arXiv subjects
Publications and source records attributed to Masanobu Yahiro.
Recently, state-of-art LQCD calculations were done for $π$-meson and $ρ$-meson screening mass, ${M_π^{\rm scr}}(T)$ and ${M_ρ^{\rm scr}}(T)$. We consider the two-flavor system, and focus on temperature dependence $T$ of ${M_π^{\rm scr}}(T)$ and ${M_ρ^{\rm scr}}(T)$. Our aim is to construct a model consistent with LQCD data on ${M_ρ^{\rm scr}}(T)$ and ${M_π^{\rm scr}}(T)$.
Background: Using the chiral (Kyushu) $g$-matrix folding model with the densities calculated with Gogny-HFB (GHFB) with the angular momentum projection (AMP), we determined the central values of matter radius and neutron skin from the central values of reaction cross sections $σ_{\rm R}({\rm EXP})$ of p+$^{40,48}$Ca and p+$^{208}$Pb scattering. As for p+$^{58}$Ni scattering, $σ_{\rm R}({\rm EXP})$ are available as a function of incident energy $E_{\rm in}$. Aim: Our aim is to determine matter radius $r_{m}$ and skin $r_{\rm skin}$ for $^{58}$Ni from the $σ_{\rm R}({\rm EXP})$ of p+$^{58}$Ni scattering by using the Kyushu $g$-matrix folding model with the GHFB+AMP densities. Results: For p+$^{58}$Ni scattering, the Kyushu $g$-matrix folding model with the GHFB+AMP densities reproduces $σ_{\rm R}({\rm EXP})$ in $8.8 \leq E_{\rm in} \leq 81$MeV. For $E_{\rm in}=81$MeV, we define the factor $F$ as $F=σ_{\rm R}({\rm EXP})/σ_{\rm R}({\rm AMP})=0.9775$. The $Fσ_{\rm R}({\rm AMP})$ be much the same as the center values of $σ_{\rm R}({\rm EXP})$ in $8.8 \leq E_{\rm in} \leq 81$MeV. We then determine $r_{\rm m}({\rm EXP})$ from the center values of $σ_{\rm R}({\rm EXP})$, using $σ_{\rm R}({\rm EXP})=C r_{m}^{2}({\rm EXP})$ with $C=r_{m}^{2}({\rm AMP})/ (Fσ_{\rm R}({\rm AMP}))$. The $r_{m}({\rm EXP})$ thus obtained are averaged over $E_{\rm in}$. The averaged value is $r_{m}({\rm EXP})=3.697$fm. Eventually, we obtain $r_{\rm skin}({\rm EXP})=0.023$fm from $r_{\rm m}=3.697$fm and $r_p({\rm EXP})=3.685$fm of electron scattering.
{\bf Background:} Using the chiral (Kyushu) $g$-matrix folding model with the densities calculated with GHFB+AMP, we determined $r_{\rm skin}^{208}=0.25$fm from the central values of $σ_{\rm R}$ of p+$^{208}$Pb scattering in $E_{\rm in}=40-81$MeV. The high-resolution $E1$ polarizability experiment ($E1$pE) yields $r_{\rm skin}^{48}(E1{\rm pE}) =0.14-0.20$fm. The data on $σ_{\rm R}$ are available as a function of $E_{\rm in}$ for $p$+$^{48}$Ca scattering. {\bf Aim:} Our aim is to determine $r_{\rm skin}^{48}$ from the central values of $σ_{\rm R}$ for $p$+$^{48}$Ca scattering by using the folding model. {\bf Results:} As for $^{48}$Ca, we determine $r_n(E1{\rm pE})=3.56$fm from the central value 0.17fm of $r_{\rm skin}^{48}(E1{\rm pE})$ and $r_p({\rm EXP})=3.385$fm of electron scattering, and evaluate $r_m(E1{\rm pE})=3.485$fm from the $r_n(E1{\rm pE})$ and the $r_p({\rm EXP})$ of electron scattering. The folding model with GHFB+AMP densities reproduces $σ_{\rm R}$ in $23 \leq E_{\rm in} \leq 25.3$ MeV in one-$σ$ level, but slightly overestimates the central values of $σ_{\rm R}$ there. In $23 \leq E_{\rm in} \leq 25.3$MeV, the small deviation allows us to scale the GHFB+AMP densities to the central values of $r_p({\rm EXP})$ and $r_n(E1{\rm pE})$. The $σ_{\rm R}(E1{\rm pE})$ obtained with the scaled densities almost reproduce the central values of $σ_{\rm R}$ when $E_{\rm in}=23-25.3$MeV, so that the $σ_{\rm R}({\rm GHFB+AMP})$ and the $σ_{\rm R}(E1{\rm pE})$ are in 1-$σ$ of $σ_{\rm R}$ there. In $E_{\rm in}=23-25.3$MeV, we determine the $r_{m}({\rm EXP})$ from the central values of $σ_{\rm R}$ and take the average for the $r_{m}({\rm EXP})$. The averaged value is $r_{m}({\rm EXP})=3.471$fm. Eventually, we obtain $r_{\rm skin}^{48}({\rm EXP})=0.146$fm from $r_{m}({\rm EXP})=3.471$fm and $r_p({\rm EXP})=3.385$fm.
