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T. Hatsuda

Publications and source records attributed to T. Hatsuda.

At least 19 recordsLinked to original sources
arXiv2024

Order of the SU(N_f) x SU(N_f) chiral transition via the functional renormalization group

Renormalization group flows of the $SU(N_f)\times SU(N_f)$ symmetric Ginzburg-Landau potential are calculated for a general number of flavors, $N_f$. Our approach does not rely on the $ε$ expansion, but uses the functional renormalization group, formulated directly in $d=3$ spatial dimensions, with the inclusion of all possible (perturbatively) relevant and marginal operators, whose number is considerably larger than those in $d=4$. We find new, potentially infrared stable fixed points spanned throughout the entire $N_f$ range. By conjecturing that the thermal chiral transition is governed by these ``flavor continuous" fixed points, stability analyses show that for $N_f\geq 5$ the chiral transition is of second-order, while for $N_f=2,3,4$, it is of first-order. We argue that the $U_{\rm A}(1)$ anomaly controls the strength of the first-order chiral transition for $N_f=2,3,4$, and makes it almost indistinguishable from a second-order one, if it is sufficiently weak at the critical point. This could open up a new strategy to investigate the strength of the $U_{\rm A}(1)$ symmetry breaking around the critical temperature.

hep-ph↗
arXiv2022

Probing $ΞN$ interaction through inversion of spin-doublets in $ΞN αα$ nuclei

A new way to study the spin-isospin dependence of the $ΞN$ interaction is explored through the energy levels of $ΞNα$ and $ΞNαα$ systems with $α$ being a spectator to attract the $ ΞN$ pair without changing its spin-isospin structure. By using the Gaussian expansion method (GEM) with the state-of-the-art $ΞN$ potential obtained from lattice QCD calculations, it is found that $ΞNαα$ has spin-doublet bound states with $J^π={1^-}$ and $2^-$ in both isospin triplet and singlet channels. The inversion of the $1^-$-$2^-$ spin-doublet between the iso-triplet and the iso-singlet is found to be strongly correlated with the relative strengths of the $ΞN$ interaction in the $^{11}{\rm S}_0, ^{13}{\rm S}_1,^{31}{\rm S}_0$ and $^{33}{\rm S}_1$ channels. The $(K^-, K^+)$ and $(K^-,K^0)$ reactions on the $^{10}$B target are proposed to produce those bound states.

nucl-th↗
arXiv2021

Femtoscopic study of coupled-channel $NΞ$ and $ΛΛ$ interactions

The momentum correlation functions of S = -2 baryon pairs (p Xi^- and Lambda Lambda) produced in high-energy pp and pA collisions are investigated on the basis of the coupled-channel formalism. The strong interaction is described by the coupled-channel HAL QCD potential obtained by the lattice QCD simulations near physical quark masses, while the hadronic source function is taken to be a static Gaussian form. The coupled-channel effect, the threshold difference, the realistic strong interaction, and the Coulomb interaction are fully taken into account for the first time in the femtoscopic analysis of baryon-baryon correlations. The characteristic features of the experimental data for the p Xi^- and Lambda Lambda pairs at LHC are reproduced quantitatively with a suitable choice of non-femtoscopic parameters and the source size. The agreement between theory and experiment indicates that the N Xi (Lambda Lambda) interaction is moderately (weakly) attractive without having a quasi-bound (bound) state.

hep-ph↗
arXiv2020

Possible lightest $Ξ$ Hypernucleus with Modern $ΞN$ Interactions

Experimental evidence exists that the $Ξ$-nucleus interaction is attractive. We search for $NNΞ$ and $NNNΞ$ bound systems on the basis of the AV8 $NN$ potential combined with either a phenomenological Nijmegen $ΞN$ potential or a first principles HAL QCD $ΞN$ potential. The binding energies of the three-body and four-body systems (below the $d+Ξ$ and $^3{\rm H}$/$^3{\rm He}+Ξ$ thresholds, respectively) are calculated by a high precision variational approach, the Gaussian Expansion Method. Although the two $ΞN$ potentials have significantly different isospin ($T$) and spin ($S$) dependence, the $NNNΞ$ system with quantum numbers $(T=0, J^π=1^+$) appears to be bound (one deep for Nijmegen and one shallow for HAL QCD) below the $^3{\rm H}$/$^3{\rm He}+Ξ$ threshold. Experimental implications for such a state are discussed.

