# Shape functions from B{yields}X{sub c}l{nu}{sub l}

## Abstract

We study inclusive semileptonic B{yields}X{sub c}l{nu}{sub l} decay using the power counting m{sub c}{approx}{radical}({lambda}{sub QCD}m{sub b}). Assuming this scaling for the charm-quark mass, the decay kinematics can be chosen to access the shape-function region even in b{yields}c transitions. To apply effective field theory methods in this region we extend soft-collinear effective theory to describe massive collinear quarks. We calculate the tree-level decay rate, including O({lambda}{sub QCD}/m{sub b}) power corrections, and show that it factorizes into a convolution of jet and shape functions. We identify a certain kinematical variable whose decay spectrum is proportional to the universal leading-order shape function familiar from b{yields}u decay, and speculate as to whether information about this shape function can be extracted from data on b{yields}c decay.

- Authors:

- Theoretische Physik 1, Fachbereich Physik, Universitaet Siegen, D-57068 Siegen (Germany)

- Publication Date:

- OSTI Identifier:
- 20776695

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevD.73.036003; (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; B MESONS; C QUARKS; CORRECTIONS; JET MODEL; NEUTRINOS; QUANTUM CHROMODYNAMICS; REST MASS; S QUARKS; SEMILEPTONIC DECAY

### Citation Formats

```
Boos, H., Feldmann, T., Mannel, T., and Pecjak, B.D.
```*Shape functions from B{yields}X{sub c}l{nu}{sub l}*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevD.73.036003.

```
Boos, H., Feldmann, T., Mannel, T., & Pecjak, B.D.
```*Shape functions from B{yields}X{sub c}l{nu}{sub l}*. United States. doi:10.1103/PhysRevD.73.036003.

```
Boos, H., Feldmann, T., Mannel, T., and Pecjak, B.D. Wed .
"Shape functions from B{yields}X{sub c}l{nu}{sub l}". United States.
doi:10.1103/PhysRevD.73.036003.
```

```
@article{osti_20776695,
```

title = {Shape functions from B{yields}X{sub c}l{nu}{sub l}},

author = {Boos, H. and Feldmann, T. and Mannel, T. and Pecjak, B.D.},

abstractNote = {We study inclusive semileptonic B{yields}X{sub c}l{nu}{sub l} decay using the power counting m{sub c}{approx}{radical}({lambda}{sub QCD}m{sub b}). Assuming this scaling for the charm-quark mass, the decay kinematics can be chosen to access the shape-function region even in b{yields}c transitions. To apply effective field theory methods in this region we extend soft-collinear effective theory to describe massive collinear quarks. We calculate the tree-level decay rate, including O({lambda}{sub QCD}/m{sub b}) power corrections, and show that it factorizes into a convolution of jet and shape functions. We identify a certain kinematical variable whose decay spectrum is proportional to the universal leading-order shape function familiar from b{yields}u decay, and speculate as to whether information about this shape function can be extracted from data on b{yields}c decay.},

doi = {10.1103/PhysRevD.73.036003},

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

number = 3,

volume = 73,

place = {United States},

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

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

}