Constraining solar hidden photons using HPGe detector
aa r X i v : . [ h e p - e x ] M a r Constraining solar hidden photons using HPGe detector
R. Horvat, D. Kekez ∗ , M. Krˇcmar, Z. Kreˇcak, A. Ljubiˇci´c Rudjer Boˇskovi´c Institute, P.O.Box 180, 10002 Zagreb, Croatia
Abstract
In this Letter we report on the results of our search for photons from a U(1) gauge factor in the hidden sector of thefull theory. With our experimental setup we observe the single spectrum in a HPGe detector arising as a result of thephotoelectric-like absorption of hidden photons emitted from the Sun on germanium atoms inside the detector. The mainingredient of the theory used in our analysis, a severely constrained kinetic mixing from the two U(1) gauge factors andmassive hidden photons, entails both photon into hidden state oscillations and a minuscule coupling of hidden photonsto visible matter, of which the latter our experimental setup has been designed to observe. On a theoretical side, fullaccount was taken of the effects of refraction and damping of photons while propagating in Sun’s interior as well asin the detector. We exclude hidden photons with kinetic couplings χ > (2 . × − − × − ) in the mass region0 . . m γ ′ .
30 keV. Our constraints on the mixing parameter χ in the mass region from 20 eV up to 15 keV proveeven slightly better then those obtained recently by using data from the CAST experiment, albeit still somewhat weakerthan those obtained from solar and HB stars lifetime arguments. Keywords:
Hidden photon, Kinetic mixing, Sun
PACS: χ must be small. The fact that both in field theory andin string theory settings an appreciable amount of χ canbe generated [1], one may recognize the kinetic mixing op-erator as an important ingredient in these fundamentaltheories.Introduction of an explicit mass term for hidden pho-tons (thereby not upsetting the renormalizability of thetheory) together with the kinetic mixing term mentionedabove would lead to a model of photon oscillations (photons-hidden photons) [2] similar to the much more popular neu-trino flavor oscillations. To this end, one gets rid of thekinetic mixing term by the appropriate rotation of states,introducing in such a manner a truly sterile state withrespect to gauge interactions. This generates a nondiag-onal mass matrix in the sector of two photons, a neces- ∗ Corresponding author.
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[email protected] (D. Kekez) sary ingredient for the oscillation phenomenon. A thor-ough analysis of finding appropriate propagating states invacua as well as in a matter background has been done re-cently [3, 4]. Thus, the flavor (or interacting) states (onetruly sterile while the other with the full gauge couplingto charged matter particles) can be expressed as a linearcombination of propagating states in vacua/matter. As aconsequence, a sterile propagating state would gain a tinycoupling to ordinary matter of order χ in vacua, whilein matter such a coupling depends on both the real andimaginary part of the photon self-energy at finite temper-ature/density. This is crucial for our experimental setup(see below), since after being oscillated into a sterile stateand (presumably) quick absorption of the active compo-nent in ordinary matter, it is just the sterile propagat-ing state that leaves material background and travels un-scathed towards a region where it is to be detected.In the present Letter, we aim to observe sterile pho-ton states (hereafter denoted as γ ′ ) in a few keV rangeand coming from the Sun by observing the photoelectric-like process on germanium atoms inside the HPGe detec-tor. So far the most stringent limits on the hidden-photonmixing, in the mass region relevant for our investigation,are obtained by experiments using the Sun as a source ofhidden photons [3] as well as by astrophysical argumentsregarding the solar lifetime [3] and HB stars lifetime [5].The low-energy effective Lagrangian for the two-photon Preprint submitted to Elsevier October 19, 2018 ystem with kinetic mixing reads [6] L = − F µν F µν − F ′ µν F ′ µν − χ F µν F ′ µν + 12 m γ ′ A ′ µ A ′ µ − eA µ J µ , (1)where F µν and F ′ µν are the photon ( A µ ) and hidden pho-ton ( A ′ µ ) field strengths, respectively, J µ is the current ofelectrically charged matter while m γ ′ is the hidden-photonmass that could arise from a Higgs or St¨uckelberg mech-anism [7]. For transversely polarized hidden photons ofenergy sufficiently above the plasma frequency ω p (in thesolar model, 1 eV . ω p .
