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Physics of Fundamental Symmetries and Interactions {PSI2010 A torsion pendulum based axion search
Available online at www.sciencedirect.com
Physics Procedia 17 (2011) 96–99
Physics of Fundamental Symmetries and Interactions – PSI2010 A torsion pendulum based axion search S.A. Hoedl, E.G. Adelberger, B.R. Heckel Center for Experimental Nuclear Physics and Astrophysics, University of Washington, Seattle, WA, USA
Abstract Despite two decades of experimental effort, the elusive axion has yet to be discovered. Nevertheless, it remains a well-motivated solution to the strong CP problem and a promising dark matter candidate. Most searches use the axion-two-photon coupling to probe for axions that are generated in the sun, remnants from the big-bang or created in the laboratory. Using techniques inspired by torsion pendulum based tests of gravity, we have constructed a new torsion pendulum experiment that looks for a macroscopic parity and time-violating force mediated by virtual axions. For an axion mass of 1 meV, we have improved the limit on this force by ten orders of magnitude, and thus, have opened another path to look for very heavy axions. Keywords: axion, axion-like particle, torsion pendulum
1. Introduction Modern torsion balance experiments impose tight constraints on the fundamental forces of nature. The E¨ ot-Wash group at the University of Washington has developed techniques that push the frontier of torsion pendulum technology. Typically, our experiments convert an oscillating force or an oscillating acceleration acting on a torsion pendulum into an oscillating rotation that√is observed with an auto-collimator. Most of our experiments have an angular noise of about 1 nano-rad/ day. Expressed as a force per atom in the pendulum, this noise corresponds to the electrostatic repulsive force between two electrons separated by 100 light-years. This sensitivity enables us to probe many interesting questions pertaining to gravitational scale particle physics. We have performed experiments that test the equivalence principle [1], the gravitational inverse square law [2] and Lorentz symmetry [3]. The results from these experiments constrain many interesting extensions to the standard model, such as scalars predicted by string theories, extra space [4] and time [5] dimensions, non-commutative geometries [6, 7], and the exchange of scalar, pseudoscalar or vector particles. Recent publications [8, 9] summarize our research on these and other questions. A number of extensions to the standard model predict the existence of light pseudo-scalar particles. Typically, these particles are the result of the spontaneous breaking of a global symmetry at a very high energy scale. Such particles include axions, familions, majorons, arions and omions. The axion [10, 11] is the most well-motivated pseudoscalar, and several experimental searches are actively underway. A discovery of the axion would identify at least one component of the dark matter and explain why the neutron electric dipole moment is observed to be so small. Quantum chromodynamics (QCD) explicitly violates the product of charge and parity (CP) reversal symmetry, so that the CP violating parameter, θQCD , is expected to be of order unity. However, bounds on the electric dipole moment of the neutron [12] and the Hg atom [13] constrain θQCD ≤ 3 × 10−10 . To solve this so-called Strong-CP problem, Peccei and Quinn (PQ) proposed a
1875-3892 © 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Organising Committee of the 2nd International Workshop on the Physics of fundamental Symmetries and Interactions doi:10.1016/j.phpro.2011.06.023
S.A. Hoedl et al. / Physics Procedia 17 (2011) 96–99
97
new symmetry [14] that spontaneously broke in the very early Universe, dynamically minimized θQCD and generated the axion through the so-called misalignment mechanism [15]. Today, these axions would compose at least some of the cold dark matter. Note that the axion is only one of many light pseudo-scalar particles with similar properties, referred to as axion-like particles (ALPs). For example, string theories also predict ALPs [16]. If discovered, an ALP other than the axion would also be an attractive dark matter candidate. Cosmology, astrophysics and laboratory experiments constrain the axion’s mass and its coupling to matter and photons. Predictions for the present-day density of axionic dark matter depend on the axion mass and the model of the early Universe. In most cosmologies, the present day axion density scales with 7/6 the axion mass as 1/ma , and an axion mass of about 10 μeV accounts for all of the dark matter [15]. If other particles also constitute some of the dark matter, then the axion would be expected to be even heavier. Axions