An axially symmetric ansatz is proposed to investigate the properties of baryon in a uniform magnetic field. The baryon number is shown to be conserved, while the baryon shape is stretched along the magnetic field. It is found that with increasing magnetic field strength, the static mass of the baryon first decreases and then increases, while the size of the baryon first increases and then decreases. Finally, in the core part of the magnetar, the equation of state strongly depends on the magnetic field, which modifies the mass limit of the magnetar.PACS numbers: 12.39. Dc, 12.39.Fe, 11.30.Rd Introduction.-The behavior of hadrons in an ultrastrong magnetic field is very rich and subtle. On one hand, recent experiments have observed that a strong magnetic field exists in non-central heavy-ion collisions. On the other hand, an ultrastrong magnetic field widely exists in the early universe and in magnetars. Thus, a number of studies have been performed in the last few years [1]. Generally, in an ultrastrong magnetic field background, hadrons have two important features: (i) the SO(3) space and SU (2) flavour symmetry of the hadron is explicitly broken by the magnetic field, and (ii) the hadron is strongly deformed in a strong magnetic field. Recently, several models have been developed that predict the mass and shape change of the meson in a uniform magnetic field. For example, lattice quantum chromodynamics (QCD) calculations imply the quark potential changes in the magnetic field background [2]; however, because it is difficult to predict the charge radii of baryons in a vacuum using lattice QCD calculations [3], the shape of the baryon in a strong magnetic field background is still unclear.In this letter, the focus is to study the baryon mass and shape under the confinement phase in a strong magnetic field background. Because the pion does not condense in a strong magnetic field, Skyrme showed that the properties of a baryon could be evaluated by constructing a soliton object in mesonic models [4]. The skyrmion preserves both energy and shape, which helps in understanding the baryon properties in strong magnetic field backgrounds. In the present study, the baryon number is shown to be always conserved, as the presence of the magnetic field does not break the U (1) V symmetry. It is found that the shape of the baryon is stretched along the magnetic field, considered as the z-axis, as the symmetry of SO(3) space is explicitly broken to SO(2) space in a strong magnetic field background. Furthermore, with increasing magnetic field strength, the dominant role shifts from the linear term of the magnetic field to the quadratic term of the magnetic field; consequently, the static mass of the baryon first decreases and then increases. Finally, because the mass and shape of the baryon are both influenced by the magnetic field, the equation of state (EOS) for magnetars

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...

We propose to study the mass spectrum of the heavy-light mesons to probe the structure of the spin-isospin correlation in the nuclear medium. We point out that the spin-isospin correlation in the nuclear medium generates a mixing among the heavy-light mesons carrying different spins and isospins such as D + , D 0 , D * + , and D * 0 mesons. We use two types of correlations motivated by the skyrmion crystal and the chiral density wave as typical examples to obtain the mass splitting caused by the mixing. Our result shows that the structure of the mixing reflects the pattern of the correlation, i.e., the remaining symmetry. Furthermore, the magnitude of the mass modification provides information of the strength of the correlation.PACS numbers: 21.65. Jk, 14.40.Lb, 12.39.Fe, 21.10.Hw. Studying the dense hadronic medium is one of the interesting subjects for understanding the quantum chromodynamics (QCD) in the low-energy region. It will provide an important clue to describe the equation of state inside neutron stars [1], and also it may give some information on the structure of the chiral symmetry breaking [2].Heavy-light mesons made of a heavy quark and a light quark are expected to be good probes of the properties of nuclear medium. Although the medium modifications of the properties of heavy-light mesons have been widely studied [3], to the best of our knowledge, there is no explicit statement on the mixing as a single state among heavy-light mesons carrying different spins, such as the pseudoscalar D and the vector D * mesons, in medium in the literature.In this Brief Report, we shall discuss the mixing between the heavy-light mesons carrying different spins such as D and D * mesons in the nuclear medium caused by the existence of the spin-isospin correlation which is expected in, e.g., the skyrmion crystal [4], the chiral density wave phase [5], and so on. In the literature, the density at which the spin-isospin correlation becomes significant depends on the model. In the recent Skyrme model calculation including the vector meson effect [6], the pion has a p-wave condensation whose size becomes on the order of a few 100 MeV at about the normal nuclear density ρ 0 . In the chiral density wave phase, on the other hand, the pion develops the position-dependent vacuum expectation value (VEV) in the high density region above 2.4ρ 0 [5]. This VEV implies the existence of the strong spin-isospin correlation.We start with a set of heavy-light mesons which makes two doublets of isospin as well as two doublets of heavyquark spin symmetry such as D + , D 0 , D * + , and D * 0 . In the heavy quark limit, the set is characterized by the spin of the light cloud surrounding the heavy quark [7]: When the spin of the light cloud is J l , the set of heavy-light mesons are made of mesons of spin J l + 1/2 and J l − 1/2.Since the set carries isospin 1/2, it includes 2(4J l + 2) states, which are all degenerated in mass at the heavy quark limit and the isospin limit. For example, D and D * mesons are specified by J l = 1/2, and...

We study the effects of light scalar mesons on the skyrmion properties by constructing and examining a mesonic model including pion, rho meson, and omega meson fields as well as two-quark and four-quark scalar meson fields. In our model, the physical scalar mesons are defined as mixing states of the two- and four-quark fields. We first omit the four-quark scalar meson field from the model and find that when there is no direct coupling between the two-quark scalar meson and the vector mesons, the soliton mass is smaller and the soliton size is larger for lighter scalar mesons; when direct coupling is switched on, as the coupling strength increases, the soliton becomes heavy, and the radius of the baryon number density becomes large, as the repulsive force arising from the $\omega$ meson becomes strong. We then include the four-quark scalar meson field in the model and find that mixing between the two-quark and four-quark components of the scalar meson fields also affects the properties of the soliton. When the two-quark component of the lighter scalar meson is increased, the soliton mass decreases and the soliton size increases.Comment: 9 pages, 6 figure

Abstract. We summarize our recent work in which we develope the holographic mean field approach to study the dense baryonic matter in a bottom-up holographic QCD model including baryons and scalar mesons in addition to vector mesons. We first show that, at zero density, the rate of the chiral invariant mass of nucleon is controlled by the ratio of the infrared boundary values of two baryon fields included in the model. Then, at non-zero density, we find that the chiral condensate decreases with the increasing density indicating the partial restoration of the chiral symmetry. Our result shows that the more amount of the proton mass comes from the chiral symmetry breaking, the faster the effective nucleon mass decrease with density.