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Dru B. Renner
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As algorithms and computing power have advanced, lattice QCD has become a precision technique for many QCD observables. However, the calculation of nucleon matrix elements remains an open challenge. I summarize the status of the lattice effort by examining one observable that has come to represent this challenge, average-x: the fraction of the nucleons momentum carried by its quark constituents. Recent results confirm a long standing tendency to overshoot the experimentally measured value. Understanding this puzzle is essential to not only the lattice calculation of nucleon properties but also the broader effort to determine hadron structure from QCD.
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In the past year, we calculated with lattice QCD three quantities that were unknown or poorly known. They are the $q^2$ dependence of the form factor in semileptonic $Dto Kl u$ decay, the decay constant of the $D$ meson, and the mass of the $B_c$ meson. In this talk, we summarize these calculations, with emphasis on their (subsequent) confirmation by experiments.
In this report, the most recent and precise estimates of masses of ground state baryons using lattice QCD are discussed. Considering the prospects in the heavy baryon sector, lattice estimates for these are emphasized. The first and only existing lattice determination of the highly excited $Omega_c$ excitations in relation to the recent LHCb discovery is also discussed.
The $OmegaOmega$ system in the $^1S_0$ channel (the most strange dibaryon) is studied on the basis of the (2+1)-flavor lattice QCD simulations with a large volume (8.1 fm)$^3$ and nearly physical pion mass $m_{pi}simeq 146$ MeV at a lattice spacing $asimeq 0.0846$ fm. We show that lattice QCD data analysis by the HAL QCD method leads to the scattering length $a_0 = 4.6 (6)(^{+1.2}_{-0.5}) {rm fm}$, the effective range $r_{rm eff} = 1.27 (3)(^{+0.06}_{-0.03}) {rm fm}$ and the binding energy $B_{Omega Omega} = 1.6 (6) (^{+0.7}_{-0.6}) {rm MeV}$. These results indicate that the $OmegaOmega$ system has an overall attraction and is located near the unitary regime. Such a system can be best searched experimentally by the pair-momentum correlation in relativistic heavy-ion collisions.
We present ground state spectra of mesons containing a charm and a bottom quark. For the charm quark we use overlap valence quarks while a non-relativistic formulation is utilized for the bottom quark on a background of 2+1+1 flavors HISQ gauge configurations generated by the MILC collaboration. The hyperfine splitting between $1S$ states of $B_c$ mesons is found to be $56^{+4}_{-3}$ MeV. We also study the baryons containing only charm and bottom quarks and predict their ground state masses. Results are obtained at three lattice spacings.
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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