Advancing the Detection of Ultralight Vector Dark Matter through Novel Analytical Strategies

Table of Links

Abstract and 1 Introduction

2 Calculating the Stochastic Wave Vector Dark Matter Signal

2.1 The Dark Photon Field

2.2 The Detector Signal

3 Statistical Analysis and 3.1 Signal Likelihood

3.2 Projected Exclusions

4 Application to Accelerometer Studies

4.1 Recasting Generalised Limits onto B − L Dark Matter

5 Future Directions

6 Conclusions, Acknowledgments, and References

A Equipartition between Longitudinal and Transverse Modes

B Derivation of Marginal Likelihood with Stochastic Field Amplitude

C Covariance Matrix

D The Case of the Gradient of a Scalar

6 Conclusions

We have provided an analysis strategy for inferring the properties of ultralight vector dark matter from terrestrial experiments, taking into account the stochastic and vector nature of the field (see Fig. 1). Our main results are suited for observation times that are longer than a sidereal day, but shorter than the coherence time. They are as follows:

• We focused on the signal in Fourier space, deriving the power spectral density that such dark matter is expected to leave on an axial sensor that is sensitive to its oscillatory signal. Accounting for the rotation of the Earth, we found that the signal manifests as three peaks at definite frequencies but with random amplitudes (see Fig. 2).

• We derived the likelihoods in each of the signal-containing bins in Fourier space. We did this by considering the marginal likelihood after integrating out the six random variables exhibited by the ULDM signal in the coherent regime: the three Rayleigh amplitudes and the three uniformly distributed DM phases (see Eq. (3.2) and Fig. 3). We found that the general elliptical motion of the vector field afforded us a significantly simpler analysis in Fourier space than the linear polarization assumption since, in the former, all peaks become statistically uncorrelated.

• We drew exclusion limits on a generalised, dimensionless parameter that can be reinterpreted in the context of a concrete sensor setup and dark matter model. We did this via a series of log-likelihood ratio tests following a hybrid frequentist-Bayesian approach. Crucially, we found that, unlike analyses focusing on only a single peak, our approach retains constraining power for experimental setups at all latitudes. This is because we make use of the entire DM signal, which is distributed across all three peaks, instead of constraining ourselves to the signal in any one peak, which is dependent on the latitude of the experiment (see Fig. 4).

• We considered a specific sensor technology (the optomechanical light cavity) and dark matter model (ultralight dark matter stemming from a new gauged U(1)B−L symmetry) as a concrete application of our analysis strategy. We recast our general limit onto one on the gauge coupling of this model, gB−L, finding that long-exposure cavities can rule out previously unexplored regions of the B −L parameter space (see Fig. 5).

In this work, we have established a framework for future experimental efforts in the detection of ultralight vector dark matter. Novel direct-detection probes require an understanding of how the signal of ultralight vector dark matter behaves in our local neighborhood and manifests itself in a sensor. We hope that our work aids in (i) designing search strategies using emerging detector technologies that are not traditionally used for dark matter searches, and (ii) in understanding how well a given model can be tested in the context of calls for Big Science projects using quantum sensing [62].

Acknowledgments

We would like to thank Andrew Long for insightful discussions throughout this work, as well as John Carlton, Daniel Carney, Zhen Liu, and Yue Zhao for their valuable feedback. DA would like to thank Yunan Gao and Juehang Qin for helpful discussions regarding our statistical treatment. CT & DA are supported by the National Science Foundation under award 2046549. MA & MJ were partly supported by DOE grant DE-SC0021619, and MJ is currently supported by a Leverhulme Trust Research Project (RPG-2022-145).

References

[1] G. Bertone and D. Hooper, History of dark matter, Rev. Mod. Phys. 90 (2018) 045002 [1605.04909].

[2] K. Freese, Status of Dark Matter in the Universe, Int. J. Mod. Phys. 1 (2017) 325 [1701.01840].

[3] T.D. Brandt, Constraints on MACHO Dark Matter from Compact Stellar Systems in Ultra-Faint Dwarf Galaxies, Astrophys. J. Lett. 824 (2016) L31 [1605.03665].

[4] N. Dalal and A. Kravtsov, Excluding fuzzy dark matter with sizes and stellar kinematics of ultrafaint dwarf galaxies, Phys. Rev. D 106 (2022) 063517 [2203.05750].

