Search

With the development of lattice QCD in recent years, a determination of decay rates for inclusive semileptonic decays from lattice correlators now seems viable. We report on the calculation of the inclusive semileptonic decay of the $D_s$ meson on the lattice. We simulate the $D_s \rightarrow X_s\ell\nu_\ell$ process with M\"obius domain-wall charm and strange quarks, whose masses were approximately tuned to the physical values. We cover the whole kinematical region. We present a general overview on how the inclusive decays are treated on the lattice and discuss ongoing challenges, such as the estimation of systematic errors and future prospects of the project., Comment: 7 pages, 2 figures, Presented at the 12th Workshop on the CKM Unitarity Triangle, 18-22 September 2023, Santiago de Compostela

We present a study on the nonperturbative calculation of observables for inclusive semileptonic decays of $B_{(s)}$ mesons using lattice QCD. We focus on the comparison of two different methods to analyse the lattice data of Euclidean correlation functions, specifically Chebyshev and Backus-Gilbert approaches. This type of computation may eventually provide new insight into the long-standing tension between the inclusive and exclusive determinations of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_{cb}|$ and $|V_{ub}|$. We report the results from a pilot lattice computation for the decay $B_s \rightarrow X_c \, l\nu_l$, where the valence quark masses are approximately tuned to their physical values using the relativistic-heavy quark action for the $b$ quark and the domain-wall formalism for the other valence quarks. We address the computation of the total decay rate as well as leptonic and hadronic moments, discussing similarities and differences between the two analysis techniques., Comment: 10 pages, 6 figures, 40th International Symposium on Lattice Field Theory - Lattice2023

We report on the calculation of the inclusive semileptonic decay of the $D_s$ meson on the lattice. We simulate the $D_s \rightarrow X_s\ell\nu_\ell$ process with M\"obius domain-wall charm and strange quarks, whose masses were approximately tuned to the physical values. We cover the whole kinematical region. The focus of this work is on the systematic error due to finite-volume effects. We construct a model of two-body final states to describe the data on a finite volume lattice of $L \simeq 0.055 \, \text{fm}$ to investigate the extrapolation to the infinite-volume limit.

We address the nonperturbative calculation of the inclusive decay rate of semileptonic $B_{(s)}$-meson decays from lattice QCD. Precise Standard-Model predictions are key ingredients in searches for new physics, and this type of computation may eventually provide new insight into the long-standing tension between the inclusive and exclusive determinations of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_{cb}|$ and $|V_{ub}|$. We present results from a pilot lattice computation for $B_s \rightarrow X_c\, l \nu_l$, where the initial $b$ quark described by the relativistic-heavy-quark (RHQ) formalism on the lattice and the other valence quarks discretised with domain-wall fermions are simulated approximately at their physical quark masses. We compare two different methods for computing the decay rate from lattice data of Euclidean $n$-point functions, namely Chebyshev and Backus-Gilbert approaches. We further study how much the ground-state meson dominates the inclusive decay rate and indicate our strategy towards a computation with a more comprehensive systematic error budget., Comment: 43 pages, 18 figures. Add missing references, fix typos

Semileptonic $B_s \to K \ell \nu$ decays provide an alternative $b$-decay channel to determine the CKM matrix element $|V_{ub}|$, and to obtain a $R$-ratio to investigate lepton-flavor-universality violations. Results for the CKM matrix element may also shed light on the discrepancies seen between analyses of inclusive or exclusive decays. We calculate the decay form factors using lattice QCD with domain-wall light quarks and a relativistic $b$-quark. We analyze data at three lattice spacings with unitary pion masses down to $268\,\mathrm{MeV}$. Our numerical results are interpolated/extrapolated to physical quark masses and to the continuum to obtain the vector and scalar form factors $f_+(q^2)$ and $f_0(q^2)$ with full error budgets at $q^2$ values spanning the range accessible in our simulations. We provide a possible explanation of tensions found between results for the form factor from different lattice collaborations. Model- and truncation-independent $z$-parameterization fits following a recently proposed Bayesian-inference approach extend our results to the entire allowed kinematic range. Our results can be combined with experimental measurements of $B_s \to D_s$ and $B_s\to K$ semileptonic decays to determine $|V_{ub}|=3.8(6)\times 10^{-3}$. The error is currently dominated by experiment. We compute differential branching fractions and two types of $R$ ratios, the one commonly used as well as a variant better suited to test lepton-flavor universality., Comment: Version accepted and published (Phys. Rev. D 107, 114512) 30 pages, 13 Figures, supplementary data file

