Minijet clustering algorithm using transverse-momentum seeds in high-energy nuclear collisions

We propose an algorithm to detect minijet clusters in high-energy nuclear collisions, by selecting a high-transverse-momentum ($p_T$) particle as a seed and assigning a clustering radius ($R$) in the pseudorapidity and azimuthal-angle space. Our pythia simulations for $p+p$ collisions show that a scheme with a seeding $p_T$ of around 0.5 GeV/$c$ and $R$ of approximately 0.6 satisfactorily identifies minijet clusters. The correlation between clusters obtained in pythia calculations using the algorithm exhibits the proper behavior of hard-scattering-like processes, suggesting its usefulness in isolating minijet-like clusters from nonhard-scattering soft processes when applied to actual nuclear-collision data, thereby allowing a closer examination of both the minijet and the soft mechanisms.

Figure 1

The correlation function $C\left(\mathrm{\Delta }\varphi \right)$.

Figure 2

Examples with $p_{T0}=0.5$ GeV/$c$. The seed particles are shown as red points.

Figure 3

Particle distributions in (a) $\eta$, (b) $\varphi$, and (c) $p_T$ for unbiased pythia events. The upper narrow panels of the $\eta$ and $\varphi$ distributions show an amplified view of the distributions.

Figure 4

Particle $p_T$ distributions for pythia events selected with (a) $p_{T0}=0.5$ and (b) 1.5 GeV/$c$.

Figure 5

Ratio of the two-particle correlation ($\mathrm{\Delta }\varphi \text{−}\mathrm{\Delta }\eta$) function for the same events to that for the mixed events with $p_{T0}=0.5$ (upper) and 1.5 GeV/$c$ (lower).

Figure 6

Number of clusters, $K$, as a function of multiplicity $M$ for the same events (red circles) and the mixed events (blue triangles), and the ratio (black circles) of the same events to the mixed events for $p_{T0}=$ (a) 0.5 GeV/$c$ and (b) 1.5 GeV/$c$.

Figure 7

Two-cluster correlation ($\mathrm{\Delta }\varphi \text{−}\mathrm{\Delta }\eta$) for the same events (upper) and the mixed events (lower) with $p_{T0}=0.5$ GeV/$c$ and $K=2$.

Figure 8

Two-cluster correlation ($\mathrm{\Delta }\varphi \text{−}\mathrm{\Delta }\eta$) for the same events (upper) and the mixed events (lower) with $p_{T0}=1.5$ GeV/$c$ and $K=2$.

Figure 9

Ratio of the two-cluster correlation ($\mathrm{\Delta }\varphi \text{−}\mathrm{\Delta }\eta$) function for the same events to that for the mixed events for events selected with $K=2$ for $p_{T0}=0.5$ (upper) and 1.5 GeV/$c$ (lower).

Figure 10

Ratio of the two-cluster correlation ($\mathrm{\Delta }\varphi \text{−}\mathrm{\Delta }\eta$) function for the same events to that for the mixed events with $p_{T0}=1$ GeV/$c$, and $K=2$ (upper), 3 (middle), and 4 (lower).

Figure 11

Ratio of the (a) two-particle or (b) two-cluster correlation ($\mathrm{\Delta }\varphi$) function for the same events to that for the mixed events with $p_{T0}=0.5$ GeV/$c$ for the multiplicity ranges of $[5,8]$ (left), $[9,12]$ (middle), and $[13,16]$ (right).

Figure 12

Same as Fig. 11, except for $p_{T0}=1.5$ GeV/$c$.

Figure 13

An example pythia event with $M=17, K=6$, and $p_{T0}=1$ GeV/$c$.