# Resummation of soft gluon logarithms in the DGLAP evolution of fragmentation functions

## Abstract

We define a general scheme for the evolution of fragmentation functions which resums both soft gluon logarithms and mass singularities in a consistent manner and to any order, and requires no additional theoretical assumptions. Using the double logarithmic approximation and the known perturbative results for the splitting functions, we present our scheme with the complete contribution from the double logarithms, being the largest soft gluon logarithms. We show that the resulting approximation is more complete than the modified leading logarithm approximation even with the fixed order contribution calculated to leading order only, and find, after using it to fit quark and gluon fragmentation functions to experimental data, that this approximation in our scheme gives a good description of the data from the largest x{sub p} values to the peak region in {xi}=ln(1/x{sub p}), in contrast to other approximations. In addition, we develop a treatment of hadron mass effects which gives additional improvements at large {xi}.

- Authors:

- II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)
- (Werner-Heisenberg-Institut), Foehringer Ring 6, 80805 Munich (Germany)

- Publication Date:

- OSTI Identifier:
- 20776867

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevD.73.054020; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; APPROXIMATIONS; GLUONS; HADRONS; QUARKS; REST MASS; SINGULARITY

### Citation Formats

```
Albino, S., Kniehl, B.A., Kramer, G., Ochs, W., and Max-Planck-Institut fuer Physik.
```*Resummation of soft gluon logarithms in the DGLAP evolution of fragmentation functions*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevD.73.054020.

```
Albino, S., Kniehl, B.A., Kramer, G., Ochs, W., & Max-Planck-Institut fuer Physik.
```*Resummation of soft gluon logarithms in the DGLAP evolution of fragmentation functions*. United States. doi:10.1103/PhysRevD.73.054020.

```
Albino, S., Kniehl, B.A., Kramer, G., Ochs, W., and Max-Planck-Institut fuer Physik. Wed .
"Resummation of soft gluon logarithms in the DGLAP evolution of fragmentation functions". United States.
doi:10.1103/PhysRevD.73.054020.
```

```
@article{osti_20776867,
```

title = {Resummation of soft gluon logarithms in the DGLAP evolution of fragmentation functions},

author = {Albino, S. and Kniehl, B.A. and Kramer, G. and Ochs, W. and Max-Planck-Institut fuer Physik},

abstractNote = {We define a general scheme for the evolution of fragmentation functions which resums both soft gluon logarithms and mass singularities in a consistent manner and to any order, and requires no additional theoretical assumptions. Using the double logarithmic approximation and the known perturbative results for the splitting functions, we present our scheme with the complete contribution from the double logarithms, being the largest soft gluon logarithms. We show that the resulting approximation is more complete than the modified leading logarithm approximation even with the fixed order contribution calculated to leading order only, and find, after using it to fit quark and gluon fragmentation functions to experimental data, that this approximation in our scheme gives a good description of the data from the largest x{sub p} values to the peak region in {xi}=ln(1/x{sub p}), in contrast to other approximations. In addition, we develop a treatment of hadron mass effects which gives additional improvements at large {xi}.},

doi = {10.1103/PhysRevD.73.054020},

journal = {Physical Review. D, Particles Fields},

number = 5,

volume = 73,

place = {United States},

year = {Wed Mar 01 00:00:00 EST 2006},

month = {Wed Mar 01 00:00:00 EST 2006}

}