Abstract
We study the spin correlations to probe time-reversal (T) asymmetries in the decays of Λb→ ΛV (V = ϕ, ρ0, ω, K∗0). The eigenstates of the T-odd operators are obtained along with definite angular momenta. We obtain the T-odd spin correlations from the complex phases among the helicity amplitudes. We give the angular distributions of Λb→ Λ(→ pπ−)V (→ PP′) and show the corresponding spin correlations, where P(′) are the pseudoscalar mesons. Due to the helicity conservation of the s quark in Λ, we deduce that the polarization asymmetries of Λ are close to −1. Since the decay of Λb→ Λϕ in the standard model (SM) is dictated by the single weak phase from the product of CKM elements, {V}_{tb}{V}_{ts}^{ast } , the true T and CP asymmetries are suppressed, providing a clean background to test the SM and search for new physics. In the factorization approach, as the helicity amplitudes in the SM share the same complex phase, T-violating effects are absent. Nonetheless, the experimental branching ratio of Br(Λb→ Λϕ) = (5.18 ± 1.29) × 10−6 suggests that the nonfactorizable effects or some new physics play an important role. By parametrizing the nonfactorizable contributions with the effective color number, we calculate the branching ratios and direct CP asymmetries. We also explore the possible T-violating effects from new physics.
Highlights
Results in Λb → J/ψΛ are well compatible with those in the covariant confined quark model [18, 30]
We have shown that all the relative complex phases among a± and b± can be interpreted as the T-odd correlations
By subtracting the effects from the final state interactions (FSIs), we have defined the true T-violating observables, which could be measured in the experiments
Summary
The decay distributions in two body decays are often described by the helicity amplitudes [48]. Λf are chosen as the momenta and spins of the particles, resulting in expanding the amplitudes with the Dirac spinors and polarization vector, given as ξμ∗uΛ. A (b) indicates the vector meson is longitudinally (transversely) polarized, while the subscripts denote the angular momenta in the p1 direction, read as J · p1 = λ1 − λ2 = ±1/2. We take Λb → Λ(→ pπ−)ρ0(→ π+π−) as a concrete example In this case, θ, θ1, and θ2 are defined as the angles between (nΛb, pΛ), (pΛ, pp), and (pρ0 , pπ+), respectively, where nΛb is the unit vector pointing toward the polarization of Λb, pΛ,ρ0 is the 3-momentum defined in the rest frame of Λb, and pp (pπ+) is defined in the helicity frame of Λ (ρ0). Aiming on probing T-violation, the partial angular analysis of Λb → Λφ has been studied at LHCb. [32], the effects of the FSIs have not been considered
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