We present our calculations for the $I$ = 1/2 and 3/2 $K-\pi$ s-wave scattering length with physical quark masses, extracted from the interaction energy of Euclidean two-point functions. We use the domain wall fermion action with physical quark masses at a single lattice spacing. We are specifically interested in the systematic effects due to around-the-world terms on the overall determination of the scattering length. We present our progress and discuss the various systematic effects in our preliminary results., Comment: 39th International Symposium on Lattice Field Theory

There is increasing interest in the study of nonperturbative aspects of three-dimensional quantum field theories (QFT). They appear as holographic dual to theories of (strongly coupled) gravity. For instance, in Holographic Cosmology, the two-point function of the Energy-Momentum Tensor (EMT) of a particular class of three-dimensional QFTs can be mapped into the power spectrum of the Cosmic Microwave Background in the gravitational theory. However, the presence of divergent contact terms poses challenges in extracting a renormalised EMT two-point function on the lattice. Using a $\phi^4$ theory of adjoint scalars valued in the $\mathfrak{su}(N)$ Lie Algebra as a proof-of-concept motivated by Holographic Cosmology, we apply a novel method for filtering out such contact terms by making use of infinitely differentiable "bump" functions which enforce a smooth window that excludes contributions at zero spatial separation. The process effectively removes the local contact terms and allows us to extract the continuum limit behaviour of the renormalised EMT two-point function., Comment: Proceedings for the 39th International Symposium on Lattice Field Theory

We report on the physical-point RBC/UKQCD calculation of the leading isospin-breaking corrections to light-meson leptonic decays. This is highly relevant for future precision tests in the flavour physics sector, in particular the first-row unitarity of the Cabibbo-Kobayashi-Maskawa matrix containing the elements $V_{us}$ and $V_{ud}$. The simulations were performed using Domain-Wall fermions for $2+1$ flavours, and with isospin-breaking effects included perturbatively in the path integral through order $\alpha$ and $(m_u - m_d)/\Lambda _{\mathrm{QCD}}$. We use QED$_{\mathrm{L}}$ for the inclusion of electromagnetism, and discuss here the non-locality of this prescription which has significant impact on the infinite-volume extrapolation., Comment: Proceedings for The 39th International Symposium on Lattice Field Theory, 8th-13th August, 2022, Rheinische Friedrich-Wilhelms-Universit\"at Bonn, Bonn, Germany

We perform a non-perturbative lattice calculation of the decay rates for inclusive semi-leptonic decays of charmed mesons. In view of the long-standing tension in the determination of the CKM matrix elements $|V_{ub}|$ and $|V_{cb}|$ from exclusive and inclusive processes, recently, the use of lattice QCD has been extended towards the description of inclusive decays. Since the determination of hadronic input parameters from QCD based methods require independent tests, we focus on the charm sector, since it not only offers experimental data, but also well determined CKM parameters. We carry out a pilot lattice simulation for the $D_s \rightarrow X_s \ell\nu$ and explore the improvement of existing techniques. Our simulation employs M\"obius domain-wall charm and strange quarks whose masses are tuned to be approximately physical and we cover the whole kinematical region. We report on our progress in analyzing different sources of systematic effects, such as the extrapolation of the kernel function chosen for the Chebsyhev approximation as well as the influence on the analysis in the region close to the kinematical limit., Comment: 9 pages, 6 figures, Proceedings of the 39th International Symposium on Lattice Field Theory, 8th-13th August 2022, Bonn, Germany

We address the non-perturbative calculation of the decay rate of inclusive semi-leptonic $B_{(s)}$ mesons decays from lattice QCD. Precise theoretical Standard Model predictions are key ingredients in searches for new physics. This type of computation may eventually provide new insight into the long-standing tension between the inclusive and exclusive determinations of the CKM matrix elements $|V_{cb}|$ and $|V_{ub}|$. We perform a pilot lattice computation for $B_s \rightarrow X_c \, l \nu_l$ and improve on existing techniques. The valence-quark masses in our simulations are approximately physical for the domain-wall strange and charm quarks as well as for the bottom quark, for which we use a relativistic heavy quark effective action. We report on our progress and discuss future plans towards a first study with fully controlled systematic effects., Comment: 10 pages, 6 figures, Proceedings of the 39th International Symposium on Lattice Field Theory, 8th-13th August 2022, Bonn, Germany

