Initial state $qqg$ correlations as a background for the chiral magnetic effect in collision of small systems

Motivated by understanding the background to chiral magnetic effect in proton-nucleus collisions from first principles, we compute the three particle correlation in the projectile wave function. We extract the correlations between two quarks and one gluon in the framework of the color glass condensate. This is related to the same-charge correlation of the conventional observable for the chiral magnetic effect. We show that there are two different contributions to this correlation function. One contribution is rapidity-independent and as such can be identified with the pedestal; while the other displays rather strong rapidity dependence. The pedestal contribution and the rapidity-dependent contribution at large rapidity separation between the two quarks result in the negative same charge correlations, while at small rapidity separation the second contribution changes sign. We argue that the computed initial state correlations might be partially responsible for the experimentally observed signal in proton-nucleus collisions.

Figure 1

The diagrammatic representation of two distinct contributions in Eq. (13). The black blobs denote the gluon sources, $\rho$. The grey blob in the gluon splitting vertex accounts for the instantaneous interaction too.

Figure 2

The sign of the correlator as a function of $c_p$ and $\mathrm{\Delta }\eta$. The curves illustrate the sign change, or the zeroes of the corresponding contributions. The shaded region show the negative values of the corresponding contributions.

Figure 3

The correlator as a function of $\mathrm{\Delta }\eta$. The black solid line is the sum, the red dashed line is the contribution proportional to from $I_1^2$ and the blue is the part from $I_2^2$. The normalization coefficient $C^{-1}=\mathcal{N}(2\pi {)}^7{g}^{10}{\mu }^6(m)\frac{(N_c^2-1{)}^2}{2N_c}$.

Figure 4

The trace $-\frac{m^4}{2}\mathrm{Tr}{I}_1(\mathrm{\Delta }\eta ,-m,p)I_1(-\mathrm{\Delta }\eta ,m,p)+m\to -m$ as a function of the angle between the momentum of quark $p$ and the momentum of the gluon $m$ for $|p|=|m|$ and different $\mathrm{\Delta }\eta$.

Figure 5

The trace $-\frac{m^4}{2}\mathrm{Tr}{I}_2(\mathrm{\Delta }\eta ,m,p)I_2^{†}(-\mathrm{\Delta }\eta ,m,p)$ as a function of the angle between the momentum of quark $p$ and the momentum of the gluon $m$ for $c_p\equiv |p|/|m|=0.2$ (left), $c_p\equiv |p|/|m|=1$ (center), $c_p\equiv |p|/|m|=5$ (right), and different $\mathrm{\Delta }\eta$.

Figure 6

$m^2\mathrm{Tr}{I}_1(\mathrm{\Delta }{\varphi }_p)$ as a function of $\mathrm{\Delta }{\varphi }_p$ for three values of $|p|/|m|=c_p=0.5$, 1, 1.5.

Figure 7

The leading order contribution to the three particle correlation involving quark, antiquark and gluon. The black blobs denote the gluon sources, $\rho$. The grey blob in the gluon splitting vertex accounts for the instantaneous interaction too.