arXiv subjects

Simone Bacchio

Publications and source records attributed to Simone Bacchio.

64 records · Page 4Linked to original sources

arXiv2021

The pion and kaon $\langle x^3 \rangle$ from lattice QCD and PDF reconstruction from Mellin moments

We present a calculation of the pion and kaon Mellin moment $\langle x^3 \rangle$ extracted directly in lattice QCD using a three-derivative local operator. We use one ensemble of gauge configurations with two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with clover improvement. The ensemble reproduces a pion mass $\sim260$ MeV, and a kaon mass $\sim530$ MeV. Excited-states contamination is evaluated using four values of the source-sink time separation within the range of $1.12-1.67$ fm. We use an operator that is free of mixing, and apply a multiplicative renormalization function calculated non-perturbatively. Our results are converted to the $\overline{\rm MS}$ scheme and evolved at a scale of 2 GeV, using three-loop expressions in perturbation theory. The final values are $\langle x^3 \rangle_π^{u^+}=0.024(18)_{\rm stat}(2)_{\rm syst}$, $\langle x^3 \rangle_K^{u^+}=0.035(6)_{\rm stat}(3)_{\rm syst}$, and $\langle x^3 \rangle_K^{s^+}=0.075(5)_{\rm stat}(1)_{\rm syst}$, where the systematic error is the uncertainty due to excited state contamination. We combine $\langle x^3 \rangle$ with the two lower moments to obtain the ratios $\langle x^3 \rangle/\langle x \rangle$ and $\langle x^3 \rangle/\langle x^2 \rangle$, as well as ratios between the pion and kaon moments. In addition, we reconstruct the $x$-dependence of the pion and kaon PDFs via 2- and 3-parameter fits to our results. We find that the reconstruction is feasible and that our lattice data favor a large $x$-dependence that falls as $(1-x)^2$ for both the pion and kaon PDFs. We integrate the reconstructed PDFs to extract the higher moments with $4\leq n\leq 6$. Finally, we compare the pion and kaon PDFs, as well as the ratios of their moments, to address the effect of SU(3) flavor symmetry breaking.

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arXiv2021

The Mellin moments $\langle x \rangle$ and $\langle x^2 \rangle$ for the pion and kaon from lattice QCD

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 $\langle x \rangle^π_{u^+}=0.261(3)_{\rm stat}(6)_{\rm syst}$, $\langle x \rangle^K_{u^+}=0.246(2)_{\rm stat}(2)_{\rm syst}$, and $\langle x \rangle^K_{s^+}=0.317(2)_{\rm stat}(1)_{\rm syst}$. For the third Mellin moments we find $\langle x^2 \rangle^π_{u^+}=0.082(21)_{\rm stat}(17)_{\rm syst}$, $\langle x^2 \rangle^K_{u^+}=0.093(5)_{\rm stat}(3)_{\rm syst}$, 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 $x$.

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arXiv2019

Investigating volume effects for N$_f$=2 twisted clover fermions at the physical point

In this work we present preliminary results on the nucleon axial and tensor charges, the quark momentum fraction and the first moment of the helicity distribution. The simulations have been performed using two $N_f{=}2$ and $N_f{=}2{+}1{+}1$ ensembles. Both ensembles have a twisted mass action with a clover term with the quark masses fixed at their physical values (physical point) and volumes of $64^3{\times}128$. The extracted quantities are compared with results from an existing $N_f{=}2$ ($48^3{\times}96$) ensemble. This comparison allows one to address volume and quenching effects.

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arXiv2018

Simulating twisted mass fermions at physical light, strange and charm quark masses

We present the QCD simulation of the first gauge ensemble of two degenerate light quarks, a strange and a charm quark with all quark masses tuned to their physical values within the twisted mass fermion formulation. Results for the pseudoscalar masses and decay constants confirm that the produced ensemble is indeed at the physical parameters of the theory. This conclusion is corroborated by a complementary analysis in the baryon sector. We examine cutoff and isospin breaking effects and demonstrate that they are suppressed through the presence of a clover term in the action.

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arXiv2018

Multigrid approach in shifted linear systems for the non-degenerated twisted mass operator

Application of multigrid solvers in shifted linear systems is studied. We focus on accelerating the rational approximation needed for simulating single flavor operators. This is particularly useful, in the case of twisted mass fermions for mass non-degenerate quarks and can be employed to accelerate the $N_f=1+1$ sector of $N_f=2+1+1$ twisted mass fermion simulations. The multigrid solver is accelerated by employing suitable initial guesses. We propose a novel strategy for proposing initial guesses for shifted linear systems based on the Lagrangian interpolation of the previous solutions.

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arXiv2017

Simulation of an ensemble of $N_f=2+1+1$ twisted mass clover-improved fermions at physical quark masses

We present a general strategy aimed at generating $N_f=2+1+1$ configurations with quarks at their physical mass using maximally twisted mass fermions to ensure automatic $O(a)$ improvement, in the presence of a clover term tuned to reduce the charged to neutral pion mass difference. The target system, for the moment, is a lattice of size $64^3 \times 128$ with a lattice spacing $a\sim 0.08$ fm. We show preliminary results on the pion and kaon mass and decay constants.

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arXiv2017

Multigrid accelerated simulations for Twisted Mass fermions

Simulations at physical quark masses are affected by the critical slowing down of the solvers. Multigrid preconditioning has proved to deal effectively with this problem. Multigrid accelerated simulations at the physical value of the pion mass are being performed to generate $N_f = 2$ and $N_f = 2 + 1 + 1$ gauge ensembles using twisted mass fermions. The adaptive aggregation-based domain decomposition multigrid solver, referred to as DD-$α$AMG method, is employed for these simulations. Our simulation strategy consists of an hybrid approach of different solvers, involving the Conjugate Gradient (CG), multi-mass-shift CG and DD-$α$AMG solvers. We present an analysis of the multigrid performance during the simulations discussing the stability of the method. This significant speeds up the Hybrid Monte Carlo simulation by more than a factor $4$ at physical pion mass compared to the usage of the CG solver.

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arXiv2017

Computation of parton distributions from the quasi-PDF approach at the physical point

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 $N_f=2$ twisted mass clover-improved fermions and a proton boosted with momentum $|\vec{p}|=0.83\mbox{ GeV}$. 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.

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arXiv2016

Adaptive Aggregation-based Domain Decomposition Multigrid for Twisted Mass Fermions

The Adaptive Aggregation-based Domain Decomposition Multigrid method (arXiv:1303.1377) is extended for two degenerate flavors of twisted mass fermions. By fine-tuning the parameters we achieve a speed-up of the order of hundred times compared to the conjugate gradient algorithm for the physical value of the pion mass. A thorough analysis of the aggregation parameters is presented, which provides a novel insight into multigrid methods for lattice QCD independently of the fermion discretization.

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arXiv2016

DDalphaAMG for Twisted Mass Fermions

We present the Adaptive Aggregation-based Domain Decomposition Multigrid method extended to the twisted mass fermion discretization action. We show comparisons of results as a function of tuning the parameters that enter the twisted mass version of the DDalphaAMG library (https://github.com/sbacchio/DDalphaAMG). Moreover, we linked the DDalphaAMG library to the tmLQCD software package and give details on the performance of the multigrid solver during HMC simulations at the physical point.

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