The decreasing uncertainties in theoretical predictions and experimental measurements of several hadronic observables related to weak processes, which in many cases are now smaller than $\mathrm{O}(1\%)$, require theoretical calculations to include subleading corrections that were neglected so far. Precise determinations of leptonic and semi-leptonic decay rates, including QED and strong isospin-breaking effects, can play a central role in solving the current tensions in the first-row unitarity of the CKM matrix. In this work we present the first RBC/UKQCD lattice calculation of the isospin-breaking corrections to the ratio of leptonic decay rates of kaons and pions into muons and neutrinos. The calculation is performed with $N_\mathrm{f}=2+1$ dynamical quarks close to the physical point and domain wall fermions in the M\"obius formulation are employed. Long-distance QED interactions are included according to the $\mathrm{QED_L}$ prescription and the crucial role of finite-volume electromagnetic corrections in the determination of leptonic decay rates, which produce a large systematic uncertainty, is extensively discussed. Finally, we study the different sources of uncertainty on $|V_\mathrm{us}|/|V_\mathrm{ud}|$ and observe that, if finite-volume systematics can be reduced, the error from isospin-breaking corrections is potentially sub-dominant in the final precision of the ratio of the CKM matrix elements., Comment: 66 pages, 23 figures and 4 tables

Lattice quantum chromodynamics has proven to be an indispensable method to determine nonperturbative strong contributions to weak decay processes. In this white paper for the Snowmass community planning process we highlight achievements and future avenues of research for lattice calculations of weak $b$ and $c$ quark decays, and point out how these calculations will help to address the anomalies currently in the spotlight of the particle physics community. With future increases in computational resources and algorithmic improvements, percent level (and below) lattice determinations will play a central role in constraining the standard model or identifying new physics., Comment: contribution to Snowmass 2021; 19 pages; v2 corrected typo and added references

In the holographic approach to cosmology, cosmological observables are described in terms of correlators of a three-dimensional boundary quantum field theory. As a concrete model, we study the $3D$ massless $SU(N)$ scalar matrix field theory with a $\phi^4$ interaction. On the lattice, the energy-momentum tensor (EMT) in this theory can mix with the operator $\phi^2$. We utilize the Wilson Flow to renormalize the EMT on the lattice, and present numerical results for the mixing coefficient for $N = 2$. Obtaining the renormalized EMT will allow us to make predictions for the CMB power spectra in the regime where the dual QFT is non-perturbative., Comment: 10 pages, 3 figures, presented at the 38th International Symposium on Lattice Field Theory - LATTICE2021 - 26-30 July, 2021, Massachusetts Institute of Technology

We present the status of our project to calculate $D \to \pi \ell \nu$, $D \to K \ell \nu$ and $D_s \to K \ell \nu$ semileptonic form factors using domain wall fermions for both heavy and light quarks. Our computations are performed using RBC/UKQCD's set of 2+1 flavour domain wall fermion and Iwasaki gauge field ensembles. We plan to calculate three-point functions covering the full, physically allowed kinematic range. Given that the signal decays faster than the noise, unambiguously and reliably extracting the ground state is critical for success. We include an analysis of operator diagonalisation within several possible $2 \times 2$ operator bases and find an admixture of gauged fixed wall and $\mathbb{Z} \left( 2 \right)$ wall sources to be acceptable at both zero and non-zero momentum. Initial results for semileptonic form factors are presented for first ensembles., Comment: 11 pages, 9 figures, to be published in Proceedings of Science, The 38th International Symposium on Lattice Field Theory

An investigation of the performance of the multilevel algorithm in the approach to criticality has been undertaken using the Ising model, performing simulations across a range of temperatures. Numerical results show that the performance of multilevel in this system deteriorates as the correlation length is increased with respect to the lattice size. The statistical error of the longest correlator in the system is reduced in a multilevel setup when the correlation length is less than one-tenth of the lattice size, while for longer correlation lengths multilevel performs more poorly than a computer-time equivalent single level algorithm. A theoretical model of this performance scaling is outlined, and shows remarkable accuracy when compared to numerical results. This theoretical model may be applied to other systems with more complex spectra to predict if multilevel techniques are likely to result in improved statistics., Comment: 9 pages, 4 figures, a proceedings paper for a talk given at the 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021. Submitted to Proceedings of Science, see https://pos.sissa.it/

