## Simple and precise factorization of the Jarlskog invariant for neutrino oscillations in matter

## Abstract

For neutrino propagation in matter, we show that the Jarlskog invariant, which controls the size of true CP violation in neutrino oscillation appearance experiments, factorizes into three pieces: the vacuum Jarlskog invariant times two simple two-flavor matter resonance factors that control the matter effects for the solar and atmospheric resonances independently. If the solar effective matter potential and the atmospheric effective Δm ^{2} are chosen carefully for these two resonance factors, then the fractional corrections to this factorization are an impressive 0.04% or smaller. We also show that the inverse of the square of the Jarlskog in matter (1/J ^{^2}) is a fourth order polynomial in the matter potential which guarantees that it can be factored into two quadratics which immediately implies the functional form of our approximate, factorized expression.

- Authors:

- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Publication Date:

- Research Org.:
- Brookhaven National Lab. (BNL), Upton, NY (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1561336

- Alternate Identifier(s):
- OSTI ID: 1529342; OSTI ID: 1562465

- Report Number(s):
- arXiv:1902.07185; FERMILAB-PUB-19-072-T; BNL-212090-2019-JAAM

Journal ID: ISSN 2470-0010; PRVDAQ; oai:inspirehep.net:1720818

- Grant/Contract Number:
- AC02-07CH11359; SC0012704

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 5; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; neutrino; CP; violation; quarks; lepton; neutrinos; Jarlskog

### Citation Formats

```
Denton, Peter B., and Parke, Stephen J. Simple and precise factorization of the Jarlskog invariant for neutrino oscillations in matter. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.053004.
```

```
Denton, Peter B., & Parke, Stephen J. Simple and precise factorization of the Jarlskog invariant for neutrino oscillations in matter. United States. doi:10.1103/PhysRevD.100.053004.
```

```
Denton, Peter B., and Parke, Stephen J. Wed .
"Simple and precise factorization of the Jarlskog invariant for neutrino oscillations in matter". United States. doi:10.1103/PhysRevD.100.053004.
```

```
@article{osti_1561336,
```

title = {Simple and precise factorization of the Jarlskog invariant for neutrino oscillations in matter},

author = {Denton, Peter B. and Parke, Stephen J.},

abstractNote = {For neutrino propagation in matter, we show that the Jarlskog invariant, which controls the size of true CP violation in neutrino oscillation appearance experiments, factorizes into three pieces: the vacuum Jarlskog invariant times two simple two-flavor matter resonance factors that control the matter effects for the solar and atmospheric resonances independently. If the solar effective matter potential and the atmospheric effective Δm2 are chosen carefully for these two resonance factors, then the fractional corrections to this factorization are an impressive 0.04% or smaller. We also show that the inverse of the square of the Jarlskog in matter (1/J^2) is a fourth order polynomial in the matter potential which guarantees that it can be factored into two quadratics which immediately implies the functional form of our approximate, factorized expression.},

doi = {10.1103/PhysRevD.100.053004},

journal = {Physical Review D},

number = 5,

volume = 100,

place = {United States},

year = {2019},

month = {9}

}

DOI: 10.1103/PhysRevD.100.053004