Search

To accelerate the HMC with field transformation, we consider a variant of the trivializing map, the decimation map, which can be regarded as a coarse-graining transformation. Using the 2D $U(1)$ pure gauge model, combined with the guided Monte Carlo algorithm, we show that the integrated autocorrelation time of the topological charge can be exponentially improved in the wall clock time. Our study indicates that incorporating renormalization group picture is a powerful and essential ingredient to accelerate the HMC at large $\beta$., Comment: 11 pages, 7 figures, talk presented at the 40th International Symposium on Lattice Field Theory (Lattice 2023)

Measurements of nucleon and nuclei Electric Dipole Moments (EDMs) play an important role in probing CP violation and exploring physics beyond the Standard Model. We extract the neutron EDM by measuring the energy shift of the nucleon two-point correlation function in the presence of a background field. The UV divergence of the topological charge density operator is mitigated using gradient flow, and the diffusion effect induced by the gradient flow process is included into the fit ansatz. Our calculations were carried out on two 2+1 DWF fermion, Iwasaki, gauge field ensembles generated by the RBC/UKQCD collaborations with inverse lattice spacing 1.73 GeV and pion masses of about 340 and 420 MeV., Comment: 8 pages, 3 figures, Proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31st - August 4th, 2023, Fermi National Accelerator Laboratory

We present a lattice calculation of the $K\to\pi\pi$ matrix elements and amplitudes with both the $\Delta I = 3/2$ and 1/2 channels and $\varepsilon'$, the measure of direct $CP$ violation. We use periodic boundary conditions (PBC), where the correct kinematics of $K\to\pi\pi$ can be achieved via an excited two-pion final state. To overcome the difficulty associated with the extraction of excited states, our previous work \cite{Bai:2015nea,RBC:2020kdj} successfully employed G-parity boundary conditions, where pions are forced to have non-zero momentum enabling the $I=0$ two-pion ground state to express the on-shell kinematics of the $K\to\pi\pi$ decay. Here instead we overcome the problem using the variational method which allows us to resolve the two-pion spectrum and matrix elements up to the relevant energy where the decay amplitude is on-shell. In this paper we report an exploratory calculation of $K\to\pi\pi$ decay amplitudes and $\varepsilon'$ using PBC on a coarser lattice size of $24^3\times64$ with inverse lattice spacing $a^{-1}=1.023$ GeV and the physical pion and kaon masses. The results are promising enough to motivate us to continue our measurements on finer lattice ensembles in order to improve the precision in the near future.

The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment, $(g-2$)/2, is computed in the infinite volume QED framework with lattice QCD. We report $a_\mu^\text{HLbL}=12.47(1.15)(0.99) \times 10^{-10}$ where the first error is statistical and the second systematic. The result is mainly based on the 2+1 flavor M\"obius domain wall fermion ensemble with inverse lattice spacing $a^{-1} = 1.73~\mathrm{GeV}$, lattice size $L=5.5~\mathrm{fm}$, and $m_\pi = 139~\mathrm{MeV}$, generated by the RBC-UKQCD collaborations. The leading systematic error of this result comes from the lattice discretization. This result is consistent with previous determinations., Comment: 29 pages

The two pion channel in Lattice QCD has long been a primary testing ground for studying multiparticle scattering in finite volume QCD. With the development of sophisticated techniques such as distillation, it is possible to carefully study two-pion scattering in order to constrain associated low-energy constants. In this work, correlation functions with multiparticle interpolating operators are constructed to compute pion scattering phase shifts and scattering lengths in the isospin 0 and 2 channels with both sea and valence quarks at physical mass. Contamination from vacuum and thermal contributions are explicitly quantified with dedicated calculations and the results obtained after subtracting these nuisance terms are compared with the traditional correlator time series subtraction method. Two physical point ensembles with different lattice actions are used, and our finest ensemble gives results for scattering lengths and phase shifts consistent with phenomenology to within the reported statistical uncertainty.

A study of two-pion scattering for the isospin channels, $I=0$ and $I=2$, using lattice QCD is presented. M\"obius domain wall fermions on top of the Iwasaki-DSDR gauge action for gluons with periodic boundary conditions are used for the lattice computations which are carried out on two ensembles of gauge field configurations generated by the RBC and UKQCD collaborations with physical masses, inverse lattice spacings of 1.023 and 1.378 GeV, and spatial extents of $L=4.63$ and 4.58 fm, respectively. The all-to-all propagator method is employed to compute a matrix of correlation functions of two-pion operators. The generalized eigenvalue problem (GEVP) is solved for a matrix of correlation functions to extract phase shifts with multiple states, two pions with a non-zero relative momentum as well as two pions at rest. Our results for phase shifts for both $I=0$ and $I=2$ channels are consistent with and the Roy Equation and chiral perturbation theory, though at this preliminary stage our errors for $I=0$ are large. An important outcome of this work is that we are successful in extracting two-pion excited states, which are useful for studying $K\to\pi\pi$ decay, on physical-mass ensembles using GEVP.

