J H E P 0 3 ( 2 0 2 0 ) 1 6 5 Published for SISSA by Springer Received: January 28, 2020 Revised: March 3, 2020 Accepted: March 11, 2020 Published: March 27, 2020 SU(3)F analysis for beauty baryon decays Avital Dery, Mitrajyoti Ghosh, Yuval Grossman and Stefan Schacht Department of Physics, LEPP, Cornell University, Ithaca, NY 14853, U.S.A. E-mail: avital.dery@cornell.edu, mg2338@cornell.edu, yg73@cornell.edu, ss3843@cornell.edu Abstract: We perform a general SU(3)F analysis of b → cc̄s(d) decays of members of the beauty baryon antitriplet to a member of the light baryon octet and a singlet. Under several reasonable assumptions we found ∣∣A(Ξ0b → ΛS)/A(Ξ0b → Ξ0S)∣∣ ≈ 1/√6 |V ∗cbVcd/(V ∗cbVcs)| and ∣∣A(Λb → Σ0S)/A(Λb → ΛS)∣∣ ∼ 0.02. These two relations have been recently probed by LHCb for the case of S = J/ψ. The former agrees with the measurement, while for the latter our prediction lies close to the upper bound set by LHCb. Keywords: Heavy Quark Physics, CP violation ArXiv ePrint: 2001.05397 Open Access, c© The Authors. Article funded by SCOAP3. https://doi.org/10.1007/JHEP03(2020)165 mailto:avital.dery@cornell.edu mailto:mg2338@cornell.edu mailto:yg73@cornell.edu mailto:ss3843@cornell.edu https://arxiv.org/abs/2001.05397 https://doi.org/10.1007/JHEP03(2020)165 J H E P 0 3 ( 2 0 2 0 ) 1 6 5 Contents 1 Introduction 1 2 SU(3)F analysis 2 2.1 General SU(3)F decomposition 2 2.2 Assumptions on CKM hierarchy and rescattering 6 2.3 Isospin and U-spin decompositions 7 2.4 CP asymmetry sum rules 9 2.5 SU(3)F breaking 10 3 Σ0–Λ mixing in Λb decays 12 3.1 General considerations 12 3.2 Anatomy of Σ0–Λ mixing 14 3.3 The dynamic contribution 15 3.4 Prediction for B(Λb → Σ0J/ψ) 16 4 Comparison with recent data 16 5 Conclusions 17 1 Introduction A tremendous amount of b-baryons is produced at the LHC [1]. This allows for angular analyses of Λb decays at LHCb [2] and ATLAS [3] and has led to evidence of CP violation in Λb decays [4]. It is now feasible to scrutinize rare or suppressed b-baryon decays: recent results include the first observation of Λb → Λγ [5] and the analysis of the isospin suppressed Λb → Σ0J/ψ decay and the Cabibbo-suppressed decay Ξ0b → ΛJ/ψ [6]. These increasingly precise measurements of baryon decays motivate us to perform an SU(3)F analysis of b → cc̄q (with q = s,d) decays of the heavy b-baryon 3 to the light baryon 8 and an SU(3)F singlet, 3b → 8b ⊗ 1. From the perspective of SU(3)F it makes no difference if the singlet, which we denote as S, is a J/ψ or any final state particle that does not carry any SU(3)F flavor, for example, a photon or a lepton pair. We start our analysis using two separate assumptions: (1) We work in the SU(3)F limit and (2) we treat the Λ and Σ0 as isospin eigenstates. We emphasize that these assumptions are not connected to each other. We later relax these assumptions and take into account corrections to the SU(3)F limit as well as deviations of the mass eigenstates of Λ and Σ 0 from their isospin eigenstates. At leading order the decays 3b → 8b⊗1 are mediated by tree-level b → cc̄q transitions. These correspond to a 3 operator. In full generality however, we have to take into account – 1 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 additional contributions from loops that generate effective b → tt̄q and b → uūq transitions. The contribution from b → tt̄q can be neglected as it is a penguin and therefore suppressed and it gives only another 3 under SU(3)F . In contrast, the up quarks in b → uūq can induce intermediate on-shell states leading to nontrivial effects from rescattering. Specifically, the b → uūq transition has a more complicated isospin and SU(3)F structure and induces the higher SU(3)F representations 6 and 15. Therefore, as higher SU(3)F representations stem from rescattering, in the literature it is often assumed that these are suppressed. Our strategy is to start with a very general model-independent viewpoint and then introduce additional assumptions step by step. While we mainly concentrate in this paper on the case where S = J/ψ, the general nature of our results make it possible to apply them also to radiative and semileptonic decays. CKM-leading SU(3)F limit Clebsch-Gordan coefficients for 3b → 8b ⊗ 1 in b → s transitions have been presented in refs. [7–9]. In refs. [8, 10–12] hadronic models based on QCD factorization have been utilized, and in refs. [9, 13] a covariant confined quark model has been applied. An SU(3)F analysis of b-baryon antitriplet decays to the light baryon octet and the η1 singlet can be found in ref. [14]. Further applications of SU(3)F to b baryon decays can be found in refs. [15–20]. Works on b baryon decays beyond their SU(3)F treatment are given in refs. [21–25]. Applications of SU(3)F methods on non-b baryon decays can be found in refs. [26–37]. Further literature on baryon decays is given in refs. [38–40]. Discussions of baryonic form factors can be found in refs. [41–50]. We present our SU(3)F analysis including isospin and SU(3)F breaking in section 2. After that we estimate in section 3 the effect of Σ0–Λ mixing in Λb decays, which is in general scale- and process-dependent, i.e. non-universal. We compare with recent experimental results in section 4 and conclude in section 5. 2 SU(3)F analysis 2.1 General SU(3)F decomposition The b → cc̄q (with q = s,d) decays of Λb, Ξ−b and Ξ 0 b, which form the heavy baryon 3̄, into a singlet S (e.g. S = J/ψ, γ, l+l−, . . . ) and a member of the light baryon 8, share a common set of reduced SU(3)F matrix elements after the application of the Wigner-Eckart theorem. These decays are specifically: • b → scc̄ transitions: Λb → ΛS , Λb → Σ0S , Ξ0b → Ξ 0S , Ξ−b → Ξ −S . (2.1) • b → dcc̄ transitions: Ξ0b → ΛS , Ξ 0 b → Σ 0S , Λb → nS , Ξ−b → Σ −S . (2.2) Note that there are two additional allowed decays Λb → Ξ0J/ψ and Ξ0b → nJ/ψ which are however highly suppressed by two insertions of weak effective operators, so we do not – 2 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 Particle Quark Content SU(3)F State Isospin U-spin Hadron Mass [MeV] u u |3〉1 2 ,1 2 ,1 3 ∣∣1 2 , 1 2 〉 I |0,0〉U n/a d d |3〉1 2 ,−1 2 ,1 3 ∣∣1 2 ,−1 2 〉 I ∣∣1 2 , 1 2 〉 U n/a s s |3〉0,0,−2 3 |0,0〉I ∣∣1 2 ,−1 2 〉 U n/a |Λb〉 udb |3̄〉0,0,2 3 |0,0〉I ∣∣1 2 , 1 2 〉 U 5619.60±0.17∣∣Ξ−b 〉 dsb |3̄〉1 2 ,−1 2 ,−1 3 ∣∣1 2 ,−1 2 〉 I |0,0〉U 5797.0±0.9∣∣Ξ0b〉 usb |3̄〉1 2 ,1 2 ,−1 3 ∣∣1 2 , 1 2 〉 I ∣∣1 2 ,−1 2 〉 U 5791.9±0.5 |Λ〉 uds |8〉0,0,0 |0,0〉I √ 3 2 |1,0〉U− 1 2 |0,0〉U 1115.683±0.006∣∣Σ0〉 uds |8〉1,0,0 |1,0〉I 12 |1,0〉U + √32 |0,0〉U 1192.642±0.024 |Σ−〉 dds |8〉1,−1,0 |1,−1〉I ∣∣1 2 , 1 2 〉 U 1197.449±0.0030 |Σ+〉 uus |8〉1,1,0 |1,1〉I ∣∣1 2 ,−1 2 〉 U 1189.37±0.07∣∣Ξ0〉 uss |8〉1 2 ,1 2 ,−1 ∣∣1 2 , 1 2 〉 I |1,−1〉U 1314.86±0.20 |Ξ−〉 dss |8〉1 2 ,−1 2 ,−1 ∣∣1 2 ,−1 2 〉 I ∣∣1 2 ,−1 2 〉 U 1321.71±0.07 |n〉 udd |8〉1 2 ,−1 2 ,1 ∣∣1 2 ,−1 2 〉 I |1,1〉U 939.565413±0.000006 |p〉 uud |8〉1 2 ,1 2 ,1 ∣∣1 2 , 1 2 〉 I ∣∣1 2 , 1 2 〉 U 938.2720813±0.0000058 |J/ψ〉 cc̄ |1〉0,0,0 |0,0〉I |0,0〉U 3096.900±0.006 Table 1. SU(3)F , isospin and U-spin wave functions [54, 58, 124–126] and masses [58]. For the indices of the SU(3)F states we use the convention |µ〉I,I3,Y . The lifetimes of the mem- bers of the heavy baryon triplet are τΛb/τB0 = 0.964±0.007, where τB0 = (1519±4)×10 −15s, τΞ0 b = (1.480±0.030)×10−12 s, τΞ− b = (1.572±0.040)·10−12 s, [58]. Note that the exact form of the Σ0–Λ mixing is phase convention dependent [126]. Our convention agrees with refs. [126, 127]. Another convention can be found e.g. in ref. [128] in the form of |Λ〉= √ 3 2 |1,0〉U− 1 2 |0,0〉U and∣∣Σ0〉 =−1 2 |1,0〉U− √ 3 2 |0,0〉U . consider them in our study here. The SU(3)F quantum numbers and masses are given in table 1. In this section we discuss the SU(3)F limit, SU(3)F -breaking effects are treated in section 2.5. We can write the SU(3)F structure of the relevant b → s and b → d Hamiltonians as [51] Hb→s = λcs(c̄b)(s̄c)+λus(ūb)(s̄u)+λts(t̄b)(s̄t) = λcs (3) c 0,0,−2 3 +λus ( (3) u 0,0,−2 3 +(6̄) u 1,0,−2 3 + √ 6 (15) u 1,0,−2 3 + √ 3 (15) u 0,0,−2 3 ) , (2.3) Hb→d = λcd(c̄b)(d̄c)+λud(ūb)(d̄u)+λtd(t̄b)(d̄t) = λcd (3) c 1 2 ,−1 2 ,1 3 +λud ( (3) u 1 2 ,−1 2 ,1 3 − ( 6 )u 1 2 ,−1 2 ,1 3 + √ 8 (15) u 3 2 ,−1 2 ,1 3 +(15) u 1 2 ,−1 2 ,1 3 ) . (2.4) See also refs. [52] and [53] for the application of these Hamiltonians to B → J/ψK and B → DD, respectively. The notation for the subindices are such that (N)I,I3,Y refers to – 3 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 the irreducible representation N of SU(3)F using the quantum numbers of strong isospin I, I3 and strong hypercharge Y . In the standard basis of the Gell-Mann matrices I3 and Y correspond to the eigenvalues of λ3 and λ8, respectively. We further use the notation λcs ≡ V ∗cbVcs ∼ λ 2 , λus ≡ V ∗ubVus ∼ λ 4 , λts ≡ V ∗tbVts ∼ λ 2 , (2.5) λcd ≡ V ∗cbVcd ∼ λ 3 , λud ≡ V ∗ubVud ∼ λ 3 , λtd ≡ V ∗tbVtd ∼ λ 3 , (2.6) for the CKM matrix element combinations, where we indicate the hierarchies using the Wolfenstein parameter λ. Note that in eqs. (2.3) and (2.4) it is understood that SU(3)F operators in front of different CKM matrix elements have to be differentiated as they stem from different underlying operators. For instance, even if the two triplets generate linearly dependent Clebsch-Gordan coefficients, the respective matrix elements themselves are independent. They can, for example, have a relative strong phase. We write the reduced SU(3)F limit matrix elements as A k q , where k is the respective SU(3)F representation in the Hamiltonian and q denotes the operator it stems from. The initial state