295 eV) we can write the differ-ential flux at the Earth as [3] d Φ γ ′ dE γ ′ = 1 π R Z R ⊙ dr r E γ ′ q E γ ′ − ω e E γ ′ / ( k B T ) − × χ m γ ′ (cid:16) ω − m γ ′ (cid:17) + ( E γ ′ Γ) Γ , (2)where E γ ′ is the hidden-photon energy, the plasma fre-quency ω p = p παN e /m e , k B is the Boltzmann constant, T is the solar plasma temperature, R ⊙ is the solar radius, R Earth ≈ . × cm is the average Sun–Earth distance,and Γ is the damping factor given by [3]Γ = 16 π α m E γ ′ r πm e k B T N e (cid:20) − exp( − E γ ′ k B T ) (cid:21) × X i Z N i ¯ g ff,i + 8 πα m N e . (3)The first term is the bremsstrahlung contribution to thedamping, where index “i” designates protons or alphas,while the second term is the Compton contribution. Hereit is assumed that all hydrogen and helium are completelyionized. The thermally averaged Gaunt factors ¯ g ff,i aretaken from [8] which presents an accurate analytic fittingformula for the nonrelativistic exact Gaunt factor. Thecalculation is also checked using another exact formula(with numerical integration over Maxwellian distribution)[9]. The r -dependent quantities, T , N e , N p , and N α arecalculated using BS05 Standard Solar Model [10]. Our ex-periment is the most sensitive to hidden photons of around1.6 keV (see below), and since they are created mostly inSun’s inner layers (as shown in Fig. 1), Eqs. (2) and (3)(ionization neglected) can be reliably applied to calculatethe expected flux of hidden photons. The contribution ofdifferent solar layers to the hidden-photons flux, depictedin Fig. 1 for m γ ′ = 100 eV, exhibits a narrow peak at r = 0 . R ⊙ corresponding to the resonant contribution, ω ( r ) = m γ ′ , in the integrand of Eq. (2). The plasmonmass is maximal at Sun’s center, ω p (0) ≃
290 eV. For m γ ′ &
290 eV there is no resonant contribution in Eq. (2)(and there would have been no peak in Fig. 1 had it drawnfor m γ ′ &
290 eV). This causes a sudden drop in sensitiv-ity for m γ ′ &
290 eV what can be clearly seen in Fig. 3. = r (cid:144) R Ÿ l og HH d F Γ ’ (cid:144) d E Γ ’ dy L (cid:144) k e V - c m - s - L Figure 1: Flux of solar hidden photons at the Earth as a functionof the normalized radial coordinate y = r/R ⊙ for E γ ′ = 1 . keV , m γ ′ = 100 eV , and χ = 3 · − . Our experiment involves searching for the particularenergy spectrum in the measured data, dN γ ′ dE γ ′ = d Φ γ ′ dE γ ′ σ γ ′ Ge → Ge ∗ e ( E γ ′ ) N Ge t , (4)produced if the hidden photons from the Sun are detectedvia photoelectric-like effect on germanium atoms. Here N Ge is the number of germanium atoms in the detectorand t is the data collection time. The cross section for thehidden-photon absorption, γ ′ + Ge → Ge ∗ + e, can be ex-pressed via the cross section for the ordinary photoelectricabsorption as (see, e.g., Ref. [11]) σ γ ′ Ge → Ge ∗ e ( E γ ′ ) = χ β γ ′ σ γ Ge → Ge ∗ e ( E γ ′ ) , (5)where χ = χ (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) m γ ′ m γ ′ + 2 E γ ′ ( n ( E γ ′ ) − (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) , (6)and β γ ′ = q − m γ ′ /E γ ′ is the velocity of the hidden pho-tons and the data for σ γ Ge → Ge ∗ e are taken from Ref. [12].The effective mixing parameter χ eff takes into accountthe media (germanium) influence on the photon–hidden-photon mixing. This is essentially the fraction in the sec-ond line of Eq. (2) with ω p and Γ expressed via the morecommonly used complex refractive index n as 2 E γ ′ (1 − n ) = ω − iE γ ′ Γ (see, e.g. , Ref. [13]). The germaniumrefractive index data are taken from Ref. [14]. Because inour experimental setup the target and the detector are thesame, the efficiency of the system for the expected signalis ≈
1. The X-rays accompanying the photoelectric-like ef-fect will be thereafter absorbed in the same crystal, so theenergy of the particular outgoing signal equals the totalenergy of the incoming hidden photon.The experimental setup used in this search for solarhidden photons has been described elsewhere [15–17]. Here2e only recall that the HPGe detector with an active tar-get mass of 1.5 kg was placed at ground level, inside alow-radioactivity iron box with a wall thickness rangingfrom 16 to 23 cm. The box was lined outside with 1 cmthick lead. A low threshold on the output provided theonline trigger, ensuring that all the events down to theelectronic noise were recorded. Various calibrated sourceshave been used to study the linearity and energy resolu-tion and, in particular, in the lowest-energy region mainlya
Am source. The detector resolution was about 820 eVfor the 13.9 keV gamma-rays and 660 eV for their 3.9 keVescape peak. Data were accumulated in a 1024-channelanalyzer, with an energy dispersion of 63.4 eV/channeland with data collection time of 2 . × s. In theselong-term running conditions, the knowledge of the energyscale is allocated by continuously monitoring the positionsand resolution of indium X-ray peaks of 24.14 keV and27.26 keV, which are present in the measured spectra.
