On the use of the reciprocal basis in neutral meson mixing

Abstract

In the presence of CP violation, the effective Hamiltonian matrix describing a neutral meson anti-meson system does not commute with its hermitian conjugate. As a result, this matrix cannot be diagonalized by a unitary transformation and one needs to introduce a reciprocal basis. Although known, this fact is seldom discussed and almost never used. Here, we use this concept to highlight a parametrization of the Hamiltonian matrix in terms of physical observables, and we show that using it reduces a number of long and tedious derivations into simple matrix multiplications. These results have a straightforward application for propagation in matter. We also comment on the (mathematical) relation with neutrino oscillations.

15 pages, no figures

References in corpus (4)

• Violation of Time-Reversal Invariance and CPLEAR Measurements
• New CP-violating parameters in cascade decays
• Detecting new physics contributions to the D0-D0bar mixing through their effects on B decays
• Disentangling violations of CPT from other new-physics effects

Cited by in corpus (15)

• Oscillations of neutrinos and mesons in quantum field theory
• CPT, T, and Lorentz Violation in Neutral-Meson Oscillations
• Dispersive and Absorptive CP Violation in $D^0-\overline{D^0}$ Mixing
• Can the CP asymmetries in $B\to \psi K_S$ and $B\to \psi K_L$ differ?
• CP asymmetry in $\tau \to K_S\pi {\nu }_{\tau }$ decays within the Standard Model and beyond
• Subtleties in the BaBar measurement of time-reversal violation
• $CP$ asymmetry in the angular distribution of $\tau \to K_S\pi {\nu }_{\tau }$ decays
• $CP$ asymmetry in the angular distributions of $\tau \to K_S\pi {\nu }_{\tau }$ decays -- II: general effective field theory analysis
• Consistent Probabilistic Description of the Neutral Kaon System
• The heavy-quark pole masses in the Hamiltonian approach
• Is there a paradox in CP asymmetries of tau to K_{L,S} pi nu decays?
• Unsterile-Active Neutrino Mixing: Consequences on Radiative Decay and Bounds from the X-ray Background
• CP, T and CPT analyses in EPR - correlated $B^0{\bar{B}}^0$ decays
• CPT Violation in ${\mathbf{B}}_{\mathbf{s}}^0$--${\bar{\mathbf{B}}}_{\mathbf{s}}^0$ mixing and the measurement of CP Violation in ${\mathbf{B}}_{\mathbf{s}}\to {\mathbf{K}}^{+}{\mathbf{K}}^{-}$
• About neutral kaons and similar systems; from quantum field theory to effective mass matrices