can also be created in, and then easily escape from, the hot plasmas found in stars and supernovae. Estimations of stellar and supernovae energy loss rates impose an upper bound on the coupling of axions to electrons, nucleons and photons. Generically, these couplings are proportional to ma , and the astrophysical constraints imply an upper bound of about 10 meV on the axion mass [17]. Heavier axions that couple so strongly that they do not escape from stars or supernovae are precluded by laboratory-based particle physics experiments [18] and by limits on hot dark matter [19]. The constraints on the mass and couplings of ALPs other than axions must be evaluated for each model individually. Nevertheless, the axion mass bounds cited above define an axion-window where most axion and ALP search efforts are focused. In the remainder of this paper, we refer to both axions and axion-like particles as ALPs. Most ALP search efforts [20, 21, 22] look for the conversion of an ALP into a photon in the presence of a static magnetic field. Alternatively, any ALP, such as the axion, that couples with both scalar and pseudoscalar vertices to fundamental fermions would mediate a parity and time-reversal symmetry violating (PTV) force [23] between polarized and unpolarized particles. For the case of a force between polarized electrons and unpolarized nucleons, the PTV force is described by the potential: gsN gpe 1 1 2 (ˆ σ · rˆ) + e−r/λalp , V (ˆ σ , rˆ) = 8πme c λalp r r2 where r is the electron-atom separation vector, λalp = malp /c is the Compton wavelength of the ALP, gpe is the ALP pseudo-scalar coupling constant to a polarized electron, gsN is the ALP scalar coupling constant to a nucleon, and σ ˆ and me are the spin unit-vector and mass of the polarized electron respectively. If the ALP is sufficiently massive, the ALP mediated force will be macroscopic and possibly accessible with a torsion pendulum. Even though gsN gpe is expected to be very small (for the axion, gsN ∝ θQCD ), PTV force searches have three advantages over more conventional ALP experiments: they do not rely on cosmological or astrophysical production mechanisms to provide a source of ALPs; they are sensitive to ALPs that do not couple to photons, and most importantly, they simultaneously probe the entire axion-window without needing to tune the experiment. Several efforts have looked for the PTV force between polarized electrons and unpolarized atoms with a range within the axion window. Ni et al. [24] looked for an induce magnetization in a paramagnetic salt that was correlated with the position of a heavy copper mass. Hammond et al. [25] observed the motion of three copper cylinders suspended within magnetic shields that were positioned in the gaps of a split toroidal electromagnet. The magnetic shields were the source of polarized electrons. Others have used ultra-cold neutrons (UCN) and 3 He to look for the PTV force between polarized and unpolarized nucleons with a range within the axion-window. Baeßler et al. [26] looked for a deviation from the expected energy levels of UCN in the Earth’s gravitational field. Serebrov et al. [27] looked for a change in the UCN precession frequency due to the PTV force. Petukov et al. [28] looked for a change in the spin relaxation time of 3 He induced by the PTV force.
S.A. Hoedl et al. / Physics Procedia 17 (2011) 96–99
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2. The axion torsion pendulum To probe for the PTV force within the axionwindow, we constructed a dedicated torsion pendulum [29] sensitive to the PTV force (see Fig. 1). This apparatus consisted of two parts: a split toroidal electromagnet that provided the source of polarized electrons and a planar torsion pendulum suspended between the two magnet halves that provided the source of unpolarized nucleons. The magnet halves were fixed to the apparatus, and the pendulum was free to rotate about the fiber axis. A change in the pendulum’s equilibrium angle, when the magnetic field reversed direction from the clockwise to counter-clockwise orientation, suggested the presence of the PTV force. Spurious signals associated with the strong magnetic field (3.6 kG) and the finite magnetic susceptibility of the silicon dominated the data. However, the PTV force has a unique signature: it must strengthen as the pendulum approaches either magnet half. Thus, by measuring the change in the pendulum’s equilibrium angle at different pendulum positions, we could distinguish a true PTV force from spurious signals. No evidence for the PTV force was observed. Figure 2 shows our constraints. 3. Conclusion
Figure 1: A diagram of the ALP pendulum. The gap between the magnet halves is exagerated for clarity. The inner radius of the magnet was 3 cm, the outer radius of the magnet was 6 cm.
