Searching for monopole-dipole interaction mediated by axions: the QUAX-gpgs experiment

N.Crescini1,2, E.Berto1, C.Braggio1, F.Calaon1, G.Carugno1,P.Falferi3, A.Ortolan2, M.Romanato1,G.Ruoso2,M. Tessaro1

1INFN Sezione di Padova and Dipartimento di Fisica e Astronomia, Via Marzolo 8, I-35131 Padova (Italy). 2Laboratori Nazionali di Legnaro, Viale dell’Università 2, 35020 Legnaro, Padova (Italy).

3 Istituto di Fotonica e Nanotecnologie, CNR|Fondazione Bruno Kessler, and INFN-TIFPA, I-38123 Povo, Trento (Italy)

INTRODUCTION

The QCD axion is a pseudo-Goldstone boson arising from the breaking of the Peccei-Quinn symmetry [1] and it is of interest as a possible component of cold dark matter. It could also mediate forces which are dependent on its coupling with matter fields. In this respect, J.E. Moody and F. Wilczek [2] showed that a new long-range force affecting particle spins arises, and that such a P and T violating force can be described in terms of an effective magnetic field. Through the scalar ( ) and pseudo-scalar ( ) couplings with ordinary matter, axions can mediate a coherent interaction over macroscopic distances, provided that their mass is sufficiently small (~10−5 eV). Therefore, many attempts have been done to measure this force in laboratory experiments [2].

The single particle monopole-dipole coupling (e.g. of a spin of a polarized electron with an unpolarized nucleus) is described by the potential

g g

⋅ e , (1)

where / is the Compton wavelength of the axion (interaction range), and are the coupling constants of

the Yukawa interaction, is the speed of light in vacuum, is the Pauli matrices vector, and ≡ is the position vector joining the monopole and the dipole. The scalar product ⋅ violates P and T symmetries. Note that here “unpolarized nuclei” means “randomly polarized nuclear spins” with respect to any quantization axis.

THE QUAX-GPGS EXPERIMENT

The experiment (see ref. [3] for details) is performed by measuring the magnetization of a sample of paramagnetic Gadolinium silicate GSO crystal (point-like dipole detector) induced by Ns lead masses M (monopole sources with Ns=4 or Ns=24). The distance between the center of mass of M and the GSO crystal is modulated in time by mounting the masses M on a rotating aluminum wheel as illustrated in Fig. 1.

Integrating the potential given in Eq. (1) over bulk matter of M, in our case a cylinder of height and diameter and nucleon density , results in a total potential . The minimum distance between source and detector is reached when the cylinder center of mass is at a distance ≃ 3.5 cm from the GSO. Thus the maximum value of the total potential reads

≅

e e , (2)

and it correspond to the pseudo-magnetic field along the direction ≡ ⋅ , where is the Bohr magneton of electron. In this configuration, the monopole source and the dipole detector are at the closest positions. The approximation neglects sub-leading exponential terms and is well justified due to the dimensions of the apparatus ( ) and the range of interest of the parameter λ and distance z ( , ≪ ). It also corresponds to simplifying the integration of the source over an infinite plane ( → ∞). The pseudomagnetic field interacts with electron spins of the GSO crystal, and its z component g g 4⁄ e ⁄ 1 e ⁄ can be detected by

measuring the induced changes of the macroscopic magnetization of GSO by means of a dc SQUID operated as a megnetometer. A pick-up coil is wound on the GSO and connected to the input coil of the SQUID. As the rotating tooth wheel changes the distance between the center of mass of the cylinder from the GSO crystal, the pseudomagnetic field is modulated in time. This modulation has a carrier frequency equal to the angular velocity of the wheel multiplied by the number of the cylinders Ns (4 for the upper

Fig.1. Schematic of the experimental set-up to measure the gp-gs interaction. The cryostat (pink) housing the GSO crystal and the tooth wheel (clear blue) with Ns=24 lead masses are shown.

limit discussed hereafter). Due to the spatial exponential decay of the amplitude of the pseudomagnetic field, the waveform of ranges from a square wave to a pure sinusoidal wave, depending on the value of λ, as illustrated in Fig. 2. The dependence of effective amplitude of on λ at the modulation frequency can be simply taken into account by means of a correction factor ranging from 1 (pure sinusoids if ) to 1.5 (square waves if ).

MEASUREMENTS

To measure the GSO magnetization induced by the source

we use a Magnicon C6XXL1W dc-SQUID based magnetometer. The calibration of the apparatus was performed using a large external coil providing a uniform magnetic field over the pick-up of the GSO. Such field was varied in known amplitudes and frequencies to calculate the transfer function from to the SQUID output voltage. The SQUID output signal and the phase of the monopole sources (i.e. the phase of the rotating tooth wheel) were acquired simultaneously with the LeCroy HDO6000 high definition oscilloscope. Then we performed a phase sensitive integration using a digital lock-in amplifier that provides amplitude and phase of the output with respect the reference frequency given by 4 / 2 . The presence of a signal due to change of GSO magnetization in phase with the reference can be detected looking at the statistical distribution of the lock-in output amplitudes. In Fig. 3 we report the Allan standard deviation of the lock-in output with reference frequency 10 Hz, and the calibrated power spectrum of the SQUID signal, expressed in equivalent magnetic field at the GSO pickup coil. In the present experimental setup, the dominant noise source is the SQUID flux noise, and it currently limits the magnetic field sensitivity to / ~3 10 /√ in the (5÷15) Hz frequency band. The long term stability of our apparatus

allows us to integrate the lock-in output for 104 s around

10 Hz and calculate the corresponding mean 3.4 10 T and standard deviation 5.1 10 T, expressed in equivalent magnetic field at the SQUID pickup coil. The mean value is compatible with zero within one standard deviation, and so we conclude that we have observed no induced magnetization in the GSO crystal due to monopole-dipole interaction mediated by axions. Thus we are able to set an upper limit on the corresponding coupling amplitude g g / 8 10 ,at 95% confidence level, and within the range 4 20 cm. This measure is a factor of 10 better than other measurements reported in the literature in the same range of [4,5,6]. We think that a further increase of sensitivity

of a factor 103 can be achieved by exploiting a high-Q resonant readout circuit and a higher signal frequency

, which is feasible with the 24 tooth wheel.

AKNOWLEDGEMENTS

It is a pleasure to thank Clive Speake and Wei-Tou Ni for stimulating discussions on theoretical and experimental aspects concerning the measure of monopole-dipole coupling.

[1] R.D. Peccei and H.R.Quinn, Phys. Rev. Lett. 38 1440 (1977). [2] J.E.Moody and F.Wilczek, Phys. Rev. D 30, 130 (1984). [3] N. Crescini, et al., NIM A 842, 109-113 (2016). [4] W.-T. Ni, et al., Phys. Rev. Lett. 82, 2439–2442 (1999). [5] S. A. Hoedl, et al., Phys. Rev. Lett. 106, 041801 (2011). [6] A. N. Youdin, et al., Phys. Rev. Lett. 77, 2170–2173 (1996).

Fig.2. Time profile of B(t) with different values of . Tooth wheel diameter 30 cm; Diameter, thickness and mass of the4 lead cylinders, 9.5 cm, 2.5 cm, and 1.95Kg, respectively. Pink curve =5 cm; clear blue curve 1 cm; brown curve 0.2 cm.

Fig.3. (a) Allan standard deviation of the calibrated lock-in output. The fitting function (red) is 3 10 /√ . . (b) Power spectral density of the calibrated SQUID output.