is always a ∣∣3〉 and the final state is always a |8〉, so that we are left with four reduced matrix elements in the SU(3)F limit: A3c , A 3 u , A 6 u , A 15 u . (2.7) The SU(3)F limit decomposition is given in table 2. The CKM-leading part of the b → s transitions agrees with refs. [7–9]. The Clebsch-Gordan coefficients are obtained using refs. [54–56]. The normalization of the amplitudes is such that B(B1 → B2S) = |A(B1 → B2S)|2 ×P(B1,B2,S) , (2.8) with the two-body decay phase space factors P(B1,B2,S) ≡ τB1 16πm3B1 √ (m2B1 − (mB2 −mS) 2)(m2B1 − (mB2 + mS) 2) . (2.9) Note that in cases where the SU(3)F singlet S is a multibody state, e.g. S = l +l−, we imply the appropriate phase space integration in eq. (2.8). Note further, that we still work in the SU(3)F limit of the decay amplitudes. Eq. (2.9) only accounts for the trivial SU(3)F breaking from phase space effects. Additional SU(3)F breaking contributions are discussed in section 2.5. Therein, we estimate SU(3)F breaking effects to be of order 20%. Note that the amplitudes in eq. (2.8) have a mass dimension, but we always care about ratios, so we can think about them as dimensionless quantities. Note that phase space effects are of order 3% and thus they are well within the errors and could or could not be taken into account. For a model-dependent way to estimate these effects one can, for example, employ form factor results in refs. [9, 57]. The reduced SU(3)F matrix elements can in principle be matched on a color suppressed tree diagram C, an exchange diagram E and penguin diagrams Pq with quark q running in the loop. As examples we show the topological diagrams for Λb → ΛJ/ψ and Λb → Σ0J/ψ in figure 1. In the following, however, we only perform the group theory treatment. – 4 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 Decay ampl. A A3c A3u A6u A15u b → s A(Λb → ΛS) √ 2 3 λcs √ 2 3 λus 0 √ 6 5 λus A(Λb → Σ0S) 0 0 − √ 2 3 λus 2 √ 2 5 λus A(Ξ0b → Ξ 0S) λcs λus √ 1 3 λus √ 1 5 λus A(Ξ−b → Ξ −S) λcs λus − √ 1 3 λus − 3√ 5 λus b → d A(Ξ0b → ΛS) − √ 1 6 λcd − √ 1 6 λud − 1√2λud √ 3 10 λud A(Ξ0b → Σ 0S) 1√ 2 λcd 1√ 2 λud − 1√6λud √ 5 2 λud A(Λb → nS) λcd λud 1√3λud 1√ 5 λud A(Ξ−b → Σ −S) λcd λud − 1√3λud − 3√ 5 λud Table 2. SU(3)F -limit decomposition. J/ψ b u d s u d c c̄ Λb Λ (a) C J/ψ b u d s u d c c̄ Λb Λ,Σ (b) E J/ψ b u d s u d c c̄ Λb Λ u, c, t (c) Pq Figure 1. Topological diagrams for the decays Λb → ΛJ/ψ and Λb → ΣJ/ψ. Note that in the exchange diagram one gluon alone can not create the J/ψ because it is a color singlet. – 5 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 The combined matrix of Clebsch-Gordan coefficients of b → s and b → d decays in table 2 has matrix rank four, i.e., there are four sum rules, which read − √ 3 2 A(Λb→ΛS)+ 1 √ 2 A(Λb→Σ0S)+A(Ξ0b →Ξ 0S) = 0, (SU(3)F sum rule) (2.10)√ 3 2 A(Ξ0b →ΛS)− 1 √ 2 A(Ξ0b →Σ 0S)+A(Λb→nS) = 0, (SU(3)F sum rule) (2.11) − √ 2A(Λb→Σ0S) λud λus + √ 6A(Ξ0b →ΛS)+A(Λb→nS) = 0, (SU(3)F sum rule) (2.12)√ 3 2 A(Λb→ΛS) λud λus − 3 √ 2 A(Λb→Σ0S) λud λus −A(Ξ−b →Ξ −S) λud λus + √ 6A(Ξ0b →ΛS)+A(Ξ − b →Σ −S) = 0, (SU(3)F sum rule) (2.13) all of which are SU(3)F sum rules, and there is no isospin sum rule. Note that there are two sum rules which mix b → s and b → d decays and two which do not. These sum rules are valid in the SU(3)F limit irrespective of the power counting of the CKM matrix elements, assumptions on the reduced matrix elements, or the particular SU(3)F singlet S, i.e. they are completely generic. 2.2 Assumptions on CKM hierarchy and rescattering We now make some assumptions, which are not completely generic, i.e. their validity can for example depend on the particular considered SU(3)F singlet S, e.g. if S = J/ψ or S = γ. We first neglect the CKM-suppressed amplitude in b → s decays, that is we set λus/λcs → 0. In the isospin and SU(3)F limit for b → s decays we have then only one contributing reduced matrix element: A(Λb → Σ0S) = 0 , (isospin sum rule) (2.14) A(Ξ0b → Ξ 0S) = A(Ξ−b → Ξ −S) , (isospin sum rule) (2.15) A(Ξ0b → Ξ 0S) = √ 3 2 A(Λb → ΛS) . (SU(3)F sum rule) (2.16) We now move to make another assumption and that is to also neglect the λud terms for the b → d transitions. Despite the formal power counting eq. (2.6), that is |λud| ' |λcd|, numerically we actually have [58] ∣∣∣∣λudλcd ∣∣∣∣ ≈ 0.38 . (2.17) Moreover, it is plausible that A6u and A 15 u are suppressed because they result from light quarks stemming from b → uūs(d) which induce intermediate on-shell states that rescatter into cc̄, see also refs. [59–63]. Under the assumption that these terms are more or equally suppressed as SU(3)F -breaking effects we have many more relations. All seven non-zero decays we considered in table 2 are then simply related by the Clebsch-Gordan coefficients – 6 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 in the first column. In addition to the sum rules eqs. (2.14)–(2.16), we have then √ 2A(Ξ0b → Σ 0S) = A(Ξ−b → Σ −S) , (isospin sum rule) (2.18) A(Ξ0b → Ξ 0S) = − √ 6A(Ξ0b → ΛS) λcs λcd , (SU(3)F sum rule) (2.19) − √ 6A(Ξ0b → ΛS) = √ 2A(Ξ0b → Σ 0S) , (SU(3)F sum rule) (2.20)√ 2A(Ξ0b → Σ 0S) = A(Λb → nS) , (SU(3)F sum rule) (2.21) A(Λb → nS) = A(Ξ−b → Σ −S) . (SU(3)F sum rule) (2.22) 2.3 Isospin and U-spin decompositions For comprehensiveness, we give also the isospin and U-spin decompositions of the Hamil- tonians, which read Hb→s = λcs(0, 0)cI + λus ((0, 0) u I + (1, 0) u I ) (2.23) = λcs ( 1 2 ,− 1 2 )c U + λus ( 1 2 ,− 1 2 )u U , (2.24) and Hb→d = λcd ( 1 2 ,− 1 2 )c I + λud (( 3 2 ,− 1 2 )u I + ( 1 2 ,− 1 2 )u I ) (2.25) = λcd ( 1 2 , 1 2 )c U + λud ( 1 2 , 1 2 )u U , (2.26) where we use the notation (i,j) q I ≡O ∆I=i ∆I3=j , (i,j) q U ≡O ∆U=i ∆U3=j , (2.27) where q denotes the quark content of the operator the representation stems from and we absorbed Clebsch-Gordan coefficients into operators. Using the isospin and U-spin states in table 1, we obtain the isospin decompositions in tables 3 and 4 and the U-spin decomposition in table 5. We note that the SU(3)F decomposition includes more information than the isospin and U-spin tables each on their own. An example is the ratio∣∣∣∣ A(Ξ0b → ΛS)A(Ξ0b → Ξ0S) ∣∣∣∣ = 1√2 ∣∣∣∣∣〈0| 1 2 ∣∣1 2 〉〈 1 2 ∣∣ 0 ∣∣1 2 〉 ∣∣∣∣∣ ∣∣∣∣λcdλcs ∣∣∣∣ , (2.28) where the appearing reduced matrix elements are not related, e.g. the final states belong to different isospin representations. That means we really need SU(3)F to find the relation eq. (2.19). We can make this completely transparent by writing out the implications of eq. (2.14) for the corresponding U-spin decomposition. From table 5 and eq. (2.14) it follows for the U-spin matrix elements − √ 3 2 √ 2 〈 0 ∣∣∣∣12 ∣∣∣∣ 12 〉c + 1 2 √ 2 〈 1 ∣∣∣∣12 ∣∣∣∣ 12 〉c = 0 . (2.29) – 7 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 b → s Decay Ampl. A 〈0|0 |0〉c 〈 1 2 ∣∣ 0 ∣∣1 2 〉c 〈0|0 |0〉u 〈1|1 |0〉u 〈1 2 ∣∣ 1 ∣∣1 2 〉u 〈1 2 ∣∣ 0 ∣∣1 2 〉u A(Λb → ΛS) λcs 0 λus 0 0 0 A(Λb → Σ0S) 0 0 0 λus 0 0 A(Ξ0b → Ξ 0S) 0 λcs 0 0 − √ 1 3 λus λus A(Ξ−b → Ξ −S) 0 λcs 0 0 √ 1 3 λus λus Table 3. Isospin decomposition for b → s transitions. b → d Decay ampl. A 〈0| 1 2 ∣∣1 2 〉c 〈0| 1 2 ∣∣1 2 〉u 〈1| 1 2 ∣∣1 2 〉c 〈1| 1 2 ∣∣1 2 〉u 〈1 2 ∣∣ 1 2 |0〉c 〈 1 2 ∣∣ 1 2 |0〉u 〈1| 3 2 ∣∣1 2 〉u A(Ξ0b → ΛS) − 1√ 2 λcd − 1√2λud 0 0 0 0 0 A(Ξ0b → Σ 0S) 0 0 1√ 2 λcd 1√ 2 λud 0 0 − 1√2λud A(Λb → nS) 0 0 0 0 λcd λud 0 A(Ξ−b → Σ −S) 0 0 λcd λud 0 0 1 2 λud Table 4. Isospin decomposition for b → d transitions. Decay ampl. A 〈0| 1 2 ∣∣1 2 〉c 〈0| 1 2 ∣∣1 2 〉u 〈1| 1 2 ∣∣1 2 〉c 〈1| 1 2 ∣∣1 2 〉u 〈1 2 ∣∣ 1 2 |0〉c 〈 1 2 ∣∣ 1 2 |0〉u b → s A(Λb → ΛS) 12√2λcs 1 2 √ 2 λus √ 3 2 √ 2 λcs √ 3 2 √ 2 λus 0 0 A(Λb → Σ0S) − √ 3 2 √ 2 λcs − √ 3 2 √ 2 λus 1 2 √ 2 λcs 1 2 √ 2 λus 0 0 A(Ξ0b → Ξ 0S) 0 0 λcs λus 0 0 A(Ξ−b → Ξ −S) 0 0 0 0 λcs λus b → d A(Ξ0b → ΛS) − 1 2 √ 2 λcd − 12√2λud √ 3 2 √ 2 λcd √ 3 2 √ 2 λud 0 0 A(Ξ0b → Σ 0S) √ 3 2 √ 2 λcd √ 3 2 √ 2 λud 1 2 √ 2 λcd 1 2 √ 2 λud 0 0 A(Λb → nS) 0 0 λcd λud 0 0 A(Ξ−b → Σ −S) 0 0 0 0 λcd λud Table 5. U-spin decomposition. – 8 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 Inserting this relation into the U-spin decomposition of the decay Ξ0b → ΛS in table 5, we obtain A(Ξ0b → ΛS) = 1 √ 6 λcd 〈 1 ∣∣∣∣12 ∣∣∣∣ 12 〉c . (2.30) Comparing this expression with the U-spin decomposition of the decay Ξ0b → Ξ 0S in table 5, we arrive again at the sum rule eq. (2.19). In order that eq. (2.19) holds we need not only the suppression of other SU(3)F limit contributions as discussed above, but also the suppression of both isospin and U-spin vio- lating contributions. A non-vanishing dynamic isospin breaking contribution to Λb → Σ0S would also be reflected in isospin and SU(3)F -breaking violations of eq. (2.19). We make this correlation explicit in section 2.5. 