Extending the CRESST-II commissioning run limits to lower masses
OOUTP-11-50-P
Extending the CRESST-II commissioning run limits to lower masses
Andrew Brown, ∗ Sam Henry, Hans Kraus, and Christopher McCabe Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP, UK (Dated: October 14, 2018)Motivated by the recent interest in light WIMPs of mass ∼O (10 GeV/c ), an extension of theelastic, spin-independent WIMP-nucleon cross-section limits resulting from the CRESST-II com-missioning run (2007) are presented. Previously, these data were used to set cross-section limitsfrom 1000 GeV/c down to ∼
17 GeV/c , using tungsten recoils, in 47.9 kg-days of exposure of cal-cium tungstate. Here, the overlap of the oxygen and calcium bands with the acceptance region ofthe commissioning run data set is reconstructed using previously published quenching factors. Theresulting elastic WIMP cross-section limits, accounting for the additional exposure of oxygen andcalcium, are presented down to 5 GeV/c . I. INTRODUCTION
Among the outstanding problems in astro-particlephysics is to identify the non-baryonic dark matter thatmakes up ∼
80% of the matter in the Universe [1]. A well-motivated class of dark matter candidates are WeaklyInteracting Massive Particles (WIMPs), which may bedirectly detected via their elastic scattering with nucleiin terrestrial detectors.In the CRESST-II commissioning run of 2007 [2], lim-its on elastic, spin-independent, WIMP-nucleon cross-sections for WIMP masses from 1000 GeV/c down to ∼
17 GeV/c were presented. However, light WIMPs,with a mass ∼O (10 GeV/c ) have been suggested asa possible interpretation to the experimental results ofDAMA, CoGeNT and CRESST-II (2011) [3–5]. At thesame time, several other experiments [6–11] partially orcompletely exclude the light WIMP interpretations of[3–5]. Therefore, it is of interest to see how data fromthe commissioning run compare to these results whenextended to examine such light WIMP scenarios. II. INCLUDING OXYGEN AND CALCIUM
The CRESST-II commissioning run data set [2] con-sists of 47.9 kg-days exposure of calcium tungstate(CaWO ), taken between the 27 th of March and the 23 rd of July, 2007. The data were obtained from two indepen-dent modules, labelled by their phonon detector / lightdetector names: “Zora/SOS23” and “Verena/SOS21”,collecting 23 . . produce different amounts of light, relative to the energydeposited. Gamma and beta interactions, causing elec- ∗ Electronic address: [email protected]
Energy [keV] 0 10 20 30 40 50 L i gh t y i e l d -0.2-0.100.10.20.30.4 Acceptance region of [2] s Tungsten 1 s Calcium 1 s Oxygen 1Acceptance region of [2] s Tungsten 1 s Calcium 1 s Oxygen 1
FIG. 1: Acceptance region and nuclear recoil band diagramfor Zora/SOS23. The black line indicates the light yield( L γ /E ) limit for the acceptance region in [2], and the verticaldashed lines the acceptance region’s lower and upper energythresholds. 1 σ regions for observing recoiling oxygen (green),calcium (red) and tungsten (blue) nuclei are indicated, usinglight detector resolution parameters in Table I and quench-ing factors from [13]. A similar diagram may be drawn forVerena/SOS21. tron recoils, produce more light than nuclear recoils. Byconvention the light produced per unit energy (the ‘lightyield’) of electron recoils L γ /E , is calibrated to those ofgamma interactions at 122 .
06 keV, which is normalisedto a value of one. Nuclear recoils see a reduction in lightcompared to electron recoils, quantified by a quenchingfactor, Q i , dependent upon the species i of recoiling nu-cleus.The limits of [2] resulted from assuming all recoilsin the acceptance region, the region in which WIMP-nucleon interactions are searched for, were from tung-sten alone. However, due to the effects of a finite lightdetector resolution, recoils from both calcium and oxy-gen may also be seen within the same acceptance re-gion. This effect is illustrated in Figure 1. The addi- a r X i v : . [ a s t r o - ph . C O ] J a n Parameter Zora/SOS23 Verena/SOS21 σ (keV) 0.784 1.508 σ (keV ) 1.064 0.610 σ P (keV) 0.56 0.11 P σ , σ and σ are light detector resolution parameters determined from [2],using the method outlined in Appendix A. P and P are thephonon energy resolution parameters from [14]. tional exposure provided by the parts of calcium andoxygen bands that fall within the acceptance region canstrengthen cross-section limits for light WIMPs, withmass ∼O (10 GeV/c ). In [2], the acceptance region waschosen so that tungsten recoils would have been seen withminimal electron recoil band overlap. In energy, this wasbetween 10 and 40 keV. In light yield, the upper limitwas set so that 90% of tungsten recoils would occur inthe acceptance region. Here, we use this same acceptanceregion, so that we do not introduce non-blind elementsinto the analysis.To consider oxygen and calcium recoils in this region,the fraction of each nuclear species’ recoils that fall withinthe acceptance region must be estimated. This requiresseveral pieces of information. The first is the light detec-tor resolution of the observed electron recoil band, as afunction of