1 Weak radiative decays of hyperons and of charm and beauty baryons ∗ Paul Singer Department of Physics, Technion-Israel Institute of Technology, 32000 Haifa, Israel A review is presented of the weak radiative decays of baryons. It includes an analysis of the possible contri- butions of electromagnetic penguins to these decays, a survey of the difficulties still encountered in the sector of hyperon decays and a short account on some new developments on this topic. The theoretical treatments on charm and beauty baryon decays are summarized, with a good outlook for their detection. 1. INTRODUCTION Although hyperon decays have been under scrutiny for some three decad the subject still carries the burden of a major puzzle and of dis- crepancies between existing data and a variety of theoretical models [1,2]. At the other end of quarks spectrum, there are no data yet on weak radiative decays of heavy baryons; however, esti- mates [3-6] for some of these modes allows us to anticipate optimistically their future detection. In the (s,d,u) sector, the interesting weak ra- diative processes are two-body decays. These de- cays proceed with branching ratios of the order of (1−3)×10−3, like Σ+ → pγ, Λ → nγ, Ξ0 → Σ0γ, or of the order 10−4, like Ξ− → Σ−γ and the expected Ω− → Ξ−γ[7]. The three-body de- cays Λ → pπ−γ, Σ+,− → nπ+,−γ proceed as expected for inner bremsstrahling processes with branching ratios close to 10−3 and are not of our concern here. On the other hand, the two- body exclusive heavy baryon weak radiative pro- cesses like Λb → Λ0γ, Ξ−b → Ξ−γ are not nec- essarily dominating the radiative channel and as we shall see one expects these modes to be sub- stantially smaller than the inclusive ones, e.g. BR[Λb → X(s)γ] >> BR[Λb → Λ0γ]. Never- theless, the study of the exclusive channels could provide important physical insights. These weak radiative processes result from an interplay of electroweak and gluonic interactions. Presently, their theoretical treatment requires the inclusion of separate short-distance (SD) and long ∗Research supported in part by a grant from the Ministry of Science and the Arts and by the Fund for Promotion of Research at the Technion. distance (LD) contributions [8,9,10,5]. The es- timate of the relative size of the two types of processes is an issue to be determined for every specific process. If, for instance, one is confi- dent that in a certain process the long-distance emission is a rather small perturbation, like in B → X(x)γ, B → K∗γ, such processes may be assigned the strategic role of testing the Standard Model [11,12] as well as the testing of theories be- yond it [13]. The next section surveys the possible role of the SD single-quark transition Q → qγ in the weak radiative decays of strange, charm and beauty baryons. 2. ELECTROWEAK PENGUINS IN BARYON RADIATIVE WEAK DE- CAYS At the quark level there are three types of pro- cesses which contribute to the weak radiative de- cays of baryons, classified [14,15] as single-, two- , and three-quark transitions. The two-quark transition corresponds to W− exchange, with the photon radiated by the participating quarks, and it is essentially a long-distance process. The three-quark transition, where the quark not par- ticipating in W-exchange radiates a photon, is strongly suppressed [15]. The single-quark tran- sition involves a SD contribution due to the elec- tromagnetic (EM) penguin diagrams [10,11,12] as well as possible LD contributions [16,17]. Before turning to the role of the EM pen- guins in the weak radiative baryon decays, one should mention the powerful analysis of Gilman and Wise (GW)[14]. In their paper, GW checked 2 the hypothesis that all weak radiative hyperon decays in the 