Outcome from spontaneous CP violation for B decays.

In the aspon model solution of the strong CP problem, there is a gauged U(1) symmetry, spontaneously broken by the same vacuum expectation value which breaks CP , whose massive gauge boson provides an additional mechanism of weak CP violation. We calculate the CP asymmetries in B decays for the aspon model and show that they are typically smaller than those predicted from the standard model. A linear relation between the CP asymmetries of different decay processes is obtained. Typeset using REVTEX 1 The violation of CP symmetry was a surprising experimental discovery made almost thirty years ago in the neutral kaon system [1]. In field theory, one profound question about CP is whether it is explicitly broken in the fundamental lagrangian or only spontaneously broken by the vacuum. Within the standard model explicit CP violation can be accommodated in the flavor mixing of three families by the Kobayashi-Maskawa (KM) mechanism [2]. The experimental information regarding CP violation still comes only from the neutral kaon system and is inadequate to determine whether the KM mechanism is the correct underpinning of CP violation. In dedicated B studies, with more than 10 samples of B (B̄) decay, it will be possible [3] to test this assumption stringently by measuring the angles of the well-known unitarity triangle whose sides correspond to the complex terms of the equation V ∗ ubVud + V ∗ tbVtd + V ∗ cbVcd = 0. (1) If CP is spontaneously broken, the outcome of these measurements will be different from the standard model. It is the purpose of the present Letter to illustrate this in the context of the aspon model [4,5]. The standard model contains 19 parameters of which two, commonly denoted by θ̄ and δ, pertain to CP violation. The value of θ̄, the strong CP violation parameter, is restricted by the neutron electric dipole moment to be: θ̄ < ∼ 2× 10 . The KM mechanism offers no solution of this fine-tuning which is generally explained by an independent mechanism. In the aspon model which solves the strong CP problem, there is a new gauged U(1) symmetry which is spontaneously broken by the same vacuum expectation value that breaks CP . The resulting massive gauge boson, the aspon, provides an additional mechanism for weak CP violation. The three angles of the unitarity triangle (conventionally defined as α, β, γ between the first and second, second and third, and third and first sides in (1), respectively) can be separately measured for the standard model by the time-dependent CP asymmetry [6], af(t) = Γ(B(t) → f)− Γ(B̄(t) → f) Γ(B(t) → f) + Γ(B̄(t) → f) (2) 2 where the final state f is a CP eigenstate. We define q, p in B–B̄0 mixing by the mass eigenstates B1,2: |B1,2〉 = p|B 〉 ± q|B̄〉 (3) and similarly for K1,2 in the kaon system. A, Ā are the decay amplitudes: A, Ā = 〈f |H|B, B̄〉 (4) Let us consider the specific cases of f = ππ, ψKS from Bd decay and f = ρKS from Bs decay. We define λ(f) by λ(ππ) = (