Extraction of from charged pion asymmetries

## Cross-section

A leading order expression for charged pion semi-inclusive pion electro-production cross section, represented as a sum of the and cross sections, using proton or neutron targets can be written, using Eq. 9 & 10 from Ref.<ref name="Christova9907265"> Christova, E., & Leader, E. (1999). Semi-inclusive production-tests for independent fragmentation and for polarized quark densities. hep-ph/9907265.</ref>, as:

Independent fragmentation identifies the process in which quarks fragment into hadrons, independent of the photon-quark scattering process. In other words, the fragmentation process is independent of the initial quark environment, which initiates the hadronization process. Assuming independent fragmentation and using isospin ( and ) and charge () conjugation invariance for the fragmentation functions, the following equality holds:

Strange quark contributions to the above SIDIS cross-section become ignorable due to the dominant contributions from the up and down quarks as x_{Bj} increases beyond 0.3

## Helicity Difference Cross Section

The polarized cross section difference is defined as :

using the polarized cross section where refers to the lepton helicity and to the target helicity.

The charged pion helicity difference can be written using equations 6 and 7 from Reference <ref name="Christova9907265"> </ref> as

The analogous expressions for the case of a Deuteron target are

and unpolarized:

## GSRV

The polarized cross section difference is defined as :

using the polarized cross section where refers to the lepton helicity and to the target helicity.

The charged pion helicity difference can be written using equations 6 and 7 from Reference <ref name="Christova9907265"> </ref> as

The analogous expressions for the case of a Deuteron target are

and unpolarized:

The charged pion asymmetry may be defined as

where the fragmentations functions do not contribute if independent fragmentation, and isospin and charge conjugation are invariant.

Independent fragmentation identifies the process in which quarks fragment into hadrons, independent of the photon-quark scattering process. In other words, the fragmentation process is independent of the initial quark environment, which initiates the hadronization process. Assuming independent fragmentation and using isospin ( and ) and charge () conjugation invariance for the fragmentation functions, the following equality holds:

The polarized and unpolarized cross sections for pion electroproduction can be written in terms of valence quark distribution functions in the valence region as:

and unpolarized:

In the valence region (), where the sea quark contribution is minimized, the above asymmetries can be expressed in terms of polarized and unpolarized valence quark distributions:

The ratio of polarized to unpolarized valence up and down quark distributions may then be written as

and

The ratio of polarized to unpolarized valence quark distribution functions can be extracted using the last two equations.

# Next to leading Order (NLO)

<ref name="Sissakian074032"> A.N. Sissakian, O. Yu. Shevchenko, and O.N. Ivanov Phys Rev D 70 (074032) 2004 https://arxiv.org/abs/hep-ph/0411243</ref>

Towards semi-inclusive deep inelastic scattering at next-to-next-to-leading order, Daniele Anderle https://arxiv.org/pdf/1612.01293.pdf

D. de Florian, R. Sassot, M. Epele, R. J. Herna ́ndez-Pinto, M. Stratmann. Phys. Rev. D 91 014035 (2015).

Global extraction of the parton-to-pion fragmentation functions at NLO accuracy in QCD R. J. Herna ́ndez-Pinto 2016 https://arxiv.org/pdf/1609.02455.pdf

2014Next-to-Leading Order QCD Factorization for Semi-Inclusive Deep Inelastic Scattering at Twist 4, Zhong-Bo Kang, Enke Wang, Xin-Nian Wang, and Hongxi Xing Phys. Rev. Lett. 112, 102001 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.102001

# References

2009 talk by Xiodong Jiang, kinematic cuts identified (Q2 >1GeV2,W >2GeV,W' (missing mass of undetected hadrons) >1.5GeV,xF >0,pπ >2GeV/c) , http://www.int.washington.edu/talks/WorkShops/int_09_3/People/Jiang_X/Jiang.pdf

</references>

## Documents

SIDIS cross sections