/home/www/ftp/data/hep-ph/dir_0011265/0011265.dvi Hyperons, Charm and Beauty Hadrons: Conclusion and Outlook José Bernabéua aDep. de F́ısica Teòrica, Univ. de València, Dr. Moliner 50, E-46100, Burjassot, València, Spain In this concluding talk, the advances in the Flavour Problem studies are discussed, following the structure of the presentations in the Conference. The subjects touched are organized as follows: Baryons, K-physics, Charm and Beauty production, Charm and Beauty decays, B-Mixing and CP-Violation, Heavy Quarkonium. 1. Introduction. The subjects presented in the Conference [1] have in common their contribution to the un- derstanding of the Flavour Problem ”from be- low”, i.e., from detailed studies of the structures, regularities and differences among the flavoured hadrons. In this edition, many new interesting re- sults have been presented and my discussion will be necessarily limited in scope. I apologize for the omissions or simplifications in the conclusions given here. The quarks carry (among other properties) the flavour quantum number conserved by strong and electroweak neutral current interactions to lead- ing order. They are organized in three fami- lies which appear as replicas. Besides the an- thropic statement that three families is the min- imum number able to build a Universe with the prospect of being understood by humans through science, we do not have still an explanation for the mistery of this replication. Except for weak charged current interactions, the other fundamen- tal forces are unable to connect the families each other. In the Standard Model, the CKM Mixing Matrix gives account of this problem according to the scheme in Fig. 1. The second mistery in the Flavour Problem is the hierarchy of mixings, with intensities of order λ, λ2, λ3 for the transitions shown in the Fig. 1. In the step from quarks to hadrons, however, the different quark masses pro- vide an essential difference between the structure λ2 λ3 b λ u c s Figure 1. CKM Mixing Matrix scheme. of light hadrons (u, d and s) and that of heavy sys- tems (c, b and t). The plan of this contribution is as follows. In Section 2, we discuss Baryons, with some emphasis on Hyperons. Section 3 is devoted to K-physics, with the highlight of the last two years: KTeV and NA48 confirm the 3.5 σ NA31 result of direct CP-violation. In Section 4, charm and beauty production, the study of the fragmentation function provides the link between quarks and hadrons. Section 5 discusses charm and beauty decays, including semileptonic, purely leptonic, hadronic and rare decays. The prob- lem of B (and D) Mixing and CP Violation is presented in Section 6, with the novel results of BaBar at PEP-II and Belle at KEK B. Heavy Quarkonium is discussed in Section 7. Finally, Section 8 gives some Outlook. Table 1 Comparison between the predicted and experi- mental values of the inclusive semileptonic widths of Λc and Λb. BRSL(%) Model Experiment Λc 5.5 4.5 ± 1.7 Λb 10.7 9 + 3.1 − 3.8 2. Baryons. The study of semileptonic decays of heavy baryons has been addressed [2] in a consistent quark model describing baryons. A single set of parameters is used for the whole spectra and the resulting structure is tested with decays. The investigation of inclusive semileptonic Λb decays can provide information on the CKM matrix el- ements Vcb and Vub, as well as on the structure of Λb. The approach is that of a potential model with physical values of the couplings. The sum over final hadronic states is treated by means of duality. The predicted value of the inclu- sive semileptonic widths of Λc and Λb are con- fronted to the experiment [3] in Table 1, where the branching ratios are given. The exclusive/inclusive ratio RE of semilep- tonic Λb → Λc decay has been compared with the corresponding ratio for the meson B → D + D∗, with the conclusion [4] that it should be larger. One needs the