We present our results of the $K_{l3}$ form factors on the volume whose spatial extent is more than $L=$10 fm, with the physical pion and kaon masses using the stout-smearing clover $N_f = 2+1$ quark action and Iwasaki gauge action at $a^{-1}\approx2.3$ GeV. The $K_{l3}$ form factor at zero momentum transfer is obtained from fit based on the next-to-leading (NLO) formula in SU(3) chiral perturbation theory. We estimate systematic errors of the form factor, mainly coming from the finite lattice spacing effect. We also determine the value of $|V_{us}|$ by combining our result with the experiment and check the consistency with the standard model prediction. The result is compared with the previous lattice calculations.
We present a method to couple finite-volume QCD to infinite-volume QED by an appropriate twist-averaging procedure. We demonstrate the prescription numerically for the leading-order hadronic contribution to the anomalous magnetic moment of the muon and the electro-magnetic pion mass splitting.
A comparative study between the Lüscher's finite volume method and the time-dependent HAL QCD method is given for the $ΞΞ$($^1\mathrm{S}_0$) interaction as an illustrative example. By employing the smeared source and the wall source for the interpolating operators, we show that the effective energy shifts $ΔE_{\rm eff} (t)$ in Lüscher's method do not agree between different sources, yet both exhibit fake plateaux. On the other hand, the interaction kernels $V(\vec{r})$ obtained from the two sources in the HAL QCD method agree with each other already for modest values of $t$. We show that the e…
Using the infinite-volume photon propagator, we developed a method which allows us to calculate electromagnetic corrections to stable hadron masses with only exponentially suppressed finite-volume effects. The key idea is that the infinite volume hadronic current-current correlation function with large time separation between the two currents can be reconstructed by its value at modest time separation, which can be evaluated in finite volume with only exponentially suppressed errors. This approach can be extended to other possible applications such as QED corrections to (semi-)leptonic decays …
The standard approach to determine the parameters of a resonance is based on the study of the volume dependence of the energy spectrum. In this work we study a non-linear sigma model coupled to a scalar field in which a resonance emerges. Using an analysis method introduced recently, based on the concept of probability distribution, it is possible to determine the mass and the width of the resonance.
We present the three-pion spectrum with maximal isospin in a finite volume determined from lattice QCD, including excited states in addition to the ground states across various irreducible representations at zero and nonzero total momentum. The required correlation functions, from which the spectrum is extracted, are computed using a newly implemented algorithm which speeds up the computation by more than an order of magnitude. On a subset of the data we extract a nonzero value of the three-pion threshold scattering amplitude using the $1/L$ expansion of the three-particle quantization conditi…
Within a multi-channel formulation of $ππ$ scattering, we investigate the use of the finite-volume Hamiltonian approach to resolve scattering observables from lattice QCD spectra. The asymptotic matching of the well-known Lüscher formalism encodes a unique finite-volume spectrum. Nevertheless, in many practical situations, such as coupled-channel systems, it is advantageous to interpolate isolated lattice spectra in order to extract physical scattering parameters. Here we study the use of the Hamiltonian framework as a parameterisation that can be fit directly to lattice spectra. We find that …
First-principles calculations of multi-hadron dynamics are a crucial goal in lattice QCD. Significant progress has been achieved in developing, implementing, and applying theoretical tools that connect finite-volume quantities to their infinite-volume counterparts. Here, I review some recent theoretical developments and numerical results regarding multi-particle quantities in a finite volume. These results include $Nπ$ scattering, systems of two and three mesons at maximal isospin, three-body resonances in a toy model, and the formulation of effective theories in finite volume for multi-nucleo…
We present results for the spectrum of excited mesons obtained from temporal correlations of spatially-extended single-hadron and multi-hadron operators computed in lattice QCD. The stochastic LapH algorithm is implemented on anisotropic, dynamical lattices for isovectors for pions of mass $390$ MeV. A large correlation matrix with single-particle and two-particle probe operators is diagonalized to identify resonances. The masses of excited states in the $I=1, S=0, T_{1u}^+$ channel as well as the mixing of single and multi-particle probe operators are presented.
Knowledge of the electric polarizability is crucial to understanding the interactions of hadrons with electromagnetic fields. The neutron polarizability is very sensitive to the quark mass and is expected to diverge in the chiral limit. Here we present results for the electric polarizability of the neutron, neutral pion, and neutral kaon on eight ensembles with nHYP-smeared clover dynamical fermions with two different pion masses (227 and 306 MeV). These are currently the lightest pion masses used in polarizability studies. For each pion mass we compute the polarizability at four different vol…
In this work we consider the $SU(N)$ gauge theory with two Dirac fermions in the adjoint representation, in the limit of large $N$. In this limit the infinite-volume physics of this model can be studied by means of the corresponding twisted reduced model defined on a single site lattice. Making use of this strategy we study the reduced model for various values of $N$ up to 289. By analyzing the eigenvalue distribution of the adjoint Dirac operator we test the conformality of the theory and extract the corresponding mass anomalous dimension.