[Background]: In our previous paper, we predicted $r_{\rm skin}$, $r_{\rm p}$, $r_{\rm n}$, $r_{\rm m}$ for $^{40-60,62,64}$Ca after determining the neutron dripline, using the Gogny-D1S HFB with and without the angular momentum projection (AMP). We found that effects of the AMP are small. Very lately, Tanaka {\it et al.} measured interaction cross sections $σ_{\rm I}$ for $^{42-51}$Ca, determined $r_{\rm m}$ from the $σ_{\rm I}$, and deduced skin $r_{\rm skin}$ and $r_{\rm n}$ from the $r_{\rm m}$ and the $r_{\rm p}(\rm {exp})$ evaluated from the electron scattering. Comparing our results with the data, we find for $^{42-48}$Ca that GHFB and GHFB+AMP reproduce the data on $r_{\rm skin}$, $r_{\rm n}$, $r_{\rm m}$, but not for $r_{\rm p}(\rm {exp})$. [Aim]: Our purpose is to determine a value of $r_{\rm skin}^{48}$ by using GHFB+AMP and the constrained GHFB (cGHFB) in which the calculated value is fitted to $r_{\rm p}(\rm {exp})$. [Results]: For $^{42,44,46,48}$Ca, cGHFB hardly changes $r_{\rm skin}$, $r_{\rm m}$, $r_{\rm n}$ calculated with GHFB+AMP, except for $r_{\rm skin}^{48}$. For $r_{\rm skin}^{48}$, the cGHFB result is $r_{\rm skin}^{48}=0.190$fm, while $r_{\rm skin}^{48}=0.159$fm for GHFB+AMP. We should take the upper and the lower bound of GHFB+AMP and cGHFB. The result $r_{\rm skin}^{48}=0.159-0.190$fm consists with the $r_{\rm skin}^{48}(σ_{\rm I})$ and the data $r_{\rm skin}^{48}(\rm $E1$pE)$ obtained from high-resolution $E1$ polarizability experiment ($E1$pE). Using the $r_{\rm skin}^{48}$-$r_{\rm skin}^{208}$ relation with strong correlation of Ref.[3], we transform the data $r_{\rm skin}^{208}$ determined by PREX and $E1$pE to the corresponding values, $r_{\rm skin}^{48}(\rm tPREX)$ and $r_{\rm skin}^{48}(\rm t$E1$pE)$. Our result is consistent also for $r_{\rm skin}^{48}(\rm tPREX)$ and $r_{\rm skin}^{48}(\rm t$E1$pE)$.
We apply the cluster-folding (CF) model for $\vec{p}+^{6}$He scattering at 200 MeV, where the potential between $\vec{p}$ and $^{4}$He is fitted to data on $\vec{p}+^{4}$He scattering at 200 MeV. For $\vec{p}+^{6}$He scattering at 200 MeV, the CF model reproduces measured differential cross section with no free parameter, We then predict the analyzing power $A_y(q)$ with the CF model, where $q$ is the transfer momentum. Johnson, Al-Khalili and Tostevin construct a theory for one-neutron halo scattering, taking (1) the adiabatic approximation and (2) neglecting the interaction between a valence neutron and a target, and yield a simple relationship between the elastic scattering of a halo nucleus and of its core under certain conditions. We improve their theory with (3) the eikonal approximation in order to determine $A_y(q)$ for $^{6}$He from the data on $A_y(q)$ for $^{4}$He. The improved theory is accurate, when approximation (1)--(3) are good. Among the three approximations, approximation (2) is most essential. The CF model shows that approximation (2) is good in $0.9 < q < 2.4$ fm$^{-1}$. In the improved theory, the $A_y(q)$ for $^{6}$He is the same as that for $^{4}$He. In $0.9 < q < 2.4$ fm$^{-1}$, we then predict $A_y(q)$ for $\vec{p}+^{6}$He scattering at 200 MeV from measured $A_y(q)$ for $\vec{p}+^{4}$He scattering at 200 MeV. We thus predict $A_y(q)$ with the model-dependent and the model-independent prescription. The ratio of differential cross sections measured for $^{6}$He to that for $^{4}$He is related to the wave function of $^{6}$He. We then determine the radius between $^{4}$He and the center-of-mass of valence two neutrons in $^{6}$He. The radius is 5.77 fm.
