Huey-Wen Lin — USQCD All Hands' Meeting
Lattice Parton Physics Project (LP3) https://www.pa.msu.edu/~hwlin/LP3/ Huey-Wen Lin (PI) Xiangdong Ji Luchang Jin Peng Sun Yi-Bo Yang (MSU) (UMD) (BNL) (MSU) (MSU) International collaborators Yong Zhao (MIT) Jiunn-Wei Chen Tomomi Ishikawa Jian-Hui Zhang (NTU) (SJTU) (Regensburg) Huey-Wen Lin — USQCD All Hands' Meeting
Parton Distribution Functions § PDFs are universal quark/gluon distributions of nucleon Many ongoing/planned experiments (BNL, JLab, J-PARC, COMPASS, GSI, EIC, LHeC , …) Imaging of the proton How are the sea quarks and gluons, and their spins, distributed in space and momentum inside the nucleon? EIC White Paper, 1212.1701 Huey-Wen Lin — USQCD All Hands' Meeting
Parton Distribution Functions § PDFs are universal quark/gluon distributions of nucleon Many ongoing/planned experiments (BNL, JLab, J-PARC, COMPASS, GSI, EIC, LHeC , …) § Important inputs to discern new physics at LHC Currently dominate errors in Higgs production Huey-Wen Lin — USQCD All Hands' Meeting
Global Analysis § Discrepancies appear when data is scarce § Many groups have tackled the analysis CTEQ, MSTW, ABM, JR, NNPDF, etc. Jimenez-Delgado, Melnitchouk, Owens, J.Phys. G40 (2013) 09310 Huey-Wen Lin — USQCD All Hands' Meeting
Global Analysis § Discrepancies appear when data is scarce § Many groups have tackled the analysis CTEQ, MSTW, ABM, JR, NNPDF, etc. § A first joint workshop with global-fitting community to address key LQCD inputs http://www.physics.ox.ac.uk /confs/PDFlattice2017 Whitepaper will study the needed precision of lattice PDFs in the large- 𝑦 region Jimenez-Delgado, Melnitchouk, Owens, J.Phys. G40 (2013) 09310 Huey-Wen Lin — USQCD All Hands' Meeting
A Pro romi misi sing Ne New Dir irec ectio tion Huey-Wen Lin — USQCD All Hands' Meeting
PDFs on the Lattice Long existing obstacles! § Lattice calculations rely on operator product expansion, 1 only provide moments 〈 x n 〉 𝑦 𝑜 𝑟 = න 𝑒𝑦 𝑦 𝑜 𝑟 𝑦 −1 § For higher moments, all ops mix with lower-dimension ops No practical proposal to overcome this New Strategy (LaMET): § Calculate finite-momentum boosted quark distribution In P z →∞ limit, parton distribution is recovered For finite P z , corrections are needed § Feasible with today’s resources! Xiangdong Ji, Phys. Rev. Lett. 111, 039103 (2013) Huey-Wen Lin — USQCD All Hands' Meeting
Parton Distribution Functions Large-Momentum Effective Theory for PDFs Γ Γ ∈ {𝛿 𝑨 , 𝛿 𝑨 𝛿 5 , 𝛿 𝑨 𝛿 ⊥ 𝛿 5 } 𝑅 2 = 0 𝑞(𝑄 𝑨 ) 𝑞(𝑄 𝑨 ) 𝑨 →∞ limit 𝑄 2 𝑄 2 + 𝒫 2 2 Τ Τ 𝑟 𝑦, 𝜈 = 𝑟 𝑦, 𝜈, 𝑄 𝑨 + 𝒫 𝛽 𝑡 + 𝒫 𝑁 𝑂 Λ QCD 𝑄 𝑨 𝑨 X. Xiong et al., 1310.7471; J.-W. Chen et al, 1603.06664 Huey-Wen Lin — USQCD All Hands' Meeting
Sea Flavor Asymmetry Sea Flavor Asymmetry § First time in LQCD history to study antiquark distribution! 𝑁 𝜌 ≈ 310 MeV HWL et al. 1402.1462 𝑟 𝑦 = −𝑟 −𝑦 ത Lost resolution in small- x region Future improvement: larger lattice volume 𝑣 𝑦 − ҧ න 𝑒𝑦 ത 𝑒(𝑦) ≈ −0.16(7) R. Towell et al. (E866/NuSea), Phys.Rev. D64, 052002 (2001) 𝒚 Huey-Wen Lin — USQCD All Hands' Meeting