56-multiplet of SU(6) are driven by the single-quark transition s → dγ. They de- termined the strength from the Σ+ → pγ decay and proceeded to calculate from this the expected branching ratios for Λ → nγ, Ξ0 → Σ0γ, Ξ0 → Λγ, Ξ− → Σ−γ, Ω− → Ξ−γ and Ω− → Ξ−∗γ. Their predictions exceed the experimental rates by one or two orders of magnitude for the vari- ous decays. Thus, the hypothesis that all these decays proceed via the single-quark transition is untenable. However, it must be stressed that the analysis of GW does not preclude substantial con- tributions from s → dγ, whether SD [18,19] or LD [17], in only some of the hyperon radiative decays. In the standard electroweak model, the flavour- changing Qqγ vertex with the Q,q quarks on the mass-shell has the form Γµ = e 4π2 GF√ 2 (q) ∑ λ V ∗λQVλq[F1,λ(k 2)(kµk/ − k2γµ) 1 − γ5 2 + F2,λ(k 2)iσµνk ν(mQ 1 + γ5 2 + mq 1 − γ5 2 )](Q). (1) F1(q2) and F2(q2) are the charge radius and mag- netic form factors respectively, calculated [20] in electroweak theory in terms of masses of quarks and W ; Vab are Cabibbo-Kabayashi-Maskawa (CKM) matrices. For (sdγ) and (bsγ) one has λ = u,c,t and for (cuγ) the contribution is from λ = d,s,b. The F1 term does not contribute to decays with real photons. It is, however, relevant in de- cays involving leptons like B → X(s)`+`− [21], Σ+ → p`+`− [22], Ω− → Ξ−`+`−[19]. In this pa- per we restrict our discussion to decays with real photons, to which only F2 contributes. The quantity of physical interest is the Qqγ ver- tex with QCD corrections. The effective hamilto- nian has the form Heff = − GF√ 2 λ ∑ Ci(µ)Oi(µ) (2) where λ represents symbolically products of CKM matrices, Oi(µ) is a complete set of dimension- six operators and Ci(µ) are Wilson coefficients. Explicit expressions for the strange, charm and beauty sectors are given in Refs. [23], [24] and [12] respectively. O1,2 are current-current opera- tors, O3 − O6 are strong penguin operators and O7,O8 are magnetic operators, of EM and gluonic type respectively. In particular the EM penguin operator required by Eq. (1) has the form O7 = e 8π2 (q̄)ασ µν[mQ(1 + γ5) + mq(1 − γ5)](Q)αFµν . (3) The application of the QCD corrections using the renormalization group equations endows (3) with a coefficient Ceff7 , which is a linear combi- nation of Ci(µ) and has been calculated for all three sectors, at least to leading order. We are thus in a position to determine quantitatively the contribution of the EM penguin to the baryonic radiative weak decays. In the strangeness sector, the replacement by the QCD-corrections of a quadratic GIM cancel- lation by logarithmic dependence, increases F2 by about three orders of magnitude [2,10]. The value of Ceff7 (sdγ) has been reevaluated recently with better accuracy [17,25]. Using the new value we estimate the SD contribution to the typical pole decay Σ+ → pγ and to the decays which have been singled out [18] as potential windows to s → dγ, namely Ω− → Ξ−γ and Ξ− → Σ−γ. Using wave functions of Ref. [14] we find Γ(Σ+ → pγ)SDs→dγ/Γ(Σ+ → pγ)exp = 2 × 10−5 (4) Hence in hyperon radiative decays driven by LD poles the s → dγ transition does not play a no- ticeable role. On the other hand, one finds Γ(Ω− → Ξ−γ)SDs→dγ = 6.4 × 10−12eV . (5) Using the recently determined [26] upper limit Γ(Ω− → Ξ−γ)exp < 3.7 × 10−9eV one concludes [17] that in this decay the amplitude ratio SD/LD is larger than 1/25. Obviously, this is a remark- able result. A similar calculation for Ξ− → Σ−γ gives Γ(Ξ− → Σ−γ)SDs→dγ = 8.3 × 10−13eV , (6) which indicates a contribution of SD of about 4% in the amplitude of this decay. 