[5] S. Hawking, Gravitationally collapsed objects of very low mass, Mon. Not. Roy. Astron. Soc. 152 (1971) 75.

[6] G.F. Chapline, Cosmological effects of primordial black holes, Nature 253 (1975) 251.

[7] W. Hu, R. Barkana and A. Gruzinov, Cold and fuzzy dark matter, Phys. Rev. Lett. 85 (2000) 1158 [astro-ph/0003365].

[8] P.H. Frampton, M. Kawasaki, F. Takahashi and T.T. Yanagida, Primordial Black Holes as All Dark Matter, JCAP 04 (2010) 023 [1001.2308].

[9] B. Carr, K. Kohri, Y. Sendouda and J. Yokoyama, Constraints on primordial black holes, Rept. Prog. Phys. 84 (2021) 116902 [2002.12778].

[10] B. Carr and F. Kuhnel, Primordial Black Holes as Dark Matter: Recent Developments, Ann. Rev. Nucl. Part. Sci. 70 (2020) 355 [2006.02838].

[11] S. Weinberg, A New Light Boson?, Phys. Rev. Lett. 40 (1978) 223.

[12] F. Wilczek, Problem of Strong P and T Invariance in the Presence of Instantons, Phys. Rev. Lett. 40 (1978) 279.

[13] L. Di Luzio, M. Giannotti, E. Nardi and L. Visinelli, The landscape of QCD axion models, Phys. Rept. 870 (2020) 1 [2003.01100].

[14] A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, String Axiverse, Phys. Rev. D 81 (2010) 123530 [0905.4720].

[15] A. Ringwald, Axions and Axion-Like Particles, in 49th Rencontres de Moriond on Electroweak Interactions and Unified Theories, pp. 223–230, 2014 [1407.0546].

[16] L. Hui, J.P. Ostriker, S. Tremaine and E. Witten, Ultralight scalars as cosmological dark matter, Phys. Rev. D 95 (2017) 043541 [1610.08297].

[17] E.G.M. Ferreira, Ultra-light dark matter, Astron. Astrophys. Rev. 29 (2021) 7 [2005.03254].

[18] J. Jaeckel, A force beyond the Standard Model - Status of the quest for hidden photons, Frascati Phys. Ser. 56 (2012) 172 [1303.1821].

[19] M. Fabbrichesi, E. Gabrielli and G. Lanfranchi, The Dark Photon, 2005.01515.

[20] P.W. Graham, J. Mardon and S. Rajendran, Vector Dark Matter from Inflationary Fluctuations, Phys. Rev. D 93 (2016) 103520 [1504.02102].

[21] P. Agrawal, N. Kitajima, M. Reece, T. Sekiguchi and F. Takahashi, Relic Abundance of Dark Photon Dark Matter, Phys. Lett. B 801 (2020) 135136 [1810.07188].

[22] R.T. Co, A. Pierce, Z. Zhang and Y. Zhao, Dark Photon Dark Matter Produced by Axion Oscillations, Phys. Rev. D 99 (2019) 075002 [1810.07196].

[23] J.A. Dror, K. Harigaya and V. Narayan, Parametric Resonance Production of Ultralight Vector Dark Matter, Phys. Rev. D 99 (2019) 035036 [1810.07195].

[24] M. Bastero-Gil, J. Santiago, L. Ubaldi and R. Vega-Morales, Vector dark matter production at the end of inflation, JCAP 04 (2019) 015 [1810.07208].

[25] A.J. Long and L.-T. Wang, Dark Photon Dark Matter from a Network of Cosmic Strings, Phys. Rev. D 99 (2019) 063529 [1901.03312].

[26] E.W. Kolb and A.J. Long, Completely dark photons from gravitational particle production during the inflationary era, JHEP 03 (2021) 283 [2009.03828].

[27] R.T. Co, K. Harigaya and A. Pierce, Gravitational waves and dark photon dark matter from axion rotations, JHEP 12 (2021) 099 [2104.02077].

[28] P. Adshead, K.D. Lozanov and Z.J. Weiner, Dark photon dark matter from an oscillating dilaton, Phys. Rev. D 107 (2023) 083519 [2301.07718].