In recent years, lattice determinations of non-perturbative quantities such as $f_K$ and $f_\pi$, which are relevant for $V_{us}$ and $V_{ud}$, have reached an impressive precision of $\mathcal{O}(1\%)$ or better. To make further progress, electromagnetic and strong isospin breaking effects must be included in lattice QCD simulations. We present the status of the RBC/UKQCD lattice calculation of isospin-breaking corrections to light meson leptonic decays. This computation is performed in a (2+1)-flavor QCD simulation using Domain Wall Fermions with near-physical quark masses. The isospin-breaking effects are implemented via a perturbative expansion of the action in $\alpha$ and $(m_u-m_d)$. In this calculation, we work in the electro-quenched approximation and the photons are implemented in the Feynman gauge and $\text{QED}_\text{L}$ formulation., Comment: 11 pages, 4 figures; Updated Author(s) metadata

We report on our determinations of $B\to \pi\ell\nu$, $B_s\to K \ell \nu$ and $B_s\to D_s \ell \nu$ semileptonic form factors. In addition we discuss the determination of $R$-ratios testing lepton-flavor universality and suggest an improved ratio. Our calculations are based on the set of 2+1 flavor domain-wall Iwasaki gauge field configurations generated by the RBC/UKQCD collaboration with three lattice spacings of $1/a = 1.78$, $2.38$, and $2.79\,\text{GeV}$. We use the relativistic heavy quark action for $b$ quarks and charm quarks are simulated with the M\"obius domain-wall fermion action., Comment: 11 pages, 7 figures. Lattice 2021 contribution 306 (combines 306 and 501)

Partially twisted boundary conditions are widely used for improving the momentum resolution in lattice computations of hadronic correlation functions. The method is however expensive since every additional twist requires computing additional propagators. We propose a novel variance reduction technique that exploits statistical correlations to reduce the overall cost for computing correlators with additional twist angles. We explain and demonstrate the method for meson 2pt and 3pt functions.

We are presenting our ongoing Lattice QCD study on $B - \bar{B}$ mixing on several RBC/UKQCD and JLQCD ensembles with 2+1 dynamical-flavour domain-wall fermions, including physical-pion-mass ensembles. We are extracting bag parameters $B_{B_d}$ and $B_{B_s}$ using the full 5-mixing-operator basis to study both Standard-Model mixing as well as Beyond the Standard Model mixing, using a fully correlated combined fit to two-point functions and ratios of three-point and two-point functions. Using 15 different lattice ensembles we are simulating a range of heavy-quark masses from below the charm-quark mass to just below the bottom-quark mass.

Precise theoretical predictions derived from the Standard Model are a key ingredient in searches for new physics in the flavor sector. The large mass and long lifetime of the $b$ quark make processes involving $b$ quarks of particular interest. We use lattice simulations to perform nonperturbative QCD calculations for semileptonic $B_{(s)}$ decays. We present results from our determinations of $B_s\to D_s \ell \nu$ and $B_s\to K \ell \nu$ semileptonic form factors and provide an outlook for our $B\to \pi\ell\nu$ calculation. In addition we discuss the determination of $R$-ratios testing lepton-flavor universality and suggest use of an improved ratio. Our calculations are based on the set of 2+1 flavor domain wall Iwasaki gauge field configurations generated by the RBC-UKQCD collaboration featuring three lattice spacings of $1/a = 1.78$, $2.38$, and $2.79\,\text{GeV}$. Heavy $b$-quarks are simulated using the relativistic heavy quark action., Comment: 6 pages, 3 figures, Proceedings of The 40th International Conference on High Energy Physics, ICHEP-2020; Jul 28-Aug 6, 2020, Prague, Czech Republic

A nonperturbative determination of the energy-momentum tensor is essential for understanding the physics of strongly coupled systems. The ability of the Wilson flow to eliminate divergent contact terms makes it a practical method for renormalizing the energy-momentum tensor on the lattice. In this paper, we utilize the Wilson flow to define a procedure to renormalize the energy-momentum tensor for a three-dimensional massless scalar field in the adjoint of $SU(N)$ with a $\varphi^4$ interaction on the lattice. In this theory the energy-momentum tensor can mix with $\varphi^2$ and we present numerical results for the mixing coefficient for the $N=2$ theory., Comment: 29 pages, 9 figures

