arXiv subjects

P. A. Boyle

Publications and source records attributed to P. A. Boyle.

At least 19 recordsLinked to original sources

arXiv2026

A note on momentum subtraction schemes for quark bilinears and semileptonic operators

In this work we examine a family of regularization invariant (RI) symmetric momentum (SMOM) schemes for semi-leptonic operators. By working with chirally symmetric and massless QCD, we relate the semi-leptonic operators with their corresponding flavor-changing vector currents, whose renormalization in pure QCD is protected by the Ward identity. For the latter, we extend the original RI/SMOM scheme [Sturm et al. 2009] to a family projectors suitable to be promoted to the semi-leptonic case and demonstrate their equivalence to Ref. [Gorbahn et al. 2023], relevant in particular for the perturbative calculation of the corresponding Wilson coefficients.

hep-lat↗

arXiv2024

The long-distance window of the hadronic vacuum polarization for the muon g-2

We provide the first ab-initio calculation of the Euclidean long-distance window of the isospin symmetric light-quark connected contribution to the hadronic vacuum polarization for the muon $g-2$ and find $a_μ^{\rm LD,iso,conn,ud} = 411.4(4.3)(2.4) \times 10^{-10}$. We also provide the currently most precise calculation of the total isospin symmetric light-quark connected contribution, $a_μ^{\rm iso,conn,ud} = 666.2(4.3)(2.5) \times 10^{-10}$, which is more than 4$σ$ larger compared to the data-driven estimates of Boito et al. 2022 and 1.7$σ$ larger compared to the lattice QCD result of BMW20.

hep-lat↗

arXiv2023

Simulating rare kaon decays $K^{+}\toπ^{+}\ell^{+}\ell^{-}$ using domain wall lattice QCD with physical light quark masses

We report the first calculation using physical light-quark masses of the electromagnetic form factor $V(z)$ describing the long-distance contributions to the $K^+\toπ^+\ell^+\ell^-$ decay amplitude. The calculation is performed on a 2+1 flavor domain wall fermion ensemble with inverse lattice spacing $a^{-1}=1.730(4)$GeV. We implement a Glashow-Iliopoulos-Maiani cancellation by extrapolating to the physical charm-quark mass from three below-charm masses. We obtain $V(z=0.013(2))=-0.87(4.44)$, achieving a bound for the value. The large statistical error arises from stochastically estimated quark loops.

hep-lat↗

arXiv2023

An update of Euclidean windows of the hadronic vacuum polarization

We compute the standard Euclidean window of the hadronic vacuum polarization using multiple independent blinded analyses. We improve the continuum and infinite-volume extrapolations of the dominant quark-connected light-quark isospin-symmetric contribution and address additional sub-leading systematic effects from sea-charm quarks and residual chiral-symmetry breaking from first principles. We find $a_μ^{\rm W} = 235.56(65)(50) \times 10^{-10}$, which is in $3.8σ$ tension with the recently published dispersive result of Colangelo et al., $a_μ^{\rm W} = 229.4(1.4) \times 10^{-10}$, and in agreement with other recent lattice determinations. We also provide a result for the standard short-distance window. The results reported here are unchanged compared to our presentation at the Edinburgh workshop of the g-2 Theory Initiative in 2022.

hep-lat↗

arXiv2022

Lattice determination of $I= 0$ and 2 $ππ$ scattering phase shifts with a physical pion mass

Phase shifts for $s$-wave $ππ$ scattering in both the $I=0$ and $I=2$ channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of $32^3\times 64$. These results support our recent study of direct CP violation in $K\toππ$ decay \cite{Abbott:2020hxn}, improving our earlier 2015 calculation \cite{Bai:2015nea}. The phase shifts are determined for both stationary and moving $ππ$ systems, at three ($I=0$) and four ($I=2$) different total momenta. We implement several $ππ$ interpolating operators including a scalar bilinear "$σ$" operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem (GEVP) method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy.

hep-lat↗

arXiv2019

QED corrections to leptonic decay rates

RBC/UKQCD is preparing a calculation of leptonic decay rates including isospin breaking corrections using a perturbative approach to include NLO contributions from QED effects. We present preliminary numerical results for a contribution to the leptonic pion decay rate and report on exploratory studies of computational techniques based on all-to-all propagators.

hep-lat↗

arXiv2018

Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment

We present a first-principles lattice QCD+QED calculation at physical pion mass of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. The total contribution of up, down, strange, and charm quarks including QED and strong isospin breaking effects is found to be $a_μ^{\rm HVP~LO}=715.4(16.3)(9.2) \times 10^{-10}$, where the first error is statistical and the second is systematic. By supplementing lattice data for very short and long distances with experimental R-ratio data using the compilation of Ref. [1], we significantly improve the precision of our calculation and find $a_μ^{\rm HVP~LO} = 692.5(1.4)(0.5)(0.7)(2.1) \times 10^{-10}$ with lattice statistical, lattice systematic, R-ratio statistical, and R-ratio systematic errors given separately. This is the currently most precise determination of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. In addition, we present the first lattice calculation of the light-quark QED correction at physical pion mass.

