The chemical-potential dependence of pi and sigma meson masses is analyzed at both real and imaginary chemical potentials, $μ_\mathrm{R}$ and $μ_\mathrm{I}$, by using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model that possesses both the extended ${\mathbb Z}_3$ symmetry and the chiral symmetry. In the $μ_\mathrm{I}$ region, the meson masses have the Roberge-Weiss periodicity. Assuming that the meson masses will be measured at finite $μ_\mathrm{I}$ by lattice QCD in future, we simulate how meson masses at finite $μ_\mathrm{R}$ are extracted from those at finite $μ_\mathrm{I}$, and propose a reliable extraction method.
We first extend our formulation for the calculation of $π$- and $σ$-meson screening masses to the case of finite chemical potential $μ$. We then consider the imaginary-$μ$ approach, which is an extrapolation method from imaginary chemical potential ($μ=i μ_{\rm I}$) to real one ($μ=μ_{\rm R}$). The feasibility of the method is discussed based on the entanglement Polyakov-loop extended Nambu--Jona-Lasinio (EPNJL) model in 2-flavor system. As an example, we investigate how reliable the imaginary-$μ$ approach is for $π$- and $σ$-meson screening masses, comparing "screening masses at $μ_{\rm R}$ i…
Constraining the QCD phase diagram by tricritical lines at imaginary chemical potential
我们从QCD的晶格模拟中得到了三种简并夸克在（T，m）相图中两个三临界点的明确证据，其中一个在轻质量区，另一个在重质量区，虚质量μ/T=iπ/3 mod 2π/3是固定的.这些代表的边界的手性和decenclosure临界线继续虚化学势，分别。结果表明，实化学势解禁闭临界线的形状是由三临界标度决定的，并意味着实化学势解禁闭跃迁的减弱.讨论了非简并夸克质量和轻夸克质量的推广。
By employing QCD inequalities, we discuss appearance of the pion condensate for both real and imaginary isospin chemical potentials, taking also into account imaginary quark chemical potential. We show that the charged pion can condense for real isospin chemical potential, but not for imaginary one. Furthermore, we evaluate the expectation value of the neutral-pion field for imaginary isospin chemical potential by using framework of the twisted mass. As a result, it is found that the expectation value becomes zero for the finite current-quark mass, whereas the Banks-Casher relation is obtained…
Properties of QCD at finite imaginary chemical potential are revisited to utilize for the model building of QCD in low energy regimes. For example, the electric holonomy which is closely related to the Polyakov-loop drastically affects thermodynamic quantities beside the Roberge-Weiss transition line. To incorporate several properties at finite imaginary chemical potential, it is important to introduce the holonomy effects to the coupling constant of effective models. This extension is possible by considering the entanglement vertex. We show justifications of the entanglement vertex based on t…
At finite imaginary values of the chemical potential, QCD is free of the sign problem. Moreover, at high temperatures the partition function exhibits a new symmetry (the Roberge-Weiss symmetry) connecting phases with different orientations of the Polyakov loop, and the corresponding phase transitions between these. In this contribution we investigate the perturbative one-loop effective potential for the Polyakov loop in the presence of imaginary isospin as well as baryon chemical potentials. This leads to a novel phase diagram, which reveals an interesting insight about the rich phase structur…
The first principle lattice QCD methods allow to calculate the thermodynamic observables at finite temperature and imaginary chemical potential. These can be compared to the predictions of various phenomenological models. We argue that Fourier coefficients with respect to imaginary baryochemical potential are sensitive to modeling of baryonic interactions. As a first application of this sensitivity, we consider the hadron resonance gas (HRG) model with repulsive baryonic interactions, which are modeled by means of the excluded volume correction. The Fourier coefficients of the imaginary part o…
We investigate the phase structure of two-color QCD at both real and imaginary chemical potentials mu, performing lattice simulations and analyzing the data with the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. Lattice QCD simulations are done on an 8^3 times 4 lattice with the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. We test the analytic continuation of physical quantities from imaginary mu to real mu by comparing lattice QCD results calculated at real mu with the result of analytic function the coefficients of w…
We investigate the order of the finite temperature chiral symmetry restoration transition for QCD with two massless fermions, by using a novel method, based on simulating imaginary values of the quark chemical potential $μ=iμ_i,μ_i\in\mathbb{R}$. Our method exploits the fact that, for low enough quark mass $m$ and large enough chemical potential $μ_i$, the chiral transition is decidedly first order, then turning into crossover at a critical mass $m_c(μ)$. It is thus possible to determine the critical line in the $m - μ^2$ plane, which can be safely extrapolated to the chiral limit by taking ad…
We discuss analytic continuation as a tool to extract the cumulants of the quark number fluctuations in the strongly interacting medium from lattice QCD simulations at imaginary chemical potentials. The method is applied to $N_f = 2+1$ QCD, discretized with stout improved staggered fermions, physical quark masses and the tree level Symanzik gauge action, exploring temperatures ranging from 135 up to 350 MeV and adopting mostly lattices with $N_t = 8$ sites in the temporal direction. The method is based on a global fit of various cumulants as a function of the imaginary chemical potentials. We …
We present here the results from an ongoing determination of the critical quark mass in simulations of (2+1)-flavor QCD with an imaginary chemical potential. Studies with unimproved actions found the existence of a critical quark mass value at which the crossover transition ends on a second order phase transition and becomes first order for smaller values of the quark mass for the case of both vanishing and imaginary chemical potential. We use the Highly Improved Staggered Quark (HISQ) action and perform calculations in the Roberge-Weiss (RW) plane, where the value of the critical mass is expe…
We present results from an ongoing study of the phase diagram of (2+1)-flavor QCD using the HISQ action with smaller than physical light quark masses in the Roberge-Weiss (RW) plane on lattices with temporal extent $N_τ=4$. We find that the endpoint of the $1^{st}$ order RW transition line remains $2^{nd}$ order at least down to light quark masses corresponding to Goldstone pion masses of $55$ MeV. Furthermore, we show that the chiral condensate is sensitive to the RW transition and may serve as a energy-like operator characterizing universal behavior close to the RW endpoint.