We present updates for our nonperturbative lattice QCD calculations to determine semileptonic form factors for exclusive $B\to \pi\ell\nu$, $B\to D \ell\nu$, $B_s\to K\ell \nu$, and $B_s\to D_s\ell\nu$ decays. Our calculation is based on RBC-UKQCD's set of $2+1$-dynamical-flavor gauge field ensembles. In the valence sector we use domain wall fermions for up/down, strange and charm quarks, whereas bottom quarks are simulated with the relativistic heavy quark action. The continuum limit is based on three lattice spacings. Using kinematical $z$ expansions we aim to obtain form factors over the full $q^2$ range. These form factors are the basis for predicting ratios addressing lepton flavor universality or, when combined with experimental results, to obtain CKM matrix elements $|V_{ub}|$ and $|V_{cb}|$., Comment: 14 pages, 10 figures, Proceedings of the 37th International Symposium on Lattice Field Theory, 16-22 June 2019, Wuhan, China

In order to reach (sub-)per cent level precision in lattice calculations of the hadronic vacuum polarisation, isospin breaking corrections must be included. This requires introducing QED on the lattice, and the associated finite-size effects are potentially large due to the absence of a mass gap. This means that the finite-size effects scale as an inverse polynomial in $L$ rather than being exponentially suppressed. Considering the $\mathcal{O}(\alpha)$ corrected hadronic vacuum polarisation in QED$_{\mathrm{L}}$ with scalar QED as an effective theory, we show that the first possible term, which is of order $1/L^{2}$, vanishes identically so that the finite-size effects start at order $1/L^{3}$. This cancellation is understood from the neutrality of the currents involved, and we show that this cancellation is universal by also including form factors for the pions. We find good numerical agreement with lattice perturbation theory calculations, as well as, up to exponentially suppressed terms, scalar QED lattice simulations., Comment: Proceedings for 37th International Symposium on Lattice Field Theory - Lattice2019, 16-22 June 2019, Wuhan, China

In the holographic approach to cosmology, cosmological observables are described in terms of correlators of a three-dimensional boundary quantum field theory. As a concrete model, we study the 3$d$ massless $SU(N)$ scalar matrix field theory. In this work, we focus on the renormalisation of the energy-momentum tensor 2-point function, which can be related to the CMB power spectra. Here we present a non-perturbative procedure to remove divergences resulting from the loss of translational invariance on the lattice, by imposing Ward identities. This will allow us to make predictions for the CMB power spectra in the regime where the dual QFT is non-perturbative., Comment: 7 pages, 2 figures, presented at the 37th International Symposium on Lattice Field Theory - LATTICE2019 - 16-22 June, 2019, Wuhan, China

Semi-leptonic $B_s \to K \ell \nu$ and $B_s \to D_s \ell \nu$ decays provide an alternative $b$-decay channel to determine the CKM matrix elements $|V_{ub}|$ and $|V_{cb}|$ or to obtain $R$-ratios to investigate lepton flavor universality violations. In addition, these decays may shed further light on the discrepancies seen in the analysis of inclusive vs. exclusive decays. Using the nonperturbative methods of lattice QCD, theoretical results are obtained with good precision and full control over systematic uncertainties. This talk will highlight ongoing efforts of the $B$-physics program by the RBC-UKQCD collaboration., Comment: Talk presented at The 36th Annual International Symposium on Lattice Field Theory, 22-28 July, 2018, Michigan State University, East Lansing, Michigan, USA; 7 pages, 5 figures

A determination of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon from lattice QCD aiming at a precision of $1\%$ requires to include isospin breaking corrections in the computation. We present a lattice calculation of the QED and strong isospin breaking corrections to the hadronic vacuum polarization with Domain Wall fermions. The results are obtained using quark masses which are tuned such that pion and kaon masses agree with their physical values including isospin breaking corrections., Comment: 7 pages, 4 figures, presented at the 36th Annual International Symposium on Lattice Field Theory - LATTICE2018 - 22-28 July, 2018, Michigan State University, East Lansing, Michigan, USA

