Cavity Search for dark-matter Axion Francisco Elohim Becerra Chavez Department of Physics, University of Maryland, College Park, Maryland 20742, USA (12 March 2007) Many different experiments have been searching for axion-like forces and some sign of existence of the axion. The axion is a hypothetical elementary particle that would solve two major problems in science. It was originally a consequence of a solution to explain the lack of CP-violation in the physics of quarks and gluons, the fundamental constituents of objects such as protons and neutrons. Later, it was recognized to be a good dark matter candidate. Today, it remains as one of the leading dark matter candidates. The ADMX experiment is the only experiment able to probe realistic dark matter axion models with sufficient sensitivity in the expected mass regime. I. Introduction Axion is a hypothetical elementary particle postulated by Peccei and Quinn in 1977 to resolve the strong-CP problem in quantum chromodynamics (QCD). This theory possesses a non-trivial vacuum structure that, in principle, permits the violation of the combined symmetries of charge conjugation and parity, collectively known as CP. The effective strong CP violating parameter in the QCD Lagrangian, Θ, appears as a Standard Model (SM) input parameter that must be measured. But generic CP-violation in the strongly interacting sector would create the electric dipole moment for the neutron, while experimental constraints on neutron’s dipole electric moment imply CP violation from QCD be extremely tiny, and then Θ (periodic parameter 0<Θ<2π) extremely small or absent; one part in 109 [1]. A solution for this problem is called Peccei-Quinn mechanism [2] which promotes the parameter Θ to a dynamic field by adding a new global symmetry to the SM. It becomes spontaneously broken resulting in a new particle known as axion that relaxes the CP violation parameter to zero [3]. The mass of the axion is constrained by cosmology to be larger than 1 μeV and by the neutrino signal from Supernova (1987a) to be less than 10 meV (20μm < λAxion < 20cm, mc/h=λ) and is a good cold dark matter candidate [4]. Since the axion interacts only very weakly with ordinary matter, it is very difficult to detect. Nevertheless, there are different experiments searching for the axion by very different methods. Some of them only constrain the strength of the related axion parameters and others are able to probe axion models. There are several groups interested in the interaction associated with the exchange of a light or massless pseudoscalar Goldstone boson, or similar interactions as the axion in mass-spin interactions [5-8]. Moody and Wilczek [9] proposed an interaction potential generated by a boson with spin zero, describing these axion-like interactions: λλσπ/2211ˆˆ8)(reseperrrmggrV−⎟⎠⎞⎜⎝⎛+⋅=h (1) where gs is the coupling strength at the scalar vertex (nucleon) and gpe the coupling strength at the pseudoscalar vertex (electron) [8] . If the mass of the exchange particle is m, the range of interaction is given by mc/h=λ. This potential violates parity P and time reversal T. At the moment the axion is the most likely candidate particle for generating such a new interaction [8]. In the experiments searching for these kind of interactions (gsgpe)Axion < 6 θ/λ3310−×2, where θ is constrained by experimental limits on the dipole moment on the neutron to be less than 10-9 [1]. A number of experiments have placed constrains on the strength gsgpe as a function of range testing deviations from the potential described by Eq. (1). Heckel et al. [5] used a torsion balance with an attached spin polarized test mass to set the strongest constraint achieved at ranges larger than 1 m. Youdin et al. [6] set the best constraint in the range 10cm <λ< 1 m, comparing the relative precession frequencies of Hg and Cs magnetometers as a function of the position of masses with respect to an applied magnetic field. Ni and his colleges [7] used SQUID in an attempt to detect the change in polarization induced in a paramagnetic salt induced by the motion of a source mass setting the strongest constraints in the range 5mm <λ< 10 cm. Hammond et al. [8] used a spherical superconducting torsion balance with suspended test cylindrical masses and a spin source. They used a toroidal electromagnet to measure the oscillation of the torsion balance coherent with the sinusoidal current driving the spin source, setting the best constraints at a range of 1 mm. The range and sensitivity of all these experiments are far from the axion regime. Even though there is a proposal with higher sensitivity using superconductive accelerometers in a Spin-Mass Interaction Low-Temperature Experiment (SMILE) able to test some axion-like interactions near the axion regime [10]. In contrast, Sikivie devised a method to find these axions via conversion into photons within a tunable 1microwave cavity threaded with a static magnetic field via Primacoff effect [11]. The conversion into microwave photons is then enhanced by the resonant cavity (with quality factor about 105) and the strength of the static magnetic field; the excess microwave photons above thermal background from axion conversion are detected by a low noise pre-amplifier coupled to the cavity. This excess in power constitutes the candidates for detected axions. The expected signature of the axion signal are narrow peaks of excess power at frequency f = mac2/h with width ~10-6 due to virialized motion of galactic axions in the halo, or ~10-11 due to the recent capture of extra-galactic axions by the gravitational potential of our galaxy. Then it is necessary to increase the signal-to-noise ratio of the converted axions minimizing the noise of the detectors . II. Theory The axions can be detected by stimulating their conversion to photons in a strong magnetic field. The axion-to-photon conversion is governed by the interaction Lagrangian [3]: BEfxagLaarr⋅=)(παγγγ (2) where E is the cavity electric field to be detected from the conversion and B is the external magnetic field, α is the fine structure constant, fa is the axion decay constant, a(x) is the axion field and gγ is the model-dependent coupling equals to -0.97 and 0.36 in the KSVZ and DFSZ model, respectively [3]. A configuration suitable to maximize this term consist of a large superconducting solenoid and a high Q microwave cavity [11].