# Neutrinoless double beta decay in chiral effective field theory: lepton number violation at dimension seven

## Abstract

Here, we analyze neutrinoless double beta decay (0νββ) within the framework of the Standard Model Effective Field Theory. Apart from the dimension-five Weinberg operator, the first contributions appear at dimension seven. We classify the operators and evolve them to the electroweak scale, where we match them to effective dimension-six, -seven, and -nine operators. In the next step, after renormalization group evolution to the QCD scale, we construct the chiral Lagrangian arising from these operators. We then develop a power-counting scheme and derive the two-nucleon 0νββ currents up to leading order in the power counting for each lepton-number-violating operator. We argue that the leading-order contribution to the decay rate depends on a relatively small number of nuclear matrix elements. We test our power counting by comparing nuclear matrix elements obtained by various methods and by different groups. We find that the power counting works well for nuclear matrix elements calculated from a specific method, while, as in the case of light Majorana neutrino exchange, the overall magnitude of the matrix elements can differ by factors of two to three between methods. We also calculate the constraints that can be set on dimension-seven lepton-number-violating operators from 0νββ experiments and study the interplaymore »

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); New Mexico Consortium, Los Alamos, NM (United States)
- Nikhef, Amsterdam (Netherlands)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Dutch Organization for Scientific Research

- OSTI Identifier:
- 1416309

- Report Number(s):
- LA-UR-17-27799

Journal ID: ISSN 1029-8479; TRN: US1800913

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 12; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Atomic and Nuclear Physics; Neutrinoless double beta decay

### Citation Formats

```
Cirigliano, V., Dekens, W., de Vries, J., Graesser, M. L., and Mereghetti, E..
```*Neutrinoless double beta decay in chiral effective field theory: lepton number violation at dimension seven*. United States: N. p., 2017.
Web. doi:10.1007/JHEP12(2017)082.

```
Cirigliano, V., Dekens, W., de Vries, J., Graesser, M. L., & Mereghetti, E..
```*Neutrinoless double beta decay in chiral effective field theory: lepton number violation at dimension seven*. United States. doi:10.1007/JHEP12(2017)082.

```
Cirigliano, V., Dekens, W., de Vries, J., Graesser, M. L., and Mereghetti, E.. Fri .
"Neutrinoless double beta decay in chiral effective field theory: lepton number violation at dimension seven". United States.
doi:10.1007/JHEP12(2017)082. https://www.osti.gov/servlets/purl/1416309.
```

```
@article{osti_1416309,
```

title = {Neutrinoless double beta decay in chiral effective field theory: lepton number violation at dimension seven},

author = {Cirigliano, V. and Dekens, W. and de Vries, J. and Graesser, M. L. and Mereghetti, E.},

abstractNote = {Here, we analyze neutrinoless double beta decay (0νββ) within the framework of the Standard Model Effective Field Theory. Apart from the dimension-five Weinberg operator, the first contributions appear at dimension seven. We classify the operators and evolve them to the electroweak scale, where we match them to effective dimension-six, -seven, and -nine operators. In the next step, after renormalization group evolution to the QCD scale, we construct the chiral Lagrangian arising from these operators. We then develop a power-counting scheme and derive the two-nucleon 0νββ currents up to leading order in the power counting for each lepton-number-violating operator. We argue that the leading-order contribution to the decay rate depends on a relatively small number of nuclear matrix elements. We test our power counting by comparing nuclear matrix elements obtained by various methods and by different groups. We find that the power counting works well for nuclear matrix elements calculated from a specific method, while, as in the case of light Majorana neutrino exchange, the overall magnitude of the matrix elements can differ by factors of two to three between methods. We also calculate the constraints that can be set on dimension-seven lepton-number-violating operators from 0νββ experiments and study the interplay between dimension-five and -seven operators, discussing how dimension-seven contributions affect the interpretation of 0νββ in terms of the effective Majorana mass m ββ .},

doi = {10.1007/JHEP12(2017)082},

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

number = 12,

volume = 2017,

place = {United States},

year = {Fri Dec 15 00:00:00 EST 2017},

month = {Fri Dec 15 00:00:00 EST 2017}

}

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