Model independent new physics analysis in $$\Lambda _b\rightarrow \Lambda \mu ^+\mu ^-$$ Λ b → Λ μ + μ - decay

Abstract

We study the rare b → μ + μ − decay in the Standard Model and beyond. Beyond the Standard Model we include new vector and axial-vector operators, scalar and pseudo-scalar operators, and tensor operators in the effective Hamiltonian. Working in the helicity basis and using appropriate parametrization of the b → hadronic matrix elements, we give expressions of hadronic and leptonic helicity amplitudes and derive expression of double differential branching ratio with respect to dilepton invariant mass squared and cosine of lepton angle. Appropriately integrating the differential branching ratio over the lepton angle, we obtain the longitudinal polarization fraction and the leptonic forward-backward asymmetry and sequentially study the observables in the presence of the new couplings. To analyze the implications of the new vector and axial-vector couplings, we follow the current global fits to b → sμ + μ − data. While the impacts of scalar couplings can be significant, exclusiveB → X s μ + μ − data imply stringent constraints on the tensor couplings and hence the effects on b → μ + μ − are negligible.

On the angular distribution of Λb → Λ(→ N π)τ +τ − decay

“…When m = 0, following the steps in ref. [18] we obtain the following non-zero expressions of the leptonic helicity…”

“…[15]. For our need of the form factors at large q 2 or low recoil, we use the results from the calculations in lattice QCD [16,17] In a recent paper [18] we presented a model independent NP analysis of Λ b → Λ + − decay where the NP operators include new vector and axial vector (VA) operators, scalar and pseudo-scalar (SP) operators, and tensor operators. In this analysis the mass of the final state leptons was neglected considering di-muon in the final state.…”

“…Going beyond the SM operator basis, we also include new VA operators and SP operators. Therefore our Lagrangian reads [18] …”

“…The VA and the SP couplings will be considered separately. Due to nonavailability of any data on JHEP07(2018)063 [14,15] 0.31 ± 0.03 0.350 ± 0.007 −0.120 ± 0.016 −0.309 ± 0.009 [15,16] 0.39 ± 0.03 0.354 ± 0.009 −0.149 ± 0.017 −0.304 ± 0.009 [16,18] 0.93 ± 0.06 0.353 ± 0.010 −0.180 ± 0.015 −0.289 ± 0.009 [18,20] 0.83 ± 0.05 0.346 ± 0.010 −0.173 ± 0.010 −0.227 ± 0.009 [15,20] 2.16 ± 0.13 0.351 ± 0.009 −0.171 ± 0.014 −0.268 ± 0.008 [14,15] 0.041 ± 0.005 −0.0026 ± 0.0030 −0.0148 ± 0.0086 [15,16] 0.052 ± 0.006 −0.0037 ± 0.0036 −0.0243 ± 0.0089 [16,18] 0.067 ± 0.006 −0.0053 ± 0.0035 −0.0446 ± 0.0075 [18,20] 0.084 ± 0.005 −0.0053 ± 0.0028 −0.0827 ± 0.0050 [15,20] 0.071 ± 0.005 −0.0050 ± 0.0031 −0.0055 ± 0.0067 Table 2. The values of the observables in different q 2 bins (in GeV 2 ).…”

“…For the operators (2.2), the hadronic matrix elements parametrization in terms of the spinor bilinears are summarized in appendix D. The spinor bilinears can be found in the appendix of [18]. The helicity amplitudes are defined as the projection of the hadronic matrix elements on to the direction of the polarization of the virtual gauge boson that decays to a dilepton pair.…”