Analysis of Angular Observables of ${\Lambda }_b\to \Lambda (\to p\pi ){\mu }^{+}{\mu }^{-}$ Decay in Standard and $Z^{\prime }$ Models

Abstract

In 2015, the LHCb collaboration has measured $\frac{d\mathcal{B}}{d{q}^2}$, the lepton- and hadron-side forward-backward asymmetries, denoted by $A_{FB}^{\ell }$ and $A_{FB}^{\Lambda }$, 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 ${\Lambda }_b\to \Lambda (\to p\pi ){\mu }^{+}{\mu }^{-}$ angular observables at large- and low-recoil in the SM and in a family non-universal $Z^{\prime }$ model. In the present study we use the recently performed high-precision lattice QCD calculations of the form factors that have well controlled uncertainties especially in $15<s<20$ GeV${}^2$ bin. Using the full four-folded angular distribution of ${\Lambda }_b\to \Lambda (\to p\pi ){\mu }^{+}{\mu }^{-}$ decay, firstly we calculate the values of these measured quantitites in the SM and compare their numerical values with the measurements in appropriate bins of $s$. In case of the possible discrepancy between the SM prediction and measurements, we try to see if these can be accommodated though the extra neutral $Z^{\prime }$ boson. In addition, the fraction of longitudinal polarization of the dimuon $F_L$ is measured to be $0.61_{-0.14}^{+0.11}\pm 0.03$ 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 a number of other observables whose values are calculated in different bins of $s$ in the SM and $Z^{\prime }$ model. We illustrate that the experimental observations of these observables in several bins of $s$ can help to test the predictions of the SM and unravel NP contributions arises due to $Z^{\prime }$ model in these decays.

Comments: 28 pages, 4 figures, A version accepted for Publication in PTEP