arXiv subjects

Christopher T. Sachrajda

Publications and source records attributed to Christopher T. Sachrajda.

At least 19 recordsLinked to original sources

arXiv2026

First Lattice QCD Determination of Lepton-Flavor-Universality Ratios in Light-Meson Leptonic Decays

The ratio of electronic to muonic leptonic decay widths, $R_{e/μ}$, for the light mesons $π$ and $K$, provides a clean test of lepton flavor universality (LFU) and a sensitive probe of physics beyond the Standard Model. Its Standard-Model prediction is exceptionally precise, with the leading uncertainty associated with the structure-dependent (SD) radiative correction of $O(0.1\%)$. As experiments such as PIONEER and NA62 aim for unprecedented precision, this SD correction has become an essential ingredient in precision experiment--theory comparisons. We present the first lattice QCD$+$QED calculation of this SD correction at the physical pion mass and in the continuum limit. We employ the infinite-volume reconstruction (IVR) method with Coulomb-gauge photons, significantly reducing both statistical errors and finite-volume effects. We obtain the Standard-Model predictions, $R_{e/μ}=1.23501(10)\times10^{-4}$ for $π$ and $R_{e/μ}=2.47653(34)\times10^{-5}$ for $K$. Our results reduce the hadronic uncertainty in $R_{e/μ}$, provide the most precise Standard-Model predictions to date, and establish first-principles benchmarks for future high-precision tests of LFU.

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arXiv2026

Lattice Calculation of Light Meson Radiative Leptonic Decays

In this work, we perform a lattice QCD calculation of the branching ratios and the form factors of radiative leptonic decays $P \to \ell ν_\ell γ$ ($P = π, K$) using $N_f=2+1$ domain wall fermion ensembles generated by the RBC and UKQCD collaborations at the physical pion mass. We adopt the infinite volume reconstruction (IVR) method, which extends lattice data to infinite volume and effectively controls the finite volume effects. This study represents a first step toward a complete calculation of radiative corrections to leptonic decays using the IVR method, including both real photon emissions and virtual photon loops. For decays involving a final state electron, collinear radiative corrections, enhanced by the large logarithmic factors such as $\ln(m_π^2/m_e^2)$ and $\ln(m_K^2/m_e^2)$, can reach the level of $O(10\%)$ and are essential at the current level of theoretical and experimental precision. After including these corrections, our result for $π\to eν_eγ$ agrees with the PIBETA measurement; for $K \to eν_eγ$, our results are consistent with the KLOE data and exhibit a $1.7σ$ tension with E36; and for $K \to μν_μγ$, where radiative corrections are negligible, our results confirm the previously observed discrepancies between lattice results and the ISTRA/OKA measurements at large photon energies, and with the E787 results at large muon photon angles.

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arXiv2024

Lattice calculation of electromagnetic corrections to $K\ell3$ decay

We describe a first-principles method to apply lattice QCD to compute the order $α_{\mathrm{EM}}$ corrections to $K\toπ\ellν_\ell$ decay. This method formulates the calculation in infinite volume with the conventional infinite-volume, continuum treatment of QED. Infinite volume reconstruction is used to replace the QCD components of the calculation with finite-volume amplitudes which can be computed in Euclidean space using lattice QCD, introducing finite-volume errors which vanish exponentially as the volume used in the QCD calculation is increased. This approach has also been described in an appendix to the recent paper: arXiv:2304.08026.

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arXiv2023

Long-distance contribution to $ε_K$ from lattice QCD

A lattice QCD approach to the calculation of the long-distance contributions to $ε_K$ is presented. This parameter describes indirect CP violation in $K\toππ$ decay. While the short-distance contribution to $ε_K$ can be accurately calculated in terms of standard model parameters and a single hadronic matrix element, $B_K$, there is a long-distance part which is estimated to be approximately $5\%$ of the total and is more difficult to determine. A method for determining this small but phenomenologically important contribution to $ε_K$ using lattice QCD is proposed and a complete exploratory calculation of the contribution is presented. This exploratory calculation uses an unphysical light quark mass corresponding to a 339 MeV pion mass and an unphysical charm quark mass of 968 MeV, expressed in the $\overline{\mathrm{MS}}$ scheme at 2 GeV. This calculation demonstrates that future work should be able to determine this long-distance contribution from first principles with a controlled error of 10\% or less.