We construct an approximate trivializing map by using a Schwinger-Dyson equation. The advantage of this method is that: (1) The basis for the flow kernel can be chosen arbitrarily by hand. (2) It can be applied to the general action of interest. (3) The coefficients in the kernel are determined by lattice estimates of the observables, which does not require analytic calculations beforehand. We perform the HMC with the effective action obtained by the Schwinger-Dyson method, and show that we can have better control of the effective action than the known $t$-expansion construction. However, the algorithmic overhead is still large and overwhelming the gain though faster decorrelation is observed for long-range observables in some cases. This contribution reports the preliminary results of this attempt., Comment: 19 pages, 12 figures, talk presented at the 39th International Symposium on Lattice Field Theory (Lattice 2022)

Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure and spectrum, to serve as a numerical laboratory to reach beyond the Standard Model, or to invent and improve state-of-the-art computational paradigms, the lattice-gauge-theory program is in a prime position to impact the course of developments and enhance discovery potential of a vibrant experimental program in High-Energy Physics over the coming decade. This projection is based on abundant successful results that have emerged using lattice gauge theory over the years: on continued improvement in theoretical frameworks and algorithmic suits; on the forthcoming transition into the exascale era of high-performance computing; and on a skillful, dedicated, and organized community of lattice gauge theorists in the U.S. and worldwide. The prospects of this effort in pushing the frontiers of research in High-Energy Physics have recently been studied within the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021), and the conclusions are summarized in this Topical Report., Comment: 57 pages, 1 figure. Submitted to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021). Topical Group Report for TF05 - Lattice Gauge Theory

Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021)., Comment: 27 pp. main text, 4 pp. appendices, 29 pp. references, 1 p. index

The search for new physics requires a joint experimental and theoretical effort. Lattice QCD is already an essential tool for obtaining precise model-free theoretical predictions of the hadronic processes underlying many key experimental searches, such as those involving heavy flavor physics, the anomalous magnetic moment of the muon, nucleon-neutrino scattering, and rare, second-order electroweak processes. As experimental measurements become more precise over the next decade, lattice QCD will play an increasing role in providing the needed matching theoretical precision. Achieving the needed precision requires simulations with lattices with substantially increased resolution. As we push to finer lattice spacing we encounter an array of new challenges. They include algorithmic and software-engineering challenges, challenges in computer technology and design, and challenges in maintaining the necessary human resources. In this white paper we describe those challenges and discuss ways they are being dealt with. Overcoming them is key to supporting the community effort required to deliver the needed theoretical support for experiments in the coming decade., Comment: Contribution to Snowmass 2021. 22 pages

The decays and mixing of $K$ mesons are remarkably sensitive to the weak interactions of quarks and leptons at high energies. They provide important tests of the standard model at both first and second order in the Fermi constant $G_F$ and offer a window into possible new phenomena at energies as high as 1,000 TeV. These possibilities become even more compelling as the growing capabilities of lattice QCD make high-precision standard model predictions possible. Here we discuss and attempt to forecast some of these capabilities., Comment: submitted to the Rare Processes and Precision, Theory and Computational Frontiers for the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021)

Static electric dipole moments of nondegenerate systems probe mass scales for physics beyond the Standard Model well beyond those reached directly at high energy colliders. Discrimination between different physics models, however, requires complementary searches in atomic-molecular-and-optical, nuclear and particle physics. In this report, we discuss the current status and prospects in the near future for a compelling suite of such experiments, along with developments needed in the encompassing theoretical framework., Comment: Contribution to Snowmass 2021; updated with community edits and endorsements

We calculate $K\to\pi\pi$ matrix elements using periodic boundary conditions as an independent calculation from our previous study with G-parity boundary conditions. We present our preliminary results for $K\to\pi\pi$ three-point functions and matrix elements on a $24^3, a^{-1} = 1$~GeV, $2+1$-flavor M\"obius DWF ensemble at physical pion and kaon masses generated by the RBC and UKQCD collaborations and discuss the prospect for high-precision computation of $\varepsilon'$ with periodic boundary conditions., Comment: Proceedings of the 38th International Symposium on Lattice Field Theory (Lattice 2021), July 26-30, 2021, Zoom/Gather@MIT