Torsion pendulum experiments are powerful tools to probe for physics beyond the standard model. Despite centuries of use, they remain the premier method for testing the fundamental forces of nature at laboratory distance scales, and they can make many interesting statements about physics at energy scales present only in the very early Universe. We have constructed a dedicated torsion pendulum to look for a massive pseudo-scalar particle, such as the axion. Our constraints on the force mediated by such a particle are more than a factor of 1010 more restrictive than previous efforts for pseudoscalars heavier than 1 meV. Future improvement is likely, and thus, we have opened another path to search for heavy axion-like particles. 4. Acknowledgments This work was primarily supported by NSF grant PHY0653863 and secondarily via DOE support for the Center for Experimental Nuclear Physics and Astrophysics at the University of Washington. 5. References [1] [2] [3] [4] [5] [6] [7]
S. Schlamminger, et al., Phys. Rev. Lett. 100 (2008) 041101. D. Kapner, et al., Phys. Rev. Lett. 98 (2007) 021101. B. Heckel, et al., Phys. Rev. D 78 (2008) 092006. N. Arkani-Hamed, S. Dimopoulis, G. Dvali, Phys. Lett. B 436 (1998) 257. G. Dvali, G. Gabadadze, G. Senjanovic, arXiv:hep-ph/9910207. I. Hinchliffe, N. Kersting, Y. Ma, Int. J. Mod. Phys. (2004) 179. A. Anisimov, T. Banks, M. Dine, M. Graesser, Phys. Rev. D 65 (2002) 085032.
S.A. Hoedl et al. / Physics Procedia 17 (2011) 96–99
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Figure 2: The 2-σ exclusion plot on an axion mediated force. The exclusion limits from Hammond and Ni are presented in Ref [25] and Ref [24] respectively.
[8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
E. Adelberger, et al., Prog. Part. Nucl. Phys. 62 (2009) 102. E. Adelberger, et al., Phys. Rev. Lett. 98 (2007) 131104. S. Weinberg, Phys. Rev. Lett. 40 (1978) 223. F. Wilczek, Phys. Rev. Lett. 40 (1978) 279. C. Baker, et al., Phys. Rev. Lett. 97 (2006) 131801. W. Griffith, et al., Phys. Rev. Lett. 102 (2009) 101601. R. Peccei, H. Quinn, Phys. Rev. D 16 (1977) 1791. S. Asztalos, et al., Phys. Rev. D 69 (2004) 011101(R). P. Svrcek, E. Witten, J. High Energy Phys. 0606 (2006) 051. G. Raffelt, Ann. Rev. Nucl. Part. Sci. 49 (1999) 163. J. Kim, Physics Reports 150 (1987) 1. S. Hannestad, et al., JCAP 08 (2010) 1. S. Asztalos, et al., Phys. Rev. Lett. 104 (2010) 041301. E. Arik, et al., JCAP 02 (2009) 008. K. Ehert, et al., Phys. Lett. B 689 (2010) 149. J. Moody, F. Wilczek, Phys. Rev. D 30 (1984) 130. W.-T. Ni, et al., Phys. Rev. Lett. 82 (1999) 2439. G. Hammond, C. Speake, C. Trenkel, A. Paton, Phys. Rev. Lett. 98 (2007) 081101. S. Baeßler, et al., Phys. Rev. D 75 (2007) 075006. A. Serebrov, et al., JETP Letters 91 (2010) 6–10. A. Petukhov, et al., Phys. Rev. Lett. 105 (2010) 170401. S. Hoedl, et al., Phys. Rev. Lett. 106 (2011) 041801.
