[Paper Review] On the ridge-like structures in the nuclear and hadronic reactions

Sergey Troshin, N. E. Tyurin|arXiv (Cornell University)|Sep 27, 2010

Nuclear physics research studies3 citations

TL;DR

The paper proposes that ridge-like structures in two-particle correlation functions in high-multiplicity pp and nuclear collisions arise from coherent rotation of a transient, strongly interacting quark-pion liquid formed in peripheral collisions. This rotation, driven by initial orbital angular momentum at non-zero impact parameters, produces narrow Δφ and broad Δη correlations, explaining the ridge phenomenon as a collective effect analogous to that seen at RHIC, with implications for multiplicity and transverse momentum correlations in pp collisions at the LHC.

ABSTRACT

We briefly comment on the ridge-like structure origin in the nuclear and hadronic reactions emphasizing that this structure in the two-particle correlation function can result from the rotation of the transient state of matter.

Motivation & Objective

• To explain the origin of ridge-like structures in two-particle correlation functions observed in high-multiplicity pp and peripheral nuclear collisions at LHC energies.
• To investigate whether the same collective mechanism seen in RHIC's AA collisions—coherent rotation of transient matter—applies to pp collisions.
• To connect the observed ridge structure to dynamical selection of peripheral collisions via impact parameter-dependent inelastic overlap functions.
• To explore the implications of rotating transient matter for directed flow (v₁), elliptic flow (v₂), and the correlation between mean transverse momentum and multiplicity.

Proposed method

• Modeling the transient state as a rotating, strongly interacting quark-pion liquid formed in the overlap region of hadronic collisions at non-zero impact parameters.
• Using the inelastic overlap function $ h_{ ext{inel}}(s,b) $ to show dynamical selection of peripheral collisions at $ ext{LHC} \sqrt{s} = 7 $ TeV, favoring high-multiplicity events.
• Applying the unitarity condition $ \text{Im}f(s,b) = h_{\text{el}}(s,b) + h_{\text{inel}}(s,b) $ to describe the elastic and inelastic amplitude contributions.
• Assuming that the transient matter's orbital angular momentum leads to coherent rotation in the xz-plane, inducing strong momentum correlations in the azimuthal angle (Δφ).
• Deriving the correlation structure via the spatial extension $ V_{\bar{R}} $ of the excited region, which allows broad Δη correlations due to momentum component variation.
• Predicting a linear correlation $ \langle p_T \rangle(s) = a + b\langle n \rangle(s) $ between average transverse momentum and mean multiplicity, consistent with experimental data.

Experimental results

Research questions

• RQ1 Can the ridge-like structure in pp collisions at LHC energies be explained by a collective mechanism similar to that in RHIC's nuclear collisions?
• RQ2 What role does the non-zero impact parameter play in generating coherent rotation of the transient matter and producing the ridge structure?
• RQ3 How does the rotation of the transient quark-pion liquid lead to narrow Δφ and broad Δη correlations in two-particle correlations?
• RQ4 What is the connection between the multiplicity of secondary particles and their average transverse momentum in high-multiplicity pp events?
• RQ5 Does the rotation mechanism predict measurable collective flow effects such as $ v_1 $ and $ v_2 $ in pp collisions?

Key findings

• The ridge-like structure in two-particle correlation functions in pp collisions at $ \sqrt{s} = 7 $ TeV is attributed to coherent rotation of a transient, strongly interacting quark-pion liquid formed in peripheral collisions.
• The narrow Δφ correlation arises due to the rotational coherence of the transient matter, which aligns momentum distributions in the azimuthal plane.
• The broad Δη correlation results from the spatial extension of the excited region, allowing variation in transverse momentum components.
• The model predicts a linear correlation $ \langle p_T \rangle(s) = a + b\langle n \rangle(s) $, which is in good agreement with experimental data from CMS.
• The mechanism naturally explains the observed directed flow $ v_1 $ and affects elliptic flow $ v_2 $, indicating collective behavior in pp collisions.
• The transient matter's rotational dynamics lead to centrifugal effects, reducing central density and enhancing transverse momentum at the periphery, consistent with observed multiplicity-momentum correlations.