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Axion Dark Matter Search Using the Storage Ring EDM Method

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Axion Dark Matter Search Using the Storage Ring EDM Method Axion dark matter search using the storage ring EDM method Seung Pyo Chang,1, 2 Selcuk Haciomeroglu,2 On Kim,1, 2 Soohyung Lee,2 Seongtae Park,2, ∗ and Yannis K. Semertzidis1, 2 1Department of Physics,KAIST,Daejeon 34141, Republic of Korea 2Center for Axion and Precision Physics Research, IBS, Daejeon 34051, Republic of Korea (Dated: October 2, 2018) We propose using the storage ring EDM method to search for the axion dark matter induced EDM oscillation in nucleons. The method uses a combination of B and E-fields to produce a resonance between the g − 2 spin precession frequency and the background axion field oscillation to greatly enhance sensitivity to it. An axion frequency range from 10−9 Hz to 100 MHz can in principle be 13 30 scanned with high sensitivity, corresponding to an fa range of 10 GeV ≤ fa ≤ 10 GeV, the breakdown scale of the global symmetry generating the axion or axion like particles (ALPs). I. INTRODUCTION internal atomic field. By combining Eq. (1) and Eq. (2) with a possible static EDM, one can write the Peccei and Quinn proposed a dynamic oscillating total EDM as, field to solve the strong CP problem [1] and that os- d(t)= dDC + dAC cos(mat + ϕax), (3) cillating field is called an axion [2–8]. An axion in 11 13 the parameter range of 10 GeV ≤ fa ≤ 10 GeV where dDC and dAC are the magnitudes of the static is potentially observable using microwave cavity res- and oscillating parts of EDM, respectively, and ϕax onators, where fa is the global symmetry break- is the phase of the axion field. In this paper, we down scale [9–12]. This method detects photons propose using the storage ring technique to probe from the axion dark matter conversion in the pres- the oscillating EDM signal [18–20], with some mod- ence of strong magnetic fields [10, 13–16]. In the ification of storage ring conditions depending on the next decade it is expected that the axion frequency axion frequency. Instead of completely zeroing the range of 0.1-50 GHz may be covered using microwave g − 2 frequency, we just control and tune it to be cavity and/or open cavity resonators [17]. However, in resonance with the axion background field oscil- this method cannot be used for higher values of fa lation frequency. We propose searching for the os- (lower mass region) because the axion-photon cou- cillating EDM term by using a resonance with the 2 pling is suppressed by fa ∼ 1/fa and the required g − 2 precession frequency. This method is expected resonance structures would be impractically large. to be more sensitive, and the systematic errors are For the higher values of the scale, including MGUT easier to handle than in the frozen spin storage ring 16 19 (∼ 10 GeV) - MPL (∼ 10 GeV), axion-gluon cou- EDM method. Using the storage ring method, one pling can be considered, which gives a time varying can scan the frequency range from 10−9 Hz up to electric dipole moment (EDM) to nucleons [11, 12]. 100 MHz, which corresponds to an axion parameter 13 30 For example, in the nucleon case, the EDM can be space of about 10 GeV ≤ fa ≤ 10 GeV. expressed as a × −16 ∼ × −35 · II. RESONANCE OF AXION INDUCED arXiv:1710.05271v2 [hep-ex] 14 Jun 2018 dn =2.4 10 (9 10 ) cos(mat)[e cm] , fa OSCILLATING EDM WITH g − 2 SPIN (1) PRECESSION IN STORAGE RINGS a(t)= a0 cos(mat), (2) The previously proposed storage ring EDM exper- where a(t) is the axion dark matter field and ma is iment is optimized for a DC (fixed in time) nucleon the axion mass. Graham and Rajendran proposed EDM, applied to protons and deuterons [18–20]. It a method that measures the small energy shift with is designed to keep (freeze) the particle spin direc- the form E~ ·d~n in an atom as a probe of the oscillating tion along the momentum direction for the duration axion field [11]. In this case, the electric field is an of the storage time, typically for 103 s, the stored beam polarization coherence time [20, 21]. In this case, the radial electric field in the particle rest frame is precessing the particle spin in the vertical plane. ∗ corresponding author; [email protected] The precession frequency in the presence of both E and B fields is expressed by the T-BMT equation In this idea of resonant axion induced EDM with Eq. (4)-(6) [22, 23]. g − 2 spin precession, one can utilize the strong ef- fective electric field E~∗ = E~ + cβ~ × B~ , which comes from the B field due to particle motion, as expressed ~ω = ~ωa + ~ωd, (4) in Eq. (6). In this case, the effective electric field is about one or two orders of magnitude larger than the applied external E field which can be up to 10 MV/m and has an apparent technical limitation in e 1 β~ × E~ ~ω = − aB~ − a − , (5) strength. a m γ2 − 1 c " # e η E~ III. SENSITIVITY CALCULATION ~ωd = − + β~ × B~ , (6) m " 2 c !