Study of semileptonic and nonleptonic decays of the B<Subscript>c</Subscript><Superscript>-</Superscript> meson

We evaluate semileptonic and two-meson nonleptonic decays of the B _c ^- meson in the framework of a nonrelativistic quark model. The former are done in spectator approximation using one-body current operators at the quark level. Our model reproduces the constraints of heavy-quark spin symmetry obtained in the limit of infinite heavy-quark mass. For the two-meson nonleptonic decays we work in factorization approximation. We compare our results to the ones obtained in different relativistic approaches.     

QCD sum rules for heavy quark systems

In this paper we present in a detailed and coherent fashion our work on QCD sum rules for equal mass heavy quark meson states. We discuss the technical procedures used to calculate the perturbative and non-perturbative contributions to the vacuum polarization, which have been calculated for all currents up to and including spin 2⁺⁺. Using dispersion relations, sum rules are derived. Extensive applications are made to the lowest lying states of the charmonium and upsilon systems. The masses of the S- and P-wave charmonium levels are reproduced to a high degree of accuracy, and the mass of the ¹P₁ level is predicted at 3.51 GeV. For the upsilon system it only appears to be possible to predict the γ-η_b splitting which gives 60 MeV. Very accurate values are given for the current quark masses at p² = ?m_q²: m_c = 1.28 GeV and m_b = 4.25 GeV.     

Gluon condensate in charmonium sum rules with three-loop corrections

Charmonium sum rules are analyzed with the primary goal to obtain the restrictions on the value of the dimension 4 gluon condensate. The moments M _n (Q ² ) of the polarization operator of the vector charm currents are calculated and compared with the experimental data. The three-loop () perturbative corrections, the contribution of the gluon condensate with corrections and the contribution of the dimension 6 operator G³ are accounted. It is shown that the sum rules for the moments do not work at Q ² = 0, where the perturbation series diverges and the G³ contribution is large. The domain in the (n, Q ² ) plane where the sum rules are legitimate is found. A strong correlation of the values of gluon condensate and charm quark mass is determined. The absolute limits are found to be for the gluon condensate and for the charm quark mass in the scheme. Received: 16 July 2002 / Revised version: 6 November 2002 / Published online: 24 January 2003 RID="a" ID="a" e-mail: ioffe@vitep1.itep.ru RID="b" ID="b" e-mail: zyablyuk@heron.itep.ru     

<Emphasis Type="Italic">B</Emphasis>→<Emphasis Type="Italic">D</Emphasis><Superscript>(*)</Superscript> form factors from QCD light-cone sum rules

We derive new QCD sum rules for B→D and B→D ^* form factors. The underlying correlation functions are expanded near the light-cone in terms of B-meson distribution amplitudes defined in HQET, whereas the c-quark mass is kept finite. The leading-order contributions of two- and three-particle distribution amplitudes are taken into account. From the resulting light-cone sum rules we calculate all B→D ^(*) form factors in the region of small momentum transfer (maximal recoil). In the infinite heavy-quark mass limit the sum rules reduce to a single expression for the Isgur–Wise function. We compare our predictions with the form factors extracted from experimental B→^(*) l ν _l decay rates fitted to dispersive parameterizations.     

Isospin breaking in nuclear physics: The Nolen-Schiffer effect

Using the QCD sum rules we calculate the neutron-proton mass difference at zero density as a function of the difference in bare quark massm _d—m _u. We confirm results of Hatsuda, Høgaasen and Prakash that the largest term results from the difference in up and down quark condensates, the explicitC(m _d—m _u) entering with the opposite sign. The quark condensates are then extended to finite density to estimate the Nolen-Schiffer effect. The neutron-proton mass difference is extremely density dependent, going to zero at roughly nuclear matter density.The Ioffe formula for the nucleon mass is interpreted as a derivation, within the QCD sum rule approach, of the Nambu-Jona-Lasinio formula. This clarifies theN _c counting and furthermore provides an alternative interpretation of the Borel mass.     