2.4 CP asymmetry sum rules Due to a general sum rule theorem given in ref. [64] that relates direct CP asymmetries of decays connected by a complete interchange of d and s quarks [64–67], we can directly write down two U-spin limit sum rules: adirCP (Ξ 0 b → Ξ 0S) adirCP (Λb → nS) = − τ(Ξ0b) τ(Λb) B(Λb → nS) B(Ξ0b → Ξ0S) , (2.31) adirCP (Ξ − b → Ξ −S) adirCP (Ξ − b → Σ−S) = − B(Ξ−b → Σ −S) B(Ξ−b → Ξ−S) , (2.32) where the branching ratios imply CP averaging. Note that the general U-spin rule lead- ing to eqs. (2.31) and (2.32) also applies to multi-body final states, as pointed out in refs. [26, 64, 68]. It follows that eqs. (2.31) and (2.32) apply also when S is a multi-body state like S = l+l−. Note that although the quark content of the Λ and Σ is uds, this does not mean that a complete interchange of d and s quarks gives the identity. The reason is given by the underlying quark wave functions [69] |Λ〉∼ 1 √ 2 (ud−du) s, ∣∣Σ0〉 ∼ 1√ 2 (ud + du) s, (2.33) where we do not write the spin wave function. Eq. (2.33) shows explicitly that a complete interchange of d and s quarks in Λ or Σ0 does not result again in a Λ or Σ0 wave function, respectively. This is similar to the situation for η and η′, where no respective particles correspond to a complete interchange of d and s quarks [70], see e.g. the quark wave functions given in ref. [71]. We can put this into a different language, namely that in the U-spin basis the large mixing of |1, 0〉U and |0, 0〉U to the U-spin states of Λ and Σ 0, see table 1, destroys two sum rules which exist for the U-spin eigenstates. To be explicit, we define U-spin eigenstates which are not close to mass eigenstates |X〉 = |0, 0〉U , |Y 〉 = |1, 0〉U . (2.34) – 9 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 Decay ampl. A 〈0| 1 2 ∣∣1 2 〉c 〈0| 1 2 ∣∣1 2 〉u 〈1| 1 2 ∣∣1 2 〉c 〈1| 1 2 ∣∣1 2 〉u 〈1 2 ∣∣ 1 2 |0〉c 〈 1 2 ∣∣ 1 2 |0〉u b → s A(Λb → XS) − 1√2λcs − 1√ 2 λus 0 0 0 0 A(Λb → Y S) 0 0 1√2λcs 1√ 2 λus 0 0 b → d A(Ξ0b → XS) 1√ 2 λcd 1√ 2 λud 0 0 0 0 A(Ξ0b → Y S) 0 0 1√ 2 λcd 1√ 2 λud 0 0 Table 6. (Unpractical) U-spin decomposition for the U-spin eigenstates |X〉 and |Y 〉, see eq. (2.34) and discussion in the text. For these, we obtain the U-spin decomposition given in table 6. From that it is straight- forward to obtain another two CP asymmetry sum rules. These are however impractical, because there is no method available to prepare Λ and Σ0 as U-spin eigenstates, instead of approximate isospin eigenstates. Consequently, we are left only with the two CP asymme- try sum rules eqs. (2.31) and (2.32). Note that CKM-leading SU(3)F breaking by itself cannot contribute to CP violation, because it comes only with relative strong phases but not with the necessary relative weak phase. Therefore, the individual CP asymmetries can be written as adirCP = Im λuq λcq Im Au Ac , (2.35) where Au,c have only a strong phase and to leading order in Wolfenstein-λ we have [58] Im ( λus λcs ) ≈ λ2η̄ ≈ 0.02 , Im ( λud λcd ) ≈ η̄ ≈ 0.36 . (2.36) Additional suppression from rescattering implies that on top of eq. (2.36) we have |Au|� |Ac|, i.e. the respective imaginary part is also expected to be small. This im- plies that we do not expect to see a nonvanishing CP asymmetry in these decays any time soon. The other way around, this prediction is also a test of our assumption that the λuq-amplitude is suppressed. 2.5 SU(3)F breaking We consider now isospin and SU(3)F breaking effects in the CKM-leading part of the b → s and b → d Hamiltonians. This will become useful once we have measurements of several b-baryon decays that are precise enough to see deviations from the SU(3)F limit sum rules. SU(3)F breaking effects for charm and beauty decays have been discussed in the literature for a long time [26, 52, 72–86]. They are generated through the spurion  mu Λ −2 3 α 0 0 0 md Λ + 1 3 α 0 0 0 ms Λ + 1 3 α   = 1 3 mu+md+ms Λ 1− 1 2 ( md−mu Λ +α ) λ3 + 1 2 √ 3 ( mu+md−2ms Λ −α ) λ8 , (2.37) – 10 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 with the unity 1 and the Gell-Mann matrices λ3 and λ8. The part of eq. (2.37) that is proportional to 1 can be absorbed into the SU(3)F limit part. It follows that the isospin and SU(3)F -breaking tensor operator is given as δ (8)1,0,0 + ε (8)0,0,0 , (2.38) with δ = 1 2 ( md −mu Λ + α ) , ε = 1 2 √ 3 ( mu + md − 2ms Λ −α ) , (2.39) where α is the electromagnetic coupling and we generically expect the size of isospin and SU(3)F breaking to be δ ∼ 1% and ε ∼ 20%, respectively. Note that the scale-dependence of the quark masses, as well as the fact that we do not know how to define the scale Λ make it impossible to quote decisive values for δ and ε. Eventually, they will have to be determined experimentally for each process of interest separately as they are not universal. For the tensor products of the perturbation with the CKM-leading SU(3)F limit op- erator it follows: (8)1,0,0 ⊗ (3)c0,0,−2 3 = √ 1 2 ( 6 ) 1,0,−2 3 + √ 1 2 (15)1,0,−2 3 , (2.40) (8)0,0,0 ⊗ (3)c0,0,−2 3 = 1 2 (3)0,0,−2 3 + √ 3 2 (15)0,0,−2 3 , (2.41) (8)1,0,0 ⊗ (3)c1 2 ,−1 2 ,1 3 = √ 3 4 (3) 1 2 ,−1 2 ,1 3 − √ 1 8 ( 6 ) 1 2 ,−1 2 ,1 3 − √ 1 48 (15) 1 2 ,−1 2 ,1 3 + √ 2 3 (15) 3 2 ,−1 2 ,1 3 , (2.42) (8)0,0,0 ⊗ (3)c1 2 ,−1 2 ,1 3 = − 1 4 (3) 1 2 ,−1 2 ,1 3 − √ 3 8 ( 6 ) 1 2 ,−1 2 ,1 3 + 3 4 (15) 1 2 ,−1 2 ,1 3 , (2.43) so that we arrive at the SU(3)F breaking Hamiltonians Hb→sX ≡ λcs δ (√ 1 2 ( 6 ) 1,0,−2 3 + √ 1 2 (15)1,0,−2 3 ) + λcs ε ( 1 2 (3)0,0,−2 3 + √ 3 2 (15)0,0,−2 3 ) , (2.44) Hb→dX ≡ λcd δ (√ 3 4 (3) 1 2 ,−1 2 ,1 3 − √ 1 8 ( 6 ) 1 2 ,−1 2 ,1 3 − √ 1 48 (15) 1 2 ,−1 2 ,1 3 + √ 2 3 (15) 3 2 ,−1 2 ,1 3 ) + λcd ε ( − 1 4 (3) 1 2 ,−1 2 ,1 3 − √ 3 8 ( 6 ) 1 2 ,−1 2 ,1 3 + 3 4 (15) 1 2 ,−1 2 ,1 3 ) . (2.45) This gives rise to three additional matrix elements B3 , B6 , B15 . (2.46) – 11 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 Decay ampl. A A3c B3 B15 B6 b → s A(Λb → ΛS)/λcs √ 2 3 1 2 √ 1 3 ε √ 3 10 ε 0 A(Λb → Σ0S)/λcs 0 0 √ 2 15 δ − √ 1 3 δ A(Ξ0b → Ξ 0S)/λcs 1 1 2 ε √ 1 15 δ − 1 2 √ 5 ε √ 1 6 δ A(Ξ−b → Ξ −S)/λcs 1 1 2 ε − √ 1 15 δ − 1 2 √ 5 ε − √ 1 6 δ b → d A(Ξ0b → ΛS)/λcd − 1√ 6 − 1 4 √ 2 δ + 1 4 √ 6 ε − 1 4 √ 10 δ + 3 4 √ 3 10 ε −1 4 δ − √ 3 4 ε A(Ξ0b → Σ 0S)/λcd 1√ 2 1 4 √ 3 2 δ − 1 4 √ 2 ε 11 4 √ 30 δ − 1 4 √ 10 ε − 1 4 √ 3 δ − 1 4 ε A(Λb → nS)/λcd 1 √ 3 4 δ − 1 4 ε − 1 4 √ 15 δ + 3 4 √ 5 ε 1 2 √ 6 δ + 1 2 √ 2 ε A(Ξ−b → Σ −S)/λcd 1 √ 3 4 δ − 1 4 ε −1 4 √ 5 3 δ − 1 4 √ 5 ε − 1 2 √ 6 δ − 1 2 √ 2 ε Table 7. CKM-leading SU(3)F decomposition including isospin- and SU(3)F -breaking. The CKM-leading decomposition for b → s and b → d decays including isospin and SU(3)F breaking is given in table 7. The complete 4×4 matrix of the b → s matrix has rank four, i.e. there is no b → s sum rule to this order. As discussed in section 2 after eq. (2.30) we see from table 7 explicitly that isospin breaking contributions to A(Λb → Σ0S) lead at the same time to a deviation of the ratio |A(Ξ0b → ΛS)|/|A(Ξ 0 b → Ξ 0S)| from the result eq. (2.19). Comparing to results present in the literature, in ref. [14] two separate coefficient matrices of b → s and b → d decays are given in terms of the isoscalar coefficients, i.e. where the isospin quantum number is still kept in the corresponding reduced matrix element. We improve on that by giving instead the SU(3)F Clebsch-Gordan coefficient table that makes transparent the corresponding sum rules in a direct way and furthermore reveals directly the correlations between b → s and b → d decays. We also find the complete set of sum rules, and discuss how further assumptions lead to additional sum rules. We note that the first two sum rules in eq. (43) in ref. [14] are sum rules for coefficient matrix vectors but do not apply to the corresponding amplitudes because of the different CKM factors involved. 3 Σ0–Λ mixing in Λb decays 3.1 General considerations In this section we study the ratio R ≡ A(Λb → Σ0physJ/ψ) A(Λb → ΛphysJ/ψ) = 〈 J/ψΣ0phys ∣∣∣H|Λb〉 〈J/ψΛphys|H|Λb〉 . (3.1) – 12 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 In order to do this we need the matrix elements appearing in eq. (3.1). In the limit where isospin is a good symmetry and Σ0phys is an isospin eigenstate, R vanishes, and therefore we are interested in the deviations from that limit. We study leading order effects in isospin breaking. We first note that we can neglect the deviation of Λb from its isospin limit. The reason is that regarding the mixing of heavy baryons, for example Σb–Λb, Ξ 0 c–Ξ ′0 c or Ξ + c –Ξ ′+ c , in the quark model one obtains a suppression of the mixing angle with the heavy quark mass [87–92]. It follows that for our purposes we can safely neglect the mixing between Λb and Σb as it is not only isospin suppressed but on top suppressed by the b quark mass. We now move to discuss the mixing of the light baryons. It has already been pointed out in ref. [91], that a description with a single mixing angle captures only part of the effect. The reason is because isospin breaking contributions will affect not only the mixing between the states but also the decay amplitude. The non-universality is also reflected in the fact that the Λb → Σ0 transition amplitude vanishes in the heavy quark limit at large recoil, i.e. in the phase space when Σ0 carries away a large fraction of the energy [47], see also ref. [25] for the heavy quark limit of similar classes of decays. To leading order in isospin breaking we consider two effects, the mixing between Λ and Σ0 as well as the correction to the Hamiltonian. We discuss these two effects below. Starting with the wave function mixing angle θm, this is defined as the mixing angle between the isospin limit states ∣∣Σ0〉 = |1, 0〉I and |Λ〉 = |0, 0〉I, see eq. (2.33), into the physical states (see refs. [93–98]) |Λphys〉 = cos θm |Λ〉− sin θm ∣∣Σ0〉 , (3.2)∣∣Σ0phys〉 = sin θm |Λ〉 + cos θm ∣∣Σ0〉 . (3.3) The effect stems from the non-vanishing mass difference md − mu as well as different electromagnetic charges [69] which lead to a hyperfine mixing between the isospin limit states. A similar mixing effect takes place for the light mesons in form of singlet octet mixing of π0 and η( ′) [99–104]. As for the Hamiltonian, we write H = H0 + H1 where H0 is the isospin limit one and H1 is the leading order breaking. In general for decays into final states Λf and Σ0f we can write〈 f Σ0phys ∣∣H|Λb〉 = sin θm 〈f Λ|H|Λb〉 + cos θm 〈f Σ0∣∣H|Λb〉 (3.4) ≈ θm 〈f Λ|H0 |Λb〉 + 〈 f Σ0 ∣∣H1 |Λb〉 , 〈f Λphys|H|Λb〉 = cos θm 〈f Λ|H|Λb〉− sin θm 〈 f Σ0 ∣∣H|Λb〉 ≈ 〈f Λ|H0 |Λb〉 , where we use the isospin eigenstates |Λ〉 and ∣∣Σ0〉. It follows that we can write R ≈ θf ≡ θm + θ dyn f , θ dyn f ≡ 〈 f Σ0 ∣∣H1 |Λb〉 〈f Λ|H0 |Λb〉 . (3.5) We learn that the angle θf has contributions from two sources: a universal part θm from wave function overlap, which we call “static” mixing, and a non-universal contribution – 13 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 θ dyn f that we call “dynamic” mixing. We can think of θf as a decay dependent “effective” mixing angle relevant for the decay Λb → Σ0f. It follows B(Λb → Σ0J/ψ) B(Λb → ΛJ/ψ) = P(Λb, Σ0,J/ψ) P(Λb, Λ,J/ψ) ×|θf| 2 . (3.6) Our aim in the next section is to find θf . 