hep-lat↗

arXiv2017

Heavy Domain Wall Fermions: The RBC and UKQCD charm physics program

We review the domain wall charm physics program of the RBC and UKQCD collaborations based on simulations including ensembles with physical pion mass. We summarise our current set-up and present a status update on the decay constants $f_D$, $f_{D_s}$, the charm quark mass, heavy-light and heavy-strange bag parameters and the ratio $ξ$.

hep-lat↗

arXiv2017

Neutral kaon mixing beyond the Standard Model with nf=2+1 chiral fermions part II: Non Perturbative Renormalisation of the $ΔF=2$ four-quark operators

We compute the renormalisation factors (Z-matrices) of the $ΔF=2$ four-quark operators needed for Beyond the Standard Model (BSM) kaon mixing. We work with nf=2+1 flavours of Domain-Wall fermions whose chiral-flavour properties are essential to maintain a continuum-like mixing pattern. We introduce new RI-SMOM renormalisation schemes, which we argue are better behaved compared to the commonly-used corresponding RI-MOM one. We find that, once converted to MS, the Z-factors computed through these RI-SMOM schemes are in good agreement but differ significantly from the ones computed through the RI-MOM scheme. The RI-SMOM Z-factors presented here have been used to compute the BSM neutral kaon mixing matrix elements in the companion paper [1]. We argue that the renormalisation procedure is responsible for the discrepancies observed by different collaborations, we will investigate and elucidate the origin of these differences throughout this work.

hep-lat↗

arXiv2016

Domain wall QCD with physical quark masses

We present results for several light hadronic quantities ($f_π$, $f_K$, $B_K$, $m_{ud}$, $m_s$, $t_0^{1/2}$, $w_0$) obtained from simulations of 2+1 flavor domain wall lattice QCD with large physical volumes and nearly-physical pion masses at two lattice spacings. We perform a short, O(3)%, extrapolation in pion mass to the physical values by combining our new data in a simultaneous chiral/continuum `global fit' with a number of other ensembles with heavier pion masses. We use the physical values of $m_π$, $m_K$ and $m_Ω$ to determine the two quark masses and the scale - all other quantities are outputs from our simulations. We obtain results with sub-percent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including: $f_π$ = 130.2(9) MeV; $f_K$ = 155.5(8) MeV; the average up/down quark mass and strange quark mass in the $\bar {\rm MS}$ scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, $B_K$, in the RGI scheme, 0.750(15) and the $\bar{\rm MS}$ scheme at 3 GeV, 0.530(11).

hep-lat↗

arXiv2016

Lattice calculation of the leading strange quark-connected contribution to the muon $g-2$

We present results for the leading hadronic contribution to the muon anomalous magnetic moment due to strange quark-connected vacuum polarisation effects. Simulations were performed using RBC--UKQCD's $N_f=2+1$ domain wall fermion ensembles with physical light sea quark masses at two lattice spacings. We consider a large number of analysis scenarios in order to obtain solid estimates for residual systematic effects. Our final result in the continuum limit is $a_μ^{(2)\,{\rm had},\,s}=53.1(9)\left(^{+1}_{-3}\right)\times10^{-10}$.

hep-lat↗

arXiv2016

Erratum: Standard-model prediction for direct CP violation in $K\toππ$ decay

In this document we address an error discovered in the ensemble generation for our calculation of the $I=0$ $K\toππ$ amplitude (Phys. Rev. Lett. 115, 212001 (2015), arXiv:1505.07863) whereby the same random numbers were used for the two independent quark flavors, resulting in small but measurable correlations between gauge observables separated by 12 units in the y-direction. We conclude that the effects of this error are negligible compared to the overall errors on our calculation.

hep-lat↗

arXiv2016

Standard-model prediction for direct CP violation in $K\toππ$ decay

We report the first lattice QCD calculation of the complex kaon decay amplitude $A_0$ with physical kinematics, using a $32^3\times 64$ lattice volume and a single lattice spacing $a$, with $1/a= 1.3784(68)$ GeV. We find Re$(A_0) = 4.66(1.00)(1.26) \times 10^{-7}$ GeV and Im$(A_0) = -1.90(1.23)(1.08) \times 10^{-11}$ GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re$(A_0) = 3.3201(18) \times 10^{-7}$ GeV while the second can be used to compute the direct CP violating ratio Re$(\varepsilon'/\varepsilon)=1.38(5.15)(4.59)\times 10^{-4}$, which is $2.1σ$ below the experimental value $16.6(2.3)\times 10^{-4}$. The real part of $A_0$ is CP conserving and serves as a test of our method while the result for Re$(\varepsilon'/\varepsilon)$ provides a new test of the standard-model theory of CP violation, one which can be made more accurate with increasing computer capability.