Sea Flavor Asymmetry Sea Flavor Asymmetry § First time in LQCD history to study antiquark distribution! 𝑁 𝜌 ≈ 310 MeV HWL et al. 1402.1462 𝑟 𝑦 = −𝑟 −𝑦 ത Lost resolution in small- x region Future improvement: A milestone for lattice QCD! larger lattice volume First sea flavor asymmetry ever 𝑣 𝑦 − ҧ න 𝑒𝑦 ത 𝑒(𝑦) ≈ −0.16(7) calculated! R. Towell et al. (E866/NuSea), Phys.Rev. D64, 052002 (2001) 𝒚 Huey-Wen Lin — USQCD All Hands' Meeting
Sea Flavor Asymmetry Sea Flavor Asymmetry § Lattice exploratory study Compared with E866 𝑁 𝜌 ≈ 310 MeV Too good to be true? HWL et al 1402.1462 Lost resolution in small- x region Future improvement to Similar results repeated have larger lattice volume by ETMC, at 𝑁 𝜌 ≈ 373 MeV 𝑣 𝑦 − ҧ න 𝑒𝑦 ത 𝑒(𝑦) ≈ −0.16(7) ETMC, 1504.07455 R. Towell et al. (E866/NuSea), Phys.Rev. D64, 052002 (2001) 𝒚 Huey-Wen Lin — USQCD All Hands' Meeting
Transversity Distribution Pos(LATTICE 2013), § Exploratory study 𝑁 𝜌 ≈ 310 MeV 1603.06664 The calculation was also Removing repeated by ETMC, n / P n ) errors + O ( α s ) O ( M N at 𝑁 𝜌 ≈ 373 MeV z Preliminary + O ( Λ 2 2 ) QCD / P ETMC, 1610.03689 z 1505.05589; 1503.03495 𝜀ത 𝑟 𝑦 = −𝜀𝑟 −𝑦 𝑣 𝑦 − 𝜀 ҧ න 𝑒𝑦 𝜀ത 𝑒(𝑦) ≈ −0.10(8) We found sea asymmetry of Chiral quark-soliton model P . Schweitzer et al., PRD 64, 034013 (2001) SoLID at JLab, Drell- Yan exp’t at FNAL (E1027+E1039), EIC, ... Huey-Wen Lin — USQCD All Hands' Meeting
Pro rogress ress Last st Yea ear: r: Sy Syst stem emati atics cs Huey-Wen Lin — USQCD All Hands' Meeting
Power Divergence § Improved quasi-quark distribution ∞ 𝑒𝑨 ൻ𝑞 ത 4𝜌 𝑓 𝑗𝑨𝑙 𝑨 −𝜀𝑛 𝑨 𝑟 imp 𝑦, Λ, 𝑞 𝑨 = 𝜔 0,0 ⊥ , 𝑨 𝛿 𝑨 𝑀 𝑨, 0 𝜔 0 𝑞 ൿ −∞ § Wilson-line renormalization to remove power divergence 𝑏 ≈ 0.09 fm , 𝑀 ≈ 6 fm , 𝑁 𝜌 ≈ 130 MeV , clover/HISQ Jian-Hui Zhang Plot by Jian-Hui Zhang Luchang Jin Huey-Wen Lin — USQCD All Hands' Meeting
Renormalization § Ongoing investigation of renormalization Investigating RI’MOM scheme renormalization (Yang) RI’MOM to MS matching (Zhao) § Preliminary result Test case: 𝑏 ≈ 0.12 fm , 𝑁 𝜌 ≈ 310 MeV , clover/HISQ Yi-Bo Yang Preliminary Yong Zhao Plot by Yi-Bo Yang Huey-Wen Lin — USQCD All Hands' Meeting
20 2017 17/1 /18 Alloc ocati ation on Huey-Wen Lin — USQCD All Hands' Meeting
Proposed Calculation § Proposed ensemble N f = 2+1+1 clover/HISQ lattices (MILC) M π ≈ 130 MeV , a ≈ 0.09 fm ( L ≈ 6 fm) § Proposed physics case t sep At least 3 𝑢 sep , multiple mom. source smearing Extended unpol. PDFs to larger 𝑞 𝑨 (w/mom. source) and polarized structure (helicity + transversity) First LQCD study of x - dep’t GPDs ( 3D Spatial Maps of the Nucleon ) “The Tomography of the Nucleon — Spatial Imaging of Gluons and Sea Quarks” Huey-Wen Lin — USQCD All Hands' Meeting
Proposed Calculation § Proposed ensemble N f = 2+1+1 clover/HISQ lattices (MILC) M π ≈ 130 MeV , a ≈ 0.09 fm ( L ≈ 6 fm) § Proposed physics case t sep At least 3 𝑢 sep , multiple mom. source smearing Extended unpol. PDFs to larger 𝑞 𝑨 (w/mom. source) and polarized structure (helicity + transversity) First LQCD study of x - dep’t GPDs ( 3D Spatial Maps of the Nucleon ) Huey-Wen Lin — USQCD All Hands' Meeting
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