Pion electromagnetic form factor at high πΉ π from lattice QCD Bipasha Chakraborty [With Raul Briceno, Robert Edwards, Adithia Kusno, Kostas Orginos, David Richards, Frank Winter] GHP 2017, Washington, D.C. 2 nd Feb, 2017 1
Definition + Ο Simplest hadron p 1 πΏ Space like β π β: q π 2 = (π 2 β π 1 ) 2 β€ 0 p 2 + π 2 = βπ 2 Ο (in units of β π β) 2
Interplay between hard and soft scales Hard tail (Q 2 β β ) from pQCD: 16ᴨα π‘ π 2 π Ο 2 πΊ π (π 2 ) β π 2 G. P. Lepage, S.J.Brodsky, Phys. Lett. 87B(1979)359 Soft part ( π 2 < 1 GeV 2 ): vector meson dominance with πΊ π (0) = 1, data fits well G. Huber and D. Gaskell Need better understanding of the transition to the asymptotic region 3
JLAB 12 GeV upgrade G. Huber and E. Gaskell πΊ π measurements at π 2 ~ 6 GeV 2 : E12-06-101 at JLAB Hall C Can we get some insight from first principles lattice QCD calculations to the question - where does the transition to pQCD happen? 4
Lattice recipe for meson correlators β’ Expectation values of observables : β’ 4-D space-time lattice β’ Gauge configurations : gluons + sea quarks β’ Discretise : β’ Inversion of Dirac matrix : propagator β’ 2-point, 3-point correlation functions : extract meson properties β’ Corrections for lattice artifacts 5
Two-point correlator construction β’ Basis of operators π’ 1 π’ 2 β’ Optimized operator for state |π > in a variational sense by solving generalized eigenvalue problem- β’ Diagonalize the correlation matrix β eigenvalues Ξ» π π’ = exp [βπΉπ π’ β π’ 0 ] 6
Two-point correlator construction Correlator Construction: smearing of quark fields - βdistillationβ with Low lying hadron states Meson creation operator : Parambulators by inverting the Dirac matrix + Operator construction with momentum projection 7
Meson Spectrum Tools well established for spectroscopy Hadron Spectrum Collaboration Jozef J. Dudek et. al . Phys.Rev. D88 (2013) 8
Form factor calculation Need three-point correlator + (π 2 )|πΎ π + (π 1 ) > = π(π 1 + π 2 ) π πΊ π (π 2 ) π π < π π (0)|π Z V calculated using F Ο (q 2 = 0) = 1 9
Pion electromagnetic form factor: up to πΉ π = π GeV 2 Amendolia et. al. JLAB expt. JLAB (Had. Spec.) Phys.Rev. D91 (2015) JLAB lattice ongoing π Ο = 750 MeV In agreement with recent lattice result from HPQCD (up to 0.25 GeV 2 ) Phys.Rev. D93 (2016) π Ο = 450 MeV Anisotropy π π‘ = 3.44 π π‘ = 0.12 fm, π π’ 10
Towards higher πΉ π More difficult on lattice for higher momenta Signal-to-noise ratio: Ο Ο Noise Ο Ο 2-point correlators : exp [β(πΉ π (π) β 2π π )π’] Minimize energies 3-point correlators : for a given π 2 to get better signal exp [β(πΉ π (ππ) + πΉ π (ππ) β 2π π )π’/2] in the middle of the plateau 11
Towards higher πΉ π Dispersion relation: β¦ β¦. Achieve maximum π 2 by using Breit frame : π π = β π π 12
Outlook Immediate goals: ο Pion form factor at π 2 β₯ 6 GeV 2 ο Extend to more ensembles with lighter pion masses , multiple volumes, multiple lattice spacings ο Take care of lattice artifacts Long term goals: ο Hadron structure program β distribution amplitude, PFDs, Quasi PDFs ο Extend to nulceons & more β charges, moments, TMDs, GPDs β¦. 13
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