METHODS TO DETERMINE THE $B_d - \bar{B}_d $ MIXING PARAMETERS

Abstract

The phenomenology of [Formula: see text] mixing involves four parameters: average width Γ, mixing ratio |q|p|, mass difference proportional to x, and width difference proportional to y. We point out the types of experimental inputs that are eventually needed in order to determine the four parameters completely and in a model-independent way. For the sign of y we suggest the measurement (at ϒ(4S) factories) of a certain time-asymmetry when one of the neutral B mesons is tagged and the other decays to a CP-eigenstate. For the sign of x we propose similar time-asymmetries when one of the B mesons undergoes the chain decay: B→KJ/ψ, and the neutral kaon →πlν or π+π−.

Bs→DsKas a probe ofCPTviolation

“…CPTV in the B systems, and its possible signatures, have been already investigated by several authors [11,12]. It was shown that the lifetime difference of the two mass eigenstates, or the direct CP asymmetries and semileptonic observables, may be affected by such new physics.…”

Decay-time asymmetries at the B-factories

“…To be specific, we shall define the state B 2 to be that which decays to the CP-odd state J/ψK S . Methods suggested [9] to fix the sign of x need the timing of kaon decay in the decays B d → J/ψK S at a B-Factory. Here the idea is to exploit the strangeness oscillations to serve as 'analysers' of bottom oscillations to decide the sign of x.…”

“…An asymmetry which would eventually shed light on the small parameter y in eq. ( 12), can be constructed [9] from the time dependence of the B d and Bd decays into the same CP eigenstate f . If t denotes the time of decay B/ B → f and t ′ the lepton-tag time, then the relative time τ = (t − t ′ ) can be either positive or negative, whereas the sum T = (t + t ′ ) must be greater than |τ |.…”

NewCP-violating parameters in cascade decays

“…In 1989, Azimov [4] pointed out that additional tests could be performed by looking for B d → J/ψK → J/ψ[f ] K 'cascade decays', involving the neutral B d and neutral kaon systems in succession. This idea has been followed by Dass and Sarma [5]. Recently, cascade decays have received renewed attention.…”