# High Energy Physics - Lattice Publications (50)

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## High Energy Physics - Lattice Publications

We consider the Weyl quantum walk in 3+1 dimensions, that is a discrete-time walk describing a particle with two internal degrees of freedom moving on a Cayley graph of the group $\mathbb Z^3$, that in an appropriate regime evolves according to Weyl's equation. The Weyl quantum walk was recently derived as the unique unitary evolution on a Cayley graph of $\mathbb Z^3$ that is homogeneous and isotropic. The general solution of the quantum walk evolution is provided here in the position representation, by the analytical expression of the propagator, i. Read More

The type IIB matrix model has been investigated as a possible nonperturbative formulation of superstring theory. In particular, it was found by Monte Carlo simulation of the Lorentzian version that the 9-dimensional rotational symmetry of the spatial matrices is broken spontaneously to the 3-dimensional one after some "critical time". In this paper we develop a new simulation method based on the effective theory for the submatrices corresponding to the late time. Read More

We apply the higher order tensor renormalization group to two and three dimensional relativistic fermion systems on the lattice. In order to perform a coarse-graining of tensor networks including Grassmann variables, we introduce Grassmann higher order tensor renormalization group. We test the validity of the new algorithm by comparing its results with those of exact or previous methods. Read More

3+1 dimensional Causal Dynamical Triangulations (CDT) describe a quantum theory of fluctuating geometries without the introduction of a background geometry. If the topology of space is constrained to be that of a three-dimensional torus we show that the system will fluctuate around a dynamically formed background geometry which can be understood from a simple minisuperspace action which contains both a classical part and a quantum part. We determine this action by integrating out degrees of freedom in the full model, as well as by transfer matrix methods. Read More

We obtain the next-to-leading order correction to the spectrum of a SU(N) Yang-Mills theory in four dimensions and we show agreement well-below 1% with respect to the lattice computations for the ground state and one of the higher states. Read More

**Affiliations:**

^{1}Kyoto U.

We propose a new theoretical method of "matter-antimatter coexistence (MAC) method" or "charge conjugation method" for the practical lattice QCD calculation at finite density, as a possible solution of the sign problem in finite-density QCD. For the matter system $M$ with $\mu > 0$, we also prepare in the other spatial location the anti-matter system $\bar M$ which is the charge conjugation of $M$, and aim to generate the gauge systems charge-conjugation symmetric under the exchange of $M$ and $\bar M$ in the lattice QCD framework. In this coexistence system, the total fermionic determinant is found to be real and non-negative in the Euclidean space-time, so that no sign problem appears and the practical numerical calculation can be performed in lattice QCD. Read More

We present results for the form factors of the isovector axial vector current in the nucleon state using large scale simulations of lattice QCD. The calculations were done using eight ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings $a \approx 0. Read More

We present the perturbative renormalization group functions of $O(n)$-symmetric $\phi^4$ theory in $4-2\varepsilon$ dimensions to the sixth loop order in the minimal subtraction scheme. In addition, we estimate diagrams without subdivergences up to 11 loops and compare these results with the asymptotic behaviour of the beta function. Furthermore, we perform a resummation to obtain estimates for critical exponents in three and two dimensions. Read More

It is a common problem in lattice QCD calculations of hadron masses with annihilation channels that the signal falls off in time while the noise remains constant. In addition, the disconnected insertion calculation in the three-point function and the calculation of the neutron electric dipole moment with the $\theta$ terms suffer from a noise due to the $\sqrt{V}$ fluctuation. We identify these problems to have the same origin and the $\sqrt{V}$ problem can be resolved by utilizing the cluster decomposition principle. Read More

Smoothing of field configurations is highly important for precision calculations of physical quantities on the lattice. We present a cooling method based on Stochastic Quantization with a built-in UV momentum cutoff. The latter is implemented via a UV-regularized, hence colored, noise term. Read More

