[Paper Review] News from bottomonium spectral functions in thermal QCD

Sam Offler, Gert Aarts+7 more|arXiv (Cornell University)|Dec 30, 2019

High-Energy Particle Collisions Research4 citations

TL;DR

This paper presents new lattice QCD results for bottomonium spectral functions at nonzero temperature using FASTSUM Generation 2L ensembles with physical pion mass, showing weak dependence on light quark mass. It introduces Kernel Ridge Regression (KRR), a machine learning technique, for spectral function reconstruction from Euclidean correlators, achieving consistent first-peak positions with Maximum Entropy Method (MEM) and revealing thermal suppression of the ground state peak above 187 MeV in both methods.

ABSTRACT

New results on bottomonium at nonzero temperature are presented, using the FASTSUM Generation 2L ensembles. Preliminary results for spectral function reconstruction using Kernel Ridge Regression, a machine learning technique, are shown as well and compared to results from the Maximum Entropy Method.

Motivation & Objective

• To study bottomonium spectral functions in thermal QCD with improved light quark masses (mπ = 236 MeV) on new FASTSUM Generation 2L ensembles.
• To investigate the role of light quarks by comparing results to previous ensembles with heavier pions (mπ = 384 MeV).
• To explore machine learning techniques, specifically Kernel Ridge Regression (KRR), for spectral function reconstruction from lattice Euclidean correlators.
• To compare KRR results with established Maximum Entropy Method (MEM) and assess the reliability and consistency of ML-based spectral reconstruction.
• To evaluate the potential of KRR as a complementary or improved alternative to MEM for analytic continuation in lattice QCD.

Proposed method

• The study uses anisotropic lattices with Nf=2+1 Wilson-clover quarks, aτ⁻¹ = 5.997(34) GeV, and ξ = 3.453(6), with mπ = 236(2) MeV and physical strange quark mass.
• Bottomonium correlators are computed using NRQCD with the non-relativistic dispersion relation tuned to the experimental Υ(1S) mass, fixing E₀ = 7464.5 MeV.
• Spectral functions are reconstructed using Kernel Ridge Regression (KRR), which maps Euclidean correlators to spectral functions via a kernel matrix of squared differences between correlators.
• KRR employs ridge regularization with hyperparameters σ and λ, optimized via cross-validation to prevent overfitting.
• The training set uses 9000 correlator-spectral function pairs; predictions are made for new correlators using the learned αopt matrix.
• Results are compared with Maximum Entropy Method (MEM) reconstructions on the same data, using identical input correlators and temperature points.

Experimental results

Research questions

• RQ1 How does the spectral function of bottomonium evolve with temperature in a thermal medium with physical pion mass?
• RQ2 To what extent does the thermal modification of bottomonium depend on the pion mass, compared to previous ensembles with heavier pions?
• RQ3 Can Kernel Ridge Regression (KRR) successfully reconstruct spectral functions from actual lattice QCD data, and how does it compare to the Maximum Entropy Method (MEM)?
• RQ4 Does KRR reveal consistent thermal suppression of the ground state peak in the Υ channel compared to MEM?
• RQ5 What is the reliability of secondary spectral features, such as a potential second peak, in KRR-reconstructed spectral functions?

Key findings

• The position of the first spectral peak in the Υ channel coincides with the mass obtained from conventional exponential fits at the lowest temperature (m(1S) = 9.460 GeV).
• Both KRR and MEM show a significant reduction in the size of the first spectral peak above T = 187 MeV, indicating thermal suppression of the ground state.
• The area under the spectral function remains constant across temperatures, implying redistribution of spectral weight to higher energies at elevated temperatures.
• KRR reconstruction reveals a more pronounced second peak at higher temperatures, though this feature is not yet considered reliable and requires further investigation.
• The agreement in the position and thermal evolution of the first peak between KRR and MEM suggests consistency between the two methods, despite different algorithmic approaches.
• This is the first application of Kernel Ridge Regression to actual lattice QCD data for spectral function reconstruction, demonstrating its feasibility and potential as a complementary method to MEM.