We report a first principle lattice calculation of the pion electric polarizability $\alpha_\pi$ at the physical pion mass. First, we derive the master formula, which relates the pion polarizabilities with the position space hadronic Compton tensor, $\langle \pi | J_\mu(x) J_\nu(0) | \pi \rangle$. The finite volume error of the master formula is exponentially suppressed by the spatial extent of the lattice. Then, the hadronic tensor is calculated using domain wall fermions (DWF) directly at physical pion mass. The gauge ensembles are generated by the RBC-UKQCD collaborations., Comment: 9 pages, 5 figures. Talk presented at the 38th International Symposium on Lattice Field Theory (Lattice 2021), 26-30 July, 2021, Zoom/Gather@Massachusetts Institute of Technology

We propose using Normalizing Flows as a trainable kernel within the molecular dynamics update of Hamiltonian Monte Carlo (HMC). By learning (invertible) transformations that simplify our dynamics, we can outperform traditional methods at generating independent configurations. We show that, using a carefully constructed network architecture, our approach can be easily scaled to large lattice volumes with minimal retraining effort. The source code for our implementation is publicly available online at https://github.com/nftqcd/fthmc., Comment: 7 pages, 6 figures, presented at The 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather @ Massachusetts Institute of Technology

Proton decay is a major prediction of Grand-Unified Theories (GUT) and its observation would indicate baryon number violation that is required for baryogenesis. Many decades of searching for proton decay have constrained its rate and ruled out some of the simplest GUT models. Apart from the baryon number-violating interactions, this rate also depends on transition amplitudes between the proton and mesons or leptons produced in the decay, which are matrix elements of three-quark operators. We report nonperturbative calculation of these matrix elements for the most studied two-body decay channels into a meson and antilepton done on a lattice with physical light and strange quark masses and lattice spacings $a\approx0.14$ and 0.20 fm. We perform nonperturbative renormalization and excited state analysis to control associated systematic effects. Our results largely agree with previous lattice calculations done with heavier quark masses and thus remove ambiguity in ruling out some simple GUT theories due to quark mass dependence of hadron structure., Comment: 34 pages, 18 figures

We provide a modification to the quantum phase estimation algorithm (QPEA) inspired on classical windowing methods for spectral density estimation. From this modification we obtain an upper bound in the cost that implies a cubic improvement with respect to the algorithm's error rate. Numerical evaluation of the costs also demonstrates an improvement. Moreover, with similar techniques, we detail an iterative projective measurement method for ground state preparation that gives an exponential improvement over previous bounds using QPEA. Numerical tests that confirm the expected scaling behavior are also obtained. For these numerical tests we have used a Lattice Thirring model as testing ground. Using well-known perturbation theory results, we also show how to more appropriately estimate the cost scaling with respect to state error instead of evolution operator error., Comment: 18 pages, 11 figures

Electric dipole moments (EDMs) of nucleons and nuclei are actively considered as direct evidence of the CP violation. Calculations of nucleon EDMs on lattice are required to connect the quark- and hadron- level effective CP violating interactions within QCD or other CP violating sources in new physics beyond the standard model. Among them, the theta-induced nucleon EDM, that is the only such renormalizable interaction, has widely been investigated on a lattice. In the report, we review recent developments of the lattice calculations of nucleon EDM induced QCD theta term., Comment: Proceedings of the 37th International Symposium on Lattice Field Theory -- Lattice2019, 16-22 June 2019, Wuhan, China; 15 pages, 11 figures

We perform a digital quantum simulation of a gauge theory with a topological term in Minkowski spacetime, which is practically inaccessible by standard lattice Monte Carlo simulations. We focus on $1+1$ dimensional quantum electrodynamics with the $\theta$-term known as the Schwinger model. We construct the true vacuum state of a lattice Schwinger model using adiabatic state preparation which, in turn, allows us to compute an expectation value of the fermion mass operator with respect to the vacuum. Upon taking a continuum limit we find that our result in massless case agrees with the known exact result. In massive case, we find an agreement with mass perturbation theory in small mass regime and deviations in large mass regime. We estimate computational costs required to take a reasonable continuum limit. Our results imply that digital quantum simulation is already useful tool to explore non-perturbative aspects of gauge theories with real time and topological terms., Comment: 13 pages, 6 figures; v3: accepted version in PRD

We report the first result for the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment with all errors systematically controlled. Several ensembles using 2+1 flavors of physical mass M\"obius domain-wall fermions, generated by the RBC/UKQCD collaborations, are employed to take the continuum and infinite volume limits of finite volume lattice QED+QCD. We find $a_\mu^{\rm HLbL} = 7.87(3.06)_\text{stat}(1.77)_\text{sys}\times 10^{-10}$. Our value is consistent with previous model results and leaves little room for this notoriously difficult hadronic contribution to explain the difference between the Standard Model and the BNL experiment.

