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S. Dalley
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Ideas and recent results for light-front Hamiltonian quantisation of lattice gauge theories.
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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 give a status report of our work on light cone Hamiltonian lattice QCD. We have derived an effective Hamiltonian $H_{eff}$ which is only quadratic in the momenta and therefore can be simulated by standard methods. For this Hamiltonian we determine variationally an approximate ground state wave functional in the light cone limit.
Using the approach proposed a few years ago by X. Ji, it has become feasible to extract parton distribution functions (PDFs) from lattice QCD, a task thought to be extremely difficult before Jis proposal. In this talk, we discuss this approach, in particular different systematic effects that need to be controlled to ultimately have precise determinations of PDFs. Special attention is paid to the analysis of excited states. We emphasize that it is crucial to control excited states contamination and we show an analysis thereof for our lattice data, used to calculate quasi-PDFs and finally light-cone PDFs in the second part of this proceeding (C. Alexandrou et al., Quasi-PDFs from Twisted mass fermions at the physical point).
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