Can we reach the Zeptouniverse with rare K and B s,d decays?

Abstract

Abstract:The Large Hadron Collider (LHC) will directly probe distance scales as short as 10 −19 m, corresponding to energy scales at the level of a few TeV. In order to reach even higher resolutions before the advent of future high-energy colliders, it is necessary to consider indirect probes of New Physics (NP), a prime example being ∆F = 2 neutral meson mixing processes, which are sensitive to much shorter distance scales. However ∆F = 2 processes alone cannot tell us much about the structure of NP beyond the LHC scales. To identify for instance the presence of new quark flavour-changing dynamics of a left-handed (LH) or right-handed (RH) nature, complementary results from ∆F = 1 rare decay processes are vital. We therefore address the important question of whether NP could be seen up to energy scales as high as 200 TeV, corresponding to distances as small as O(10 −21 ) m -the Zeptouniverse -in rare K and B s,d decays, subject to present ∆F = 2 constraints and perturbativity. We focus in particular on a heavy Z gauge boson. If restricted to purely LH or RH Z couplings to quarks, we find that rare K decays, in particular K + → π + νν and K L → π 0 νν, allow us to probe the Zeptouniverse. On the other hand rare B s and B d decays, which receive stronger ∆F = 2 constraints, allow us to reach about 15 TeV. Allowing for both LH and RH couplings a loosening of the ∆F = 2 constraints is possible, and we find that the maximal values of M Z at which NP effects could be found that are consistent with perturbative couplings are approximately 2000 TeV for K decays and 160 TeV for rare B s,d decays. Because Z exchanges in the B s,d → µ + µ − rare decays are helicity suppressed, we also consider tree-level scalar exchanges for these decays, for which we find that scales close to 1000 TeV can be probed for the analogous pure and combined LH and RH scenarios. We further present a simple idea for an indirect determination of M Z that could be realised at the next linear e + e − or µ + µ − collider and with future precise flavour data.

The Revival of Kaon Flavour Physics

“…In particular the recent indications from the dual QCD approach that FSI are much less relevant for ε /ε than previously expected and the upper bounds on B (1/2) 6 and B (3/2) 8 from this approach diminished significantly hopes that improved lattice calculations would bring the SM prediction for ε /ε to agree with the experimental data, opening thereby an arena for important NP contributions to this ratio. The latest analyses of such contributions in the context of models with tree-level Z and Z exchanges like 331 models, Littlest Higgs model with T-parity can be found in [36,37,[40][41][42]. The analyses in supersymmetric models can be found in [43][44][45].…”

“…Even scales of O(100) TeV can be probed in this manner [35]. The present status of K + → π + νν and K L → π 0 νν within the SM has been presented in [24] with the result…”

“…These formulae should be useful for monitoring the numerical values for these branching ratios within the SM when the CKM input improves. On the other hand the results for both decays obtained in simplified models with flavour violating couplings of the SM Z and of a heavy Z can be found in [36]. A more general study of such models, performed in [37], will be discussed now.…”

Search for \(K^{ + } \to \pi ^{ + }\nu \bar{\nu }\) at the NA62 Experiment at CERN

“…Simultaneous measurements of the K + → π + νν and K L → π 0 νν branching ratio provides determination of the CKM matrix elements in a complementary and independent way with respect to the study of B meson decays. In the SM scenario the expected values of the branching ratio (BR) are [2]:…”

Search forK+→π+νν̄at the NA62 experiment

“…These elements give the largest uncertainty to the BR. Using tree-level observables, one obtains [1,2]: These values are not polluted by contributions from the NP and hence are suitable for a NP search as a deviation from the SM BR value. More precise calculation with the loop-level measurements of the CKM elements assumes the absence of NP and provides the best accuracy for further recalculation of CKM elements from the comparison of theoretical and experimental BR values:…”