We report nucleon mass, isovector vector and axial-vector charges, and tensor and scalar couplings, calculated using two recent 2+1-flavor dynamical domain-wall fermions lattice-QCD ensembles generated jointly by the RIKEN-BNL-Columbia and UKQCD collaborations. These ensembles were generated with Iwasaki $\times$ dislocation-suppressing-determinant-ratio gauge action at inverse lattice spacing of 1.378(7) GeV and pion mass values of 249.4(3) and 172.3(3) MeV. The nucleon mass extrapolates to a value $m_N = 0.950(5)$ GeV at physical point. The isovector vector charge renormalizes to unity in the chiral limit, narrowly constraining excited-state contamination in the calculation. The ratio of the isovector axial-vector to vector charges shows a deficit of about ten percent. The tensor coupling no longer depends on mass and extrapolates to 1.04(5) in $\overline {\rm MS}$ 2-GeV renormalization at physical point, in a good agreement with the value obtained at the lightest mass in our previous calculations and other calculations that followed. The scalar charge, though noisier, does not show mass dependence and is in agreement with other calculations., Comment: Accepted for publication in Physical Review D, 11 pages, 13 figures and 7 tables. arXiv admin note: text overlap with arXiv:1710.06656

The Hadronic Vacuum Polarization (HVP) is a dominant contribution to the theoretical uncertainty of the muon anomalous magnetic moment. The uncertainty in a lattice QCD calculation of the connected light-quark contribution to the HVP is dominated by the long-distance region of the vector correlation function. Explicit studies of the exclusive channels of the HVP diagram make it possible to reconstruct the long-distance behavior of the correlation function. This removes most of the statistical uncertainty of the correlation function. In these proceedings, preliminary results of an exclusive study of the isospin symmetric connected-only vector-vector correlation function using a hybrid of distillation and A2A techniques are presented. The computation is performed on 2+1 flavor M\"obius Domain Wall Fermion ensembles with physical pion mass. Reconstruction of the long-distance correlation function will enable lattice-only calculations of the HVP to achieve precision similar to estimates of the HVP from the R-ratio method on the timescale of the new experimental measurements of the muon anomalous magnetic moment., Comment: 7 pages, 4 figures; Presented at the 37th International Symposium on Lattice Field Theory, 16-22 June 2019, Wuhan, China

We report preliminary results for the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment. Several ensembles using 2+1 flavors of M\"obius domain-wall fermions, generated by the RBC/UKQCD collaborations, are employed to take the continuum and infinite volume limits of finite volume lattice QED+QCD. We find $a_\mu^{\rm HLbL} = (7.41\pm6.33)\times 10^{-10}$, Comment: 8 pages, 19 figures, to appear in the proceedings of Rencontres de Moriond (EW)

We present a lattice QCD study of valence parton distribution inside the pion within the framework of Large Momentum Effective Theory. We use a mixed action approach with 1-HYP smeared valence Wilson clover quarks on 2+1 flavor HISQ sea with the valence quark mass tuned to 300 MeV pion mass. We use $48^3 \times 64$ lattice at a fine lattice spacing $a=0.06$ fm for this computation. We renormalize the quasi-PDF matrix element in the non-perturbative RI-MOM scheme. As a byproduct, we test the validity of 1-loop matching procedure by comparing the RI-MOM renormalized quasi-PDF matrix element with off-shell quark external states as computed in the continuum 1-loop perturbation theory with the lattice results at $a=0.04$ and 0.06 fm. By applying the RI-MOM to ${\bar{\rm MS}}$ one-loop matching, implemented through a fit to phenomenologically motivated PDFs, we obtain the valence PDF of pion., Comment: 25 pages, 22 figures; version published in PRD