[29] D. Cyncynates and Z.J. Weiner, Detectable, defect-free dark photon dark matter, 2310.18397.

[30] O. Ozsoy and G. Tasinato, ¨ Vector dark matter, inflation and non-minimal couplings with gravity, 2310.03862. [31] M.A. Amin, M. Jain, R. Karur and P. Mocz, Small-scale structure in vector dark matter, JCAP 08 (2022) 014 [2203.11935].

[32] M. Gorghetto, E. Hardy, J. March-Russell, N. Song and S.M. West, Dark photon stars: formation and role as dark matter substructure, JCAP 08 (2022) 018 [2203.10100].

[33] M. Jain, M.A. Amin, J. Thomas and W. Wanichwecharungruang, Kinetic relaxation and Bose-star formation in multicomponent dark matter, Phys. Rev. D 108 (2023) 043535 [2304.01985].

[34] A. Pierce, K. Riles and Y. Zhao, Searching for Dark Photon Dark Matter with Gravitational Wave Detectors, Phys. Rev. Lett. 121 (2018) 061102 [1801.10161].

[35] L. Badurina et al., AION: An Atom Interferometer Observatory and Network, JCAP 05 (2020) 011 [1911.11755].

[36] D. Carney, A. Hook, Z. Liu, J.M. Taylor and Y. Zhao, Ultralight dark matter detection with mechanical quantum sensors, New J. Phys. 23 (2021) 023041 [1908.04797].

[37] Y. Michimura, T. Fujita, S. Morisaki, H. Nakatsuka and I. Obata, Ultralight vector dark matter search with auxiliary length channels of gravitational wave detectors, Phys. Rev. D 102 (2020) 102001 [2008.02482].

[38] J. Manley, M.D. Chowdhury, D. Grin, S. Singh and D.J. Wilson, Searching for vector dark matter with an optomechanical accelerometer, Phys. Rev. Lett. 126 (2021) 061301 [2007.04899].

[39] Y. Chen, M. Jiang, J. Shu, X. Xue and Y. Zeng, Dissecting axion and dark photon with a network of vector sensors, Phys. Rev. Res. 4 (2022) 033080 [2111.06732].

[40] A. Caputo, A.J. Millar, C.A.J. O’Hare and E. Vitagliano, Dark photon limits: A handbook, Phys. Rev. D 104 (2021) 095029 [2105.04565].

[41] M. Abe, P. Adamson, M. Borcean, D. Bortoletto, K. Bridges, S.P. Carman et al., Matter-wave atomic gradiometer interferometric sensor (magis-100), Quantum Science and Technology 6 (2021) 044003.

[42] H. Nakatsuka, S. Morisaki, T. Fujita, J. Kume, Y. Michimura, K. Nagano et al., Stochastic effects on observation of ultralight bosonic dark matter, 2205.02960.

[43] J.W. Foster, N.L. Rodd and B.R. Safdi, Revealing the Dark Matter Halo with Axion Direct Detection, Phys. Rev. D 97 (2018) 123006 [1711.10489].

[44] LIGO Scientific, KAGRA, Virgo collaboration, Constraints on dark photon dark matter using data from LIGO’s and Virgo’s third observing run, Phys. Rev. D 105 (2022) 063030 [2105.13085].

[45] M. Lisanti, M. Moschella and W. Terrano, Stochastic properties of ultralight scalar field gradients, Phys. Rev. D 104 (2021) 055037 [2107.10260].[46] L. Badurina, D. Blas and C. McCabe, Refined ultralight scalar dark matter searches with compact atom gradiometers, Phys. Rev. D 105 (2022) 023006 [2109.10965].

[47] L. Badurina, V. Gibson, C. McCabe and J. Mitchell, Ultralight dark matter searches at the sub-Hz frontier with atom multigradiometry, Phys. Rev. D 107 (2023) 055002 [2211.01854].

[48] L. Badurina, A. Beniwal and C. McCabe, Super-Nyquist ultralight dark matter searches with broadband atom gradiometers, Phys. Rev. D 108 (2023) 083016 [2306.16477].

[49] A.L. Miller and L. Mendes, First search for ultralight dark matter with a space-based gravitational-wave antenna: LISA Pathfinder, Phys. Rev. D 107 (2023) 063015 [2301.08736].