3 The transition c → uγ has been treated in detail, including QCD corrections, only recently [24]. Contributions from all three quark loops are comparable in size, like in the strangeness sector. Likewise, the QCD corrections enhance also here enormously the transition, leading to a c → uγ width which is increased by five orders of magni- tude. However, even with increased strength the c → uγ EM penguin is too small to play a role in weak hadronic radiative decays. The b → sγ transition has been treated in great theoretical detail [12,27]. In this case, the contri- bution of the t-quark loop is strongly dominant so that other contributions are usually omitted. The recent measurements by CLEO of B → K∗γ[28] and B → X(γ [29] confirm the original expecta- tions [11] that these modes are dominated by the EM penguin transition b → sγ. We expect there- fore b → sγ to play a central role also in beauty baryon decays [5]. Hence, the role of the SD Q → qγ transition in the baryonic weak radiative decays is of differ- ent nature in each of the three sectors: it is to- tally negligible in the charm sector, it dominates the appropriate decays in the beauty sector, and plays a modest role in some of the hyperon decays like Ω− → Ξ−γ and Ξ− → Σ−γ. 3. THE HYPERON SECTOR The amplitude for the transition B(p) → B′(p′) + γ(k) is M(B → B′γ) = ieGF ū(p′)σµν(A + Bγ5)� µkνu(p) (7) where A(B) are the parity-conserving (-violating) amplitudes. The angular distribution of the de- cay is characterized by an asymmetry parameter αh, given by αh = 2Re(A ∗B)/(|A|2 + |B|2) . (8) Table 1 summarizes the experimental situation, based on Ref. [7] except for the entry on Ω− → Ξ−γ which is based on a new experiment [26]. The recent analysis on the Σ+ → pγ width based on 31900 events [30], not included in Table 1, gives BR(Σ+ → pγ) = (1.20±0.06±0.05)×10−3. A puzzling feature is the large negative asym- metry detected in Σ+ → pγ. According to Hara’s theorem [31], in the limit of SU(3)-flavour symmetry the PV-amplitudes in Σ+ → pγ and Ξ− → Σ−γ should vanish, causing a vanishing asymmetry. Many articles have been devoted to this question as exemplified by Ref. [32]. It has also been argued [33] that in a quark description the Hara theorem does not hold and the problem could lie in the “translation” of the quark basis to the hadronic world. So far, there is no convincing explanation for this large SU(3)-breaking. A large number of models have been construc- ted to treat the processes of Table 1, most of them attempting a “unified” picture for the ra- diative hyperon decays. Among these models, there are pole models [34], quark models [15], skirmion models [35], Vector Meson Dominance models [36] and chiral models [37]. In many of these attempts, one accomplishes firstly a fit to the well measured Σ+ → pγ mode, and predic- tions are made for other decays, though Refs. [35], [37] do not follow this pattern. Unfortunately, none of the existing models can reproduce simul- taneously all the features in Table 1. In fact, comparing various models (see, e.g. Table 7.1 of Ref. [1] and Table II of Ref. [2]) one finds strong disagreements for the yet unmeasured quantities. In the following, we restrict ourselves to an anal- ysis of the better understood physical features in these decays. The analysis of Section 2 has shown that the contribution of SD emission is negligible in the four decays proceeding at the 10−3 level, namely Σ+ → pγ, Λ → nγ, Ξ0 → Σ0(Λ0)γ. It also can account for only a fraction of the decays proceeding at the 10−4 level or lower, Ξ− → Σ−γ, Ω− → Ξ−γ, Ω− → Ξ∗−γ, as already established for Ξ− → Σ−γ[9]. Thus, in all hyperon radiative decays the LD emission plays the predominant role. A further dynamical distinct arises from the valence quark structure of the hyperons and the explicit form of H∆S=1eff (Eq. [2]). For