First-principles studies of strongly-interacting hadronic systems using lattice quantum chromodynamics (QCD) have been complemented in recent years with the inclusion of quantum electrodynamics (QED). The aim is to confront experimental results with more precise theoretical determinations, e.g. for the anomalous magnetic moment of the muon and the CP-violating parameters in the decay of mesons. Quantifying the effects arising from enclosing QED in a finite volume remains a primary target of investigations. To this end, finite-volume corrections to hadron masses in the presence of QED have been carefully studied in recent years. This paper extends such studies to the self-energy of moving charged hadrons, both on and away from their mass shell. In particular, we present analytical results for leading finite-volume corrections to the self-energy of spin-0 and spin-$\frac{1}{2}$ particles in the presence of QED on a periodic hypercubic lattice, once the spatial zero mode of the photon is removed, a framework that is called $\mathrm{QED}_{\mathrm{L}}$. By altering modes beyond the zero mode, an improvement scheme is introduced to eliminate the leading finite-volume corrections to masses, with potential applications to other hadronic quantities. Our analytical results are verified by a dedicated numerical study of a lattice scalar field theory coupled to $\mathrm{QED}_{\mathrm{L}}$. Further, this paper offers new perspectives on the subtleties involved in applying low-energy effective field theories in the presence of $\mathrm{QED}_{\mathrm{L}}$, a theory that is rendered non-local with the exclusion of the spatial zero mode of the photon, clarifying recent discussions on this matter., Comment: 57 pages, 10 figures, version accepted for publication in Phys. Rev. D

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

We present results for the QED and strong isospin breaking corrections to the hadronic vacuum polarization using $N_f=2+1$ Domain Wall fermions. QED is included in an electro-quenched setup using two different methods, a stochastic and a perturbative approach. Results and statistical errors from both methods are directly compared with each other., Comment: 8 pages, 6 figures, presented at the 35th International Symposium on Lattice Field Theory (Lattice 2017), Granada, Spain, June 18-24, 2017

We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among physical observables thus tackling the critical slowing down towards the continuum limit. We present a comparison of costs of the new algorithms with the standard HMC evolution for pure gauge fields, studying the autocorrelation times for various quantities including the topological charge., Comment: 8 pages, 2 figures, Lattice 2017 conference proceedings

The Wilson-Fisher fixed point with $O(N)$ universality in three dimensions is studied using the renormalisation group. It is shown how a combination of analytical and numerical techniques determine global fixed point solutions to leading order in the derivative expansion for real or purely imaginary fields with moderate numerical effort. Universal and non-universal quantitites such as scaling exponents and mass ratios are computed, for all $N$, together with local fixed point coordinates, radii of convergence, and parameters which control the asymptotic behaviour of the effective action. We also explain when and why finite-$N$ results do not converge pointwise towards the exact infinite-$N$ limit. In the regime of purely imaginary fields, a new link between singularities of fixed point effective actions and singularities of their counterparts by Polchinski are established. Implications for other theories are indicated., Comment: 28 pages, 10 figures, v2: explanations and refs added, to appear (NPB)

We present an exploratory study of the electromagnetic corrections to meson masses and the hadronic vacuum polarization using $N_f=2+1$ Domain Wall fermions. These corrections are estimated with two different approaches, a stochastic approach using $U(1)$ gauge configurations for the photon fields, and a perturbative approach through a QED perturbative expansion of the QCD+QED path integral. We compare results and statistical errors from both methods., Comment: 14 pages, 11 figures, presented at the 34th annual International Symposium on Lattice Field Theory, 24-30 July 2016, University of Southampton, UK

We present RBC/UKQCD's charm project using $N_f=2+1$ flavour ensembles with inverse lattice spacings in the range $1.73-2.77\,\mathrm{GeV}$ and two physical pion mass ensembles. Domain wall fermions are used for the light as well as the charm quarks. We discuss our strategy for the extraction of the decay constants $f_D$ and $f_{D_s}$ and their extrapolation to the continuum limit, physical pion masses and the physical heavy quark mass. Our preliminary results are $f_D=208.7(2.8)\,\mathrm{MeV}$ and $f_{D_s}=246.4(1.9)\,\mathrm{MeV}$ where the quoted error is statistical only. We outline our current approach to extend the reach in the heavy quark mass and present preliminary results., Comment: 7 pages, 4 figures, Lattice 2016

We present preliminary results for the strange leading-order hadronic contribution to the anomalous magnetic moment of the muon using RBC/UKQCD physical point domain wall fermions ensembles. We discuss various analysis strategies in order to constrain the systematic uncertainty in the final result.

