arXiv subjects

Norikazu Yamada

Publications and source records attributed to Norikazu Yamada.

At least 19 recordsLinked to original sources

arXiv2026

A kernel-derived orthogonal basis for spectral functions from Euclidean correlators

Spectral functions play a central role in the characterization of a wide range of physical systems, including strongly interacting quantum field theories and many-body systems. Their non-perturbative determination from Euclidean correlation functions constitutes a well-known ill-posed inverse problem and has motivated the development of numerous reconstruction techniques. In this work, we propose a systematic, prior-free framework for representing spectral functions using an orthogonal functional basis derived directly from the kernel of Euclidean two-point correlation functions. We identify a set of lattice-accessible constraints together with the associated basis functions. These functions can be reorganized into an orthogonal basis within which the spectral function may be approximated in a controlled manner. Using several model spectral functions, we demonstrate that the proposed expansion captures global spectral features and reproduces low-energy transport coefficients with good accuracy. While the numerical implementation requires high-precision Euclidean correlator data, the present framework is intended not as a direct reconstruction method, but rather as a tool for extracting robust constraints and overall spectral structures. The approach may therefore serve as a complementary ingredient or preprocessing step for existing spectral reconstruction techniques.

hep-lat↗

arXiv2025

$θ$ dependence of $T_c$ in SU(2) Yang-Mills theory

We present an exploratory study to determine the confinement-deconfinement transition temperature at finite $θ$, $T_c(θ)$, for the 4d \SU(2) pure Yang-Mills theory. Lattice numerical simulations are performed on three spatial sizes $N_S=24$, $32$, $48$ with a fixed temporal size $N_T=8$. We introduce a non-zero $θ$-angle by the sub-volume method to mitigate the sign problem. By taking advantage of the universality in the second order phase transition and the Binder cumulant of the order parameter, the $θ$-dependence of $T_c$ is determined to be $T_c(θ)/T_c(0)=1-0.16(2)\,(θ/π)^2-0.03(4)\,(θ/π)^4$ up to $θ\sim 0.9\,π$. The reliability of the extrapolations in the sub-volume method is extensively checked. We also point out that the temperature dependence of the topological susceptibility should exhibit a singularity with the exponent for the specific heat.

hep-lat↗

arXiv2024

Subvolume method for SU(2) Yang-Mills theory at finite temperature: topological charge distributions

We apply the previously-developed sub-volume method to study the $θ$-dependence of the four-dimensional SU(2) Yang-Mills theory at finite temperature. We calculate the first two coefficients, the topological susceptibility $χ$ and the fourth cumulant $b_2$, in the $θ$-expansion of the free energy density around the critical temperature ($T_c$) for the confinement-deconfinement transition. Lattice calculations are performed with three different spatial sizes $24^3,32^3,48^3$ to monitor finite size effects, while the temporal size is fixed to be $8$. The systematic uncertainty associated with the sub-volume extrapolation is studied with special care. The sub-volume method allows us to determine the values of $b_2$ much more accurately than the standard full-volume method, and we successfully identify the temperature dependence of $b_2$ around $T_c$. Our numerical results suggest that the $θ$-dependence of the free energy density near $θ=0$ changes from $4χ(1-\cos(θ/2))$ to $χ(1-\cosθ)$ as the temperature crosses $T_c$.

hep-lat↗

arXiv2022

$θ$ dependence of $T_c$ in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large $N$ limit

The phase diagram on the $θ$-$T$ plane in four dimensional SU(3) Yang-Mills theory is explored. We revisit the $θ$ dependence of the deconfinement transition temperature, $T_c(θ)$, on the lattice through the constraint effective potential for Polyakov loop. The $θ$ term is introduced by the reweighting method, and the critical $β$ is determined to $θ\sim 0.75$, where the interpolation in $β$ is carried out by the multipoint reweighting method. The $θ$ dependence of $T_c$ obtained here turns out to be consistent with the previous result by D'Elia and Negro \cite{DElia:2012pvq,DElia:2013uaf}. We also derive $T_c(θ)$ by classifying configurations into the high and low temperature phases and applying the Clausius-Clapeyron equation. It is found that the potential barrier in the double well potential at $T_c(θ)$ becomes higher with $θ$, which suggests that the first order transition continues robustly above $θ\sim 0.75$. Using information obtained here, we try to depict the expected $θ$ dependence of the free energy density at $T < T_c(0)$, which crosses the first order transition line at an intermediate value of $θ$. Finally, how the Lee-Yang zeros associated with the spontaneous CP violation appear is discussed formally in the large $N$ limit, and the locations of them are found to be $(θ_R,θ_I)=\left( (2m+1)π, \frac{2n+1}{2χV_4} \right)$ with $n$ and $m$ arbitrary integers.

