The leading-order electromagnetic and strong isospin-breaking corrections to the ratio of K_{μ2} and π_{μ2} decay rates are evaluated for the first time on the lattice, following a method recently ...proposed. The lattice results are obtained using the gauge ensembles produced by the European Twisted Mass Collaboration with N_{f}=2+1+1 dynamical quarks. Systematic effects are evaluated and the impact of the quenched QED approximation is estimated. Our result for the correction to the tree-level K_{μ2}/π_{μ2} decay ratio is -1.22(16)%, to be compared to the estimate of -1.12(21)% based on chiral perturbation theory and adopted by the Particle Data Group.
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
→
π
transition at zero momentum transfer as well as the ratio
f
K
/
f
π
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)
L
×SU(2)
R
and SU(3)
L
×SU(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 Sect. 1.2, but we stress the importance of the detailed discussion that underlies these results and constitutes the bulk of the present review.
The leading electromagnetic (e.m.) and strong isospin-breaking corrections to the π+→μ+νγ and K+→μ+νγ leptonic decay rates are evaluated for the first time on the lattice. The results are obtained ...using gauge ensembles produced by the European Twisted Mass Collaboration with Nf=2+1+1 dynamical quarks. The relative leading-order e.m. and strong isospin-breaking corrections to the decay rates are 1.53(19)% for πμ2 decays and 0.24(10)% for Kμ2 decays. Using the experimental values of the πμ2 and Kμ2 decay rates and updated lattice QCD results for the pion and kaon decay constants in isosymmetric QCD, we find that the Cabibbo-Kobayashi-Maskawa matrix element |Vus|=0.22538(46), reducing by a factor of about 1.8 the corresponding uncertainty in the particle data group review. Our calculation of |Vus| allows also an accurate determination of the first-row Cabibbo-Kobayashi-Maskawa unitarity relation |Vud|2+|Vus|2+|Vub|2=0.99988(46). Theoretical developments in this paper include a detailed discussion of how QCD can be defined in the full QCD+QED theory and an improved renormalization procedure in which the bare lattice operators are renormalized nonperturbatively into the regularization independent momentum subtraction (RI'-MOM) scheme and subsequently matched perturbatively at O(αemαs(MW)) into the W-regularization scheme appropriate for these calculations.
We present a nonperturbative lattice calculation of the form factors which contribute to the amplitudes for the radiative decays P → ℓνℓγ, where P is a pseudoscalar meson and ℓ is a charged lepton. ...Together with the nonperturbative determination of the corrections to the processes P → ℓνℓ due to the exchange of a virtual photon, this allows accurate predictions at O(αem) to be made for leptonic decay rates for pseudoscalar mesons ranging from the pion to the Ds meson. We are able to separate unambiguously and nonpertubatively the pointlike contribution, from the structure-dependent, infrared-safe, terms in the amplitude. The fully nonperturbative O(a) improved calculation of the inclusive leptonic decay rates will lead to the determination of the corresponding Cabibbo-Kobayashi-Maskawa matrix elements also at O(αem). Prospects for a precise evaluation of leptonic decay rates with emission of a hard photon are also very interesting, especially for the decays of heavy D and B mesons for which currently only model-dependent predictions are available to compare with existing experimental data.
By imposing twisted boundary conditions on quark fields it is possible to access components of momenta other than integer multiples of 2π/L on a lattice with spatial volume L3. We use chiral ...perturbation theory to study finite-volume effects with twisted boundary conditions for quantities without final-state interactions, such as meson masses, decay constants and semileptonic form factors, and confirm that they remain exponentially small with the volume. We show that this is also the case for partially twisted boundary conditions, in which (some of) the valence quarks satisfy twisted boundary conditions but the sea quarks satisfy periodic boundary conditions. This observation implies that it is not necessary to generate new gluon configurations for every choice of the twist angle, making the method much more practicable. For K→ππ decays we show that the breaking of isospin symmetry by the twisted boundary conditions implies that the amplitudes cannot be determined in general (on this point we disagree with a recent claim).