nucl-th↗
arXiv2019

Flows of multicomponent scalar models with U(1) gauge symmetry

We investigate the renormalization group flows of multicomponent scalar theories with $U(1)$ gauge symmetry using the functional renormalization group method. The scalar sector is built up from traces of matrix fields that belong to simple, compact Lie algebras. We find that in general these theories are non-renormalizable even at zero gauge coupling, but if we add a $U(1)$ factor to the Lie algebra structure, then they are consistent. In accordance with our earlier findings, fluctuations introduce anomalous, regulator dependent gauge contributions, which are only consistent with the flow equation for a given set of gauge fixing parameters. We establish connections between regularization procedures in the standard covariant and the $R_ξ$ gauges arguing that one is not tied by introducing regulators at the level of the functional integral, and it is allowed to switch between schemes at different levels of the calculations. We calculate $β$ functions, classify fixed points, and clarify compatibility of the flow equation and the Ward-Takahashi identity between the scalar wavefunction renormalization and the charge rescaling factor.

hep-ph↗
arXiv2018

Doubly magic nuclei from Lattice QCD forces at $M_{PS}=$469 MeV/c$^2$

We perform ab initio self-consistent Green's function calculations of the closed shell nuclei $^{\rm 4}$He, $^{\rm 16}$O and $^{\rm 40}$Ca, based on two-nucleon potentials derived from Lattice QCD simulations, in the flavor SU(3) limit and at the pseudo-scalar meson mass of 469~MeV/c$^{\rm 2}$. The nucleon-nucleon interaction is obtained using the HAL QCD method and its short-distance repulsion is treated by means of ladder resummations outside the model space. Our results show that this approach diagonalises ultraviolet degrees of freedom correctly. Therefore, ground state energies can be obtained from infrared extrapolations even for the relatively hard potentials of HAL QCD. Comparing to previous Brueckner Hartree-Fock calculations, the total binding energies are sensibly improved by the full account of many-body correlations. The results suggest an interesting possible behaviour in which nuclei are unbound at very large pion masses and islands of stability appear at first around the traditional doubly-magic numbers when the pion mass is lowered toward its physical value. The calculated one-nucleon spectral distributions are qualitatively close to those of real nuclei even for the pseudo-scalar meson mass considered here.

nucl-th↗
arXiv2017

Renormalization group flows of the N-component Abelian Higgs model

Flows of the couplings of a theory of an N-component (complex) scalar field coupled to electrodynamics is investigated using the functional renormalization group formalism in d dimensions in covariant gauges. We find charged fixed points for any number of components in d=3, in accordance with the findings of [G. Fejos and T. Hatsuda, Phys. Rev. D 93, 121701 (2016)] for N=1. It is argued that the appropriate choice of the regulator matrix is indispensible to obtain such a result. Ward-Takahashi identites are analyzed in the presence of the regulator, and their compatibility with the flow equation is investigated in detail.

hep-ph↗
arXiv2016

Fixed point structure of the Abelian Higgs model

The order of the superconducting phase transition is analyzed via the functional renormalization group approach. For the first time, we derive fully analytic expressions for the $β$ functions of the charge and the self-coupling in the Abelian Higgs model with one complex scalar field in $d=3$ dimensions that support the existence of two charged fixed points: an infrared (IR) stable fixed point describing a second-order phase transition and a tritical fixed point controlling the region of the parameter space that is attracted by the former one. It is found that the region separating first- and second-order transitions can be uniquely characterized by the Ginzburg-Landau parameter $κ$, and the system undergoes a second order transition, only if $κ>κ_c \approx 0.62/\sqrt2$.

