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Register a new userVisualization of semileptonic form factors from lattice QCD
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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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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 $|V_{ub}| = 3.55(25)(50) times 10^{-3}$.
In this work we present the first non-perturbative determination of the hadronic susceptibilities that constrain the form factors entering the semileptonic $B to D^{(*)} ell u_ell $ transitions due to unitarity and analyticity. The susceptibilities are obtained by evaluating moments of suitable two-point correlation functions obtained on the lattice. Making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing ($a simeq 0.062, 0.082, 0.089$ fm) and with pion masses in the range $simeq 210 - 450$ MeV, we evaluate the longitudinal and transverse susceptibilities of the vector and axial-vector polarization functions at the physical pion point and in the continuum and infinite volume limits. The ETMC ratio method is adopted to reach the physical $b$-quark mass $m_b^{phys}$. At zero momentum transfer for the $b to c$ transition we get $chi_{0^+}(m_b^{phys}) = 7.58,(59) cdot 10^{-3}$, $chi_{1^-}(m_b^{phys}) = 6.72,(41) cdot 10^{-4}$ GeV$^{-2}$, $chi_{0^-}(m_b^{phys}) = 2.58,(17) cdot 10^{-2}$ and $chi_{1^+}(m_b^{phys}) = 4.69,(30) cdot 10^{-4}$ GeV$^{-2}$ for the scalar, vector, pseudoscalar and axial susceptibilities, respectively. In the case of the vector and pseudoscalar channels the one-particle contributions due to $B_c^*$- and $B_c$-mesons are evaluated and subtracted to improve the bounds, obtaining: $chi_{1^-}^{sub}(m_b^{phys}) = 5.84,(44) cdot 10^{-4}$ GeV$^{-2}$ and $chi_{0^-}^{sub}(m_b^{phys}) = 2.19,(19) cdot 10^{-2}$.
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.
Precision computation of hadronic physics with lattice QCD is becoming feasible. The last decade has seen percent-level calculations of many simple properties of mesons, and the last few years have seen calculations of baryon masses, including the nucleon mass, accurate to a few percent. As computational power increases and algorithms advance, the precise calculation of a variety of more demanding hadronic properties will become realistic. With this in mind, I discuss the current lattice QCD calculations of generalized parton distributions with an emphasis on the prospects for well-controlled calculations for these observables as well. I will do this by way of several examples: the pion and nucleon form factors and moments of the nucleon parton and generalized-parton distributions.
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.
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