Physics Procedia 17 (2011) 96–99
Physics of Fundamental Symmetries and Interactions – PSI2010 A torsion pendulum based axion search S.A. Hoedl, E.G. Adelberger, B.R. Heckel Center for Experimental Nuclear Physics and Astrophysics, University of Washington, Seattle, WA, USA
Abstract Despite two decades of experimental effort, the elusive axion has yet to be discovered. Nevertheless, it remains a well-motivated solution to the strong CP problem and a promising dark matter candidate. Most searches use the axion-two-photon coupling to probe for axions that are generated in the sun, remnants from the big-bang or created in the laboratory. Using techniques inspired by torsion pendulum based tests of gravity, we have constructed a new torsion pendulum experiment that looks for a macroscopic parity and time-violating force mediated by virtual axions. For an axion mass of 1 meV, we have improved the limit on this force by ten orders of magnitude, and thus, have opened another path to look for very heavy axions. Keywords: axion, axion-like particle, torsion pendulum
1. Introduction Modern torsion balance experiments impose tight constraints on the fundamental forces of nature. The E¨ ot-Wash group at the University of Washington has developed techniques that push the frontier of torsion pendulum technology. Typically, our experiments convert an oscillating force or an oscillating acceleration acting on a torsion pendulum into an oscillating rotation that√is observed with an auto-collimator. Most of our experiments have an angular noise of about 1 nano-rad/ day. Expressed as a force per atom in the pendulum, this noise corresponds to the electrostatic repulsive force between two electrons separated by 100 light-years. This sensitivity enables us to probe many interesting questions pertaining to gravitational scale particle physics. We have performed experiments that test the equivalence principle [1], the gravitational inverse square law [2] and Lorentz symmetry [3]. The results from these experiments constrain many interesting extensions to the standard model, such as scalars predicted by string theories, extra space [4] and time [5] dimensions, non-commutative geometries [6, 7], and the exchange of scalar, pseudoscalar or vector particles. Recent publications [8, 9] summarize our research on these and other questions. A number of extensions to the standard model predict the existence of light pseudo-scalar particles. Typically, these particles are the result of the spontaneous breaking of a global symmetry at a very high energy scale. Such particles include axions, familions, majorons, arions and omions. The axion [10, 11] is the most well-motivated pseudoscalar, and several experimental searches are actively underway. A discovery of the axion would identify at least one component of the dark matter and explain why the neutron electric dipole moment is observed to be so small. Quantum chromodynamics (QCD) explicitly violates the product of charge and parity (CP) reversal symmetry, so that the CP violating parameter, θQCD , is expected to be of order unity. However, bounds on the electric dipole moment of the neutron [12] and the Hg atom [13] constrain θQCD ≤ 3 × 10−10 . To solve this so-called Strong-CP problem, Peccei and Quinn (PQ) proposed a
1875-3892 © 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Organising Committee of the 2nd International Workshop on the Physics of fundamental Symmetries and Interactions doi:10.1016/j.phpro.2011.06.023
S.A. Hoedl et al. / Physics Procedia 17 (2011) 96–99
97
new symmetry [14] that spontaneously broke in the very early Universe, dynamically minimized θQCD and generated the axion through the so-called misalignment mechanism [15]. Today, these axions would compose at least some of the cold dark matter. Note that the axion is only one of many light pseudo-scalar particles with similar properties, referred to as axion-like particles (ALPs). For example, string theories also predict ALPs [16]. If discovered, an ALP other than the axion would also be an attractive dark matter candidate. Cosmology, astrophysics and laboratory experiments constrain the axion’s mass and its coupling to matter and photons. Predictions for the present-day density of axionic dark matter depend on the axion mass and the model of the early Universe. In most cosmologies, the present day axion density scales with 7/6 the axion mass as 1/ma , and an axion mass of about 10 μeV accounts for all of the dark matter [15]. If other particles also constitute some of the dark matter, then the axion would be expected to be even heavier. Axions can also be created in, and then easily escape from, the hot plasmas