high from lattice QCD Bipasha Chakraborty [With Raul Briceno, - - PowerPoint PPT Presentation

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high from lattice QCD Bipasha Chakraborty [With Raul Briceno, - - PowerPoint PPT Presentation

Sep 08, 2022 209 likes β€’352 views

Pion electromagnetic form factor at high 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 +

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Pion electromagnetic form factor at high π‘ΉπŸ‘ from lattice QCD

Bipasha Chakraborty [With Raul Briceno, Robert Edwards, Adithia Kusno, Kostas Orginos, David Richards, Frank Winter]

GHP 2017, Washington, D.C. 2nd Feb, 2017

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Definition

p1 p2 q

Space like β€œπ‘Ÿβ€: π‘Ÿ2 = (π‘ž2 – π‘ž1)2 ≀ 0 𝑅2 = βˆ’π‘Ÿ2

(in units of β€˜π‘“β€™) Simplest hadron Ο€

+

Ο€

+

𝛿

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Interplay between hard and soft scales

  • G. Huber and D. Gaskell

Need better understanding of the transition to the asymptotic region Hard tail (Q2 β†’ ∞) from pQCD:

𝐺𝜌(𝑅2) β†’

16ᴨα𝑑 𝑅2 𝑔π

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𝑅2

  • G. P. Lepage, S.J.Brodsky,
  • Phys. Lett. 87B(1979)359

Soft part (𝑅2 < 1 GeV2): vector meson dominance with 𝐺𝜌(0) = 1, data fits well

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JLAB 12 GeV upgrade

  • G. Huber and E. Gaskell

𝐺𝜌 measurements at 𝑅2 ~ 6 GeV2: 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?

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Lattice recipe for meson correlators

  • Expectation values of observables :
  • 4-D space-time lattice
  • Gauge configurations : gluons + sea quarks
  • Discretise :
  • Inversion of Dirac matrix : propagator
  • 2-point, 3-point correlation functions : extract meson properties
  • Corrections for lattice artifacts
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Two-point correlator construction

  • Optimized operator for state |π‘œ >

in a variational sense by solving generalized eigenvalue problem-

  • Basis of operators

𝑒1 𝑒2

  • Diagonalize the correlation matrix – eigenvalues

Ξ»π‘œ 𝑒 = exp [βˆ’πΉπ‘œ 𝑒 βˆ’ 𝑒0 ]

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Two-point correlator construction

Correlator Construction: smearing of quark fields - β€˜distillation’ with Meson creation operator : Parambulators by inverting the Dirac matrix Operator construction with momentum projection Low lying hadron states

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Meson Spectrum

Tools well established for spectroscopy

Jozef J. Dudek et. al. Phys.Rev. D88 (2013) Hadron Spectrum Collaboration

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Form factor calculation

Need three-point correlator π‘Žπ‘Š < 𝜌

+ (π‘ž2)|𝐾𝜈 𝜌(0)|𝜌 + (π‘ž1) > = 𝑓(π‘ž1 + π‘ž2)𝜈𝐺𝜌(π‘Ÿ2)

ZV calculated using FΟ€(q2 = 0) = 1

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Pion electromagnetic form factor: up to π‘ΉπŸ‘ = 𝟐 GeV2

Amendolia et. al. JLAB expt. JLAB (Had. Spec.) Phys.Rev. D91 (2015) JLAB lattice ongoing

Anisotropy 𝑏𝑑 = 0.12 fm, 𝑏𝑑 𝑏𝑒 = 3.44

In agreement with recent lattice result from HPQCD (up to 0.25 GeV2) Phys.Rev. D93 (2016) 𝑛π = 750 MeV 𝑛π = 450 MeV

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Towards higher π‘ΉπŸ‘

More difficult on lattice for higher momenta Signal-to-noise ratio: 2-point correlators : exp [βˆ’(𝐹𝜌(π‘ž) βˆ’ 2π‘›πœŒ)𝑒] 3-point correlators :

exp

[βˆ’(𝐹𝜌(π‘žπ‘—) + 𝐹𝜌(π‘žπ‘”) βˆ’ 2π‘›πœŒ)𝑒/2] in the middle of the plateau Minimize energies for a given 𝑅2 to get better signal Ο€ Ο€ Ο€ Ο€ Noise

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Towards higher π‘ΉπŸ‘

Achieve maximum 𝑅2 by using Breit frame : 𝑄𝑔 = βˆ’ 𝑄𝑗 Dispersion relation:

….

…

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Outlook

Immediate goals:

  • Pion form factor at 𝑅2 β‰₯ 6 GeV2
  • Extend to more ensembles with lighter pion masses ,

multiple volumes, multiple lattice spacings

  • Take care of lattice artifacts

Long term goals:

  • Hadron structure program – distribution amplitude,

PFDs, Quasi PDFs

  • Extend to nulceons & more – charges, moments, TMDs,

GPDs ….