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Probing penguin coefficients with the lifetime ratio<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mi>τ</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:…
We calculate penguin contributions to the lifetime splitting between the ${B}_{s}$ and the ${B}_{d}$ meson. In the standard model the penguin effects are found to be opposite in sign, but of similar magnitude as the contributions of the current-current operators, despite the smallness of the penguin coefficients. We predict $\ensuremath{\tau}{(B}_{s})/\ensuremath{\tau}{(B}_{d})\ensuremath{-}1=(\ensuremath{-}1.2\ifmmode\pm\else\textpm\fi{}10.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}{(f}_{{B}_{s}}/190\mathrm{MeV}{)}^{2},$ …