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Register a new userSecond Moment of the Pion Light-cone Distribution Amplitude from Lattice QCD
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We present the results of a lattice study of the second moment of the light-cone pion distribution amplitude using two flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to $m_pisim 150 , mathrm {MeV}$. At lattice spacings between $0.06 , mathrm {fm}$ and $0.08 , mathrm {fm}$ we find for the second Gegenbauer moment the value $a_2 = 0.1364(154)(145)$ at the scale $mu=2 , mathrm {GeV}$ in the $overline{mathrm{MS}}$ scheme, where the first error is statistical including the uncertainty of the chiral extrapolation, and the second error is the estimated uncertainty coming from the nonperturbatively determined renormalization factors.
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Using the second moment of the pion distribution amplitude as an example, we investigate whether lattice calculations of matrix elements of local operators involving covariant derivatives may benefit from the recently proposed momentum smearing technique for hadronic interpolators. Comparing the momentum smearing technique to the traditional Wuppertal smearing we find - at equal computational cost - a considerable reduction of the statistical errors. The present investigation was carried out using $N_f=2+1$ dynamical non-perturbatively order $a$ improved Wilson fermions on lattices of different volumes and pion masses down to 220 MeV.
We present the results of a lattice study of the normalization constants and second moments of the light-cone distribution amplitudes of longitudinally and transversely polarized $rho$ mesons. The calculation is performed using two flavors of dynamical clover fermions at lattice spacings between $0.060,text{fm}$ and $0.081,text{fm}$, different lattice volumes up to $m_pi L = 6.7$ and pion masses down to $m_pi=150,text{MeV}$. Bare lattice results are renormalized non-perturbatively using a variant of the RI-MOM scheme and converted to the $overline{text{MS}}$ scheme. The necessary conversion coefficients, which are not available in the literature, are calculated. The chiral extrapolation for the relevant decay constants is worked out in detail. We obtain for the ratio of the tensor and vector coupling constants $f_rho^T/f_rho^{vphantom{T}} = 0.629(8)$ and the values of the second Gegenbauer moments $a_2^parallel = 0.132(27)$ and $a_2^perp = 0.101(22)$ at the scale $mu = 2,text{GeV}$ for the longitudinally and transversely polarized $rho$ mesons, respectively. The errors include the statistical uncertainty and estimates of the systematics arising from renormalization. Discretization errors cannot be estimated reliably and are not included. In this calculation the possibility of $rhotopipi$ decay at the smaller pion masses is not taken into account.
We present lattice QCD results for the wave function normalization constants and the first moments of the distribution amplitudes for the lowest-lying baryon octet. The analysis is based on a large number of $N_f=2+1$ ensembles comprising multiple trajectories in the quark mass plane including physical pion (and kaon) masses, large volumes, and, most importantly, five different lattice spacings down to $a=0.039,mathrm{fm}$. This allows us to perform a controlled extrapolation to the continuum and infinite volume limits by a simultaneous fit to all available data. We demonstrate that the formerly observed violation of flavor symmetry breaking constraints can, indeed, be attributed to discretization effects that vanish in the continuum limit.
We present the first lattice determination of the two lowest Gegenbauer moments of the leading-twist pion and kaon light-cone distribution amplitudes with full control of all errors. The calculation is carried out on 35 different CLS ensembles with $N_f=2+1$ flavors of dynamical Wilson-clover fermions. These cover a multitude of pion and kaon mass combinations (including the physical point) and 5 different lattice spacings down to $a=0.039,$fm. The momentum smearing technique and a new operator basis are employed to reduce statistical fluctuations and to improve the overlap with the ground states. The results are obtained from a combined chiral and continuum limit extrapolation that includes three separate trajectories in the quark mass plane. The present arXiv version (v3) includes an Addendum where we update the results using the recently calculated three-loop matching factors for the conversion from the RI/SMOM to the $overline{text{MS}}$ scheme. We find $a_2^pi=0.116^{+19}_{-20}$ for the pion, $a_1^K=0.0525^{+31}_{-33}$ and $a_2^K=0.106^{+15}_{-16}$ for the kaon. We also include the previous values, which were obtained with two-loop matching.
We present the first determination of the $x$-dependent pion gluon distribution from lattice QCD using the pseudo-PDF approach. We use lattice ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration, at two lattice spacings $aapprox 0.12$ and 0.15~fm and three pion masses $M_piapprox 220$, 310 and 690 MeV. We use clover fermions for the valence action and momentum smearing to achieve pion boost momentum up to 2.29 GeV. We find that the dependence of the pion gluon parton distribution on lattice spacing and pion mass is mild. We compare our results from the lightest pion mass ensemble with the determination by JAM and xFitter global fits.
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