We investigate inhomogeneous chiral condensates, such as the so-called dual chiral density wave of dense quark matter, under an external magnetic field at finite real and imaginary chemical potentials. In a model-independent manner, we find that analytic continuation from imaginary to real chemical potential is not possible due to the singularity induced by inhomogeneous chiral condensates at zero chemical potential. From the discussion on the non-analyticity and methods used in lattice QCD simulations, e.g., Taylor expansion, and the analytic continuation with an imaginary chemical potential,…
We investigate the influence of the allowed unphysical meson decay into a quark-antiquark pair of the three flavour Nambu--Jona-Lasinio (NJL) model on its parameter fixing. This decay manifests in a non-vanishing imaginary part of the corresponding meson propagator and its polarisation loop, respectively. In order to handle the emerging divergent integrals, we focus on the Pauli-Villars, three- and four momentum cutoff regularisation method. Here, we fix the parameters to certain observables, which are effected by the non-vanishing imaginary part. The resulting parameter-sets for each regulari…
We investigate temperature ($T$) dependence of quark number densities ($n_q$) at imaginary and real chemical potential ($μ$) by using $N_f = 2$ lattice QCD and the hadron resonance gas (HRG) model. Quark number densities are calculated at imaginary $μ$ with lattice QCD on an $8^2 \times 16 \times 4$ lattice with the clover-improved $N_f =2$ Wilson fermion action and the renormalization-group-improved Iwasaki gauge action. The results are consistent with the previous results of the staggered-type quark action. The $n_q$ obtained are extrapolated to real $μ$ by assuming the Fourier series for th…
In characterizing the chiral phase-structure of pseudoscalars ($J^{pc}=0^{-+}$), scalars ($J^{pc}=0^{++}$), vectors ($J^{pc}=1^{--}$) and axial-vectors ($J^{pc}=1^{++}$) meson states and their dependence on temperature, chemical potential, and magnetic fields, we utilize SU($3$) Polyakov linear-sigma model (PLSM) in mean-field approximation. We first determine the chiral (non)strange quark condensates, $σ_l$ and $σ_s$ and the corresponding deconfinement order parameters, $ϕ$ and $ϕ^*$, respectively, in thermal and dense (finite chemical potential) medium and finite magnetic field. The temperat…
We evaluate the finite temperature scalar sunset diagram with imaginary square masses, that appears in the Gribov-Zwanziger approach to Yang-Mills (YM) theory beyond one-loop order. Since YM theory at finite temperature is governed by center-symmetry and the Polyakov loop, we also include the possibility of a constant temporal background gauge field in the form of color-dependent imaginary chemical potentials.
Thermodynamic geometry in hadron resonance gas model at real and imaginary baryon chemical potential and a simple sufficient condition for quark deconfinement
Saga University（佐贺大学）；Khazar University（阿塞拜疆坎扎尔大学）；Fukuoka Institute of Technology（福冈工业大学）
In order to study the fate of mesons in thermal QCD at finite baryon chemical potential, we consider light mesonic correlation functions using the Taylor expansion to ${\cal O}((μ/T)^2)$, in both the hadronic and quark-gluon plasma phases. We use the FASTSUM anisotropic fixed-scale lattices with $N_f = 2+1$ flavours of Wilson fermion. We find that mesonic correlators are sensitive to finite-density corrections and that the second-order terms indicate the chiral crossover in the vector and axial-vector channels.
Phase structure of magnetized quark matter at imaginary chemical potential
Instituto de Física La Plata, CONICET − - Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La PLata（拉普拉塔物理研究所，阿根廷国家科学研究委员会，拉普拉塔国立大学理学院物理系）；CONICET（阿根廷国家科学研究委员会）；Physics Department, Comisión Nacional de Energía Atómica（阿根廷国家原子能委员会物理系）
Light meson ( $π,\ σ,\ a_0$) properties in the environment with chiral imbalance are analyzed with the help of meson effective Lagrangian associated with QCD. New spatial parity violating decays of scalar mesons arise as a result of mixing of $π$ and $a_0$ mesons under influence of chiral charge density. The pion electromagnetic form-factor gets an unusual parity-odd contribution. Pion effective masses depend on their velocities and may vanish in flight. The possible determination of chiral chemical potential in heavy ion collisions based on above mentioned phenomena is discussed.