hep-lat↗

arXiv2021

Peeking into the $θ$ vacuum

We propose a subvolume method to study the $θ$ dependence of the free energy density of the four-dimensional SU($N$) Yang-Mills theory on the lattice. As an attempt, the method is first applied to SU(2) Yang-Mills theory at $T=1.2\,T_c$ to understand the systematics of the method. We then proceed to the calculation of the vacuum energy density and obtain the $θ$ dependence qualitatively different from the high temperature case. The numerical results combined with the theoretical requirements provide the evidence for the spontaneous CP violation at $θ= π$, which is in accordance with the large $N$ prediction and indicates that the similarity between 4d SU($N$) and 2d CP$^{N-1}$ theories does not hold for $N$=2.

hep-lat↗

arXiv2021

Is $N=2$ Large?

We study $θ$ dependence of the vacuum energy for the 4d SU(2) pure Yang-Mills theory by lattice numerical simulations. The response of topological excitations to the smearing procedure is investigated in detail, in order to extract topological information from smeared gauge configurations. We determine the first two coefficients in the $θ$ expansion of the vacuum energy, the topological susceptibility $χ$ and the first dimensionless coefficient $b_2$, in the continuum limit. We find consistency of the SU(2) results with the large $N$ scaling. By analytic continuing the number of colors, $N$, to non-integer values, we infer the phase diagram of the vacuum structure of SU(N) gauge theory as a function of $N$ and $θ$. Based on the numerical results, we provide quantitative evidence that 4d SU(2) Yang-Mills theory at $θ= π$ is gapped with spontaneous breaking of the CP symmetry.

hep-lat↗

arXiv2017

Topological susceptibility with a single light quark flavour

One of the historical suggestions to tackle the strong CP problem is to take the up quark mass to zero while keeping $m_d$ finite. The $θ$ angle is then supposed to become irrelevant, i.e. the topological susceptibility vanishes. However, the definition of the quark mass is scheme-dependent and identifying the $m_u=0$ point is not trivial, in particular with Wilson-like fermions. More specifically, up to our knowledge there is no theoretical argument guaranteeing that the topological susceptibility exactly vanishes when the PCAC mass does. We will present our recent progresses on the empirical check of this property using $N_f=1+2$ flavours of clover fermions, where the lightest fermion is tuned very close to $m^{PCAC}_u$=0 and the mass of the other two is kept of the order of magnitude of the physical $m_s$. This choice is indeed expected to amplify any unknown non-perturbative effect caused by $m_u\not=m_d$. The simulation is repeated for several $β$s and those results, although preliminary, give a hint about what happens in the continuum limit.

hep-lat↗

arXiv2017

$θ=π$ in $SU(N)/\mathbb{Z}_N$ gauge theories

In $SU(N)$ gauge theory, it is argued recently that there exists a "mixed anomaly" between the CP symmetry and the 1-form $\mathbb{Z}_N$ symmetry at $θ=π$, and the anomaly matching requires CP to be spontaneously broken at $θ=π$ if the system is in the confining phase. In this paper, we elaborate on this discussion by examining the large volume behavior of the partition functions of the $SU(N)/\mathbb{Z}_N$ theory on $T^4$ a la 't Hooft. The periodicity of the partition function in $θ$, which is not $2π$ due to fractional instanton numbers, suggests the presence of a phase transition at $θ=π$. We propose lattice simulations to study the distribution of the instanton number in $SU(N)/\mathbb{Z}_N$ theories. A characteristic shape of the distribution is predicted when the system is in the confining phase. The measurements of the distribution may be useful in understanding the phase structure of the theory.

hep-th↗

arXiv2016

$N_f=1+2$ mass dependence of the topological susceptibility

A massless up quark has long been proposed as a solution to the strong CP problem. While this solution is sometimes thought to have been excluded, it is actually still ill-defined. In this work, we study the mass dependence of the physical observable $χ_t$, the topological susceptibility. Assigning an unphysically large value to the down mass allows to be more sensitive to the non-perturbative effects behind the $m_u=0$ ambiguity. Preliminary results are presented for four masses of clover fermions.

