Abstract
The K → μ+μ− decay is often considered to be uninformative of fundamental theory parameters since the decay is polluted by long-distance hadronic effects. We demonstrate that, using very mild assumptions and utilizing time-dependent interference effects, ℬ(KS → μ+μ−)ℓ=0 can be experimentally determined without the need to separate the ℓ = 0 and ℓ = 1 final states. This quantity is very clean theoretically and can be used to test the Standard Model. In particular, it can be used to extract the CKM matrix element combination mid {V}_{ts}{V}_{td}sin left(beta +{beta}_sright)mid approx mid {A}^2{lambda}^5overline{eta}mid with hadronic uncertainties below 1%.
Highlights
Working with decays that involve charged leptons is much simpler than the above-mentioned neutrino modes
We demonstrate that, using very mild assumptions and utilizing time-dependent interference effects, B(KS → μ+μ−) =0 can be experimentally determined without the need to separate the = 0 and = 1 final states
What we show in this work is that under some mild assumptions we can extract the rate, that is, B(KS → (μ+μ−) =0) without separating the = 0 and = 1 final states
Summary
We use the following standard notation [67], where the two neutral kaon mass eigenstates, |KS and |KL , are linear combinations of the flavor eigenstates:. The time dependence for a beam of initial |K0 into a CP-even final state is given by the coefficients. We can draw an important conclusion from the above assumption: AC1 P-odd = 0 This implies that the number of unknown parameters is reduced by two, leaving a single parameter, |AC1 P-even|, for the = 1 final state. As portrayed in eq (2.6), the time-dependent decay rate for an arbitrary neutral kaon initial state is given in general by the sum of four independent functions of time that depend on the experimentally extracted parameters. Within our assumptions, these coefficients depend on the following four theory parameters. We move to discuss the theoretical calculation of B(KS → μ+μ−) =0
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