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arXiv2023

Radiative corrections to leptonic decays using infinite-volume reconstruction

Lattice QCD calculations of leptonic decay constants have now reached sub-percent precision so that isospin-breaking corrections, including QED effects, must be included to fully exploit this precision in determining fundamental quantities, in particular the elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, from experimental measurements. A number of collaborations have performed, or are performing, such computations. In this paper we develop a new theoretical framework, based on Infinite-Volume Reconstruction (IVR), for the computation of electromagnetic corrections to leptonic decay widths. In this method, the hadronic correlation functions are first processed theoretically in infinite volume, in such a way that the required matrix elements can be determined non-perturbatively from lattice QCD computations with finite-volume uncertainties which are exponentially small in the volume. The cancellation of infrared divergences in this framework is performed fully analytically. We also outline how this IVR treatment can be extended to determine the QED effects in semi-leptonic kaon decays with a similar degree of accuracy.

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arXiv2023

The $I$ = 1/2 and 3/2 $K-π$ scattering length with domain wall fermions at physical pion mass with all-to-all propagators

We present our calculations for the $I$ = 1/2 and 3/2 $K-π$ 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.

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arXiv2020

Direct CP violation and the $ΔI=1/2$ rule in $K\toππ$ decay from the Standard Model

We present a lattice QCD calculation of the $ΔI=1/2$, $K\toππ$ decay amplitude $A_0$ and $\varepsilon'$, the measure of direct CP-violation in $K\toππ$ decay, improving our 2015 calculation of these quantities. Both calculations were performed with physical kinematics on a $32^3\times 64$ lattice with an inverse lattice spacing of $a^{-1}=1.3784(68)$ GeV. However, the current calculation includes nearly four times the statistics and numerous technical improvements allowing us to more reliably isolate the $ππ$ ground-state and more accurately relate the lattice operators to those defined in the Standard Model. We find ${\rm Re}(A_0)=2.99(0.32)(0.59)\times 10^{-7}$ GeV and ${\rm Im}(A_0)=-6.98(0.62)(1.44)\times 10^{-11}$ GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result ${\rm Re}(A_0)=3.3201(18)\times 10^{-7}$ GeV. These results for $A_0$ can be combined with our earlier lattice calculation of $A_2$ to obtain ${\rm Re}(\varepsilon'/\varepsilon)=21.7(2.6)(6.2)(5.0) \times 10^{-4}$, where the third error represents omitted isospin breaking effects, and Re$(A_0)$/Re$(A_2) = 19.9(2.3)(4.4)$. The first agrees well with the experimental result of ${\rm Re}(\varepsilon'/\varepsilon)=16.6(2.3)\times 10^{-4}$. A comparison of the second with the observed ratio Re$(A_0)/$Re$(A_2) = 22.45(6)$, demonstrates the Standard Model origin of this "$ΔI = 1/2$ rule" enhancement.

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arXiv2020

Finite-volume effects in long-distance processes with massless leptonic propagators

In Ref. [1], a method was proposed to calculate QED corrections to hadronic self energies from lattice QCD without power-law finite-volume errors. In this paper, we extend the method to processes which occur at second-order in the weak interaction and in which there is a massless (or almost massless) leptonic propagator. We demonstrate that, in spite of the presence of the propagator of an almost massless electron, such an infinite-volume reconstruction procedure can be used to obtain the amplitude for the rare kaon decay $K^+\toπ^+ν\barν$ from a lattice quantum chromodynamics computation with only exponentially small finite-volume corrections.