slope parameter ρ2B of the Isgur- Wise form factor FB (ω) in Λb → Λc lν FB (ω) = 1 − ρ2B (ω − 1) + c (ω − 1)2 + · · · (1) and an upper bound is taken from the spectator quark model limit ρ2B ≤ 2 ρ2M − 1 2 (2) with the experimental value [3] ρ2M = 0.70±0.10. From QCD sum rules, 0.65 ≤ ρ2B ≤ 0.85, and one finds a ratio 0.81 ≤ RE (baryon) ≤ 0.92 to be compared with RE (meson) = 66%. Table 2 Comparison between the predicted and experi- mental values of the b hadron lifetime ratios. Experiment Theory τ (B+) τ (Bd) 1.065 ± 0.023 1 + 0.05 ( fB 200 MeV )2 τ (Bs) τ (Bd) 0.937 ± 0.040 1 ± 0.01 τ (b baryon) τ (Bd) 0.773 ± 0.036 0.9 The exclusive process Λb → Λc lνl has been experimentally searched by DELPHI Collabora- tion [5], with the analysis addressed to measure the slope parameter ρ2B of the form factor (1). With appropiate cuts in pl and p⊥, the invariant masses M(Λc e), M(Λc µ), a candidate is taken as the sign of l opposite to that of Λc. They find 57 ± 8 events and the measure of the slope pa- rameter gives ρ2B = 1.6 ± 0.6 (sta) ± 0.6 (syst) (3) when the absolute event rate is included in the fit. A review on the b hadron lifetimes was pre- sented [6] by Wasserbaech, ALEPH Coll. Recent measurements from LEP, SLD and CDF indicate that we have still a problem with the lifetime of Λb. From the theoretical side, the measurement of the individual lifetimes of B+, Bd, Bs and Λb yields information about nonspectator mech- anisms. The experimental results for the lifetime ratios are given in Table 2, together with the theo- retical predictions from QCD-based Heavy Quark expansions. A theoretical study [7] of the lifetime problem in the light-front quark model suggests that the Fermi motion of the b quark inside Λb can pro- duce a reduction of about 12±2%, accounting for a significant fraction of the discrepancy. The measurement of the ratio of meson life- times has also been considered recently [8] by SLD, with the result τ(B+)/τ(Bd) = 1.037±0.04, to be compared with the value in Table 2. The Hyperon Working Group of the KTeV Col- laboration at Fermilab has studied [9] the Ξ0 beta decay branching ratio Ξ0 −→ Σ+ + e− + ν̄e ↪→ p + π0 (4) with a signal of 626±25 events and a background of 45 ± 18 events. The process is described by the hadronic vertex of Fig. 2 with 6 form fac- 0 Σ + e− νe Ξ us s s u u Figure 2. Hadronic vertex for Ξ0 → Σ+ e− ν̄e. tors, 3 vector and 3 axial. The pseudotensor (or weak electricity) form factor cannot be generated in the standard model with quark constituents. The scalar and pseudoscalar form factors give contributions proportional to the electron mass and thus negligible. This argument is not valid for muons. The Collaboration aims for the ex- traction of the three forms: vector, magnetic and axial, for Ξ0 beta decay with 2000 events. The present result for the branching ratio is BR(e) = ( 2.60 ± 0.11 ± 0.16 ) × 10−4 (5) to be compared to the theoretical SU(3)f pre- dicted value (2.61±0.11)×10−4. In the CM of Σ+, and using the 98% analyzing power of Σ+ → pπ0, the angular correlation between p and e− is the decay asymmetry. For the muonic channel, with a few events, the measured branching ratio is BR(µ) = ( 3.5 + 2− 1 + 0.5 − 1 ) × 10−6 (6) The KTeV Hyperon Program also includes the measurement [10] of the Hyperon Radiative De- cays. The 1997 run has emphasized the chan- nel Ξ0 → Σ0 + γ, with a preliminary result B.R. = (3.34±0.12)×10−3. To obtain the asym- metry parameter, one must study a three stage process: Ξ0 → Σ0 + γ , Σ0 → Λ + γ , Λ → p + π− (7) The detected particles are p,π from the Λ decay, a γ from the Σ0 decay and a γ from the Ξ0 decay. The present value for the asymmetry is α = −0.65 ± 0.13 (8) More data is expected from the 1999 run. The theoretical studies of Ξ0 → Σ0 γ are based on the quark diagrams in Fig. 3 corresponding to the penguin diagrams (s → d FCNC transition) plus the exchange diagram. The