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Register a new userB Meson Semileptonic Form Factors from Unquenched Lattice QCD
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The semileptonic process, B --> pi l u, is studied via full QCD Lattice simulations. We use unquenched gauge configurations generated by the MILC collaboration. These include the effect of vacuum polarization from three quark flavors: the $s$ quark and two very light flavors ($u/d$) of variable mass allowing extrapolations to the physical chiral limit. We employ Nonrelativistic QCD to simulate the $b$ quark and a highly improved staggered quark action for the light sea and valence quarks. We calculate the form factors $f_+(q^2)$ and $f_0(q^2)$ in the chiral limit for the range 16 GeV$^2 leq q^2 < q^2_{max}$ and obtain $int^{q^2_{max}}_{16 GeV^2} [dGamma/dq^2] dq^2 / |v_{ub}|^2 = 1.46(35) ps^{-1}$. Combining this with a preliminary average by the Heavy Flavor Averaging Group (HFAG05) of recent branching fraction data for exclusive B semileptonic decays from the BaBar, Belle and CLEO collaborations, leads to $|V_{ub}| = 4.22(30)(51) times 10^{-3}$. PLEASE NOTE APPENDIX B with an ERRATUM, to appear in Physical Review D, to the published version of this e-print (Phys.Rev.D 73, 074502 (2006)). Results for the form factor $f_+(q^2)$ in the chiral limit have changed significantly. The last two sentences in this abstract should now read; We calculate the form factor $f_+(q^2)$ and $f_0(q^2)$ in the chiral limit for the range 16 Gev$^2 leq q^2 < q^2_{max}$ and obtain $int^{q^2_{max}}_{16 GeV^2} [dGamma/dq^2] dq^2 / |V_{ub}|^2 = 2.07(57)ps^{-1}$. Combining this with a preliminary average by the Heavy Flavor Averagibg Group (HFAG05) of recent branching fraction data for exclusive B semileptonic decays from the BaBar, Belle and CLEO collaborations, leads to $|V_{ub}| = 3.55(25)(50) times 10^{-3}$.
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We update the lattice calculation of the $Btopi$ semileptonic form factors, which have important applications to the CKM matrix element $|V_{ub}|$ and the $Btopiell^+ell^-$ rare decay. We use MILC asqtad ensembles with $N_f=2+1$ sea quarks and over a range of lattice spacings $a approx 0.045$--$0.12$ fm. We perform a combined chiral and continuum extrapolation of our lattice data using SU(2) staggered chiral perturbation theory in the hard pion limit. To extend the results for the form factors to the full kinematic range, we take a functional approach to parameterize the form factors using the Bourrely-Caprini-Lellouch formalism in a model-independent way. Our analysis is still blinded with an unknown off-set factor which will be disclosed when we present the final results.
We study the exclusive semileptonic $B$-meson decays $Bto K(pi)ell^+ell^-$, $Bto K(pi) ubar u$, and $Btopitau u$, computing observables in the Standard model using the recent lattice-QCD results for the underlying form factors from the Fermilab Lattice and MILC Collaborations. These processes provide theoretically clean windows into physics beyond the Standard Model because the hadronic uncertainties are now under good control for suitably binned observables. For example, the resulting partially integrated branching fractions for $Btopimu^+mu^-$ and $Bto Kmu^+mu^-$ outside the charmonium resonance region are 1-2$sigma$ higher than the LHCb Collaborations recent measurements, where the theoretical and experimental errors are commensurate. The combined tension is 1.7$sigma$. Combining the Standard-Model rates with LHCbs measurements yields values for the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_{td}|=7.45{(69)}times10^{-3}$, $|V_{ts}|=35.7(1.5)times10^{-3}$, and $|V_{td}/V_{ts}|=0.201{(20)}$, which are compatible with the values obtained from neutral $B_{(s)}$-meson oscillations and have competitive uncertainties. Alternatively, taking the CKM matrix elements from unitarity, we constrain new-physics contributions at the electroweak scale. The constraints on the Wilson coefficients ${rm Re}(C_9)$ and ${rm Re}(C_{10})$ from $Btopimu^+mu^-$ and $Bto Kmu^+mu^-$ are competitive with those from $Bto K^* mu^+mu^-$, and display a 2.0$sigma$ tension with the Standard Model. Our predictions for $Bto K(pi) ubar u$ and $Btopitau u$ are close to the current experimental limits.
We study $B_d$ and $B_s$ mixing in unquenched lattice QCD employing the MILC collaboration gauge configurations that include u, d, and s sea quarks based on the improved staggered quark (AsqTad) action and a highly improved gluon action. We implement the valence light quarks also with the AsqTad action and use the nonrelativistic NRQCD action for the valence b quark. We calculate hadronic matrix elements necessary for extracting CKM matrix elements from experimental measurements of mass differences $Delta M_d$ and $Delta M_s$. We find $xi = f_{B_s} sqrt{hat{B}_{B_s}} / f_{B_d} sqrt{hat{B}_{B_d}} = 1.258(33)$, $f_{B_d} sqrt{hat{B}_{B_d}} = 216(15)$ MeV and $f_{B_s} sqrt{hat{B}_{B_s}} = 266(18)$ MeV. We also update previous results for decay constants and obtain $f_{B_d} = 190(13)$ MeV, $f_{B_s} = 231(15)$ MeV and $f_{B_s}/f_{B_d} = 1.226(26)$. The new lattice results lead to updated values for the ratio of CKM matrix elements $|V_{td}|/|V_{ts}|$ and for the Standard Model prediction for $Br(B_s rightarrow mu^+ mu^-)$ with reduced errors. We determine $|V_{td}|/|V_{ts}| = 0.214(1)(5)$ and $Br(B_s rightarrow mu^+ mu^-) = 3.19(19) times 10^{-9}$.
Comparisons of lattice-QCD calculations of semileptonic form factors with experimental measurements often display two sets of points, one each for lattice QCD and experiment. Here we propose to display the output of a lattice-QCD analysis as a curve and error band. This is justified, because lattice-QCD results rely in part on fitting, both for the chiral extrapolation and to extend lattice-QCD data over the full physically allowed kinematic domain. To display an error band, correlations in the fit parameters must be taken into account. For the statistical error, the correlation comes from the fit. To illustrate how to address correlations in the systematic errors, we use the Becirevic-Kaidalov parametrization of the D -> pi l nu and D -> K l nu form factors, and a analyticity-based fit for the B -> pi l nu form factor f_+.
We compute the $Btopiell u$ semileptonic form factors and update the determination of the CKM matrix element $|V_{ub}|$. We use the MILC asqtad ensembles with $N_f=2+1$ sea quarks at four different lattice spacings in the range $a approx 0.045$~fm to $0.12$~fm. The lattice form factors are extrapolated to the continuum limit using SU(2) staggered chiral perturbation theory in the hard pion limit, followed by an extrapolation in $q^2$ to the full kinematic range using a functional $z$-parameterization. The extrapolation is combined with the experimental measurements of the partial branching fraction to extract $|V_{ub}|$. Our preliminary result is $|V_{ub}|=(3.72pm 0.14)times 10^{-3}$, where the error reflects both the lattice and experimental uncertainties, which are now on par with each other.
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