3.2 Anatomy of Σ0–Λ mixing We start with θm. Because of isospin and SU(3)F breaking effects, the physical states |Λphys〉 and ∣∣∣Σ0phys〉 deviate from their decomposition into their SU(3)F eigenstates both in the U-spin and in the isospin basis. As isospin is the better symmetry, we expect generically the scaling θm ∼ δ ε . (3.7) This scaling can be seen explicitly in some of the estimates of the effect. In the quark model, the QCD part of the isospin breaking corrections comes from the strong hyperfine interaction generated by the chromomagnetic spin-spin interaction as [89] θm = √ 3 4 md −mu ms − (mu + md)/2 , (3.8) see also refs. [69, 105–109], and where constituent quark masses are used. Eq. (3.8) agrees with our generic estimate from group-theory considerations, eq. (3.7). The same analytic result, eq. (3.8), is also obtained in chiral perturbation theory [106, 110]. Within the quark model, the mixing angle can also be related to baryon masses via [89, 94, 96] tan θm = (mΣ0 −mΣ+ ) − (mn −mp)√ 3(mΣ −mΛ) , (3.9) or equally [89, 96, 111] tan θm = (mΞ− −mΞ0 ) − (mΞ∗− −mΞ∗0 ) 2 √ 3(mΣ −mΛ) . (3.10) In ref. [89] eqs. (3.8)–(3.10) have been derived within the generic “independent quark model” [112, 113]. Furthermore, ref. [89] provides SU(3)-breaking corrections to eq. (3.9) within this model. Note that eqs. (3.9) and (3.10) automatically include also QED cor- rections through the measured baryon masses. Recently, lattice calculations of θm have become available that include QCD and QED effects [98], and which we consider as the most reliable and robust of the quoted results. The various results for the mixing angle from the literature are summarized in table 8. It turns out that the quark-model predictions agree quite well with modern lattice QCD calculations. Note however, that the lattice result of ref. [98] (see table 8) demonstrates that the QED correction is large, contrary to the quark model expectation in ref. [69], and amounts to about 50% of the total result [98]. – 14 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 Method Mixing Angle θm [ ◦] Ref. Quark model: Relation to Baryon masses 0.86 ± 0.06 [94, 96] Quark model: Hyperfine splitting + EM interactions ' 0.57 [69] Lattice QCD+QED A 1.00 ± 0.32 [98] Lattice QCD+QED B 0.96 ± 0.31 [98] Lattice QCD without QED 0.55 ± 0.03 [98] Table 8. Results for the Σ0–Λ mixing angle. Note that we adjusted the sign conventions for the results to match always the one of ref. [94], see also the corresponding comment in ref. [98]. For older lattice results for the “QCD only” scenario see refs. [95, 97]. Note that with alternate quark mass input taken from ref. [129] the result for the “Lattice QCD without QED” scenario is changed to θm = 0.65 ± 0.03 [98]. In the literature the mixing angle has often been assumed to be universal and employed straight forward for the prediction of decays, see refs. [94, 109, 114, 115]. It was already pointed out in refs. [109, 116] that the Σ0–Λ mixing angle can also be extracted from semileptonic Σ− → Λl−ν decays. The angle has also been directly related to the π–η mixing angle [115, 117]. The ratio on the right hand side of eq. (3.8) can be extracted from η → 3π decays [117] or from the comparison of K+ → π0e+νe and K0L → π −e+νe [117]. For pseudoscalar mesons it has been shown [118, 119] that the reduction of isospin violation from (md − mu)/(md + mu) to the ratio in eq. (3.8) is related to the Adler-Bell-Jackiw anomaly [120, 121] of QCD. Note that in principle also θm is scale dependent [109], as was observed for the similar case of π0–η mixing in ref. [122]. Furthermore, θm has an electromagnetic component. Depending on the relevant scale of the process in principle the QED correction can be large. We see from the lattice results in table 8 that this is the case for θm. Very generally, at high energy scales electromagnetic interactions will dominate over QCD ones [123]. 3.3 The dynamic contribution The dynamical contributions to isospin breaking can be parametrized as part of the isospin- and SU(3)F -breaking expansion, see section 2.5. Explicitly we found θ dyn J/ψ ≡ 〈 J/ψ Σ0 ∣∣H1 |Λb〉 〈J/ψ Λ|H0 |Λb〉 = δ × [√ 1 5 B15 A3c − √ 1 2 B6̄ A3c ] . (3.11) We expect that B15 ∼ B6̄ ∼ A3c. The important result is that these effects are order δ. Taking everything into account, very schematically we expect therefore the power counting θf ∼ ( δ ε ) m + δf ∼ θm [1 + O(εf )] , (3.12) where δf and εf refer to isospin and SU(3) breaking parameters that depend on f. – 15 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 3.4 Prediction for B(Λb → Σ0J/ψ) We see from the power counting in eq. (3.12) that the static component θm dominates, as it is relatively enhanced by the inverse of the size of SU(3)F breaking. Employing this assumption we obtain for θf ∼ θm ∼ 1◦ (3.13) the prediction ∣∣∣∣A(Λb → Σ0J/ψ)A(Λb → ΛJ/ψ) ∣∣∣∣ = |θf| ∼ 0.02 . (3.14) A confirmation of our prediction would imply the approximate universality of the Σ0–Λ mixing angle in b-baryon decays. In that case we would expect that likewise∣∣∣∣A(Λb → Σ0J/ψ)A(Λb → ΛJ/ψ) ∣∣∣∣ = ∣∣∣∣A(Λb → Σ0γ)A(Λb → Λγ) ∣∣∣∣ = ∣∣∣∣A(Λb → Σ0l+l−)A(Λb → Λl+l−) ∣∣∣∣ = ∣∣∣∣ A(Σ0b → ΛJ/ψ)A(Σ0b → Σ0J/ψ) ∣∣∣∣ ∼ 0.02 , (3.15) up to SU(3)F breaking. Note that Λb and Σb are not in the same SU(3)F multiplet, so that there is no relation between their reduced matrix elements. The above predictions are based on the assumption that the dynamic contribution is smaller by a factor of the order of the SU(3) breaking. In practice, these effects may be large enough to be probed experimentally. Thus, we can hope that precise measurements of these ratios will be able to test these assumptions. 4 Comparison with recent data We move to compare the general results of sections 2 and 3 to the recent LHCb data for the case S = J/ψ [6]. Particularly relevant to the experimental findings is the sum rule eq. (2.19) which we rephrase as∣∣∣∣ A(Ξ0b → ΛJ/ψ)A(Ξ0b → Ξ0J/ψ) ∣∣∣∣ = 1√6 (1 + O(ε)) ∣∣∣∣λcdλcs ∣∣∣∣ ≈ 0.41 ∣∣∣∣λcdλcs ∣∣∣∣ , (4.1) where in the last step we only wrote the central value. The error is expected to be roughly of order ε ∼ 20%. The estimate in eq. (4.1) agrees very well with the recent measurement [6]∣∣∣∣ A(Ξ0b → ΛJ/ψ)A(Ξ0b → Ξ0J/ψ) ∣∣∣∣ = (0.44 ± 0.06 ± 0.02) ∣∣∣∣λcdλcs ∣∣∣∣ . (4.2) This suggests that the assumptions made in section 2 are justified. However, from the SU(3)F -breaking contributions which we calculated in section 2.5, we expect generically an order 20% correction to eq. (4.1). The measurement eq. (4.2) is not yet precise enough to probe and learn about the size of these corrections. However, SU(3)F breaking seems also not to be enhanced beyond the generic 20%. – 16 – J H E P 0 3 ( 2 0 2 0 ) 1 6 5 The only other theory result for the ratio eq. (4.2) that we are aware of in the literature can be obtained from the branching ratios provided in ref. [9], where a covariant confined quark model has been employed. From the branching ratios given therein we extract the central value ∣∣∣∣ A(Ξ0b → ΛJ/ψ)A(Ξ0b → Ξ0J/ψ) ∣∣∣∣ ∼ 0.34 λcdλcs , (4.3) where an error of ∼ 20% is quoted in ref. [9] for the branching ratios. This estimate is also in agreement with the data, eq. (4.2) (see for details in ref. [9]). Finally, our prediction eq. (3.14)∣∣∣∣A(Λb → Σ0J/ψ)A(Λb → ΛJ/ψ) ∣∣∣∣ = |θf| ∼ 0.02 , (4.4) is only about a factor two below the bound provided in ref. [6],∣∣∣∣A(Λb → Σ0J/ψ)A(Λb → ΛJ/ψ) ∣∣∣∣ < 1/20.9 = 0.048 at 95% CL. (4.5) A deviation from eq. (3.14) would indicate the observation of a non-universal contribution to the effective mixing angle, i.e. an enhancement of isospin violation in the dynamical contribution θ dyn J/Ψ . It seems that a first observation of isospin violation in Λb decays is feasible for LHCb in the near future. 5 Conclusions We perform a comprehensive SU(3)F analysis of two-body b → cc̄s(d) decays of the b- baryon antitriplet to baryons of the light octet and an SU(3)F singlet, including a discussion of isospin and SU(3)F breaking effects as well as Σ 0–Λ mixing. Our formalism allows us to interpret recent results for the case S = J/ψ by LHCb, which do not yet show signs of isospin violation or SU(3)F breaking. We point out several sum rules which can be tested in the future and give a prediction for the ratios |A(Λb → Σ0J/ψ)|/|A(Λb → ΛJ/ψ)| ∼ 0.02 and ∣∣A(Ξ0b → ΛJ/ψ)/A(Ξ0b → Ξ0J/ψ)∣∣ ≈ 1/√6 |V ∗cbVcd/(V ∗cbVcs)|. More measurements are needed in order to probe isospin and SU(3)F breaking corrections to these and many more relations that we laid out in this work. Acknowledgments We thank Sheldon Stone for discussions. The work of YG is supported in part by the NSF grant PHY1316222. SS is supported by a DFG Forschungsstipendium under contract no. SCHA 2125/1-1. Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. – 17 – https://creativecommons.org/licenses/by/4.0/ J H E P 0 3 ( 2 0 2 0 ) 1 6 5 References [1] A. Cerri et al., Report from Working Group 4, CERN Yellow Rep. Monogr. 