We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at O(α) are universal; i.e. they are independent of the ...structure of the meson. This is analogous to a similar result for the spectrum but with some fundamental differences, most notably the presence of infrared divergences in decay amplitudes. The leading nonuniversal, structure-dependent terms are of O(1/L2) compared to the O(1/L3) leading nonuniversal corrections in the spectrum. We calculate the universal finite-volume effects, which requires an extension of previously developed techniques to include a dependence on an external three-momentum (in our case, the momentum of the final-state lepton). The result can be included in the strategy proposed in Ref. N. Carrasco et al.,Phys. Rev. D 91, 074506 (2015). for using lattice simulations to compute the decay widths at O(α), with the remaining finite-volume effects starting at order O(1/L2). The methods developed in this paper can be generalized to other decay processes, most notably to semileptonic decays, and hence open the possibility of a new era in precision flavor physics.
We present a lattice QCD calculation of the ΔI = 1/2, K → π π decay amplitude A 0 and ϵ ′, the measure of direct C P violation in K → π π decay, improving our 2015 calculation 1 of these quantities. ...Both calculations were performed with physical kinematics on a 323 × 64 lattice with an inverse lattice spacing of a−1 = 1.3784(68) GeV . However, the current calculation includes nearly 4 times the statistics and numerous technical improvements allowing us to more reliably isolate the π π ground state and more accurately relate the lattice operators to those defined in the standard model. We find Re(A0) = 2.99(0.32)(0.59) × 10−7 GeV and Im(A0) = − 6.98(0.62)(1.44) × 10−11 GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result Re(A0) = 3.3201(18) × 10−7 GeV . These results for A0 can be combined with our earlier lattice calculation of A2 2 to obtain Re(ϵ′/ϵ) = 21.7(2.6)(6.2)(5.0) × 10−4, where the third error represents omitted isospin breaking effects, and Re(A0) / Re(A2) = 19.9(2.3)(4.4). The first agrees well with the experimental result of Re(ϵ′/ϵ) = 16.6(2.3) × 10−4. A comparison of the second with the observed ratio Re(A0) / Re(A2) = 22.45(6), demonstrates the standard model origin of this " ΔI = 1/2 rule" enhancement.
We present results for several light hadronic quantities (f sub(pi), f sub(K), B sub(K), m sub(ud), m sub(s), t super(1/2) sub(0), w sub(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 sub(pi), m sub(K) and m sub(Omega) to determine the two quark masses and the scale-all other quantities are outputs from our simulations. We obtain results with subpercent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including f sub(pi)=130.2(9)MeV; f sub(K)=155.5(8)MeV; the average up/down quark mass and strange quark mass in the MS scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, BK, in the renormalization group invariant scheme, 0.750(15) and the MS scheme at 3 GeV, 0.530(11).
We present a comparison of existing experimental data for the radiative leptonic decays P → ℓνℓγ, where P = K or π and ℓ = e or μ, from the KLOE, PIBETA, E787, ISTRA+ and OKA collaborations with ...theoretical predictions based on the recent non-perturbative determinations of the structure-dependent vector and axial-vector form factors, FV and FA respectively. These were obtained using lattice QCD + QED simulations at order O(αem) in the electromagnetic coupling. We find good agreement with the KLOE data on K → eνeγ decays from which the form factor F+ = FV + FA can be determined. For K → μνμγ decays we observe differences of up to –34 standard deviations at large photon energies between the theoretical predictions and the data from the E787, ISTRA + and OKA experiments and similar discrepancies in some kinematical regions with the PIBETA experiment on radiative pion decays. A global study of all the kaon-decay data within the Standard Model results in a poor fit, largely because at large photon energies the KLOE and E787 data cannot be reproduced simultaneously in terms of the same form factor F+. The discrepancy between the theoretical and experimental values of the form factor F− = FV − FA is even more pronounced. These observations motivate future improvements of both the theoretical and experimental determinations of the structure-dependent form factors F+ and F−, as well as further theoretical investigations of models of "new physics" which might for example, include possible flavor changing interactions beyond V − A and/or nonuniversal corrections to the lepton couplings.
We report the first lattice QCD calculation of the complex kaon decay amplitude A_{0} with physical kinematics, using a 32³×64 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)×10(-7) GeV and Im(A_{0})=-1.90(1.23)(1.08)×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)×10(-7) GeV, while the second can be used to compute the direct CP-violating ratio Re(ϵ^{'}/ϵ)=1.38(5.15)(4.59)×10^{-4}, which is 2.1σ below the experimental value 16.6(2.3)×10(-4). The real part of A_{0} is CP conserving and serves as a test of our method while the result for Re(ϵ^{'}/ϵ) provides a new test of the standard model theory of CP violation, one which can be made more accurate with increasing computer capability.
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