# What are the low- $Q$ and large- $x$ boundaries of collinear QCD factorization theorems?

## Abstract

Familiar factorized descriptions of classic QCD processes such as deeply-inelastic scattering (DIS) apply in the limit of very large hard scales, much larger than nonperturbative mass scales and other nonperturbative physical properties like intrinsic transverse momentum. Since many interesting DIS studies occur at kinematic regions where the hard scale, $$Q \sim$$ 1-2 GeV, is not very much greater than the hadron masses involved, and the Bjorken scaling variable $$x_{bj}$$ is large, $$x_{bj} \gtrsim 0.5$$, it is important to examine the boundaries of the most basic factorization assumptions and assess whether improved starting points are needed. Using an idealized field-theoretic model that contains most of the essential elements that a factorization derivation must confront, we retrace in this paper the steps of factorization approximations and compare with calculations that keep all kinematics exact. We examine the relative importance of such quantities as the target mass, light quark masses, and intrinsic parton transverse momentum, and argue that a careful accounting of parton virtuality is essential for treating power corrections to collinear factorization. Finally, we use our observations to motivate searches for new or enhanced factorization theorems specifically designed to deal with moderately low-$Q$ and large-$$x_{bj}$$ physics.

- Authors:

- Old Dominion Univ., Norfolk, VA (United States). Dept. of Physics
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1360679

- Report Number(s):
- JLAB-THY-17-2413

Journal ID: ISSN 2470-0010

- Grant/Contract Number:
- AC05-06OR23177

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 95; Journal Issue: 9; 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

```
Moffat, E., Melnitchouk, W., Rogers, T. C., and Sato, N.
```*What are the low-Q and large-x boundaries of collinear QCD factorization theorems?*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.95.096008.

```
Moffat, E., Melnitchouk, W., Rogers, T. C., & Sato, N.
```*What are the low-Q and large-x boundaries of collinear QCD factorization theorems?*. United States. doi:10.1103/PhysRevD.95.096008.

```
Moffat, E., Melnitchouk, W., Rogers, T. C., and Sato, N. 2017.
"What are the low-Q and large-x boundaries of collinear QCD factorization theorems?". United States.
doi:10.1103/PhysRevD.95.096008.
```

```
@article{osti_1360679,
```

title = {What are the low-Q and large-x boundaries of collinear QCD factorization theorems?},

author = {Moffat, E. and Melnitchouk, W. and Rogers, T. C. and Sato, N.},

abstractNote = {Familiar factorized descriptions of classic QCD processes such as deeply-inelastic scattering (DIS) apply in the limit of very large hard scales, much larger than nonperturbative mass scales and other nonperturbative physical properties like intrinsic transverse momentum. Since many interesting DIS studies occur at kinematic regions where the hard scale, $Q \sim$ 1-2 GeV, is not very much greater than the hadron masses involved, and the Bjorken scaling variable $x_{bj}$ is large, $x_{bj} \gtrsim 0.5$, it is important to examine the boundaries of the most basic factorization assumptions and assess whether improved starting points are needed. Using an idealized field-theoretic model that contains most of the essential elements that a factorization derivation must confront, we retrace in this paper the steps of factorization approximations and compare with calculations that keep all kinematics exact. We examine the relative importance of such quantities as the target mass, light quark masses, and intrinsic parton transverse momentum, and argue that a careful accounting of parton virtuality is essential for treating power corrections to collinear factorization. Finally, we use our observations to motivate searches for new or enhanced factorization theorems specifically designed to deal with moderately low-$Q$ and large-$x_{bj}$ physics.},

doi = {10.1103/PhysRevD.95.096008},

journal = {Physical Review D},

number = 9,

volume = 95,

place = {United States},

year = 2017,

month = 5

}