Chiral-partner D mesons in a heat bath within QCD sum rules

Abstract

Utilizing QCD sum rules, we extract the temperature dependences of the spectral properties of the pseudo-scalar and scalar D mesons regarded as chiral partners. Besides the masses also decay constants are analyzed as the D meson yields in heavy-ion collisions may be sensitive to their altered decay properties in an ambient strongly interacting medium. Our findings are (i) a decreasing scalar D meson mass for growing temperatures while its pseudo-scalar partner meson seems hardly affected, which is in qualitative agreement with hadronic model calculations; (ii) inferring an equally weak temperature dependence of the pseudo-scalar D meson decay properties the decreasing residua and decay constants of the scalar particle point towards partial chiral restoration. As a bonus of our analysis in the pseudo-scalar sector we determine the pseudo-scalar decay constant at vanishing temperature. Due to the connection to particular leptonic branching fractions this decay constant is of great interest allowing for the determination of the off-diagonal CKM matrix element |V cd | at zero temperature. arXiv:1801.01472v1 [nucl-th] 4 Jan 2018 etc. Further interesting aspects of open flavor mesons are rare CP-violating decays [10] and their role w. r. t. exotic quantum numbers [11]. In this paper, we utilize the QCD sum rule (QSR) tool [12] and compare chiral-partner open-charm mesons, that is the pseudo-scalar (P) D meson and the scalar (S) D meson. Mass modificationsChiral partners in the light-quark sector, e. g. the spectra of ρ and a 1 mesons, should become mass degenerate under chiral restoration [13,14], but also the individual fate of a member in the chiral multiplet under chiral restoration is of interest [15][16][17]. As mentioned above, also the open-charm mesons are subject to chiral restoration, albeit in a different manner.Studying patterns of dynamical chiral symmetry breaking (DχSB) with mesons containing a heavy and a light quark seems to be superimposed by the explicit symmetry breaking due to the non-negligible heavy-quark mass. However, the original light-quark problem can be translated into the heavy-light sector, if the chiral symmetry transformations are restricted to the light-quark content. As exemplified in Appendix A for the D 0 meson, the respective pseudo-scalar current can be transformed into the scalar current by a finite chiral transformation with a specific set of rotation parameters. Thus, the pseudo-scalar and scalar D 0 mesons are qualified as chiral partners, which would have degenerate spectral properties in a chirally symmetric world. In contrast, the experimentally verified masses [3], m P = 1.865 GeV and m S = 2.318 GeV, deviate by about 450 MeV (similar to the a 1 -ρ mass splitting) signaling the dynamical breakdown of chiral symmetry which is driven by order parameters [18-21], e. g. most prominently by the chiral condensate 〈qq〉 as well as by chirally odd four-quark condensates which vanish in a chiral restoration scenario. The DχSB phenomenology, e. g. the splitting of chiral partner mass...

D meson mass and heavy quark potential at finite temperature

“…The sign in front of the γ E (the Euler-Mascheroni constant) term is different from the expression given in Ref. [22], which can be traced back to a mistake/typo in Eq. (65) of Ref.…”

“…For our purposes, we can identify the imaginary part of the time ordered correlator with the spectral density as the thermal factor tanh √ s/(2T ) in the integrand on the right-hand side for the temperature and energy values considered here ( √ s > ∼ m D and T < ∼ T c ) is close to 1 and can be safely neglected (see also the discussion in Ref. [22]).…”

Impact of a thermal medium on $D$ mesons and their chiral partners

“…Therefore, in this sector we cannot conclude that masses of opposite parity states become degenerate close to T χ , although the temperatures studied might be still low for the chiral symmetry restoration. In [36] a large reduction in the mass of the positive-parity D meson partner, of around 150 MeV, is found at T = 150 MeV, but using a constant D mass as an input of the sum-rule analysis. An even larger reduction of close to 200 MeV is seen in the results of [35].…”

D mesons as a probe of Casimir effect for chiral symmetry breaking

“…Furthermore, the relation between D meson masses and the chiral condensate (or σ-mean field) at finite temperature/density has been discussed by using phenomenological approaches such as QCD sum rules [13,[17][18][19][20][21][22][23][24][25] and effective models [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] (see Refs. [43] for a recent review).…”