Survey of heavy-meson observables

Abstract

We employ a Dyson-Schwinger equation model to effect a unified and uniformly accurate description of light- and heavy-meson observables, which we characterise by heavy-meson leptonic decays, semileptonic heavy-to-heavy and heavy-to-light transitions - B -> D*, D, rho, pi; D -> K*, K, pi, radiative and strong decays - B(s)* -> B(s) gamma; D(s)* -> D(s) gamma, D pi, and the rare B-> K* gamma flavour-changing neutral-current process. We elucidate the heavy-quark limit of these processes and, using a model-independent mass formula valid for all nonsinglet pseudoscalar mesons, demonstrate that their mass rises linearly with the mass of their heaviest constituent. In our numerical calculations we eschew a heavy-quark expansion and rely instead on the observation that the dressed c,b-quark mass functions are well approximated by a constant, interpreted as their constituent-mass: we find M_c=1.32 GeV and M_b=4.65 GeV. The calculated heavy-meson leptonic decay constants and transition form factors are a necessary element in the experimental determination of CKM matrix elements. The results also show that this framework, as employed hitherto, is well able to describe vector meson polarisation observables.Comment: 32 pages, 7 figures, REVTEX. Some quantitative modification of tables and figures: calculation of additional processes. To appear in Phys. Rev.

Hadron properties and Dyson–Schwinger equations

“…The existence of a sensible truncation of the DSEs [41,42] has enabled proof via that identity of a body of exact results for pseudoscalar mesons. They relate even to radial excitations and/or hybrids [43,44,45], and heavy-light [46,47] and heavy-heavy mesons [39]. The results have been illustrated using a renormalisation-group-improved rainbow-ladder truncation [38,48], which also provided a prediction of the electromagnetic pion form factor [49].…”

Unifying Aspects of Light- and Heavy-Systems

“…The chiral limit gap equation also admits a Nambu-Goldstone mode solution whose p 2 ≃ 0 properties are unambiguously related to those of the m = 0 solution, a feature also evident in QCD [11]. A complete solution of Eq.…”

“…(47) - (49) are valid for any values of the current-quark masses, and the generalisation to N f quark flavours is [6,10,11] …”

“…The ellipsis represents terms whose leading contribution is O(g 4 ); viz., the crossed-box and two-rung dressed-gluon ladder diagrams, and also terms of higher leading-order. This expansion of S 2 K, with its implications for other n-point functions, yields an ordered truncation of the DSEs that guarantees, term-by-term, the preservation of vector and axial-vector Ward-Takahashi identities, a feature that has been exploited [5,10,11] to establish exact results in QCD. It is readily seen that inserting Eq.…”

“…The DSE methods described hitherto have been applied to mesons involving heavy-quarks [11,54,55] and in this case there is a natural simplification. To begin, one focuses on the fact that mesons, whether heavy or light, are bound states of a dressed-quark and -antiquark, with the dressing described by the gap equation, Eq.…”