found in stars and supernovae. Estimations of stellar and supernovae energy loss rates impose an upper bound on the coupling of axions to electrons, nucleons and photons. Generically, these couplings are proportional to ma , and the astrophysical constraints imply an upper bound of about 10 meV on the axion mass [17]. Heavier axions that couple so strongly that they do not escape from stars or supernovae are precluded by laboratory-based particle physics experiments [18] and by limits on hot dark matter [19]. The constraints on the mass and couplings of ALPs other than axions must be evaluated for each model individually. Nevertheless, the axion mass bounds cited above define an axion-window where most axion and ALP search efforts are focused. In the remainder of this paper, we refer to both axions and axion-like particles as ALPs. Most ALP search efforts [20, 21, 22] look for the conversion of an ALP into a photon in the presence of a static magnetic field. Alternatively, any ALP, such as the axion, that couples with both scalar and pseudoscalar vertices to fundamental fermions would mediate a parity and time-reversal symmetry violating (PTV) force [23] between polarized and unpolarized particles. For the case of a force between polarized electrons and unpolarized nucleons, the PTV force is described by the potential: gsN gpe 1 1 2 (ˆ σ · rˆ) + e−r/λalp , V (ˆ σ , rˆ) = 8πme c λalp r r2 where r is the electron-atom separation vector, λalp = malp /c is the Compton wavelength of the ALP, gpe is the ALP pseudo-scalar coupling constant to a polarized electron, gsN is the ALP scalar coupling constant to a nucleon, and σ ˆ and me are the spin unit-vector and mass of the polarized electron respectively. If the ALP is sufficiently massive, the ALP mediated force will be macroscopic and possibly accessible with a torsion pendulum. Even though gsN gpe is expected to be very small (for the axion, gsN ∝ θQCD ), PTV force searches have three advantages over more conventional ALP experiments: they do not rely on cosmological or astrophysical production mechanisms to provide a source of ALPs; they are sensitive to ALPs that do not couple to photons, and most importantly, they simultaneously probe the entire axion-window without needing to tune the experiment. Several efforts have looked for the PTV force between polarized electrons and unpolarized atoms with a range within the axion window. Ni et al. [24] looked for an induce magnetization in a paramagnetic salt that was correlated with the position of a heavy copper mass. Hammond et al. [25] observed the motion of three copper cylinders suspended within magnetic shields that were positioned in the gaps of a split toroidal electromagnet. The magnetic shields were the source of polarized electrons. Others have used ultra-cold neutrons (UCN) and 3 He to look for the PTV force between polarized and unpolarized nucleons with a range within the axion-window. Baeßler et al. [26] looked for a deviation from the expected energy levels of UCN in the Earth’s gravitational field. Serebrov et al. [27] looked for a change in the UCN precession frequency due to the PTV force. Petukov et al. [28] looked for a change in the spin relaxation time of 3 He induced by the PTV force.
S.A. Hoedl et al. / Physics Procedia 17 (2011) 96–99
98
2. The axion torsion pendulum To probe for the PTV force within the axionwindow, we constructed a dedicated torsion pendulum [29] sensitive to the PTV force (see Fig. 1). This apparatus consisted of two parts: a split toroidal electromagnet that provided the source of polarized electrons and a planar torsion pendulum suspended between the two magnet halves that provided the source of unpolarized nucleons. The magnet halves were fixed to the apparatus, and the pendulum was free to rotate about the fiber axis. A change in the pendulum’s equilibrium angle, when the magnetic field reversed direction from the clockwise to counter-clockwise orientation, suggested the presence of the PTV force. Spurious signals associated with the strong magnetic field (3.6 kG) and the finite magnetic susceptibility of the silicon dominated the data. However, the PTV force has a unique signature: it must strengthen as the pendulum approaches either magnet half. Thus, by measuring the change in the pendulum’s equilibrium angle at different pendulum positions, we could distinguish a true PTV force from spurious signals. No evidence for the PTV force was observed. Figure 2 shows our constraints. 3. Conclusion
Figure 1: A diagram of the ALP pendulum. The gap between the magnet halves is exagerated for clarity. The inner radius of the magnet was 3 cm, the outer radius of the magnet was 6 cm.