Extracting muon momentum scale corrections for hadron collider experiments

The quark condensate is calculated within the world-line effective-action formalism, by using for the Wilson loop an ansatz provided by the stochastic vacuum model. Starting with the relation between the quark and the gluon condensates in the heavy-quark limit, we diminish the current quark mass down to the value of the inverse vacuum correlation length, finding in this way a 64?% decrease in the absolute value of the quark condensate. In particular, we find that the conventional formula for the heavy-quark condensate cannot be applied to the c-quark, and that the corrections to this formula can reach 23?% even in the case of the b-quark. We also demonstrate that, for an exponential parametrization of the two-point correlation function of gluonic field strengths, the quark condensate does not depend on the non-confining non-perturbative interactions of the stochastic background Yang?CMills fields.     

The top quark, others new phenomena observed at the CDF in {ie359-1} collisions at √s = 1.96 TeV (Review)

Upgraded Tevatron luminosity in Run-II (started 2001) has opened a new level of modern heavy-quark studies compared to that one of Run-I. Now top event samples contain hundreds of event statistics for investigation. This review mainly covers the mass measurements of the top quark produced at √s = 1.96 TeV in {ie359-2} collisions at the Collider Detector of Fermilab with the integrated luminosity samples up to 1 fb^?1. As an example of the top quark mass measurements we consider so-called Matrix Element method in “lepton + jets” and “dilepton” channels of the top-quark decay. The CDF top quark mass obtained in lepton +jets mode is the world most precise single measurement of this important physics parameter. The review summarizes the essential results of the CDF top-quark mass measurement achieved and published for the recent 2003–2008 period. We consider also b-quark baryon discoveries like Σ _b , Σ _b ^* , Θ _b as well as first observation of {ie359-3} oscillations. Let us mention here that a CDF/JINR-group created significant contribution to the new CDF complex and physics investigation.     

B c-meson decays and lifetime within QCD sum rules

On the basis of three-point sum rules, the form factors for the semileptonic decays B _c ⁺ → B _s(B _s ^* )l ⁺ ν _l are calculated with allowance for α _s/v Coulomb corrections for the heavy quarkonium. Generalized relations associated with spin symmetry within the approach combining heavy-quark effective theory and nonrelativistic QCD are derived for form factors in the region of recoil momenta close to zero. The nonleptonic decays of the B _c meson are studied on the basis of the factorization hypothesis. By summing the main exclusive modes of c-quark decays and by using the results of a previous analysis of b-quark decays, the B _c-meson lifetime is estimated within QCD sumrules and within nonrelativistic QCD.     

Screening of heavy quark free energies at finite temperatureand non-zero baryon chemical potential

We analyze the dependence of heavy quark free energies on the baryon chemical potential μ_b in 2-flavor QCD by performing a 6th order Taylor expansion in the chemical potential which circumvents the sign problem. The bare quark mass at corresponds to a pion mass of about 770 MeV and is thus not in the range of physical quark masses but the quark mass dependence is known to be small above T_c. At N_τ = 4 the lattices are coarse, however, we are using improved (p4 staggered) fermions. The Taylor expansion coefficients of color singlet and color averaged free energies are calculated and from this the expansion coefficients for the corresponding screening masses are determined. We find that for small μ_b the free energies of a static quark-antiquark pair decrease in a medium with a net excess of quarks and that screening is well described by a screening mass which increases with increasing μ_b. The μ_b-dependent corrections to the screening masses are well described by perturbation theory for T ≳ 2T_c. In particular, we find for all temperatures above T_c that the expansion coefficients for singlet and color averaged screening masses differ by a factor 2. PACS. 11.15.Ha, 11.10.Wx, 12.38Gc, 12.38.Mh     

Decay constants of the B and D mesons from QCD-duality sum rules

We show that various (non-) relativistic versions of QCD duality sum rules lead to a unique prediction ƒ_b ⋍ (1.38 ± 0.14) ƒ_π for the decay constant of the pseudoscalar B-meson. We also obtain ƒ_D ⋍(1.31 ± 0.12) ƒ_π from relativistic Laplace (Borel) sum rules and show that the SU (3)_F-breaking effects tend to increase the decay corresponding of the corresponding mesons containing a strange quark. In view of our results, we re-examine some qualitative arguments predicting the mass behaviour of the decay constant of heavy-light quark bound states.     

