# Unitarity and bounds on the scale of fermion mass generation

## Abstract

The scale of fermion mass generation can, as shown by Appelquist and Chanowitz, be bounded from above by relating it to the scale of unitarity violation in the helicity nonconserving amplitude for fermion-anti-fermion pairs to scatter into pairs of longitudinally polarized electroweak gauge bosons. In this paper, we examine the process tt{yields}W{sub L}{sup +}W{sub L}{sup -} in a family of phenomenologically-viable deconstructed Higgsless models and we show that scale of unitarity violation depends on the mass of the additional vectorlike fermion states that occur in these theories (the states that are the deconstructed analogs of Kaluza-Klein partners of the ordinary fermions in a five-dimensional theory). For sufficiently light vector fermions, and for a deconstructed theory with sufficiently many lattice sites (that is, sufficiently close to the continuum limit), the Appelquist-Chanowitz bound can be substantially weakened. More precisely, we find that, as one varies the mass of the vectorlike fermion for fixed top-quark and gauge-boson masses, the bound on the scale of top-quark mass generation interpolates smoothly between the Appelquist-Chanowitz bound and one that can, potentially, be much higher. In these theories, therefore, the bound on the scale of fermion mass generation is independent of the bound on the scale ofmore »

- Authors:

- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824 (United States)

- Publication Date:

- OSTI Identifier:
- 21020255

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 7; Other Information: DOI: 10.1103/PhysRevD.75.073018; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; BOSONS; CHIRALITY; HELICITY; KALUZA-KLEIN THEORY; QUARK-QUARK INTERACTIONS; REST MASS; STANDARD MODEL; T QUARKS; UNITARITY

### Citation Formats

```
Chivukula, R. Sekhar, Christensen, Neil D., Coleppa, Baradhwaj, and Simmons, Elizabeth H.
```*Unitarity and bounds on the scale of fermion mass generation*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.073018.

```
Chivukula, R. Sekhar, Christensen, Neil D., Coleppa, Baradhwaj, & Simmons, Elizabeth H.
```*Unitarity and bounds on the scale of fermion mass generation*. United States. doi:10.1103/PHYSREVD.75.073018.

```
Chivukula, R. Sekhar, Christensen, Neil D., Coleppa, Baradhwaj, and Simmons, Elizabeth H. Sun .
"Unitarity and bounds on the scale of fermion mass generation". United States.
doi:10.1103/PHYSREVD.75.073018.
```

```
@article{osti_21020255,
```

title = {Unitarity and bounds on the scale of fermion mass generation},

author = {Chivukula, R. Sekhar and Christensen, Neil D. and Coleppa, Baradhwaj and Simmons, Elizabeth H.},

abstractNote = {The scale of fermion mass generation can, as shown by Appelquist and Chanowitz, be bounded from above by relating it to the scale of unitarity violation in the helicity nonconserving amplitude for fermion-anti-fermion pairs to scatter into pairs of longitudinally polarized electroweak gauge bosons. In this paper, we examine the process tt{yields}W{sub L}{sup +}W{sub L}{sup -} in a family of phenomenologically-viable deconstructed Higgsless models and we show that scale of unitarity violation depends on the mass of the additional vectorlike fermion states that occur in these theories (the states that are the deconstructed analogs of Kaluza-Klein partners of the ordinary fermions in a five-dimensional theory). For sufficiently light vector fermions, and for a deconstructed theory with sufficiently many lattice sites (that is, sufficiently close to the continuum limit), the Appelquist-Chanowitz bound can be substantially weakened. More precisely, we find that, as one varies the mass of the vectorlike fermion for fixed top-quark and gauge-boson masses, the bound on the scale of top-quark mass generation interpolates smoothly between the Appelquist-Chanowitz bound and one that can, potentially, be much higher. In these theories, therefore, the bound on the scale of fermion mass generation is independent of the bound on the scale of gauge-boson mass generation. While our analysis focuses on deconstructed Higgsless models, any theory in which top-quark mass generation proceeds via the mixing of chiral and vector fermions will give similar results.},

doi = {10.1103/PHYSREVD.75.073018},

journal = {Physical Review. D, Particles Fields},

number = 7,

volume = 75,

place = {United States},

year = {Sun Apr 01 00:00:00 EDT 2007},

month = {Sun Apr 01 00:00:00 EDT 2007}

}