# STOUT SMEARING FOR TWISTED FERMIONS.

## Abstract

The effect of Stout smearing is investigated in numerical simulations with twisted mass Wilson quarks. The phase transition near zero quark mass is studied on 12{sup 3} x 24, 16{sup 3} x 32 and 24{sup 3} x 48 lattices at lattice spacings a {approx_equal} 0.1-0.125 fm. The phase structure of Wilson fermions with twisted mass ({mu}) has been investigated in [1,2]. As it is explained there, the observed first order phase transition limits the minimal pion mass which can be reached in simulations at a given lattice spacing: m{sub k}{sup min} {approx_equal} {theta}(a). The phase structure is schematically depicted in the left panel of Fig. I . The phase transition can be observed in simulations with twisted mass fermions, for instance, as a ''jump'' or even metastabilities in the average plaquette value as a function of the hopping parameter ({kappa}). One possibility to weaken the phase transition and therefore allow for lighter pion masses at a given lattice spacing is to use an improved gauge action like the DBW2, Iwasaki, or tree-level Symanzik (tlSym) improved gauge action instead of the simple Wilson gauge action. This has been successfully demonstrated in [3,4,5]. Here we report on our attempts to use amore »

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- Doe - Office Of Science

- OSTI Identifier:
- 922236

- Report Number(s):
- BNL-79711-2007-CP

R&D Project: 12705; KA1401020; TRN: US0801022

- DOE Contract Number:
- DE-AC02-98CH10886

- Resource Type:
- Conference

- Resource Relation:
- Conference: XXV INTERNATIONAL SYMPOSIUM ON LATTICE FIELD THEORY; REGENSBURG, GERMANY; 20070730 through 20070804

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGORITHMS; DIRAC OPERATORS; DISLOCATIONS; EIGENVALUES; FERMIONS; FLUCTUATIONS; LATTICE FIELD THEORY; PIONS; QUARKS; SLOWING-DOWN

### Citation Formats

```
SCHOLZ, W, JANSEN, K, McNEILE, C, MONTVAY, I, RICHARDS, C, URBACH, C, and WENGER, U.
```*STOUT SMEARING FOR TWISTED FERMIONS.*. United States: N. p., 2007.
Web.

```
SCHOLZ, W, JANSEN, K, McNEILE, C, MONTVAY, I, RICHARDS, C, URBACH, C, & WENGER, U.
```*STOUT SMEARING FOR TWISTED FERMIONS.*. United States.

```
SCHOLZ, W, JANSEN, K, McNEILE, C, MONTVAY, I, RICHARDS, C, URBACH, C, and WENGER, U. Mon .
"STOUT SMEARING FOR TWISTED FERMIONS.". United States. https://www.osti.gov/servlets/purl/922236.
```

```
@article{osti_922236,
```

title = {STOUT SMEARING FOR TWISTED FERMIONS.},

author = {SCHOLZ, W and JANSEN, K and McNEILE, C and MONTVAY, I and RICHARDS, C and URBACH, C and WENGER, U},

abstractNote = {The effect of Stout smearing is investigated in numerical simulations with twisted mass Wilson quarks. The phase transition near zero quark mass is studied on 12{sup 3} x 24, 16{sup 3} x 32 and 24{sup 3} x 48 lattices at lattice spacings a {approx_equal} 0.1-0.125 fm. The phase structure of Wilson fermions with twisted mass ({mu}) has been investigated in [1,2]. As it is explained there, the observed first order phase transition limits the minimal pion mass which can be reached in simulations at a given lattice spacing: m{sub k}{sup min} {approx_equal} {theta}(a). The phase structure is schematically depicted in the left panel of Fig. I . The phase transition can be observed in simulations with twisted mass fermions, for instance, as a ''jump'' or even metastabilities in the average plaquette value as a function of the hopping parameter ({kappa}). One possibility to weaken the phase transition and therefore allow for lighter pion masses at a given lattice spacing is to use an improved gauge action like the DBW2, Iwasaki, or tree-level Symanzik (tlSym) improved gauge action instead of the simple Wilson gauge action. This has been successfully demonstrated in [3,4,5]. Here we report on our attempts to use a smeared gauge field in the fermion lattice Dirac operator to further reduce the strength of the phase transition. This is relevant in simulations with N{sub f} = 2 + 1 + 1 (u,d,s,c) quark flavors [6] where the first order phase transition becomes stronger compared to N{sub f} = 2 simulations. The main impact of the above mentioned improved gauge actions on the gauge fields occurring in simulations is to suppress short range fluctuations (''dislocations'') and the associated ''exceptionally small'' eigenvalues of the fermion matrix. The same effect is expected from smearing the gauge field links in the fermion action. The cumulated effect of the improved gauge action and smeared links should allow for a smaller pion mass at a given lattice spacing and volume. Our choice is the Stout smearing procedure as introduced in [7], since it can easily be implemented in the Hybrid Monte Carlo (HMC) based updating algorithms we are currently using. One should keep in mind that a possible caveat of this procedure is ''oversmearing'', i.e., removing too many small eigenvalues by applying too many smearing steps and/or using a too high value for the smearing parameter-because not every small eigenvalue is ''unphysical''. In addition, after many smearing steps the fermion action can become too delocalized which can lead to an unwanted slowing down of the approach to the continuum limit. In order to avoid this caveat we choose to work with only one step of very mild Stout smearing. Moreover we keep these smearing parameters fixed as we change the lattice spacing. In Section 1 we will shortly review the smearing procedure and the twisted mass formulation, as well as some details concerning the used updating algorithms. Section 2 is devoted to the presentation of the results of our numerical simulations using N{sub f} = 2 and N{sub f} = 2 + 1 + 1 flavors of twisted mass quarks.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2007},

month = {7}

}