# Stochastic reconstructions of spectral functions: Application to lattice QCD

## Abstract

Here, we present a detailed study of the applications of two stochastic approaches, stochastic optimization method (SOM) and stochastic analytical inference (SAI), to extract spectral functions from Euclidean correlation functions. SOM has the advantage that it does not require prior information. On the other hand, SAI is a more generalized method based on Bayesian inference. Under mean field approximation SAI reduces to the often-used maximum entropy method (MEM), and for a specific choice of the prior SAI becomes equivalent to SOM. To test the applicability of these two stochastic methods to lattice QCD, Firstly, we apply these methods to various reasonably chosen model correlation functions, and present detailed comparisons of the reconstructed spectral functions obtained from SOM, SAI and MEM. Next, we present similar studies for charmonia correlation functions obtained from lattice QCD computations using clover-improved Wilson fermions on large, fine, isotropic lattices at 0:75 and 1:5 *T _{c}*,

*T*being the deconfinement transition temperature of a pure gluon plasma. We find that SAI and SOM give consistent results to MEM at these two temperatures.

_{c}- Authors:

- Central China Normal Univ., Wuhan (China)
- Central China Normal Univ., Wuhan (China); Univ. Bielefeld, Bielefeld (Germany)
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Brookhaven National Lab. (BNL), Upton, NY (United States); Univ. of Tsukuba, Ibaraki (Japan)

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1462432

- Alternate Identifier(s):
- OSTI ID: 1436822

- Report Number(s):
- BNL-207877-2018-JAAM

Journal ID: ISSN 2470-0010; PRVDAQ

- Grant/Contract Number:
- SC0012704; SC001270

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 9; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

### Citation Formats

```
Ding, H. -T., Kaczmarek, O., Mukherjee, Swagato, Ohno, H., and Shu, H. -T.
```*Stochastic reconstructions of spectral functions: Application to lattice QCD*. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.97.094503.

```
Ding, H. -T., Kaczmarek, O., Mukherjee, Swagato, Ohno, H., & Shu, H. -T.
```*Stochastic reconstructions of spectral functions: Application to lattice QCD*. United States. doi:10.1103/PhysRevD.97.094503.

```
Ding, H. -T., Kaczmarek, O., Mukherjee, Swagato, Ohno, H., and Shu, H. -T. Thu .
"Stochastic reconstructions of spectral functions: Application to lattice QCD". United States.
doi:10.1103/PhysRevD.97.094503.
```

```
@article{osti_1462432,
```

title = {Stochastic reconstructions of spectral functions: Application to lattice QCD},

author = {Ding, H. -T. and Kaczmarek, O. and Mukherjee, Swagato and Ohno, H. and Shu, H. -T.},

abstractNote = {Here, we present a detailed study of the applications of two stochastic approaches, stochastic optimization method (SOM) and stochastic analytical inference (SAI), to extract spectral functions from Euclidean correlation functions. SOM has the advantage that it does not require prior information. On the other hand, SAI is a more generalized method based on Bayesian inference. Under mean field approximation SAI reduces to the often-used maximum entropy method (MEM), and for a specific choice of the prior SAI becomes equivalent to SOM. To test the applicability of these two stochastic methods to lattice QCD, Firstly, we apply these methods to various reasonably chosen model correlation functions, and present detailed comparisons of the reconstructed spectral functions obtained from SOM, SAI and MEM. Next, we present similar studies for charmonia correlation functions obtained from lattice QCD computations using clover-improved Wilson fermions on large, fine, isotropic lattices at 0:75 and 1:5Tc, Tc being the deconfinement transition temperature of a pure gluon plasma. We find that SAI and SOM give consistent results to MEM at these two temperatures.},

doi = {10.1103/PhysRevD.97.094503},

journal = {Physical Review D},

number = 9,

volume = 97,

place = {United States},

year = {Thu May 10 00:00:00 EDT 2018},

month = {Thu May 10 00:00:00 EDT 2018}

}