Abstract
In recent years, the gauge group \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) has received a lot of attention since it can, in principle, account for the observed excess in the anomalous muon magnetic moment (g − 2)μ, as well as the Hubble tension. Due to unavoidable, loop-induced kinetic mixing with the SM photon and Z, the \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) gauge boson A′ can contribute to stellar cooling via decays into neutrinos. In this work, we perform for the first time an ab initio computation of the neutrino emissivities of white dwarf stars due to plasmon decay in a model of gauged \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \). A key result is that current observations of the early-stage white dwarf neutrino luminosity at the 30% level exclude previously allowed regions of the parameter space favoured by a simultaneous explanation of the (g – 2)μ and H0 anomalies. In this work, we present the relevant white dwarf cooling limits over the entire A′ mass range. In particular, we have performed a rigorous computation of the luminosities in the resonant regime, where the A′ mass is comparable to the white dwarf plasma frequencies.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Foot, New physics from electric charge quantization?, Mod. Phys. Lett. A 6 (1991) 527 [INSPIRE].
X.G. He, G.C. Joshi, H. Lew and R.R. Volkas, New Z′ phenomenology, Phys. Rev. D 43 (1991) 22 [INSPIRE].
X.-G. He, G.C. Joshi, H. Lew and R.R. Volkas, Simplest Z′ model, Phys. Rev. D 44 (1991) 2118 [INSPIRE].
R. Foot, X.G. He, H. Lew and R.R. Volkas, Model for a light Z′ boson, Phys. Rev. D 50 (1994) 4571 [hep-ph/9401250] [INSPIRE].
J. Heeck and W. Rodejohann, Gauged Lμ – Lτ symmetry at the electroweak scale, Phys. Rev. D 84 (2011) 075007 [arXiv:1107.5238] [INSPIRE].
K. Asai et al., Minimal gauged \( U{(1)}_{L_{\alpha }-{L}_{\beta }} \) models driven into a corner, Phys. Rev. D 99 (2019) 055029 [arXiv:1811.07571] [INSPIRE].
M. Bauer, P. Foldenauer and M. Mosny, Flavor structure of anomaly-free hidden photon models, Phys. Rev. D 103 (2021) 075024 [arXiv:2011.12973] [INSPIRE].
C. Majumdar et al., Neutrino mass, mixing and muon g – 2 explanation in \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) extension of left-right theory, JHEP 09 (2020) 010 [arXiv:2004.14259] [INSPIRE].
L. Singh, M. Kashav and S. Verma, Gauged \( U{(1)}_{L_{\mu }-{L}_{\tau }} \) symmetry and two-zero textures of inverse neutrino mass matrix in light of muon (g – 2), Mod. Phys. Lett. A 37 (2022) 2250202 [arXiv:2207.08415] [INSPIRE].
S. Arora, M. Kashav, S. Verma and B.C. Chauhan, Muon (g – 2) in \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) scotogenic model extended with vector like fermion, Phys. Scripta 98 (2023) 025304 [arXiv:2206.12828] [INSPIRE].
S. Baek and P. Ko, Phenomenology of \( U{(1)}_{L_{\mu }-{L}_{\tau }} \) charged dark matter at PAMELA and colliders, JCAP 10 (2009) 011 [arXiv:0811.1646] [INSPIRE].
S. Baek, Dark matter and muon (g – 2) in local \( U{(1)}_{L_{\mu }-{L}_{\tau }} \) -extended Ma model, Phys. Lett. B 756 (2016) 1 [arXiv:1510.02168] [INSPIRE].
A. Biswas, S. Choubey and S. Khan, Neutrino mass, dark matter and anomalous magnetic moment of muon in a \( U{(1)}_{L_{\mu }-{L}_{\tau }} \) model, JHEP 09 (2016) 147 [arXiv:1608.04194] [INSPIRE].
A. Biswas, S. Choubey and S. Khan, FIMP and muon (g – 2) in a \( U{(1)}_{L_{\mu }-{L}_{\tau }} \) model, JHEP 02 (2017) 123 [arXiv:1612.03067] [INSPIRE].
P. Foldenauer, Light dark matter in a gauged \( U{(1)}_{L_{\mu }-{L}_{\tau }} \) model, Phys. Rev. D 99 (2019) 035007 [arXiv:1808.03647] [INSPIRE].
N. Okada and O. Seto, Inelastic extra U(1) charged scalar dark matter, Phys. Rev. D 101 (2020) 023522 [arXiv:1908.09277] [INSPIRE].
