Abstract
The exchange of a pair of neutrinos between two objects, seperated by a distance r, leads to a long-range effective potential proportional to 1/r5, assuming massless neutrinos and four-fermion contact interactions. In this paper, we investigate how this known form of neutrino-mediated potentials might be altered if the distance r is sufficiently short, corresponding to a sufficiently large momentum transfer which could invalidate the contact interactions. We consider two possible scenarios to open up the contact interactions by introducing a t-channel or an s-channel mediator. We derive a general formula that is valid to describe the potential in all regimes as long as the external particles remain non-relativistic. In both scenarios, the potential decreases as 1/r5 in the long-range limit as expected. In the short-range limit, the t-channel potential exhibits the Coulomb-like behavior (i.e. proportional to 1/r), while the s-channel potential exhibits 1/r4 and 1/r2 behaviors.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H.A. Bethe and R.F. Bacher, Nuclear physics A. stationary states of nuclei, Rev. Mod. Phys. 8 (1936) 82.
D. Iwanenko and A. Sokolow, Zur wechselwirkung der schweren teilchen, Z. Phys. 102 (1936) 119.
G. Gamow and E. Teller, Some Generalizations of the beta Transformation Theory, Phys. Rev. 51 (1937) 289 [INSPIRE].
G. Feinberg and J. Sucher, Long-Range Forces from Neutrino-Pair Exchange, Phys. Rev. 166 (1968) 1638 [INSPIRE].
G. Feinberg, J. Sucher and C.K. Au, The Dispersion Theory of Dispersion Forces, Phys. Rept. 180 (1989) 83 [INSPIRE].
S.D.H. Hsu and P. Sikivie, Long range forces from two neutrino exchange revisited, Phys. Rev. D 49 (1994) 4951 [hep-ph/9211301] [INSPIRE].
G. Feinberg and J. Sucher, Long-Range Electromagnetic Forces on Neutral Particles, Phys. Rev. 139 (1965) B1619.
A. Segarra, Neutrino-Pair Exchange Long-Range Force Between Aggregate Matter, Master’s thesis, Universitat de València (2015) [arXiv:1606.05087] [INSPIRE].
Q. Le Thien and D.E. Krause, Spin-Independent Two-Neutrino Exchange Potential with Mixing and C P -Violation, Phys. Rev. D 99 (2019) 116006 [arXiv:1901.05345] [INSPIRE].
Z.-z. Xing, Flavor structures of charged fermions and massive neutrinos, Phys. Rept. 854 (2020) 1 [arXiv:1909.09610] [INSPIRE].
J.A. Grifols, E. Masso and R. Toldra, Majorana neutrinos and long range forces, Phys. Lett. B 389 (1996) 563 [hep-ph/9606377] [INSPIRE].
A. Segarra and J. Bernabéu, Absolute neutrino mass and the Dirac/Majorana distinction from the weak interaction of aggregate matter, Phys. Rev. D 101 (2020) 093004 [arXiv:2001.05900] [INSPIRE].
A. Costantino and S. Fichet, The Neutrino Casimir Force, JHEP 09 (2020) 122 [arXiv:2003.11032] [INSPIRE].
M. Lusignoli and S. Petrarca, Remarks on the forces generated by two-neutrino exchange, Eur. Phys. J. C 71 (2011) 1568 [arXiv:1010.3872] [INSPIRE].
T. Asaka, M. Tanaka, K. Tsumura and M. Yoshimura, Precision electroweak shift of muonium hyperfine splitting, arXiv:1810.05429 [INSPIRE].
N. Orlofsky and Y. Zhang, Neutrino as the dark force, Phys. Rev. D 104 (2021) 075010 [arXiv:2106.08339] [INSPIRE].
S. Fichet, Quantum Forces from Dark Matter and Where to Find Them, Phys. Rev. Lett. 120 (2018) 131801 [arXiv:1705.10331] [INSPIRE].
P. Brax, S. Fichet and G. Pignol, Bounding Quantum Dark Forces, Phys. Rev. D 97 (2018) 115034 [arXiv:1710.00850] [INSPIRE].
A. Costantino, S. Fichet and P. Tanedo, Exotic Spin-Dependent Forces from a Hidden Sector, JHEP 03 (2020) 148 [arXiv:1910.02972] [INSPIRE].