hep-lat↗

arXiv2015

Calculation of the hadronic vacuum polarization disconnected contribution to the muon anomalous magnetic moment

We report the first lattice QCD calculation of the hadronic vacuum polarization disconnected contribution to the muon anomalous magnetic moment at physical pion mass. The calculation uses a refined noise-reduction technique which enabled the control of statistical uncertainties at the desired level with modest computational effort. Measurements were performed on the $48^3 \times 96$ physical-pion-mass lattice generated by the RBC and UKQCD collaborations. We find $a_μ^{\rm HVP~(LO)~DISC} = -9.6(3.3)(2.3)\times 10^{-10}$, where the first error is statistical and the second systematic.

hep-lat↗

arXiv2015

The Low Energy Constants of $SU(2)$ Partially Quenched Chiral Perturbation Theory from $N_{f}=2+1$ Domain Wall QCD

We have performed fits of the pseudoscalar masses and decay constants, from a variety of RBC-UKQCD domain wall fermion ensembles, to $SU(2)$ partially quenched chiral perturbation theory at next-to leading order (NLO) and next-to-next-to leading order (NNLO). We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low energy constants, which we compare to other lattice and phenomenological determinations. We discuss the size of successive terms in the chiral expansion and use our large set of low energy constants to make predictions for mass splittings due to QCD isospin breaking effects and the S-wave $ππ$ scattering lengths. We conclude that, for the range of pseudoscalar masses explored in this work, $115~\mathrm{MeV} \lesssim m_{\rm PS} \lesssim 430~\mathrm{MeV}$, the NNLO $SU(2)$ expansion is quite robust and can fit lattice data with percent-scale accuracy.

hep-lat↗

arXiv2015

$K \rightarrow ππ$ $ΔI=3/2$ decay amplitude in the continuum limit

We present new results for the amplitude $A_2$ for a kaon to decay into two pions with isospin $I=2$: Re$A_2 = 1.50(4)_\mathrm{stat}(14)_\mathrm{syst}\times 10^{-8}$ GeV; Im$A_2 = -6.99(20)_\mathrm{stat}(84)_\mathrm{syst}\times 10^{-13}$ GeV. These results were obtained from two ensembles generated at physical quark masses (in the isospin limit) with inverse lattice spacings $a^{-1}=1.728(4)$ GeV and $2.358(7)$ GeV. We are therefore able to perform a continuum extrapolation and hence largely to remove the dominant systematic uncertainty from our earlier results, that due to lattice artefacts. The only previous lattice computation of $K\toππ$ decays at physical kinematics was performed using an ensemble at a single, rather coarse, value of the lattice spacing ($a^{-1}\simeq 1.37(1)$ GeV). We confirm the observation that there is a significant cancellation between the two dominant contributions to Re$A_2$ which we suggest is an important ingredient in understanding the $ΔI=1/2$ rule, Re$A_0$/Re$A_2\simeq 22.5$, where the subscript denotes the total isospin of the two-pion final state. Our result for $A_2$ implies that the electroweak penguin contribution to $ε^\prime/ε$ is Re($ε^\prime/ε)_\textrm{EWP}=-(6.6\pm 1.0)\times 10^{-4}$.

hep-lat↗

arXiv2014

Conserved currents for Mobius Domain Wall Fermions

We derive the exactly conserved vector, and almost conserved axial currents for rational approximations to the overlap operator with a general Mobius kernel. The approach maintains manifest Hermiticity, and allows matrix elements of the currents to be constructed at no extra cost after solution of the usual 5d system of equations, similar to the original approach of Furman and Shamir for domain wall Fermions.

hep-lat↗

arXiv2014

A Combined NNLO Lattice-Continuum Determination of $L_{10}^r$

The renormalized next-to-leading-order (NLO) chiral low-energy constant, $L_{10}^r$, is determined in a complete next-to-next-to-leading-order (NNLO) analysis, using a combination of lattice and continuum data for the flavor $ud$ $V-A$ correlator and results from a recent chiral sum-rule analysis of the flavor-breaking combination of $ud$ and $us$ $V-A$ correlator differences. The analysis also fixes two combinations of NNLO low-energy constants, the determination of which is crucial to the precision achieved for $L_{10}^r$. Using the results of the flavor-breaking chiral $V-A$ sum rule obtained with current versions of the strange hadronic $τ$ branching fractions as input, we find $L_{10}^r(m_ρ)\, =\, -0.00346(32)$. This result represents the first NNLO determination of $L_{10}^r$ having all inputs under full theoretical and/or experimental control, and the best current precision for this quantity.

hep-ph↗