the above group of four decays Heff induces pole diagrams [e.g. Σ → (p,N∗) → pγ, etc.], which dominate over multiparticle intermediate states. A suitable combination of the 1 2 + baryons and 1 2 − resonance poles can lead to large asymmetries. However, the 4 Table 1 The experimental status of the hyperon radiative decays Decay Branching Ratio(10−3) Asymmetry Parameter Σ+ → pγ 1.25 ± 0.07 −0.76 ± 0.08 Λ → nγ 1.75 ± 0.15 Ξ0 → Σ0γ 3.5 ± 0.4 0.20 ± 0.32 Ξ0 → Λ0γ 1.06 ± 0.16 0.4 ± 0.4 Ξ− → Σ−γ 0.127 ± 0.023 Ω− → Ξ−γ < 0.46 Ω− → Ξ−∗γ poor knowledge of some of the couplings involved leads to a widely divergent spectrum of predic- tions. The second group of three decays involves par- ticles Ω−(sss), Ξ−(ssd), Σ−(sdd) with no u- valent quark, i.e. there are no W-exchange di- agrams to generate poles. These decays will then proceed via two-hadron intermediate states. Glu- onic penguins may also contribute; explicit calcu- lations [38] indicate that such penguin contribu- tions are considerably suppressed. Thus, from a dynamical point of view, there are two distinct groups: the “pole decays” (Σ+ → pγ, Λ → nγ, Ξ0 → Σ0γ, Ξ0 → Λ0γ) and the “non-pole decays” (Ξ− → Σ−γ, Ω− → Ξ−γ, Ω− → Ξ∗−γ), which are driven by different mech- anisms. As an example of a “non-pole” calcula- tion we mention Ξ− → Σ−γ [8], where the main LD contribution is due to the (Λπ−) intermediate state. The imaginary part of Eq. (7) is then ImM(Ξ− → Σ−γ) = 1 2 ∫ d4k (2π)2 δ(k2 − m2π)δ[(p − k)2 − M2Λ]M(Ξ− → Λπ−) · T (π−Λ → γΣ−) (9) giving [9] ImALD = 0.94MeV, ImBLD = −8.3 MeV. For the real part, dominated by an infrared log divergence in the chiral limit, one finds ReALD = 0, ReBLD = −6.9MeV. Including uncerta one obtains [9] Γ(Ξ− → Σ−γ) Γ(Ξ− → all) = (1.8 ± 0.4) × 10 −4; αh(Ξ − → Σ−γ) = −0.13 ± 0.07 . (10) The value for the width agrees well with experi- ment; the measurement of the asymmetry is re- quired to confirm the physical picture. 4. A VECTOR MESON DOMINANCE APPROACH FOR LONG DISTANCE TRANSITIONS Q → qγ A new approach to the calculation of the LD contributions to the radiative decays b → s(d)γ has been suggested recently [16] and was applied to s → dγ and hyperon radiative decays in Ref. [17]. The basic idea is to calculate the LD emis- sion via the t-channel, assuming the vector meson dominance (VMD) of the hadronic electromag- netic current [39]. A hybrid approach is employed in converting from the nonleptonic hamiltonian expressed in terms of quark operators to the pro- cess Q → qV → qγ. It should be mentioned that an older “s-channel” attempt to calculate the LD contribution to s → dγ [40] uses a problematic mixture of particles and quarks on equal footing in intermediate loops. Let us present the new approach [16,17] by considering the relevant O1,O2 operators in the ∆S = 1 sector of Eq. (2) H∆S=1eff = GF√ 2 ∑ η=u,c,t VηsV ∗ ηd(C1,ηO1,η + C2,ηO2,η) + H.C. (11) O1,η = d̄γµ(1 − γ5)ηβη̄βγµ(1 − γ5)s , (12a) O2,η = d̄γµ(1 − γ5)ηη̄γµ(1 − γ5)s . (12b) Using factorization, one obtains the amplitude for Q → qV proportional to a2gV , where 〈V (k)|η̄γµη| 0〉 = igV (k2)�+µ (k) and a2 = c1 + C2N , N being the number of colors. For the hyperon decays, 5 the η = t contribution is negligible and using VcsV ∗ cd ' −VusV ∗ud and the Gordon decomposi- tion to extract the transverse part, one has A s→dγ LD = − eGF√ 2 VcsV ∗ cda2(µ 2) [ 2 3 ∑ i g2ψi (0) m2ψi − 1 2 g2ρ(0) m2ρ − 1 6 g2ω(0) m2ω ] . 