[50] Z. Ahmed et al., Quantum Sensing for High Energy Physics, in First workshop on Quantum Sensing for High Energy Physics, 3, 2018 [1803.11306].

[51] M.S. Safronova, D. Budker, D. DeMille, D.F.J. Kimball, A. Derevianko and C.W. Clark, Search for new physics with atoms and molecules, Rev. Mod. Phys. 90 (2018) 025008.

[52] J. Beckey, D. Carney and G. Marocco, Quantum measurements in fundamental physics: a user’s manual, 2311.07270.

[53] D. Carney et al., Mechanical Quantum Sensing in the Search for Dark Matter, Quantum Sci. Technol. 6 (2021) 024002 [2008.06074].

[54] G. Higgins, S. Kalia and Z. Liu, Maglev for Dark Matter: Dark-photon and axion dark matter sensing with levitated superconductors, 2310.18398.

[55] C.G. Baker, W.P. Bowen, P. Cox, M.J. Dolan, M. Goryachev and G. Harris, Optomechanical Dark Matter Direct Detection, 2306.09726.

[56] E. Kilian et al., Dark Matter Searches with Levitated Sensors, 2401.17990.

[57] D.C. Moore and A.A. Geraci, Searching for new physics using optically levitated sensors, Quantum Sci. Technol. 6 (2021) 014008 [2008.13197].

[58] F. Monteiro, G. Afek, D. Carney, G. Krnjaic, J. Wang and D.C. Moore, Search for composite dark matter with optically levitated sensors, Phys. Rev. Lett. 125 (2020) 181102 [2007.12067].

[59] M. Blencowe, Quantum electromechanical systems, Physics Reports 395 (2004) 159.

[60] M. Aspelmeyer, T.J. Kippenberg and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86 (2014) 1391.

[61] O. Buchmueller et al., Snowmass 2021: Quantum Sensors for HEP Science – Interferometers, Mechanics, Traps, and Clocks, in Snowmass 2021, 3, 2022 [2203.07250].

[62] Windchime collaboration, Snowmass 2021 White Paper: The Windchime Project, in Snowmass 2021, 3, 2022 [2203.07242].

[63] P.W. Graham, D.E. Kaplan, J. Mardon, S. Rajendran and W.A. Terrano, Dark Matter Direct Detection with Accelerometers, Phys. Rev. D 93 (2016) 075029 [1512.06165].

[64] M. Jain and M.A. Amin, Polarized solitons in higher-spin wave dark matter, Phys. Rev. D 105 (2022) 056019 [2109.04892].

[65] M.A. Fedderke, P.W. Graham, D.F.J. Kimball and S. Kalia, Earth as a transducer for dark-photon dark-matter detection, Phys. Rev. D 104 (2021) 075023 [2106.00022].

[66] PPTA collaboration, High-precision search for dark photon dark matter with the Parkes Pulsar Timing Array, Phys. Rev. Res. 4 (2022) L012022 [2112.07687].

[67] M.A. Fedderke, P.W. Graham, D.F. Jackson Kimball and S. Kalia, Search for dark-photon dark matter in the SuperMAG geomagnetic field dataset, Phys. Rev. D 104 (2021) 095032 [2108.08852].

[68] J. Frerick, J. Jaeckel, F. Kahlhoefer and K. Schmidt-Hoberg, Riding the dark matter wave: Novel limits on general dark photons from LISA Pathfinder, Phys. Lett. B 848 (2024) 138328 [2310.06017].

[69] C. Beaufort, M. Bastero-Gil, A. Catalano, D.-S. Erfani-Harami, O. Guillaudin, D. Santos et al., Directional detection of meV dark photons with Dandelion, 2310.16505.

[70] L. Sun, B.J.J. Slagmolen and J. Qin, Search for ultralight vector dark matter with a Torsion Pendulum Dual Oscillator, 2402.08935.

[71] H.-Y. Zhang, M. Jain and M.A. Amin, Polarized vector oscillons, Phys. Rev. D 105 (2022) 096037 [2111.08700].

[72] M. Jain, Soliton stars in Yang-Mills-Higgs theories, Phys. Rev. D 106 (2022) 085011 [2205.03418].

