Sprecher
Beschreibung
Starting from the momentum-space dilute-dilute computation of single-inclusive gluon production in the CGC framework [1,2], where the leading-order cross section is written as convolution of two unintegrated gluon distributions through the Lipatov vertex, I show that this result is just the zeroth order of a gradient expansion in the transverse positions entering the two dipole amplitudes. This expansion produces a ladder of scalar and tensor structures [3], built from the local dipole amplitudes and their transverse derivatives, which we can combined into an extended gluon production formula. In this way, I obtained a $k_T$-factorized ansatz that retains the spatial dependence of the two colliding sources and a factorized form of the original result.
I exemplify this result by obtaining a simplified formula for a simple Gaussian (GBW-type) dipole with position-dependent saturation scale, a gradient corrected analog to the simple parametrical formula used in Ref. [4]. I also discuss how the coupling of the gradients of the saturation scales to the produce gluon momenta generate momentum-space anisotropies, by creating a transverse pressure imbalance, $T^{xx}-T^{yy}\neq 0$ and shear components $T^{xy}$. This effect presents itself more pronounced in fluctuation-dominated systems such as O+O and Ne+Ne, and may be relevant in the question of how thermalization occurs in such systems.
References
[1] A. Dumitru and L. D. McLerran, Nucl. Phys. A 700 (2002), 492-508
[2] J. P. Blaizot, F. Gelis and R. Venugopalan, Nucl. Phys. A 743 (2004), 13-56
[3] O. Garcia-Montero, In preparation.
[4] N. Borghini, M. Borrell, N. Feld, H. Roch, S. Schlichting and C. Werthmann, Phys. Rev. C 107 (2023) no.3, 034905