We review recent experimental and theoretical progress in understanding the microscopic details of clustering in nuclei. We discuss recent experimental results on alpha-conjugate systems, alpha-states in heavy systems, molecular structures in neutron-rich nuclei, and constraints for ab initio theory. We then examine nuclear clustering in a wide range of theoretical methods, including the resonating group and generator coordinate methods, antisymmetrized molecular dynamics, fermionic molecular dynamics, Tohsaki-Horiuchi-Schuck-R\"opke wave function and container model, no-core shell model methods, continuum quantum Monte Carlo, lattice effective field theory, and several approaches to clustering in heavier systems. Read More

We present a lattice calculation of the nucleon iso-vector axial and induced pseudoscalar form factors on the CLS ensembles using $N_{\rm f}=2$ dynamical flavours of non-perturbatively $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved axial current together with the pseudoscalar density. Excited-state effects in the extraction of the form factors are treated using a variety of methods, with a detailed discussion of their respective merits. The chiral and continuum extrapolation of the results is performed both using formulae inspired by Heavy Baryon Chiral Perturbation Theory (HBChPT) and a global approach to the form factors based on a chiral effective theory (EFT) including axial vector mesons. Read More

The mass and the lifetime of a gluon are evaluated from first principles at finite temperature across the deconfinement transition of pure SU(3) Yang-Mills theory, by a direct calculation of the pole of the propagator in the complex plane, using the finite temperature extension of a massive expansion in Landau gauge. Even at T=0 the quasigluon lifetime is finite and the gluon is canceled from the asymptotic states, yielding a microscopic proof of confinement from first principles. Above the transition the damping rate is a linear increasing function of temperature as predicted by standard perturbation theory. Read More

We propose a strategy for large volume non-perturbative renormalization which alleviates the window problem by reducing cut-off effects. We perform a proof-of-concept study using position space renormalization scheme and the CLS $N_f=2+1$ ensembles generated at 5 different lattice spacings. We show that in the advocated strategy results for the renormalization constants are to a large extend independent of the specific lattice direction used to define the renormalization condition. Read More

In this paper, for a given Markov chain Monte Carlo algorithm we introduce a distance between two configurations that quantifies the difficulty of transition from one configuration to the other configuration. We argue that the distance takes a universal form for the class of algorithms which generate local moves in the configuration space. We explicitly calculate the distance for the Langevin algorithm, and show that it certainly has desired and expected properties. Read More

We summarize the current status of the determination of the CKM matrix elements |V_ud| and |V_us|, which is at the precision frontier of CKM phenomenology. We also review recent progress on the study of charm (semi)leptonic decays, and the determination of |V_cd| and |V_cs|. Read More

We report a comprehensive analysis of the light and strange disconnected-sea quarks contribution to the nucleon magnetic moment, charge radius, and the electric and magnetic form factors. The lattice QCD calculation includes ensembles across several lattice volumes and lattice spacings with one of the ensembles at the physical pion mass. We adopt a model-independent extrapolation of the nucleon magnetic moment and the charge radius. Read More

Motivated by the claimed possibility of a large contribution of the first radial excitation of the $D^{(\ast )}$ to the $B$ semileptonic decay into charmed mesons, also invoked to solve the "$1/2$ vs. $3/2$ semileptonic puzzle", we discuss the transitions to heavy-light radial excitations by a heavy $b \to c$ quark current. We first consider a HQET sum rule, which provides a bound on the slopes of Isgur-Wise functions which we then calculate in the Bakamjian-Thomas framework which both guaranties covariance in the heavy quark limit and satisfies a set of HQET sum rules. Read More

Semileptonic transitions $\overline{B} \to D^{(n)} \ell \overline{\nu}$, where $D^{(n)} (n \not = 0)$ is a radially excited meson, have recently attracted much attention as a way to understand some puzzles between theory and data. Following closely the formalism of Falk and Neubert for the elastic case, we study the $1/m_Q$ corrections to the heavy quark limit, in which the inelastic Isgur-Wise function vanishes at zero recoil, $\xi^{(n)}(1) = 0\ (n \not = 0)$. We find simple formulas that involve the derivative $\xi^{(n)'}(1)$, and we propose a number of ways of isolating this quantity in practice. Read More

We propose a new approach to circumvent the sign problem in which the integral path is optimized to control the sign problem. We give a trial function specifying the integration path in the complex plane and tune it to optimize the cost function which represents the seriousness of the sign problem. We call it path optimization method. Read More