We consider finite volume effects on the electromagnetic form factor of the pion. We compute the peudoscalar-vector-pseudoscalar correlator in the $ε$ expansion of chiral perturbation theory up to the next-to-leading order and find a way to remove the dominant part, which comes from a contribution of the pion zero-mode. Inserting non-zero momentum to relevant operators (or taking a subtraction of the correlators at different time-slices), and taking an appropriate ratio of them, one can automatically cancel the zero-mode's contribution, which becomes non-perturbatively large $\sim \mathcal{O}(…
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-co…
We study the finite volume effects on the electric polarizability for the neutron, neutral pion, and neutral kaon using eight dynamically generated two-flavor nHYP-clover ensembles at two different pion masses: 306(1) and 227(2) MeV. An infinite volume extrapolation is performed for each hadron at both pion masses. For the neutral kaon, finite volume effects are relatively mild. The dependence on the quark mass is also mild and a reliable chiral extrapolation can be performed along with the infinite volume extrapolation. Our result is $α_{K^0}^\mbox{phys}=0.356(74) \times 10^{-4} \mbox{fm}^3$.…
We study the convergence of the derivative expansion in HAL QCD method from the finite volume analysis. Employing the (2+1)-flavor lattice QCD data obtained at nearly physical light quark masses $(m_π, m_K) \simeq (146, 525)$ MeV and the physical charm quark mass, we study two representative systems, $ΩΩ$ and $Ω_{ccc}Ω_{ccc}$ in the $^1S_0$ channel, where both systems were found to have a shallow bound state in our previous studies. The HAL QCD potentials are determined at the leading-order in the derivative expansion, from which finite-volume eigenmodes are obtained. Utilizing the eigenmode p…
It has been proposed that four-dimensional QCD with fermions in the adjoint representation exhibits volume-independence in the large-N limit. If correct, this would mean that results for physical quantities could be obtained from the single-site version of the model. A necessary condition for volume-independence is that the (Z_N)^4 center-symmetry of the single-site theory is unbroken. We explore the phase diagram of the theory with a single Dirac fermion using Wilson fermions for a number of colors in the range N=8-15, and identify the region in the parameter space of quark mass and gauge cou…
We derive the relations necessary for the extraction of matrix elements of multi-hadron systems from finite-volume QCD calculations. We focus on systems of $n \ge 2$ weakly interacting identical particles without spin. These results will be useful in extracting physical quantities from lattice QCD measurements of such matrix elements in many-pion and many-kaon systems
Strong three-body interactions above threshold govern the dynamics of many exotics and conventional excited mesons and baryons. Three-body finite-volume energies calculated from lattice QCD promise an ab-initio understanding of these systems. We calculate the three-$π^+$ spectrum unraveling the three-body dynamics that is tightly intertwined with the $S$-matrix principle of three-body unitarity and compare it with recent lattice QCD results. For this purpose, we develop a formalism for three-body systems in moving frames and apply it numerically.
We calculate finite-volume corrections to the low-energy constants $Σ$ and $F$ in the epsilon-regime of QCD using partially quenched chiral perturbation theory in the supersymmetry formulation without a singlet particle. We comment on how to minimize these corrections in lattice simulations of QCD.
