Direct CP Violation in K→μ+μ−

Abstract

A rare decay KL → µ + µ − has been measured precisely, while a rare decay KS → µ + µ − will be observed by an upgrade of the LHCb experiment. Although both processes are almost CPconserving decays, we point out that an interference contribution between KL and KS in the kaon beam emerges from a genuine direct CP violation. It is found that the interference contribution can change KS → µ + µ − standard-model predictions at O(60%). We also stress that an unknown sign of A(KL → γγ) can be determined by a measurement of the interference, which can much reduce a theoretical uncertainty of B(KL → µ + µ − ). We also investigate the interference in a new physics model, where the K / K tension is explained by an additional Z-penguin contribution.

Probing SUSY effects in K0 S → μ+μ−

“…In the following, we derive some relations between the two branching fractions, for a better interpretation of the results of our scans. In the case in which new physics enters only inC S andC P =C S (pure lefthanded MSSM scenario), the following relations between the branching fractions of K 0 S and K 0 L decaying into µ + µ − can be established: 21) and 22) where m d terms are discarded for simplicity. The long-distance term Re N LD L holds the unknown sign from A µ Lγγ , which changes the correlation significantly, as will be shown.…”

“…Experimentally, one can also access an effective branching ratio of K 0 S → µ + µ − [21] which includes an interference contribution with K 0 L → µ + µ − in the neutral kaon sample. We obtain 26) where the dilution factor D is a measure of the initial (t = 0) K 0 -K 0 asymmetry,…”

“…A pure K 0 L → µ + µ − background can be subtracted by a combination of simultaneous measurement of K 0 S → π + π − events and knowledge of the observed value of B(K 0 L → µ + µ − ) in eq. (2.25) [21]. The decay-time acceptance of the LHCb detector is parametrized by ε(t) = exp(−βt) with β 86 ns −1 , and the range of the detector for selecting K 0 → µ + µ − is t min = 8.95 ps= 0.1τ S and t max = 130 ps = 1.45τ S .…”

“…Given the potential measurement of an effective branching ratio by different dilution factors D > 0 and D < 0 using K − tagging and K + tagging [21], respectively, the direct CP asymmetry can be measured using the difference…”

“…The Standard Model (SM) expectation is (5.18 ± 1.50 LD ± 0.02 SD ) × 10 −12 [19][20][21], where the first uncertainty comes from the long-distance (LD) contribution and the second one comes from the short-distance (SD) contribution. On the other hand, the current experimental upper bound is 8 × 10 −10 at 90% C.L., using 3 fb −1 of LHCb data [22].…”