The complex vacuum configurations contribute to an extra non-perturbative term in the QCD Lagrangian[1],

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1 Detection of Axions LI, LONG Duke University October 18, 2017 Abstract Physicsts proposed axions as a solution to the strong-cp problem of QCD. Axions turn out also to be a candidate of dark matter which constitutes 26.8% of total mass-energy of the universe. Axions have not been observed by experiments so far. In this paper, the concept of axions is introduced and multiple axion direct direction experiments are discussed. Keywords: axions 1 Introduction The complex vacuum configurations contribute to an extra non-perturbative term in the QCD Lagrangian[1], L QCD = L PERT + Θ g2 32π 2 Gαµν G αµν, Θ = Θ + Arg det M (1) where G αµν is the gluon field strength tensor, G αµν is the dual of G αµν, Θ is an arbitrary parameter to generate "the Θ-vacuum": Θ = Σ n e inθ n, and M is the quark mass matrix. This extra term cause QCD violating CP, and leads to a neutron electric dipole moment of order d n Θ e cm. The experimental bound on d n constrains Θ to be less than The problem why Θ is so small is called strong-cp problem. Peccei and Quinn in 1977 proposed a compelling solution[2]. The key idea is to introduce an additional global, chiral symmetry, known as PQ symmetry, which is spontaneously broken at a scale f PQ. This drives Θ to be zero, but in the mean time, there must be a Nambu-Goldstone boson, "the axion", associated with this spontaneous symmetry breaking. The mass of axion is of order Λ 2 QCD / f PQ. Because f PQ is arbitrary (somewhere between 1

2 100GeV and GeV), this leaves the axion mass varying from 1MeV to ev, a very broad spectrum! The relationship between the axion mass m a and PQ symmetry-breaking scale f PQ is given by m a = z 1 + z f π m π f PQ /N 0.62eV 107 GeV f PQ /N (2) where z is the ratio of up quark mass and down quark mass z m u /m d 0.56, m π and f π are the mass and decay constant of pion, and N is the color anomaly of the PQ symmetry. The axion field a is related to Θ by a = ( f PQ /N) Θ (3) Thus, the interaction Lagrangian between axions and ordinary matter (protons, neutrons, electrons and photons) is L int = i g ann 2m N µ a( Nγ µ γ 5 N) + i g aee 2m e µ a(ēγ µ γ 5 e) + g aγγ a E B (4) Here N is either a proton or a neutron. The coupling constant g aii, not surprisingly, is proportional to the axion mass. Therefore, experiments have a way to set limits or discover the axion. 2 Direct searches for axions Although cosmology observations including SN 1987A and red giants can exclude a wide range of the axion mass[3], in this paper, only direct searcher of axions are discussed. 2.1 The CAST experiment The Sun is a powerful nuclear reactor and thus a strong axion source. The Sun can generate axions through the Primakoff process (see Fig.1)[4]. This is possible because axions can couple to two photons with coupling strength g aγγ. Therefore, stars are able to produce axions from thermal photons in the fluctuating EM fields of the stellar plasma. Assuming the standard solar model, the axion flux seen at the Earth is[3]: dφ a de = g cm 2 s 1 kev 1 E e E/1.205 (5) E is the axion energy in kev and g 10 = g aγγ /(10 10 GeV 1 ). The average energy is 4.2keV. The integrated flux is Φ a = g cm 2 s 1 (6) 2

3 Figure 1: Primakoff Effect: axions convert to photons in the EM field and vice versa The CERN Axion Solar Telescope (CAST) is such an experiment that is trying to observe axions from the Sun. The detection principal is the reverse how axions are generated in the Sun (see Fig.2)[5]. The CAST has Figure 2: Sketch of the CAST helioscope utilized an LHC prototype dipole magnet with two parallel straight pipes. The 9T magnet can move by ±8 vertically and ±40 horizontally. This allows the system to follow the Sun for 1.5h at both sunrise and sunset. At both ends of the magnet, X-ray detectors can detect photons coming from axion conversion inside the magnet when it is pointing to the Sun. Background calibration is performed when the magnet is not tracking the Sun. The new implemented X-ray telescope (XRT) improved the background level of sunrise (SR) system significantly (down to 10 6 cm 2 s 1 kev 1 ). The detectors were gaseous time projection chambers filled with 1.4bar Ar and 2% isoutane. The data contains two parts[5]. One is the counting from background and the other is from tracking runs. Fig.3 shows the counting rate spectrum of two data sets from background runs with 1 σ statistical error bars on 3

4 Figure 3: The count rate of background in the SR detector each bin. By integrating measured count rate in the 2 7keV region, the CAST observed 0 and 3 counts excess from tracking runs in K and L data sets. The axion-γ conversion probability in the CAST is P a γ = (g aγγ B sin(ql/2) ) 2 (7) q where q is the momentum transfer. B and L are the magnet field and the length of the magnet. The CAST loses its sensitivity for m a > 0.02eV because of losing coherence in the axion-γ conversion. Since the flux is known from Eq.5, for axion mass m a < 0.02eV, the upper limit of coupling constant g aγγ from the CAST experiment is g aγγ < GeV 1 at 95% CL (8) In the 2-D g aγγ m a plane, the result is shown in Fig.4 The black line is from old data sets from 2003 to The red line is the latest work in 2015[5]. 4

5 Figure 4: CAST excluded region (blue) 2.2 The CDMS experiment The hypothesis that the mass of the universe is dominated by dark matter is supported by several astrophysical arguments. Among these are the rotation curves of galaxies, measurements of the cosmic microwave background (CMB) and observations of the collision of large clusters of galaxies. While the Standard Model cannot explain these phenomena, new theories propose some candidates that can be dark matter. Weakly interacting massive particles (WIMPs) are one of them and axions are another. Astrophysics has already put upper limits on the axion mass m a < ev which is corresponding to f PQ > 10 9 GeV[3]. This makes axions couple to ordinary matter weakly, which is an important property of dark matter. If axions were produced in the early universe, its contribution to the energy density of the universe today is Ω a ( 5µeV m a ) 7/6 (9) 5