7 (2019) 867 [arXiv:1812.07638] [INSPIRE]. [2] LHCb collaboration, Measurements of the Λ0b → J/ψΛ decay amplitudes and the Λ 0 b polarisation in pp collisions at √ s = 7 TeV, Phys. Lett. B 724 (2013) 27 [arXiv:1302.5578] [INSPIRE]. [3] ATLAS collaboration, Measurement of the parity-violating asymmetry parameter αb and the helicity amplitudes for the decay Λ0b → J/ψ + Λ 0 with the ATLAS detector, Phys. Rev. D 89 (2014) 092009 [arXiv:1404.1071] [INSPIRE]. [4] LHCb collaboration, Measurement of matter-antimatter differences in beauty baryon decays, Nature Phys. 13 (2017) 391 [arXiv:1609.05216] [INSPIRE]. [5] LHCb collaboration, First Observation of the Radiative Decay Λ0b → Λγ, Phys. Rev. Lett. 123 (2019) 031801 [arXiv:1904.06697] [INSPIRE]. [6] LHCb collaboration, Isospin amplitudes in Λ0b → J/ψΛ(Σ 0) and Ξ0b → J/ψΞ 0(Λ) decays, Phys. Rev. Lett. 124 (2020) 111802 [arXiv:1912.02110] [INSPIRE]. [7] M.B. Voloshin, Remarks on measurement of the decay Ξ−b → Λbπ −, arXiv:1510.05568 [INSPIRE]. [8] Fayyazuddin and M.J. Aslam, Hadronic weak decay Bb( 12 + ) →B( 1 2 + , 3 2 + ) + V , Phys. Rev. D 95 (2017) 113002 [arXiv:1705.05106] [INSPIRE]. [9] T. Gutsche, M.A. Ivanov, J.G. Körner and V.E. Lyubovitskij, Nonleptonic two-body decays of single heavy baryons ΛQ, ΞQ and ΩQ (Q = b,c) induced by W emission in the covariant confined quark model, Phys. Rev. D 98 (2018) 074011 [arXiv:1806.11549] [INSPIRE]. [10] Y.K. Hsiao, P.Y. Lin, C.C. Lih and C.Q. Geng, Charmful two-body anti-triplet b-baryon decays, Phys. Rev. D 92 (2015) 114013 [arXiv:1509.05603] [INSPIRE]. [11] Y.K. Hsiao, P.Y. Lin, L.W. Luo and C.Q. Geng, Fragmentation fractions of two-body b-baryon decays, Phys. Lett. B 751 (2015) 127 [arXiv:1510.01808] [INSPIRE]. [12] J. Zhu, Z.-T. Wei and H.-W. Ke, Semileptonic and nonleptonic weak decays of Λ0b , Phys. Rev. D 99 (2019) 054020 [arXiv:1803.01297] [INSPIRE]. [13] T. Gutsche, M.A. Ivanov, J.G. Körner, V.E. Lyubovitskij, V.V. Lyubushkin and P. Santorelli, Theoretical description of the decays Λb → Λ(∗)( 12 ± , 3 2 ± ) + J/ψ, Phys. Rev. D 96 (2017) 013003 [arXiv:1705.07299] [INSPIRE]. [14] S. Roy, R. Sinha and N.G. Deshpande, Nonleptonic beauty baryon decays and CP asymmetries based on an SU(3) -flavor analysis, Phys. Rev. D 101 (2020) 036018 [arXiv:1911.01121] [INSPIRE]. [15] M. Gronau and J.L. Rosner, Flavor SU(3) and Λb decays, Phys. Rev. D 89 (2014) 037501 [Erratum ibid. D 91 (2015) 119902] [arXiv:1312.5730] [INSPIRE]. [16] M. He, X.-G. He and G.-N. Li, CP-Violating Polarization Asymmetry in Charmless Two-Body Decays of Beauty Baryons, Phys. Rev. D 92 (2015) 036010 [arXiv:1507.07990] [INSPIRE]. [17] X.-G. He and G.-N. Li, Predictive CP violating relations for charmless two-body decays of beauty baryons Ξ −, 0 b and Λ 0 b with flavor SU(3) symmetry, Phys. Lett. B 750 (2015) 82 [arXiv:1501.00646] [INSPIRE]. – 18 – https://doi.org/10.23731/CYRM-2019-007.867 https://arxiv.org/abs/1812.07638 https://inspirehep.net/search?p=find+EPRINT+arXiv:1812.07638 https://doi.org/10.1016/j.physletb.2013.05.041 https://arxiv.org/abs/1302.5578 https://inspirehep.net/search?p=find+EPRINT+arXiv:1302.5578 https://doi.org/10.1103/PhysRevD.89.092009 https://doi.org/10.1103/PhysRevD.89.092009 https://arxiv.org/abs/1404.1071 https://inspirehep.net/search?p=find+EPRINT+arXiv:1404.1071 https://doi.org/10.1038/nphys4021 https://arxiv.org/abs/1609.05216 https://inspirehep.net/search?p=find+EPRINT+arXiv:1609.05216 https://doi.org/10.1103/PhysRevLett.123.031801 https://doi.org/10.1103/PhysRevLett.123.031801 https://arxiv.org/abs/1904.06697 https://inspirehep.net/search?p=find+EPRINT+arXiv:1904.06697 https://doi.org/10.1103/PhysRevLett.124.111802 https://arxiv.org/abs/1912.02110 https://inspirehep.net/search?p=find+EPRINT+arXiv:1912.02110 https://arxiv.org/abs/1510.05568 https://inspirehep.net/search?p=find+EPRINT+arXiv:1510.05568 https://doi.org/10.1103/PhysRevD.95.113002 https://doi.org/10.1103/PhysRevD.95.113002 https://arxiv.org/abs/1705.05106 https://inspirehep.net/search?p=find+EPRINT+arXiv:1705.05106 https://doi.org/10.1103/PhysRevD.98.074011 https://arxiv.org/abs/1806.11549 https://inspirehep.net/search?p=find+EPRINT+arXiv:1806.11549 https://doi.org/10.1103/PhysRevD.92.114013 https://arxiv.org/abs/1509.05603 https://inspirehep.net/search?p=find+EPRINT+arXiv:1509.05603 https://doi.org/10.1016/j.physletb.2015.10.013 https://arxiv.org/abs/1510.01808 https://inspirehep.net/search?p=find+EPRINT+arXiv:1510.01808 https://doi.org/10.1103/PhysRevD.99.054020 https://doi.org/10.1103/PhysRevD.99.054020 https://arxiv.org/abs/1803.01297 https://inspirehep.net/search?p=find+EPRINT+arXiv:1803.01297 https://doi.org/10.1103/PhysRevD.96.013003 https://doi.org/10.1103/PhysRevD.96.013003 https://arxiv.org/abs/1705.07299 https://inspirehep.net/search?p=find+EPRINT+arXiv:1705.07299 https://doi.org/10.1103/PhysRevD.101.036018 https://arxiv.org/abs/1911.01121 https://inspirehep.net/search?p=find+EPRINT+arXiv:1911.01121 https://doi.org/10.1103/physrevd.91.119902 https://arxiv.org/abs/1312.5730 https://inspirehep.net/search?p=find+EPRINT+arXiv:1312.5730 https://doi.org/10.1103/PhysRevD.92.036010 https://arxiv.org/abs/1507.07990 https://inspirehep.net/search?p=find+EPRINT+arXiv:1507.07990 https://doi.org/10.1016/j.physletb.2015.08.048 https://arxiv.org/abs/1501.00646 https://inspirehep.net/search?p=find+EPRINT+arXiv:1501.00646 J H E P 0 3 ( 2 0 2 0 ) 1 6 5 [18] R. Arora, G.K. Sidana and M.P. Khanna, SU(3) predictions for nonleptonic weak decays of bottom baryons, Phys. Rev. D 45 (1992) 4121 [INSPIRE]. [19] D.-S. Du and D.-X. Zhang, SU(3) breaking effects in nonleptonic decays of the bottom baryons, Phys. Rev. D 50 (1994) 2058 [INSPIRE]. [20] J.G. Korner, M. Krämer and D. Pirjol, Heavy baryons, Prog. Part. Nucl. Phys. 33 (1994) 787 [hep-ph/9406359] [INSPIRE]. [21] Y.K. Hsiao and C.Q. Geng, Direct CP-violation in Λb decays, Phys. Rev. D 91 (2015) 116007 [arXiv:1412.1899] [INSPIRE]. [22] M. Gronau and J.L. Rosner, S-wave nonleptonic hyperon decays and Ξ−b → π −Λb, Phys. Rev. D 93 (2016) 034020 [arXiv:1512.06700] [INSPIRE]. [23] M. Gronau and J.L. Rosner, From Ξb → Λbπ to Ξc → Λcπ, Phys. Lett. B 757 (2016) 330 [arXiv:1603.07309] [INSPIRE]. [24] D.A. Egolf, R.P. Springer and J. Urban, SU(3) predictions for weak decays of doubly heavy baryons including SU(3) breaking terms, Phys. Rev. D 68 (2003) 013003 [hep-ph/0211360] [INSPIRE]. [25] A.K. Leibovich, Z. Ligeti, I.W. Stewart and M.B. Wise, Predictions for nonleptonic Lambda(b) and Theta(b) decays, Phys. Lett. B 586 (2004) 337 [hep-ph/0312319] [INSPIRE]. [26] Y. Grossman and S. Schacht, U-Spin Sum Rules for CP Asymmetries of Three-Body Charmed Baryon Decays, Phys. Rev. D 99 (2019) 033005 [arXiv:1811.11188] [INSPIRE]. [27] C.-D. Lü, W. Wang and F.-S. Yu, Test flavor SU(3) symmetry in exclusive Λc decays, Phys. Rev. D 93 (2016) 056008 [arXiv:1601.04241] [INSPIRE]. [28] C.Q. Geng, Y.K. Hsiao, C.-W. Liu and T.-H. Tsai, Three-body charmed baryon Decays with SU(3) flavor symmetry, Phys. Rev. D 99 (2019) 073003 [arXiv:1810.01079] [INSPIRE]. [29] C.-P. Jia, D. Wang and F.-S. Yu, Charmed baryon decays in SU(3)F symmetry, arXiv:1910.00876 [INSPIRE]. [30] M.J. Savage and R.P. Springer, SU(3) Predictions for Charmed Baryon Decays, Phys. Rev. D 42 (1990) 1527 [INSPIRE]. [31] M.J. Savage and R.P. Springer, Very charming baryons, Int. J. Mod. Phys. A 6 (1991) 1701 [INSPIRE]. [32] R.-M. Wang, M.-Z. Yang, H.-B. Li and X.-D. Cheng, Testing SU(3) Flavor Symmetry in Semileptonic and Two-body Nonleptonic Decays of Hyperons, Phys. Rev. D 100 (2019) 076008 [arXiv:1906.08413] [INSPIRE]. [33] C.Q. Geng, Y.K. Hsiao, C.-W. Liu and T.-H. Tsai, SU(3) symmetry breaking in charmed baryon decays, Eur. Phys. J. C 78 (2018) 593 [arXiv:1804.01666] [INSPIRE]. [34] C.Q. Geng, Y.K. Hsiao, C.-W. Liu and T.-H. Tsai, Antitriplet charmed baryon decays with SU(3) flavor symmetry, Phys. Rev. D 97 (2018) 073006 [arXiv:1801.03276] [INSPIRE]. [35] C.Q. Geng, Y.K. Hsiao, C.-W. Liu and T.-H. Tsai, Charmed Baryon Weak Decays with SU(3) Flavor Symmetry, JHEP 11 (2017) 147 [arXiv:1709.00808] [INSPIRE]. [36] H.J. Zhao, Y.