hep-lat↗

arXiv2016

Exploring the nature of chiral phase transition in two-flavor QCD using extra heavy quarks

Chiral phase transition of two flavor QCD at finite quark masses is known to be crossover except near the chiral limit, but it can turn to a first order transition when adding many extra flavors. This property is used to explore the nature of the phase transition of massless two flavor QCD using lattice numerical simulations. The extra heavy flavors being incorporated in the form of the hopping parameter expansion through the reweighting, the number of the extra flavors and their masses appear only in a single parameter, defined by $h$. We determine the critical value of the parameter, at which the first order and the crossover regions are separated, and examine its dependence on the two flavor mass. The lattice calculations are carried out at $N_t$=4, and show that the critical value does not depend on the two flavor mass in the range we have studied ($0.46 \le m_π/m_ρ\le 0.66$) and appears to remain finite and positive in the chiral limit, suggesting that the phase transition of massless two flavor QCD is of second order.

hep-lat↗

arXiv2016

Many flavor approach to study the nature of chiral phase transition of two-flavor QCD

We perform lattice numerical simulations to study the phase transition of QCD at finite temperature to clarify the nature of the transition of massless two flavor QCD. We investigate QCD with two light and Nf heavy quarks instead of two-flavor QCD, and focus on the light quark mass dependence of the critical heavy mass, below which the transition is of first order. The heavy quarks are incorporated into two flavor configurations in the form of the hopping parameter expansion through the reweighting technique. The nature of the transition is identified by the shape of the constraint effective potential at the critical temperature. Our result indicates that the critical heavy mass remains finite in the chiral limit of the two flavors, suggesting the phase transition of massless two-flavor QCD is of second order.

hep-lat↗

arXiv2016

Critical point search from an extended parameter space of lattice QCD at finite temperature and density

Aiming to understand the phase structure of lattice QCD at nonzero temperature and density, we study the phase transitions of QCD in an extended parameter space, where the number of flavor and quark masses are considered as parameters. Performing simulations of 2 flavor QCD and using the reweighting method, we investigate (2+Nf) flavor QCD at finite density, where two light flavors and Nf massive flavors exist. Calculating probability distribution functions, we determine the critical surface terminating first order phase transitions in the parameter space of the light quark mass, the heavy quark mass and the chemical potential. Through the study of the many flavor system, we discuss the phase structure of QCD at finite density.

hep-lat↗

arXiv2015

Many flavor approach to study the critical point in finite density QCD

We discuss the QCD critical point at finite density through the study of many flavor QCD, in which two light flavors and Nf massive flavors exist. Performing simulations of QCD with two flavors of improved Wilson fermions, we calculate probability distribution functions of many flavor QCD at finite temperature and density. The dynamical effects of massive flavors and the chemical potential are added using the reweighting technique. From the shape of the distribution functions, we determine the critical surface separating the first order transition and crossover regions in the parameter space of the light and massive quark masses and the chemical potentials. It is found that the critical massive quark mass becomes larger as the chemical potential increases in (2+Nf) flavor QCD. The indication to the (2+1) flavor QCD is then discussed.

hep-lat↗

arXiv2015

Topology in QCD and the axion abundance

The temperature dependence of the topological susceptibility in QCD, chi_t, essentially determines the abundance of the QCD axion in the Universe, and is commonly estimated, based on the instanton picture, to be a certain negative power of temperature. While lattice QCD should be able to check this behavior in principle, the temperature range where lattice QCD works is rather limited in practice, because the topological charge is apt to freezes at high temperatures. In this work, two exploratory studies are presented. In the first part, we try to specify the temperature range in the quenched approximation. Since our purpose here is to estimate the range expected in unquenched QCD through quenched simulations, hybrid Monte Carlo (HMC) algorithm is employed instead of heatbath algorithm. We obtain an indication that unquenched calculations of chi_t encounter the serious problem of autocorrelation already at T~2Tc or even below with the plain HMC. In the second part, we revisit the axion abundance. The absolute value and the temperature dependence of chi_t in real QCD can be significantly different from that in the quenched approximation, and is not well established above the critical temperature. Motivated by this fact and precedent arguments which disagree with the conventional instanton picture, we estimate the axion abundance in an extreme case where chi_t decreases much faster than the conventional power-like behavior. We find a significant enhancement of the axion abundance in such a case.