last amplitude u s s u u s s u u s s u W s d W γ g s d W γ γ Figure 3. Quark diagrams for Ξ0 → Σ0 γ. occurs for hyperons containing a u-quark. The radiative Ξ0 decays, in the modes Ξ0 → Λ γ and Ξ0 → Σ0 γ, have also been considered by the NA48 Collaboration [11]. NA48, designed to measure �′/�, has two beam lines to generate KS and KL simultaneously and obtains the neutral hyperons from the KS -Target. The results from 1997 Data are, in units of 10−3, BR(Ξ0 → Λγ) = (1.9 ± 0.34 ± 0.19) BR(Ξ0 → Σ0γ) = (3.14 ± 0.76 ± 0.32) (9) They can be measured with ∼ 5% accuracy. In 2002, the high intensity KS run will produce a statistical gain by a factor of at least ∼ 100. NA48 has also found about 60 events of the semileptonic Beta Decay of Ξ0. The future NA48 programs for KS and Hy- peron rare decays have been discussed by Fan- techi [12], in competition with KLOE and KTeV, respectively. A novelty is the aim to look for di- rect CP violation by means of an asymmetry in the Dalitz plot density of the three-body decays K± → π±π+π− and K± → π±π0π0. Sensitivi- ties of the order 10−4 are envisaged for the later phase. An exotic role of the hyperons in Astrophysics has been presented by Miralles [13]. The pres- ence of hyperons allows a scenario in which a proto-neutron star is formed and emits neutrinos during tens of seconds. After deleptonization, it collapses to a black hole. This mechanism can be invoked to explain the lack of a neutron star rem- nant in the SN1987A and the detection of neutri- nos from the supernova explosion. 3. K-physics. The present world average for �′/� has been discussed [14] by Unal, from the NA48 Collab- oration. With the results of the last two years, KTeV and NA48 have confirmed the original 3.5σ finding by NA31 of direct CP-violation in the K0−K̄0 system. With indirect CP-violation, i.e., in the ∆S = 2 mixing, established since 1964, the mass eigenstates KS,L are not pure CP eigen- states (K±): KS ≈ K+ + �K− KL ≈ K− + �K+ (10) where |�| = (2.28 ± 0.02) × 10−3. To generate Direct CP-violation, i.e., in the de- cay amplitude |A(K0 → ff̄)| 6= |A(K̄0 → ff̄)|, one needs the interference of two decay ampli- tudes. The final state of two pions has contribu- tions from isospin I = 0 and I = 2, A0 and A2. The imaginary part of the interference generated by weak CP phases (besides the strong phases) leads to the �′ parameter �′ = i√ 2 Im ( A2 A0 ) ei(δ2−δ0) (11) The ratio of amplitudes from KL and KS has contributions from � and �′ A(KL → π+π−) A(KS → π+π−) ≡ η+− = � + �′ A(KL → π0π0) A(KS → π0π0) ≡ η00 = � − 2�′ (12) In order to separate �′ experimentally, one con- siders the ratio of ratios of decay rates R = Γ(KL → π0π0) Γ(KS → π+π−) Γ(KS → π0π0) Γ(KL → π+π−) = 1 − 6 Re ( �′ � ) (13) To establish Direct CP Violation, one needs R 6= 1. In the standard model, � is generated from the box diagram whereas �′ gets its dominant value from gluonic and electroweak penguin diagrams. The experimental situation is pictured in the Figure 4. ’ R e( / ) x 1 0 ε - 4 +-19.2 2.5 ε 30 NA31 E731 KTEV NA48 10 15 25 5 Figure 4. Experimental measurements of �′/�. One realizes from the world average value that �′/� 6= 0 is well established, but the actual value is probably not. As illustrated in Figure 4, the χ2 is poor. More results from NA48, KTeV and KLOE, which uses a different method, will clarify the experimental situation. The establishment of Direct CP-violation tells us that a superweak [15] explanation is ruled out, and that the K-system needs a milliweak model to describe CP violation. In the standard model, this description is understood in terms of the rel- ative magnitudes of the sides of the unitary tri- angle, shown in Fig 5. The CP-asymmetries are cd cs * ~λ |V V | ud us * ~λ |V V | |V V |td ts * ~ λ 5 Figure 5. The (sd) unitarity triangle. thus expected to be of order λ4. The calculation of the two isospin amplitudes A0,2 makes use