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Register a new userTesting CP and Time Reversal Symmetries with $Lambda_b to Lambda V(1-)$ Decays
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In this letter, an overview is given for interesting tests of both CP and Time Reversal symmetries with the beauty baryon $Lambda_b $. Extensive use of the helicity formalism and HQET is done for all calculations. Then, emphasis is put on sophisticated methods like analysis of resonance polarizations and particular angle distributions which can exhibit a clear signal of TR violation.
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Putting together kinematical and dynamical analysis, a complete study of the decay channels $Lambda_b to {Lambda} V(1^-)$, with $Lambda to p {pi}^-$ and $V (J/psi) to {ell}^+ {ell}^-$ or $V ({rho}^0) to {pi}^+ {pi}^-,$ is performed. An intensive use of the helicity formalism is involved on the kinematical side, while on the dynamical side, Heavy Quark Effective Theory (HQET) is applied for an accurate determination of the hadronic matrix elements between the baryons $Lambda_b$ and $Lambda$. Emphasis is put on the major role of the $Lambda_b$ polarization for constructing T-odd observables and the standard ${rho}^0-{omega}$ mixing has the benefit effect of amplifying the process of direct CP violation between $Lambda_b mathrm{and} {bar Lambda}_b$ decays.
Weak decays of beauty baryons like Lambda_b into Lambda V(J^P=1^-), where the produced resonances are polarized, offer interesting opportunity to perform tests of Time-Reversal Invariance. This paper emphasizes the particular role of the resonance polarization-vectors and their physical properties by symmetry transformations. In particular, it is shown that the normal component of a polarization-vector, as defined in the Jacksons frame, is Lorentz invariant and could get large values, notably in the case of J/psi production.
It is shown that interference of the amplitudes for the decays $Lambda_b to Lambda D$ and $Lambda_b to Lambda bar{D}^0$ gives rise to CP-violation.
A complete study of the angular distributions of the processes, $Lambda_b to {Lambda} V(1^-)$, with $Lambda to p {pi}^-$ and $V (J/{Psi}) to {ell}^+ {ell}^-$ or $V ({rho}^0,omega) to {pi}^+ {pi}^-,$ is performed. Emphasis is put on the initial $Lambda_b$ polarization produced in the proton-proton collisions. The polarization density-matrices as well as angular distributions are derived and help to construct T-odd observables which allow us to perform tests of both Time-Reversal and CP violation.
We present the prospects of an angular analysis of the $Lambda_b to Lambda(1520)ell^+ell^-$ decay. Using the expected yield in the current dataset collected at the LHCb experiment, as well as the foreseen ones after the LHCb upgrades, sensitivity studies are presented to determine the experimental precision on angular observables related to the lepton distribution and their potential to identify New Physics. The forward-backward lepton asymmetry at low dilepton invariant mass is particularly promising. NP scenarios favoured by the current anomalies in $bto sell^+ell^-$ decays can be distinguished from the SM case with the data collected between the Run 3 and the Upgrade 2 of the LHCb experiment.
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