The study of excited hadron spectra using Lattice QCD is currently evolving. An important step toward obtaining resonance parameters from Lattice QCD is the calculation of finite volume energy spectra. Somewhat more rigorous studies of finite volume spectra are currently possible and should be completed in the near future. The inclusion of disconnected diagrams is increasingly commonplace and the simplest systems which involve mixing between single- and multi-hadron interpolating fields are being studied. Advances in all-to-all algorithms which have been crucial in this progress are reviewed a…
We non-perturbatively determine the renormalization constant and the improvement coefficients relating the renormalized current and subtracted quark mass in O(a) improved two-flavour lattice QCD. We employ the Schrödinger functional scheme and fix the physical extent of the box by working at a constant value of the renormalized coupling. Our calculation yields results which cover two regions of bare parameter space. One is the weak-coupling region suitable for volumes of about half a fermi. By making simulations in this region, quarks as heavy as the bottom can be propagated with the full rela…
We present results for the isovector nucleon form factors measured on a $96^4$ lattice at almost the physical pion mass with a lattice spacing of 0.085 fm in 2+1 flavor QCD. The configurations are generated with the stout-smeared $O(a)$-improved Wilson quark action and the Iwasaki gauge action at $β$=1.82. The pion mass at the simulation point is about 146 MeV. A large spatial volume of $(8.1~{\rm fm})^3$ allows us to investigate the form factors in the small momentum transfer region. We determine the isovector electric radius and magnetic moment from nucleon electric ($G_E$) and magnetic ($G_…
We study the two-point Topological Charge Density Correlator (TCDC) in lattice QCD with two degenerate flavours of naive Wilson fermions and unimproved Wilson gauge action at two values of lattice spacings and different volumes, for a range of quark masses. Configurations are generated with DDHMC algorithm and smoothed with HYP smearing. In order to shed light on the mechanisms leading to the observed suppression of topological susceptibility with respect to the decreasing quark mass and decreasing volume, in this work, we carry out a detailed study of the two-point TCDC. We have shown that, (…
We study the scaling behavior of the two-flavor chiral phase transition using an effective quark-meson model. We investigate the transition between infinite-volume and finite-volume scaling behavior when the system is placed in a finite box. We can estimate effects that the finite volume and the explicit symmetry breaking by the current quark masses have on the scaling behavior which is observed in full QCD lattice simulations. The model allows us to explore large quark masses as well as the chiral limit in a wide range of volumes, and extract information about the scaling regimes.In particula…
We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at $O(α)$ are universal, i.e. they are independent of the structure of the meson. This is analogous to a similar result for the spectrum but with some fundamental differences, most notably the presence of infrared divergences in decay amplitudes. The leading non-universal, structure-dependent terms are of $O(1/L^2)$ (compared to the $O(1/L^3)$ leading non-universal corrections in the spectrum). We calculate the universal finite-volume effects, which requir…
Lattice QCD simulations tend to get stuck in a single topological sector at fine lattice spacing, or when using chirally symmetric quarks. In such cases computed observables differ from their full QCD counterparts by finite volume corrections, which need to be understood on a quantitative level. We extend a known relation from the literature between hadron masses at fixed and at unfixed topology by incorporating in addition to topological finite volume effects, also ordinary finite volume effects. We present numerical results for SU(2) Yang-Mills theory.
We present preliminary results from a lattice QCD calculation of the H-dibaryon using two flavors of $\mathcal{O}(a)$ improved Wilson fermions. We employ local six-quark interpolating operators at the source with a combination of local six-quark and two-baryon operators at the sink with the appropriate quantum numbers of the H-dibaryon and its coupling to the two-baryon channels. We find that the two-baryon operators provide an improved overlap onto the ground state in comparison to the local six-quark operators. We also apply Lüscher's finite volume formalism to obtain information on the natu…
The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effec…
SU(3) gauge theory with eight massless fundamental fermions seems to be near the conformal boundary, and is a candidate theory of walking technicolor. Along the series of study by LatKMI collaboration using HISQ fermions, S-parameter and vector decay constant, which provide important constraints in the model of electroweak symmetry breaking, are calculated for this theory. Use of various volumes allows a systematic investigation of finite volume effects. A strong sensitivity of the S-parameter to the volume is found.
Using the Coulomb gauge formulation of QED we present a lattice QCD procedure to calculate the $π^+π^+$ scattering phase shift including the effects of the Coulomb potential which appears in this formulation. The approach described here incorporates the effects of relativity and avoids finite-volume corrections that vanish as a power of the volume in which the lattice calculation is performed. This is the first step in developing a complete lattice QCD calculation of the electromagnetic and isospin-breaking light-quark mass contributions to $\varepsilon'$, the parameter describing direct CP vi…
Finite-volume effects in Quantum Chromodynamics (QCD) have been a subject of much theoretical interest for more than two decades. They are in particular important for the analysis and interpretation of QCD simulations on a finite, discrete space-time lattice. Most of these effects are closely related to the phenomenon of spontaneous breaking of the chiral flavor symmetry and the emergence of pions as light Goldstone bosons. These long-range fluctuations are strongly affected by putting the system into a finite box, and an analysis with different methods can be organized according to the interp…
Inclusion of QED in lattice QCD calculations can lead to power-law volume artifacts as a consequence of the long-range nature of the interaction. Such artifacts must be removed by extrapolation in order to attain reliable infinite volume estimates of observables and quantities derived from them. As an alternative to this methodology, we consider the use of a photon mass term as an infrared regulator for QCD+QED, and explore the viability of its use in determining hadron mass shifts and splittings.