[73] M. Jain and M.A. Amin, i-SPin: an integrator for multicomponent Schr¨odinger-Poisson systems with self-interactions, JCAP 04 (2023) 053 [2211.08433].

[74] P. Arias, D. Cadamuro, M. Goodsell, J. Jaeckel, J. Redondo and A. Ringwald, WISPy Cold Dark Matter, JCAP 06 (2012) 013 [1201.5902].

[75] G. Alonso-Alvarez, T. Hugle and J. Jaeckel, ´ Misalignment \& Co.: (Pseudo-)scalar and vector dark matter with curvature couplings, JCAP 02 (2020) 014 [1905.09836].

[76] B. Himmetoglu, C.R. Contaldi and M. Peloso, Instability of anisotropic cosmological solutions supported by vector fields, Phys. Rev. Lett. 102 (2009) 111301 [0809.2779].

[77] B. Himmetoglu, C.R. Contaldi and M. Peloso, Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature, Phys. Rev. D 80 (2009) 123530 [0909.3524].

[78] M. Karciauskas and D.H. Lyth, On the health of a vector field with (R Aˆ2)/6 coupling to gravity, JCAP 11 (2010) 023 [1007.1426].

[79] G.P. Centers et al., Stochastic fluctuations of bosonic dark matter, Nature Commun. 12 (2021) 7321 [1905.13650].

[80] E.J. Groth, Probability distributions related to power spectra., ApJS 29 (1975) 285.

[81] G. Cowan, K. Cranmer, E. Gross and O. Vitells, Asymptotic formulae for likelihood-based tests of new physics, Eur. Phys. J. C 71 (2011) 1554 [1007.1727].

[82] H. Chernoff, On the Distribution of the Likelihood Ratio, Ann. Math. Stat. 25 (1954) 573.

[83] S. Algeri, J. Aalbers, K. Dundas Mor˚a and J. Conrad, Searching for new phenomena with profile likelihood ratio tests, Nature Rev. Phys. 2 (2020) 245 [1911.10237].

[84] M.E. Peskin and D.V. Schroeder, An Introduction to quantum field theory, Addison-Wesley, Reading, USA (1995).

[85] L. Basso, A. Belyaev, S. Moretti and C.H. Shepherd-Themistocleous, Phenomenology of the minimal B-L extension of the Standard model: Z’ and neutrinos, Phys. Rev. D 80 (2009) 055030 [0812.4313]. [86] S. Kanemura, T. Matsui and H. Sugiyama, Neutrino mass and dark matter from gauged U(1)B−L breaking, Phys. Rev. D 90 (2014) 013001 [1405.1935].

[87] A.A. Clerk, M.H. Devoret, S.M. Girvin, F. Marquardt and R.J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Rev. Mod. Phys. 82 (2010) 1155 [0810.4729].

[88] LIGO Scientific collaboration, LIGO: The Laser interferometer gravitational-wave observatory, Rept. Prog. Phys. 72 (2009) 076901 [0711.3041]. [89] MICROSCOPE collaboration, MICROSCOPE Mission: Final Results of the Test of the Equivalence Principle, Phys. Rev. Lett. 129 (2022) 121102 [2209.15487].

[90] T.A. Wagner, S. Schlamminger, J.H. Gundlach and E.G. Adelberger, Torsion-balance tests of the weak equivalence principle, Class. Quant. Grav. 29 (2012) 184002 [1207.2442].

[91] P. Mocz, M. Vogelsberger, V.H. Robles, J. Zavala, M. Boylan-Kolchin, A. Fialkov et al., Galaxy formation with BECDM – I. Turbulence and relaxation of idealized haloes, Mon. Not. Roy. Astron. Soc. 471 (2017) 4559 [1705.05845].

[92] F. Edwards, E. Kendall, S. Hotchkiss and R. Easther, PyUltraLight: A Pseudo-Spectral Solver for Ultralight Dark Matter Dynamics, JCAP 10 (2018) 027 [1807.04037].

[93] M. Jain, M.A. Amin and H. Pu, Integrator for general spin-s Gross-Pitaevskii systems, Phys. Rev. E 108 (2023) 055305 [2305.01675].

[94] P. Adshead and K.D. Lozanov, Self-gravitating Vector Dark Matter, Phys. Rev. D 103 (2021) 103501 [2101.07265].