We present a simple version of hadron-quark hybrid (HQH) model in the $μ_B$--$T$ plain, where $T$ is temperature and $μ_{B}$ is the baryon-number chemical potential. The model is composed of the independent-quark model for quark-gluon states and an improved version of excluded-volume hadron resonance gas (EV-HRG) model for hadronic states. In the improved version of EV-HRG, the pressure has charge conjugation and is obtained by a simple analytic form. The switching function from hadron states to quark-gluon states in the present model has no chemical potential dependence. The simple HQH model is successful in reproducing LQCD results on the transition region of chiral crossover and the EoS in $μ_{B} \leq 400$ MeV. We then predict the chiral-crossover region in $400 \leq μ_{B} \leq 800$ MeV. We also predict a transition line derived from isentropic trajectories in $0 \leq μ_{B} \leq 800$ MeV and find that the effect of strangeness neutrality is small there.
The persistent homology analysis is applied to the effective Polyakov-line model on a rectangular lattice to investigate the confinement-deconfinement nature. The lattice data are mapped onto the complex Polyakov-line plane without taking the spatial average and then the plane is divided into three domains. This study is based on previous studies for the clusters and the percolation properties in lattice QCD, but the mathematical method of the analyses are different. The spatial distribution of the data in the individual domain is analyzed by using the persistent homology to obtain information of the multiscale structure of center clusters. In the confined phase, the data in the three domains show the same topological tendency characterized by the birth and death times of the holes which are estimated via the filtration of the alpha complexes in the data space, but do not in the deconfined phase. By considering the configuration averaged ratio of the birth and death times of holes, we can construct the nonlocal order-parameter of the confinement-deconfinement transition from the multiscale topological properties of center clusters.
We first predict the ground-state properties of Ca isotopes, using the Gogny-D1S Hartree-Fock-Bogoliubov (GHFB) with and without the angular momentum projection (AMP). We find that $^{64}$Ca is an even-dripline nucleus and $^{59}$Ca is an odd-dripline nucleus, using $A$ dependence of the one-neutron separation energy $S_{1}$ and the two-neutron separation energy, $S_{2}$. As for $S_{1}$, $S_{2}$ and the binding energies $E_{\rm B}$, our results agree with the experimental data in $^{40-58}$Ca. As other ground-state properties of $^{40-60,62,64}$Ca, we predict charge, proton, neutron, matter radii, neutron skin and deformation. As for charge radii, our results are consistent with the experimental data in $^{40-52}$Ca. For $^{48}$Ca, our results on proton, neutron, matter radii agree with the experimental data. Very lately, Tanaka et. al. measured interaction cross sections for $^{42-51}$Ca scattering on a $^{12}$C target at an incident energy per nucleon of $E_{\rm lab}=280$MeV. Secondly, we predict reaction cross sections $σ_{\rm R}$ for $^{40-60,62,64}$Ca, using a chiral $g$-matrix double-folding model (DFM). To show the reliability of the present DFM for $σ_{\rm R}$, we apply the DFM for the data on $^{12}$C scattering on $^{9}$Be, $^{12}$C, $^{27}$Al targets in $30 < E_{\rm lab} < 400 $MeV, and show that the present DFM is good in $30 < E_{\rm lab} < 100 $MeV and $250 < E_{\rm lab} < 400 $MeV. For $110 < E_{\rm lab} < 240 $MeV, our results have small errors. To improve the present DFM for $σ_{\rm R}$, we propose two prescriptions.
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 $μ_{\rm R}$ in the method" with "those calculated directly at $μ_{\rm R}$". We finally propose the new extrapolation method and confirm its efficiency.
