New physics patterns in ε′/ε and ε K with implications for rare kaon decays and ∆M K

Abstract

Abstract:The Standard Model (SM) prediction for the ratio ε /ε appears to be significantly below the experimental data. Also ε K in the SM tends to be below the data. Any new physics (NP) removing these anomalies will first of all have impact on flavour observables in the K meson system, in particular on rare decaysRestricting the operators contributing to ε /ε to the SM ones and to the corresponding primed operators, NP contributions to ε /ε are quite generally dominated either by QCD penguin (QCDP) operators Q 6 (Q 6 ) or electroweak penguin (EWP) operators Q 8 (Q 8 ) with rather different implications for other flavour observables. Our presentation includes general models with tree-level Z and Z flavour violating exchanges for which we summarize known results and add several new ones. We also briefly discuss few specific models. The correlations of ε /ε with other flavour observables listed above allow to differentiate between models in which ε /ε can be enhanced. Various DNA-tables are helpful in this respect. We find that simultaneous enhancements of ε /ε, ε K , B(K L → π 0 νν) and B(K + → π + νν) in Z scenarios are only possible in the presence of both left-handed and right-handed flavour-violating couplings. In Z scenarios this is not required but the size of NP effects and the correlation between B(K L → π 0 νν) and B(K + → π + νν) depends strongly on whether QCDP or EWP dominate NP contributions to ε /ε. In the QCDP case possible enhancements of both branching ratios are much larger than for EWP scenario and take place only on the branch parallel to the Grossman-Nir bound, which is in the case of EWP dominance only possible in the absence of NP in ε K . We point out that QCDP and EWP scenarios of NP in ε /ε can also be uniquely distinguished by the size and the sign of NP contribution to ∆M K , elevating the importance of the precise calculation of ∆M K in the SM. We emphasize the importance of the theoretical improvements not only on ε /ε, ε K and ∆M K but also on K L → µ + µ − , K L → π 0 + − , and the K → ππ isospin amplitudes ReA 0 and ReA 2 which would in the future enrich our analysis.

Lattice study of largeNcQCD

“…[59]. ) We also recall the recent discussion by Buras [60] about connections between lattice [61,62] and large-N c [63] calculations of kaon weak matrix elements. The lattice calculations An issue with large N c simulations that we have not resolved is simply that they are expensive.…”

331 Models Facing the Tensions in ΔF = 2 Processes with the Impact on ε ′ /ε, B s → μ + μ − and B →K ∗ μ + μ −

“…This appears presently problematic in view of the findings in [7][8][9]39] that a significant upwards shift ε /ε of at least 5 × 10 −4 is required to bring the theory to agree with the data from from NA48 [10] and KTeV [11,12] collaborations. The question then arises whether including Z − Z mixing we can obtain the required positive shift in ε /ε.…”

Simultaneous interpretation of K and B anomalies in terms of chiral-flavorful vectors

“…The size of the real part for g 12 ρL actually turns out to be constrained severely by the Kaon system measurements such as the indirect CP violation K , and K L → µ + µ − , to be extremely tiny ( O(10 −6 )) (for instance, see Ref. [29]). In contrast, its imaginary part can be moderately larger, which will account for the presently reported / anomaly (deviated by about 3 sigma [7][8][9][10]).…”

“…see Refs. [29,30]). The base transformation among the gauge-and flavor-eigenstates can be made by rotating fields as (under the assumption that neutrinos are massless)…”