of the ∆S = 1 effective hamil- tonian, which leads to four-quark operators of the current-current form (Q1,2), QCD penguin (Q3→6) and electroweak penguin (Q7→10) dia- grams. In conventional notation, Q6 and Q8 are most important, but their matrix elements have opposite signs. Possible cancellations are thus a potential danger in the theoretical calculations. In fact, Im A0 is dominated by Q6 whereas Im A2 is dominated by Q8. It is well known that, around 500 MeV, the π π interaction is very strong in the scalar-isoscalar channel. The role of final state interactions is thus very important [16] for the A0-amplitude. What is a subject of debate [17] is whether the dis- persive computation has enough reliability. This is a difficult problem, but the Omnès resumma- tion of chiral logarithms [16] gives a 50% en- hancement. In this case, A0 and thus Q6, is the primary problem. This leads to an estimate �′/� = (15±5)×10−4, compatible with the present experimental value. Models of low energy dynamics point towards a connection between the ∆I = 1/2 rule and a ”large” �′/�. Lattice QCD simulations will tell us whether this suggestion has a firm ground. A review on the final CPLEAR results on CP, T and CPT in the neutral kaon system was pre- sented by Zavrtanik [18]. For the 2π decay chan- nel, this experiment has observed for the first time a difference in the time dependence of the K0 and K̄0 decay rates. CP violation implies T viola- tion or CPT violation or both. Is T-violated? CPLEAR has measured the Kabir asymmetry [19], by comparing K0 → K̄0 versus K̄0 → K0. The flavour tag at the production time is defined by the charged kaon pp̄ → K−π+K0, K+π−K̄0. The strangeness of the neutral kaon at the de- cay time is defined by the lepton charge in the semileptonic decay (∆S = ∆Q). The Kabir asymmetry is a genuine T-violating observable, which needs both T-violation and ∆Γ 6= 0. This method works thus for neutral kaons, due to the difference in KS and KL lifetimes. CPLEAR re- sults are compatible with equal CP and T viola- tions and CPT invariance. 4. Charm and Beauty production In the production of heavy hadrons, the frag- mentation function [20] is the link between the heavy quark and the heavy hadron. It is parametrized by the probability f(z) that a hadron shares a fraction z of the quark momen- tum z = (E + p‖)H (E + p)Q (14) The problem with the variable z is the denomi- nator, which refers to the quark before fragmen- tation, so that z is not accessible on a event-by- event basis. New variables which are experimen- tally accessible are defined as the hadron energy with respect to the beam energy xE ≡ EH Ebeam (15) There are recent results on 〈xB〉 for the B meson from ALEPH, DELPHI, OPAL and from SLD, with values for the leading B energy ranging from 0.72 → 0.74. The methodology follows different strategies, and still one has to understand the consistency of the different analyses. At SLD, the polarization of the electron beam is used to tag b-quarks with 100% efficiency [8]. The re- construction of the secondary vertex by exploit- ing the kinematics leads to a measurement of the mean energy of weakly-decaying B hadrons, with a value 〈xB〉 = 0.714 ± 0.009. The SELEX experiment [21] emphasizes the understanding of charm production in the for- ward hemisphere. QCD factorization predicts that heavy quarks hadronize through jet fragmen- tation functions independently of the initial state. The experimental data show that the produced charm (anticharm) quark combines with a pro- jectile valence quark. Λ+c is a leading particle when produced by the 3 beams π−, p, Σ−. The Λc hadroproduction has a hard xF distribution. There is a strong production asymmetry in favour of Λ+c over Λ − c for baryon beams. It is less strong for a π− beam. 5. Charm and Beauty decays The semileptonic b-decay studies have the dou- ble objective of the understanding of the