Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1996-05-09
Phys.Rev.D83:119902,2011; Erratum-ibid.D83:119902,2011
Physics
High Energy Physics
High Energy Physics - Phenomenology
24 pages, LaTeX, 1 figure as uudecoded file
Scientific paper
10.1103/PhysRevD.54.4419 10.1103
We use the heavy quark expansion to investigate the width difference $\Delta\Gamma_{B_s}$ between the $B_s$ mass eigenstates. The corrections of ${\cal O}(\Lambda_{QCD}/m_b)$ and ${\cal O}(m_s/m_b)$ to the leading order expression in the operator product expansion are derived and estimated to yield a sizable reduction of the leading result for $\Delta\Gamma_{B_s}$ by typically $30\%$. For completeness we also quantify small effects due to penguin operators and CKM suppressed contributions. Based on our results we discuss the prediction for $(\Delta\Gamma/\Gamma)_{B_s}$ with particular emphasis on theoretical uncertainties. We find $(\Delta\Gamma/\Gamma)_{B_s}=0.16^{+0.11}_{-0.09}$, where the large error is dominated by the uncertainty in hadronic matrix elements. An accuracy of about $10\%$ in $(\Delta\Gamma/\Gamma)_{B_s}$ should be within reach, assuming continuing progress in lattice calculations. In addition we address phenomenological issues and implications of a $\Delta\Gamma_{B_s}$ measurement for constraints on $\Delta M_{B_s}$ and CKM parameters. We further consider in some detail the lifetime ratio $\tau(B_s)/\tau(B_d)$ and estimate that, most likely, $|\tau(B_s)/\tau(B_d)-1|<1\%$.
Beneke Martin
Buchalla Gerhard
Dunietz Isard
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