We present a procedure for reconstructing the decision function of an artificial neural network as a simple function of the input, provided the decision function is sufficiently symmetric. In this case one can easily deduce the quantity by which the neural network classifies the input. The procedure is embedded into a pipeline of machine learning algorithms able to detect the existence of different phases of matter, to determine the position of phase transitions and to find explicit expressions of the physical quantities by which the algorithm distinguishes between phases. Read More

The value of the parton to hadron fragmentation function in QCD in vacuum (for example from proton-proton collisions at high energy colliders) is directly/indirectly used in the literature to study the jet quenching and the hadron production from quark-gluon plasma at RHIC and LHC. In this paper we show that this is not possible because, unlike the perturbative propagator in non-equilibrium QCD, the parton to hadron fragmentation function is a non-perturbative quantity in QCD and hence it is not possible to decompose the fragmentation function in non-equilibrium QCD into the vacuum part and the medium part. Read More

It is known since 1980's that the instanton-induced 't Hooft effective Lagrangian not only can solve the so called $U(1)a$ problem, by making the $\eta'$ meson heavy etc, but it can also lead to chiral symmetry breaking. In 1990's it was demonstrated that, taken to higher orders, this Lagrangian correctly reproduces effective forces in a large set of hadronic channels, mesonic and baryonic ones. Recent progress in understanding gauge topology at finite temperatures is related with the so called {\em instanton-dyons}, the constituents of the instantons. Read More

We describe a calculation of the spectrum of flavour-SU(3) octet and decuplet baryons, their parity partners, and the radial excitations of these systems, made using a symmetry-preserving treatment of a vector-vector contact interaction as the foundation for the relevant few-body equations. Dynamical chiral symmetry breaking generates nonpointlike diquarks within these baryons and hence, using the contact interaction, flavour-antitriplet scalar, pseudoscalar and vector, and flavour-sextet axial-vector quark-quark correlations can all play an active role. The model yields reasonable masses for all systems studied, and Faddeev amplitudes for ground states and associated parity partners that sketch a realistic picture of their internal structure: ground-state, even parity baryons are constituted, almost exclusively, from like-parity diquark correlations; but orbital angular momentum plays an important role in the rest-frame wave functions of odd-parity baryons, whose Faddeev amplitudes are dominated by odd-parity diquarks. Read More

We perform a high precision measurement of the static $q\bar{q}$ potential in three-dimensional SU($N$) gauge theory with $N=2,3$ and compare the results to the potential obtained from the effective string theory. In particular, we show that the exponent of the leading order correction in $1/R$ is 4, as predicted, and obtain accurate results for the continuum limits of the string tension and the non-universal boundary coefficient $\bar{b}_2$, including an extensive analysis of all types of systematic uncertainties. We find that the magnitude of $\bar{b}_2$ decreases with increasing $N$, leading to the possibility of a vanishing $\bar{b}_2$ in the large $N$ limit. Read More

Beyond perturbation theory the number of gauge copies drastically increases due to the Gribov-Singer ambiguity. Any way of treating them defines, in principle, a new, non-perturbative gauge, and the gauge-dependent correlation functions can vary between them. Herein various such gauges will be constructed as completions of the Landau gauge inside the first Gribov region. Read More

We discuss two problems in complexified auxiliary fields in fermionic effective models, the auxiliary sign problem associated with the repulsive vector-field and the choice of the cut for the scalar field appearing from the logarithmic function. In the fermionic effective models with attractive scalar and repulsive vector-type interaction, the auxiliary scalar and vector fields appear in the path integral after the bosonization of fermion ilinears. When we make the path integral well-defined by the Wick rotation of the vector field, the oscillating Boltzmann weight appears in the partition function. Read More

We present results on the nucleon axial and induced pseudo-scalar form factors using an ensemble of two degenerate twisted mass clover-improved fermions generated at the physical value of the pion mass. We evaluate the isovector and the isoscalar, as well as, the strange and the charm axial form factors. The disconnected contributions are evaluated using recently developed methods that include deflation of the lower eigenstates, allowing us to extract the isoscalar, strange and charm axial form factors. Read More

