Analysis of angular observables of |$Lambda_b o Lambda (o ppi)mu^{+}mu^{-}$| decay in the standard and |$Z^{prime}$| models

摘要

In 2015, the LHCb collaboration measured the differential branching ratio |$rac{d{mathcal{B}}}{dq^2}$|?, the lepton- and hadron-side forward–backward asymmetries, denoted by |$A^ell_{m FB}$| and |$A^{Lambda}_{m FB}$|?, respectively, in the range |$15 q^2(=s) 20$| GeV|$^2$| with 3 fb|$^{-1}$| of data. Motivated by these measurements, we perform an analysis of |$q^2$|-dependent |$Lambda_b o Lambda (o p pi ) mu^+mu^-$| angular observables at large- and low- recoil in the standard model (SM) and in a family non-universal |$Z^{prime}$| model. The exclusive |$Lambda_{b}o Lambda$| transition is governed by the form factors, and in the present study we use the recently performed high-precision lattice QCD calculations that have well-controlled uncertainties, especially in the |$15 s 20$| GeV|$^2$| bin. Using the full four-folded angular distribution of |$Lambda_b o Lambda (o p pi ) mu^+mu^-$| decay, first of all we focus on calculations of the experimentally measured |$rac{d{mathcal{B}}}{ds}$|?, |$A^ell_{m FB}$|?, and |$A^{Lambda}_{m FB}$| in the SM and compare their numerical values with the measurements in appropriate bins of |$s$|?. In case of a possible discrepancy between the SM prediction and the measurements, we try to see if these can be accommodated though the extra neutral |$Z^{prime}$| boson. We find that in the dimuon momentum range |$15 s 20$| GeV|$^2$| the value of |$rac{d{mathcal{B}}}{ds}$| and central value of |$A^ell_{m FB}$| in the |$Z^{prime}$| model is compatible with the measured values. In addition, the fraction of longitudinal polarization of the dimuon |$F_{L}$| was measured to be |$0.61^{+0.11}_{-0.14}pm 0.03$| in |$15 s 20$| GeV|$^2$| at the LHCb. We find that in this bin the value found in the |$Z^{prime}$| model is close to the observed values. After comparing the results of these observables, we have proposed other observables such as |${lpha}_{i}$| and |$lpha^{(prime)}_{i}$| with |$i =heta_{ell},; heta_{Lambda},; phi,;L,; U$| and coefficients of different foldings |$mathcal{P}_{1, ldots, 9}$| in different bins of |$s$| in the SM and |$Z^{prime}$| model. We illustrate that the experimental observations of the |$s$|-dependent angular observables calculated here in several bins of |$s$| can help to test the predictions of the SM and unravel new physics contributions arising due to the |$Z^{prime}$| model in |$Lambda_b o Lambda (o p pi ) mu^+mu^-$| decays.