hep-ph↗

arXiv2015

First order transition regions in the quark masses and chemical potential parameter space of QCD

We investigate the phase transitions of (2+Nf)-flavor QCD, where two light flavors and Nf massive flavors exist, aiming to understand the phase structure of (2+1)-flavor QCD. Performing simulations of 2-flavor QCD with improved staggered and Wilson fermions and using the reweighting method, we calculate probability distribution functions in the many-flavor QCD. Through the shape of distribution functions, we determine the critical surface terminating first order phase transitions in the parameter space of the light quark mass, heavy quark mass and the chemical potential, and find that the first order region becomes larger with Nf. We then study the critical surface at finite density for large Nf and the first order region is found to become wider with the increasing chemical potential. On the other hand, the light quark mass dependence of the critical mass of heavy quarks seems weak in the region we investigated. The result of this weak dependence suggests that the critical mass of heavy quark remains finite in the chiral limit of 2-flavors and there exists a second order transition region on the line of the 2-flavor massless limit above the tri-critical point. Moreover, we extend the study of 2-flavor QCD at finite density to the case of a complex chemical potential and investigate the singularities where the partition function vanishes, so-called Lee-Yang zeros. The plaquette effective potential is computed in the complex plane. We find that the shape of the effective potential changes from single-well on the real axis to double-well at large imaginary chemical potential and the double-well potential causes the singularities.

hep-lat↗

arXiv2015

Linking $U(2)\times U(2)$ to $O(4)$ model via decoupling

The nature of chiral phase transition of massless two flavor QCD depends on the fate of flavor singlet axial symmetry $U_A(1)$ at the critical temperature ($T_c$). Assuming that a finite $U_A(1)$ breaking remains at $T_c$, the corresponding three dimensional effective theory is composed of four massless and four massive scalar fields. We study the renormalization group flow of the effective theory in the $ε$-expansion, using a mass dependent renormalization scheme, and determine the region of the attractive basin flowing into the $O(4)$ fixed point with a focus on its dependence on the size of the $U_A(1)$ breaking. The result is discussed from a perspective of the decoupling of massive fields. It is pointed out that, although the effective theory inside the attractive basin eventually reaches the $O(4)$ fixed point, the approaching rate, one of the universal exponents, is different from that of the standard $O(4)$ model. We present the reason for this peculiarity, and propose a novel possibility for chiral phase transition in two-flavor QCD.

hep-lat↗

arXiv2015

The First Estimates of Kinematically Forbidden D Meson Decays

The weak hadronic decay D^+ -> K^0\bar a_1^+ is kinematically forbidden at the peak mass values of the particles involved. However, occurrence of this decay has been reported with branching fraction (9.1 \plusminus 1.8) \cross 10^{-3} in the analysis of D^+ -> K^\bar0 4 πdecay data. This is due to smearing effects on this decay caused mainly by the large width of a_1-resonance, which extends the phase space and allows this decay. Using a factorization model to evaluate decay amplitudes for external and internal W-emission diagrams, and incorporating Breit-Wigner smearing using the total a_1 width of 400 MeV, we obtain the first estimate for branching fraction of this decay to be 3.3 \cross 10^{-3} and 7.0 \cross 10^{-3}, for |V_1^{Da1} (0)|=0.40 and 1.50 respectively corresponding to different theoretical models, where |V_1^{Da1} (q^2)| is the vector form factor appearing in the D -> a_1 s-wave transition. The estimates are of the desired order of magnitude. We also predict branching fractions of its counterpart decays D^0 -> K^-\bar a_1^+ and D^0 -> K^0\bar a_1^0.

hep-ph↗

arXiv2015

Renormalization group flow of linear sigma model with $U_A(1)$ anomaly

In the presence of finite $U_A(1)$ breaking, chiral phase transition of massless two-flavor QCD is studied by tracing the renormalization group flow of the corresponding effective theory. In the framework of the $ε$ expansion, it is found that the nature of the phase transition depends on the initial condition for the parameters of the effective theory and that, when it undergoes second order phase transition, one of the universal exponents shows a different value from that in the standard $O(4)$ linear sigma model. We discuss that the origin of the difference is attributed to a non-decoupling effect. The present status of the calculation of the effective potential is presented.

hep-lat↗