Light-front quark model and analysis of the spectrum of photons from inclusive B → X s γ decays

The electroweak-decay width Γ(B → X _s γ) is investigated in a light-front (LF) constituent quark model. A new partonlike formula is derived that establishes a simple relation between Γ(B → X _s γ) and the b → sγ decay width. A treatment of the b quark as an on-mass-shell particle and the inclusion of effects that arise from the transverse motion of the b quark in the B meson are basic features of this approach. Adopting different b-quark LF distribution functions, both phenomenological ones and those that are derived from constituent quark models, and neglecting perturbative corrections, we compute the photon energy spectra and the moments of the shape function. It is shown that the LF approach can be matched completely with a heavy-quark expansion (HQE), provided that the constituent b-quark mass is redefined in a way similar to that used in HQE to define the pole mass of the b quark. In this way, the correction to first order in 1/m _b can be eliminated from the total width in agreement with the general statement of HQE. We also show that the photon energy spectra calculated in the LF approach agree well with those obtained in the model of Altarelli et al., provided that the same distribution function is used as an input in both cases. Despite the simplicity of the model, our results are in fairly good agreement both with HQE predictions and with available experimental data.     

Sum rule estimate of the subleading non-perturbative contributions to Bs–$\bar{ B}_{s}$ mixing

We use QCD sum rules to compute the matrix elements of the ΔB=2 operators appearing in the heavy-quark expansion of the width difference of the B _s mass eigenstates. The main focus of our analysis is on the subleading operators R ₂ and R ₃, which appear at next-to-leading order in the 1/m _b expansion. The matrix elements of these operators are already essential for precise phenomenology, but their calculation in lattice QCD is lacking and the values given here provide a first estimate of their values. We conclude that the violation of the factorization approximation for these matrix elements due to non-perturbative vacuum condensates is as low as 1–2%.     

Decay of Bc (3S) → B D

The decay constant for the vector state of 3S-level in the heavy (

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c)-quarkonium is evaluated in the framework of sum rules for the mesonic currents. A scaling relation for the constants of vector quarkonia with different quark contents is derived. The numerical estime gives Γ (B^*+_c(3S) → B⁺ D⁰) = 90 ± 35 MeV.     

Properties of doubly heavy baryons in the relativistic quark model

Mass spectra and semileptonic decay rates of baryons consisting of two heavy (b or c) and one light quark are calculated in the framework of the relativistic quark model. The doubly heavy baryons are treated in the quark-diquark approximation. The ground and excited states of both the diquark and quark-diquark bound systems are considered. The quark-diquark potential is constructed. The light quark is treated completely relativistically, while the expansion in the inverse heavy-quark mass is used. The weak transition amplitudes of heavy diquarks bb and bc going, respectively, to bc and cc are explicitly expressed through the overlap integrals of the diquark wave functions in the whole accessible kinematic range. The relativistic baryon wave functions of the quark-diquark bound system are used for the calculation of the decay matrix elements, the Isgur-Wise function, and decay rates in the heavy-quark limit.     