-L. Wang, Y.K. Hsiao and Y. Yu, A diagrammatic analysis of two-body charmed baryon decays with flavor symmetry, JHEP 02 (2020) 165 [arXiv:1811.07265] [INSPIRE]. – 19 – https://doi.org/10.1103/PhysRevD.45.4121 https://inspirehep.net/search?p=find+J+%22Phys.Rev.,D45,4121%22 https://doi.org/10.1103/PhysRevD.50.2058 https://inspirehep.net/search?p=find+J+%22Phys.Rev.,D50,2058%22 https://doi.org/10.1016/0146-6410(94)90053-1 https://doi.org/10.1016/0146-6410(94)90053-1 https://arxiv.org/abs/hep-ph/9406359 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9406359 https://doi.org/10.1103/PhysRevD.91.116007 https://doi.org/10.1103/PhysRevD.91.116007 https://arxiv.org/abs/1412.1899 https://inspirehep.net/search?p=find+EPRINT+arXiv:1412.1899 https://doi.org/10.1103/PhysRevD.93.034020 https://doi.org/10.1103/PhysRevD.93.034020 https://arxiv.org/abs/1512.06700 https://inspirehep.net/search?p=find+EPRINT+arXiv:1512.06700 https://doi.org/10.1016/j.physletb.2016.04.020 https://arxiv.org/abs/1603.07309 https://inspirehep.net/search?p=find+EPRINT+arXiv:1603.07309 https://doi.org/10.1103/PhysRevD.68.013003 https://arxiv.org/abs/hep-ph/0211360 https://inspirehep.net/search?p=find+EPRINT+hep-ph/0211360 https://doi.org/10.1016/j.physletb.2004.02.033 https://arxiv.org/abs/hep-ph/0312319 https://inspirehep.net/search?p=find+EPRINT+hep-ph/0312319 https://doi.org/10.1103/PhysRevD.99.033005 https://arxiv.org/abs/1811.11188 https://inspirehep.net/search?p=find+EPRINT+arXiv:1811.11188 https://doi.org/10.1103/PhysRevD.93.056008 https://doi.org/10.1103/PhysRevD.93.056008 https://arxiv.org/abs/1601.04241 https://inspirehep.net/search?p=find+EPRINT+arXiv:1601.04241 https://doi.org/10.1103/PhysRevD.99.073003 https://arxiv.org/abs/1810.01079 https://inspirehep.net/search?p=find+EPRINT+arXiv:1810.01079 https://arxiv.org/abs/1910.00876 https://inspirehep.net/search?p=find+EPRINT+arXiv:1910.00876 https://doi.org/10.1103/PhysRevD.42.1527 https://doi.org/10.1103/PhysRevD.42.1527 https://inspirehep.net/search?p=find+J+%22Phys.Rev.,D42,1527%22 https://doi.org/10.1142/S0217751X91000903 https://inspirehep.net/search?p=find+J+%22Int.J.Mod.Phys.,A6,1701%22 https://doi.org/10.1103/PhysRevD.100.076008 https://doi.org/10.1103/PhysRevD.100.076008 https://arxiv.org/abs/1906.08413 https://inspirehep.net/search?p=find+EPRINT+arXiv:1906.08413 https://doi.org/10.1140/epjc/s10052-018-6075-7 https://arxiv.org/abs/1804.01666 https://inspirehep.net/search?p=find+EPRINT+arXiv:1804.01666 https://doi.org/10.1103/PhysRevD.97.073006 https://arxiv.org/abs/1801.03276 https://inspirehep.net/search?p=find+EPRINT+arXiv:1801.03276 https://doi.org/10.1007/JHEP11(2017)147 https://arxiv.org/abs/1709.00808 https://inspirehep.net/search?p=find+EPRINT+arXiv:1709.00808 https://doi.org/10.1007/JHEP02(2020)165 https://arxiv.org/abs/1811.07265 https://inspirehep.net/search?p=find+EPRINT+arXiv:1811.07265 J H E P 0 3 ( 2 0 2 0 ) 1 6 5 [37] M. Gronau, J.L. Rosner and C.G. Wohl, Overview of Λc decays, Phys. Rev. D 97 (2018) 116015 [arXiv:1808.03720] [INSPIRE]. [38] D. Ebert and W. Kallies, Nonleptonic Decays of Charmed Baryons in the MIT Bag Model, Phys. Lett. 131B (1983) 183 [Erratum ibid. B 148 (1984) 502] [INSPIRE]. [39] I.I.Y. Bigi, Weak Annihilation in Charm Baryon Decays: A Reevaluation, Z. Phys. C 9 (1981) 197 [INSPIRE]. [40] I.I. Bigi, Probing CP Asymmetries in Charm Baryons Decays, arXiv:1206.4554 [INSPIRE]. [41] N. Isgur and M.B. Wise, Heavy baryon weak form-factors, Nucl. Phys. B 348 (1991) 276 [INSPIRE]. [42] A. Khodjamirian, C. Klein, T. Mannel and Y.M. Wang, Form Factors and Strong Couplings of Heavy Baryons from QCD Light-Cone Sum Rules, JHEP 09 (2011) 106 [arXiv:1108.2971] [INSPIRE]. [43] Y.-M. Wang and Y.-L. Shen, Perturbative Corrections to Λb → Λ Form Factors from QCD Light-Cone Sum Rules, JHEP 02 (2016) 179 [arXiv:1511.09036] [INSPIRE]. [44] T. Husek and S. Leupold, Radiative corrections for the decay Σ0 → Λe+e−, Eur. Phys. J. C 80 (2020) 218 [arXiv:1911.02571] [INSPIRE]. [45] C. Granados, S. Leupold and E. Perotti, The electromagnetic Sigma-to-Lambda hyperon transition form factors at low energies, Eur. Phys. J. A 53 (2017) 117 [arXiv:1701.09130] [INSPIRE]. [46] B. Kubis and U.G. Meissner, Baryon form-factors in chiral perturbation theory, Eur. Phys. J. C 18 (2001) 747 [hep-ph/0010283] [INSPIRE]. [47] T. Mannel and Y.-M. Wang, Heavy-to-light baryonic form factors at large recoil, JHEP 12 (2011) 067 [arXiv:1111.1849] [INSPIRE]. [48] W. Detmold, C.J.D. Lin, S. Meinel and M. Wingate, Λb → Λ`+`− form factors and differential branching fraction from lattice QCD, Phys. Rev. D 87 (2013) 074502 [arXiv:1212.4827] [INSPIRE]. [49] W. Detmold and S. Meinel, Λb → Λ`+`− form factors, differential branching fraction and angular observables from lattice QCD with relativistic b quarks, Phys. Rev. D 93 (2016) 074501 [arXiv:1602.01399] [INSPIRE]. [50] F.U. Bernlochner, Z. Ligeti, D.J. Robinson and W.L. Sutcliffe, Precise predictions for Λb → Λc semileptonic decays, Phys. Rev. D 99 (2019) 055008 [arXiv:1812.07593] [INSPIRE]. [51] D. Zeppenfeld, SU(3) Relations for B Meson Decays, Z. Phys. C 8 (1981) 77 [INSPIRE]. [52] M. Jung, Determining weak phases from B → J/ψP decays, Phys. Rev. D 86 (2012) 053008 [arXiv:1206.2050] [INSPIRE]. [53] M. Jung and S. Schacht, Standard model predictions and new physics sensitivity in B → DD decays, Phys. Rev. D 91 (2015) 034027 [arXiv:1410.8396] [INSPIRE]. [54] J.J. de Swart, The Octet model and its Clebsch-Gordan coefficients, Rev. Mod. Phys. 35 (1963) 916 [Erratum ibid. 37 (1965) 326] [INSPIRE]. [55] T.A. Kaeding, Tables of SU(3) isoscalar factors, Atom. Data Nucl. Data Tabl. 61 (1995) 233 [nucl-th/9502037] [INSPIRE]. – 20 – https://doi.org/10.1103/PhysRevD.97.116015 https://doi.org/10.1103/PhysRevD.97.116015 https://arxiv.org/abs/1808.03720 https://inspirehep.net/search?p=find+EPRINT+arXiv:1808.03720 https://doi.org/10.1016/0370-2693(83)91117-6 https://inspirehep.net/search?p=find+J+%22Phys.Lett.,B131,183%22 https://doi.org/10.1007/BF01410658 https://doi.org/10.1007/BF01410658 https://inspirehep.net/search?p=find+J+%22Z.Physik,C9,197%22 https://arxiv.org/abs/1206.4554 https://inspirehep.net/search?p=find+EPRINT+arXiv:1206.4554 https://doi.org/10.1016/0550-3213(91)90518-3 https://inspirehep.net/search?p=find+J+%22Nucl.Phys.,B348,276%22 https://doi.org/10.1007/JHEP09(2011)106 https://arxiv.org/abs/1108.2971 https://inspirehep.net/search?p=find+EPRINT+arXiv:1108.2971 https://doi.org/10.1007/JHEP02(2016)179 https://arxiv.org/abs/1511.09036 https://inspirehep.net/search?p=find+EPRINT+arXiv:1511.09036 https://doi.org/10.1140/epjc/s10052-020-7710-7 https://doi.org/10.1140/epjc/s10052-020-7710-7 https://arxiv.org/abs/1911.02571 https://inspirehep.net/search?p=find+EPRINT+arXiv:1911.02571 https://doi.org/10.1140/epja/i2017-12324-4 https://arxiv.org/abs/1701.09130 https://inspirehep.net/search?p=find+EPRINT+arXiv:1701.09130 https://doi.org/10.1007/s100520100570 https://doi.org/10.1007/s100520100570 https://arxiv.org/abs/hep-ph/0010283 https://inspirehep.net/search?p=find+EPRINT+hep-ph/0010283 https://doi.org/10.1007/JHEP12(2011)067 https://doi.org/10.1007/JHEP12(2011)067 https://arxiv.org/abs/1111.1849 https://inspirehep.net/search?p=find+EPRINT+arXiv:1111.1849 https://doi.org/10.1103/PhysRevD.87.074502 https://arxiv.org/abs/1212.4827 https://inspirehep.net/search?p=find+EPRINT+arXiv:1212.4827 https://doi.org/10.1103/PhysRevD.93.074501 https://doi.org/10.1103/PhysRevD.93.074501 https://arxiv.org/abs/1602.01399 https://inspirehep.net/search?p=find+EPRINT+arXiv:1602.01399 https://doi.org/10.1103/PhysRevD.99.055008 https://arxiv.org/abs/1812.07593 https://inspirehep.net/search?p=find+EPRINT+arXiv:1812.07593 https://doi.org/10.1007/BF01429835 https://inspirehep.net/search?p=find+J+%22Z.Physik,C8,77%22 https://doi.org/10.1103/PhysRevD.86.053008 https://doi.org/10.1103/PhysRevD.86.053008 https://arxiv.org/abs/1206.2050 https://inspirehep.net/search?p=find+EPRINT+arXiv:1206.2050 https://doi.org/10.1103/PhysRevD.91.034027 https://arxiv.org/abs/1410.8396 https://inspirehep.net/search?p=find+EPRINT+arXiv:1410.8396 https://doi.org/10.1103/RevModPhys.35.916 https://doi.org/10.1103/RevModPhys.35.916 https://inspirehep.net/search?p=find+J+%22Rev.Mod.Phys.,35,916%22 https://doi.org/10.1006/adnd.1995.1011 https://doi.org/10.1006/adnd.1995.1011 https://arxiv.org/abs/nucl-th/9502037 https://inspirehep.net/search?p=find+EPRINT+nucl-th/9502037 J H E P 0 3 ( 2 0 2 0 ) 1 6 5 [56] T.A. Kaeding and H.T. Williams, Program for generating tables of SU(3) coupling coefficients, Comput. Phys. Commun. 98 (1996) 398 [nucl-th/9511025] [INSPIRE]. [57] T. Gutsche, M.A. Ivanov, J.G. Körner, V.E. Lyubovitskij and P. Santorelli, Polarization effects in the cascade decay Λb → Λ(→ pπ−) + J/ψ(→ `+`−) in the covariant confined quark model, Phys. Rev. D 88 (2013) 114018 [arXiv:1309.7879] [INSPIRE]. [58] Particle Data Group collaboration, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE]. [59] O.F. Hernandez, D. London, M. Gronau and J.L. Rosner, Measuring strong and weak phases in time independent B decays, Phys. Lett. B 333 (1994) 500 [hep-ph/9404281] [INSPIRE]. [60] M. Gronau, J.L. Rosner and D. London, Weak coupling phase from decays of charged B mesons to πK and ππ, Phys. Rev. Lett. 73 (1994) 21 [hep-ph/9404282] [INSPIRE]. [61] M. Gronau, O.F. Hernandez, D. London and J.L. Rosner, Decays of B mesons to two light pseudoscalars, Phys. Rev. D 50 (1994) 4529 [hep-ph/9404283] [INSPIRE]. [62] M. Gronau, O.F. Hernandez, D. London and J.L. Rosner, Broken SU(3) symmetry in two-body B decays, Phys. Rev. D 52 (1995) 6356 [hep-ph/9504326] [INSPIRE]. [63] M. Neubert and J.L. Rosner, Determination of the weak phase gamma from rate measurements in B± → πK,ππ decays, Phys. Rev. Lett. 81 (1998) 5076 [hep-ph/9809311] [INSPIRE]. [64] M. Gronau, U spin symmetry in charmless B decays, Phys. Lett. B 492 (2000) 297 [hep-ph/0008292] [INSPIRE]. [65] R. Fleischer, New strategies to extract Beta and gamma from Bd → π+π− and BS → K+K−, Phys. Lett. B 459 (1999) 306 [hep-ph/9903456] [INSPIRE]. [66] M. Gronau and J.L. Rosner, The Role of Bs → Kπ in determining the weak phase γ, Phys. Lett. B 482 (2000) 71 [hep-ph/0003119] [INSPIRE]. [67] X.