This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for Lattice Quantum Chromodynamics (LQCD) in the research frontier in fundamental symmetries and signals for new physics. LQCD, in synergy with effective field theories and nuclear many-body studies, provides theoretical support to ongoing and planned experimental programs in searches for electric dipole moments of the nucleon, nuclei and atoms, decay of the proton, $n$-$\overline{n}$ oscillations, neutrinoless double-$\beta$ decay of a nucleus, conversion of muon to electron, precision measurements of weak decays of the nucleon and of nuclei, precision isotope-shift spectroscopy, as well as direct dark matter detection experiments using nuclear targets. This whitepaper details the objectives of the LQCD program in the area of Fundamental Symmetries within the USQCD collaboration, identifies priorities that can be addressed within the next five years, and elaborates on the areas that will likely demand a high degree of innovation in both numerical and analytical frontiers of the LQCD research., Comment: A whitepaper by the USQCD Collaboration, 30 pages, 9 figures

Proton decay is one of possible signatures of baryon number violation, which has to exist to explain the baryon asymmetry and the existence of nuclear matter. Proton decays must be mediated through effective low-energy baryon number violating operators made of three quarks and a lepton. We calculate matrix elements of these operators between the proton and various meson final states using the direct method. We report on preliminary results of matrix element calculation done with the 2+1 dynamical flavor domain wall fermions at the physical point for the first time., Comment: 7 pages, 5 figures, 1 table

We present preliminary study of parton distribution inside the pion using mixed action approach with HYP smeared valence clover quarks on HISQ sea within the framework of Large Momentum Effective Theory. We use 2+1 flavor $48^3 \times 64$ HISQ lattices with lattices spacing of a=0.06 fm and valence quark masses corresponding to pion mass of 300 MeV., Comment: Proceedings of XIIth Conference on Quark Confinement and Hadron Spectrum, July 31-August 6, 2018, Maynooth University, Ireland, 8 pages

Hadronic spectral functions of $\tau$ decays have been used in the past to provide an alternative determination of the LO Hadronic Vacuum Polarization relevant for the (g-2) of the muon. Following recent developments and results in Lattice QCD+QED calculations, we explore the possibility of studying the isospin breaking corrections of $\tau$ spectral functions for this prediction. We present preliminary results at physical pion mass based on Domain Wall Fermion ensembles generated by the RBC/UKQCD collaboration., Comment: 7 pages, 6 figures. Talk presented at The 36th Annual International Symposium on Lattice Field Theory

We study the finite-volume correction on the hadronic vacuum polarization contribution to the muon g-2 ($a_\mu^{\rm hvp}$) in lattice QCD at (near) physical pion mass using two different volumes: $(5.4~{\rm fm})^4$ and $(8.1~{\rm fm})^4$. We use an optimized AMA technique for noise reduction on $N_f=2+1$ PACS gauge configurations with stout-smeared clover-Wilson fermion action and Iwasaki gauge action at a single lattice cut-off $a^{-1}=2.33$ GeV. The calculation is performed for the quark-connected light-quark contribution in the isospin symmetric limit. We take into account the effects of backward state propagation by extending a temporal boundary condition. In addition we study a quark-mass correction to tune to the exactly same physical pion mass on different volume and compare those correction with chiral perturbation. We find $10(26)\times10^{-10}$ difference for light quark $a_\mu^{\rm hvp}$ between $(5.4~{\rm fm})^4$ and $(8.1~{\rm fm})^4$ lattice in 146 MeV pion.

We propose and apply a new approach to determining $|V_{us}|$ using dispersion relations with weight functions having poles at Euclidean (space-like) momentum which relate strange hadronic $\tau$ decay distributions to hadronic vacuum polarization functions (HVPs) obtained from lattice QCD. We show examples where spectral integral contributions from the region where experimental data have large errors or do not exist are strongly suppressed but accurate determinations of the relevant lattice HVP combinations remain possible. The resulting $|V_{us}|$ agrees well with determinations from $K$ physics and 3-family CKM unitarity. Advantages of this new approach over the conventional hadronic $\tau$ decay determination employing flavor-breaking sum rules are also discussed., Comment: 10 pages, 11 figures. References added and minor modifications. Accepted for publication in Physical Review Letters

In a large-momentum nucleon state, the matrix element of a gauge-invariant Euclidean Wilson line operator accessible from lattice QCD can be related to the standard light-cone parton distribution function through the large-momentum effective theory (LaMET) expansion. This relation is given by a factorization theorem with a non-trivial matching coefficient. Using the operator product expansion we prove the large-momentum factorization of the quasi-parton distribution function in LaMET, and show that the more recently discussed Ioffe-time distribution approach also obeys an equivalent factorization theorem. Explicit results for the coefficients are obtained and compared at one-loop. Our proof clearly demonstrates that the matching coefficients in the $\overline{\rm MS}$ scheme depend on the large partonic momentum rather than the nucleon momentum., Comment: 19 pages, 4 figures

