Testing the CKM parameters with parity violating longitudinal muon polarization in K+ → π+μ+μ−

Rare kaon decays

“…However, while the muon pair couples via a vector current (μµ) V in the photon amplitude, the electroweak shortdistance mechanism also contains an axial vector piece (μµ) A . The interference term between these contributions is odd under parity and gives rise to a parity-violating longitudinal µ + polarization, which can be observed as an asymmetry [44][45][46][47]. Γ R(L) denotes the rate of producing a right-(left-) handed…”

LAB observables for the muon polarization in K+→π+μ+μ−

“…One can define the longitudinal µ + polarization asymmetry ∆ (rest) long by using an expression similar to (5), and taking the polarization vectors s + to be parallel to the µ + three-momenta in the kaon rest frame. As we have discussed below, ∆ (rest) long will in general be different from ∆ (LAB) long , defined by taking s + parallel to p + in the LAB system, if the decaying K L are in flight.…”

“…In the Standard Model (SM), the effect arises from the interference between the one-photon amplitude and one-loop Z-penguin and W -box Feynman diagrams [1,5,6]. It has been shown [1] that the muon polarizations can be predicted in terms of the well-known K l3 semileptonic decay form factors, and a parameter ξ that carries "clean" information (that means, relatively free from nonperturbative effects) on the quark masses and mixing angles.…”

Precise determinations of the CKM matrix from CP-asymmetries in B-decays and

“…As a recent analysis [30] shows it will be difficult to reach ∆η = ±0.03 this way if | V cb | is determined in tree level Bdecays. Our strategy then is to find η from CP asymmetries in B decays and use in K + → π + µμ [32,33,34] are also theoretically rather clean and are useful in this respect. In particular as demonstrated in [30],…”