-G. He, SU(3) analysis of annihilation contributions and CP-violating relations in B → PP decays, Eur. Phys. J. C 9 (1999) 443 [hep-ph/9810397] [INSPIRE]. [68] B. Bhattacharya, M. Gronau and J.L. Rosner, CP asymmetries in three-body B± decays to charged pions and kaons, Phys. Lett. B 726 (2013) 337 [arXiv:1306.2625] [INSPIRE]. [69] N. Isgur, Isospin violating mass differences and mixing angles: the role of quark masses, Phys. Rev. D 21 (1980) 779 [Erratum ibid. D 23 (1981) 817] [INSPIRE]. [70] D. Wang, Sum rules for CP asymmetries of charmed baryon decays in the SU(3)F limit, Eur. Phys. J. C 79 (2019) 429 [arXiv:1901.01776] [INSPIRE]. [71] B. Bhattacharya and J.L. Rosner, Charmed meson decays to two pseudoscalars, Phys. Rev. D 81 (2010) 014026 [arXiv:0911.2812] [INSPIRE]. [72] G. Hiller, M. Jung and S. Schacht, SU(3)-flavor anatomy of nonleptonic charm decays, Phys. Rev. D 87 (2013) 014024 [arXiv:1211.3734] [INSPIRE]. [73] Y. Grossman and S. Schacht, The emergence of the ∆U = 0 rule in charm physics, JHEP 07 (2019) 020 [arXiv:1903.10952] [INSPIRE]. [74] S. Müller, U. Nierste and S. Schacht, Sum Rules of Charm CP Asymmetries beyond the SU(3)F Limit, Phys. Rev. Lett. 115 (2015) 251802 [arXiv:1506.04121] [INSPIRE]. – 21 – https://doi.org/10.1016/0010-4655(96)00085-9 https://arxiv.org/abs/nucl-th/9511025 https://inspirehep.net/search?p=find+EPRINT+nucl-th/9511025 https://doi.org/10.1103/PhysRevD.88.114018 https://arxiv.org/abs/1309.7879 https://inspirehep.net/search?p=find+EPRINT+arXiv:1309.7879 https://doi.org/10.1103/PhysRevD.98.030001 https://doi.org/10.1103/PhysRevD.98.030001 https://inspirehep.net/search?p=find+J+%22Phys.Rev.,D98,030001%22 https://doi.org/10.1016/0370-2693(94)90174-0 https://arxiv.org/abs/hep-ph/9404281 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9404281 https://doi.org/10.1103/PhysRevLett.73.21 https://arxiv.org/abs/hep-ph/9404282 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9404282 https://doi.org/10.1103/PhysRevD.50.4529 https://arxiv.org/abs/hep-ph/9404283 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9404283 https://doi.org/10.1103/PhysRevD.52.6356 https://arxiv.org/abs/hep-ph/9504326 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9504326 https://doi.org/10.1103/PhysRevLett.81.5076 https://arxiv.org/abs/hep-ph/9809311 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9809311 https://doi.org/10.1016/S0370-2693(00)01119-9 https://arxiv.org/abs/hep-ph/0008292 https://inspirehep.net/search?p=find+EPRINT+hep-ph/0008292 https://doi.org/10.1016/S0370-2693(99)00640-1 https://arxiv.org/abs/hep-ph/9903456 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9903456 https://doi.org/10.1016/S0370-2693(00)00508-6 https://doi.org/10.1016/S0370-2693(00)00508-6 https://arxiv.org/abs/hep-ph/0003119 https://inspirehep.net/search?p=find+EPRINT+hep-ph/0003119 https://doi.org/10.1007/s100529900064 https://arxiv.org/abs/hep-ph/9810397 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9810397 https://doi.org/10.1016/j.physletb.2013.08.062 https://arxiv.org/abs/1306.2625 https://inspirehep.net/search?p=find+EPRINT+arXiv:1306.2625 https://doi.org/10.1103/PhysRevD.21.779 https://inspirehep.net/search?p=find+J+%22Phys.Rev.,D21,779%22 https://doi.org/10.1140/epjc/s10052-019-6925-y https://arxiv.org/abs/1901.01776 https://inspirehep.net/search?p=find+EPRINT+arXiv:1901.01776 https://doi.org/10.1103/PhysRevD.81.014026 https://doi.org/10.1103/PhysRevD.81.014026 https://arxiv.org/abs/0911.2812 https://inspirehep.net/search?p=find+EPRINT+arXiv:0911.2812 https://doi.org/10.1103/PhysRevD.87.014024 https://arxiv.org/abs/1211.3734 https://inspirehep.net/search?p=find+EPRINT+arXiv:1211.3734 https://doi.org/10.1007/JHEP07(2019)020 https://doi.org/10.1007/JHEP07(2019)020 https://arxiv.org/abs/1903.10952 https://inspirehep.net/search?p=find+EPRINT+arXiv:1903.10952 https://doi.org/10.1103/PhysRevLett.115.251802 https://arxiv.org/abs/1506.04121 https://inspirehep.net/search?p=find+EPRINT+arXiv:1506.04121 J H E P 0 3 ( 2 0 2 0 ) 1 6 5 [75] S. Müller, U. Nierste and S. Schacht, Topological amplitudes in D decays to two pseudoscalars: A global analysis with linear SU(3)F breaking, Phys. Rev. D 92 (2015) 014004 [arXiv:1503.06759] [INSPIRE]. [76] J. Brod, Y. Grossman, A.L. Kagan and J. Zupan, A Consistent Picture for Large Penguins in D → π+π−,K+K−, JHEP 10 (2012) 161 [arXiv:1203.6659] [INSPIRE]. [77] Y. Grossman, A.L. Kagan and J. Zupan, Testing for new physics in singly Cabibbo suppressed D decays, Phys. Rev. D 85 (2012) 114036 [arXiv:1204.3557] [INSPIRE]. [78] Y. Grossman, A.L. Kagan and Y. Nir, New physics and CP-violation in singly Cabibbo suppressed D decays, Phys. Rev. D 75 (2007) 036008 [hep-ph/0609178] [INSPIRE]. [79] A.F. Falk, Y. Grossman, Z. Ligeti and A.A. Petrov, SU(3) breaking and D0-D̄0 mixing, Phys. Rev. D 65 (2002) 054034 [hep-ph/0110317] [INSPIRE]. [80] M.J. Savage, SU(3) violations in the nonleptonic decay of charmed hadrons, Phys. Lett. B 257 (1991) 414 [INSPIRE]. [81] I. Hinchliffe and T.A. Kaeding, Nonleptonic two-body decays of D mesons in broken SU(3), Phys. Rev. D 54 (1996) 914 [hep-ph/9502275] [INSPIRE]. [82] M. Jung and T. Mannel, General Analysis of U-Spin Breaking in B Decays, Phys. Rev. D 80 (2009) 116002 [arXiv:0907.0117] [INSPIRE]. [83] M. Gronau, Y. Grossman, G. Raz and J.L. Rosner, Suppression of flavor symmetry breaking in B decay sum rules, Phys. Lett. B 635 (2006) 207 [hep-ph/0601129] [INSPIRE]. [84] D. Pirtskhalava and P. Uttayarat, CP Violation and Flavor SU(3) Breaking in D-meson Decays, Phys. Lett. B 712 (2012) 81 [arXiv:1112.5451] [INSPIRE]. [85] F. Buccella, A. Paul and P. Santorelli, SU(3)F breaking through final state interactions and CP asymmetries in D → PP decays, Phys. Rev. D 99 (2019) 113001 [arXiv:1902.05564] [INSPIRE]. [86] Y. Grossman and D.J. Robinson, SU(3) Sum Rules for Charm Decay, JHEP 04 (2013) 067 [arXiv:1211.3361] [INSPIRE]. [87] L.A. Copley, N. Isgur and G. Karl, Charmed Baryons in a Quark Model with Hyperfine Interactions, Phys. Rev. D 20 (1979) 768 [Erratum ibid. D 23 (1981) 817] [INSPIRE]. [88] K. Maltman and N. Isgur, Baryons With Strangeness and Charm in a Quark Model With Chromodynamics, Phys. Rev. D 22 (1980) 1701 [INSPIRE]. [89] J. Franklin, D.B. Lichtenberg, W. Namgung and D. Carydas, Wave Function Mixing of Flavor Degenerate Baryons, Phys. Rev. D 24 (1981) 2910 [INSPIRE]. [90] M.J. Savage and M.B. Wise, SU(3) Predictions for Nonleptonic B Meson Decays to Charmed Baryons, Nucl. Phys. B 326 (1989) 15 [INSPIRE]. [91] C.G. Boyd, M. Lu and M.J. Savage, Heavy baryon mixing in chiral perturbation theory, Phys. Rev. D 55 (1997) 5474 [hep-ph/9612441] [INSPIRE]. [92] M. Karliner, B. Keren-Zur, H.J. Lipkin and J.L. Rosner, The Quark Model and b Baryons, Annals Phys. 324 (2009) 2 [arXiv:0804.1575] [INSPIRE]. [93] S.R. Coleman and S.L. Glashow, Electrodynamic properties of baryons in the unitary symmetry scheme, Phys. Rev. Lett. 6 (1961) 423 [INSPIRE]. – 22 – https://doi.org/10.1103/PhysRevD.92.014004 https://doi.org/10.1103/PhysRevD.92.014004 https://arxiv.org/abs/1503.06759 https://inspirehep.net/search?p=find+EPRINT+arXiv:1503.06759 https://doi.org/10.1007/JHEP10(2012)161 https://arxiv.org/abs/1203.6659 https://inspirehep.net/search?p=find+EPRINT+arXiv:1203.6659 https://doi.org/10.1103/PhysRevD.85.114036 https://arxiv.org/abs/1204.3557 https://inspirehep.net/search?p=find+EPRINT+arXiv:1204.3557 https://doi.org/10.1103/PhysRevD.75.036008 https://arxiv.org/abs/hep-ph/0609178 https://inspirehep.net/search?p=find+EPRINT+hep-ph/0609178 https://doi.org/10.1103/PhysRevD.65.054034 https://arxiv.org/abs/hep-ph/0110317 https://inspirehep.net/search?p=find+EPRINT+hep-ph/0110317 https://doi.org/10.1016/0370-2693(91)91917-K https://doi.org/10.1016/0370-2693(91)91917-K https://inspirehep.net/search?p=find+J+%22Phys.Lett.,B257,414%22 https://doi.org/10.1103/PhysRevD.54.914 https://arxiv.org/abs/hep-ph/9502275 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9502275 https://doi.org/10.1103/PhysRevD.80.116002 https://doi.org/10.1103/PhysRevD.80.116002 https://arxiv.org/abs/0907.0117 https://inspirehep.net/search?p=find+EPRINT+arXiv:0907.0117 https://doi.org/10.1016/j.physletb.2006.02.066 https://arxiv.org/abs/hep-ph/0601129 https://inspirehep.net/search?p=find+EPRINT+hep-ph/0601129 https://doi.org/10.1016/j.physletb.2012.04.039 https://arxiv.org/abs/1112.5451 https://inspirehep.net/search?p=find+EPRINT+arXiv:1112.5451 https://doi.org/10.1103/PhysRevD.99.113001 https://arxiv.org/abs/1902.05564 https://inspirehep.net/search?p=find+EPRINT+arXiv:1902.05564 https://doi.org/10.1007/JHEP04(2013)067 https://arxiv.org/abs/1211.3361 https://inspirehep.net/search?p=find+EPRINT+arXiv:1211.3361 https://doi.org/10.1103/PhysRevD.23.817.3 https://inspirehep.net/search?p=find+J+%22Phys.Rev.,D20,768%22 https://doi.org/10.1103/PhysRevD.22.1701 https://inspirehep.net/search?p=find+J+%22Phys.Rev.,D22,1701%22 https://doi.org/10.1103/PhysRevD.24.2910 https://inspirehep.net/search?p=find+J+%22Phys.Rev.,D24,2910%22 https://doi.org/10.1016/0550-3213(89)90432-X https://inspirehep.net/search?p=find+J+%22Nucl.Phys.,B326,15%22 https://doi.org/10.1103/PhysRevD.55.5474 https://arxiv.org/abs/hep-ph/9612441 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9612441 https://doi.org/10.1016/j.aop.2008.05.003 https://arxiv.org/abs/0804.1575 https://inspirehep.net/search?p=find+EPRINT+arXiv:0804.1575 https://doi.org/10.1103/PhysRevLett.6.423 https://inspirehep.net/search?p=find+J+%22Phys.Rev.Lett.,6,423%22 J H E P 0 3 ( 2 0 2 0 ) 1 6 5 [94] R.H. Dalitz and F. Von Hippel, Electromagnetic Λ −σ0 mixing and charge symmetry for the Λ-hyperon, Phys. Lett. 10 (1964) 153 [INSPIRE]. [95] R. Horsley et al., Lattice determination of Sigma-Lambda mixing, Phys. Rev. D 91 (2015) 074512 [arXiv:1411.7665] [INSPIRE]. [96] A. Gal, Comment on “Lattice determination of Σ-Λ mixing”, Phys. Rev. D 92 (2015) 018501 [arXiv:1506.01143] [INSPIRE]. [97] QCDSF-UKQCD collaboration, Reply to “Comment on ‘Lattice determination of Σ-Λ mixing”’, Phys. Rev. D 92 (2015) 018502 [arXiv:1507.07825] [INSPIRE]. [98] CSSM/QCDSF/UKQCD collaboration, Electromagnetic contribution to Σ-Λ mixing using lattice QCD+QED, Phys. Rev. D 101 (2020) 034517 [arXiv:1911.02186] [INSPIRE]. [99] T. Feldmann and