# The statistical error in the EDM for proton or where a = (g − 2) /2 is the magnetic anomaly with deuteron can be expressed with the following equa- a = −0.14 for deuterons. Here, other terms are tion [19, 20]. omitted by assuming the conditions β~·E~ = β~·B~ = 0. The parameter η shown in the equation is related 2~s ~ σd = ∗ , (7) to the electric dipole moment d as d = ηe /4mc. P AE NcκTtotτp Since we are dealing with a time varying EDM due to the oscillating axion background field, η is also a p where P is the degree of polarization, A the analyz- function of time. The ~ωa is the angular frequency, ∗ i.e., 2π times the g −2 frequency, describing the spin ing power, E the effective electric field that causes precession in the horizontal plane relative to the mo- the EDM precession, Nc the number of particles mentum precession. stored per cycle, κ the detection efficiency of the polarimeter, τ is the polarization life time, and T The term ~ω is due to the EDM and the corre- p tot d the total experiment running time. The s in the sponding precession takes place in the vertical plane. numerator is 1/2 for protons and 1 for deuterons. For a time independent nucleon EDM, the spin vec- One can easily calculate the sensitivity of nucleon tor will precess vertically for the duration of the stor- EDM measurement using this formula with the cor- age time if the horizontal spin component is fixed to responding experimental parameters. the momentum direction [20]. This condition can be achieved by setting the E and B fields properly, and In this study, we used the following method to cal- is called the frozen spin condition. culate the sensitivities of the axion EDM measure- With a nonzero g − 2 frequency, the average EDM ment including the oscillation effect. First, we chose precession angle becomes zero for the static EDM the target axion frequency and then calculated the case because the relative E field direction to the spin corresponding E and B-fields for the particle stor- vector changes within every cycle of g−2 precession. age, which give the same g − 2 frequency as the cho- For example, the spin tilts in one direction (up or sen axion frequency. Then, the axion oscillation and down) due to the EDM within one half cycle and g − 2 spin precession will be on resonance and the then tilts in the opposite direction for the other half EDM precession angle in the vertical plane can keep cycle, resulting in an average accumulation of zero. accumulating during the measurement time. With The presence of a static EDM will only slightly tilt the chosen axion frequency and the axion quality the g − 2 precession plane away from the horizon- factor Qax, we estimated the statistical error and tal plane, without a vertical spin accumulation. In the resulting error was used to calculate the ex- contrast, for an oscillating EDM, when the axion periment sensitivity along with the effective electric frequency (ωax) is the same as the g − 2 frequency field. This method can be used not only for nucleons with the appropriate phase, the precession angle can like deuterons or protons but it can also be used for be accumulated in one direction. This is possible be- other leptonic particles like muons, provided there cause the EDM direction flips every half cycle due to is a coupling between the oscillating θQCD induced the axion filed oscillation and the relative direction by the background axion dark matter field and the between the E field and the EDM d always remains particle EDM. the same. As shown in Eq. (6), the EDM part of the preces- 2 sion rate can be rewritten as Eq. (8) R ≡ N(ψ, 0) = nNA∆ΩζI0(ψ)[1 − PyAy(ψ)], (13) dθ d ∗ respectively. After simple algebra one can obtain the ωd = = − E , dt s~ (8) left-right asymmetry ǫ for the vertically polarized ∗ E = E + cβB, beam as follows where s is 1/2 for protons and 1 for deuterons. Ac- L − R s~ ǫ(t)= (t)= P Aθ(t), (14) cordingly, d = E∗ ωd, and the error for the EDM d L + R can be written as Eq. (9). where A is the analyzing power, θ(t) is the accu- s~ mulated EDM precession angle in the vertical plane σ = σ , (9) d E∗ ωd and L and R are the number of hits on the left and right detectors, respectively.
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