Sparse modeling approach to obtaining the shear viscosity from smeared correlation functions
- PDF / 6,733,966 Bytes
- 32 Pages / 595.276 x 841.89 pts (A4) Page_size
- 58 Downloads / 202 Views
Springer
Received: April 27, 2020 Accepted: June 15, 2020 Published: July 1, 2020
Sparse modeling approach to obtaining the shear viscosity from smeared correlation functions
a
Department of Physics and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521, Japan b Department of Mathematics and Physics, Kochi University, 2-5-1 Akebono-cho, Kochi 780-8520, Japan c Research Center for Nuclear Physics (RCNP), Osaka University, 10-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan d CCSE, Japan Atomic Energy Agency, 178-4-4, Wakashiba, Kashiwa, Chiba, 277-0871, Japan e Mathematical Science Team, RIKEN Center for Advanced Intelligence Project (AIP), 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan
E-mail: [email protected], [email protected] Abstract: We propose the sparse modeling method to estimate the spectral function from the smeared correlation functions. We give a description of how to obtain the shear viscosity from the correlation function of the renormalized energy-momentum tensor (EMT) measured by the gradient flow method (C(t, τ )) for the quenched QCD at finite temperature. The measurement of the renormalized EMT in the gradient flow method reduces a statistical uncertainty thanks to its property of the smearing. However, the smearing breaks the sum rule of the spectral function and the over-smeared data in the correlation function may have to be eliminated from the analyzing process of physical observables. In this work, we demonstrate the sparse modeling analysis in the intermediate-representation basis (IR basis), which connects between the Matsubara frequency data and real frequency data. It works well even using very limited data of C(t, τ ) only in the fiducial window of the gradient flow. We utilize the ADMM algorithm which is useful to solve the LASSO problem under some constraints. We show that the obtained spectral function reproduces the input smeared correlation function at finite flow-time. Several systematic and statistical errors and the flow-time dependence are also discussed. Keywords: Lattice QCD, Quark-Gluon Plasma ArXiv ePrint: 2004.02426
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)007
JHEP07(2020)007
Etsuko Itoua,b,c and Yuki Nagaid,e
Contents 1 Introduction
1
2 Sparse modeling method
4
4 Simulation setup
13
5 Results of the sparse modeling method for the central value of C(t, τ /a)
14
6 Error estimations 6.1 ωcut dependence 6.2 τ -regime dependence and the fiducial window of the gradient flow 6.3 Statistical errors 6.4 Flow-time dependence of the shear viscosity
18 18 18 20 23
7 Summary
24
A ADMM algorithm
25
B Analysis in the trash: usage of whole τ -regime data of C(t, τ /a) at a finite flow-time 26 C Nτ dependence of the singular values
1
27
Introduction
One of the most important results obtained by RHIC (Relativistic Heavy Ion Collider) experiment is an elliptic flow of QCD particles [1, 2]. The elliptic flow data using a Boltzmann-type equation
Data Loading...
