Longitudinal structure function from the parton parameterization
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Regular Article - Theoretical Physics
Longitudinal structure function from the parton parameterization B. Rezaeia , G. R. Borounb Physics Department, Razi University, Kermanshah 67149, Iran
Received: 4 June 2020 / Accepted: 26 September 2020 / Published online: 15 October 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Communicated by Andre Peshier
Abstract We present a certain theoretical model to describe data based on the DGLAP evolution equations at low values of x. This model is based on a hard-pomeron exchange in the next-to-next-to-leading order of the perturbative theory. The behavior of the DIS cross section ratio R(x, Q 2 ) and FL (x, Q 2 )/F2 (x, Q 2 ) is studied and compared with the experimental data. These behaviors are controlled by the color dipole model bound. These results show good agreement with the DIS experimental data throughout the low values of x. The results can be applied to the LHeC region for analyses of ultra-high-energy processes.
1 Introduction The reduced cross section is defined in terms of the transverse and longitudinal structure functions, F2 (x, Q 2 ) and FL (x, Q 2 ), by the following: σ (x, Q 2 ) = F2 (x, Q 2 ) −
y2 FL (x, Q 2 ), Y+
(1)
where Y+ = 1 + (1 − y)2 , y = Q 2 /xs denotes the inelasticity and s stands for the center-of-mass squared energy of incoming electrons and protons. As usual x is the Bjorken scaling parameter and Q 2 is the four momentum transfer in a deep-inelastic scattering process. For fixed Q 2 , the reduced cross section increases with decreasing x. However, at highy (very low x) a characteristic bending of the reduced cross section is observed, which it is attributed to the contribution due to the longitudinal structure function. The longitudinal structure function FL is proportional to the cross section for the interaction of the longitudinally polarized virtual photon with a proton. This observable is a e-mail:
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of interest since it is directly sensitive to the gluon density. The longitudinal structure function FL (x, Q 2 ) is obtained as a consequence of the violation of the Callan–Gross relation [1] and is defined as FL (x, Q 2 ) = F2 (x, Q 2 )−2x F1 (x, Q 2 ). Beyond the parton model the FL effects can be sizable, hence it can no longer be neglected. Also, the longitudinal structure function is predominant in cosmic neutrino–hadron cross section scattering [2]. This behavior for the longitudinal structure function will be checked in high-energy processes such as the Large Hadron electron Collider (LHeC) project, which runs to beyond a TeV in center-of-mass energy [3]. Data on FL are generally difficult to extract from reduced cross section measurements. This procedure requires highprecision cross section measurements at the same values of x and Q 2 but at different center-of-mass energy of the incoming beams [4]. Recently, the new data on the proton longitudinal structure function has been taken f
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