The Charm and Beauty of Strong Interactions

Abstract

Abstract. We briefly review common features and overlapping issues in hadron and flavor physics focussing on continuum QCD approaches to heavy bound states, their mass spectrum and weak decay constants in different strong interaction models. Hadron and Flavor Physics: a twofold motivation, a unified approach?Hadron and flavor physics are often thought of as different research fields though they have in common the underlying theory which describes strong interactions in flavored and non-flavored hadrons, namely Quantum Chromodynamics (QCD). In particular confinement, one of QCD's paradigmatic hallmarks, may not be appreciated enough in flavor physics. Undoubtedly, in nonrelativistic QCD and effective field theory approaches to quarkonia and the fauna of new XYZ states the main focus is on spectroscopy and production mechanisms, where most efforts concentrate on nonrelativistic perturbative aspects, effective theories or potentials models [1][2][3][4].While certain quarkonia provide a relatively clean environment to probe strong dynamics, and the mass spectrum of their confined quarks is reasonably well described in nonrelativistic perturbative QCD (pQCD), many of the heavier XYZ states close to threshold may not be pureqq states but admixtures of meson molecules and a core of quarks. Moreover, it is desirable to unify the meson and baryon spectrum with a unique confining framework that correctly describes the dynamical chiral symmetry breaking (DCSB) pattern which occurs to varying degrees in hadrons. In particular, DCSB may still play an important role in charmonia where nonperturbative O(Λ QCD /m c ) contributions can be non negligible. On the other hand, the study of weak B-meson decays, once driven by factorization theorems [5] and soft collinear effective field theory [6], appears to be nowadays dominated by the quest for new physics largely motivated by recurrent announcements of the LHCb collaboration [7][8][9]. Still, it is exactly in the case of heavy-light mesons where our understanding of their QCD dynamics and emerging properties are the least well understood within continuum QCD approaches [10][11][12][13][14][15][16][17][18][19]. The reason for this is obviously the important difference in quark masses and the energetic light mesons produced in their decays, both of which are at the origin of a wide array of energy scales [20,21] which effective theories can merely separate.More generally, the main object of study in flavor physics is the origin of CP-violating phases in weak decays of flavored quarks confined in hadrons, where the Cabibbo-Kobayashi-Maskawa (CKM) mechanism has been established as the dominant Standard Model source of CP violation in heavymeson decays. On the other hand, the overwhelming bulk of visible matter is made of baryons containing light quarks. DCSB due to gluon self-interactions has by now been established to be the most important mass generating mechanism for visible matter in the Universe, which implies that for most observed matter the Higgs mechanism is almost irrelevan...

Distribution amplitudes of heavy mesons and quarkonia on the light front

“…and N (α) and N (β) are both as in Eq. (47). The even and odd components of the distribution amplitudes are then determined independently by separately minimizing,…”

“…In the infinite-mass limit these distribution amplitudes tend towards a δ-like function, though this limit is far from being reached at the bottommass scale. The transition from concavely shaped distribution amplitudes to convex-concave ones occurs between the strange and charm quark, a mass-scale region known for the onset of important flavor-symmetry breaking effects [43][44][45][46][47].…”

Interplay of dynamical and explicit chiral symmetry breaking effects on a quark

“…The renormalization conditions (4) and (5) are imposed at µ = 19 GeV for the vertices in Eqs. (11), (12) and (14) for both the MT and QC interactions. The bare vertex is multiplied by a renormalization constant Z 2 as in Eq.…”

“…The bare vertex is multiplied by a renormalization constant Z 2 as in Eq. (11), which introduces a renormalization factor Z 2 2 on the right-hand-side of Eq. (9).…”

“…Moreover, while the weak decay constants of light pseudoscalar and vector mesons increase with the light current-quark mass, they level off somewhere between the strange-and charm-quark mass and fall off for heavier quark masses as f M = 1/ √ M M [1,8]. On the other hand, the weak decay constants of radially excited quarkonia can be shown to vanish in the chiral limit but though suppressed, their values increase again in a mass range somewhere between thess andcc quarkonia [9][10][11]. Clearly, dynamical effects on the dressed-mass function in the intermediate range between these two current-quark mass scales have a substantial impact on hadronic observables; an analogue observation is that SU(4) F flavor symmetry is badly broken compared with SU(3) F [12][13][14].…”