Memorino on the ‘1/2 versus 3/2 puzzle’ in B̄→lν̄X<Subscript>c</Subscript> – a year later and a bit wiser

The OPE treatment that has been so successful in describing inclusive B̄→lν̄X_c decays yields sum rules (in particular the Uraltsev sum rule and its higher moments) implying the dominance of the P wave j_q=3/2 charm states in X_c over their j_q=1/2 counterparts. This prediction is supported by other general arguments as well as quark model calculations, which illustrate the OPE results, and by preliminary lattice findings. Its failure would indicate a significant limitation in our theoretical understanding of B̄→lν̄X_c. Some experimental issues have been clarified since a preliminary version of this note had appeared; yet, the verdict on the composition of the final states beyond D, D^* and the two narrow j_q=3/2 resonances remains unsettled. Establishing which hadronic configurations – D/D^*+π,D/D^*+2π,... – contribute, what their quantum numbers are, and their mass distributions will require considerable experimental effort. We explain the theoretical issues involved and why a better understanding of them will be of considerable value. Having significant contributions from a mass continuum distribution below 2.5 GeV raises serious theoretical questions for which we have no good answer. Two lists are given, one with measurements that need to be done and one with items of theoretical homework. Some of the latter can be done by employing existing theoretical tools, whereas others need new ideas.     

Photo-absorption sum rules σ<Subscript>–1</Subscript> in different environments (Atoms,nuclei, nucleons)

Combining the spin-dependent dispersion GDH-sum rule, the isotopic-spin-dependent Cabibbo-Radicati sum rule, and the relativistic dipole-moment-fluctuation (i.e. generalized Gottfried) sum rule with the three valence quark configuration of nucleons taken into account for the composition of the ground and the excited states of the nucleon, the relevant moments of the distribution and correlation functions of the quark electric dipole moment operators in the nucleon ground state are expressed via the experimentally measurable nucleon resonance photo-excitation amplitudes.These functions are of interest for checking detailed quark-configuration structure of the nucleon state vector. Within the non-relativistic approach to photo-absorption sum rules for the 3N-nuclei a new σ_–1 sum rule proposed which is based on general charge-symmetry (CS) consequences for the “CS-conjugated” triton and ³He.     

<Emphasis Type="Italic">B</Emphasis> and <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">s</Emphasis></Subscript> decay constants from moments of finite energy sum rules in QCD

We use an appropriate combination of moments of finite energy sum rules in QCD in order to compute the B _q -meson decay constants f _B and . We perform the calculation using a two-loop computation of the imaginary part of the pseudoscalar two point function in terms of the running bottom quark mass. The results are stable against the so-called QCD duality threshold, and they are in agreement with the estimates obtained from Borel transform QCD sum rules and lattice computations.Received: 28 July 2004, Revised: 10 September 2004, Published online: 23 November 2004PACS: 12.38.Bx, 12.38.LgSupported by MCYT-FEDER under contract FPA2002-00612.     

Effects of explicit SUf(3) breaking on the quark condensates

Effects of the explicit breaking of flavour symmetry on the quark condensates in the large-N_c limit are examined with the use of a QCD-motivated effective lagrangian. It is shown that, as the current mass increases, the non-perturbative quark condensate decreases in the absolute values, which agrees well with that obtained from QCD sum rules, not only qualitatively but also quantitatively. The condensatesat finite temperature are also investigated in relation to the chiral transition.     

Electric quadrupole and magnetic octupole moments of the light decuplet baryons within light cone QCD sum rules

The electric quadrupole and magnetic octupole moments of the light decuplet baryons are calculated in the framework of the light cone QCD sum rules. The obtained non-vanishing values for the electric quadrupole and magnetic octupole moments of these baryons show nonspherical charge distribution. The sign of electric quadrupole moment is positive for Ω⁻, Ξ^*−, Σ^*− and negative for Σ^*+, which correspond to the prolate and oblate charge distributions, respectively. A comparison of the obtained results with the predictions of non-covariant quark model which shows a good consistency between two approaches is also presented. Comparison of the obtained results on the multipole moments of the decuplet baryons containing strange quark with those of Δ baryons shows a large SU(3) flavor symmetry breaking.     

Ultrasoft contribution to heavy-quark pair production near threshold

We compute the third-order correction to the heavy-quark current correlation function due to the emission and absorption of an ultrasoft gluon. Our result supplies a missing contribution to top-quark pair production near threshold and the determination of the bottom quark mass from QCD sum rules.