We demonstrate that two-dimensional nonlinear sigma models on the lattice in the large-N limit admit convergent weak-coupling expansions in powers of t'Hooft coupling and its logarithms, reminiscent of re-summed perturbation theory in thermal field theory and resurgent trans-series without exponential terms. Such a double-series structure arises due to the bare mass proportional to the t'Hooft coupling, which stems from the Jacobian in the path integral measure and is absent in the scale-invariant classical action. This term renders the perturbative expansion infrared-finite even for infinite lattice size, which allows to study it directly in the large-N and infinite-volume limits using the Diagrammatic Monte-Carlo approach. Read More

The most popular and widely used subtract-with-borrow generator, also known as RANLUX, is reimplemented as a linear congruential generator using large integer arithmetic with the modulus size of 576 bits. Modern computers, as well as the specific structure of the modulus inferred from RANLUX, allow for the development of a fast modular multiplication -- the core of the procedure. This was previously believed to be slow and have too high cost in terms of computing resources. Read More

Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of building chains which can explore probability densities efficiently. The method emerges from physics and geometry and these links have been extensively studied by a series of authors through the last thirty years. Read More

Multi-particle states with additional pions are expected to be a non-negligible source of excited-state contamination in lattice simulations at the physical point. It is shown that baryon chiral perturbation theory can be employed to calculate the contamination due to two-particle nucleon-pion states in various nucleon observables. Leading order results are presented for the nucleon axial, tensor and scalar charge and three Mellin moments of parton distribution functions (quark momentum fraction, helicity and transversity moment). Read More

We discuss possible vacuum structures of $SU(n)\times SU(n)$ gauge theories with bifundamental matters at finite $\theta$ angles. In order to give a precise constraint, a mixed 't Hooft anomaly is studied in detail by gauging the center $\mathbb{Z}_n$ one-form symmetry of the bifundamental gauge theory. We propose phase diagrams that are consistent with the constraints, and also give a heuristic explanation of the result based on the dual superconductor scenario of confinement. Read More

A new approach to description of hadron spectroscopy is proposed. By assumption, the form of spectrum is dictated by the trace of energy momentum tensor in QCD. This provides the relativistic and renormalization invariance of hadron masses. Read More

We present results on QCD with four dynamical flavors in the temperature range $0.9 \lesssim T/T_c \lesssim 2$. We have performed lattice simulations with Wilson fermions at maximal twist and measured the topological charge with gluonic and fermionic methods. Read More

We present a calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, $a_\mu^{\mathrm hvp}$, in lattice QCD employing dynamical up and down quarks. We focus on controlling the infrared regime of the vacuum polarization function. To this end we employ several complementary approaches, including Pad\'e fits, time moments and the time-momentum representation. Read More

We show that quasi-PDFs may be treated as hybrids of PDFs and primordial rest-frame momentum distributions of partons. This results in a complicated convolution nature of quasi-PDFs that necessitates using large p_3~ 3 GeV momenta to get reasonably close to the PDF limit. As an alternative approach, we propose to use pseudo-PDFs P(x, z_3^2) that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time distributions M (\nu, z_3^2), the functions of the Ioffe time \nu = p_3 z_3 and the distance parameter z_3^2 with respect to which it displays perturbative evolution for small z_3. Read More

We extend the $D4$-$D8$ holographic construction to include three chiral and one heavy flavor, to describe heavy-light baryons with strangeness and their exotics. At strong coupling, the heavy meson always binds to the bulk instanton in the form of a flavor zero mode in the fundamental representation. We quantize the ensuing bound states using the collective quantization method, to obtain the spectra of heavy and strange baryons with both explicit and hidden charm and bottom. Read More

We present an improved result of lattice computation of the proton decay matrix elements in $N_f=2+1$ QCD. In this study, the significant improvement of statistical accuracy by adopting the error reduction technique of All-mode-averaging, is achieved for relevant form factor to proton (and also neutron) decay on the gauge ensemble of $N_f=2+1$ domain-wall fermions in $m_\pi=0.34$--0. Read More