1 M2s − M2d d̄σµν(MsR − MdL)sFµν . (13) A phenomenological value a2(µ2) ≥ 0.5 is as- sumed [17]. Ms, Md are constituent quark masses, R,L projection operators and the sum- mation covers the six narrow 1−ψ states. The Ω− → Ξ−γ decay is calculated [17] from (13) using the formalism of Ref. [14]. Using the experimental bound [26] of Γexp(Ω− → Ξ−γ) < 3.7 × 10−9eV one obtains the relation |CVMD| = ∣∣∣∣∣ 23 Σi ∑ i g2ψi (0) m2ψi − 1 2 g2ρ(0) m2ρ − 1 6 g2ω(0) m2ω ∣∣∣∣ < 0.01GeV2 . (14) The relation (14) represents a remarkable cancel- lation at the 30% level. It also determines∑ i g 2 ψi (0)/m2ψi = 0.045 ± 0.016GeV2, implying a strong k2 dependence in the ψi − γ couplings which reduces their value by a factor of ' 6 from k2 = m2ψi to k 2 = 0. This conclusion agrees well with independent determinations of gψi (0) from photoproduction and decays [16]. We expect |CVMD| to be quite close to the up- per limit value (15), which in turn implies that BR(Ω− → Ξ−γ) should be close to the exper- imental upper limit of Table 1. The two-body intermediate states contribute [8] to the BR of this decay only 0.8 × 10−5. The application of this approach to Ξ− → Σ−γ gives for the LD contribution to the rate from s → dV an upper limit of 80%. For a pole decay like Σ+ → pγ the same contribution is less than 1%. These values confirm the consistency of the dynamical picture discussed in this section. 5. CHARM BARYON DECAYS Charm baryons containing one c quark are usu- ally classified according to the SU(3) representa- tion of the two light quarks, which can form a symmetric sextet (with spin 1) or an antisym- metric antitriplet (with spin 0). The spin 1 2 an- titriplet is composed of B̄3c (Λ + c , Ξ + c , Ξ 0 c). The sextet baryons have spin 1 2 (B6c ) or spin 3 2 (B6∗c ). The particles forming it are (Σ++c , Σ + c , Σ 0 c, Ξ ,+ c , Ξ,0? Ω 0 c). The B̄ 3 c particles and Ω 0 c decay weakly, while the rest of sextet particles decay strongly (Σ++,+,0c → Λ+c π+,0,−) or electromagnetically (Σ+c → Λ+c γ, Ξ,+,0c → Ξ+,0γ. In the following, we shall consider only two-body weak radiative decays of charm baryons. The SD contribution from c → uγ to the ra- diative decays was shown to be negligible [24], hence the main mechanism for the decays is W-exchange. Since the radiative decays are “cleaner” than other weak multiparticle decay channels of Bc to strongly interacting particles, one may hope that their estimate will be quite reliable. We start our considerations by firstly classifying these decays according to their CKM strength: CKM allowed decays (∆C = ∆S = −1): Λ+c → Σ+γ; Ξ0c → Ξ0γ. CKM forbidden decays (∆C = −1; ∆S = 0): Λ+c → pγ; Ξ+c → Σ+γ; Ξ0c → Λ(Σ0)γ; Ξ0c → Ξ0γ. CKM doubly-forbidden decays (∆C = −∆S = −1): Ξ+c → pγ; Ξ−c → nγ; Ω0c → Λ0(Σ0)γ. The photon energy in these decays is consider- ably larger than in the hyperon decays, ranging between 833 MeV in Λc → Σ+γ to 1124 MeV in Ω0c → Λγ. Kamal has pioneered [3] this field by calcu- lating Λ+c → Σ+γ from two-quark W-exchange bremsstrahlung transitions of type c+d → s+u+ γ. Summing all relevant diagrams one obtains an effective Hamiltonian which is used to calculate the amplitudes A,B of Eq. (7). Using harmonic oscillator wave functions for the baryons involved, a branching ratio of nearly 10−4 is obtained. Up- pal and Verma [4] have improved the relativistic corrections of this calculation and have also intro- duced strong flavour dependence in the harmonic oscillator wave functions. The results of their two 6 Table 2. Theoretical Estimates for Charm Baryon Decays Branching Ratio (10−4) Asymmetry Decay Mode Ref. [3] Ref. [4] Ref. [4] Ref. [5] Ref. [4] Ref. [4] Ref. [5] I II I II Λc → Σ+γ 0.67 0.45 2.9 0.49 -0.013 0.02 -0.86 Ξ0c → Σ0γ 0.19 1.3 0.31 -0.042 -0.01 -0.86 models, together with an updated value of Ref. [3] and results from a heavy-quark effective theory calculation [5] with c and s quarks as heavy are presented in Table 2 for the CKM allowed decays. Branching ratios for the CKM-forbidden de- cays Λ+c → pγ, Ξ+c → Σ+γ, Ξ0c → Λγ, Ω0c → Ξ0γ were also estimated in