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 $m_\pi=0.34$--0.69 GeV on 2.7~fm$^3$ lattice as used in our previous work \cite{Aoki:2013yxa}. We improve total accuracy of matrix elements to 10--15\% from 30--40\% for $p\rightarrow\pi e^+$ or from 20--40\% for $p\rightarrow K \bar\nu$. The accuracy of the low energy constants $\alpha$ and $\beta$ in the leading-order baryon chiral perturbation theory (BChPT) of proton decay are also improved. The relevant form factors of $p\rightarrow \pi$ estimated through the "direct" lattice calculation from three-point function appear to be 1.4 times smaller than those from the "indirect" method using BChPT with $\alpha$ and $\beta$. It turns out that the utilization of our result will provide a factor 2--3 larger proton partial lifetime than that obtained using BChPT. We also discuss the use of these parameters in a dark matter model., Comment: 28 pages, 14 figures, 6 tables

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. We present numerical results for the case when the quark loop is replaced by a muon loop, finding the expected exponential approach to the infinite volume limit and consistency with the known analytic result. We have implemented an improved weighting function which reduces both discretization and finite volume effects arising from the hadronic part of the amplitude., Comment: 12 pages

We present initial results of computing nucleon electric dipole moment induced by quark chromo-EDM, CP-violating quark-gluon coupling. Using chirally-symmetric domain wall and M\"obius fermions with pion mass $m_\pi=172\text{ MeV}$, we calculate the connected part of the electric dipole form factor $F_3(Q^2)$. In addition, we perform an exploratory study of the method to calculate EDM using uniform background electric field on a lattice introduced without breaking the periodicity in the time direction., Comment: 7 pages, 9 figures Proceedings of the 34th annual International Symposium on Lattice Field Theory, 24-30 July 2016, University of Southampton, UK

Semi-leptonic $B$ decays provide promising channels to test the Standard Model, search for signs of new physics, or determine fundamental parameters like CKM matrix elements. We present an update on our calculation of short distance contributions to GIM suppressed rare $B$ decays focusing in particular on $B_s\to \phi \ell^+ \ell^-$ decays. Furthermore we show first results for our calculation of $B_{(s)}\to D_{(s)}^{(*)}\ell\nu$ semi-leptonic decays involving $b\to c$ transitions. Our calculations are based on RBC-UKQCD's 2+1 flavor domain-wall fermion and Iwasaki gauge field configurations featuring three lattice spacings in the range $1.73$ GeV $\le a^{-1} \le 2.77$ GeV and pion masses down to the physical value. We calculate the form factors by simulating $b$-quarks using the relativistic heavy quark action, create light $u/d$ and $s$ quarks with standard domain-wall kernel, and use optimised M\"obius domain-wall fermions for charm quarks., Comment: 13 pages, 2 tables, 6 figures, presented at the 34th annual International Symposium on Lattice Field Theory (Lattice2016), 24-30 July 2016, University of Southampton, UK

We report our recent lattice calculation of hadronic light-by-light contribution to muon $g-2$ using our recently developed moment method. The connected diagrams and the leading disconnected diagrams are included. The calculation is performed on a $48^3 \times 96$ lattice with physical pion mass and 5.5 fm box size. We expect sizable finite volume and finite lattice spacing corrections to the results of these calculations which will be estimated in calculations to be carried out over the next 1-2 years., Comment: 34th annual International Symposium on Lattice Field Theory, 24-30 July 2016, University of Southampton, UK. 7 pages

We report a lattice QCD calculation of the hadronic light-by-light contribution to the muon anomalous magnetic moment at physical pion mass. The calculation includes the connected diagrams and the leading, quark-line-disconnected diagrams. We incorporate algorithmic improvements developed in our previous work. The calculation was performed on the $48^3 \times 96$ ensemble generated with a physical-pion-mass and a 5.5 fm spatial extent by the RBC and UKQCD collaborations using the chiral, domain wall fermion (DWF) formulation. We find $a_\mu^{\text{HLbL}} = 5.35 (1.35) \times 10^{- 10}$, where the error is statistical only. The finite-volume and finite lattice-spacing errors could be quite large and are the subject of on-going research. The omitted disconnected graphs, while expected to give a correction of order 10\%, also need to be computed., Comment: 6 pages