dynam- ics of heavy quark decays plus the extraction of the CKM coupling constants Vcb, Vub. The inclu- sive BR(b)SL has been discussed by Margoni [22], with different strategies of b-lifetime and lepton tags exploited at LEP. For the first time, DEL- PHI has explicitly separated by direct measure- ment BR(b → c̄ → l−). At present the analyses to extract Vcb are mainly limited by theory (b → l, b → c → l decay models). The most precise de- termination in the OPE approach to analyze the LEP data gives |Vcb|inclLEP = ( 40.76 ± 0.41 (exp.) ± 2.04 (theo) ) × 10−3 (16) The alternative to the inclusive decay is the study of the exclusive B0 → D∗ lν decay as a function of the D∗ recoil dΓ dω = K(ω) F 2(ω) |Vcb|2 (17) where K(ω) is a phase space factor and F(ω) is the Isgur-Wise form factor, for which the heavy- quark-effective-theory value for no recoil ω = 1 is estimated. The problem is that, due to K(ω), the decay rate vanishes at ω = 1. The procedure is thus the measurement of dΓ dω to fit it and extrap- olate to ω = 1 to obtain F(1) |Vcb|. These mea- surements at LEP have been presented by Terem [23]. There is a problem with b → D∗∗ lν, fol- lowed by D∗∗ → D∗+ X, which is an important systematic effect. ALEPH and DELPHI fit to D∗ and D∗∗ contributions gives Br(B− → D∗∗0 ( → D∗+π− ) lν) = ( 1.24 ± 0.19 ± 0.04 ) % (18) The LEP average for the exclusive analysis gives |F(1)Vcb| = (34.9 ± 1.7) × 10−3, with higher ex- perimental error than (16) due to small samples, but much cleaner theoretical approach. The determinations of Vub can come from either the exclusive B → π,ρlν decays, where the main limitation is statistics or the inclusive lepton end- point analysis, above the process b → clν. This method, limited by theoretical uncertainties, ex- tracts [24] a measurement of the branching ratio for inclusive charmless semi-leptonic b decays Br(b → Xu lν) = ( 1.67 ± 0.60 ) × 10−3 (19) from ALEPH, DELPHI and L3 at LEP. The LEP average for the Vub value derived using HQET is |Vub| = ( 4.04 +0.62−0.74 ) × 10−3 (20) ALEPH takes 4 million e+ e− → Z → q q̄ events to measure [25] the branching fractions for Ds → τ ν (τ → eνν̄ or τ → µν ν̄) and Ds → µν. Due to chirality suppression in the pseudoscalar decay of Fig. 6 the Ds → eν decay is not acces- ν D sf W l Figure 6. Pseudoscalar decay Ds → l ν̄. sible. The two leptonic τ decay channels, which give consistent signals, measure Br(Ds → τ ν) = ( 5.79 ± 0.76 ± 1.78 )% (21) whereas the Ds → µν analysis gives Br(Ds → µν) = ( 0.68 ± 0.11 ± 0.18 )% (22) The two results (21) and (22) are consistent with the chirality suppression and phase space factors m2l ( 1 − m 2 l M2 Ds )2 and provide a proof of leptonic universality in charged current decays. Combinig them, one gets for the decay constant fDs = ( 285 ± 20 ± 40 ) MeV (23) which can be used to check the validity of its pre- diction by different theoretical models. Lattice QCD predicts a value 240+ 30− 25 MeV. Hadronic decays B∗ → B π, D∗ → D π allow [26] the extraction of the physical coupling 〈B0(p) π+(q)|B∗+(p′)〉 = gB∗Bπ(q2) �µ qµ (24) gB = lim q2→m2π gB∗Bπ(q 2) and analogously for the D∗ D transition. These B* B π Figure 7. Vertex B∗-B-π. form factors have been obtained theoretically from QCD sum rules [27]. They cannot be de- scribed by a monopole function. Two different methods give consistent results and one gets for the coupling constants gD = 5.7 ± 0.4 , gB = 14.5 ± 3.9 (25) The excited states of D, Ds, B and Bs mesons have been studied [28] in the framework of the relativistic heavy chiral quark model, with the de- termination of spectrum and wavefunctions. The 1/mh-effects are relevant for the calculation of the decay amplitudes of B∗∗ → B + η, π and K. De- cay channels of B∗∗ are useful for flavour tagging in particle detectors. The decays D+, D+s → π−π+π+ were studied experimentally by the E791 Collaboration [29], at Fermilab fixed target programme. The