Ref. [4] and found to be generally of the order of 10−5. Finally, we comment on the weak radiative decays of heavy baryons with several c quarks. Among these, of particular interest is Ξ+cc → Ξ+c γ which is CKM allowed and expected with a 10−4 branching ratio. There are also a couple decays which cannot proceed via W-exchange. These are Ξ++cc → Σ++c γ and Ω++ccc → Ξ++cc γ, which could be driven by the c → uγ transition. Since the SD contribution is very small, these decays would constitute a direct window to the LD c → uγ pro- cess, or possibly to effects beyond the standard model. 6. BEAUTY BARYON DECAYS As it was explained in Section 2, the SD con- tribution plays a prominent role in the b-sector. Therefore, we shall classify the beauty baryon two-body weak radiative decays as follows: (A) SD decays driven by the EM penguin b → sγ, which includes Λ0b → Λ0γ; Λ0b → Σ0γ; Ξ0b → Ξ0γ; Ξ−b → Ξ−γ; Ω−b → Ω−γ. (B) LD decays which are described on the quark level by two-quark W-exchange transitions accompanied by photon radiation. To this group belong Λ0b → Σ0cγ; Ξ0b → Ξ0cγ; Ξ0b → Ξ,0c γ. The decays in both groups are CKM doubly-forbidden, the matrix el- ement being proportional to VtbV ∗ts ∼ λ2 for group (A) and to VudV ∗bc ∼ λ2 for group (B). The pho- ton energies are in the several GeV range, e.g. Eγ = 2.71GeV for Λ0b → Λ0γ. Theoretical calculations for these decays were performed only recently [5,6]. For group (A) the transition amplitude for Bi → Bfγ is given by the short-distance QCD-corrected O7 operator M(Bi → Bfγ) = iGF√ 2 e 4π2 Ceff7 VtbV ∗ tb� µkν 〈B̄f|s̄σµν[mb(1 + γ5) + ms(1 − γ5)]b|Bi〉 (15) where Cefff = 0.31 [24,27]. The LD contribution to the b → sγ transition is estimated to be at the level of a few percent only [16,17], which al- lows us to neglect it. The authors of Ref. [5] use two methods to treat the Λb → Λγ decay, - the heavy quark symmetry scheme with both b and s treated as heavy, and the MIT bag mo In the first method, they obtain for the A,B amplitudes of Eq. (7) A,B = Ceff7 4 √ 2π2 VtbV ∗ ts ( 1 ± ms mb − Λ̄h 2ms ) ξ(v · v′) (16) where ξ(v·v′) is the Isgur-Wise function and h is a function of v·v′. Allowing for reasonable variation of the various parameters involved, Cheng et al. [5] conclude that BR(Λ0b → Λ0γ) = (0.5 − 1.5) × 10−5 (17) ¿From their amplitude, one obtains αh(Λ0b → Λ0γ) = 0.9. In the heavy s quark limit, Λ0 behaves as an an- titriplet heavy baryon while Σ0 as a sextet heavy baryon. Λ0b belongs to an antitriplet. Accord- ingly, b → sγ will not induce in the limiting case Λ0b → Σ0γ which is a sextet-antitriplet transition and one is led to Γ(Λ0b → Σ0γ) << Γ(Λ0b → Λ0γ) (18) 7 The other decays of group (A) are more difficult to treat (several heavy quarks baryon). In any case, branching ratios somewhat smaller than in Eq. (17) are expected, also due to wave function overlap suppression especially in Ω−b → Ω−γ. For the transitions of group (B) an effective Lagrangian is constructed [5] from the diagrams of the W-exchange bremsstrahlung processes b + u → c + d + γ, b + d̄ → c + ū + γ. Branching ratios smaller by at least one order of magnitude than in group (A) are obtained [5], even if max- imal overlap for the static bag wave functions is assumed: BR(Ξ0b → Ξ0cγ) = 6.4 × 10−8; αh = −0.47 BR(Ξ0b → Ξ,0c γ) = 5.7 × 10−7; αh = −0.98 BR(Λ0b → Σ0cγ) = 1.2 × 10−6; αh = −0.98 The basic decay mechanism b → sγ actually leads to a multitude of exclusive states in the ra- diative Λb decay, like Λb → Λ(1405)γ, Λ(1520)γ, Λ(nπ)γ, Ληγ, Λη′γ, etc. Hence it is of interest to estimate the expected Λ0b → X(s)γ branching ratio and the percentage of it of the lowest exclu- sive mode, Λ0b → Λ0γ. We use the measured [29] B → X(s)γ to calculate Γ(b → sγ) = (1±0.35)× 