Authors:
(1) Dorian W. P. Amaral, Department of Physics and Astronomy, Rice University and These authors contributed approximately equally to this work;
(2) Mudit Jain, Department of Physics and Astronomy, Rice University, Theoretical Particle Physics and Cosmology, King’s College London and These authors contributed approximately equally to this work;
(3) Mustafa A. Amin, Department of Physics and Astronomy, Rice University;
(4) Christopher Tunnell, Department of Physics and Astronomy, Rice University. 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 Abstract: (Ultra)light spin-1 particles—dark photons—can constitute all of dark matter (DM) and have beyond Standard Model couplings. This can lead to a coherent, oscillatory signature in terrestrial detectors that depends on the coupling strength. We provide a signal analysis and statistical framework for inferring the properties of such DM by taking into account (i) the stochastic and (ii) the vector nature of the underlying field, along with (iii) the effects due to the Earth’s rotation. On time scales shorter than the coherence time, the DM field vector typically traces out a fixed ellipse. Taking this ellipse and the rotation of the Earth into account, we highlight a distinctive three-peak signal in Fourier space that can be used to constrain DM coupling strengths. Accounting for all three peaks, we derive latitude-independent constraints on such DM couplings, unlike those stemming from single-peak studies. We apply our framework to the search for ultralight B − L DM using optomechanical sensors, demonstrating the ability to delve into previously unprobed arXiv:2403.02381v1 [hep-ph] 4 Mar 2024 regions of this DM candidate’s parameter space. 1 Introduction A widely pursued DM candidate is the light/ultralight vector dark matter (VDM) particle. Several early-universe production mechanisms exist for such dark matter [20–30] and, recently, numerical simulations of structure formation of light, vector dark matter in the nonlinear regime have been carried out (e.g. [31–33]). Our focus here is on the detection prospects of this kind of dark matter. Many dedicated studies have been conducted on the detection or exclusion of vectors [34–42] as well as scalars [35, 39, 42–49]. However, for the vector case, the analyses focusing on the Fourier space signal did not fully account for the vector nature and stochastic aspects of the field in their statistical treatment, and nor did they model the effect of the rotation of the Earth [36, 38]. In this work, we take these effects into account when studying the sensitivity of mono-directional accelerometers to ultralight vector dark matter. Given the recent and substantial research and development efforts in quantum technologies, we are specifically interested in timely studies aimed at understanding the potential of quantum optomechanical sensors in the direct detection of dark matter. Mechanical detectors have a rich history in tests of gravity, including LIGO, and in recent years there has been a surge in efforts to explore their potential in quantum sensing for fundamental physics investigations (see reviews [50–52]). We are only beginning to understand the new opportunities for dark matter searches [53–58] in light of significant advances in quantum readout and control of mechanical sensing devices using optical or microwave light [59– 61]. Accurately modeling the dark matter signal and the associated statistics is crucial for drawing representative inferences, guiding these quantum research and development efforts and aiding in experimental design. This is particularly relevant for large-scale accelerometer projects, such as the one proposed by the Windchime collaboration [62]. Such sensors have demonstrated potential as powerful probes for the wavelike signature produced by ultralight dark matter [63]. In this paper, we devise the analysis strategy for ultralight vector dark matter in the coherent regime to draw more representative exclusion inferences in the future. We begin by laying the theoretical groundwork for this DM paradigm in Section 2, where we derive the DM signal in both the time and frequency domains, taking into account both its stochastic and polarization properties, as well as accounting for the rotation of the Earth. We then perform statistical analyses of the DM signal in the frequency domain in Section 3. We derive a limit on a generalised parameter that is independent of the vector dark matter model and experimental parameters, which can be recast to concrete choices of them. Unlike other studies that focus solely on a single peak, our findings reveal that the signal power is distributed across three distinct peaks. Accounting for this distribution ensures the retention of constraining power, regardless of the experiment’s location on Earth. Finally, in Section 4, we apply our framework to a concrete dark matter model and sensor: B − L dark matter and the canonical optomechanical light cavity. This paper is available on arxiv under CC BY-SA 4.0 DEED license. Authors: (1) Dorian W. P. Amaral, Department of Physics and Astronomy, Rice University and These authors contributed approximately equally to this work; (2) Mudit Jain, Department of Physics and Astronomy, Rice University, Theoretical Particle Physics and Cosmology, King’s College London and These authors contributed approximately equally to this work; (3) Mustafa A. Amin, Department of Physics and Astronomy, Rice University; (4) Christopher Tunnell, Department of Physics and Astronomy, Rice University. Authors: Authors: (1) Dorian W. P. Amaral, Department of Physics and Astronomy, Rice University and These authors contributed approximately equally to this work; (2) Mudit Jain, Department of Physics and Astronomy, Rice University, Theoretical Particle Physics and Cosmology, King’s College London and These authors contributed approximately equally to this work; (3) Mustafa A. Amin, Department of Physics and Astronomy, Rice University; (4) Christopher Tunnell, Department of Physics and Astronomy, Rice University. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Calculating the Stochastic Wave Vector Dark Matter Signal 2.1 The Dark Photon Field 2.1 The Dark Photon Field 2.2 The Detector Signal 2.2 The Detector Signal 3 Statistical Analysis and 3.1 Signal Likelihood 3 Statistical Analysis and 3.1 Signal Likelihood 3.2 Projected Exclusions 3.2 Projected Exclusions 4 Application to Accelerometer Studies 4 Application to Accelerometer Studies 4.1 Recasting Generalised Limits onto B − L Dark Matter 4.1 Recasting Generalised Limits onto B − L Dark Matter 5 Future Directions 5 Future Directions 6 Conclusions, Acknowledgments, and References 6 Conclusions, Acknowledgments, and References A Equipartition between Longitudinal and Transverse Modes A Equipartition between Longitudinal and Transverse Modes B Derivation of Marginal Likelihood with Stochastic Field Amplitude B Derivation of Marginal Likelihood with Stochastic Field Amplitude C Covariance Matrix C Covariance Matrix D The Case of the Gradient of a Scalar D The Case of the Gradient of a Scalar Abstract: (Ultra)light spin-1 particles—dark photons—can constitute all of dark matter (DM) and have beyond Standard Model couplings. This can lead to a coherent, oscillatory signature in terrestrial detectors that depends on the coupling strength. We provide a signal analysis and statistical framework for inferring the properties of such DM by taking into account (i) the stochastic and (ii) the vector nature of the underlying field, along with (iii) the effects due to the Earth’s rotation. On time scales shorter than the coherence time, the DM field vector typically traces out a fixed ellipse. Taking this ellipse and the rotation of the Earth into account, we highlight a distinctive three-peak signal in Fourier space that can be used to constrain DM coupling strengths. Accounting for all three peaks, we derive latitude-independent constraints on such DM couplings, unlike those stemming from single-peak studies. We apply our framework to the search for ultralight B − L DM using optomechanical sensors, demonstrating the ability to delve into previously unprobed arXiv:2403.02381v1 [hep-ph] 4 Mar 2024 regions of this DM candidate’s parameter space. 1 Introduction A widely pursued DM candidate is the light/ultralight vector dark matter (VDM) particle. Several early-universe production mechanisms exist for such dark matter [20–30] and, recently, numerical simulations of structure formation of light, vector dark matter in the nonlinear regime have been carried out (e.g. [31–33]). Our focus here is on the detection prospects of this kind of dark matter. Many dedicated studies have been conducted on the detection or exclusion of vectors [34–42] as well as scalars [35, 39, 42–49]. However, for the vector case, the analyses focusing on the Fourier space signal did not fully account for the vector nature and stochastic aspects of the field in their statistical treatment, and nor did they model the effect of the rotation of the Earth [36, 38]. In this work, we take these effects into account when studying the sensitivity of mono-directional accelerometers to ultralight vector dark matter. Given the recent and substantial research and development efforts in quantum technologies, we are specifically interested in timely studies aimed at understanding the potential of quantum optomechanical sensors in the direct detection of dark matter. Mechanical detectors have a rich history in tests of gravity, including LIGO, and in recent years there has been a surge in efforts to explore their potential in quantum sensing for fundamental physics investigations (see reviews [50–52]). We are only beginning to understand the new opportunities for dark matter searches [53–58] in light of significant advances in quantum readout and control of mechanical sensing devices using optical or microwave light [59– 61]. Accurately modeling the dark matter signal and the associated statistics is crucial for drawing representative inferences, guiding these quantum research and development efforts and aiding in experimental design. This is particularly relevant for large-scale accelerometer projects, such as the one proposed by the Windchime collaboration [62]. Such sensors have demonstrated potential as powerful probes for the wavelike signature produced by ultralight dark matter [63]. In this paper, we devise the analysis strategy for ultralight vector dark matter in the coherent regime to draw more representative exclusion inferences in the future. We begin by laying the theoretical groundwork for this DM paradigm in Section 2, where we derive the DM signal in both the time and frequency domains, taking into account both its stochastic and polarization properties, as well as accounting for the rotation of the Earth. We then perform statistical analyses of the DM signal in the frequency domain in Section 3. We derive a limit on a generalised parameter that is independent of the vector dark matter model and experimental parameters, which can be recast to concrete choices of them. Unlike other studies that focus solely on a single peak, our findings reveal that the signal power is distributed across three distinct peaks. Accounting for this distribution ensures the retention of constraining power, regardless of the experiment’s location on Earth. Finally, in Section 4, we apply our framework to a concrete dark matter model and sensor: B − L dark matter and the canonical optomechanical light cavity. This paper is available on arxiv under CC BY-SA 4.0 DEED license. This paper is available on arxiv under CC BY-SA 4.0 DEED license. available on arxiv

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