exper- iment runs for 500 GeV π−-nucleon interactions and the signals yield (1240 ± 51) D+ events and (858 ± 49) D+s events. Besides the branching ra- tios, a detailed analysis of the Dalitz plots has been perfomed. The invariant mass M2 π+π− dis- tribution for D+s → π−π+π+ is completely dom- inated by f0(980) and f0(1370), as shown in the Fig. 8, with a negligible non-resonant contribu- tion. The behaviour of the M2 π+π− distribution +π− 2M (GeV )π 2 0 1 2 3 150 100 50 0 Figure 8. M2 π+π− distribution for D + s → π−π+π+. for D+ → π−π+π+ is however completely dif- ferent, with a dominant non-resonant contribu- tion shown in Fig. 9. What is the origin of the low mass peak? One is led naturally to the σ- meson, the scalar-isoscalar predicted by Nambu and Jona-Lasinio in a linear realization of the chi- ral Lagrangian. Experimentally, it has suffered all kinds of up’s and down’s in the Review of particle properties along the years. The inclusion of the σ in the fit leads to an spectacular improvement and to the determination of its mass (483 ± 30) MeV and width (338±50) MeV. The light σ(500), in spite of its broadness, is up again ! +π−M (GeV ) 2 2 π 0 0 1 2 3 150 100 50 Figure 9. M2 π+π− distribution for D + → π−π+π+. Rare decays are a good probe for searching new physics. The branching ratios for the inclusive B → Xs l+ l− and exclusive B → K(∗) l+ l− de- cays are smaller in the standard model than the experimental bounds, so that there is room for contributions from models beyond the standard theory. In particular, there is a very interest- ing property [30] in B → K∗ l+ l−: the zero of the forward-backward asymmetry provides a dis- crimination between the standard model and su- persymmetry. The very rare ∆S = 2 process b → ssd̄ is de- scribed in the standard model by the box diagram of Fig. 10. with a branching ratio of the order b W W s d s Figure 10. Standard Model box diagram for b → ssd̄. 10−11. Whereas the MSSM squark-gaugino box q ~q g~ g~ ~ b s d s Figure 11. MSSM squark-gaugino box diagram for b → ssd̄. diagram in Fig. 11 can increase [31] the theoret- ical branching ratio to levels of 10−8, the MSSM with R parity violating couplings induced by the sneutrino, see Fig. 12, is not restricted. On the ∼ν db s s Figure 12. MSSM sneutrino-mediated diagram for b → ssd̄. contrary, data from LEP1, around the Z reso- nance, allow the search for B− → K− K− π+ [32]. The upper limit of ∼ 10−4 for the branching ratio leads to new limits on the contribution of R parity violating couplings in this process. 6. B(D) mixing and CP-violation For charm mesons, the two parameters of mix- ing x = ∆M Γ , y = ∆Γ 2 Γ (26) are small. The experimental methods to see x or y are either by mixing, with wrong sign final lepton, or comparing the lifetime of CP eigenstates. The last method takes into account the expectation that CP-violation for the charm sector is small. FOCUS(E831) selects [33] the two channels D0 → K+ K− (CP +) D0 → K− π+ (CP + : CP − = 1 : 1) (27) and the direct comparison of CP final state life- times finds yCP as yCP = τ(D → K π) τ(D → K K) − 1 (28) The experimental result is (3.42 ± 1.39 ± 0.74)%. The standard model predicts that direct CP vi- olation in D decay rates is the largest in singly Cabbibo-suppressed decays D+ → K− K+ π+, D0 → K− K+, π− π+. The CP asymmetry re- sults [33] show no evidence for CP violation at the level of few percent. In the b sector, the problems of Bd and Bs mix- ing allow the extraction of Vtd and Vtd/Vts matrix elements of the CKM matrix. In the time inte- grated approach, the Bd-mixing leads to a world average ∆md = 0.484 ± 0.015 ps−1, but the Bs- mixing has no sensitivity to ∆ms. The method used [34,38] needs a time dependent experimen- tal approach. The time dependent mixing gener- ates a periodic signal. The amplitude fit method measures the oscillation amplitude A at fixed fre- quency ∆ms. One