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Register a new userDetermination of $Lambda_{overline{textrm{MS}}}^{(n_f=2)}$ and analytic parameterization of the static quark-antiquark potential
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While lattice QCD allows for reliable results at small momentum transfers (large quark separations), perturbative QCD is restricted to large momentum transfers (small quark separations). The latter is determined up to a reference momentum scale $Lambda$, which is to be provided from outside, e.g. from experiment or lattice QCD simulations. In this article, we extract $Lambda_{overline{textrm{MS}}}$ for QCD with $n_f=2$ dynamical quark flavors by matching the perturbative static quark-antiquark potential in momentum space to lattice results in the intermediate momentum regime, where both approaches are expected to be applicable. In a second step, we combine the lattice and the perturbative results to provide a complete analytic parameterization of the static quark-antiquark potential in position space up to the string breaking scale. As an exemplary phenomenological application of our all-distances potential we compute the bottomonium spectrum in the static limit.
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We determine the strong coupling constant $alpha_s(M_Z)$ from the static QCD potential by matching a lattice result and a theoretical calculation. We use a new theoretical framework based on operator product expansion (OPE), where renormalons are subtracted from the leading Wilson coefficient. We find that our OPE prediction can explain the lattice data at $Lambda_{rm QCD} r lesssim 0.8$. This allows us to use a larger window in matching, which leads to a more reliable determination. We obtain $alpha_s(M_Z)=0.1179^{+0.0015}_{-0.0014}$.
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.
We extend HPQCDs earlier $n_f=4$ lattice-QCD analysis of the ratio of $overline{mathrm{MSB}}$ masses of the $b$ and $c$ quark to include results from finer lattices (down to 0.03fm) and a new calculation of QED contributions to the mass ratio. We find that $overline{m}_b(mu)/overline{m}_c(mu)=4.586(12)$ at renormalization scale $mu=3$,GeV. This result is nonperturbative. Combining it with HPQCDs recent lattice QCD$+$QED determination of $overline{m}_c(3mathrm{GeV})$ gives a new value for the $b$-quark mass: $overline{m}_b(3mathrm{GeV}) = 4.513(26)$GeV. The $b$-mass corresponds to $overline{m}_b(overline{m}_b, n_f=5) = 4.202(21)$GeV. These results are the first based on simulations that include QED.
The existing theory of hard exclusive QCD processes is based on two assumptions: (i) $factorization$ into a $hard,block$ times light front distribution amplitudes (DAs); (ii) use of perturbative gluon exchanges within the hard block. However, unlike DIS and jet physics, the characteristic momentum transfer $Q$ involved in the factorized block is not large enough for this theory to be phenomenologically successful. In this work, we revisit the latter assumption (ii), by explicitly calculating the $instanton-induced$ contributions to the hard block, and show that they contribute substantially to the vector, scalar and gravitational form factors of the pseudoscalar, scalar and vector mesons, over a wide range of momentum transfer.
We study the analytic properties of the t Hooft coupling expansion of the beta-function at the leading nontrivial large-$N_f$ order for QED, QCD, Super QED and Super QCD. For each theory, the t Hooft coupling expansion is convergent. We discover that an analysis of the expansion coefficients to roughly 30 orders is required to establish the radius of convergence accurately, and to characterize the (logarithmic) nature of the first singularity. We study summations of the beta-function expansion at order $1/N_f$, and identify the physical origin of the singularities in terms of iterated bubble diagrams. We find a common analytic structure across these theories, with important technical differences between supersymmetric and non-supersymmetric theories. We also discuss the expected structure at higher orders in the $1/N_f$ expansion, which will be in the future accessible with the methods presented in this work, meaning without the need for resumming the perturbative series. Understanding the structure of the large-$N_f$ expansion is an essential step towards determining the ultraviolet fate of asymptotically non-free gauge theories.
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