<Emphasis Type="Italic">B</Emphasis>-meson physics: <Emphasis Type="Italic">CP</Emphasis> violation and semileptonic decays

The paper represents a review of our present knowledge on the phenomenology of weak decays of quarks and their role in the determination of the parameters of the Standard Model. Specifically, we focus on CP violation in B decays and the determination of the Cabibbo-Kobayashi-Maskawa matrix element V_cb from exclusive and inclusive semileptonic B decays. We also briefly discuss phenomeno-logical applications concerning the electron energy spectra in inclusive semileptonic B and B_c decays.     

A determination of the CKM-matrix element ratio |V ts |/|V cb | from the rareB-decaysB→K *+γ andB→X s +γ

Implications of the recent CLEO observation [1] of the rare decay modeB→K ^*+γ having a combined branching ratio BR(B→K ^*+γ)=(4.5±1.5±0.9)×10^?5 and an improved upper limit on the inclusive branching ratio BR(B→X _s +γ)<5.4×10^?4 (95% C.L.) [2] are discussed in the context of the Standard Model (SM). Using the unitarity of the CKM-matrix and taking into account QCD radiative corrections in the decay rate and the inclusive photon energy spectrum we obtain an improved upper limit on the inclusive branching ratio BR(B→X _s +γ)<4.8×10^?4 (95% C.L.). This can be used to constrain possible non-SM contributions to the inclusive branching ratio, giving BR(B→X _s +γ) (non-SM)<3.0×10^?4 form _t >-108 GeV. Within the SM, we show that the resulting experimental upper limit can be interpreted as a corresponding limit on the CKM-matrix element ratio yielding |V _ts |/|V _cb |<1.67, with the top quark mass assumed to weigh less than 200 GeV. We calculate the relative exclusive to inclusive branching ratioR(K ^*/X _s )≡Γ(B→K ^*+γ)/Γ(B→X _s +γ), based on the inclusive hadronic invariant mass distribution inB→X _s +γ. Estimating theK ^*-contribution from this distribution in the threshold region (m _K +m _π)≤m _{X s} ≤0.97 GeV and using experimental measurements from the semileptonicD-decaysD→K+π+?v _? in the same mass interval, we obtainR(K ^*/X _s )=0.13±0.03. This enables us to put a lower bound on the ratio |V _ts |/|V _cb | from the 95% C.L. lower limit on the branching ratio BR(B→K ^*+γ)>1.6×10^?5 [1,2]. Combining the exclusive and inclusive decay rates, we determine 0.50≤|V _ts |/|V _cb |≤1.67 (at 95% C.L.).     

Role of the pion mass in triple-Regge physics

This paper is an extension of the investigations of Abarbanel et al., who examined asymptotic total cross sections in a multiperipheral model and obtained the surprising result that the scale for the cross sections is provided not by μ, the mass of the exchanged pion (as anticipated on geometrical grounds) but by m_V, the central mass of the dominant low energy ππ resonance entering the kernel. In this paper the role of the pion mass in triple-Regge physics is clarified by examining the pion pole dominance model for the triple-Regge couplings g_ijk. It is found that m_V provides the scale for the inclusive link and that for this reason the couplings g_ijk depend very little on the intercept α_k of the exchanged reggeon. In the exclusive links if i = j = pomeron, m_V once again is the only active energy scale, whereas if i = j = R, the reggeons of intercept 0.5 or less, the pion mass enters the couplings g_RRk in an essential way. It is shown that the smallness of μ²/m_V² is responsible for the largeness of the ratios g_RRk/g_PPk. These features of the model, which are in qualitative agreement with experiment, are put to a quantitative test.     