cond-mat.supr-con↗
arXiv2014

Spin-Orbit Force from Lattice QCD

We present a first attempt to determine nucleon-nucleon potentials in the parity-odd sector, which appear in 1P1, 3P0, 3P1, 3P2-3F2 channels, in Nf=2 lattice QCD simulations. These potentials are constructed from the Nambu-Bethe-Salpeter wave functions for J^P=0^-, 1^- and 2^-, which correspond to A1^-, T1^- and T2^- + E^- representation of the cubic group, respectively. We have found a large and attractive spin-orbit potential VLS(r) in the isospin-triplet channel, which is qualitatively consistent with the phenomenological determination from the experimental scattering phase shifts. The potentials obtained from lattice QCD are used to calculate the scattering phase shifts in 1P1, 3P0, 3P1 and 3P2-3F2 channels. The strong attractive spin-orbit force and a weak repulsive central force in spin-triplet P-wave channels lead to an attraction in the 3P2 channel, which is related to the P-wave neutron paring in neutron stars.

hep-lat↗
arXiv2013

Phase shifts in I=2 ππ-scattering from two lattice approaches

We present a lattice QCD study of the phase shift of $I{=}2$ $ππ$ scattering on the basis of two different approaches: the standard finite volume approach by Luscher and the recently introduced HAL QCD potential method. Quenched QCD simulations are performed on lattices with extents $N_s{=}16,24,32,48$ and $N_t{=}128$ as well as lattice spacing $a{\sim}0.115\,\mathrm{fm}$ and a pion mass of $m_π{\sim}940\,\mathrm{MeV}$. The phase shift and the scattering length are calculated in these two methods. In the potential method, the error is dominated by the systematic uncertainty associated with the violation of rotational symmetry due to finite lattice spacing. In Luscher's approach, such systematic uncertainty is difficult to be evaluated and thus is not included in this work. A systematic uncertainty attributed to the quenched approximation, however, is not evaluated in both methods. In case of the potential method, the phase shift can be calculated for arbitrary energies below the inelastic threshold. The energy dependence of the phase shift is also obtained from Luscher's method using different volumes and/or nonrest-frame extension of it. The results are found to agree well with the potential method.

hep-lat↗
arXiv2012

Probability distribution functions in the finite density lattice QCD

We study the phase structure of QCD at high temperature and density by lattice QCD simulations adopting a histogram method. We try to solve the problems which arise in the numerical study of the finite density QCD, focusing on the probability distribution function (histogram). As a first step, we investigate the quark mass dependence and the chemical potential dependence of the probability distribution function as a function of the Polyakov loop when all quark masses are sufficiently large, and study the properties of the distribution function. The effect from the complex phase of the quark determinant is estimated explicitly. The shape of the distribution function changes with the quark mass and the chemical potential. Through the shape of the distribution, the critical surface which separates the first order transition and crossover regions in the heavy quark region is determined for the 2+1-flavor case.

hep-lat↗
arXiv2012

Application of fixed scale approach to static quark free energies in quenched and 2+1 flavor lattice QCD with improved Wilson quark action

Free energies between static quarks and Debye screening masses in the quark-gluon plasma are studied on the basis of Polyakov-line correlations in lattice simulations of 2+1 flavors QCD with the renormalization-group improved gluon action and the $O(a)$-improved Wilson quark action. We perform simulations at $m_{\rm PS}/m_{\rm V} = 0.63$ (0.74) for light (strange) flavors with lattice sizes of $32^3 \times N_t$ with $N_t=4$--12. We adopt the fixed-scale approach, where temperature can be varied without changing the spatial volume and renormalization factor. We find that, at short distance, the free energies of static quarks in color-singlet channel converge to the static-quark potential evaluated from the Wilson-loop at zero-temperature, in accordance with the expected insensitivity of short distance physics to the temperature. At long distance, the free energies of static quarks approach to twice the single-quark free energies, implying that the interaction between static quarks is fully screened. The screening properties can be well described by the screened Coulomb form with appropriate Casimir factor at high temperature. We also discuss a limitation of the fixed-scale approach at high temperature.

