We present the first determination of the binding energy of the $H$ dibaryon in the continuum limit of lattice QCD. The calculation is performed at five values of the lattice spacing $a$, using O($a$)-improved Wilson fermions at the SU(3)-symmetric p
oint with $m_pi=m_Kapprox 420$ MeV. Energy levels are extracted by applying a variational method to correlation matrices of bilocal two-baryon interpolating operators computed using the distillation technique. Our analysis employs Luschers finite-volume quantization condition to determine the scattering phase shifts from the spectrum and vice versa, both above and below the two-baryon threshold. We perform global fits to the lattice spectra using parametrizations of the phase shift, supplemented by terms describing discretization effects, then extrapolate the lattice spacing to zero. The phase shift and the binding energy determined from it are found to be strongly affected by lattice artifacts. Our estimate of the binding energy in the continuum limit of three-flavor QCD is $B_H=3.97pm1.16_{rm stat}pm0.86_{rm syst}$ MeV.
Nonlocal quark bilinear operators connected by link paths are used for studying parton distribution functions (PDFs) and transverse momentum-dependent PDFs of hadrons using lattice QCD. The nonlocality makes it difficult to understand the renormaliza
tion and improvement of these operators using standard methods. In previous work, we showed that by introducing an auxiliary field on the lattice, one can understand an on-axis Wilson-line operator as the product of two local operators in an extended theory. In this paper, we provide details about the calculation in perturbation theory of the factor for conversion from our lattice-suitable renormalization scheme to the MS-bar scheme. Extending our work, we study Symanzik improvement of the extended theory to understand the pattern of discretization effects linear in the lattice spacing, $a$, which are present even if the lattice fermion action exactly preserves chiral symmetry. This provides a prospect for an eventual $O(a)$ improvement of lattice calculations of PDFs. We also generalize our approach to apply to Wilson lines along lattice diagonals and to piecewise-straight link paths.
It would be very useful to find a way of reducing excited-state effects in lattice QCD calculations of nucleon structure that has a low computational cost. We explore the use of hybrid interpolators, which contain a nontrivial gluonic excitation, in
a variational basis together with the standard interpolator with tuned smearing width. Using the clover discretization of the field strength tensor, a calculation using a fixed linear combination of standard and hybrid interpolators can be done using the same number of quark propagators as a standard calculation, making this a cost-effective option. We find that such an interpolator, optimized by solving a generalized eigenvalue problem, reduces excited-state contributions in two-point correlators. However, the effect in three-point correlators, which are needed for computing nucleon matrix elements, is mixed: for some matrix elements such as the tensor charge, excited-state effects are suppressed, whereas for others such as the axial charge, they are enhanced. The results illustrate that the variational method is not guaranteed to reduce the net contribution from excited states except in its asymptotic regime, and suggest that it may be important to use a large basis of interpolators capable of isolating all of the relevant low-lying states.