Determination of meson resonance contributions to pion and kaon inclusive spectra

π- andK-meson inclusive spectra with low transverse momenta inK-meson fragmentation region inKp-interactions are determined on the basis of the assumption on a recombination mechanism of hadron production. It is shown that the pion and kaon spectra (both “direct” and from resonance decay) inK-meson fragmentation region can be expressed by structure functions of initialK-meson. Contributions from resonance decays from different meson multiplets (vector, axial and tensor) to pion and kaon inclusive spectra are determined. α=(3A _T /5A _V )=0.28±0.02 is found for the suppression factor ofP-wave meson state production as compared to theS-wave one. It is shown that with decreasing final meson mass the relative contribution of direct production to meson inclusive spectrum increases. In the limits of available experimental errors in meson resonance spectra there is found no dependence of meson yields on the value of summary spin of quark and antiquark producing meson (β=3A _P /A _V =1). It is shown that analysis of meson resonance inclusive spectra allows one to determine not only the parameters of valence quark distribution in the initialK-meson but also the sea parton distributions. For the strange sea quark distribution inK-meson there is founds _S(x) ～(1?x) ^ns wheren _S =4.8±1.0, which agrees with the prediction of the quark counting rules for this quantity.     

Spectra in the central region and the multiplicities of secondaries at high energies

The inclusive spectrum in the central region, ρ_n(x→0)/<ρ(x→0)> is considered as a function of the multiplicity of charged secondariesn/〈n〉. The calculations in framework of the quark-gluon strings model and the minijet model agree with theSppS-collider data, but both models predict a slow dependence of this value on the energy.     

Λ polarization in12C(π −,Λ) reactions atp π=4 GeV/c

We study theΛ formation cross sections andΛ polarizations based on the Regge pole amplitudes in theπ ^?+¹²C→Λ+X(inclusive) reactions and the exclusive kaon channel reactions atp _π =4 GeV/c. We found that the experimental data of inclusive cross sections can be reproduced qualitatively well by our calculation. As for the polarization, we have the experimental data that were reported by two different groups, although they have opposite sign and different magnitudes. Our calculated results do not agree with either set of data. We show that the sign of polarization is sensitive to the outgoingΛ kinetic energy in the inclusive reactions and to the outgoing kaon angle in the exclusive kaon channel reactions.     

Study of inclusive neutral current interactions of neutrinos and antineutrinos

We report on results from a study of hadron-energy distributions for ν and $\text{ν}$ inclusive neutral current interactions. There is no significant variation of the neutral to charged current total cross-section ratios R_ν and $\text{R}\text{ν}$ with neutrino energy. The space-time structure of neutral currents is dominated by V?A, with a significant admixture of V+A. The Weinberg-Salam model is in agreement with all data if sin²θ_w=0.24±0.02.     

Dependence of |V ub/Vcb| on Fermi momentump F in ACCMM model

The Gaussian width of Fermi momentum,p _F, is the most important parameter of the ACCMM model, and its value is essential in the determination of |V _ub/V_cb| because the experimental analysis is allowed only at the end-point region of inclusive semileptonicB-decay spectrum. We extract the value of |V _ub/V_cb| as a function ofp _F. We also calculate the parameterp _F in the relativistic quark model using the variational method, and obtainp _F=0.54 GeV which is much larger than the commonly used value, ∼0.3 GeV, in experimental analyses. When we usep _F=0.5 GeV instead of 0.3 GeV, the value of |V _ub/V_cb| from ACCMM model is increased by a factor 1.81, and can give a good agreement with Isgur et al. model.     

The problem of the relation between double pomeron exchange in inclusive and exclusive experiments

The pionization region of the inclusive single-particle spectrum is accounted for by double pomeron exchange in the absorptive part of a six-point amplitude. In this paper a multiperipheral model for the six-point amplitude with double pomeron exchange is used for continuation by crossing and analyticity to the physical region of the exclusive two particle → four particle production process. The cross section for π^? p → π^?(π⁺π^?)p in the double-Regge region is then calculated and compared with the experimental analysis of Lipes, Zweig and Robertson which sets an upper bound to the strength of the double pomeron exchange coupling. This upper bound, coupled with the model for continuation to the inclusive cross section, is shown to give too small a magnitude for the double pomeron exchange in the pionization region. Further avenues for investigation are discussed.     

