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 (GHFB) with and without the angular momentum projection (AMP). Using the chir
al $g$-matrix folding model, we predicted $sigma_{rm R}$ for Ca scattering on a $^{12}$C target at 280 MeV/nucleon, since Tanaka {it el al.} measured interaction cross sections $sigma_{rm I} (approx sigma_{rm R})$ for $^{42-51}$Ca in RIKEN. After our prediction, they determine $r_{rm m}({rm RIKEN})$, $r_{rm skin}({rm RIKEN})$, $r_{rm n}({rm RIKEN})$. In this paper, we reanalyses the $sigma_{rm I}$, since they assumed the Wood-Saxon densities for $^{42-51}$Ca. The $sigma_{rm R}$ calculated with the folding model with GHFB and GHFB+AMP densities almost reproduce the $sigma_{rm I}$. We then scale proton and neutron densities so that $r_{rm p}$ and $r_{rm n}$ may agree with the central values of $r_{rm p}(rm exp)$ and $r_{rm n}({rm RIKEN})$, respectively. The $sigma_{rm R}$ calculated with the scaled densities do not reproduce the central values of $sigma_{rm I}$ perfectly. We then determine the $r_{rm m}$ that agree with the central values of $sigma_{rm I}$, using the chiral $g$-matrix folding model. The fitted $r_{rm m}$ do not reproduce the central values of $r_{rm m}({rm RIKEN})$ perfectly, but are in one $sigma$ level. Finally, we show the $r_{rm skin}$, $r_{rm n}$ determined from the fitted $r_{rm m}$ are close to the original ones except for $r_{rm skin}^{48}$. The fitted $r_{rm skin}^{48}$ is 0.105 fm, while the central value of $r_{rm m}^{48}({rm RIKEN})$ is 0.146 fm. When we fit $r_{rm m}$ to the upper bound of $sigma_{rm I}$, the fitted $r_{rm skin}^{48}$ is 0.164~fm and near the central vale 0.17 fm of the high-resolution $E1$ polarizability experiment.
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 r
eproduces 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.
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 p
roperties 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$pi$-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 ($Lambda$) dependence is investigated for both nuclear matter and $^{4}$He scattering by considering two cases of $Lambda=450$ 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 isos
pin 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 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--Jon
a-Lasinio (PNJL) model. In the theoretical approach, we clarify conditions imposed on the imaginary chemical potentials $mu_{f}=itheta_{f}T$ to realize the Roberge-Weiss (RW) periodicity. We also show that the RW periodicity is broken if anyone of $theta_{f}$ 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 $theta_{u}=theta_{d}equiv theta_{l}$ for two conditions of $theta_{s}=theta_{l}$ and $theta_{s}=0$. We also consider two cases, $(mu_{u},mu_{d},mu_{s}) =(itheta_{u}T,iC_{1}T,0)$ and $(mu_{u},mu_{d},mu_{s})=(iC_{2}T,iC_{2}T,itheta_{s}T)$; here $C_{1}$ and $C_{2}$ are dimensionless constants, whereas $theta_{u}$ and $theta_{s}$ 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 $theta_{u}$ ($theta_{s}$) 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 $T_c^{chi}$ of chiral crossover and the screening-mass difference between $pi$ and $a_0$ mesons in $T > 1.1T_c^chi$ where only the $U(1)_{rm A}$-symmetry breaking survives. The model well reproduces LQCD data on screening masses $M_{xi}^{rm scr}(T)$ for both scalar and pseudoscalar mesons, particularly in $T ge T_c^{chi}$. Using this effective model, we predict meson pole masses $M_{xi}^{rm pole}(T)$ for scalar and pseudoscalar mesons. For $eta$ meson, the prediction is consistent with the experimental value at finite $T$ measured in heavy-ion collisions. We point out that the relation $M_{xi}^{rm scr}(T)-M_{xi}^{rm pole}(T) approx M_{xi}^{rm scr}(T)-M_{xi}^{rm pole}(T)$ is pretty good when $xi$ and $xi$ are scalar mesons, and show that the relation $M_{xi}^{rm scr}(T)/M_{xi}^{rm scr}(T) approx M_{xi}^{rm pole}(T)/M_{xi}^{rm pole}(T)$ is well satisfied within 20% error when $xi$ and $xi$ are pseudoscalar mesons and also when $xi$ and $xi$ are scalar mesons.
We investigate the effects of chiral three-nucleon force (3NF) on proton scattering at 65 MeV and $^{4}$He scattering at 72 MeV/nucleon from heavier targets, using the standard microscopic framework composed of the Brueckner-Hartree-Fock (BHF) method
and the $g$-matrix folding model. For nuclear matter, the $g$ matrix is evaluated from chiral two-nucleon force (2NF) of N$^{3}$LO and chiral 3NF of NNLO by using the BHF method. Since the $g$ matrix thus obtained is numerical and nonlocal, an optimum local form is determined from the on-shell and near-on-shell components of $g$ matrix that are important for elastic scattering. For elastic scattering, the optical potentials are calculated by folding the local chiral $g$ matrix with projectile and target densities. This microscopic framework reproduces the experimental data without introducing any adjustable parameter. Chiral-3NF effects are small for proton scattering, but sizable for $^{4}$He scattering at middle angles where the data are available. Chiral 3NF, mainly in the 2$pi$-exchange diagram, makes the folding potential less attractive and more absorptive for all the scattering.
We investigate a way of circumventing the sign problem in lattice QCD simulations with a theta-vacuum term, using the PNJL model. We consider the reweighting method for the QCD Lagrangian after the U_A(1) transformation. In the Lagrangian, the P-odd
mass term as a cause of the sign problem is minimized. In order to find out a good reference system in the reweighting method, we estimate the average reweighting factor by using the two-flavor PNJL model and eventually find a good reference system.
We propose a simple model with the Z_N symmetry in order to answer whether the symmetry is a good concept in QCD with light quark mass. The model is constructed by imposing the flavor-dependent twisted boundary condition (TBC) on the three-flavor Pol
yakov-loop extended Nambu-Jona-Lasinio model. In the model, the Z_N symmetry is preserved below some temperature T_c, but spontaneously broken above T_c. Dynamics of the simple model is similar to that of the original PNJL model without the TBC, indicating that the Z_N symmetry is a good concept. We also investigate the interplay between the Z_N symmetry and the emergence of the quarkyonic phase.
We propose a practical way of circumventing the sign problem in lattice QCD simulations with a theta-vacuum term. This method is the reweighting method for the QCD Lagrangian after the U_A(1) transformation. In the Lagrangian, the P-odd mass term as
a cause of the sign problem is minimized. In order to find out a good reference system in the reweighting method, we estimate the average reweighting factor by using the two-flavor NJL model and eventually find a good reference system.
