Bs(d) − $$ \overline{B} $$s(d) mixing and Bs → μ+μ− decay in the NMSSM with the Flavour Expansion Theorem

Abstract

In this paper, motivated by the observation that the Standard Model predictions are now above the experimental data for the mass difference ∆M s(d) , we perform a detailed study of B s(d) −B s(d) mixing and B s → µ + µ − decay in the Z 3 -invariant NMSSM with non-minimal flavour violation, using the recently developed procedure based on the Flavour Expansion Theorem, with which one can perform a purely algebraic mass-insertion expansion of an amplitude written in the mass eigenstate basis without performing any diagrammatic calculations in the interaction/flavour basis. Specifically, we consider the finite orders of mass insertions for neutralinos but the general orders for squarks and charginos, under two sets of assumptions for the squark flavour structures (i.e., while the flavour-conserving off-diagonal element δ LR 33 is kept in both of these two sectors, only the flavour-violating off-diagonal elements δ LL 23 and δ RR i3 (i = 1, 2) are kept in the LL and RR sectors, respectively). Our analytic results are then expressed directly in terms of the initial Lagrangian parameters in the interaction/flavour basis, making it easy to impose the experimental bounds on them. It is found numerically that the NMSSM effects with the above two assumptions for the squark flavour structures can accommodate the observed deviation for ∆M s(d) , while complying with the experimental constraints from the branching ratios of B s → µ + µ − and B → X s γ decays.

∆Ms theory precision confronts flavour anomalies

“…(1.6) for the mass differences could be the starting point of new anomalies arising in the b-sector, see e.g. [14][15][16][17][18]. In addition ∆M s poses very severe constraints on certain BSM models -in particular Z models -that address the observed anomalies in b → s transitions, see e.g.…”

The impact of nonminimal universal extra dimensional model on $$\Delta B=2$$ transitions

“…Besides, in view of the analysis of the effect of the SM Higgs mass on vacuum stability in UED model [73], we consider the sum of KKcontributions up to 5 KK-levels 11 and thereafter we add up the total KK-contributions with the SM counterpart. 12 Moreover, due to the converging 13 nature of KK-summation, the numerical values would not differ drastically whether one considers higher numbers of KK-levels during the evaluation of KK-contributions for the loop diagrams [53][54][55].…”

“…For example the Refs. [8][9][10][11][12][13] depicted how the observables are related to B = 2 transition that can constrain different BSM scenarios. In the current article we consider a class of models, namely Universal Extra Dimensional (UED) [14] scenario, with nonvanishing boundary localised terms (BLTs), where the low energy effective Hamiltonians are controlled by local operators that are same as in the SM.…”

“…In earlier studies, usually 20-30 KK-levels have been taken while adding up the contributions from KK-modes 12. We have taken M W = 80.379 GeV[62] for SM W ± boson mass and m t (m t ) = 165.25 GeV[63] for SM top quark mass 13. The summation of KK-contribution is convergent in UED type models with one extra space-like dimension, as far as one-loop calculation is concerned[74].…”

The impact of nonminimal Universal Extra Dimensional model on $ΔB=2$ transitions

“…For example the refs. [8][9][10][11][12][13] depicted how the observables are related to ∆B = 2 transition that can constrain different BSM scenarios. In the current article we consider a class of models, namely Universal Extra Dimensional (UED) [14] scenario, with nonvanishing boundary localised terms (BLTs), where the low energy effective Hamiltonians are controlled by local operators that are same as in the SM.…”