It is a current important subject to clarify properties of chiral three-nucleon forces (3NFs) not only in nuclear matter but also in scattering between finite-size nuclei. Particularly for the elastic scattering, this study has just started and the properties are not understood in a wide range of incident energies ($E_{\rm in}$). We investigate basic properties of chiral 3NFs in nuclear matter with positive energies by using the Brueckner-Hartree-Fock method with chiral two-nucleon forces of N$^{3}$LO and 3NFs of NNLO, and analyze effects of chiral 3NFs on $^{4}$He elastic scattering from targets $^{208}$Pb, $^{58}$Ni and $^{40}$Ca over a wide range of $30 \lesssim E_{\rm in}/A_{\rm P} \lesssim 200$ MeV by using the $g$-matrix folding model, where $A_{\rm P}$ is the mass number of projectile. In symmetric nuclear matter with positive energies, chiral 3NFs make the single-particle potential less attractive and more absorptive. The effects mainly come from the Fujita-Miyazawa 2$π$-exchange 3NF and slightly become larger as $E_{\rm in}$ increases. These effects persist in the optical potentials of $^{4}$He scattering. As for the differential cross sections of $^{4}$He scattering, chiral-3NF effects are large in $E_{\rm in}/A_{\rm P} \gtrsim 60$ MeV and improve the agreement of the theoretical results with the measured ones. Particularly in $E_{\rm in}/A_{\rm P} \gtrsim 100$ MeV, the folding model reproduces measured differential cross sections pretty well. Cutoff ($Λ$) dependence is investigated for both nuclear matter and $^{4}$He scattering by considering two cases of $Λ=450$ and $550$ MeV. The uncertainty coming from the dependence is smaller than chiral-3NF effects even at $E_{\rm in}/A_{\rm P}=175$ MeV.
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 in the massless limit.
We investigate the real and imaginary chemical-potential dependence of pion and $ρ$-meson screening masses in both the confinement and the deconfinement region by using two-flavor lattice QCD. The spatial meson correlators are calculated in the imaginary chemical potential region with lattice QCD simulations. We extract pion and $ρ$-meson screening masses from the correlators. The obtained meson screening masses are extrapolated to the real chemical potential region by assuming some analytic function. In the real chemical potential region, the resulting pion and $ρ$-meson screening masses monotonically increase as real chemical potential becomes large.
As an effective model corresponding to $Z_3$-symmetric QCD ($Z_3$-QCD), we construct a $Z_3$-symmetric effective Polyakov-line model ($Z_3$-EPLM) by using the logarithmic fermion effective action. Since $Z_3$-QCD tends to QCD in the zero temperature limit, $Z_3$-EPLM also agrees with the ordinary effective Polyakov-line model (EPLM) there; note that ordinary EPLM does not possess $Z_3$ symmetry. Our main purpose is to discuss a sign problem appearing in $Z_3$-EPLM. The action of $Z_3$-EPLM is real, when the Polyakov line is not only real but also its $Z_3$ images. This suggests that the sign problem becomes milder in $Z_3$-EPLM than in EPLM. In order to confirm this suggestion, we do lattice simulations for both EPLM and $Z_3$-EPLM by using the reweighting method with the phase quenched approximation. In the low-temperature region, the sign problem is milder in $Z_3$-EPLM than in EPLM. We also propose a new reweighting method. This makes the sign problem very weak in $Z_3$-EPLM.
We construct a simple model for describing the hadron-quark crossover transition by using lattice QCD (LQCD) data in the 2+1 flavor system, and draw the phase diagram in the 2+1 and 2+1+1 flavor systems through analyses of the equation of state (EoS) and the susceptibilities. In the present hadron-quark crossover (HQC) model is successful in reproducing LQCD data on the EoS and the flavor susceptibilities.We define the hadron-quark transition temperature. For the 2+1 flavor system, the transition line thus obtained is almost identical in planes that are created by temperature and the chemical potential for the baryon-number(B), the isospin(I), the hypercharge(Y), when the chemical potentials are smaller than 250 MeV. This BIY approximate equivalence persists also in the 2+1+1 flavor system. We plot the phase diagram also in planes that are created by temperature and the chemical potential for u,d,s quark number in order to investigate flavor dependence of transition lines. In the 2+1+1 flavor system, c quark does not affect the 2+1 flavor subsystem composed of u, d, s. The flavor off-diagonal susceptibilities are good indicators to see how hadrons survive as T increases, since the independent quark model hardly contributes to them.