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arXiv2019

Lattice QCD study of the rare kaon decay $K^+\toπ^+ν\barν$ at a near-physical pion mass

The rare kaon decay $K^+\toπ^+ν\barν$ is an ideal process in which to search for signs of new physics and is the primary goal of the NA62 experiment at CERN. In this paper we report on a lattice QCD calculation of the long-distance contribution to the $K^+\toπ^+ν\barν$ decay amplitude at the near-physical pion mass $m_π=170$ MeV. The calculations are however, performed on a coarse lattice and hence with a lighter charm quark mass ($m_c^{\bar{\mathrm{MS}}}(\mbox{3 GeV})=750$ MeV) than the physical one. The main aims of this study are two-fold. Firstly we study the momentum dependence of the amplitude and conclude that it is very mild so that a computation at physical masses even at a single kinematic point would provide a good estimate of the long-distance contribution to the decay rate. Secondly we compute the contribution to the branching ratio from the two-pion intermediate state whose energy is below the kaon mass and find that it is less than 1% after its exponentially growing unphysical contribution has been removed and that the corresponding non-exponential finite-volume effects are negligibly small.

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arXiv2018

Exploratory lattice QCD study of the rare kaon decay $K^+\toπ^+ν\barν$

In Ref [1] we have presented the results of an exploratory lattice QCD computation of the long-distance contribution to the $K^+\toπ^+ν\barν$ decay amplitude. In the present paper we describe the details of this calculation, which includes the implementation of a number of novel techniques. The $K^+\toπ^+ν\barν$ decay amplitude is dominated by short-distance contributions which can be computed in perturbation theory with the only required non-perturbative input being the relatively well-known form factors of semileptonic kaon decays. The long-distance contributions, which are the target of this work, are expected to be of O(5%) in the branching ratio. Our study demonstrates the feasibility of lattice QCD computations of the $K^+\toπ^+ν\barν$ decay amplitude, and in particular of the long-distance component. Though this calculation is performed on a small lattice ($16^3\times32$) and at unphysical pion, kaon and charm quark masses, $m_π=420$ MeV, $m_K=563$ MeV and $m_c^{\overline{\mathrm{MS}}}(\mbox{2 GeV})=863$ MeV, the techniques presented in this work can readily be applied to a future realistic calculation.

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arXiv2017

Effects of finite volume on the $K_L$-$K_S$ mass difference

Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher, and Lellouch and Lüscher, which determine the leading order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second order mixing of the $K^0$ and $\overline{K^0}$ states. We extend the methods of Kim, Sachrajda and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the $K_L$-$K_S$ mass difference $ΔM_K$ and the CP violating parameter $ε_K$ are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finite-volume, two-pion state.

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arXiv2017

Exploratory Lattice QCD Study of the Rare Kaon Decay $K^+\toπ^+ν\barν$

We report a first, complete lattice QCD calculation of the long-distance contribution to the $K^+\toπ^+ν\barν$ decay within the standard model. This is a second-order weak process involving two four-Fermi operators that is highly sensitive to new physics and being studied by the NA62 experiment at CERN. While much of this decay comes from perturbative, short-distance physics there is a long-distance part, perhaps as large as the planned experimental error, which involves nonperturbative phenomena. The calculation presented here, with unphysical quark masses, demonstrates that this contribution can be computed using lattice methods by overcoming three technical difficulties: (i) a short-distance divergence that results when the two weak operators approach each other, (ii) exponentially growing, unphysical terms that appear in Euclidean, second-order perturbation theory, and (iii) potentially large finite-volume effects. A follow-on calculation with physical quark masses and controlled systematic errors will be possible with the next generation of computers.

