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Register a new userComparing the QCD potential in Perturbative QCD and Lattice QCD at large distances
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We compare the perturbatively calculated QCD potential to that obtained from lattice calculations in the theory without light quark flavours. We examine E_tot(r) = 2 m_pole + V_QCD(r) by re-expressing it in the MSbar mass m = m^MSbar(m^MSbar) and by choosing specific prescriptions for fixing the scale mu (dependent on r and m). By adjusting m so as to maximise the range of convergence, we show that perturbative and lattice calculations agree up to 3*r_0 ~ 7.5 GeV^-1 (r_0 is the Sommer scale) within the uncertainty of order Lambda^3 r^2.
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We determine the strong coupling constant $alpha_s$ from the static QCD potential by matching a theoretical calculation with a lattice QCD computation. We employ a new theoretical formulation based on the operator product expansion, in which renormalons are subtracted from the leading Wilson coefficient. We remove not only the leading renormalon uncertainty of $mathcal{O}(Lambda_{rm QCD})$ but also the first $r$-dependent uncertainty of $mathcal{O}(Lambda_{rm QCD}^3 r^2)$. The theoretical prediction for the potential turns out to be valid at the static color charge distance $Lambda_{rm overline{MS}} r lesssim 0.8$ ($r lesssim 0.4$ fm), which is significantly larger than ordinary perturbation theory. With lattice data down to $Lambda_{rm overline{MS}} r sim 0.09$ ($r sim 0.05$ fm), we perform the matching in a wide region of $r$, which has been difficult in previous determinations of $alpha_s$ from the potential. Our final result is $alpha_s(M_Z^2) = 0.1179^{+0.0015}_{-0.0014}$ with 1.3 % accuracy. The dominant uncertainty comes from higher order corrections to the perturbative prediction and can be straightforwardly reduced by simulating finer lattices.
The $XiXi$ interaction in the $^1$S$_0$ channel is studied to examine the convergence of the derivative expansion of the non-local HAL QCD potential at the next-to-next-to-leading order (N$^2$LO). We find that (i) the leading order potential from the N$^2$LO analysis gives the scattering phase shifts accurately at low energies, (ii) the full N$^2$LO potential gives only small correction to the phase shifts even at higher energies below the inelastic threshold, and (iii) the potential determined from the wall quark source at the leading order analysis agrees with the one at the N$^2$LO analysis except at short distances, and thus, it gives correct phase shifts at low energies. We also study the possible systematic uncertainties in the HAL QCD potential such as the inelastic state contaminations and the finite volume artifact for the potential and find that they are well under control for this particular system.
Recent developments in non-perturbative renormalization for lattice QCD are reviewed with a particular emphasis on RI/MOM scheme and its variants, RI/SMOM schemes. Summary of recent developments in Schroedinger functional scheme, as well as the summary of related topics are presented. Comparison of strong coupling constant and the strange quark mass from various methods are made.
Our ability to resolve new physics effects is, largely, limited by the precision with which we calculate. The calculation of observables in the Standard (or a new physics) Model requires knowledge of associated hadronic contributions. The precision of such calculations, and therefore our ability to leverage experiment, is typically limited by hadronic uncertainties. The only first-principles method for calculating the nonperturbative, hadronic contributions is lattice QCD. Modern lattice calculations have controlled errors, are systematically improvable, and in some cases, are pushing the sub-percent level of precision. I outline the role played by, highlight state of the art efforts in, and discuss possible future directions of lattice calculations in flavor physics.
We briefly review and expand our recent analysis for all three invariant A,B,D gravitational form factors of the nucleon in holographic QCD. They compare well to the gluonic gravitational form factors recently measured using lattice QCD simulations. The holographic A-term is fixed by the tensor $T=2^{++}$ (graviton) Regge trajectory, and the D-term by the difference between the tensor $T=2^{++}$ (graviton) and scalar $S=0^{++}$ (dilaton) Regge trajectories. The B-term is null in the absence of a tensor coupling to a Dirac fermion in bulk. A first measurement of the tensor form factor A-term is already accessible using the current GlueX data, and therefore the tensor gluonic mass radius, pressure and shear inside the proton, thanks to holography. The holographic A-term and D-term can be expressed exactly in terms of harmonic numbers. The tensor mass radius from the holographic threshold is found to be $langle r^2_{GT}rangle approx (0.57-0.60,{rm fm})^2$, in agreement with $langle r^2_{GT}rangle approx (0.62,{rm fm})^2$ as extracted from the overall numerical lattice data, and empirical GlueX data. The scalar mass radius is found to be slightly larger $langle r^2_{GS}rangle approx (0.7,{rm fm})^2$.
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