energy. This resolution is expressed as: σ γ ( E ) = σ + σ E + σ E , (1)where E is the energy in the phonon channel. The reso-lution of the electron recoil band depends on three terms: σ , reflecting electronic noise; σ , related to the Poissondistribution of the expected number of detected photons;and σ , incorporating position dependence and other pos-sible effects seen in CRESST-II light detectors.An additional piece of information needed is the res-olution of each quenched band. At energy E , events inthe quenched band produce an average amount of light L Q i ( E ) = Q i L γ ( E ). The resolution of a quenched bandis assumed to be equal to the resolution of the electronrecoil band at energy E (cid:48) , where L Q i ( E ) = L γ ( E (cid:48) ). Theexact light detector resolutions used in [2] are unavail-able. However, these resolutions may be obtained byfitting to the acceptance region figures in [2], using themethod outlined in Appendix A. These light detector res-olutions are given in Table I. Separately, the energy res-olution of the phonon detector was modelled in [14] by∆ E = P + P E , with energy resolution parameters alsoshown in Table I.The next piece of information is the quenching factorof each target nucleus. For this, the measurements in[13] are used, with 11 . +0 . − . % for oxygen, 6 . +0 . − . % Energy [keV] 0 10 20 30 40 50 O v e r l ap w i t h a cc ep t an c e r eg i on Tungsten in [2]TungstenCalciumOxygen
FIG. 2: Estimates of the fraction of recoils of a given targetnucleus that fall within the acceptance region for Zora/SOS23in [2] as a function of energy. Oxygen is shown by greendiamonds, calcium by red crosses and tungsten by blue circles,with black showing the initial assumption of 90% of tungstenrecoils falling within the acceptance region. Vertical dashedlines at 10 and 40 keV indicate acceptance region limits inrecoil energy. for calcium and 3 . +0 . − . % for tungsten. It should benoted that the more recent measurements of light outputfor tungsten recoils in CaWO in [13] are higher than the2.5% used in [2]. This means that the amount of light fortungsten recoils is on average higher than that which wasexpected in [2], causing less than the expected 90% of alltungsten recoils to fall within the acceptance region, ascan be seen in Figure 2 for Zora/SOS23.One last piece of information would be required for acomplete description of detected light. This is the smalldeviation of observed light in the electron recoil bandfrom the normalisation of one unit of light per unit en-ergy. Two effects can cause this deviation: the depen-dence of light yield on energy in inorganic scintillators[15], and an overall calibration error. Such adjustmentsas used in the analysis of [2] are unavailable, although itis stated in [2] that the light yield is always near the nor-malisation of one. Here we use the approximation thatthe mean electron recoil light yield is one everywhere. Inan independent analysis of the commissioning run data[14], the electron recoil band behaviour and light detec-tor resolution were parameterised, with results repeatedin Appendix B. As a check on our results, we also consid-ered the resulting WIMP cross-section limits with theseparameters. They are consistent with those presentedhere to within a few percent. An oxygen quenching factor of 10 . +0 . − . % was used in [5]. Limitscalculated using this quenching factor are slightly stronger thanthose presented here, a result of a larger fraction of oxygen recoilsbeing observable within the acceptance region. ] WIMP mass [GeV/c10 C r o ss - s e c t i on [ pb ] -7 -6 -5 -4 -3 -2 -1 All recoilsTungstenCalciumOxygen
FIG. 3: 90% confidence limits on elastic, spin-independent,WIMP-nucleon cross-sections from data in [2], consideringall possible nuclear recoils within the acceptance region.The green dashed-dotted, red dashed and light-blue dottedlines result from considering WIMP interactions with oxy-gen, calcium and tungsten individually, and the solid blueline the total rate. The WIMP halo properties used are ρ DM = 0 . , v esc = 544 km/s, v = 220 km/s and v sun = 232 km/s. Resolutions from Table I and quenchingfactors from [13] were used to derive these limits. With these pieces of information, the fraction of re-coiling nuclei from each constituent of CaWO that fallswithin the acceptance region of [2] can be estimated, asshown in Figure 2 for Zora/SOS23. With these fractions,the interaction rate of WIMPs with oxygen and calciumin the commissioning run acceptance region may now becalculated. Here we follow a method analogous to that in[2]. The elastic, spin-independent WIMP-nucleon inter-action rates are calculated following [16], using the Helmform factor parameterisation as suggested in [17]. Thetotal rate expected from all target nuclei is then: dR Tot dE = A W dR W dE + A Ca dR Ca dE + A O dR O dE , (2)for the fractions A i of each species’ nuclear recoils thatmay be seen in the acceptance region. This rate is con-volved with the observed phonon energy resolution, ∆ E ,as described in [17]. III. RESULTS
Three events are observed in [2], at 16 .
89 keV,18 .
03 keV and 33 .
