A recent letter by the D0 collaboration complements the new physics paper that they released in May. As both papers carefully point out, CPT invariance in B meson systems is assumed. Dear me.

In $B^{0}$ $\overline{B^{0}}$ oscillation QM, one considers a $2 \times 2$ Hamiltonian of the form

$H = M - \frac{i}{2} \Gamma$

acting as mass and decay on a two component $(B, \overline{B})$ state. The CPT assumption makes the diagonal entries of $M$ (and $\Gamma$) equal. For a given second quark $q$ (ie. $d$ or $s$) let us call the upper off diagonal entries $M_{12}$ and $\Gamma_{12}$. Then the quantity used by D0 to compute the asymmetry

$A^{b} \equiv \frac{N^{++} - N^{--}}{N^{++} + N^{--}} = 0.506 a^{d} + 0.494 a^{s}$

in like-sign dimuon events is

$a^{q} = \frac{| \Gamma_{12} | \textrm{sin} \phi}{| M_{12} |} $

where

$\phi = \textrm{arg} (\frac{- M_{12}}{\Gamma_{12}})$.

The new measured $A^{b}$ is $-0.00957$, which is roughly $50$ times the expected Standard Model value of -0.00023. If, however, we allowed different masses for the antiparticles, then the diagonal entries of $H$ would no longer be equal. We could account for this most simply by using an average mass for the usual CPT respecting $H$, and adding a $\Delta H$ matrix with negative $B$ mass term and positive $\overline{B}$ term, as if the antiparticles were heavier. Both of these terms would encourage an excess of $(--)$ dimuon events, such as in a greater probability of $b \rightarrow \mu^{-} X$ decays for the antiparticles $\overline{B^{0}}$. This could affect both the $d$ and $s$ terms in $A^{b}$.

8 years ago

This does not seem to conflict with the recent CDF result for the $\beta_s$ parameter, which agrees with the SM/QI value of $0.0194$.

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