We provide an overview of RBC/UKQCD's charm project on 2+1 flavour physical pion mass ensembles using M\"obius Domain Wall Fermions for the light as well as for the charm quark. We discuss the analysis strategy in detail and present results at the different stages of the analysis for $D$ and $D_s$ decay constants as well as the bag and $\xi$ parameters. We also discuss future approaches to extend the reach in the heavy quark mass., Comment: 14 pages, 7 figures, The 33rd International Symposium on Lattice Field Theory (Lattice2015)

We discuss first results for the computation of short distance contributions to semileptonic form factors for the rare $B$ decays $B \to K^{*} \ell^+\ell^-$ and $B_s \to \phi \ell^+ \ell^-$. Our simulations are based on RBC/UKQCD's $N_f=2+1$ ensembles with domain wall light quarks and the Iwasaki gauge action. For the valence $b$-quark we chose the relativistic heavy quark action., Comment: 7 pages, 1 table, 3 figures, presented at the 33rd International Symposium on Lattice Field Theory (Lattice2015), July 14-18, 2015, Kobe, Japan

We develop an improved lattice action for heavy quarks based on Brillouin-type fermions, that have excellent energy-momentum dispersion relation. The leading discretization errors of $O(a)$ and $O(a^2)$ are eliminated at tree-level. We carry out a scaling study of this improved Brillouin fermion action on quenched lattices by calculating the charmonium energy-momentum dispersion relation and hyperfine splitting. We present a comparison to standard Wilson fermions and domain-wall fermions., Comment: 33 pages, 23 figures, minor changes are made, a version published in JHEP

We present steps towards the computation of the leading-order hadronic contribution to the muon anomalous magnetic moment on RBC/UKQCD physical point DWF ensembles. We discuss several methods for controlling and reducing uncertainties associated to the determination of the HVP form factor., Comment: presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, New York, NY, USA

We present results showing that Domain Wall fermions are a suitable discretisation for the simulation of heavy quarks. This is done by a continuum scaling study of charm quarks in a M\"obius Domain Wall formalism using a quenched set-up. We find that discretisation effects remain well controlled by the choice of Domain Wall parameters preparing the ground work for the ongoing dynamical $2+1f$ charm program of RBC/UKQCD., Comment: The 32nd International Symposium on Lattice Field Theory

We present scaling studies for heavy-quark observables calculated with an $O(a^2)$-improved fermion action on tree-level Symanzik improved gauge configurations. Lattices of $1/a = $ 2.0-3.8 GeV with an equal physical volume 1.6 fm are used. The results are compared with the standard domain-wall and naive Wilson fermions., Comment: 7 pages, 3 figures, presented at the 32nd International Symposium on Lattice Field Theory, 23-28 June, 2014, Colombia University, New York, USA

We compute the Adler function on the lattice from vacuum polarization data with twisted boundary conditions using numerical derivatives. The study is based on CLS ensembles with two flavours of $O(a)$ improved Wilson fermions. We extrapolate the lattice data for the Adler function to the continuum limit and to the physical pion mass and analyze its dependence on the momentum transfer. We discuss the application of this method to the extraction of the $u,d$ contribution to $a_\mu^{\mathrm{HLO}}$., Comment: 7 pages, 3 figures, presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), June 23-28 2014, New York, USA

We investigate a new class of improved relativistic fermion action on the lattice with a criterion to give excellent energy-momentum dispersion relation as well as to be consistent with tree-level $O\left(a^{2}\right)$-improvement. Main application in mind is that for heavy quark for which $ma\simeq O(0.5)$. We present tree-level results and a scaling study on quenched lattices., Comment: 7 pages, 8 figures, presented at the 31st International Symposium on Lattice Field Theory (LATTICE 2013), July 29 - August 3, 2013, Mainz, Germany