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arXiv2017

First exploratory calculation of the long-distance contributions to the rare kaon decays $K\toπ\ell^+\ell^-$

The rare decays of a kaon into a pion and a charged lepton/antilepton pair proceed via a flavour changing neutral current and therefore may only be induced beyond tree level in the Standard Model. This natural suppression makes these decays sensitive to the effects of potential New Physics. The CP conserving $K\toπ\ell^+\ell^-$ decay channels however are dominated by a single photon exchange; this involves a sizeable long-distance hadronic contribution which represents the current major source of theoretical uncertainty. Here we outline our methodology for the computation of the long-distance contributions to these rare decay amplitudes using lattice QCD and present the numerical results of the first exploratory studies of these decays in which all but the disconnected diagrams are evaluated. The domain wall fermion ensembles of the RBC and UKQCD collaborations are used, with a pion mass of $M_π\sim 430\,\mathrm{MeV}$ and a kaon mass of $M_{K}\sim 625\,\mathrm{MeV}$. In particular we determine the form factor, $V(z)$, of the $K^+\toπ^+\ell^+\ell^-$ decay from the lattice at small values of $z=q^2/M_{K}^{2}$, obtaining $V(z)=1.37(36),\, 0.68(39),\, 0.96(64)$ for the three values of $z=-0.5594(12),\, -1.0530(34),\, -1.4653(82)$ respectively.

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arXiv2016

Prospects for a lattice computation of rare kaon decay amplitudes II $K\toπν\barν$ decays

The rare kaon decays $K\toπν\barν$ are strongly suppressed in the standard model and widely regarded as processes in which new phenomena, not predicted by the standard model, may be observed. Recognizing such new phenomena requires precise standard model prediction for the braching ratio of $K\toπν\barν$ with controlled uncertainty for both short-distance and long-distance contributions. In this work we demonstrate the feasibility of lattice QCD calculation of the long-distance contribution to rare kaon decays with the emphasis on $K^+\toπ^+ν\barν$. Our methodology covers the calculation of both $W$-$W$ and $Z$-exchange diagrams. We discuss the estimation of the power-law, finite-volume corrections and two methods to consistently combine the long distance contribution determined by the lattice methods outlined here with the short distance parts that can be reliably determined using perturbation theory. It is a subsequent work of our first methodology paper on $K\toπ\ell^+\ell^-$, where the focus was made on the $γ$-exchange diagrams.

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arXiv2015

The kaon semileptonic form factor in Nf=2+1 domain wall lattice QCD with physical light quark masses

We present the first calculation of the kaon semileptonic form factor with sea and valence quark masses tuned to their physical values in the continuum limit of 2+1 flavour domain wall lattice QCD. We analyse a comprehensive set of simulations at the phenomenologically convenient point of zero momentum transfer in large physical volumes and for two different values of the lattice spacing. Our prediction for the form factor is f+(0)=0.9685(34)(14) where the first error is statistical and the second error systematic. This result can be combined with experimental measurements of K->pi decays for a determination of the CKM-matrix element for which we predict |Vus|=0.2233(5)(9) where the first error is from experiment and the second error from the lattice computation.

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arXiv2014

Review of lattice results concerning low energy particle physics

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.

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arXiv2014

Calculating the $K_L-K_S$ mass difference and $ε_K$ to sub-percent accuracy

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, $ΔM_K$ and $ε_K$ 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]

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arXiv2011

Review of lattice results concerning low energy particle physics

We review lattice results relevant for pion and kaon physics with the aim of making them easily accessible to the particle physics community. Specifically, we review the determination of the light-quark masses, the form factor f_+(0), relevant for the semileptonic K -> pi transition at zero momentum transfer as well as the ratio f_K/f_pi of decay constants and discuss the consequences for the elements V_{us} and V_{ud} of the CKM matrix. 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 B_K parameter of neutral kaon mixing. We introduce quality criteria and use these when forming averages. Although subjective and imperfect, these criteria may help the reader to judge different aspects of current lattice computations. Our main results are summarized in section 1.2, but we stress the importance of the detailed discussion that underlies these results and constitutes the bulk of the present review.

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