I. Holst, D. Hooper and G. Krnjaic, Simplest and most predictive model of muon g – 2 and thermal dark matter, Phys. Rev. Lett. 128 (2022) 141802 [arXiv:2107.09067] [INSPIRE].
S. Baek, J. Kim and P. Ko, Muon (g – 2) and thermal WIMP DM in \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) models, arXiv:2204.04889 [INSPIRE].
S. Baek, N.G. Deshpande, X.G. He and P. Ko, Muon anomalous g – 2 and gauged Lμ – Lτ models, Phys. Rev. D 64 (2001) 055006 [hep-ph/0104141] [INSPIRE].
E. Ma, D.P. Roy and S. Roy, Gauged Lμ – Lτ with large muon anomalous magnetic moment and the bimaximal mixing of neutrinos, Phys. Lett. B 525 (2002) 101 [hep-ph/0110146] [INSPIRE].
K. Harigaya et al., Muon g – 2 and LHC phenomenology in the Lμ – Lτ gauge symmetric model, JHEP 03 (2014) 105 [arXiv:1311.0870] [INSPIRE].
W. Altmannshofer, C.-Y. Chen, P.S. Bhupal Dev and A. Soni, Lepton flavor violating Z′ explanation of the muon anomalous magnetic moment, Phys. Lett. B 762 (2016) 389 [arXiv:1607.06832] [INSPIRE].
M. Escudero, D. Hooper, G. Krnjaic and M. Pierre, Cosmology with a very light Lμ – Lτ gauge boson, JHEP 03 (2019) 071 [arXiv:1901.02010] [INSPIRE].
J.A. Carpio, K. Murase, I.M. Shoemaker and Z. Tabrizi, High-energy cosmic neutrinos as a probe of the vector mediator scenario in light of the muon g – 2 anomaly and Hubble tension, Phys. Rev. D 107 (2023) 103057 [arXiv:2104.15136] [INSPIRE].
T. Araki et al., Resolving the Hubble tension in a \( U{(1)}_{L_{\mu }-{L}_{\tau }} \) model with the Majoron, PTEP 2021 (2021) 103B05 [arXiv:2103.07167] [INSPIRE].
W. Altmannshofer, S. Gori, M. Pospelov and I. Yavin, Quark flavor transitions in Lμ – Lτ models, Phys. Rev. D 89 (2014) 095033 [arXiv:1403.1269] [INSPIRE].
A. Crivellin, G. D’Ambrosio and J. Heeck, Explaining h → μ±τ∓, B → K∗μ+μ− and B → Kμ+μ−/B → Ke+e− in a two-Higgs-doublet model with gauged Lμ – Lτ, Phys. Rev. Lett. 114 (2015) 151801 [arXiv:1501.00993] [INSPIRE].
W. Altmannshofer, S. Gori, S. Profumo and F.S. Queiroz, Explaining dark matter and B decay anomalies with an Lμ − Lτ model, JHEP 12 (2016) 106 [arXiv:1609.04026] [INSPIRE].
C.-H. Chen and T. Nomura, Penguin b → sℓ′+ℓ′− and B-meson anomalies in a gauged Lμ – Lτ, Phys. Lett. B 777 (2018) 420 [arXiv:1707.03249] [INSPIRE].
S. Baek, Dark matter contribution to b → sμ+μ− anomaly in local \( U{(1)}_{L_{\mu }-{L}_{\tau }} \) model, Phys. Lett. B 781 (2018) 376 [arXiv:1707.04573] [INSPIRE].
S.-Y. Ho, J. Kim and P. Ko, Recent B+ → \( {K}^{+}\nu \overline{\nu} \) Excess and muon g – 2 illuminating light dark sector with Higgs portal, arXiv:2401.10112 [INSPIRE].
W. Altmannshofer, S.A. Gadam and S. Profumo, Probing new physics with μ+μ− → bs at a muon collider, Phys. Rev. D 108 (2023) 115033 [arXiv:2306.15017] [INSPIRE].
LHCb collaboration, Test of lepton universality in b → sℓ+ℓ− decays, Phys. Rev. Lett. 131 (2023) 051803 [arXiv:2212.09152] [INSPIRE].
LHCb collaboration, Measurement of lepton universality parameters in B+ → K+ℓ+ℓ− and B0 → K∗0ℓ+ℓ− decays, Phys. Rev. D 108 (2023) 032002 [arXiv:2212.09153] [INSPIRE].
