[Paper Review] Bose-Einstein or HBT correlations and the anomalous dimension of QCD

T. Csörgő, S. Hegyi+2 more|ArXiv.org|Dec 16, 2004

Complex Systems and Time Series Analysis19 citations

TL;DR

This paper proposes that Bose-Einstein (HBT) correlation functions in QCD jets exhibit a Lévy-stable, stretched exponential form due to the fractal structure of gluon radiation. The Lévy index of stability, derived from two-pion correlation data in NA22 and UA1 experiments, directly links to the anomalous dimension of QCD, enabling a measurement of the running QCD coupling constant αs via the relation αs = π/6 α²_BEC, yielding αs ≈ 0.24 (NA22) and 0.13 (UA1).

ABSTRACT

Bose-Einstein (or HBT) correlation functions are evaluated for the fractal structure of QCD jets. These correlation functions have a stretched exponential (or Levy-stable) form. The anomalous dimension of QCD determines the Levy index of stability, thus the running coupling constant of QCD becomes measurable with the help of two-particle Bose-Einstein correlation functions. These considerations are tested on NA22 and UA1 two-pion correlation data.

Motivation & Objective

• To establish a connection between the fractal structure of QCD jets and the functional form of Bose-Einstein correlation functions.
• To demonstrate that the Lévy index of stability in HBT correlations reflects the anomalous dimension of QCD.
• To provide a measurable link between two-particle correlation functions and the running coupling constant αs in QCD.
• To test the theoretical framework against empirical data from NA22 and UA1 experiments on two-pion correlations.

Proposed method

• Models the phase-space of QCD jets as a multifaceted, fractal surface in (rapidity, transverse momentum) space, generated by iterative gluon emission from color dipoles.
• Applies the Lévy-stable distribution to describe the source function in coordinate space, with the Lévy index α_Lévy governing the power-law decay of the tail.
• Derives the two-particle Bose-Einstein correlation function as C2(Q) = 1 + |f̃(q)|², where f̃ is the Fourier transform of the Lévy-stable source distribution.
• Introduces the τ-model to relate the invariant momentum difference Q_inv to the proper-time distribution, linking C2(Q_inv) to the square of the Fourier-transformed H(τ).
• Establishes the relation α_BEC = 2α_Lévy, and derives αs = (π/6) α²_BEC from the anomalous dimension α_Lévy = √(3αs / 2π).
• Fits the Lévy-stable form to NA22 and UA1 two-pion correlation data to extract α_BEC, then uses the derived formula to extract αs.

Experimental results

Research questions

• RQ1 Can the fractal structure of QCD jets be probed through the functional form of two-particle Bose-Einstein correlation functions?
• RQ2 Is the Lévy index of stability in HBT correlations directly related to the anomalous dimension of QCD?
• RQ3 Can the running coupling constant αs be extracted from HBT correlation data using the derived analytical relation?
• RQ4 How well do the Lévy-stable model and the τ-model describe the two-pion correlation functions in NA22 and UA1 experiments?

Key findings

• The Bose-Einstein correlation function for QCD jets takes a stretched exponential (Lévy-stable) form due to the fractal nature of gluon radiation.
• The Lévy index of stability α_Lévy is equal to the anomalous dimension of QCD, given by √(3αs / 2π).
• The exponent α_BEC of the invariant momentum-dependent correlation function is related to the Lévy index by α_BEC = 2α_Lévy.
• From the fit to NA22 data, the extracted α_BEC = 0.67 ± 0.07 leads to αs = 0.24 ± 0.05.
• From the fit to UA1 data, the extracted α_BEC = 0.49 ± 0.01 leads to αs = 0.13 ± 0.01.
• The results demonstrate that HBT correlations can be used to measure the running QCD coupling constant via the Lévy-stable source model.