Correlations between ε′/ε and rareKdecays in the Littlest Higgs model with T-parity

Abstract

We calculate the CP-violating ratio ε ′ /ε in the Littlest Higgs model with T-parity (LHT) and investigate its correlations with the branching ratios for K L → π 0 νν, K L → π 0 ℓ + ℓ − and K + → π + νν. The resulting correlations are rather strong in the case of K L decays, but less pronounced in the case of K + → π + νν. Unfortunately, they are subject to large hadronic uncertainties present in ε ′ /ε, whose theoretical prediction in the Standard Model (SM) is reviewed and updated here. With the matrix elements of Q 6 (gluon penguin) and Q 8 (electroweak penguin) evaluated in the large-N limit and m MS s (2 GeV) = 100 MeV from lattice QCD, (ε ′ /ε) SM turns out to be close to the data so that significant departures of Br(K L → π 0 νν) and Br(K L → π 0 ℓ + ℓ − ) from the SM expectations are unlikely, while Br(K + → π + νν) can be enhanced even by a factor 5. On the other hand, modest departures of the relevant hadronic matrix elements from their large-N values allow for a consistent description of ε ′ /ε within the LHT model accompanied by large enhancements of Br(K L → π 0 νν) and Br(K L → π 0 ℓ + ℓ − ), but only modest enhancements of Br(K + → π + νν). Note addedAn additional contribution to the Z penguin in the Littlest Higgs model with T-parity has been pointed out in [1,2], which has been overlooked in the present analysis. This contribution leads to the cancellation of the left-over quadratic divergence in the calculation of some rare decay amplitudes. Instead of presenting separate errata to the present work and our papers [3][4][5][6] partially affected by this omission, we have presented a corrected and updated analysis of flavour changing neutral current processes in the Littlest Higgs model with T-parity in [7].

Messages on Flavour Physics Beyond the Standard Model

“…Already in 2006 we have pointed out that in this model S ψφ as large as 0.3 could be obtained [19]. Our updated 2008 analysis [3] shows that S ψφ can easily reach in the LHT model values 0.15−0.20, while higher values are rather unlikely though not excluded.…”

“…In this note I would like to report on the results of various analyses of physics beyond the SM performed by my young and strong collaborators and myself at the Technical University Munich in 2008 [1,2,3,4,5,6,7,8,9].…”

“…There are of course many other known reasons for going beyond the SM and expecting new physics at scales probed by the LHC but I will not repeat them here. While a large fraction of particle physicists bets that this new physics will be supersymmetry, the turbulences on stock markets in this decade teach us that it is wise to have many different shares.In this note I would like to report on the results of various analyses of physics beyond the SM performed by my young and strong collaborators and myself at the Technical University Munich in 2008 [1,2,3,4,5,6,7,8,9].In view of space limitations this presentation will consist basically of a list of messages that summarizes the main results of our papers on new physics, in particular supersymmetry, the Littlest Higgs model with T-parity (LHT) and the Randall-Sundrum (RS) scenario with all particles except the Higgs propagating in the bulk.All our papers deal with flavour violating processes, in particular CP-violating ones. While in these papers we have hopefully cited properly all relevant papers, the list of references presented here is incomplete and I apologize for it.…”

New Physics Signatures in Kaon Decays

“…This ratio has been measured rather precisely [16] Re(ε /ε) exp = (1.66 ± 0.23) · 10 −3 (3.6) and can in principle place strong bounds on the possible NP effects in K L → π 0 νν and K L → π 0 + − . The correlation between ε /ε has been studied explicitly in a number of models, including supersymmetry [31], the Littlest Higgs model with T-parity [32], the Randall-Sundrum model with SM bulk gauge symmetry [33], the SM with a sequential fourth generation [34] and the modified electroweak penguin scenario [35]. The common outcome of all these studies is that in order…”

Signatures of extra gauge bosons in the littlest Higgs model withTparity at future colliders

“…A H is usually the lightest T-odd particle (LTP) which cannot further decay into the SM particles and thus plays as the dark matter candidate. With the allowed low mass scale, these extra T-odd particles have significant impacts on the phenomenology [17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]. Large Hadron Collider (LHC) at CERN has a great potential to copiously produce these new particles.…”