6 Ω a should be less than one, because the universe is not shrinking by dark matter. This sets a lower limit on the axion mass of m a > 10 6 ev. Furthermore, the weak-coupling makes axions impossible to be in thermal equilibrium with other particles. This means when they were produced, they could start to form structures around density perturbations relatively quickly. the Cryogenic Dark Matter Search (CDMS) experiment was designed to detect WIMP like dark matter. It utilizes 19 Ge (250 g each) and 11 Si (100 g each) crystal detectors at 40 mk in the Soudan Underground Laboratory. These detectors have low enough threshold to observe WIMPnuclei elastic scattering events for certain WIMP mass and energy. Since the axion is another interesting candidate, the CDMS collaboration analyzed their germanium data from two run periods and managed to put constraints on the coupling strength g aγγ for certain axion mass range. Figure 5: Solar axions conversion rate in Ge detectors as a function of time in a day (g aγγ = 10 8 GeV 1 ) The basic detection principal is the same as the CAST experiment, but with different detectors. When solar axions arrive at the Earth, due to 6

7 Column field near the nuclei, axions can convert to photons via Primakoff effect (see Fig.1). The difference in the EM field and the length scale makes CDMS Ge detectors sensitive to different axion mass. The coherence from Bragg diffraction also produces a correlation between incident axion angles and event rate in the Ge crystals. The expected event rate for a given observed photon energy E, momentum transfer q and scattering angle θ is[6] R(E) = 2c d 3 q q 2 dφ a de a [ g2 aγγ 16π 2 F(q) 2 sin 2 (2θ)]W (10) where dφ a de a is the axion flux from Eq.5, W is the detector energy resolution function, and F(q) is the Fourier transform of the electric field in a crystal:f( q) = k 2 d 3 xφ( x)e i q x. Because of the dependence on scattering angle, the event rate and the photon energy spectrum will change during a day. Fig.5 shows how it depends assuming the coupling constant g aγγ = 10 8 GeV 1. Figure 6: The count rate in Ge detectors The final result is shown in Fig.6. The count rate is in the unit of counts per day (cpd) per kg per kev. The inset is what is defined as the analysis window (2-8.5keV). Thus by fitting this spectrum with the background rate 7

8 and the expected axion conversion rate, the CDMS experiment set the limit for m a < 0.1keV g aγγ = GeV 1 at 95% CL (11) Fig.7 shows the CDMS result in the g aγγ m a 2-D plane. Figure 7: The CDMS result is represented by the red solid line 3 Conclusion Two different axion direct detection experiments were reviewed in this essay. Although they both cannot detect a clear axion signal, they managed to exclude some space predicted by the theory. Fig.8 [7] shows the combination of all axion search experiments so far, from cosmology observations to terrestrial direct detection. The theory is very flexible with g aγγ and m a. This leaves much space still untouched. However, axions are a fascinating solution to the strong-cp problem of the well tested standard model and a reasonable explanation of the mysterious dark matter. Therefore, physicist will not give up searching for axions in the following years. 8

9 Axion Coupling G Aγγ (GeV -1 ) SN 1987A LSW (OSQAR) Helioscopes (CAST) HESS Haloscopes (ADMX) Horizontal Branch Stars KSVZ DFSZ Axion Mass m A (ev) VMB (PVLAS) Telescopes Figure 8: Exclusion plots in the g aγγ m a space. Limits derived with different experiment techniques are shown. The yellow band is the region predicted by theoretical models References 1. Edward W. Kolb and Michael S. Turner. The Early Universe R. D. Peccei and H. R. Quinn. Phys. Rev. Lett., 38:1440, Georg G. Raffelt. Astrophysical Axion Bounds, pages Springer Berlin Heidelberg, Berlin, Heidelberg, R.J. Creswick, F.T. Avignone III, H.A. Farach, J.I. Collar, A.O. Gattone, S. Nussinov, and K. Zioutas. Theory for the direct detection of solar axions by coherent primakoff conversion in germanium detectors. Physics Letters B, 427(3): , arxiv: Z. Ahmed, D. S. Akerib, S. Arrenberg, C. N. Bailey, D. Balakishiyeva, L. Baudis, D. A. Bauer, J. Beaty, P. L. Brink, T. Bruch, R. Bunker, B. Cabrera, D. O. Caldwell, J. Cooley, P. Cushman, F. DeJongh, M. R. Dragowsky, L. Duong, E. Figueroa-Feliciano, J. Filippini, M. Fritts, S. R. Golwala, D. R. 9

10 Grant, J. Hall, R. Hennings-Yeomans, S. Hertel, D. Holmgren, L. Hsu, M. E. Huber, O. Kamaev, M. Kiveni, M. Kos, S. W. Leman, R. Mahapatra, V. Mandic, D. Moore, K. A. McCarthy, N. Mirabolfathi, H. Nelson, R. W. Ogburn, M. Pyle, X. Qiu, E. Ramberg, W. Rau, A. Reisetter, T. Saab, B. Sadoulet, J. Sander, R. W. Schnee, D. N. Seitz, B. Serfass, K. M. Sundqvist, M. Tarka, G. Wang, S. Yellin, J. Yoo, and B. A. Young. Search for axions with the cdms experiment. Phys. Rev. Lett., 103:141802, Oct K.A. Olive and Particle Data Group. Review of particle physics. Chinese Physics C, 38(9):090001, All equations and graphs in this essay can be found in the above references. 10