Comparative analysis of the $\Lambda_b \rightarrow \Lambda \ell^+ \ell^-$ decay in the SM, SUSY and RS model with custodial protection

arXiv:1508.03980v2 [hep-ph] 21 Dec 2015 Comparative analysis of the A5 —> A£ + £ decay in the SM, SUSY and RS model with custodial protection K. Azizi * 1 *, A. T. Olgun 2 \ Z. Tavukoglu 2 * 1 Department of Physics, Dogu§ University, Acibadem-Kadikoy, 34722 Istanbul, Turkey 2 Vocational School Kadikoy Campus, Okan University, Hasanpa§a-Kadikoy, 34722 Istanbul, Turkey Abstract We comparatively analyze the rare Aj, —>• channel in standard model, su¬ persymmetry and Randall-Sundrum model with custodial protection (RS C ). Using the parametrization of the matrix elements entering the low energy effective Hamilto¬ nian in terms of form factors, we calculate the corresponding differential decay width and lepton forward-backward asymmetry in these models. We compare the results obtained with the most recent data from LHCb as well as lattice QCD results on the considered quantities. It is obtained that the standard model, with the form factors calculated in light-cone QCD sum rules, can not reproduce some experimental data on the physical quantities under consideration but the supersymmetry can do it. The RS C model predictions are roughly the same as the standard model and there are no considerable differences between the predictions of these two models. In the case of differential decay rate, the data in the range 4 GeV 2 /c 4 < q 2 < 6 GeV 2 /c 4 can not be described by any of the considered models. PACS number(s): 12.60.-i, 12.60.Jv, 13.30.-a, 13.30.Ce, 14.20.Mr *e-mail: kazizi@dogus.edu.tr i e-mail: tugba.olgun@okan.edu.tr 1 e-mail: zeynep.tavukoglu@okan.edu.tr 1 Introduction The ATLAS and CMS Collaborations at CERN have independently reported their discovery of the Higgs boson with a mass of about 125 GeV using the samples of proton-proton collision data collected in 2011 and 2012, commonly referred to as the first LHC run [1-3]. Recently, a measurement of the Higgs boson mass based on the combined data samples of the ATLAS and CMS experiments has been presented as rrin = 125.09 ± 0.21 (stat) ±0.11(s|/st) GeV in Refs [3-7]. At the same time, all LHC searches for signals of new physics above the TeV scale have given negative results. However, the LHC constraints on new physics effects can help theoreticians in the course of searching for these new effects and answering the questions that the standard model (SM) has not answered yet. We hope that the upcoming LHC run can bring unexpected surprises to observe signals of new physics in the experiment [ 8 ], Although the SM could be valid up to some arbitrary high scale, new scenarios should exist because we are lacking a proper understanding of some important issues like origin of the matter, matter-antimatter asymmetry, dark matter and dark energy etc. [9]. In the baryonic sector, the loop-induced flavor changing neutral current (FCNC) decay of the Af, —>■ A i + £~ with l = e,n,r, which is described by the b —> s£ + £~ transition at quark level, is one of the important rare processes that can help us in the course of indirectly searching for new physics effects [10]. Recently, the differential branching fraction of the A® —> A/j, + /j,~ decay channel has been measured as a function of the square of the di-muon invariant mass (g 2 ), corresponding to an integrated luminosity of 3.0 /5 _1 using protonproton collision data collected by the LHCb experiment [11]. The measured result at 15 GeV 2 /c 4 < q 2 < 20 GeV 2 /c 4 region for the differential branching fraction is dBr(A° —y A fi + ij,~)/dq 2 = (1.18 ± 0.03 ± 0.27) x 10 ' GeV 2 /c 4 . The LHCb Collaboration has also reported the measurement on the forward-backward asymmetries of this transition at the // channel. The measured result at the 15 GeV 2 /c 4 < q 2 < 20 GeV 2 /c 4 region for the lepton forward-backward asymmetry is A BB = —0.05 ± 0.09 (stat) ± 0.03 (syst) [11]. In the literature, there are a lot of studies on this decay channel via different approaches (for some recent studies see for instance Refs. [12-17]). In the present work, we calculate the differential decay rate and lepton forward-backward asymmetry related to the FCNC A h —> A£ + £~ transition for all leptons in the SM, supersymmetry (SUSY) and Randall-Sundrum scenario with custodial protection (RS C ). We compare the results with the experimental data provided by LHCb [11] as well as the ex¬ isting lattice QCD predictions [18]. Comparison of the LHCb results with the lattice QCD 1 predictions shows that there are some deviations of data from the SM predictions. Such deviations can be attributed to the new physics effects that can contribute to such loop level processes. In this connection, we comparatively analyze the A& —y A £ + t~ decay channel in SM and some new physics scenarios. In the calculations, we use the form factors calculated via the light-cone QCD sum rules in [19]. Hence, to get ride of any misleading, we will use SMLCSR instead of SM referring to the results that are obtained via using the from factors predicted by the light-