# Lattice operators for scattering of particles with spin

## Abstract

We construct operators for simulating the scattering of two hadrons with spin on the lattice. Three methods are shown to give the consistent operators for *P N, P V, V N* and *N N* scattering, where *P, V* and *N* denote pseudoscalar, vector and nucleon. Explicit expressions for operators are given for all irreducible representations at lowest two relative momenta. Each hadron has a good helicity in the first method. The hadrons are in a certain partial wave L with total spin S in the second method. These enable the physics interpretations of the operators obtained from the general projection method. The correct transformation properties of the operators in all three methods are proven. Lastly, the total momentum of two hadrons is restricted to zero since parity is a good quantum number in this case.

- Authors:

- Univ. of Ljubljana, Ljubljana (Slovenia); Jozef Stefan Institute, Ljubljana (Slovenia); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Jozef Stefan Institute, Ljubljana (Slovenia)
- Univ. of Graz, Graz (Austria)

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

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

- OSTI Identifier:
- 1349637

- Report Number(s):
- JLAB-THY-16-2282; DOE/OR/23177-3871

Journal ID: ISSN 1029-8479; PII: 5429; TRN: US1700921

- Grant/Contract Number:
- AC05-06OR23177

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Volume: 2017; Journal Issue: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice QCD; Lattice Quantum Field Theory

### Citation Formats

```
Prelovsek, S., Skerbis, U., and Lang, C. B.
```*Lattice operators for scattering of particles with spin*. United States: N. p., 2017.
Web. doi:10.1007/JHEP01(2017)129.

```
Prelovsek, S., Skerbis, U., & Lang, C. B.
```*Lattice operators for scattering of particles with spin*. United States. doi:10.1007/JHEP01(2017)129.

```
Prelovsek, S., Skerbis, U., and Lang, C. B. Mon .
"Lattice operators for scattering of particles with spin". United States. doi:10.1007/JHEP01(2017)129. https://www.osti.gov/servlets/purl/1349637.
```

```
@article{osti_1349637,
```

title = {Lattice operators for scattering of particles with spin},

author = {Prelovsek, S. and Skerbis, U. and Lang, C. B.},

abstractNote = {We construct operators for simulating the scattering of two hadrons with spin on the lattice. Three methods are shown to give the consistent operators for P N, P V, V N and N N scattering, where P, V and N denote pseudoscalar, vector and nucleon. Explicit expressions for operators are given for all irreducible representations at lowest two relative momenta. Each hadron has a good helicity in the first method. The hadrons are in a certain partial wave L with total spin S in the second method. These enable the physics interpretations of the operators obtained from the general projection method. The correct transformation properties of the operators in all three methods are proven. Lastly, the total momentum of two hadrons is restricted to zero since parity is a good quantum number in this case.},

doi = {10.1007/JHEP01(2017)129},

journal = {Journal of High Energy Physics (Online)},

issn = {1029-8479},

number = 1,

volume = 2017,

place = {United States},

year = {2017},

month = {1}

}

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