High Energy / Nuclear Theory / RIKEN Seminars
# [RIKEN Seminar] Sparse modeling approach to obtaining the shear viscosity from smeared correlation functions

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Description

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

($C(t,\tau)$) 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 that 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 $C(t,\tau)$ 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.