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تسجيل مستخدم جديدSearch for the rare decay $K^+tomu^+ ubar u u$
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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.
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The rare pion decays ${pi}^+{rightarrow}{mu}^+{ u}_{mu}{ u}bar{ u}$ and ${pi}^+{rightarrow}e^+{ u}_{e}{ u}bar{ u}$ are allowed in the Standard Model but highly suppressed. These decays were searched for using data from the PIENU experiment. A first r
esult for ${Gamma}({pi}^+{rightarrow}{mu}^+{ u}_{mu}{ u}bar{ u})/{Gamma}({pi}^+{rightarrow}{mu}^+{ u}_{mu})<8.6{times}10^{-6}$, and an improved measurement ${Gamma}({pi}^+{rightarrow}{e}^+{ u}_{e}{ u}bar{ u})/{Gamma}({pi}^+{rightarrow}{mu}^+{ u}_{mu})<1.6{times}10^{-7}$ were obtained.
An upper limit on the branching ratio for the decay $K^+ ! rightarrow ! pi^+ u overline{ u}$ is set at $2.4 times 10^{-9}$ at the 90% C.L. using pions in the kinematic region $214~{rm MeV}/c < P_pi < 231~{rm MeV}/c$. An upper limit of $5.2 times 10^
{-10}$ is found on the branching ratio for decays $K^+ ! rightarrow ! pi^+ X^0$, where $X^0$ is any massless, weakly interacting neutral particle. Limits are also set for cases where $M_{X^0}>0$.
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.
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 imp
lementation 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 current status of the experimental study of the rare kaon decay K^+ to pi^+ u bar u at Brookhaven National Laboratory (BNL) by the E787 and E949 collaborations is reported.
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