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Register a new userExploratory Lattice QCD Study of the Rare Kaon Decay $K^+topi^+ ubar{ u}$
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We report a first, complete lattice QCD calculation of the long-distance contribution to the $K^+topi^+ ubar{ u}$ 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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In Ref [1] we have presented the results of an exploratory lattice QCD computation of the long-distance contribution to the $K^+topi^+ ubar{ u}$ decay amplitude. In the present paper we describe the details of this calculation, which includes the implementation of a number of novel techniques. The $K^+topi^+ ubar{ u}$ 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 $K^+topi^+ ubar{ u}$ decay amplitude, and in particular of the long-distance component. Though this calculation is performed on a small lattice ($16^3times32$) and at unphysical pion, kaon and charm quark masses, $m_pi=420$ 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.
The rare kaon decay $K^+topi^+ ubar{ u}$ 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 $K^+topi^+ ubar{ u}$ decay amplitude at the near-physical pion mass $m_pi=170$ 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.
The rare kaon decays $Ktopi ubar{ u}$ 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 $Ktopi ubar{ u}$ 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 $K^+topi^+ ubar{ u}$. 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 $Ktopiell^+ell^-$, where the focus was made on the $gamma$-exchange diagrams.
Evidence of the $K^+tomu^+ ubar u u$ decay was searched for using E949 experimental data with an exposure of $1.70times 10^{12}$ stopped kaons. The data sample is dominated by the backgrond process $K^+tomu^+ u_mugamma$. An upper limit on the decay rate $Gamma(K^+tomu^+ ubar u u)< 2.4times 10^{-6}Gamma(K^+to all)$ at 90% confidence level was set assuming the Standard Model muon spectrum. The data are presented in such a way as to allow calculation of rates for any assumed $mu^+$ spectrum.
We calculate, for the first time using unquenched lattice QCD, form factors for the rare decay B -> Kll in and beyond the Standard Model. Our lattice QCD calculation utilizes a nonrelativistic QCD formulation for the b valence quarks, the highly improved staggered quark formulation for the light valence quarks, and employs the MILC 2+1 asqtad ensembles. The form factor results, based on the z expansion, are valid over the full kinematic range of q^2. We construct the ratios f0/f+ and fT/f+, which are useful in constraining new physics and verifying effective theory form factor symmetry relations. We also discuss the calculation of Standard Model observables.
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