We study properties of 2+1-flavor QCD in the imaginary chemical potential region by using two approaches. One is a theoretical approach based on QCD partition function, and the other is a qualitative one based on the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. In the theoretical approach, we clarify conditions imposed on the imaginary chemical potentials $μ_{f}=iθ_{f}T$ to realize the Roberge-Weiss (RW) periodicity. We also show that the RW periodicity is broken if anyone of $θ_{f}$ is fixed to a constant value. In order to visualize the condition, we use the PNJL model as a model possessing the RW periodicity, and draw the phase diagram as a function of $θ_{u}=θ_{d}\equiv θ_{l}$ for two conditions of $θ_{s}=θ_{l}$ and $θ_{s}=0$. We also consider two cases, $(μ_{u},μ_{d},μ_{s}) =(iθ_{u}T,iC_{1}T,0)$ and $(μ_{u},μ_{d},μ_{s})=(iC_{2}T,iC_{2}T,iθ_{s}T)$; here $C_{1}$ and $C_{2}$ are dimensionless constants, whereas $θ_{u}$ and $θ_{s}$ are treated as variables. For some choice of $C_{1}$ ($C_{2}$), the number density of up (strange) quark becomes smooth in the entire region of $θ_{u}$ ($θ_{s}$) even in high $T$ region.
We propose a practical effective model by introducing temperature ($T$) dependence to the coupling strengths of four-quark and six-quark Kobayashi-Maskawa-'t Hooft interactions in the 2+1 flavor Polyakov-loop extended Nambu-Jona-Lasinio model. The $T$ dependence is determined from LQCD data on the renormalized chiral condensate around the pseudocritical temperature $T_c^χ$ of chiral crossover and the screening-mass difference between $π$ and $a_0$ mesons in $T > 1.1T_c^χ$ where only the $U(1)_{\rm A}$-symmetry breaking survives. The model well reproduces LQCD data on screening masses $M_ξ^{\rm scr}(T)$ for both scalar and pseudoscalar mesons, particularly in $T \ge T_c^χ$. Using this effective model, we predict meson pole masses $M_ξ^{\rm pole}(T)$ for scalar and pseudoscalar mesons. For $η'$ meson, the prediction is consistent with the experimental value at finite $T$ measured in heavy-ion collisions. We point out that the relation $M_ξ^{\rm scr}(T)-M_ξ^{\rm pole}(T) \approx M_{ξ'}^{\rm scr}(T)-M_{ξ'}^{\rm pole}(T)$ is pretty good when $ξ$ and $ξ'$ are scalar mesons, and show that the relation $M_ξ^{\rm scr}(T)/M_{ξ'}^{\rm scr}(T) \approx M_ξ^{\rm pole}(T)/M_{ξ'}^{\rm pole}(T)$ is well satisfied within 20% error when $ξ$ and $ξ'$ are pseudoscalar mesons and also when $ξ$ and $ξ'$ are scalar mesons.
We analyze the equation of state of 2+1 flavor lattice QCD at zero baryon density by constructing the simple quark-hadron hybrid model that has both quark and hadron components simultaneously. We calculate hadron and quark contribution separately and parameterizing those to match with LQCD data. Lattice data on the equation of state are decomposed into hadron and quark components by using the model. The transition temperature is defined by the temperature at which the hadron component is equal to the quark one in the equation of state. The transition temperature thus obtained is about 215 MeV and somewhat higher than the chiral and the deconfinement pseudocritical temperatures defined by the temperature at which the susceptibility or the absolute value of the derivative of the order parameter with respect to temperature becomes maximum.
We construct four kinds of Z3-symmetric three-dimentional (3-d) Potts models, each with different number of states at each site on a 3-d lattice, by extending the 3-d three-state Potts model. Comparing the ordinary Potts model with the four Z3-symmetric Potts models, we investigate how Z3 symmetry affects the sign problem and see how the deconfinement transition line changes in the $μ-κ$ plane as the number of states increases, where $μ$ $(κ)$ plays a role of chemical potential (temperature) in the models. We find that the sign problem is almost cured by imposing Z3 symmetry. This mechanism may happen in Z3-symmetric QCD-like theory. We also show that the deconfinement transition line has stronger $μ$-dependence with respect to increasing the number of states.