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We present our recent results on antiheavy-antiheavy-light-light tetraquark systems using lattice QCD. Our study of the b¯b¯us four-quark system with quantum numbers JP=1+ and the b¯c¯ud four-quark systems with I(JP)=0(0+) and I(JP)=0(1+) utilizes scattering operators at the sink to improve the extraction of the low-lying energy levels. We found a bound state for b¯b¯us with Ebind,b¯b¯us=(−86±22±10)MeV, but no indication for a bound state in both b¯c¯ud channels. Moreover, we show preliminary results for b¯b¯ud with I(JP)=0(1+), where we used scattering operators both at the sink and the source. We found a bound state and determined its infinite-volume binding energy with a scattering analysis, resulting in Ebind,b¯b¯ud=(−103±8)MeV.
We present our recent results on antiheavy-antiheavy-light-light tetraquark systems using lattice QCD. Our study of the b¯b¯us four-quark system with quantum numbers JP=1+ and the b¯c¯ud four-quark systems with I(JP)=0(0+) and I(JP)=0(1+) utilizes scattering operators at the sink to improve the extraction of the low-lying energy levels. We found a bound state for b¯b¯us with Ebind,b¯b¯us=(−86±22±10)MeV, but no indication for a bound state in both b¯c¯ud channels. Moreover, we show preliminary results for b¯b¯ud with I(JP)=0(1+), where we used scattering operators both at the sink and the source. We found a bound state and determined its infinite-volume binding energy with a scattering analysis, resulting in Ebind,b¯b¯ud=(−103±8)MeV.
In this work we present, for the first time, the non-perturbative renormalization for the unpolarized, helicity and transversity quasi-PDFs, in an RI′ scheme. The proposed prescription addresses simultaneously all aspects of renormalization: logarithmic divergences, finite renormalization as well as the linear divergence which is present in the matrix elements of fermion operators with Wilson lines. Furthermore, for the case of the unpolarized quasi-PDF, we describe how to eliminate the unwanted mixing with the twist-3 scalar operator.
We utilize perturbation theory for the one-loop conversion factor that brings the renormalization functions to the MS-scheme at a scale of 2 GeV. We also explain how to improve the estimates on the renormalization functions by eliminating lattice artifacts. The latter can be computed in one-loop perturbation theory and to all orders in the lattice spacing.
We apply the methodology for the renormalization to an ensemble of twisted mass fermions with Nf = 2 + 1 + 1 dynamical quarks, and a pion mass of around 375 MeV.