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1. Hadronic vacuum polarization of the muon on 2+1+1-flavor HISQ ensembles: an update.

   https://doi.org/10.22323/1.396.0526  

   Lahert, Shaun ; DeTar, Carleton ; El-Khadra, Aida X ; Gámiz, Elvira ; Gottlieb, Steven ; Kronfeld, Andreas ; Neil, Ethan ; Peterson, Curtis T. ; Van de Water, Ruth ( May 2022 , The 38th International Symposium on Lattice Field Theory (LATTICE2021))

   We give an update on the status of the Fermilab Lattice-HPQCD-MILC calculation of the con- tribution to the muon’s anomolous magnetic moment from the light-quark, connected hadronic vacuum polarization. We present preliminary, blinded results in the intermediate window for this contribution a^ll_{\mu W}. The calculation is performed on Nf = 2 + 1 + 1 highly-improved staggered quark (HISQ) ensembles from the MILC collaboration with physical pion mass at four lattice spacings between 0.15 fm and 0.06 fm. We also present preliminary results for a study of the two- pion contributions to the vector-current correlation function performed on the 0.15 fm ensemble contribution, 𝑎𝑙𝑙 . The calculation is performed on the 0.15 fm ensemble where we see a factor of four improvement over traditional noise reduction techniques. 

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2. I=3/2 nucleon-pion scattering and the Delta(1232) resonance on 2+1 flavor CLS ensembles using the stochastic LapH method

   Andersen, Christian Walther ; Bulava, John ; Hoerz, Ben ; Morningstar, Colin ( November 2019 , 37th International Symposium on Lattice Field Theory)

   Calculations of the elastic I=3/2 nucleon-pion scattering phase shifts on two lattice QCD ensembles with mπ=200MeV and 280MeV are presented. The ensembles both employ Nf=2+1 Wilson clover fermions. We determine the Δ(1232) resonance parameters from a finite volume scattering analysis. In one study the single partial wave simplification is employed to compute the ppp-wave amplitude while in the other we treat the partial wave mixing between sss- and ppp-wave contributions. Fitting our data to a Breit-Wigner resonance model we find mΔ/mπ=7.13(9) and 4.75(5) on the two ensembles respectively, showing that for a lighter quark mass the resonance mass moves from near the Nπ threshold to near the Nππ threshold, in agreement with experiment. 

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3. Pion valence quark distribution at physical pion mass of N f = 2 + 1 + 1 lattice QCD

   https://doi.org/10.1088/1361-6471/ad3162  

   Holligan, Jack ; Lin, Huey-Wen ( April 2024 , Journal of Physics G: Nuclear and Particle Physics)

   We present a state-of-the-art calculation of the unpolarized pion valence-quark distribution in the framework of large-momentum effective theory (LaMET) with improved handling of systematic errors as well as two-loop perturbative matching. We use lattice ensembles generated by the MILC collaboration at lattice spacinga≈ 0.09 fm, lattice volume 64³× 96,N_f= 2 + 1 + 1 flavors of highly-improved staggered quarks and a physical pion mass. The LaMET matrix elements are calculated with pions boosted to momentumP_z≈ 1.72 GeV with high-statistics ofO(10⁶) measurements. We study the pion PDF in both hybrid-ratio and hybrid-regularization-independent momentum subtraction (hybrid-RI/MOM) schemes and also compare the systematic errors with and without the addition of leading-renormalon resummation (LRR) and renormalization-group resummation (RGR) in both the renormalization and lightcone matching. The final lightcone PDF results are presented in the modified minimal-subtraction scheme at renormalization scaleμ= 2.0 GeV. We show that thex-dependent PDFs are compatible between the hybrid-ratio and hybrid-RI/MOM renormalization with the same improvements. We also show that systematics are greatly reduced by the simultaneous inclusion of RGR and LRR and that these methods are necessary if improved precision is to be reached with higher-order terms in renormalization and matching.

    

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4. Pion PDFs confronted by fixed-target charmonium production

   https://doi.org/10.1007/s43673-023-00085-4  

   Chang, Wen-Chen ; Hsieh, Chia-Yu ; Lian, Yu-Shiang ; Peng, Jen-Chieh ; Platchkov, Stephane ; Sawada, Takahiro ( July 2023 , AAPPS Bulletin)

   The pion, as the Goldstone boson of the strong interaction, is the lightest QCD bound state and responsible for the long-range nucleon-nucleon interaction inside the nucleus. Our knowledge on the pion partonic structure is limited by the existing Drell-Yan data which are primarily sensitive to the pion valence-quark distributions. The recent progress of global analysis of pion’s parton distribution functions (PDFs) utilizing various experimental approaches are introduced. From comparisons between the pion-induced$$J/\psi$$$J/\psi$and$$\psi (2S)$$$\psi \left(2S\right)$production data with theoretical calculations using the CEM and NRQCD models, we show how these charmonium production data could provide useful constraints on the pion PDFs.

    

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5. Gluon Parton Distribution of the Pion from Lattice QCD

   Zhouyou Fan, Huey-Wen Lin ( January 2021 , Physics letters)

   null (Ed.)

   We present the first determination of the x-dependent pion gluon distribution from lattice QCD using the pseudo-PDF approach. We use lattice ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration, at two lattice spacings a≈0.12 and 0.15~fm and three pion masses Mπ≈220, 310 and 690 MeV. We use clover fermions for the valence action and momentum smearing to achieve pion boost momentum up to 2.29 GeV. We find that the dependence of the pion gluon parton distribution on lattice spacing and pion mass is mild. We compare our results from the lightest pion mass ensemble with the determination by JAM and xFitter global fits. 

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