Abstract
For a general Hb → {H}_ctau {overline{nu}}_{tau } decay we analyze the role of the τ polarization vector {mathcal{P}}^{mu } in the context of lepton flavor universality violation studies. We use a general phenomenological approach that includes, in addition to the Standard Model (SM) contribution, vector, axial, scalar, pseudoscalar and tensor new physics (NP) terms which strength is governed by, complex in general, Wilson coefficients. We show that both in the laboratory frame, where the initial hadron is at rest, and in the center of mass of the two final leptons, a overrightarrow{mathcal{P}} component perpendicular to the plane defined by the three-momenta of the final hadron and the τ lepton is only possible for complex Wilson coefficients, being a clear signal for physics beyond the SM as well as time reversal (or CP-symmetry) violation. We make specific evaluations of the different polarization vector components for the Λb → Λc, {overline{B}}_c → ηc, J/ψ and overline{B} → D(*) semileptonic decays, and describe NP effects in the complete two-dimensional space associated with the independent kinematic variables on which the polarization vector depends. We find that the detailed study of {mathcal{P}}^{mu } has great potential to discriminate between different NP scenarios for 0− → 0− decays, but also for Λb → Λc transitions. For this latter reaction, we pay special attention to corrections to the SM predictions derived from complex Wilson coefficients contributions.
Highlights
RD∗ = 0.258 ± 0.05, are obtained from the Standard Model (SM) predictions in refs. [10,11,12,13,14]
We use a general phenomenological approach that includes, in addition to the Standard Model (SM) contribution, vector, axial, scalar, pseudoscalar and tensor new physics (NP) terms which strength is governed by, complex in general, Wilson coefficients. We show that both in the laboratory frame, where the initial hadron is at rest, and in the center of mass of the two final leptons, a P component perpendicular to the plane defined by the three-momenta of the final hadron and the τ lepton is only possible for complex Wilson coefficients, being a clear signal for physics beyond the SM as well as time reversal violation
For a given configuration of the momenta of all particles involved, we have introduced the tau spin-density matrix ρand the polarization vector Pμ associated to a general Hb → Hcτ ντ decay
Summary
Let us consider a Hb → Hcτ ντ semileptonic decay of a bottomed hadron (Hb) of mass M into a charmed one (Hc) with mass M. Defines a trace-one hermitian operator (ρ† = ρ) in the two-dimensional Hilbert space spanned by the spin states of the τ particle.. A general polarization basis (covariant spin) for the τ states with four-momentum k , can be constructed as follows. For the τ at rest, we take the two states un±1(mτ , 0 ) corresponding to spin ±1/2 along the direction defined by a normalized three vector n, apply to these states a boost of velocity k /k 0. For the given configuration of momenta, the spin-density operator ρencodes all information that can be obtained on the spin of the τ leptons produced in the Hb → Hcτ ντ decay when no other particle spin state is measured. Give the probability that in an actual measurement the τ is found in the uS±1(k ) state, as follows from eq (2.1)
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