20 40 60 80
Channel number C oun t s (cid:144) c h a nn e l Energy H keV L
100 300 500 700 900
Channel number ´ ´ ´ C oun t s (cid:144) c h a nn e l
10 20 30 40 50
Energy H keV L Figure 2: Top panel: total measured energy spectrum showing alsoX-ray peaks from various materials. Bottom panel: low-energydata shown together with the maximum of expected events dueto hidden photon-electron interactions (red line), corresponding to E γ ′ ∼ . keV . As can be seen from Fig. 2, showing the total energyspectrum, there is no evidence for any excess of photon-like events due to the hidden photon-electron interactions. Theexpected spectrum (red line) has a step at E γ ′ ∼ . N γ ′ ( k ) in every energy bin k to be less than orequal to the recorded counts N exp ( k ). Namely, N γ ′ ( k ) ≤ N bg ( k ) + N γ ′ ( k ) = N exp ( k ), where N bg ( k ) is the unknownbackground. For every fixed m γ ′ we raise the parame-ter χ till the first touch of the predicted spectrum N γ ′ ( k )with the measured spectrum N exp ( k ) in some channel k .This value of χ is our upper limit. Similar approacheshave been used elsewhere (see for instance [17–21]), wheredirect background measurement is not possible and thesignal shape is a broad spectrum on top of an unknownbackground spectrum. Figure 2 (bottom panel) shows thatour experiment is the most sensitive to the hidden photonsof energy around 1.6 keV. For fixed E γ ′ (= 1 . m γ ′ , the theoretically expected yield of hidden photon-induced events has been calculated by means of Eq. (4),where χ is the only free parameter which is then usedto fit the maximal strength of the expected spectrum,marked with red line in Fig. 2 (bottom panel), to the mea-sured one. For the highest hidden-photon masses underconsiderations, m γ ′ ∼
10 keV, the energy at which ex-pected spectrum touches the measured one, shifts fromfixed E γ ′ = 1 . E γ ′ > m γ ′ . In order to estimatea day-night variation of the flux of hidden photons in ourexperiment (performed in Zagreb, ϕ = 45 ◦ ′ N), whichis expected due to their travel through Earth’s mantle (2 R E cos ϕ ∼ × km in length), we calculated theabsorption under the most conservative assumptions thatEarth’s mantle consists only of iron, and its density is themean density of the Earth. It was found that the day-night correction does not affect our limits on the mixingparameter, for the hidden-photon mass range displayed inFig. 3.The corresponding upper limits on the mixing param-eter obtained in this work are displayed in Fig. 3 togetherwith the current hidden photon bounds [3, 5].In conclusion, we have performed an experiment to ob-tain the upper limits on the photon–hidden-photon mixingparameter χ in the eV to keV hidden-photon mass rangeby observing the photoelectric-like process on germaniumatoms inside the HPGe detector impinged by hidden pho-tons coming from the Sun. We have excluded hidden pho-tons with mixing parameters χ > (2 . × − − × − )in the mass region 0 . . m γ ′ .
30 keV. We thencompared our limits on the interaction strength χ with re-spect to the hidden-photon mass, to that derived recently Earth’s mantle is thought to be dominantly oxygen (44.8%), sili-con (21.5%), and magnesium (22.8%) with some (5.8%) iron and theremainder aluminum, calcium, sodium, and potassium. - log m Γ ’ H eV L - - - - - - - - - l og Χ CAST This WorkSolarLifetime HB - - log m Γ ’ H eV L - - - - - - - - - l og Χ Figure 3: Limits on the mixing parameter as a function of the hidden-photon mass from this experiment against the current hidden photonbounds taken from [3, 5]. For description see the text. [3] using helioscope data from the CAST experiment [22],as well as to those obtained from solar [3] and HB stars[5] lifetime arguments. It turns out that our limits in thehidden-photon mass region from 20 eV up to 15 keV areslightly better than those obtained from CAST laboratorymeasurement [3], but still somewhat weaker than thoseobtained from astrophysical considerations (solar and HBlifetimes). The relevance of our results lies in the fact thatthey constitute the best laboratory limits in the said pa-rameter range obtained to date.We would like to thank J. Redondo for useful com-ments. The authors acknowledge the support of the Croa-tian MSES Project No. 098-0982887-2872.
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