Heavy Quark Fluorescence

Abstract

Heavy hadrons containing heavy quarks (for example, Ç mesons) feature a scale separation between the heavy-quark mass and the QCD scale that controls the effective masses of lighter constituents. As in ordinary molecules, the deexcitation of the lighter, faster degrees of freedom leaves the velocity distribution of the heavy quarks unchanged, populating the available decay channels in qualitatively predictable ways. Automatically an application of the Franck-Condon principle of molecular physics explains several puzzling results of Çð5SÞ decays as measured by the Belle Collaboration, such as the high rate of B The Franck-Condon principle [1] is essential in understanding fluorescence in the decay of excited molecules. It states that, during an electronic transition, the electron orbital relaxes to the ground state in a time too short for the nuclei to react. Hence, the wave function associated with the motion of the nuclei remains the same after the transition. Since the ground-state wave functions of this motion in the two electronic adiabatic potentials (before and after the transition) are unequal, the nuclei remain in a superposition of excited states, resulting in secondary transitions (efficiently degrading excitation energy).While the Born-Oppenheimer approximation from molecular physics has already been studied for decades in the context of particle physics, we have only recently understood [2] the relevance of the Franck-Condon principle here. The key is its usefulness in analyzing open-flavor decays of heavy hadrons. Such decays are characterized by the heavy quarks from the initial hadron streaming away in separate hadrons. We take as an example the newly analyzed Çð10 860Þ ! B " B, B " B . . . decays. The momentum of the heavy quark inside the heavy hadron k b follows a quantum-mechanical probability distribution that depends on the wave function of the state. This wave function accepts a decomposition in an appropriately chosen quark-gluon basis, for example jÇi. . . One of the salient problems of hadron physics nowadays is to determine the functions i , whose size characterizes whether a state is ''mostly a quarkonium'' or otherwise. Characteristic of pure (excited) quarkonia is the presence of Sturm-Liouville zeros in the momentum distribution [3]. This follows from the Hermiticity of the QCD Hamiltonian [4], that implies orthogonality between different wave functions. Figure 1 We have divided the experimental data by known spin, isospin, and phase-space factors so it can be directly compared to the square of the top panel wave function (solid line) or to the wave function folded with a complete 3 P 0 decay-model (dashed line), that gives us an idea of the errors of order à QCD =m b involved in a naive application of the Franck-Condon principle.

Higher bottomonium zoo

“…In Ref. [66], authors just discussed the application of the Franck-Condon principle, which is common in molecular physics on the anomalous high branching ratios of B * s B * s versus B s B * s . For the Υ(11020) state, there are no experimental data in the open-bottom decay channel at present.…”

Mapping chiral symmetry breaking in the excited baryon spectrum

“…The truncated Coulomb gauge approach is equivalent to a field theory version of chiral invariant quark models [24][25][26][27][28][29][30][31][32][33][34]. Because the model includes linear confinement one can examine an excited spectrum with infinitely many excitations.…”

Phase Diagram, Scalar-Pseudoscalar Meson Behavior and Restoration of Symmetries in (2 + 1) Polyakov-Nambu-Jona-Lasinio Model

“…Usually, different approaches can also be used to compute M M and Γ M . In [95], the meson masses were calculated by supposing that the pole is near the real axis and the imaginary part of the solution in the argument of Equation (A3) of the Appendix A is neglected. In [47,51,115] only the Γ 2 M contribution coming from (M M − iΓ M /2) was neglected.…”

“…After that, several studies have addressed the peculiarities of the different versions of the model, namely the SU(2) [85][86][87] and (2 + 1)-flavors [88][89][90]. The PNJL model brings with it some changes relative to the NJL model, in both SU(2) and (2 + 1)-flavor versions, particularly concerning to a higher temperature for the position of the CEP and also a larger size of the critical region [91][92][93][94][95].…”