Recently, Grabowska and Kaplan suggested a non-perturbative formulation of a chiral gauge theory, which consists of the conventional domain-wall fermion and a gauge field that evolves by the gradient flow from one domain wall to the other. In this paper, we discuss the U(1) axial-vector current in 4 dimensions using this formulation. We introduce two sets of domain-wall fermions belonging to complex conjugate representations so that the effective theory is a 4-dimensional vector-like gauge theory. Read More

In our previous work, the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment (g - 2) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD collaboration. However, the calculation is expected to suffer from a significant finite volume error that scales like $1/L^2$ where $L$ is the spatial size of the lattice. In this paper, we demonstrate that this problem is cured by treating the muon and photons in infinite volume, continuum QED, resulting in a weighting function that is pre-computed and saved with affordable cost and sufficient accuracy. Read More

We calculate the form factors of the $K \to \pi l \nu$ semileptonic decays in three-flavor lattice QCD, and study their chiral behavior as a function of the momentum transfer and the Nambu-Goldstone boson masses. Chiral symmetry is exactly preserved by using the overlap quark action, which enables us to directly compare the lattice data with chiral perturbation theory (ChPT). We generate gauge ensembles at a lattice spacing of 0. Read More

We review theoretical aspects of quantum chromodynamics (QCD) at finite temperature. The most important physical variable to characterize hot QCD is the Polyakov loop, which is an approximate order parameter for quark deconfinement in a hot gluonic medium. Additionally to its role as an order parameter, the Polyakov loop has rich physical contents in both perturbative and non-perturbative sectors. Read More

If the QCD axion is a significant component of dark matter, and if the universe was once hotter than a few hundred MeV, the axion relic abundance depends on the function $\chi(T)$, the temperature-dependent topological susceptibility. Uncertainties in this quantity induce uncertainties in the axion mass as a function of the relic density, or vice versa. At high temperatures, theoretical uncertainties enter through the dilute instanton gas computation, while in the intermediate and strong coupling regime, only lattice QCD can determine $\chi(T)$ precisely. Read More

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. Read More

We determine the degeneracy factor and the average particle mass of particles that produce the Lattice QCD pressure and specific entropy at zero baryon chemical potential. The number of states of the gluons and the quarks are found to converge above T=230 MeV to almost constant values, close to the number of states of an ideal Quark-Gluon Phase, while their assigned masses retain high values. The number of states and the average mass of the system containing quarks are found to decrease steeply with increase of temperature between $T \sim 150$ and 160 MeV, a region contained within the region of the chiral transition. Read More

We conjecture that in Yang-Mills theories the ratio between the ground-state glueball mass squared and the string tension is proportional to the ratio of the eigenvalues of quadratic Casimir operators in the adjoint and the fundamental representations. The proportionality constant depends on the dimension of the space-time only, and is henceforth universal. We argue that this universality, which is supported by available lattice results, is a direct consequence of area-law confinement. Read More

Large momentum effective field theory provides a new direction for lattice QCD calculations of hadronic structure functions, such as parton distribution functions (PDFs), meson distribution amplitudes, and so on, directly with $x$-dependence. In the framework of lattice perturbation theory, we compute the order $\mathcal{O}\left(a^{0}\right)$ and $\mathcal{O}\left(a^{1}\right)$ corrections of one-loop quark-in-quark quasi-PDF with Wilson-Clover fermions. We confirm that the lattice perturbation theory-calculated quasi-PDF reduces to the continuum quasi-PDF in the continuum limit. Read More

A large number of experimental discoveries especially in the heavy quarkonium sector that did not at all fit to the expectations of the until then very successful quark model led to a renaissance of hadron spectroscopy. Among various explanations of the internal structure of these excitations, hadronic molecules, being analogues of light nuclei, play a unique role since for those predictions can be made with controlled uncertainty. We review experimental evidences of various candidates of hadronic molecules, and methods of identifying such structures. Read More

We study interacting Majorana fermions in two dimensions as a low-energy effective model of a vortex lattice in two-dimensional time-reversal-invariant topological superconductors. For that purpose, we implement ab-initio quantum Monte Carlo simulation to the Majorana fermion system in which the path-integral measure is given by a semi-positive Pfaffian. We discuss spontaneous breaking of time-reversal symmetry at finite temperature. Read More