expects A = 1 on a frequency equal to the true ∆ms, whereas A = 0 for a wrong frequency. The world combination leads to the conclusion that Bs oscillations have not yet been resolved, with a lower limit ∆ms > 14.6 ps−1. The standard model preferred value is close to the present reach. In the ALEPH data, there is a hint of a signal around 17 ps−1. With expected sensitivities like ∼ 19 ps−1, one can envisage very interesting results in the near future. The measurement of ∆Γs has been addressed with many methods [6]. An appreciable value would allow to see CP violation in untagged Bs, contrary to Bd in which ∆Γd ≈ 0. With the constraint Γs = Γd = Γ, the present combined experimental value by the LEP Working Group is ∆Γs Γ = 0.16+0.08−0.09. This is still an insufficient sensitivity to claim an observed width difference. The standard model preferred value is 0.05±0.03 [35], using Lattice HQET and extrapolated Lat- tice QCD. One of the highlights of the Conference is the presentation that the two B-factories and the cor- responding detectors, BABAR at PEP-II [36,37] and BELLE at KEK B [38,39], are working very well. The PEP-II 9 GeV e− against 3.1 GeV e+ collider expects a luminosity of about 6 × 1033 cm−2 s−1 around summer 2000, whereas the KEK B 8 GeV e− against 3.5 GeV e+ collider had a luminosity about 2 × 1033 cm−2 s−1 just be- fore the Conference in June 2000. Some of the many physics results which are being analyzed by the two Collaborations have been presented, in particular, the lifetimes τ(b), τ(c) and τ(τ), the mixing ∆md, the inclusive B → J/ψ X de- cay, the charmless B → ρπ decay, the dominant ”Cabibbo allowed” Br(B → D∗ π) and Br(B → D∗+s D ∗−), or the rare B → K∗ γ, B → K∗ l+ l− decays. The main objective of the B-factories is to es- tablish CP-violation outside the K-system and see whether its description obeys to the CKM mix- ing matrix in the standard model. For the (bd) unitarity triangle, the three sides mediated by u, c, t quarks are of similar size of order λ3. When the CP conserving direction is taken as a refer- ence and the associated side is normalized to one, the (bd) unitarity triangle is shown in Fig. 13. B-Physics has the power to find observables able CP (ρ.η) (t)(u) (c) CP γ α β 1 Figure 13. (bd) unitarity triangle. to overconstrain the parameters of this triangle. The separate measurement of the weak CP phases α, β, γ is possible. The value of sin(2β) is acces- sible from the CP asymmetry in B → J/ψ Ks generated from the interplay of mixing and de- cay. This method needs a flavour tag, as given by the lepton channel or others. Suppose the decay of Υ(4S) into an entangled state of two B’s: Υ(4S) → B1 B2   • B → D− e+ ν (Tag) • B̄ → J/ψ Ks ∆z (29) After a time ∆t (or length ∆z) from the tag, the CP eigenstate B− is observed: the comparison of B0 → B− versus B̄0 → B− measures CP viola- tion. Bañuls [40] has discussed the way to use these decays to look for T and CPT violation. Starting from the transition B0 → B−, one has B0 → B− B− → B0 B− → B̄0 (30) These transformed transitions need a CP tag. In order to project first on B−, the B of the other side has to be identified as B+, a difficult prob- lem. There is, however, an equivalent transition for hermitian hamiltonians. In the limit ∆Γd = 0 (an excellent approximation for Bd), the transi- tion B− → B0 is equivalent to B+ → B̄0, which is obtained from the original B0 → B− by a tem- poral exchange ∆z → −∆z of the two decay channels: leptonic and J/ψKs. Although the temporal and T-odd asymmetries are conceptu- ally different, they become equivalent in the limit ∆Γd = 0 and the temporal asymmetry is a T-odd observable. The problem of B-physics and CP-violation is a source of inspiration and dedication in the hadronic machines too. At the Conference, the prospects of CDF-II [41], BTeV [42], CKM [43], and Run II [44] at FermiLab, as well as HERA b [45] at DESY and