Interlayer tunneling spectroscopy of graphite at high magnetic field oriented parallel to the layers

Interlayer tunneling in graphite mesa-type structures is studied at a strong in-plane magnetic field H up to 55 T and low temperature T = 1.4 K. The tunneling spectrum dI/dV vs. V has a pronounced peak at a finite voltage V ₀. The peak position V ₀ increases linearly with H. To explain the experiment, we develop a theoretical model of graphite in the crossed electric E and magnetic H fields. When the fields satisfy the resonant condition E = vH, where V is the velocity of the two-dimensional Dirac electrons in graphene, the wave functions delocalize and give rise to the peak in the tunneling spectrum observed in the experiment.     

Remarks on the lifetime of charmed baryonΛ c +

The interference andW-exchange contributions toΛ _c ⁺ inclusive nonleptonic decay rate are expressed in terms of matrix elements of effective fourquark operators and evaluated in the MIT bag model. It is found that although theW-exchange is not necessarily subject to helicity and color suppression, it does not suffice to explain the measured lifetime ofΛ _c ⁺. The observed semileptonic branching ratio ofΛ _c ⁺, however, requires that its inclusive decay rate be dominated by the nonspectator contribution and thus theW-exchange be substantially enhanced by some nonperturbative effects. The implication for exclusive two-body decays ofΛ _c ⁺ is briefly discussed.     

Internal rotation in the spectrum of acetaldehyde

The geometrical structure of acetaldehyde from the microwave spectrum and torsional transitions from the far infrared spectrum have been fitted with a semirigid model in order to obtain the torsional parameters V″₃ = 415.0 and V″₆ = 22.3 cm^?1 and the torsional energy levels of the isotopic species CH₃CHO, CH₃CDO, CD₃CHO, and CD₃CDO. These have been used in fitting torsional sequences in the 182-nm system of the electronic spectra of these species to obtain the excited state parameters V′₃ = 880 and V′₆ = 77 cm^?1. Both the ground and excited state parameters are in good agreement with ab initio predictions.     

Compilation of coupling constants and low-energy parameters

The double-pomeron coupling strength in the dual resonance model is found in both the inclusive and exclusive regions by comparison with experiments. Double-pomeron coupling occurs in inclusive experiments in the Mueller diagram for the central plateau region. Its strength can also be bounded from its non-observation in the two-particle to four-particle exclusive experiments. The dual resonance model is used to perform the analytic continuation of a six-point amplitude between these regions. The results show that the coupling strength for two forward pomerons in the exclusive region must be less than $\text{1}\text{300}$ of that in the inclusive region. This is experimental evidence for substantial forward double-pomeron decoupling in exclusive processes.     

On the relation between inclusive and exclusive p⊥ distributions

Inclusive and exclusive scattering is studied within an impact parameter framework. It is shown that the inclusive p_⊥ distribution at a fixed value of c.m. longitudinal momentum, p_6;, is governed only by the impact parameter structure of the observed particle. Next we introduce to each of the produced particles a radius, which is assumed to be independent of all the other particles, including those in the initial state. This enables us, at a fixed value of p₆, to relate the elastic πN, KN and NN data, at lab momenta of less than 20 GeV, to the pion, kaon, proton and antiproton inclusive p_⊥ distributions at ISR energies.     

Urbaryon Model Approach to Unified Understanding of Large and Small PT Spectra

Single-particle distributions in the entire Peyrou plot at CERN-PS ∼ ISR energies are unifiedly described by the whole-region formula, which incorporates both parton model results at large p_T and all of the Mueller-Regge forms at small p_T. The quantum number dependence of the distributions is explained by the formula as due to the intimate relation between the energy-momentum flow and the quantum-number flow carried by valence urbaryons. A field theoretical basis of the formula is provided by a covariant model of the hadron-urbaryon amplitude which is parametrized in terms of valence urbaryon lines and pair effects. Two-body reactions at all angles are also described by the formula as the exclusive limit of inclusive reactions. The construction of a formula for inclusive two-particle distribution is briefly discussed.     

