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Non-dipolar gauge links for transverse-momentum-dependent pion wave functions
High Energy Physics - Phenomenology · Submitted 28 Dec 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim I will then turn to show that the newly proposed TMD definition with non-dipolar Wilson lines is equivalent to the one with dipolar gauge links and with a complicated soft function, to all orders of the perturbative expansion in the strong coupling, as far as the infrared behavior is concerned.
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The abstract, sentence by sentence
I discuss the factorization-compatible definitions of transverse-momentum-dependent (TMD) pion wave functions which are fundamental theory inputs entering QCD factorization formulae for many hard exclusive processes. I will first demonstrate that the soft subtraction factor introduced to remove both rapidity and pinch singularities can be greatly reduced by making the maximal use of the freedom to construct the Wilson-line paths when defining the TMD wave functions. I will then turn to show that the newly proposed TMD definition with non-dipolar Wilson lines is equivalent to the one with dipolar gauge links and with a complicated soft function, to all orders of the perturbative expansion in the strong coupling, as far as the infrared behavior is concerned.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | I discuss the factorization-compatible definitions of transverse-momentum-dependent (TMD) pion wave functions which are fundamental theory inputs entering QCD factorization formulae for many hard exclusive processes. | background 0.93 | 0.28 | 0.06 | asserted 0.94 |
| s1 | I will first demonstrate that the soft subtraction factor introduced to remove both rapidity and pinch singularities can be greatly reduced by making the maximal use of the freedom to construct the Wilson-line paths when defining the TMD wave functions. | result 0.51 | 0.81 | 0.14 | asserted 0.98 |
| s2 | I will then turn to show that the newly proposed TMD definition with non-dipolar Wilson lines is equivalent to the one with dipolar gauge links and with a complicated soft function, to all orders of the perturbative expansion in the strong coupling, as far as the infrared behavior is concerned. | result 0.95 | 0.81 | 0.69 | asserted 1.00 |
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The paper
Original abstract
I discuss the factorization-compatible definitions of transverse-momentum-dependent (TMD) pion wave functions which are fundamental theory inputs entering QCD factorization formulae for many hard exclusive processes. I will first demonstrate that the soft subtraction factor introduced to remove both rapidity and pinch singularities can be greatly reduced by making the maximal use of the freedom to construct the Wilson-line paths when defining the TMD wave functions. I will then turn to show that the newly proposed TMD definition with non-dipolar Wilson lines is equivalent to the one with dipolar gauge links and with a complicated soft function, to all orders of the perturbative expansion in the strong coupling, as far as the infrared behavior is concerned.
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References
How the literature uses it
5 arXiv papers cite this in 5 sentences
Papers citing it · 4 sentences without a confident label
Cites it as background 1 paper
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The TMD factorization for hard exclusive processes is yet to be fully understood as it requires a definite power-counting scheme for the intrinsic transverse momentum [ref] as well as a proper construction of the Wilson-line for the TMD wave functions which is necessary to circumvent the rapidity and pinch singularities in the infrared subtraction procedure [ref] .
$B\to D \ell \nu_\ell$ form factors beyond leading power and extraction of $|V_{cb}|$ and $R(D)$ · Introduction · 0.89
What it cites · 5 sentences without a confident label
Builds on 1 paper
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This definition is unique, up to the choice of the ultraviolet renormalization prescription, provided that the following criteria are satisfied [ref] . * The unsubtracted wave function only involves light-cone Wilson lines. * Each soft factor has at most one off-light-cone Wilson line. * The subtracted wave function is free of rapidity and pinch singularities and is defined as the product of the unsubtracted wave function and powers of the soft function in transverse coordinate space.
New definition of TMD parton densities · Factorization-compatible TMD wave functions · 0.94
Cites as background 10 papers
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By contrast, transverse-momentum-dependent (TMD) factorization for hard exclusive processes based upon the theory of on-shell Sudakov form factor [ref] , with the original aim of avoiding the rapidity divergences in collinear factorization for the pion electromagnetic form factor at sub-leading power [ref] , turns out to be far more sophisticated conceptually due to the absence of a definite power counting scheme and to the emergence of light-cone singularities in the infrared subtraction, and this can be already partially recognized from the troubled history of TMD wave functions [ref] .
Next-to-leading-order corrections to exclusive processes in $k_T$ factorization · Introduction · 0.95
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By contrast, transverse-momentum-dependent (TMD) factorization for hard exclusive processes based upon the theory of on-shell Sudakov form factor [ref] , with the original aim of avoiding the rapidity divergences in collinear factorization for the pion electromagnetic form factor at sub-leading power [ref] , turns out to be far more sophisticated conceptually due to the absence of a definite power counting scheme and to the emergence of light-cone singularities in the infrared subtraction, and this can be already partially recognized from the troubled history of TMD wave functions [ref] .
Gauge Invariance and k_T-Factorization of Exclusive Processes · Introduction · 0.95
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By contrast, transverse-momentum-dependent (TMD) factorization for hard exclusive processes based upon the theory of on-shell Sudakov form factor [ref] , with the original aim of avoiding the rapidity divergences in collinear factorization for the pion electromagnetic form factor at sub-leading power [ref] , turns out to be far more sophisticated conceptually due to the absence of a definite power counting scheme and to the emergence of light-cone singularities in the infrared subtraction, and this can be already partially recognized from the troubled history of TMD wave functions [ref] .
Next-to-leading-order correction to pion form factor in $k_T$ factorization · Introduction · 0.95
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