P. Kroll, Mixing of pseudoscalar mesons, Phys. Scripta T 99 (2002) 13 [hep-ph/0201044] [INSPIRE]. [100] T. Feldmann, P. Kroll and B. Stech, Mixing and decay constants of pseudoscalar mesons: The Sequel, Phys. Lett. B 449 (1999) 339 [hep-ph/9812269] [INSPIRE]. [101] T. Feldmann, P. Kroll and B. Stech, Mixing and decay constants of pseudoscalar mesons, Phys. Rev. D 58 (1998) 114006 [hep-ph/9802409] [INSPIRE]. [102] T. Feldmann and P. Kroll, Flavor symmetry breaking and mixing effects in the eta gamma and eta-prime gamma transition form-factors, Eur. Phys. J. C 5 (1998) 327 [hep-ph/9711231] [INSPIRE]. [103] J.J. Dudek, R.G. Edwards, B. Joo, M.J. Peardon, D.G. Richards and C.E. Thomas, Isoscalar meson spectroscopy from lattice QCD, Phys. Rev. D 83 (2011) 111502 [arXiv:1102.4299] [INSPIRE]. [104] K. Ottnad, Pseudoscalar flavor-singlet mesons from lattice QCD, PoS(CD2018)077 (2019) [arXiv:1905.08385] [INSPIRE]. [105] A. De Rujula, H. Georgi and S.L. Glashow, Hadron Masses in a Gauge Theory, Phys. Rev. D 12 (1975) 147 [INSPIRE]. [106] J. Gasser and H. Leutwyler, Quark Masses, Phys. Rept. 87 (1982) 77 [INSPIRE]. [107] J.F. Donoghue, E. Golowich and B.R. Holstein, Low-Energy Weak Interactions of Quarks, Phys. Rept. 131 (1986) 319 [INSPIRE]. [108] J.F. Donoghue, Light Quark Masses and Chiral Symmetry, Ann. Rev. Nucl. Part. Sci. 39 (1989) 1 [INSPIRE]. [109] G. Karl, Isospin violation and hyperon semileptonic decays, Phys. Lett. B 328 (1994) 149 [Erratum ibid. B 341 (1995) 449] [INSPIRE]. [110] J. Gasser and H. Leutwyler, Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark, Nucl. Phys. B 250 (1985) 465 [INSPIRE]. [111] A. Gal and F. Scheck, Electromagnetic mass splittings of mesons and baryons in the quark model, Nucl. Phys. B 2 (1967) 110 [INSPIRE]. [112] P. Federman, H.R. Rubinstein and I. Talmi, Dynamical derivation of baryon masses in the quark model, Phys. Lett. 22 (1966) 208 [INSPIRE]. [113] H.R. Rubinstein, F. Scheck and R.H. Socolow, Electromagnetic Properties of Hadrons in the Quark Model, Phys. Rev. 154 (1967) 1608 [INSPIRE]. – 23 – https://doi.org/10.1016/0031-9163(64)90617-1 https://inspirehep.net/search?p=find+J+%22Phys.Lett.,10,153%22 https://doi.org/10.1103/PhysRevD.91.074512 https://doi.org/10.1103/PhysRevD.91.074512 https://arxiv.org/abs/1411.7665 https://inspirehep.net/search?p=find+EPRINT+arXiv:1411.7665 https://doi.org/10.1103/PhysRevD.92.018501 https://doi.org/10.1103/PhysRevD.92.018501 https://arxiv.org/abs/1506.01143 https://inspirehep.net/search?p=find+EPRINT+arXiv:1506.01143 https://doi.org/10.1103/PhysRevD.92.018502 https://arxiv.org/abs/1507.07825 https://inspirehep.net/search?p=find+EPRINT+arXiv:1507.07825 https://doi.org/10.1103/PhysRevD.101.034517 https://arxiv.org/abs/1911.02186 https://inspirehep.net/search?p=find+EPRINT+arXiv:1911.02186 https://doi.org/10.1238/Physica.Topical.099a00013 https://arxiv.org/abs/hep-ph/0201044 https://inspirehep.net/search?p=find+EPRINT+hep-ph/0201044 https://doi.org/10.1016/S0370-2693(99)00085-4 https://arxiv.org/abs/hep-ph/9812269 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9812269 https://doi.org/10.1103/PhysRevD.58.114006 https://arxiv.org/abs/hep-ph/9802409 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9802409 https://doi.org/10.1007/s100529800848 https://arxiv.org/abs/hep-ph/9711231 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9711231 https://doi.org/10.1103/PhysRevD.83.111502 https://arxiv.org/abs/1102.4299 https://inspirehep.net/search?p=find+EPRINT+arXiv:1102.4299 https://doi.org/10.22323/1.317.0077 https://arxiv.org/abs/1905.08385 https://inspirehep.net/search?p=find+EPRINT+arXiv:1905.08385 https://doi.org/10.1103/PhysRevD.12.147 https://doi.org/10.1103/PhysRevD.12.147 https://inspirehep.net/search?p=find+J+%22Phys.Rev.,D12,147%22 https://doi.org/10.1016/0370-1573(82)90035-7 https://inspirehep.net/search?p=find+J+%22Phys.Rept.,87,77%22 https://doi.org/10.1016/0370-1573(86)90151-1 https://inspirehep.net/search?p=find+J+%22Phys.Rept.,131,319%22 https://doi.org/10.1146/annurev.ns.39.120189.000245 https://doi.org/10.1146/annurev.ns.39.120189.000245 https://inspirehep.net/search?p=find+J+%22Ann.Rev.Nucl.Part.Sci.,39,1%22 https://doi.org/10.1016/0370-2693(95)80029-W https://inspirehep.net/search?p=find+J+%22Phys.Lett.,B328,149%22 https://doi.org/10.1016/0550-3213(85)90492-4 https://inspirehep.net/search?p=find+J+%22Nucl.Phys.,B250,465%22 https://doi.org/10.1016/0550-3213(67)90122-8 https://inspirehep.net/search?p=find+J+%22Nucl.Phys.,B2,110%22 https://doi.org/10.1016/0031-9163(66)90577-4 https://inspirehep.net/search?p=find+J+%22Phys.Lett.,22,208%22 https://doi.org/10.1103/PhysRev.154.1608 https://inspirehep.net/search?p=find+J+%22Phys.Rev.,154,1608%22 J H E P 0 3 ( 2 0 2 0 ) 1 6 5 [114] E.M. Henley and G.A. Miller, A Proposed test of charge symmetry in Sigma decay, Phys. Rev. D 50 (1994) 7077 [hep-ph/9408227] [INSPIRE]. [115] K. Maltman, Strong isospin mixing effects on the extraction of ∆I = 3/2 nonleptonic hyperon decay amplitudes, Phys. Lett. B 345 (1995) 541 [hep-ph/9504253] [INSPIRE]. [116] G. Karl, Isospin violation in hyperon semileptonic decays, in Hyperon physics symposium: Hyperon 99, 27–29 September 1999, Fermi National Accelerator Laboratory, Batavia, Illinois, pp. 41–42 (1999) [hep-ph/9910418] [INSPIRE]. [117] E.S. Na and B.R. Holstein, Isospin mixing and model dependence, Phys. Rev. D 56 (1997) 4404 [hep-ph/9704407] [INSPIRE]. [118] D.J. Gross, S.B. Treiman and F. Wilczek, Light Quark Masses and Isospin Violation, Phys. Rev. D 19 (1979) 2188 [INSPIRE]. [119] P. Kroll, Isospin symmetry breaking through π0-η-η′ mixing, Mod. Phys. Lett. A 20 (2005) 2667 [hep-ph/0509031] [INSPIRE]. [120] S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 [INSPIRE]. [121] J.S. Bell and R. Jackiw, A PCAC puzzle: π0 → γγ in the σ model, Nuovo Cim. A 60 (1969) 47 [INSPIRE]. [122] K. Maltman, Q2 dependence of meson mixing in few body charge symmetry breaking: π0-η mixing to one loop in chiral perturbation theory, Phys. Lett. B 313 (1993) 203 [nucl-th/9211006] [INSPIRE]. [123] G. Berlad, A. Dar, G. Eilam and J. Franklin, Dominance of electromagnetic effects in high energy hadron and photon induced reactions, Annals Phys. 75 (1973) 461 [INSPIRE]. [124] A. Ali, C. Hambrock, A.Y. Parkhomenko and W. Wang, Light-Cone Distribution Amplitudes of the Ground State Bottom Baryons in HQET, Eur. Phys. J. C 73 (2013) 2302 [arXiv:1212.3280] [INSPIRE]. [125] W. Roberts and M. Pervin, Heavy baryons in a quark model, Int. J. Mod. Phys. A 23 (2008) 2817 [arXiv:0711.2492] [INSPIRE]. [126] W. Greiner and B. Muller, Theoretical physics. Vol. 2: Quantum mechanics. Symmetries, Springer (1989) [INSPIRE]. [127] J.L. Rosner, Magnetic Moments of Composite Baryons, Quarks and Leptons, Prog. Theor. Phys. 66 (1981) 1422 [INSPIRE]. [128] Y.V. Novozhilov, Introduction to Elementary Particle Theory, Pergamon (1975). [129] Flavour Lattice Averaging Group collaboration, FLAG Review 2019, Eur. Phys. J. C 80 (2020) 113 [arXiv:1902.08191] [INSPIRE]. – 24 – https://doi.org/10.1103/PhysRevD.50.7077 https://doi.org/10.1103/PhysRevD.50.7077 https://arxiv.org/abs/hep-ph/9408227 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9408227 https://doi.org/10.1016/0370-2693(94)01601-8 https://arxiv.org/abs/hep-ph/9504253 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9504253 https://arxiv.org/abs/hep-ph/9910418 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9910418 https://doi.org/10.1103/PhysRevD.56.4404 https://doi.org/10.1103/PhysRevD.56.4404 https://arxiv.org/abs/hep-ph/9704407 https://inspirehep.net/search?p=find+EPRINT+hep-ph/9704407 https://doi.org/10.1103/PhysRevD.19.2188 https://doi.org/10.1103/PhysRevD.19.2188 https://inspirehep.net/search?p=find+J+%22Phys.Rev.,D19,2188%22 https://doi.org/10.1142/S0217732305018633 https://doi.org/10.1142/S0217732305018633 https://arxiv.org/abs/hep-ph/0509031 https://inspirehep.net/search?p=find+EPRINT+hep-ph/0509031 https://doi.org/10.1103/PhysRev.177.2426 https://inspirehep.net/search?p=find+J+%22Phys.Rev.,177,2426%22 https://doi.org/10.1007/BF02823296 https://doi.org/10.1007/BF02823296 https://inspirehep.net/search?p=find+J+%22NuovoCim.,A60,47%22 https://doi.org/10.1016/0370-2693(93)91213-7 https://arxiv.org/abs/nucl-th/9211006 https://inspirehep.net/search?p=find+EPRINT+nucl-th/9211006 https://doi.org/10.1016/0003-4916(73)90076-6 https://inspirehep.net/search?p=find+J+%22AnnalsPhys.,75,461%22 https://doi.org/10.1140/epjc/s10052-013-2302-4 https://doi.org/10.1140/epjc/s10052-013-2302-4 https://arxiv.org/abs/1212.3280 https://inspirehep.net/search?p=find+EPRINT+arXiv:1212.3280 https://doi.org/10.1142/S0217751X08041219 https://doi.org/10.1142/S0217751X08041219 https://arxiv.org/abs/0711.2492 https://inspirehep.net/search?p=find+EPRINT+arXiv:0711.2492 https://inspirehep.net/search?p=find+IRN+2598914 https://doi.org/10.1143/PTP.66.1422 https://doi.org/10.1143/PTP.66.1422 https://inspirehep.net/search?p=find+J+%22Prog.Theor.Phys.,66,1422%22 https://doi.org/10.1140/epjc/s10052-019-7354-7 https://doi.org/10.1140/epjc/s10052-019-7354-7 https://arxiv.org/abs/1902.08191 https://inspirehep.net/search?p=find+EPRINT+arXiv:1902.08191 Introduction SU(3)(F) analysis General SU(3)(F) decomposition Assumptions on CKM hierarchy and rescattering Isospin and U-spin decompositions CP asymmetry sum rules SU(3)(F) breaking Sigma**(0)–Lambda mixing in Lambda(b) decays General considerations Anatomy of Sigma**(0)–Lambda mixing The dynamic contribution Prediction for B(Lambda(b) –> Sigma**(0) J/psi) Comparison with recent data Conclusions