We use a lattice determination of the hadronic vacuum polarization tensor to study the associated Ward identities and compute the Adler function. The vacuum polarization tensor is computed from a combination of point-split and local vector currents, using two flavours of O($a$)-improved Wilson fermions. Partially twisted boundary conditions are employed to obtain a fine momentum resolution. The modifications of the Ward identities by lattice artifacts and by the use of twisted boundary conditions are monitored. We determine the Adler function from the derivative of the vacuum polarization function over a large region of momentum transfer $q^2$. As a first account of systematic effects, a continuum limit scaling analysis is performed in the large $q^2$ regime., Comment: 7 pages, 4 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle physics community. More specifically, we report on the determination of the light-quark masses, the form factor f+(0), arising in semileptonic K -> pi transition at zero momentum transfer, as well as the decay constant ratio fK/fpi of decay constants and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)LxSU(2)R and SU(3)LxSU(3)R Chiral Perturbation Theory and review the determination of the BK parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, for this review, we focus on D- and B-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant alpha_s., Comment: Several errors of transcription in the entries of Table 1 have been corrected. The entries of Table 1 now agree with the final results quoted in the main text. 324 pages, 26 figures, 118 tables, 697 references

The CKM matrix element $|V_{us}|$ can be extracted from the experimental measurement of semileptonic $K\to\pi$ decays. The determination depends on theory input for the corresponding vector form factor in QCD. We present a preliminary update on our efforts to compute it in $N_f=2+1$ lattice QCD using domain wall fermions for several lattice spacings and with a lightest pion mass of about $170\,\mathrm{MeV}$. By using partially twisted boundary conditions we avoid systematic errors associated with an interpolation of the form factor in momentum-transfer, while simulated pion masses near the physical point reduce the systematic error due to the chiral extrapolation., Comment: 7 pages, 7 figures, Lattice 2012 PoS

We report on our ongoing project to calculate the leading hadronic contribution to the anomalous magnetic moment of the muon a_mu^HLO using two dynamical flavours of non-perturbatively O(a) improved Wilson fermions. In this study, we changed the vacuum polarisation tensor to a combination of local and point-split currents which significantly reduces the numerical effort. Partially twisted boundary conditions allow us to improve the momentum resolution of the vacuum polarisation tensor and therefore the determination of the leading hadronic contribution to (g-2)_mu. We also extended the range of ensembles to include a pion mass below 200 MeV which allows us to check the non-trivial chiral behaviour of a_mu^HLO., Comment: 7 pages, 3 figures, 1 table, talk presented at the 30th International Symposium on Lattice Field Theory (Lattice2012), Cairns, Australia

We report on our computation of the leading hadronic contribution to the anomalous magnetic moment of the muon using two dynamical flavours of non-perturbatively O(a) improved Wilson fermions. The strange quark is introduced in the quenched approximation. Partially twisted boundary conditions are applied to improve the momentum resolution in the relevant integral. Our results, obtained at three different values of the lattice spacing, allow for a preliminary study of discretization effects. We explore a wide range of lattice volumes, namely 2 fm < L < 3 fm, with pion masses from 600 to 280 MeV and discuss different chiral extrapolations to the physical point. We observe a non-trivial dependence of a_mu(HLO) on m_pi especially for small pion masses. The final result, a_mu(HLO)=618(64)*10^(-10), is obtained by considering only the quark connected contribution to the vacuum polarization. We present a detailed analysis of systematic errors and discuss how they can be reduced in future simulations., Comment: Version accepted for publication in JHEP. Discussions extended in sections 3.1 and 3.2, results unchanged. 19 pages, 7 figures, 3 tables

We compute the leading hadronic contribution to the anomalous magnetic moment of the muon a_mu^HLO using two dynamical flavours of non-perturbatively O(a) improved Wilson fermions. By applying partially twisted boundary conditions we are able to improve the momentum resolution of the vacuum polarisation, an important ingredient for the determination of the leading hadronic contribution. We check systematic uncertainties by studying several ensembles, which allows us to discuss finite size effects and lattice artefacts. The chiral behavior of a_mu^HLO turns out to be non-trivial, especially for small pion masses., Comment: 7 pages, 3 figures, 1 table, contribution to LATTICE 2011

We present a lattice determination of the leptonic decay constant F_Ds of the Ds-meson using its mass and F_K as experimental input. Setting the scale with F_K=160 MeV, our final result is F_Ds = 252(9) MeV. The error contains all uncertainties apart from the quenched approximation. Setting the scale with the nucleon mass instead leads to an increase of 3(1) MeV of the leptonic decay constant which might indicate a small quenching error., Comment: 8 pages, 1 figure, references added, mistake in the computation of the quenched scale ambiguity of the decay constant corrected