One prominent phenomenon in relativistic nucleus-nucleus collisions is jet quenching due to medium-induced partonic energy loss. The observable most directly associated with jet quenching is the suppression of the yield of hadrons with a high transverse momentum p_T, which is quantified by the nuclear modification factor, R_AA (p_T, η). It is defined as the ratio of the inclusive single-hadron yield per unit pseudorapidity η in AA collisions to the corresponding yield in pp collisions, scaled by the average number of binary nucleon-nucleon collisions. In this paper, we investigate the double nuclear modification factor, which was introduced in [1], to simultaneously probe initial and final state effects. We consider a more general case where both hard particles experience energy loss. The hypothesis of the factorization of this factor

R_AA (p_T1, η₁; p_T2, η₂) = F∙R_AA (p_T1,η₁)∙R_AA (p_T2,η₂)

is tested for different types of final-state hadrons within the framework of the HYDJET++ model.

Fig.1 The dependence of the ratio F of the double and the product of single nuclear modification factors on the minimum value of the hadron transverse momentum p_T .

The deviation F from factorization of the production pions in association with kaons and (anti-)protons as well as the production of kaons in association with (anti-)protons was calculated for central PbPb collisions at center-of-mass energy 5.02 TeV per nucleon pair (Fig. 1). Results indicate that the hypothesis of factorization holds reasonably well at moderately high p_T, provided that the effects of double parton scattering can be small or neglected. However factorization violation starts to show at very high p_T. This supports the conclusion that measurements of the double nuclear modification factors offer significant potential for further investigations.

[1] S.P. Baranov, A.V. Lipatov, M.A. Malyshev, and A.M. Snigirev, JETP Letters 119, 823 (2024)

A. S.Chernyshov, I.P. Lokhtin, A.M. Snigirev
JETP Letters 122, issue 5 (2025)