D.W.P. Amaral, D.G. Cerdeno, A. Cheek and P. Foldenauer, Confirming \( U{(1)}_{L_{\mu }-{L}_{\tau }} \) as a solution for (g – 2)μ with neutrinos, Eur. Phys. J. C 81 (2021) 861 [arXiv:2104.03297] [INSPIRE].
Y. Kaneta and T. Shimomura, On the possibility of a search for the Lμ – Lτ gauge boson at Belle-II and neutrino beam experiments, PTEP 2017 (2017) 053B04 [arXiv:1701.00156] [INSPIRE].
D.W.P. Amaral, D.G. Cerdeno, P. Foldenauer and E. Reid, Solar neutrino probes of the muon anomalous magnetic moment in the gauged \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \), JHEP 12 (2020) 155 [arXiv:2006.11225] [INSPIRE].
A. Kamada and H.-B. Yu, Coherent propagation of PeV neutrinos and the dip in the neutrino spectrum at IceCube, Phys. Rev. D 92 (2015) 113004 [arXiv:1504.00711] [INSPIRE].
A. Kamada, K. Kaneta, K. Yanagi and H.-B. Yu, Self-interacting dark matter and muon g − 2 in a gauged \( U{(1)}_{L_{\mu }-{L}_{\tau }} \) model, JHEP 06 (2018) 117 [arXiv:1805.00651] [INSPIRE].
D. Croon, G. Elor, R.K. Leane and S.D. McDermott, Supernova muons: new constraints on Z′ bosons, axions and ALPs, JHEP 01 (2021) 107 [arXiv:2006.13942] [INSPIRE].
D.G. Cerdeño, M. Cermeño and Y. Farzan, Constraints from the duration of supernova neutrino burst on on-shell light gauge boson production by neutrinos, Phys. Rev. D 107 (2023) 123012 [arXiv:2301.00661] [INSPIRE].
K. Akita, S.H. Im, M. Masud and S. Yun, Limits on heavy neutral leptons, Z′ bosons and majorons from high-energy supernova neutrinos, arXiv:2312.13627 [INSPIRE].
R.P. Feynman, N. Metropolis and E. Teller, Equations of state of elements based on the generalized Fermi-Thomas theory, Phys. Rev. 75 (1949) 1561 [INSPIRE].
E.E. Salpeter, Energy and pressure of a zero-temperature plasma, Astrophys. J. 134 (1961) 669 [INSPIRE].
M. Rotondo, J.A. Rueda, R. Ruffini and S.-S. Xue, The relativistic Feynman-Metropolis-Teller theory for white dwarfs in general relativity, Phys. Rev. D 84 (2011) 084007 [arXiv:1012.0154] [INSPIRE].
A. Mathew and M.K. Nandy, General relativistic calculations for white dwarfs, Res. Astron. Astrophys. 17 (2017) 061.
R. Fantoni, White-dwarf equation of state and structure: the effect of temperature, J. Stat. Mech. 1711 (2017) 113101 [arXiv:1709.06064] [INSPIRE].
D.E. Winget et al., A strong test of electro-weak theory using pulsating db white dwarf stars as plasmon neutrino detectors, Astrophys. J. Lett. 602 (2004) L109 [astro-ph/0312303] [INSPIRE].
E.M. Kantor and M.E. Gusakov, The neutrino emission due to plasmon decay and neutrino luminosity of white dwarfs, Mon. Not. Roy. Astron. Soc. 381 (2007) 1702 [arXiv:0708.2093] [INSPIRE].
J.D. Landstreet, Synchrotron radiation of neutrinos and its astrophysical significance, Phys. Rev. 153 (1967) 1372 [INSPIRE].
P.R. Chaudhuri, Neutrino synchrotron radiation: I. Application to white dwarfs, Astrophys. Space Sci. 8 (1970) 432.
V. Canuto, C. Chiuderi and C.K. Chou, Plasmon neutrinos emission in a strong magnetic field: I. Transverse plasmons, Astrophys. Space Sci. 7 (1970) 407.
V. Canuto, C. Chiuderi and C.K. Chou, Plasmon neutrinos emission in a strong magnetic field: II. Longitudinal plasmons, Astrophys. Space Sci. 9 (1970) 453.
D.V. Galtsov and N.S. Nikitina, Photoneutrino processes in a strong field, Zh. Eksp. Teor. Fiz. 62 (1972) 2008 [INSPIRE].
L.L. DeRaad Jr., K.A. Milton and N.D. Hari Dass, Photon decay into neutrinos in a strong magnetic field, Phys. Rev. D 14 (1976) 3326 [INSPIRE].
