Addition of boundary localised kinetic and Yukawa terms to the action of a 5-dimensional Standard Model would non-trivially modify the Kaluza-Klein spectra and some of the interactions among the Kaluza-Klein excitations compared to the minimal version of this model, in which, these boundary terms are not present. In the minimal version of this framework known as Universal Extra Dimensional model, special assumptions are made about these unknown, beyond the cut-off contributions to restrict the number of unknown parameters of the theory to a minimal. We estimate the contribution of Kaluza-Klein modes to the branching ratios of B s(d) → µ + µ − in the framework of non-minimal Universal Extra Dimensional, at one loop level. The results have been compared to the experimental data to constrain the parameters of this model. From the measured decay branching ratio of B s → µ + µ − (depending on the values of boundary localised parameters) lower limit on R −1 can be as high as 800 GeV. We have briefly reviewed the bounds on nmUED parameter space coming from electroweak precision observables. The present analysis (B s → µ + µ − ) has ruled out new regions of parameter space in comparison to the analysis of electroweak data. We have revisited the bound on R −1 in Universal Extra Dimensional model, which came out to be 454 GeV. This limit on R −1 in Universal Extra Dimensional framework is not as competitive as the limits derived from the consideration of relic density or Standard Model Higgs boson production and decay to W + W − . Unfortunately, B d → µ + µ − decay branching ratio would not set any significant limit on R −1 in a minimal or non-minimal Universal Extra Dimensional model.

We estimate contributions from Kaluza-Klein excitations of third generation quarks and gauge bosons to the branching ratio of B → X s γ decay process in 5-Dimensional Universal Extra Dimensional scenario with non-vanishing boundary localised terms. This model is conventionally known as non-minimal Universal Extra Dimensional model. We have derived the lower limit on the size of the extra dimension by comparing our theoretical estimation of the branching ratio which includes next-to-next-to leading order QCD corrections with its experimentally measured value. Coefficients of the boundary localised terms have also been constrained. 95 % C.L. lower limit on inverse of radius of compactification (R −1 ) can be as large as 670 GeV for some choice of the value of coefficients of boundary localised terms.

We estimate contributions from Kaluza-Klein excitations of gauge bosons and physical charge scalar for the explanation of the lepton flavor universality violating excess in the ratios RðDÞ and RðD Ã Þ in 5 dimensional universal extra dimensional scenario with nonvanishing boundary localized terms. This model is conventionally known as nonminimal universal extra dimensional model. We obtain the allowed parameter space in accordance with constraints coming from B c → τν decay, as well as those from the electroweak precision tests.

Non-vanishing boundary localised terms significantly modify the mass spectrum and various interactions among the Kaluza-Klein excited states of 5-Dimensional Universal Extra Dimensional scenario. In this scenario we compute the contributions of Kaluza-Klein excitations of gauge bosons and third generation quarks for the decay process B → X s + − incorporating next-to-leading order QCD corrections. We estimate branching ratio as well as ForwardBackward asymmetry associated with this decay process. Considering the constraints from some other b → s observables and electroweak precision data we show that significant amount of parameter space of this scenario has been able to explain the observed experimental data for this decay process. From our analysis we put lower limit on the size of the extra dimension by comparing our theoretical prediction for branching ratio with the corresponding experimental data. Depending on the values of free parameters of the present scenario, lower limit on the inverse of the radius of compactification (R −1 ) can be as high as ≥ 760 GeV.Even this value could slightly be higher if we project the upcoming measurement by Belle II experiment. Unfortunately, the Forward Backward asymmetry of this decay process would not provide any significant limit on R −1 in the present model. *In the present article, in order to serve our purposes we are particularly focused on an extension of SM with one flat space-like dimension (y) compactified on a circle S 1 of radius R. All the SM fields are allowed to propagate along the extra dimension y. This model is called as 5-dimensional (5D) Universal Extra Dimensional (UED) [20] scenario. The fields manifested on this manifold are usually defined in terms of towers of 4-Dimensional (4D) Kaluza-Klein (KK) states while the zero-mode of the KK-towers is designated as the corresponding 4D SM field. A discrete symmetry Z 2 (y ↔ −y) has been needed to generate chiral SM fermions in this scenario. Consequently, the extra dimension is defined as S 1 /Z 2 orbifold and eventually physical domain extends from y = 0 to y = πR. As a result, the y ↔ −y symmetry has been translated as a conserved parity which is known as KK-parity = (−1) n , where n is called the KK-number. This KK-number (n)is identified as discretised momentum along the y-direction. From the conservation of KK-parity the lightest Kaluza-Klein particle (LKP) with KK-number one (n = 1) cannot decay to a pair of SM particles and becomes absolutely stable. Hence, the LKP has been considered as a potential DM candidate in this scenario [21][22][23][24][25][26][27][28]. Furthermore, few variants of this model can address some other shortcomings of SM, for example, gauge coupling unifications [29][30][31], neutrino mass [32,33] and fermion mass hierarchy [34] etc.At the n th KK-level all the KK-state particles have the mass (m 2 + (nR −1 ) 2 ). Here, m is considered as the zero-mode mass (SM particle mass) which is very small with respect to R −1 . Therefore, this UED scenario contains almost degenerate mass...

In universal extra dimension (UED) models with one compactified extra dimension, a Z 2 symmetry, termed KK parity, ensures the stability of the lightest Kaluza-Klein particle (LKP) which could be a viable dark matter candidate. This symmetry leads to two fixed points. In nonminimal versions of UED boundary-localized (kinetic or mass) terms (BLT) for different fields are included at these fixed points and KK parity may be violated. However, BLTs with same strength at both points induce a new Z 2 symmetry which restores the stability of the LKP. We show that the BLTs serve to relax the bounds set on the compactification scale in UED by the observed dark matter relic density. At the same time, the precision of the dark matter measurements severely correlates the BLT parameters of gauge bosons and fermions. Depending on the parameter values, the LKP can be chosen to be the level-1 photon, which is essentially the B ð1Þ , or the level-1 Z boson, basically the W ð1Þ 3 . We find that in the latter case the relic density is too small if the W ð1Þ 3 has a mass $1 TeV. We also explore the prospects of direct detection of an LKP which matches the observed dark matter relic density.