A correlated-cluster model and the ridge phenomenon in hadron–hadron collisions

Abstract

A study of the near-side ridge phenomenon in hadron-hadron collisions based on a cluster picture of multiparticle production is presented. The near-side ridge effect is shown to have a natural explanation in this context provided that clusters are produced in a correlated manner in the collision transverse plane. 1 We consider a right-handed coordinate system with the z axis along the beams' direction. Cylindrical coordinates are used in the transverse plane, φ being the azimuthal angle. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan (θ/2). The (longitudinal) rapidity is defined as y = 1 2 ln ( E+p L E−p L ) and coincides with the pseudorapidity for massless particles. Here, p L is the longitudinal (along the beam axis) component of the measured particle moment.

Searching for new physics with three-particle correlations in pp collisions at the LHC

“…Hence a dependence on the cluster azimuthal angle φ c should remain in the particle densities from single-cluster decay. Then, as shown in [15], for these densities, the rapidity and azimuthal dependence can be approximately expressed in terms of Gaussians for highest boosted particles, i.e.…”

“…Finally, the last line takes into account three clusters from three hidden particles. In order to match our theoretical approach to experimental results in terms of (pseudo)rapidity and azimuthal differences (∆y ij = y i − y j and ∆φ ij = φ i − φ j , i, j = 1, 2, 3, i = j), use will be made of integration over Dirac's δ-functions as in [13,15]. Notice that only two out of the three rapidity and azimuthal intervals, are independent, chosen here as ∆φ 12…”

“…In the calculations of below, we adopt Gaussian distributions in rapidity and azimuthal spaces as usual in cluster models along with the factorization hypothesis [13,15], to express production cross sections and cluster densities. Thus, the single, double and triple HS production cross sections read…”

“…upon their rapidities. The azimuthal conditions are implemented in the Gaussians following [13,15], in order to take into account collinear emission of particles in accordance with the ridge effect.…”

Signatures of New Physics Versus the Ridge Phenomenon in Hadron–Hadron Collisions at the LHC

“…where δ hφ was interpreted as an azimuthal cluster "width" in [21] 5 . Large hidden source velocities lead to small δ hφ and thereby a more pronounced peak at φ φ h , in accordance with Eq.…”