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Register a new userDistribution Amplitudes of Heavy Mesons and Quarkonia on the Light Front
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The ladder kernel of the Bethe-Salpeter equation is amended by introducing a different flavor dependence of the dressing functions in the heavy-quark sector. Compared with earlier work this allows for the simultaneous calculation of the mass spectrum and leptonic decay constants of light pseudoscalar mesons, the $D_u$, $D_s$, $B_u$, $B_s$ and $B_c$ mesons and the heavy quarkonia $eta_c$ and $eta_b$ within the same framework at a physical pion mass. The corresponding Bethe-Salpeter amplitudes are projected onto the light front and we reconstruct the distribution amplitudes of the mesons in the full theory. A comparison with the first inverse moment of the heavy meson distribution amplitude in heavy quark effective theory is made.
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In this work we use the framework of the Dyson-Schwinger and Bethe-Salpeter equations to compute Light-Cone Distribution Amplitudes of heavy-light mesons and quarkonia. In studying the meson properties, we introduce a flavor dependence in the heavy-quark sector of the Bethe-Salpeter ladder kernel which yields improved numerical results for masses and leptonic decay constants of the pseudoscalar $D$, $D_s$, $B$ and $B_s$ mesons. Finally, the corresponding heavy-light Bethe-Salpeter amplitudes are projected onto the light front and we reconstruct the distribution amplitudes of the mesons in the full theory.
Accumulating evidence indicates that soft quark+quark (diquark) correlations play an important role in the structure and interactions of hadrons constituted from three or more valence-quarks; so, it is worth developing insights into diquark structure. Using a leading-order truncation of those equations needed to solve continuum two-valence-body bound-state problems, the leading-twist two-parton distribution amplitudes (DAs) of light-quark scalar and pseudovector diquarks are calculated. The diquark DAs are narrower and taller than the asymptotic profile that characterises mesons. Consequently, the valence quasiparticles in a diquark are less likely to carry a large light-front fraction of the systems total momentum than those in a meson. These features may both influence the form of baryon DAs and be transmitted to diquark distribution functions (DFs), in which case their impact will be felt, e.g. in the protons $u$ and $d$ valence-quark DFs.
The parton distribution functions (PDFs) of heavy mesons are evaluated from their light-front wave functions, which are obtained from a basis light-front quantization in the leading Fock sector representation. We consider the mass eigenstates from an effective Hamiltonian consisting of the confining potential adopted from light-front holography in the transverse direction, a longitudinal confinement, and a one-gluon exchange interaction with running coupling. We present the gluon and the sea quark PDFs which we generate dynamically from the QCD evolution of the valence quark distributions.
We summarize recently improved results for the pseudoscalar [1,2] and vector [3] meson decay constants and their ratios from QCD spectral sum rules where N2LO + estimate of the N3LO PT and power corrections up to d< 6 dimensions have been included in the SVZ expansion. The optimal results based on stability criteria with respect to the variations of the Laplace/Moments sum rule variables, QCD continuum threshold and subtraction constant mu are compared with recent sum rules and lattice calculations. To understand the apparent tension between some recent results for f_B*/f_B, we present in Section 8 a novel extraction of this ratio from heavy quark effective theory (HQET) sum rules by including the normalization factor (M_b/M_B)^2 relating the pseudoscalar to the universal HQET correlators for finite b-quark and B-meson masses. We obtain f_B*/f_B=1.025(16) in good agreement with the one 1.016(16) from (pseudo)scalar sum rules in full QCD [3]. We complete the paper by including new improved estimates of the scalar, axial-vector and B^*_c meson decays constants (Sections 11-13). For further phenomenological uses, we attempt to extract a Global Average of different sum rules and lattice determinations of the decay constants which are summarized in Tables 2-6. We do not found any deviation of these SM results from the present data.
We use QCD spectral sum rules (QSSR) and the factorization properties of molecule and four-quark currents to estimate the masses and couplings of the 0+ and 1+ molecules and four-quark at N2LO of PT QCD. We include in the OPE the contributions of non-perturbative condensates up to dimension-six. Within the Laplace sum rules approach (LSR) and in the MS-scheme, we summarize our results in Table 2, which agree within the errors with some of the observed XZ-like molecules or/and four-quark. Couplings of these states to the currents are also extracted. Our results are improvements of the LO ones in the existing literature.
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