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Register a new user$Btopiell u$ semileptonic form factors from unquenched lattice QCD and determination of $|V_{ub}|$
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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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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 present a lattice-QCD calculation of the $Btopiell u$ semileptonic form factors and a new determination of the CKM matrix element $|V_{ub}|$. We use the MILC asqtad 2+1-flavor lattice configurations at four lattice spacings and light-quark masses down to 1/20 of the physical strange-quark mass. We extrapolate the lattice form factors to the continuum using staggered chiral perturbation theory in the hard-pion and SU(2) limits. We employ a model-independent $z$ parameterization to extrapolate our lattice form factors from large-recoil momentum to the full kinematic range. We introduce a new functional method to propagate information from the chiral-continuum extrapolation to the $z$ expansion. We present our results together with a complete systematic error budget, including a covariance matrix to enable the combination of our form factors with other lattice-QCD and experimental results. To obtain $|V_{ub}|$, we simultaneously fit the experimental data for the $Btopiell u$ differential decay rate obtained by the BaBar and Belle collaborations together with our lattice form-factor results. We find $|V_{ub}|=(3.72pm 0.16)times 10^{-3}$ where the error is from the combined fit to lattice plus experiments and includes all sources of uncertainty. Our form-factor results bring the QCD error on $|V_{ub}|$ to the same level as the experimental error. We also provide results for the $Btopiell u$ vector and scalar form factors obtained from the combined lattice and experiment fit, which are more precisely-determined than from our lattice-QCD calculation alone. These results can be used in other phenomenological applications and to test other approaches to QCD.
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 $|V_{ub}| = 3.55(25)(50) times 10^{-3}$.
The 2012 PDG reports a tension at the level of $3 sigma$ between two exclusive determinations of $|V_{ub}|$. They are obtained by combining the experimental branching ratios of $B to tau u$ and $B to pi l u$ (respectively) with a theoretical computation of the hadronic matrix elements $fB$ and the $B to pi$ form factor $f_+(q^2)$. To understand the tension, improved precision and a careful analysis of the systematics involved are necessary. We report the results of the ALPHA collaboration for $fB$ from the lattice with 2 flavors of $O(a)$ improved Wilson fermions. We employ HQET, including $1/m_b$ corrections, with pion masses ranging down to $approx$ 190 MeV. Renormalization and matching were performed non-perturbatively, and three lattice spacings reaching $a^{-1}approx 4.1$ GeV are used in the continuum extrapolation. We also present progress towards a computation of $f_+(q^2)$, to directly compare two independent exclusive determinations of $|V_{ub}|$ with each other and with inclusive determinations. Additionally, we report on preliminary results for $fBq{s}$, needed for the analysis of $B_s to mu^+mu^-$.}
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_+.
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