09 keV. The Maximum Gap method[18] is used to calculate the resulting elastic, spin-independent, WIMP-nucleon cross-section limits. Theresults are shown in Figure 3. The extended 90% confi-dence limit improves sensitivity to low mass WIMPs withcommissioning run data. Interactions with WIMPs heav-ier than ∼
17 GeV/c in the acceptance region are dom-inated by tungsten recoils, and the cross-section limit is ] WIMP mass [GeV/c C r o ss - s e c t i on [ pb ] -8 -7 -6 -5 -4 s (2011) 2CRESST-IICoGeNT 90%DAMA 90% XENON100(S2 only)XENON10 CDMS II(low en.)CDMS II CRESST-II (2007) Extended FIG. 4: The combined 90% confidence limit on the elastic,spin-independent WIMP-nucleon cross-section from extend-ing the analysis of commissioning run data to lower WIMPmasses (solid blue). For comparison, the favoured regionsfrom DAMA, derived from [3], CoGeNT [4] and CRESST-II (2011) [5] are shown. Also shown are WIMP cross-section limits from, CDMS II [6], CDMS II (low energy) [7],XENON100 [8] and XENON10 (S2 only) [9]. well modelled by considering interactions from tungstenalone. At lower masses, calcium, then oxygen recoils be-come dominant, such that below ∼ , nearly allWIMP-nucleon interactions in the acceptance region arewith oxygen nuclei. Considering all possible nuclear re-coils then provides a significant strengthening of cross-section limits at low masses compared to tungsten alone.In Figure 4, a comparison of the combined limit ismade to the elastic WIMP interpretation of other ex-periments [3–9]. The CoGeNT, CRESST-II (2011) andDAMA results were already in tension with the results ofXENON100, XENON10 (S2 only), CDMS II, and CDMSII (low energy). The extended CRESST-II commission-ing run limits introduce further mild tension with DAMAand CRESST-II (2011).As the commissioning run and CRESST-II (2011) re-sults are with the same target nuclei with similar en-ergy thresholds, it is difficult to reduce this mild tensionby choosing different astrophysical parameters or parti-cle physics models. However, it should be noted that theCRESST-II commissioning run and CRESST-II (2011)run do not use the same acceptance region definitions.In this work, we have used the acceptance region definedin the original commissioning run analysis. While thisensures that we have not introduced non-blind elementsinto the analysis, this region has not been optimised forlight mass WIMP discovery. An additional difference be-tween runs is the design of clamps in direct contact withthe target crystals, which as noted in [5] introduced addi-tional backgrounds into the CRESST-II (2011) data set.Since the commissioning run live-time is much smallerthan in the CRESST-II (2011) run, repeating the com-missioning run experimental conditions for a longer pe-riod would allow stronger conclusions to be drawn. IV. CONCLUSIONS
The WIMP cross-section limits for the 47.9 kg-daysexposure of CaWO in the CRESST-II commissioningrun [2] have been extended down to a WIMP mass of5 GeV/c . Our analysis has accounted for possible oxy-gen and calcium recoils within the commissioning runacceptance region, using light and phonon detector reso-lutions in Table I and quenching factors from [13]. Theimprovement of cross-section limits at light masses occursbecause recoiling oxygen and calcium nuclei dominateover tungsten recoiling nuclei for light WIMPs. Extend-ing the commissioning run limits results in mild tensionwith the recent CRESST-II [5] and DAMA [3] results. Acknowledgments
We wish to thank Franz Pr¨obst for providing thefavoured region contours of recent CRESST-II results,Jens Schmaler for numerous helpful comments on thiswork, and Felix Kahlhoefer for useful discussions. Wealso wish to acknowledge the Science and Technology Fa-cilities Council, UK who funded this work.
Appendix A: Reconstructing light detectorresolutions
To estimate light detector resolutions, oxygen andtungsten acceptance regions were modelled by:Acc( Q i , E ) = Q i L γ ( E ) + N sig σ Q i ( E ) E , (A1)where Q i is the quenching factor of the considered nu-cleus, and N sig ≈ .
28 is the number of standard devia-tions allowing 90% of quenched recoils to be seen in theacceptance region. These equations were fitted simulta-neously to the tungsten and oxygen nuclear recoil accep-tance regions in Figure 8 of [2]. The tungsten quenchingfactor is set at 2.5% and L γ /E is taken to be one. The oxygen quenching factor, given as ∼ .
1% in the text of[2] is allowed to vary in the fit. A value of 11.0% is foundfrom fitting to both modules’ acceptance regions.
Appendix B: Alternative light detector resolutions
In [14], the electron recoil behaviour was modelled by: L γ ( E ) = l E e − l e E , (B1)giving electron recoil band behaviour parametersand light detector resolutions for Zora/SOS23:Parameter Zora/SOS23 l . ± . l e (keV − ) 0 . ± . σ (keV) 1 . ± . σ (keV ) 0 . ± . σ . ± . l . ± .
005 1 . ± .
003 1 . ± . l e (keV − ) 0 . ± .
001 0 . ± .
008 0 . ± . σ (keV) 3 . ± . . ± .
37 1 . ± . σ (keV ) 1 . ± .
15 0 . ± .
07 0 . ± . σ . ± .
08 0 . ± .
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