[Paper Review] Leading-Order Gluon-Pair Production from a Space-Time Dependent Chromofield

Dennis D. Dietrich, Gouranga C. Nayak+1 more|ArXiv.org|Sep 15, 2000

High-Energy Particle Collisions Research1 references3 citations

TL;DR

This paper derives the leading-order source term for gluon-pair production from a space-time dependent chromofield in 1+1 dimensions using the background field method in QCD. It shows that the dominant contribution to gluon production occurs well before the field strength drops to the QCD scale, validating the perturbative approach for modeling early-stage quark-gluon plasma formation in heavy-ion collisions at RHIC and LHC.

ABSTRACT

We describe gluon-pair production from a space-time dependent chromofield via vacuum polarization within the framework of the background field method of QCD. The processes we consider are first order in the action. We derive the corresponding source terms for gluon pair production for situations that can be described by a 1+1 dimensional approach. Especially, we observe that within the range of applicability of our approach the principal contribution to gluon production is included. Gluon production from a space-time dependent chromofield will play an important role in the production and evolution of the quark-gluon plasma in ultra relativistic heavy-ion collisions at RHIC and LHC.

Motivation & Objective

• To model gluon-pair production from a space-time dependent chromofield in the pre-equilibrium stage of ultra-relativistic heavy-ion collisions.
• To extend previous studies limited to constant chromofields by incorporating time and longitudinal spatial dependence.
• To derive a source term for gluon production applicable to non-abelian transport equations in the quark-gluon plasma formation phase.
• To assess the validity and range of applicability of perturbative QCD for describing early particle production in heavy-ion collisions.
• To compare the total probability for gluon-pair production with Schwinger's fermion-pair result and evaluate its relevance for RHIC/LHC phenomenology.

Proposed method

• Uses the background field method in QCD to compute the leading-order effective action for gluon-pair production.
• Derives the source term for gluon production from a chromofield depending on time $ t $ and longitudinal coordinate $ z $, valid in 1+1 dimensions.
• Applies the Schwinger mechanism framework to non-abelian gauge fields, accounting for color structure via the adjoint representation.
• Evaluates the total probability for real gluon-pair production from an arbitrary space-time dependent chromofield, analogous to Schwinger's fermion result.
• Considers a specific time- and space-localized field profile $ A^{a au}(x) = A^{a3}_{in} e^{-t/t_0} \theta(t+z)\theta(t-z)\theta(t) $ to compute particle density evolution.
• Integrates the production rate over time to compute the accumulated particle density $ w $, assessing when the main contribution occurs.

Experimental results

Research questions

• RQ1 What is the source term for gluon-pair production from a $ t $- and $ z $-dependent chromofield in 1+1 dimensions?
• RQ2 How does the time evolution of particle production compare to the onset of non-perturbative effects at $ gA \sim \Lambda_{QCD} $?
• RQ3 Is the main contribution to gluon production concentrated in the early, perturbative phase of the chromofield evolution?
• RQ4 How does the total probability for gluon-pair production compare to the Schwinger result for fermion pairs?
• RQ5 Can the derived source terms be reliably used in a non-abelian transport equation for modeling QGP formation at RHIC and LHC?

Key findings

• The principal contribution to gluon-pair production occurs at times significantly earlier than $ t_{\text{end}} $, when the field strength drops to $ \Lambda_{QCD}/g $, validating the perturbative approach.
• For the chosen parameters ($ t_0 = 0.5\,\text{fm}, g=1.5, A_{\text{in}}=1.5\,\text{GeV}, \Lambda_{QCD}=150\,\text{MeV} $), $ t_{\text{end}} \approx 1.3\,\text{fm} $, but the main production occurs on a time scale of order $ t_0 $, i.e., $ \sim 0.5\,\text{fm} $.
• The accumulated particle density $ w $ at $ t_{\text{end}} $ and $ z=0 $ is $ w = \frac{1}{16\pi t_0} \left[ 11(g^2 A_{\text{in}}^2 - \Lambda_{\text{QCD}}^2) + 36 t_0^2 (g^4 A_{\text{in}}^4 - \Lambda_{\text{QCD}}^4) \right] $, showing a sharp peak in the central region.
• The particle density is sharply peaked in the central region due to the small size of the expanding system at the time of peak production.
• The time scale for peak production is $ \sim t_0 $, which is $ \sim \ln(gA_{\text{in}}/\Lambda_{\text{QCD}}) \approx 2.7 $ times smaller than $ t_{\text{end}} $, confirming that most production is completed before non-perturbative effects dominate.
• The derived source terms are suitable for inclusion in a non-abelian relativistic transport equation to study QGP formation and equilibration at RHIC and LHC.