# Power corrections to the universal heavy WIMP-nucleon cross section

## Abstract

WIMP-nucleon scattering is analyzed at order $1/M$ in Heavy WIMP Effective Theory. The $1/M$ power corrections, where $$M\gg m_W$$ is the WIMP mass, distinguish between different underlying UV models with the same universal limit and their impact on direct detection rates can be enhanced relative to naive expectations due to generic amplitude-level cancellations at leading order. The necessary one- and two-loop matching calculations onto the low-energy effective theory for WIMP interactions with Standard Model quarks and gluons are performed for the case of an electroweak SU(2) triplet WIMP, considering both the cases of elementary fermions and composite scalars. The low-velocity WIMP-nucleon scattering cross section is evaluated and compared with current experimental limits and projected future sensitivities. Our results provide the most robust prediction for electroweak triplet Majorana fermion dark matter direct detection rates; for this case, a cancellation between two sources of power corrections yields a small total $1/M$ correction, and a total cross section close to the universal limit for $$M \gtrsim {\rm few} \times 100\,{\rm GeV}$$. For the SU(2) composite scalar, the $1/M$ corrections introduce dependence on underlying strong dynamics. Using a leading chiral logarithm evaluation, the total $1/M$ correction has a larger magnitude and uncertainty than in the fermionic case, with a sign that further suppresses the total cross section. These examples provide definite targets for future direct detection experiments and motivate large scale detectors capable of probing to the neutrino floor in the TeV mass regime.

- Authors:

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

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

- OSTI Identifier:
- 1422719

- Report Number(s):
- CAL-TH-2017-063; FERMILAB-PUB-17-400-T; arXiv:1801.08551

Journal ID: ISSN 0370-2693; 1650560

- DOE Contract Number:
- AC02-07CH11359

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics Letters. Section B; Journal Volume: 781; Journal Issue: C

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Chen, Chien-Yi, Hill, Richard J., Solon, Mikhail P., and Wijangco, Alexander M.
```*Power corrections to the universal heavy WIMP-nucleon cross section*. United States: N. p., 2018.
Web. doi:10.1016/j.physletb.2018.04.021.

```
Chen, Chien-Yi, Hill, Richard J., Solon, Mikhail P., & Wijangco, Alexander M.
```*Power corrections to the universal heavy WIMP-nucleon cross section*. United States. doi:10.1016/j.physletb.2018.04.021.

```
Chen, Chien-Yi, Hill, Richard J., Solon, Mikhail P., and Wijangco, Alexander M. Fri .
"Power corrections to the universal heavy WIMP-nucleon cross section". United States.
doi:10.1016/j.physletb.2018.04.021. https://www.osti.gov/servlets/purl/1422719.
```

```
@article{osti_1422719,
```

title = {Power corrections to the universal heavy WIMP-nucleon cross section},

author = {Chen, Chien-Yi and Hill, Richard J. and Solon, Mikhail P. and Wijangco, Alexander M.},

abstractNote = {WIMP-nucleon scattering is analyzed at order $1/M$ in Heavy WIMP Effective Theory. The $1/M$ power corrections, where $M\gg m_W$ is the WIMP mass, distinguish between different underlying UV models with the same universal limit and their impact on direct detection rates can be enhanced relative to naive expectations due to generic amplitude-level cancellations at leading order. The necessary one- and two-loop matching calculations onto the low-energy effective theory for WIMP interactions with Standard Model quarks and gluons are performed for the case of an electroweak SU(2) triplet WIMP, considering both the cases of elementary fermions and composite scalars. The low-velocity WIMP-nucleon scattering cross section is evaluated and compared with current experimental limits and projected future sensitivities. Our results provide the most robust prediction for electroweak triplet Majorana fermion dark matter direct detection rates; for this case, a cancellation between two sources of power corrections yields a small total $1/M$ correction, and a total cross section close to the universal limit for $M \gtrsim {\rm few} \times 100\,{\rm GeV}$. For the SU(2) composite scalar, the $1/M$ corrections introduce dependence on underlying strong dynamics. Using a leading chiral logarithm evaluation, the total $1/M$ correction has a larger magnitude and uncertainty than in the fermionic case, with a sign that further suppresses the total cross section. These examples provide definite targets for future direct detection experiments and motivate large scale detectors capable of probing to the neutrino floor in the TeV mass regime.},

doi = {10.1016/j.physletb.2018.04.021},

journal = {Physics Letters. Section B},

number = C,

volume = 781,

place = {United States},

year = {Fri Jun 01 00:00:00 EDT 2018},

month = {Fri Jun 01 00:00:00 EDT 2018}

}