Virtuality and transverse momentum dependence of the pion distribution amplitude

Radyushkin, Anatoly V.

doi:10.1103/PhysRevD.93.056002

Title: Virtuality and transverse momentum dependence of the pion distribution amplitude

Abstract

We describe basics of a new approach to transverse momentum dependence in hard exclusive processes. We develop it in application to the transition process γ*γ → π⁰ at the handbag level. Our starting point is coordinate representation for matrix elements of operators (in the simplest case, bilocal O (0,z)) describing a hadron with momentum p. Treated as functions of (pz) and z², they are parametrized through virtuality distribution amplitudes (VDA) Φ(x,σ), with x being Fourier-conjugate to (pz) and σ Laplace-conjugate to z². For intervals with z⁺ = 0, we introduce the transverse momentum distribution amplitude (TMDA) ψ(x, k), and write it in terms of VDA Φ(x,σ). The results of covariant calculations, written in terms of Φ(x, σ) are converted into expressions involving ψ(x, k). Starting with scalar toy models, we extend the analysis onto the case of spin-1/2 quarks and QCD. We propose simple models for soft VDAs/TMDAs, and use them for comparison of handbag results with experimental (BaBar and BELLE) data on the pion transition form factor. Furthermore, we discuss how one can generate high-k tails from primordial soft distributions.

Authors:

Radyushkin, Anatoly V. ^[1]

Old Dominion Univ., Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Publication Date:: Tue Mar 08 00:00:00 EST 2016

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1245173

Alternate Identifier(s):: OSTI ID: 1242580

Report Number(s):: JLAB-THY-15-2145; DOE/OR/23177-3773; arXiv:1510.02517
Journal ID: ISSN 2470-0010; PRVDAQ

Grant/Contract Number:: AC05-06OR23177; FG02-97ER41028

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 93; Journal Issue: 5; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Radyushkin, Anatoly V. Virtuality and transverse momentum dependence of the pion distribution amplitude.  United States: N. p., 2016. 
Web.  doi:10.1103/PhysRevD.93.056002.

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                    Radyushkin, Anatoly V. Virtuality and transverse momentum dependence of the pion distribution amplitude.  United States.  https://doi.org/10.1103/PhysRevD.93.056002

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                    Radyushkin, Anatoly V. Tue .  
"Virtuality and transverse momentum dependence of the pion distribution amplitude".  United States.  https://doi.org/10.1103/PhysRevD.93.056002.  https://www.osti.gov/servlets/purl/1245173.

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@article{osti_1245173,

  title        = {Virtuality and transverse momentum dependence of the pion distribution amplitude},

  author       = {Radyushkin, Anatoly V.},

  abstractNote = {We describe basics of a new approach to transverse momentum dependence in hard exclusive processes. We develop it in application to the transition process γ*γ → π0 at the handbag level. Our starting point is coordinate representation for matrix elements of operators (in the simplest case, bilocal O (0,z)) describing a hadron with momentum p. Treated as functions of (pz) and z2, they are parametrized through virtuality distribution amplitudes (VDA) Φ(x,σ), with x being Fourier-conjugate to (pz) and σ Laplace-conjugate to z2. For intervals with z+ = 0, we introduce the transverse momentum distribution amplitude (TMDA) ψ(x, k), and write it in terms of VDA Φ(x,σ). The results of covariant calculations, written in terms of Φ(x, σ) are converted into expressions involving ψ(x, k). Starting with scalar toy models, we extend the analysis onto the case of spin-1/2 quarks and QCD. We propose simple models for soft VDAs/TMDAs, and use them for comparison of handbag results with experimental (BaBar and BELLE) data on the pion transition form factor. Furthermore, we discuss how one can generate high-k tails from primordial soft distributions.},

  doi          = {10.1103/PhysRevD.93.056002},

  journal      = {Physical Review D},

  number       = 5,

  volume       = 93,

  place        = {United States},

  year         = {Tue Mar 08 00:00:00 EST 2016},

  month        = {Tue Mar 08 00:00:00 EST 2016}

}

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Virtuality distributions in application to <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi>γ</mml:mi><mml:msup><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mrow><mml:mo>⁎</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:math> transition form factor at handbag level
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Works referencing / citing this record:

A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results
journal, June 2019

Cichy, Krzysztof; Constantinou, Martha
Advances in High Energy Physics, Vol. 2019
DOI: 10.1155/2019/3036904

Pion Distribution Amplitude and Quasi-Distributions
text, January 2017

Radyushkin, Anatoly V.
arXiv
DOI: 10.48550/arxiv.1701.02688

A guide to light-cone PDFs from Lattice QCD: an overview of approaches, techniques and results
text, January 2018

Cichy, Krzysztof; Constantinou, Martha
arXiv
DOI: 10.48550/arxiv.1811.07248

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Title: Virtuality and transverse momentum dependence of the pion distribution amplitude

Abstract

Citation Formats

Transversity in hard exclusive electroproduction of pseudoscalar mesons journal, September 2011

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction journal, February 1996

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Use and misuse of QCD sum rules, factorization and related topics journal, May 1984

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Freedom at moderate energies: Masses in color dynamics journal, October 1976

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Factorization and asymptotic behaviour of pion form factor in QCD journal, July 1980

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Evolution equations for QCD string operators journal, January 1989

Pseudoscalar meson transition form factors in nonperturbative QCD approach journal, April 2012

Connection of Elastic Electromagnetic Nucleon Form Factors at Large Q 2 and Deep Inelastic Structure Functions Near Threshold journal, January 1970

Non-Lagrangian Models of Current Algebra journal, March 1969

Quantum Electrodynamics in the Infinite-Momentum Frame journal, May 1970

Exclusive processes in perturbative quantum chromodynamics journal, November 1980

Alpha representation and spectral properties of multiparton functions journal, November 1984

Nonforward parton distributions journal, November 1997

Decomposition of non-local light-cone operators into harmonic operators of definite twist journal, October 1999

The virtual Compton amplitude in the generalized Bjorken region: Twist-2 contributions journal, November 1999

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Field theory approach to processes with large momentum transfer. III. Gauge theories journal, September 1980

On Gauge Invariance and Vacuum Polarization journal, June 1951

Measurement of the γ γ * → π 0 transition form factor journal, September 2009

Measurement of γ γ * → π 0 transition form factor at Belle journal, November 2012

Shape of pion distribution amplitude journal, November 2009

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Nonforward Parton Distributions text, January 1997

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A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results journal, June 2019

Pion Distribution Amplitude and Quasi-Distributions text, January 2017

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Transversity in hard exclusive electroproduction of pseudoscalar mesons
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The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction
journal, February 1996

Meson - photon transition form factors
journal, January 1996

Use and misuse of QCD sum rules, factorization and related topics
journal, May 1984

Hard processes in quantum chromodynamics
journal, February 1980

Positivity constraints for anomalous dimensions
journal, October 1973

Vacuum corrections to QCD charmonium sum rules: Basic formalism and O(G3) results
journal, March 1983

A method for computing higher gluonic power corrections to QCD charmonium sum rules
journal, April 1982

Freedom at moderate energies: Masses in color dynamics
journal, October 1976

Exclusive processes in quantum chromodynamics: Evolution equations for hadronic wavefunctions and the form factors of mesons
journal, November 1979

Factorization and asymptotic behaviour of pion form factor in QCD
journal, July 1980

On spectral properties of parton correlation functions and multiparton wave functions
journal, November 1983

Evolution equations for QCD string operators
journal, January 1989

Pseudoscalar meson transition form factors in nonperturbative QCD approach
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Connection of Elastic Electromagnetic Nucleon Form Factors at Large $Q^{2}$ and Deep Inelastic Structure Functions Near Threshold
journal, January 1970

Non-Lagrangian Models of Current Algebra
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Transverse momentum and Sudakov effects in exclusive QCD processes: $γ^{*} γ π^{0}$ form factor
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