10−7eV. Assuming Γ(Λ0b → X(s)γ)/Γ(Λb → all) ' Γ(b → sγ)/Γ(Λb → all) and the measured Λ0b life-time[7] we estimate Γ(Λ0b → X(s)γ) Γ(Λb → all) = (1.6 ± 0.5) × 10−4 . (19) Hence, the calculations presented above lead to Γ(Λ0b → Λ0γ) Γ(Λb → X(s)γ) ' (6.0 ± 3.5)%. (20) The figure we obtained is not very different from the mesonic sector, where one has [28,29] Γ(B → K∗γ)/Γ(B → X(s)γ) = 0.2 ± 0.1 An analysis [41] of the angular distribution of the photon in Λ0b → X(s)γ with polarized Λ0b, using the heavy quark effective scheme, shows that deviations from free quark decay are gener- ally small and are significant mostly for photons emitted in the forward direction with respect to Λ0b spin. However, as a consequence of the func- tional form of the EM penguin the photons are emitted preferentially backwards. 7. CONCLUDING REMARKS We highlight here several points, some of which are of direct relevance to forthcoming and con- templated experimental programmes: # As a result of the theoretical activity of last few years, a clear picture emerges on the the im- portance of short-distance radiation in the weak radiative decays of baryons. Thus, the electro- magnetic penguin Q − qγ (with gluonic correc- tions) plays a major role in the beauty sector, dominating processes like Λb → X(s)γ, Λb → Λγ. The charm penguin c → uγ is too weak to play any noticeable role in charm baryon radiative de- cays, while the strange penguin s → dγ occupies an intermediate position, contributing to a pos- sibly detectable extent in a few hyperon decays (Ω− → Ξ−γ, Ξ− → Σ−γ, Ω− → Ξ∗−γ). # The measurements of the rate and asymme- try parameter of Ω− → Ξ−γ should be given high priority, since there is good probability that both SD and LD radiation contributes measurably to it. This decay could constitute the main desired window to the EM penguin in the strangeness sec- tor s → dγ, in addition to providing interesting information on couplings of vector mesons to pho- tons from the LD contribution. # It is difficult at present to favour any of the competing models describing pole hyperon decays like Σ+ → pγ, Ξ0 → Σ0γ, etc. Since the var- ious models diverge mostly in the prediction of the asymmetry parameter, good measurements of this parameter in Λ → nγ, Ξ0 → Λγ and Ξ0 → Σ0γ should finally alllow one to resolve the unsettled situation. # The measurement of the asymmetry param- eter in the decay Ξ− → Σ−γ will distinguish be- tween the dynamical picture [8,9] for non-pole decays which leads to Eq. (10), and alternative mechanisms [34-37]. # Theoretical estimates indicate that charm baryon CKM allowed radiative decays will oc- cur with a branching ratio of ∼ 10−4, making the search for these decays a realistic proposition. One expects BR(Λ+c → Σ+γ) = 1+1−0.5 × 10−4, BR(Ξ0c → Ξ0γ = (0.8 ± 0.5) × 10−4. The CKM- forbidden decays, like Λ+c → pγ, Ξ0c → Λ(Σ0)γ, Ξ+c → Σ+γ, Ω0c → Ξ0γ are expected to occur 8 with branching ratios of 10−5 or less. # Beauty baryons have detectable weak ra- diative decays induced by short distanc electro- magnetic penguins. The inclusive decay Λb → X(s)γ is expected to have a branching ratio of (1.6 ± 0.5) × 10−4. The most frequent exclu- sive mode is probably Λb → Λγ expected to oc- cur with a branching ratio of (1 ± 0.5) × 10−5. On the other hand, Λ0b → Σ0γ is expected from heavy quarks symmetry considerations to be be much smaller. Radiative decays to charm baryons Λ0b → Σ0cγ, Ξ0b → Ξ0cγ, Ξ0b → Ξ,0c γ are expected in the 10−6 − 10−7 range. REFERENCES 1. A detailed review on the experimental and theoretical states of weak radiative decays of hyperons is: J. Lach and P. Zenczykowski, Int. J. of Mod. Phys. A (in press). 2. P. 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