DirectCPviolation inΛb→n(Λ)π+

Abstract

We study direct CP violation in the bottom baryon decays Λ b → f ρ 0 (ω) → f π + π − (f = n or Λ). It is found that in these decays via ρ − ω mixing the CP violation could be very large when the invariant mass of the π + π − pair is in the vicinity of the ω resonance. With a typical value N c = 2 in the factorization approach, the maximum CP-violating asymmetries are more than 50% and 68% for Λ b → nπ + π − and Λ b → Λπ + π − , respectively.With the aid of heavy quark symmetry and phenomenological models for the hadronic wave functions of Λ b , Λ and the neutron, we estimate the branching ratios of Λ b → n(Λ)ρ 0 .

Localized direct CP violation in $$B^\pm \rightarrow \rho ^0 (\omega )\pi ^\pm \rightarrow \pi ^+ \pi ^-\pi ^\pm $$ B ± → ρ 0 ( ω ) π ± → π + π - π ±

“…As a consequence the physical ρ 0 and ω mesons are not eigenstates of isospin but, for example, the physical ρ 0 contains a small admixture of an I = 0 state [13]. In previous works, this phenomenon, known as ρ-ω mixing, was considered to obtain a large strong phase in B decays [14][15][16][17] and it was found that such a mixing can lead to a peak of CP violation when the invariant mass of π + π − is near ω. The differential CP asymmetry was studied in the decays B ± → ρ 0 (ω)π ± → π + π − π ± before [18][19][20].…”

CP violation induced by the double resonance for pure annihilation decay process in perturbative QCD

“…(15) that both weak and strong phase differences are responsible for CP violation. ρ-ω mixing introduces the strong phase difference and is well known for the three-body decay processes of the bottom hadron [28][29][30][31][32][33][34]. Due to ρ-ω interference from u and d quark mixing, we can write the formalism in an approximate form in terms of the first order isospin violation:…”

“…(17) and (18) compared with the case of single ρ-ω interference [28][29][30][31][32][33][34][35][36]. From Eqs.…”

Direct CP violation in $$\tau ^\pm \rightarrow K^\pm \rho ^0 (\omega )\nu _\tau \rightarrow K^\pm \pi ^+\pi ^-\nu _\tau $$ τ ± → K ± ρ 0 ( ω ) ν τ → K ± π + π - ν τ

“…ρ-ω mixing has the dual advantages that the strong phase difference is large and well known [24,25]. From a series of studies on CP violation, it has already been found that this mechanism can provide a very large strong phase difference (usually 90 degrees) when the mass of the decay product of ρ 0 (ω) , π + π − , is in the vicinity of the ω resonance in some decay channels of heavy hadrons including B, b , and D [24][25][26][27][28][29]. We will apply this mechanism to the τ lepton decay in the present paper.…”