Torsion pendulum experiments are powerful tools to probe for physics beyond the standard model. Despite centuries of use, they remain the premier method for testing the fundamental forces of nature at laboratory distance scales, and they can make many interesting statements about physics at energy scales present only in the very early Universe. We have constructed a dedicated torsion pendulum to look for a massive pseudo-scalar particle, such as the axion. Our constraints on the force mediated by such a particle are more than a factor of 1010 more restrictive than previous efforts for pseudoscalars heavier than 1 meV. Future improvement is likely, and thus, we have opened another path to search for heavy axion-like particles. 4. Acknowledgments This work was primarily supported by NSF grant PHY0653863 and secondarily via DOE support for the Center for Experimental Nuclear Physics and Astrophysics at the University of Washington. 5. References [1] [2] [3] [4] [5] [6] [7]
S. Schlamminger, et al., Phys. Rev. Lett. 100 (2008) 041101. D. Kapner, et al., Phys. Rev. Lett. 98 (2007) 021101. B. Heckel, et al., Phys. Rev. D 78 (2008) 092006. N. Arkani-Hamed, S. Dimopoulis, G. Dvali, Phys. Lett. B 436 (1998) 257. G. Dvali, G. Gabadadze, G. Senjanovic, arXiv:hep-ph/9910207. I. Hinchliffe, N. Kersting, Y. Ma, Int. J. Mod. Phys. (2004) 179. A. Anisimov, T. Banks, M. Dine, M. Graesser, Phys. Rev. D 65 (2002) 085032.
S.A. Hoedl et al. / Physics Procedia 17 (2011) 96–99
99
Figure 2: The 2-σ exclusion plot on an axion mediated force. The exclusion limits from Hammond and Ni are presented in Ref [25] and Ref [24] respectively.
[8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
E. Adelberger, et al., Prog. Part. Nucl. Phys. 62 (2009) 102. E. Adelberger, et al., Phys. Rev. Lett. 98 (2007) 131104. S. Weinberg, Phys. Rev. Lett. 40 (1978) 223. F. Wilczek, Phys. Rev. Lett. 40 (1978) 279. C. Baker, et al., Phys. Rev. Lett. 97 (2006) 131801. W. Griffith, et al., Phys. Rev. Lett. 102 (2009) 101601. R. Peccei, H. Quinn, Phys. Rev. D 16 (1977) 1791. S. Asztalos, et al., Phys. Rev. D 69 (2004) 011101(R). P. Svrcek, E. Witten, J. High Energy Phys. 0606 (2006) 051. G. Raffelt, Ann. Rev. Nucl. Part. Sci. 49 (1999) 163. J. Kim, Physics Reports 150 (1987) 1. S. Hannestad, et al., JCAP 08 (2010) 1. S. Asztalos, et al., Phys. Rev. Lett. 104 (2010) 041301. E. Arik, et al., JCAP 02 (2009) 008. K. Ehert, et al., Phys. Lett. B 689 (2010) 149. J. Moody, F. Wilczek, Phys. Rev. D 30 (1984) 130. W.-T. Ni, et al., Phys. Rev. Lett. 82 (1999) 2439. G. Hammond, C. Speake, C. Trenkel, A. Paton, Phys. Rev. Lett. 98 (2007) 081101. S. Baeßler, et al., Phys. Rev. D 75 (2007) 075006. A. Serebrov, et al., JETP Letters 91 (2010) 6–10. A. Petukhov, et al., Phys. Rev. Lett. 105 (2010) 170401. S. Hoedl, et al., Phys. Rev. Lett. 106 (2011) 041801.