# Linear sigma EFT for nearly conformal gauge theories

## Abstract

Here, we construct a generalized linear sigma model as an effective field theory (EFT) to describe nearly conformal gauge theories at low energies. The work is motivated by recent lattice studies of gauge theories near the conformal window, which have shown that the lightest flavor-singlet scalar state in the spectrum (σ) can be much lighter than the vector state (ρ) and nearly degenerate with the PNGBs (π) over a large range of quark masses. The EFT incorporates this feature. We highlight the crucial role played by the terms in the potential that explicitly break chiral symmetry. The explicit breaking can be large enough so that a limited set of additional terms in the potential can no longer be neglected, with the EFT still weakly coupled in this new range. The additional terms contribute importantly to the scalar and pion masses. In particular, they relax the inequality M ^{2} _{σ} ≥ 3M ^{2} _{π}, allowing for consistency with current lattice data.

- Authors:

- Yale Univ., New Haven, CT (United States)
- Boston Univ., Boston, MA (United States)
- Yale Univ., New Haven, CT (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of Bern, Bern (Switzerland)
- Univ. of Colorado, Boulder, CO (United States)
- Univ. of California, Davis, CA (United States)
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
- Univ. of Bern, Bern (Switzerland)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Boston Univ., Boston, MA (United States); NVIDIA Corp., Santa Clara, CA (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26); RIKEN; National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- Contributing Org.:
- Lattice Strong Dynamics (LSD) Collaboration

- OSTI Identifier:
- 1488639

- Alternate Identifier(s):
- OSTI ID: 1489357; OSTI ID: 1573356

- Report Number(s):
- RBRC-1291; BNL-210838-2019-JAAM

Journal ID: ISSN 2470-0010; PRVDAQ

- Grant/Contract Number:
- SC0012704; SC0010005; SC0010025; SC0014664; AC52-07NA27344; AC02-06CH11357

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 11; 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

```
Appelquist, Thomas, Brower, R. C., Fleming, G. T., Gasbarro, Andrew, Hasenfratz, A., Ingoldby, James, Kiskis, J., Osborn, J. C., Rebbi, C., Rinaldi, Enrico, Schaich, D., Vranas, P., Weinberg, E., and Witzel, O. Linear sigma EFT for nearly conformal gauge theories. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.98.114510.
```

```
Appelquist, Thomas, Brower, R. C., Fleming, G. T., Gasbarro, Andrew, Hasenfratz, A., Ingoldby, James, Kiskis, J., Osborn, J. C., Rebbi, C., Rinaldi, Enrico, Schaich, D., Vranas, P., Weinberg, E., & Witzel, O. Linear sigma EFT for nearly conformal gauge theories. United States. doi:10.1103/PhysRevD.98.114510.
```

```
Appelquist, Thomas, Brower, R. C., Fleming, G. T., Gasbarro, Andrew, Hasenfratz, A., Ingoldby, James, Kiskis, J., Osborn, J. C., Rebbi, C., Rinaldi, Enrico, Schaich, D., Vranas, P., Weinberg, E., and Witzel, O. Thu .
"Linear sigma EFT for nearly conformal gauge theories". United States. doi:10.1103/PhysRevD.98.114510.
```

```
@article{osti_1488639,
```

title = {Linear sigma EFT for nearly conformal gauge theories},

author = {Appelquist, Thomas and Brower, R. C. and Fleming, G. T. and Gasbarro, Andrew and Hasenfratz, A. and Ingoldby, James and Kiskis, J. and Osborn, J. C. and Rebbi, C. and Rinaldi, Enrico and Schaich, D. and Vranas, P. and Weinberg, E. and Witzel, O.},

abstractNote = {Here, we construct a generalized linear sigma model as an effective field theory (EFT) to describe nearly conformal gauge theories at low energies. The work is motivated by recent lattice studies of gauge theories near the conformal window, which have shown that the lightest flavor-singlet scalar state in the spectrum (σ) can be much lighter than the vector state (ρ) and nearly degenerate with the PNGBs (π) over a large range of quark masses. The EFT incorporates this feature. We highlight the crucial role played by the terms in the potential that explicitly break chiral symmetry. The explicit breaking can be large enough so that a limited set of additional terms in the potential can no longer be neglected, with the EFT still weakly coupled in this new range. The additional terms contribute importantly to the scalar and pion masses. In particular, they relax the inequality M2σ ≥ 3M2π, allowing for consistency with current lattice data.},

doi = {10.1103/PhysRevD.98.114510},

journal = {Physical Review D},

number = 11,

volume = 98,

place = {United States},

year = {2018},

month = {12}

}

DOI: 10.1103/PhysRevD.98.114510

*Citation information provided by*

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Web of Science

#### Figures / Tables:

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*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*