Inclusive production of neutral pions in hadronic Z decays

A measurement of the inclusive production of π⁰ mesons in hadronic Z decays is presented and compared to Monte Carlo model predictions. The analysis is based on approximately 2 million hadronic events recorded with the ALEPH detector at LEP at a centre-of-mass energy of ?s = 91.2 GeV. Neutral pions are reconstructed using photons measured in the electromagnetic calorimeter and photons from conversion pairs. The inclusive π⁰ momentum spectrum is measured in the range 0.025 < x _p = p/p _beam < 1. In this range the number of π⁰ per hadronic Z is found to be 4.80 ± 0.07(stat) ± 0.31(sys). The differential inclusive π⁰ cross section is also measured as a function of transverse momentum with respect to the event plane (p _T ⁱⁿ and p _T ^out ).     

Role of hadronic dynamics in proton decay

Aspects of hadronic dynamics which play a crucial role in proton decay (exclusive and inclusive) are examined in the context of a comprehensive Bethe-Salpeter (BS) formalism forq \(\bar q\) andqqq systems, under harmonic confinement. The BS model which is characterized by two basic parameters—the universal spring constant \(\tilde \omega \) GeV and the quark massm _q =0.28 GeV, has already provided an impressive set of agreements in respect of a large number and variety of hadronic observables (mass spectra, and an extensive list of e.m. and pionic couplings of both mesons and baryons). TheSU(5) GUT parameters, on the other hand, are kept fixed at the ‘standard’ values, (see e.g. Langacker's review). The absolute normalization of the baryon, which is rather crucial in this case, is fixed with reference to the (topologically equivalent) process of its ‘dissociation’ into three quarks by a hard photon, which makes use of the structure function sum rule \(\int\limits_0^1 {dxF_2^p (x)/x = \sum {Q_i^2 } } \) , instead of the usual BS normalization (which amounts to the conservation of charge). Thee ⁺ inclusive rate, which is about three times that of thee ⁺π⁰ mode, works out at0.54×10 ^?33 yr ^?1 which is smaller than most contemporary calculations by two orders of magnitude. Other exclusive modes are also consistent with the above estimate. The theoretical implications of these results vis a vis contemporary calculations as well as current experimental searches are discussed.     

A detailed analysis ofD-,D s - andB-meson transition form factors and the determination of |V cb |

We study various transition form factors in semi-leptonic decays ofD-,D _s -,B- andB _s -mesons using the pole dominance assumption. The vector current form factor is found to have only a negligible contribution to the decay rates involving pseudoscalar to vector transitions. In view of this fact we evaluate the form factors from present experimental data on the exclusive semi-leptonic decay rateΓ and the ratioΓ _l /Γ _T of the longitudinal and transverse partial decay rates. Some non-leptonic two-body decay rates are also investigated using the factorization ansatz. Consistency with the semi-leptonic decays is found. The transition form factors of theD- andD _s -mesons are found to contradict the predictions of quark model. In contrast, the experimental data on the transition form factors ofB-mesons are found to be consistent with the quark model predictions. The KM matrix element |V _cb | is determined to be |V _cb |=0.040±0.010, a value somewhat smaller than is usually chosen.     

Current-voltage relation and charge distribution in mixed ionic electronic solid conductors

Current-voltage relation and charge distribution in mixed ionic electronic solid conductors (MC) are evaluated for dc steady state conditions. Explicit dependence of the electronic and ionic currents on the applied voltage, V, are given for two models: (I) for a MC with a large and uniform ion disorder as, e.g., in δ-Bi₂O₃, doped CeO_2−x, stabilized and reduced ZrO₂ or α-AgI and (II) for a MC with equal concentrations of quasifree electrons and mobile ions as, e.g., in CeO_2−x. The composition of the current in model I depends on V. It is mainly electronic for V close to the polarization voltage and is mainly ionic for V → 0. In model II the current is mainly electronic. In model I the concentration of electrons, n, is not uniform when the MC is in contact with a nonunifonn surrounding. Furthermore, n and the stoichiometry depend both on V. When electrons are present dominantly in one side and holes in the other side of a MC, a p-n quasijunction is formed which depends on the applied voltage V. The charge distribution for V = 0 and for V equals the polarization voltage, is calculated.