X iv : h ep - p h / 03 07 30 7 v 2 1 2 A ug 2 00 3 T - violating triple product asymmetries in Λ b → Λ π + π − decay

We study Λb → Λπ+π−. The branching fraction is predicted to be about 4.4 ×10−8. Within the standard model, we compute T -odd triple product asymmetries to be about 1.4, 4.3, 6.5 and 7.2% respectively due to ~sΛb,Λ · (~ pΛ × ~ pπ) and ~ pΛ,π · (~sΛ × ~sΛb). PACS number(s): 11.30.Er, 13.30.Eg, 14.20.Mr [email protected] [email protected] 1 In this paper, we consider Λb → Λππ decay and study T -odd triple product correlations (TPC’s). As has been discussed in [1–4], the triple product asymmetry (TPA) is independent of strong phase. In the vanishing limit of strong phase, the TPA is maximal: AT = 1 2 (AT − ĀT ) ∼ sinφ cos δ (1) where AT (ĀT ) the net TPC [4], of the form ~v1 · (~v2 × ~v3) where vi are momentum or spin, in the decay (conjucate decay) in question and φ(δ) is weak (strong) phase. In Λb → pP (V ) where P (V ) is pseudoscalar (vector) meson, T-odd triple correlations give rise to an asymmetry of about O(10%) in certain decays while in some at O(1%) [3]. However, in beyond standard model scenarios the TPA is about 50% or so [5,6]. Thus Λb decays provides better opportunity to study CP/T violating effects. For instance, Λb-spin and the final state baryon spin are obervable in terms of which physics of the standard model and beyond it can be investigated. In the two-body decay mode, i. e., Λb → pP , TPC’s necessarily involve the polarisation of both baryons. Whereas in three-body final state such as one we consider, TPC’s are constituted by either of the baryon polarisations, (besides cases involving both). This is more feasible experimentally, despite the size being relatively smaller, than the one with two polarisations. On the other hand, with the most of the b quark polarisation being carried by the Λb baryon, polarisation of final state baryon alone can be considered in the search for CP violating effects. Hopefully, at the future colliders BTeV, LHC-b, production of about 10 ΛbΛ̄b pairs would facilitate such studies. In this work, we describe the decay using factorisation and obtain the branching ratio. Then, we look for the following TPC’s: ~sΛb,Λ · (~ pΛ × ~pπ) and ~pΛ,π · (~sΛ × ~sΛb). The effective Hamiltonion for b → uūs which underlies the decay Λb → Λππ (see [7] for other modes) is Heff = Gf √ 2 {VubV ∗ usa2 − 2VtdV ∗ ts(a3 − a5)} (s̄αγμ(1− γ5)bα)(ūβγ(1− γ5)uβ) (2)