Collinear spin correlations of final-state radiation in dense QCD matter

TL;DR

The paper investigates how collinear spin correlations in successive QCD splittings are modified when jet fragmentation occurs in a quark-gluon plasma. Using a simplified QCD antenna with one splitting inside and a collinear second splitting outside the medium, and employing the BDMPS-Z formalism, the authors derive a fully differential in-medium cross-section that extends the vacuum cos(2ψ12) modulation to include medium effects. They show that, in isotropic media, the azimuthal modulation is systematically suppressed relative to vacuum, while in anisotropic media a process-dependent phase φ_med shifts the modulation as cos(2ψ12+φ_med). These results provide theoretical guidance for implementing spin-driven interference in jet quenching studies and motivate future work to include more complete in-medium 1→3 dynamics and spin-flip effects.

Abstract

Spin correlations are required to reproduce the correct azimuthal dependence of matrix elements for successive branchings at disparate angles in QCD jets. In this paper, we study modifications to this, $\cos(2ψ_{12})$, azimuthal pattern in the presence of a quark-gluon plasma. To that end, we consider a simplified setup in which a narrow and energetic QCD antenna is formed inside a medium of fixed length and radiates a collinear emission outside it. The calculation includes both light and heavy-quarks. Further, we do not include medium-induced spin-flip interactions since they are energy suppressed in our formalism. We show that the amplitude of the azimuthal modulation in the presence of a medium is always suppressed with respect to the vacuum baseline, with its magnitude depending on the medium properties and splitting kinematics. For a medium with a momentum space anisotropy, we find that the azimuthal modulation acquires a phase shift, i.e., $\cos(2ψ_{12}) \to \cos(2ψ_{12}+φ_{\rm med })$, where $φ_{\rm med}$ is a process-dependent function that again depends on the medium properties and splitting kinematics. This work provides theory guidance for implementing spin-driven interference effects in phenomenological studies of jet quenching in heavy-ion collisions.

Figures (6)

• Figure 1: Amplitude of the spin modulation signal, $a$, defined in Eq. \ref{['eq:adef-vac']}, as a function of both energy fractions $z_i$ for two different first splittings (massless $q\rightarrow qg$ on the left and $g\rightarrow gg$ on the right), fixing the second splitting to be $g\rightarrow Q\bar{Q}$. From top to bottom we change the opening angle of the second splitting with respect to the dead-cone angle, i.e., $\tilde{\theta}_{m,2}=\theta_{m,2}/\theta_2$ with $\theta_{m,2}$ defined in Eq. \ref{['eq:deadcone-def']}.
• Figure 2: Ratio between the the spin-correlations modulation amplitude in the medium and in vacuum $a_{\rm med}/a$ as a function of the first splitting's kinematics $z_1$ and $\theta_1$. The upper panels correspond to the first splitting being $q\rightarrow qg$ and the lower ones to $g\rightarrow gg$. The medium is isotropic and we plot $\hat{q}= 1$ GeV$^2$/fm (upper panels) and $5$ GeV$^2$/fm (lower panels).
• Figure 3: Evolution of the angular modulation in Eq. \ref{['eq:p-def']} with $\hat{q}$ as a function of $\psi_{12}$ for $\theta_1 = 0.15$ (top panels) and $\theta_1 = 0.3$ (bottom panels). The remaining kinematic variables are fixed to $z_1 = 0.1$, $z_2=0.5$ and $\theta_2 = 0.05$. The left panels correspond to $q\rightarrow qg \rightarrow qgg$ and the right panels to $q\rightarrow qg \rightarrow qc\bar{c}$. Note that for a massless second splitting (left panels) there is no dependence on $\theta_2$.
• Figure 4: Modulation amplitude $a_{\rm med}$ for an anisotropic medium, divided by the isotropic result with $\hat{q} = \hat{q}^{\rm av.}$ (upper panels) as a function of the first splitting's kinematics $z_1$ and $\theta_1$, for the process $q\rightarrow qg$. The three columns correspond to three different azimuthal orientations of first splitting's plane: $\phi_1 = 0,\,\pi/4,\,\pi/2$.
• Figure 5: Same as Fig. \ref{['fig:amed_anisotropic']} but for the phase shift $\phi_{\rm med}$. The values of $\phi_1$ differ with respect to Fig. \ref{['fig:amed_anisotropic']} since $\phi_{\rm med}=0$ for $\phi_1=0,\,\pi/2$. Here we choose $\phi_1= \pi/8,\,\pi/4,\,3\pi/8$.