V.V. Skobelev, Reaction whereby a photon decays into a neutrino-antineutrino pair and a neutrino decays into a photon-neutrino pair in a strong magnetic field, Zh. Eksp. Teor. Fiz. 71 (1976) 1263.
D.G. Yakovlev and R. Tschaepe, Synchrotron neutrino-pair radiation in neutron stars, Astron. Nachr. 302 (1981) 167.
A.D. Kaminker et al., Neutrino emissivity from e− synchrotron and e−e+ annihilation processes in a strong magnetic field: general formalism and nonrelativistic limit, Phys. Rev. D 46 (1992) 3256 [INSPIRE].
M.P. Kennett and D.B. Melrose, Neutrino emission via the plasma process in a magnetized plasma, Phys. Rev. D 58 (1998) 093011 [astro-ph/9901156] [INSPIRE].
I. Bhattacharyya, Neutrino synchrotron radiation in electro-weak interaction, Astropart. Phys. 24 (2005) 100 [INSPIRE].
M. Drewes, J. McDonald, L. Sablon and E. Vitagliano, Neutrino emissivities as a probe of the internal magnetic fields of white dwarfs, Astrophys. J. 934 (2022) 99 [arXiv:2109.06158] [INSPIRE].
M. Bauer, P. Foldenauer and J. Jaeckel, Hunting all the hidden photons, JHEP 07 (2018) 094 [arXiv:1803.05466] [INSPIRE].
H.K. Dreiner, J.-F. Fortin, J. Isern and L. Ubaldi, White dwarfs constrain dark forces, Phys. Rev. D 88 (2013) 043517 [arXiv:1303.7232] [INSPIRE].
Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [Erratum ibid. 652 (2021) C4] [arXiv:1807.06209] [INSPIRE].
A.G. Riess et al., Large Magellanic cloud Cepheid standards provide a 1% foundation for the determination of the Hubble constant and stronger evidence for physics beyond ΛCDM, Astrophys. J. 876 (2019) 85 [arXiv:1903.07603] [INSPIRE].
N. Blinov, K.J. Kelly, G.Z. Krnjaic and S.D. McDermott, Constraining the self-interacting neutrino interpretation of the Hubble tension, Phys. Rev. Lett. 123 (2019) 191102 [arXiv:1905.02727] [INSPIRE].
M. Bauer and P. Foldenauer, Consistent theory of kinetic mixing and the Higgs low-energy theorem, Phys. Rev. Lett. 129 (2022) 171801 [arXiv:2207.00023] [INSPIRE].
K.R. Lynch, A note on one loop electroweak contributions to g – 2: a companion to BUHEP-01-16, hep-ph/0108081 [INSPIRE].
M. Pospelov, Secluded U(1) below the weak scale, Phys. Rev. D 80 (2009) 095002 [arXiv:0811.1030] [INSPIRE].
T. Aoyama et al., The anomalous magnetic moment of the muon in the standard model, Phys. Rept. 887 (2020) 1 [arXiv:2006.04822] [INSPIRE].
Muon g-2 collaboration, Measurement of the positive muon anomalous magnetic moment to 0.20 ppm, Phys. Rev. Lett. 131 (2023) 161802 [arXiv:2308.06230] [INSPIRE].
Muon g-2 collaboration, Measurement of the positive muon anomalous magnetic moment to 0.46 ppm, Phys. Rev. Lett. 126 (2021) 141801 [arXiv:2104.03281] [INSPIRE].
Muon g-2 collaboration, Final report of the muon E821 anomalous magnetic moment measurement at BNL, Phys. Rev. D 73 (2006) 072003 [hep-ex/0602035] [INSPIRE].
S. Borsanyi et al., Leading hadronic contribution to the muon magnetic moment from lattice QCD, Nature 593 (2021) 51 [arXiv:2002.12347] [INSPIRE].
A. Crivellin, M. Hoferichter, C.A. Manzari and M. Montull, Hadronic vacuum polarization: (g – 2)μ versus global electroweak fits, Phys. Rev. Lett. 125 (2020) 091801 [arXiv:2003.04886] [INSPIRE].
J.H. Zink and M.E. Ramirez-Quezada, Exploring the dark sectors via the cooling of white dwarfs, Phys. Rev. D 108 (2023) 043014 [arXiv:2306.00517] [INSPIRE].