The application of the Dirac operator on a spinor field, the Dslash operation, is the most computation-intensive part of the lattice QCD simulations. It is often the key kernel to optimize to achieve maximum performance on various platforms. Here we report on a project to optimize the domain wall fermion Dirac operator in Columbia Physics System (CPS) using the R-Stream source-to-source compiler. Our initial target platform is the Intel PC clusters. We discuss the optimization strategies involved before and after the automatic code generation with R-Stream and present some preliminary benchmark results., Comment: 7 pages, 4 figures. Proceedings of the 33rd International Symposium on Lattice Field Theory, July 14 -18, 2015, Kobe, Japan

We present a lattice calculation of the neutron and proton electric dipole moments (EDM's) with $N_f=2+1$ flavors of domain-wall fermions. The neutron and proton EDM form factors are extracted from three-point functions at the next-to-leading order in the $\theta$ vacuum of QCD. In this computation, we use pion masses 0.33 and 0.42 GeV and 2.7 fm$^3$ lattices with Iwasaki gauge action and a 0.17 GeV pion and 4.6 fm$^3$ lattice with I-DSDR gauge action, all generated by the RBC and UKQCD collaborations. The all-mode-averaging technique enables an efficient and high statistics calculation. Chiral behavior of lattice EDM's is discussed in the context of baryon chiral perturbation theory. In addition, we also show numerical evidence on relationship of three- and two-point correlation function with local topological distribution., Comment: 33 pages, 22 figures

The current measurement of muonic $g - 2$ disagrees with the theoretical calculation by about 3 standard deviations. Hadronic vacuum polarization (HVP) and hadronic light by light (HLbL) are the two types of processes that contribute most to the theoretical uncertainty. The current value for HLbL is still given by models. I will describe results from a first-principles lattice calculation with a 139 MeV pion in a box of 5.5 fm extent. Our current numerical strategies, including noise reduction techniques, evaluating the HLbL amplitude at zero external momentum transfer, and important remaining challenges, in particular those associated with finite volume effects, will be discussed., Comment: The 33rd International Symposium on Lattice Field Theory, 14 -18 July 2015, Kobe International Conference Center, Kobe, Japan

For reliable comparison of the standard model prediction to the muon g-2 with its experimental value, the hadronic light-by-light scattering (HLbL) contribution must be calculated by lattice QCD simulation. HLbL contribution has many types of disconnected-type diagrams. Here, we start with recalling the point that must be taken care of in every method to calculate them by lattice QCD, and present one concrete method called nonperturbative QED method., Comment: 7 pages, 12 figures. 2 tables, Proceedings of the 33rd International Symposium on Lattice Field Theory, July 14-18, 2015, Kobe, Japan

Computing plays an essential role in all aspects of high energy physics. As computational technology evolves rapidly in new directions, and data throughput and volume continue to follow a steep trend-line, it is important for the HEP community to develop an effective response to a series of expected challenges. In order to help shape the desired response, the HEP Forum for Computational Excellence (HEP-FCE) initiated a roadmap planning activity with two key overlapping drivers -- 1) software effectiveness, and 2) infrastructure and expertise advancement. The HEP-FCE formed three working groups, 1) Applications Software, 2) Software Libraries and Tools, and 3) Systems (including systems software), to provide an overview of the current status of HEP computing and to present findings and opportunities for the desired HEP computational roadmap. The final versions of the reports are combined in this document, and are presented along with introductory material., Comment: 72 pages

The quark-connected part of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment is computed using lattice QCD with chiral fermions. We report several significant algorithmic improvements and demonstrate their effectiveness through specific calculations which show a reduction in statistical errors by more than an order of magnitude. The most realistic of these calculations is performed with a near-physical, $171$ MeV pion mass on a $(4.6\;\mathrm{fm})^3$ spatial volume using the $32^3\times 64$ Iwasaki+DSDR gauge ensemble of the RBC/UKQCD Collaboration., Comment: 52 pages

The anomalous magnetic moment of muon, $g-2$, is a very precisely measured quantity. However, the current measurement disagrees with standard model by about 3 standard deviations. Hadronic vacuum polarization and hadronic light by light are the two types of processes that contribute most to the theoretical uncertainty. I will describe how lattice methods are well-suited to provide a first-principle's result for the hadronic light by light contribution, the various numerical strategies that are presently being used to evaluate it, our current results and the important remaining challenges which must be overcome., Comment: Twelfth Conference on the Intersections of Particle and Nuclear Physics. Vail Colorado at the Vail Marriott from May 19-24, 2015

