Lithuanian Journal of Physics article / Lietuvos fizikos žurnalo straipsnis

[PDF] http://dx.doi.org/10.3952/lithjphys.48206

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 48, 121–126 (2008)

ANALYTIC SOLUTION FOR THE REDUCED CROSS-SECTION AND ITS DERIVATIVES AT LOW x BASED ON GLUON AND STRUCTURE FUNCTION EXPONENTS
G.R. Boroun
Physics Department, Razi University, Kermanshah 67149, Iran
E-mail: boroun@razi.ac.ir, grboroun@gmail.com

Received 29 December 2007; revised 2 March 2008; accepted 9 June 2008

Analytic solutions for the reduced cross-section and its derivatives with respect to lny are presented at the low-x limit. The DGLAP evolution equations for singlet and gluon structure function based on Regge-like behaviour of the gluon distribution and the structure function at this limit are solved. We calculated numerically and compared our results with the HERA experiment H1 data at small x. All results can be consistently described within the framework of perturbative QCD.

Keywords: reduced cross-section, DGLAP evolution equation, small-x physics, Regge-like behaviour

PACS: 13.60.Hb, 11.55.Jy

REDUKUOTOJO SKERSPJŪVIO IR JO IŠVESTINIŲ SPRENDINYS NEDIDELĖMS x VERTĖMS, REMIANTIS GLIUONŲ IR SANDAROS FUNKCIJŲ EKSPONENTĖMIS
G.R. Boroun
Razi universitetas, Kermanšachas, Iranas

Pateiktos analizinės redukuotojo skerspjūvio ir jo išvestinių išraikos lny atžvilgiu, kai Bjorkeno parametras x yra mažas. Išspręstos DGLAP evoliucinės lygtys singletinei ir gliuonų sandaros funkcijai, grindžiamos Redže tipo gliuonų pasiskirstymo ir sandaros funkcijos elgsena šioje riboje. Skaitmeniškai gauti rezultatai palyginti su HERA bandymo H1 duomenimis, kai x maži. Visus rezultatus galima nuosekliai aprašyti naudojant perturbacinę kvantinę chromodinamiką.

References / Nuorodos

[1] R.G. Roberts, The Structure of the Proton (Cambridge University Press, Cambridge, 1990),
http://www.cambridge.org/academic/subjects/physics/theoretical-physics-and-mathematical-physics/structure-proton-deep-inelastic-scattering
[2] N. Gogitidze, Determination of the longitudinal structure function F_L at HERA, J. Phys. G 28, 751 (2002),
http://dx.doi.org/10.1088/0954-3899/28/5/303
[3] N. Ghahramany and G.R. Boroun, Extraction of the structure function F₂(x,Q²) at low x from the cross-section derivative, Phys. Lett. B 528, 239 (2002),
http://dx.doi.org/10.1016/S0370-2693(02)01227-3
[4] A.M. Cooper-Sarkar, R.C.E. Devenish, and A. De Roeck, Structure functions of the nucleon and their interpretation, Int. J. Mod. Phys. A 113, 3385 (1998),
http://dx.doi.org/10.1142/S0217751X98001670
[5] A.W. Thomas and W. Weise, The Structure of the Nucleon (Wiley-VCH, Berlin, 2001),
http://dx.doi.org/10.1002/352760314X
[6] P.D.B. Collins, An Introduction to Regge Theory and High-Energy Physics (Cambridge University Press, Cambridge, 1997),
http://www.cambridge.org/academic/subjects/physics/theoretical-physics-and-mathematical-physics/introduction-regge-theory-and-high-energy-physics
[7] A. Capella et al., Structure function and low x, Phys. Lett. B 337, 358 (1994),
http://dx.doi.org/10.1016/0370-2693(94)90988-1
[8] L. Csernai et al., From Regge behavior to DGLAP evolution, Eur. Phys. J. C 24, 205 (2002),
http://dx.doi.org/10.1007/s100520200931
[9a] Yu.L. Dokshitzer, Calculation of structure functions of deep-inelastic scattering and e⁺e^– annihilation by perturbation theory in quantum chromodynamics, Sov. Phys. JETP 46, 641 (1977),
http://www.jetp.ac.ru/cgi-bin/e/index/e/46/4/p641?a=list
[9b] G. Altarelli and G. Parisi, Nucl. Phys. B 126, 298 (1977),
http://dx.doi.org/10.1016/0550-3213(77)90384-4
[9c] V.N. Gribov and L.N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972)
[10] P. Desgrolard, A. Lengyel, and E. Martynov, Pomeron effective intercept-logarithmic derivatives of F₂(x,Q²) in DIS and Regge models, J. High Energy Phys. 02, 029 (2002)
[11] J. Gayler, on behalf of the H1 Collaboration, The rise of the proton structure function F₂ towards low x, Acta Phys. Pol. B 33, 2841 (2002),
[PDF]
[12a] G. Soyez, Global QCD fit from Q² = 0 to Q² = 30000 GeV² with Regge compatible initial condition, Phys. Rev. D 71, 076001 (2005),
http://dx.doi.org/10.1103/PhysRevD.71.076001
[12b] F. Barreiro, C. López, and F. J. Ynduráin, NLO predictions for the growth of F₂ at small x and comparison with experimental data, Z. Phys. C 72, 561 (1996),
http://dx.doi.org/10.1007/s002880050279
[13] The H1 Collaboration, C. Adloff et al., On the rise of the proton structure function F₂ towards low x, Phys. Lett. B 520, 183 (2001),
http://dx.doi.org/10.1016/S0370-2693(01)01074-7
[14] A.M. Cooper-Sarkar and R.C.E. Devenish, The rise and fall of F₂ at low x, Acta Phys. Pol. B 34, 2911 (2003),
[PDF]
[15a] R.K. Ellis, Z. Kunszt, and E.M. Levin, The evolution of parton distributions at small x, Nucl. Phys. B 420, 517 (1994),
http://dx.doi.org/10.1016/0550-3213(94)90076-0
[15b] R.K. Ellis, W.J. Stirling, and B.R. Webber, QCD and Collider Physics (Cambridge University Press, Cambridge, 1996),
http://dx.doi.org/10.1017/CBO9780511628788
[16] G.R. Boroun and B. Rezaie, Approximate method for calculating the exponent of the gluon distribution, λ_g, and the exponent of the structure function, λ_S, at low x, Phys. At. Nucl. 71, 1077 (2008),
http://dx.doi.org/10.1134/S1063778808060100
[17] The H1 Collaboration, C. Adloff et al., Deep inelastic inclusive ep scattering at low x and a determination of α_s, Eur. Phys. J. C 21, 33 (2001),
http://dx.doi.org/10.1007/s100520100720