E. Braaten and D. Segel, Neutrino energy loss from the plasma process at all temperatures and densities, Phys. Rev. D 48 (1993) 1478 [hep-ph/9302213] [INSPIRE].
S.L. Shapiro and S.A. Teukolsky, Black holes, white dwarfs, and neutron stars: the physics of compact objects, Wiley, New York, NY, U.S.A. (1983) [https://doi.org/10.1002/9783527617661] [INSPIRE].
G. Breit and E. Wigner, Capture of slow neutrons, Phys. Rev. 49 (1936) 519 [INSPIRE].
H.A. Weldon, Simple rules for discontinuities in finite temperature field theory, Phys. Rev. D 28 (1983) 2007 [INSPIRE].
G.P. Lepage, Adaptive multidimensional integration: VEGAS enhanced, J. Comput. Phys. 439 (2021) 110386 [arXiv:2009.05112] [INSPIRE].
B.M.S. Hansen et al., Constraining neutrino cooling using the hot white dwarf luminosity function in the globular cluster 47 Tucanae, Astrophys. J. 809 (2015) 141 [arXiv:1507.05665] [INSPIRE].
NA64 collaboration, First results in the search for dark sectors at NA64 with the CERN SPS high energy muon beam, Phys. Rev. Lett. 132 (2024) 211803 [arXiv:2401.01708] [INSPIRE].
G. Bellini et al., Precision measurement of the 7Be solar neutrino interaction rate in Borexino, Phys. Rev. Lett. 107 (2011) 141302 [arXiv:1104.1816] [INSPIRE].
Borexino collaboration, First simultaneous precision spectroscopy of pp, 7Be, and pep solar neutrinos with Borexino phase-II, Phys. Rev. D 100 (2019) 082004 [arXiv:1707.09279] [INSPIRE].
BaBar collaboration, Search for a muonic dark force at BABAR, Phys. Rev. D 94 (2016) 011102 [arXiv:1606.03501] [INSPIRE].
COHERENT collaboration, The COHERENT experiment at the Spallation Neutron Source, arXiv:1509.08702 [INSPIRE].
COHERENT collaboration, Observation of coherent elastic neutrino-nucleus scattering, Science 357 (2017) 1123 [arXiv:1708.01294] [INSPIRE].
W. Altmannshofer, S. Gori, M. Pospelov and I. Yavin, Neutrino trident production: a powerful probe of new physics with neutrino beams, Phys. Rev. Lett. 113 (2014) 091801 [arXiv:1406.2332] [INSPIRE].
CHARM-II collaboration, First observation of neutrino trident production, Phys. Lett. B 245 (1990) 271 [INSPIRE].
G. Krnjaic, G. Marques-Tavares, D. Redigolo and K. Tobioka, Probing muonphilic force carriers and dark matter at Kaon factories, Phys. Rev. Lett. 124 (2020) 041802 [arXiv:1902.07715] [INSPIRE].
P. Côté et al., CASTOR: the Cosmological Advanced Survey Telescope for Optical and ultraviolet Research, Proc. SPIE 8442 (2012) 844215.
N.J. Fantin, P. Côté and A.W. McConnachie, White dwarfs in the era of the LSST and its synergies with space-based missions, Astrophys. J. 900 (2020) 139 [arXiv:2007.01312].
P. Côté et al., CASTOR: a flagship Canadian space telescope, Zenodo (2019).
P. Lepage, gplepage/vegas: Vegas version 6.0, Zenodo (2024).
Acknowledgments
We would like to thank Maura E. Ramirez-Quezada for the profiles of the white dwarf used for the computation of the luminosities of this paper. We also want to acknowledge the VEGAS+ package [95] for multidimensional Monte Carlo integration. This research project was made possible through the access granted by the Galician Supercomputing Center (CESGA) to its supercomputing infrastructure. The supercomputer FinisTerrae III and its permanent data storage system have been funded by the Spanish Ministry of Science and Innovation, the Galician Government and the European Regional Development Fund (ERDF).
The work of PF was supported by the Spanish Agencia Estatal de Investigacion through the grants PID2021-125331NB-I00 and CEX2020-001007-S, funded by MCIN/AEI/10.13039/501100011033. The research of JHZ has received support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska- Curie grant agreement No 860881-HIDDeN.
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: 2405.00094
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
Foldenauer, P., Zink, J.H. How to rule out (g − 2)μ in \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) with white dwarf cooling. J. High Energ. Phys. 2024, 96 (2024). https://doi.org/10.1007/JHEP07(2024)096
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2024)096