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We show the first results for parton distribution functions within the proton at the physical pion mass, employing the method of quasi-distributions. In particular, we present the matrix elements for the iso-vector combination of the unpolarized, helicity and transversity quasi-distributions, obtained with Nf = 2 twisted mass cloverimproved fermions and a proton boosted with momentum = 0.83 GeV. The momentum smearing technique has been applied to improve the overlap with the proton boosted state. Moreover, we present the renormalized helicity matrix elements in the RI’ scheme, following the non-perturbative renormalization prescription recently developed by our group.
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.
We compute potentials of two static antiquarks in the presence of two quarks qq of finite mass using lattice QCD. In a second step we solve the Schrödinger equation, to determine, whether the resulting potentials are sufficiently attractive to host a bound state, which would indicate the existence of a stable qqb¯b¯ tetraquark. We find a bound state for qq=(ud−du)/2–√ with corresponding quantum numbers I(JP)=0(1+) and evidence against the existence of bound states with isospin I=1 or qq∈{cc,ss}.
We discuss the current developments by the European Twisted Mass Collaboration in extracting parton distribution functions from the quasi-PDF approach. We concentrate on the non-perturbative renormalization prescription recently developed by us, using the RI′ scheme. We show results for the renormalization functions of matrix elements needed for the computation of quasi-PDFs, including the conversion to the MS scheme, and for renormalized matrix elements. We discuss the systematic effects present in the Z-factors and the possible ways of addressing them in the future.
This paper traces the military role of Tibnīn and its rulers in the Latin East against the Muslims until 1187/ 583. Tibnīn played a key role in overcoming the Muslims in Tyre and controlled it in 1124. It also played a vital role in the conflict between Damascus and the Kingdom of Jerusalem. Tibnīn participated in defending Antioch, Banyas, Hebron and Transjordan several times. Furthermore, its soldiers and Knights joined the army of the Kingdom of Jerusalem to capture Ascalon in 1153, and joined the campaigns of Amaury I, King of Jerusalem, against Egypt from 1164 to1169. The military situation of Tibnīn under the rule of the royal house until its fall to the Muslims in 1187/ 583 will be studied as well
The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density
We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility Xt is measured directly, and by the slab method, which is based on the topological content of sub-volumes (“slabs”) and estimates Xt even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, ξ2). This ongoing study is based on direct measurements of Xt in L × L lattices, at L/ξ ≃6.
We investigate BB̅ systems by computing potentials of two static quarks in the presence of two quarks of finite mass using lattice QCD. By solving the Schrodinger equation we check whether these potentials are sufficiently attractive to host bound states. Particular focus is put on the experimentally most promising bottomonium-like tetraquark candidate Zb± with quantum numbers I(JP) = 1(1+).
Working in a quenched setup with Wilson twisted mass valence fermions, we explore the possibility to compute non-perturbatively the step scaling function using the coordinate (X-space) renormalization scheme. This scheme has the advantage of being on-shell and gauge invariant. The step scaling method allows us to calculate the running of the renormalization constants of quark bilinear operators. We describe here the details of this calculation. The aim of this exploratory study is to identify the feasibility of the X-space scheme when used in small volume simulations required by the step scaling technique. Eventually, we translate our final results to the continuum MS scheme and compare against four-loop analytic formulae finding satisfactory agreement.