ATLAS [46], CMS [47] and LHCb [48] at LHC [49] were given. A brilliant sce- nario appears at the near future. Contrary to the B-factory preparation, the B-production mecha- nism is thought to be here incoherent from the individual b quark, with no entanglement. One can proceed then to flavour tags, but there is no possibility of CP tags as discussed above. It is worth to emphasize that, inside the Stan- dard Model, the CP phases can be also extracted from CP conserving observables in exclusive B- decays. For example, cos α is measured in the rare B → ργ decay [50,51]. The evidence for α 6= 0 in the (bd) unitary triangle is here cos α 6= 1 in these observables, contrary to sin α 6= 0 (yes-no experiment) in the CP-odd asymmetries. The chapter of SM Physics was also addressed by Narain [52], with an excellent review of Top Quark Physics at the Tevatron (Run I and Run II) and the LHC as a top factory. 7. Heavy Quarkonium Quarkonia are special hadrons, for which a de- scription in terms of factorization between the hard and soft scales is believed to be valid. For the case of Υ, confinement effects are small and basic perturbative QCD calculations on some ob- servables [53] can be envisaged. These observ- ables refer to structure and decays. The only flavour dependent parameter is the b quark mass m at the scale of the bound state. The running of the b quark mass has been established [54]. With the velocity v ∼ α for Coulomb systems, one has a multiscale problem with m, p ∼ mv, E ∼ mv2. The separation of scales is made by means of an effective field theory [55]. There is a J/ψ and ψ′ surplus in direct pro- duction at the Tevatron. An interesting produc- tion mechanism which has been suggested is the Colour-Octet component in NRQCD. Chao [56] has discussed a test of this mechanism, which in- corporates the colour-octet gluon fragmentation shown in Fig. 14 based on the polarization of charmonium at the Tevatron. In the NRQCD factorization approach, an explicit calculation of the production cross section [57] shows that the colour-octet contributions can describe Tevatron data. The experimental J/ψ polarization at high pT is, however, in disagreement with the calcu- lation for direct J/ψ production plus the feed- down from intermediate χc and ψ′. More tests are needed to understand this problem. Figure 14. Color-octet gluon fragmentation. The inelastic J/ψ production in DIS (2 < Q2 < 80 GeV2) at HERA shows [58] that the colour- singlet contribution is below data, but the shape is in reasonable agreement. When the colour- octet contribution, as suggested by the Tevatron data, is included, the theoretical magnitude is above data and the shapes disagree. Clearly one has to conclude that the problem of the produc- tion mechanism is not understood yet. 8. Outlook The Conference was a great event. Many ex- perimental results and theoretical ideas were pre- sented and discussed. The understanding of the Flavour Problem is one of the main pending ques- tions in fundamental physics. In the quark sector, this study involves strange, charm and beauty hadrons, and so the control of the interplay be- tween electroweak and strong interactions. It is gratifying for this field that all major facilities in particle physics around the world have a strong programme in it. As a consequence, we can ex- pect important breakthroughs in the next two years and to have a fruitful rendez-vous at Van- couver 2002. 9. 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Polini, these Proceedings. λ2 λ3 b λ u c s b W W s d s q ~q g~ g~ ~ b s d s ∼ν db s s CP (ρ.η) (t)(u) (c) CP γ α β 1 0 Σ + e− νe Ξ us s s u u u s s u u s s u u s s u W s d W γ g s d W γ γ ’ R e( / ) x 1 0 ε - 4 +-19.2 2.5 ε 30 NA31 E731 KTEV NA48 10 15 25 5 cd cs * ~λ |V V | ud us * ~λ |V V | |V V |td ts * ~ λ 5 ν D sf W l B* B π +π− 2M (GeV )π 2 0 1 2 3 150 100 50 0 +π−M (GeV ) 2 2 π 0 0 1 2 3 150 100 50