hep-lat↗
arXiv2012

Equation of state in 2+1 flavor QCD with improved Wilson quarks by the fixed scale approach

We study the equation of state in 2+1 flavor QCD with nonperturbatively improved Wilson quarks coupled with the RG-improved Iwasaki glue. We apply the $T$-integration method to nonperturbatively calculate the equation of state by the fixed-scale approach. With the fixed-scale approach, we can purely vary the temperature on a line of constant physics without changing the system size and renormalization constants. Unlike the conventional fixed-$N_t$ approach, it is easy to keep scaling violations small at low temperature in the fixed scale approach. We study 2+1 flavor QCD at light quark mass corresponding to $m_π/m_ρ\simeq 0.63$, while the strange quark mass is chosen around the physical point. Although the light quark masses are heavier than the physical values yet, our equation of state is roughly consistent with recent results with highly improved staggered quarks at large $N_t$.

hep-lat↗
arXiv2012

Phase structure of finite temperature QCD in the heavy quark region

We study the quark mass dependence of the finite temperature QCD phase transition in the heavy quark region using an effective potential defined through the probability distribution function of the average plaquette. Performing a simulation of SU(3) pure gauge theory, we first confirm that the distribution function has two peaks indicating that the phase transition is of first order in the heavy quark limit, while the first order transition turns into a crossover as the quark mass decreases from infinity, where the mass dependence of the distribution function is evaluated by the reweighting method combined with the hopping parameter expansion. We determine the endpoint of the first order transition region for N_f=1, 2, 3 and 2+1 cases. The quark mass dependence of the latent heat is also evaluated in the first order transition region.

hep-lat↗
arXiv2012

Finite density QCD phase transition in the heavy quark region

We extend our previous study of the QCD phase structure in the heavy quark region to non-zero chemical potentials. To identify the critical point where the first order deconfining transition terminates, we study an effective potential defined by the probability distribution function of the plaquette and the Polyakov loop. The reweighting technique is shown to be powerful in evaluating the effective potential in a wide range of the plaquette and Polyakov loop expectation values. We adopt the cumulant expansion to overcome the sign problem in the calculation of complex phase of the quark determinant. We find that the method provides us with an intuitive and powerful way to study the phase structure. We estimate the location of the critical point at finite chemical potential in the heavy quark region.

hep-lat↗
arXiv2011

Histogram method in finite density QCD with phase quenched simulations

We propose a new approach to finite density QCD based on a histogram method with phase quenched simulations at finite chemical potential. Integrating numerically the derivatives of the logarithm of the quark determinant with respect to the chemical potential, we calculate the reweighting factor and the complex phase of the quark determinant. The complex phase is handled with a cumulant expansion to avoid the sign problem. We examine the applicability of this method.

hep-lat↗
arXiv2011

Scaling behavior of chiral phase transition in two-flavor QCD with improved Wilson quarks at finite density

We study scaling behavior of a chiral order parameter performing a simulation of two-flavor QCD with improved Wilson quarks. It has been shown that the scaling behavior of the chiral order parameter defined by a Ward-Takahashi identity agrees with the scaling function of the three-dimensional O(4) spin model at zero chemical potential. We extend the scaling study to finite density QCD. Calculating derivatives of the chiral order parameter with respect to the chemical potential in two-flavor QCD, the scaling property of chiral phase transition is discussed in the low density region. We moreover calculate the curvature of the phase boundary of the chirl phase transition in the temperature and chemical potential plane assuming the O(4) scaling relation.

hep-lat↗