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Register a new userThe width difference in the $B_s$-$bar B_s$ system: towards NNLO
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Ulrich Nierste
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The width difference $Delta Gamma$ among the two mass eigenstates of the $B_s$-$bar B_s$ system is measured with a precision of 7%. The theory prediction has a larger uncertainty which mainly stems from unknown perturbative higher-order QCD corrections. I discuss the subset of next-to-next-to-leading order diagrams proportional to $alpha_s^2, N_f$, where $N_f=5$ is the number of quark flavours. The results are published in [1].
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We consider two-loop QCD corrections to the element $Gamma_{12}^q$ of the decay matrix in $B_q-bar{B}_q$ mixing, $q=d,s$, in the leading power of the Heavy Quark Expansion. The calculated contributions involve one current-current and one penguin operator and constitute the next step towards a theory prediction for the width difference $DeltaGamma_s$ matching the precise experimental data. We present compact analytic results for all matching coefficients in an expansion in $m_c/m_b$ up to second order. Our new corrections are comparable in size to the current experimental error and slightly increase $DeltaGamma_s$.
The interference between the K+K- S-wave and P-wave amplitudes in B_s -> J/psi K+K- decays with the K+K- pairs in the region around the phi(1020) resonance is used to determine the variation of the difference of the strong phase between these amplitudes as a function of K+K- invariant mass. Combined with the results from our CP asymmetry measurements in B_s -> J/psi phi decays, we conclude that the B_s mass eigenstate that is almost CP =+1 is lighter and decays faster than the mass eigenstate that is almost CP =-1. This determines the sign of the decay width difference DeltaGamma_s == Gamma_L -Gamma_H to be positive. Our result also resolves the ambiguity in the past measurements of the CP violating phase phi_s to be close to zero rather than pi. These conclusions are in agreement with the Standard Model expectations.
Predicting the $B_s^0-bar{B}_s^0$ width difference $DeltaGamma_s$ relies on the heavy quark expansion and on hadronic matrix elements of $Delta B=2$ operators. We present the first lattice QCD results for matrix elements of the dimension-7 operators $R_{2,3}$ and linear combinations $tilde{R}_{2,3}$ using nonrelativistic QCD for the bottom quark and a highly improved staggered quark (HISQ) action for the strange quark. Computations use MILC ensembles of gauge field configuations with $2+1+1$ flavors of sea quarks with the HISQ discretization, including lattices with physically light up/down quark masses. We discuss features unique to calculating matrix elements of these operators and analyze uncertainties from series truncation, discretization, and quark mass dependence. Finally we report the first Standard Model determination of $DeltaGamma_s$ using lattice QCD results for all hadronic matrix elements through $mathcal{O}(1/m_b)$. The main result of our calculations yields the $1/m_b$ contribution $Delta Gamma_{1/m_b} = -0.022(10)~mathrm{ps}^{-1}$. Adding this to the leading order contribution, the Standard Model prediction is $Delta Gamma_s = 0.092(14)~mathrm{ps}^{-1}$.
The time-dependent CP asymmetry in B_s^0to J/psi K^+K^- decays is measured using $pp$ collision data at sqrt{s}=7TeV, corresponding to an integrated luminosity of 1.0fb^-1, collected with the LHCb detector. The decay time distribution is characterised by the decay widths Gamma_L and Gamma_H of the light and heavy mass eigenstates of the B_s^0--bar{B}_s^0 system and by a CP-violating phase phi_s. In a sample of 27,617 B_s^0to J/psi K^+K^- decays, where the dominant contribution comes from B_s^0to J/psiphi decays, these parameters are measured to be phi_s = 0.07 pm 0.09 (stat) pm 0.01 (syst) rad, Gamma_s equiv (Gamma_L+Gamma_H)/2 = 0.663 pm 0.005 (stat) pm 0.006 (syst) ps^-1, DeltaGamma_s equiv Gamma_L -Gamma_H = 0.100 pm 0.016 (stat) pm 0.003 (syst) & ps^-1, corresponding to the single most precise determination of phi_s, DeltaGamma_s and Gamma_s. The result of performing a combined analysis with B_s^{0} to J/psi pi^+pi^- decays gives phi_s = 0.01 pm 0.07 (stat) pm 0.01 (syst) rad, Gamma_s = 0.661 pm 0.004 (stat) pm 0.006 (syst) ps^-1, DeltaGamma_s = 0.106 pm 0.011 (stat) pm 0.007 (syst) & ps^-1. All measurements are in agreement with the Standard Model predictions.
The $B_s to D_s^{(*)pm} K^mp$ decays allow a theoretically clean determination of $phi_s+gamma$, where $phi_s$ is the $B^0_s$-$bar B^0_s$ mixing phase and $gamma$ the usual angle of the unitarity triangle. A sizable $B_s$ decay width difference $DeltaGamma_s$ was recently established, which leads to subtleties in analyses of the $B_s to D_s^{(*)pm} K^mp$ branching ratios but also offers new untagged observables, which do not require a distinction between initially present $B^0_s$ or $bar B^0_s$ mesons. We clarify these effects and address recent measurements of the ratio of the $B_sto D_s^pm K^mp$, $B_sto D_s^pmpi^mp$ branching ratios. In anticipation of future LHCb analyses, we apply the SU(3) flavour symmetry of strong interactions to convert the $B$-factory data for $B_dto D^{(*)pm}pi^mp$, $B_dto D_s^{pm}pi^mp$ decays into predictions of the $B_s to D_s^{(*)pm} K^mp$ observables, and discuss strategies for the extraction of $phi_s+gamma$, with a special focus on untagged observables and the resolution of discrete ambiguities. Using our theoretical predictions as a guideline, we make simulations to estimate experimental sensitivities, and extrapolate to the end of the planned LHCb upgrade. We find that the interplay between the untagged observables, which are accessible thanks to the sizable $DeltaGamma_s$, and the mixing-induced CP asymmetries, which require tagging, will play the key role for the experimental determination of $phi_s+gamma$.
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