Mass degeneracy of heavy-light mesons with chiral partner structure in the half-Skyrmion phase

Abstract

We explore the mass splitting of the heavy-light mesons with chiral partner structure in nuclear matter. In our calculation, we employed the heavy hadron chiral perturbation theory with chiral partner structure and the nuclear matter is constructed by putting skyrmions from the standard Skyrme model onto the face-centered cubic crystal and regarding the skyrmion matter as nuclear matter. We find that, although the masses of the heavy-light mesons with chiral partner structure are splitted in the matter-free space and skyrmion phase, they are degenerated in the half-skyrmion phase in which the chiral symmetry is restored globally. This observation suggests that the magnitude of the mass splitting of the heavy-light mesons with chiral partner structure can be used as a probe of the phase structure of the nuclear matter.Although the nuclear matter properties are difficult to access, it is a crucial and an interesting object to study them in both particle and nuclear physics because they are critically concerned with such issues as the equation of state (EoS) relevant to the compact-star matter and the chiral symmetry breaking/restoration in dense matter( see., e.g., Ref.[1] and references therein).Among all the approaches to the nuclear matter, skyrmion crystal is such one in which the nuclear matter properties are studied by putting skyrmions onto the crystal structure and regarding the skyrmion matter as baryonic matter [2](see also Ref.[3] and references therein). By changing the crystal size, the density effect enters. For example, in the face-centered cubic (FCC) crystal [4,5] adopted in this paper, ρ = 4/(2L) 3 with ρ and L being the nuclear matter density and crystal size, respectively. The advantage of the skyrmion crystal approach to nuclear matter is that both the nuclear matter and medium modified hadron properties can be treated in a unified way [6].In the skyrmion crystal approach, when we reduce the crystal size, or, equivalently, increase the nuclear matter density, the nuclear matter undergoes a phase transition from skyrmion phase to half-skyrmion phase in which there is a skyrmion configuration with a half baryon number at each crystal vertex [7]. And people found that, when the skyrmions are put onto the FCC crystal at low density, in the half-skyrmion phase at high density, the crystal vertices at which half-baryons are concentrated form a cubic crystal [4,5]. The order parameter which charactorizes this phase transition is the space average of the quark-antiquark condensate qq which vanishes in the half-skyrmion phase. Note that although the space average of the quark-antiquark condensate vanishes in * suenaga@hken.phys.nagoya-u.ac.jp † he@hken.phys.nagoya-u.ac.jp ‡ yongliangma@jlu.edu.cn § harada@hken.phys.nagoya-u.ac.jp the half-skyrmion phase, chiral symmetry is still locally broken since the pion decay constant in the baryonic matter f * π which charactorizes the chiral symmetry breaking does not vanish [8] and the quark-antiquark condensate is locally non-zero [9]. At this moment, properti...

Spectral functions for D¯ and D¯0* mesons in nuclear matter with partial restoration of chiral symmetry

“…Especially in relation to chiral symmetry, in Ref. [32], the masses ofD mesons in a dense matter such as the Skyrmion crystal was studied by including both chiral partner structure and heavy quark spin symmetry. The chiral partners such as aD meson (J P = 0 − ) and ā D * 0 meson (J P = 0 + ), whose parities are opposite each other, have unequal masses whose difference stems from the spontaneous breakdown of chiral symmetry [29,30].…”

Inhomogeneous quark condensate in compressed Skyrmion matter

“…Indeed, it was shown very recently in Ref. [25] by coupling the heavy-light mesons with chiralpartner structure to the leading-derivative order HLS(π), that the masses of the chiral partners of the heavy-light mesons, which are split in the skyrmion matter, become degenerate in the half-skymion phase. It would be interesting to study similar phenomena in the light meson sector.…”

Correlations between light and heavy flavors near the chiral crossover

“…There exist a number of works on the charmed mesons in nuclear matter, in the context of QCD sum rules [14,[23][24][25] and effective theories [16,[26][27][28][29][30][31][32]. In utilizing our effective theory, a central task is to introduce a reliable density dependence of the interaction parameters, which requires a more microscopic prescription [33].…”

“…The chiral partner of H is embodied as the secondlowest spin multiplets G [10,11]. The mass splitting between G and H is proportional to the chiral order parameter, and its thermal/dense evolution characterizes partial restoration of the chiral symmetry in a medium [12][13][14][15][16].…”