H. Banks and M. Mccullough, Charting the Fifth Force Landscape, Phys. Rev. D 103 (2021) 075018 [arXiv:2009.12399] [INSPIRE].
G. Feinberg and J. Sucher, The Two Photon Exchange Force Between Charged Systems. 1. Spinless Particles, Phys. Rev. D 38 (1988) 3763 [Erratum ibid. 44 (1991) 3997] [INSPIRE].
G. Feinberg and J. Sucher, Spin dependent two photon exchange forces: Spin0 particle and a charged spin 1/2 particle, Phys. Rev. D 45 (1992) 2493 [INSPIRE].
J.A. Grifols and S. Tortosa, Residual long range pseudoscalar forces between unpolarized macroscopic bodies, Phys. Lett. B 328 (1994) 98 [hep-ph/9404249] [INSPIRE].
F. Ferrer and J.A. Grifols, Long range forces from pseudoscalar exchange, Phys. Rev. D 58 (1998) 096006 [hep-ph/9805477] [INSPIRE].
J.B. Hartle, Long-range weak forces and cosmology, Phys. Rev. D 1 (1970) 394 [INSPIRE].
C.J. Horowitz and J.T. Pantaleone, Long range forces from the cosmological neutrinos background, Phys. Lett. B 319 (1993) 186 [hep-ph/9306222] [INSPIRE].
F. Ferrer, J.A. Grifols and M. Nowakowski, Long range forces induced by neutrinos at finite temperature, Phys. Lett. B 446 (1999) 111 [hep-ph/9806438] [INSPIRE].
E. Fischbach, Long range forces and neutrino mass, Annals Phys. 247 (1996) 213 [hep-ph/9603396] [INSPIRE].
A.Y. Smirnov and F. Vissani, Long range neutrino forces and the lower bound on neutrino mass, hep-ph/9604443 [INSPIRE].
A. Abada, M.B. Gavela and O. Pene, To rescue a star, Phys. Lett. B 387 (1996) 315 [hep-ph/9605423] [INSPIRE].
M. Kachelriess, Neutrino selfenergy and pair creation in neutron stars, Phys. Lett. B 426 (1998) 89 [hep-ph/9712363] [INSPIRE].
K. Kiers and M.H.G. Tytgat, Neutrino ground state in a dense star, Phys. Rev. D 57 (1998) 5970 [hep-ph/9712463] [INSPIRE].
A. Abada, O. Pene and J. Rodriguez-Quintero, Finite size effects on multibody neutrino exchange, Phys. Rev. D 58 (1998) 073001 [hep-ph/9802393] [INSPIRE].
J. Arafune and Y. Mimura, Finiteness of multibody neutrino exchange potential energy in neutron stars, Prog. Theor. Phys. 100 (1998) 1083 [hep-ph/9805395] [INSPIRE].
Y.V. Stadnik, Probing Long-Range Neutrino-Mediated Forces with Atomic and Nuclear Spectroscopy, Phys. Rev. Lett. 120 (2018) 223202 [arXiv:1711.03700] [INSPIRE].
M. Ghosh, Y. Grossman and W. Tangarife, Probing the two-neutrino exchange force using atomic parity violation, Phys. Rev. D 101 (2020) 116006 [arXiv:1912.09444] [INSPIRE].
A.Y. Smirnov and X.-J. Xu, Wolfenstein potentials for neutrinos induced by ultra-light mediators, JHEP 12 (2019) 046 [arXiv:1909.07505] [INSPIRE].
K.I. Aoki, Z. Hioki, M. Konuma, R. Kawabe and T. Muta, Electroweak Theory. Framework of On-Shell Renormalization and Study of Higher Order Effects, Prog. Theor. Phys. Suppl. 73 (1982) 1 [INSPIRE].
M. Böhm, H. Spiesberger and W. Hollik, On the One Loop Renormalization of the Electroweak Standard Model and Its Application to Leptonic Processes, Fortsch. Phys. 34 (1986) 687 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2112.03060
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Xu, XJ., Yu, B. On the short-range behavior of neutrino forces beyond the Standard Model: from 1/r5 to 1/r4, 1/r2, and 1/r. J. High Energ. Phys. 2022, 8 (2022). https://doi.org/10.1007/JHEP02(2022)008
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2022)008