Virtuality and transverse momentum dependence of the pion distribution amplitude
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 → π ^{0} 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 z ^{2}, they are parametrized through virtuality distribution amplitudes (VDA) Φ(x,σ), with x being Fourierconjugate to (pz) and σ Laplaceconjugate to z ^{2}. 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 spin1/2 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 highk tails from primordial soft distributions.
 Authors:

^{[1]}
 Old Dominion Univ., Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
 Publication Date:
 Report Number(s):
 JLABTHY152145; DOE/OR/231773773; arXiv:1510.02517
Journal ID: ISSN 24700010; PRVDAQ
 Grant/Contract Number:
 AC0506OR23177; FG0297ER41028
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 93; Journal Issue: 5; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Research Org:
 Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
 OSTI Identifier:
 1245173
 Alternate Identifier(s):
 OSTI ID: 1242580
Radyushkin, Anatoly V. Virtuality and transverse momentum dependence of the pion distribution amplitude. United States: N. p.,
Web. doi:10.1103/PhysRevD.93.056002.
Radyushkin, Anatoly V. Virtuality and transverse momentum dependence of the pion distribution amplitude. United States. doi:10.1103/PhysRevD.93.056002.
Radyushkin, Anatoly V. 2016.
"Virtuality and transverse momentum dependence of the pion distribution amplitude". United States.
doi:10.1103/PhysRevD.93.056002. https://www.osti.gov/servlets/purl/1245173.
@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 Fourierconjugate to (pz) and σ Laplaceconjugate 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 spin1/2 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 highk tails from primordial soft distributions.},
doi = {10.1103/PhysRevD.93.056002},
journal = {Physical Review D},
number = 5,
volume = 93,
place = {United States},
year = {2016},
month = {3}
}