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Register a new user$langle xrangle$ and $langle x^2rangle$ of the pion PDF from Lattice QCD with $N_f=2+1+1$ dynamical quark flavours
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Using Nf=2+1+1 lattice QCD, we determine the fermionic connected contributions to the second and third moment of the pion PDF. Based on gauge configurations from the European Twisted Mass Collaboration, chiral and continuum extrapolations are performed using pion masses in the range of 230 to 500 MeV and three values of the lattice spacing. Finite volume effects are investigated using different volumes. In order to avoid mixing under renormalisation for the third moment, we use an operator with two non-zero spatial components of momentum. Momenta are injected using twisted boundary conditions. Our final values read $langle xrangle=0.2075(106)$ and $langle x^2rangle=0.163(33)$, determined at 2 GeV in the $overline{MS}$-scheme and with systematic and statistical uncertainties summend in quadrature.
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We present a calculation of the pion quark momentum fraction, $langle x rangle$, and its third Mellin moment $langle x^2 rangle$. We also obtain directly, for the first time, $langle x rangle$ and $langle x^2 rangle$ for the kaon using local operators. We use an ensemble of two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with clover improvement. The quark masses are chosen so that they reproduce a pion mass of about 260 MeV, and a kaon mass of 530 MeV. The lattice spacing of the ensemble is 0.093 fm and the lattice has a spatial extent of 3 fm. We analyze several values of the source-sink time separation within the range of $1.12-2.23$ fm to study and eliminate excited-states contributions. The necessary renormalization functions are calculated non-perturbatively in the RI$$ scheme, and are converted to the $overline{rm MS}$ scheme at a scale of 2 GeV. The final values for the momentum fraction are $langle x rangle^pi_{u^+}=0.261(3)_{rm stat}(6)_{rm syst}$, $langle x rangle^K_{u^+}=0.246(2)_{rm stat}(2)_{rm syst}$, and $langle x rangle^K_{s^+}=0.317(2)_{rm stat}(1)_{rm syst}$. For the third Mellin moments we find $langle x^2 rangle^pi_{u^+}=0.082(21)_{rm stat}(17)_{rm syst}$, $langle x^2 rangle^K_{u^+}=0.093(5)_{rm stat}(3)_{rm syst}$, and $langle x^2 rangle^K_{s^+}=0.134(5)_{rm stat}(2)_{rm syst}$. The reported systematic uncertainties are due to excited-state contamination. We also give the ratio $langle x^2 rangle/langle x rangle$ which is an indication of how quickly the PDFs lose support at large $x$.
We study properties of the thermal transition in QCD, using anisotropic, fixed-scale lattice simulations with $N_f = 2+1$ flavours of Wilson fermion. Observables are compared for two values of the pion mass, focusing on chiral properties. Results are presented for the Polyakov loop, various susceptibilities, the chiral condensate and its susceptibility, and the onset of parity doubling in the light and strange baryonic sector.
We investigate the masses and decay constants of eta and eta mesons using the Wilson twisted mass formulation with N_f=2+1+1 dynamical quark flavours based on gauge configurations of ETMC. We show how to efficiently subtract excited state contributions to the relevant correlation functions and estimate in particular the eta mass with improved precision. After investigating the strange quark mass dependence and the continuum and chiral extrapolations, we present our results for masses and mixing angle(s) at the physical point. Using chiral perturbation theory we also extract the decay constants f_l and f_s and use them to estimate the decay widths of eta,eta to gamma gamma and the transition form factor in the limit of large momentum transfer.
We calculate the strange quark content of the nucleon in 2+1-flavor lattice QCD. Chirally symmetric overlap fermion formulation is used to avoid the contamination from up and down quark contents due to an operator mixing between strange and light scalar operators, bar{s}s and bar{u}u+bar{d}d. At a lattice spacing a=0.112(1) fm, we perform calculations at four values of degenerate up and down quark masses, which cover a range of the pion mass M_pi simeq 300-540 MeV. We employ two different methods: one is a direct method where we calculate the strange quark content by directly inserting the strange scalar operator. The other is an indirect method where the quark content is extracted from a derivative of the nucleon mass in terms of the strange quark mass. With these two methods we obtain consistent results with each other. Our best estimate f_{T_s}=0.009(15)(16) is in good agreement with our previous studies in two-flavor QCD.
We present lattice results on the valence-quark structure of the pion using a coordinate space method within the framework of Large Momentum Effective Theory (LaMET). In this method one relies on the matrix elements of a Euclidean correlator in boosted hadronic states, which have an operator product expansion at short distance that allows us to extract the moments of PDFs. We renormalize the Euclidean correlator by forming the reduced Ioffe-time distribution (rITD), and reconstruct the second and fourth moments of the pion PDF by taking into account of QCD evolution effects.
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