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., Comment: Presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, New York, NY, USA

The form factor that yields the light-by-light scattering contribution to the muon anomalous magnetic moment is computed in lattice QCD+QED and QED. A non-perturbative treatment of QED is used and is checked against perturbation theory. The hadronic contribution is calculated for unphysical quark and muon masses, and only the diagram with a single quark loop is computed. Statistically significant signals are obtained. Initial results appear promising, and the prospect for a complete calculation with physical masses and controlled errors is discussed., Comment: 5 pages, 5 figures

Neutral $B$ meson mixing matrix elements and $B$ meson decay constants are calculated. Static approximation is used for $b$ quark and domain-wall fermion formalism is employed for light quarks. The calculations are carried out on $2+1$ flavor dynamical ensembles generated by RBC/UKQCD Collaborations with lattice spacings $0.086$fm ($a^{-1}\sim 2.3$GeV) and $0.11$fm ($1.7$GeV), and a fixed physical spatial volume of about $(2.7{\rm fm})^3$. In the static quark action, link-smearings are used to improve the signal-to-noise ratio. We employ two kinds of link-smearings, HYP1 and HYP2, and their results are combined in taking the continuum limit. For the matching between the lattice and the continuum theory, one-loop perturbative $O(a)$ improvements are made to reduce discretization errors. As the most important quantity of this work, we obtain SU(3) breaking ratio $\xi=1.208(60)$, where the error includes statistical and systematic one. (Uncertainty from infinite $b$ quark mass is not included.) We also find other neutral $B$ meson mixing quantities $f_B\sqrt{\hat{B}_B}=240(22)$MeV, $f_{B_s}\sqrt{\hat{B}_{B_s}}=290(22)$MeV, $\hat{B}_B=1.17(22)$, $\hat{B}_{B_s}=1.22(13)$ and $B_{B_s}/B_B=1.028(74)$, $B$ meson decay constants $f_B=219(17)$MeV, $f_{B_s}=264(19)$MeV and $f_{B_s}/f_B=1.193(41)$, in the static limit of $b$ quark, which do not include infinite $b$ quark mass uncertainty., Comment: 33 pages, 18 figures, v3: published version

We calculate the B-meson decay constants f_B, f_Bs, and their ratio in unquenched lattice QCD using domain-wall light quarks and relativistic b-quarks. We use gauge-field ensembles generated by the RBC and UKQCD collaborations using the domain-wall fermion action and Iwasaki gauge action with three flavors of light dynamical quarks. We analyze data at two lattice spacings of a ~ 0.11, 0.086 fm with unitary pion masses as light as M_pi ~ 290 MeV; this enables us to control the extrapolation to the physical light-quark masses and continuum. For the b-quarks we use the anisotropic clover action with the relativistic heavy-quark interpretation, such that discretization errors from the heavy-quark action are of the same size as from the light-quark sector. We renormalize the lattice heavy-light axial-vector current using a mostly nonperturbative method in which we compute the bulk of the matching factor nonperturbatively, with a small correction, that is close to unity, in lattice perturbation theory. We also improve the lattice heavy-light current through O(alpha_s a). We extrapolate our results to the physical light-quark masses and continuum using SU(2) heavy-meson chiral perturbation theory, and provide a complete systematic error budget. We obtain f_B0 = 199.5(12.6) MeV, f_B+ = 195.6(14.9) MeV, f_Bs = 235.4(12.2) MeV, f_Bs/f_B0 = 1.197(50), and f_Bs/f_B+ = 1.223(71), where the errors are statistical and total systematic added in quadrature. These results are in good agreement with other published results and provide an important independent cross check of other three-flavor determinations of $B$-meson decay constants using staggered light quarks., Comment: 25 pages, 13 tables, 12 figures. Version 2 revised for PRD. Sign in Eq. (27) corrected. Chiral-continuum extrapolations of fB and fBs/fB changed. Results for fB and fBs/fB, plots, and text updated accordingly. Updated references

The real and imaginary parts of the $K_L-K_S$ mixing matrix receive contributions from all three charge-2/3 quarks: up, charm and top. These give both short- and long-distance contributions which are accessible through a combination of perturbative and lattice methods. We will discuss a strategy to compute both the mass difference, $\Delta M_K$ and $\epsilon_K$ to sub-percent accuracy, looking in detail at the contributions from each of the three CKM matrix element products $V_{id}^*V_{is}$ for $i=u, c$ and $t$ as described in Ref. [1], Comment: Presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany, 7 pages and 5 figures