Intrinsic Transverse Motion of the Pion’s Valence Quarks
Abstract
Starting with the solution to the Bethe-Salpeter equation for the pion, in a beyond rainbow-ladder truncation to QCD's Dyson-Schwinger equations, we determine the pion's $$\mathcal{l}$$z = 0 and |$$\mathcal{l}$$z| = 1 leading Fock-state light-front wave functions (LFWFs) [labeled by $$\psi$$$$\mathcal{l}$$z($$\mathcal{x}$$, $$\mathcal{k}$$$$2\atop{T}$$)]. The leading-twist time-reversal even transverse momentum dependent parton distribution function (TMD) of the pion is then directly obtained using these LFWFs. A key characteristic of the LFWFs, which is driven by dynamical chiral symmetry breaking, is that at typical hadronic scales they are broad functions in the light-cone momentum fraction $$\mathcal{x}$$. The LFWFs have a nontrivial ($$\mathcal{x}$$, $$\mathcal{k}$$$$2\atop{T}$$)) dependence and in general do not factorize into separate functions of each variable. For $$\mathcal{k}$$$$2\atop{T}$$ ≲ 1 GeV2 the $$\mathcal{k}$$$$2\atop{T}$$ dependence of the LFWFs is well described by a Gaussian; however for $$\mathcal{k}$$$$2\atop{T}$$ ≳ 10 GeV2 these LFWFs behave as $$\psi$$0∝ $$\mathcal{x}$$(1 - $$\mathcal{x}$$)/$$\mathcal{k}$$$$2\atop{T}$$ and $$\psi$$1 ∝ $$\mathcal{x}$$(1 - $$\mathcal{x}$$)/$$\mathcal{k}$$$$4\atop{T}$$ and therefore exhibit the power-law behavior predicted by perturbative QCD. The pion's TMD naturally inherits many features from the LFWFs. With this being said, the TMD evolution of our result is studied using both the b* and $$\zeta$$ prescriptions which allows a qualitative comparison with Drell-Yan data.
- Authors:
-
- Argonne National Lab. (ANL), Lemont, IL (United States)
- Publication Date:
- Research Org.:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1501855
- Alternate Identifier(s):
- OSTI ID: 1546336
- Grant/Contract Number:
- AC02-06CH11357; 2016-098-N0; 2017-058-N0
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 122; Journal Issue: 8; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Shi, Chao, and Cloët, Ian C. Intrinsic Transverse Motion of the Pion’s Valence Quarks. United States: N. p., 2019.
Web. doi:10.1103/PhysRevLett.122.082301.
Shi, Chao, & Cloët, Ian C. Intrinsic Transverse Motion of the Pion’s Valence Quarks. United States. https://doi.org/10.1103/PhysRevLett.122.082301
Shi, Chao, and Cloët, Ian C. Fri .
"Intrinsic Transverse Motion of the Pion’s Valence Quarks". United States. https://doi.org/10.1103/PhysRevLett.122.082301. https://www.osti.gov/servlets/purl/1501855.
@article{osti_1501855,
title = {Intrinsic Transverse Motion of the Pion’s Valence Quarks},
author = {Shi, Chao and Cloët, Ian C.},
abstractNote = {Starting with the solution to the Bethe-Salpeter equation for the pion, in a beyond rainbow-ladder truncation to QCD's Dyson-Schwinger equations, we determine the pion's $\mathcal{l}$z = 0 and |$\mathcal{l}$z| = 1 leading Fock-state light-front wave functions (LFWFs) [labeled by $\psi$$\mathcal{l}$z($\mathcal{x}$, $\mathcal{k}$$2\atop{T}$)]. The leading-twist time-reversal even transverse momentum dependent parton distribution function (TMD) of the pion is then directly obtained using these LFWFs. A key characteristic of the LFWFs, which is driven by dynamical chiral symmetry breaking, is that at typical hadronic scales they are broad functions in the light-cone momentum fraction $\mathcal{x}$. The LFWFs have a nontrivial ($\mathcal{x}$, $\mathcal{k}$$2\atop{T}$)) dependence and in general do not factorize into separate functions of each variable. For $\mathcal{k}$$2\atop{T}$ ≲ 1 GeV2 the $\mathcal{k}$$2\atop{T}$ dependence of the LFWFs is well described by a Gaussian; however for $\mathcal{k}$$2\atop{T}$ ≳ 10 GeV2 these LFWFs behave as $\psi$0∝ $\mathcal{x}$(1 - $\mathcal{x}$)/$\mathcal{k}$$2\atop{T}$ and $\psi$1 ∝ $\mathcal{x}$(1 - $\mathcal{x}$)/$\mathcal{k}$$4\atop{T}$ and therefore exhibit the power-law behavior predicted by perturbative QCD. The pion's TMD naturally inherits many features from the LFWFs. With this being said, the TMD evolution of our result is studied using both the b* and $\zeta$ prescriptions which allows a qualitative comparison with Drell-Yan data.},
doi = {10.1103/PhysRevLett.122.082301},
journal = {Physical Review Letters},
number = 8,
volume = 122,
place = {United States},
year = {Fri Mar 01 00:00:00 EST 2019},
month = {Fri Mar 01 00:00:00 EST 2019}
}
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