Message to the end user.
This is a guide intended to facilitate the use of CDMSlite Run 1 data. Here we describe the files containing the data, and provide instructions regarding energy scale conversion from electron equivalent energies (suffix ee ) to nuclear recoil energies (suffix nr ). We release the data corresponding to the measurement of ionization, hence in keVee units. Along with that we provide the exposure weighted efficiency as a function of ionization energy. This analysis is described in a letter accessible via this link.
The data release is composed of three files which can be found in the linked directory. There are also alternative files, with the extra suffix "_wheader" in their name, and these contain a header in the first line describing the column entries.
This file contains the energies of our WIMP search events, calibrated in keVee units. Note the K and L shell activation lines at 10.36 and 1.29 keVee. The spectra of these events are shown in Fig. 1 and 2.
This file contains the exposure multiplied by the total energy-dependent efficiency in kg-day units evaluated at a list of energies in keVee. There are two columns in this file: the first is the list of eneries in keVee and the second is the efficiency-weighted exposure evaluated at these energies. Please see additional comments in the section on energy scales.
This file contains 90% C.L. upper limit on the WIMP-nucleon spin-independent cross section versus WIMP mass. The first column is the mass in GeV/c2 and the second column is the corresponding upper limit on the cross section in units of 10-39 cm2. The limit is shown in Fig. 4. Please see additional comments in the sensitivity curve section when comparing user calculated limits with the numbers from this file.
Here we show the spectrum of WIMP-search events in ionization energy scale. The first figure is directly from our letter. The second figure is simply a blow-up of the inset from Fig. 1.
Fig. 1: Spectrum of ionization energies for WIMP-search events, expressed in raw counts per energy bin (left axis, blue line). The efficiency function is overlaid (right axis, maroon line).
Fig. 2: The low energy spectrum (inset to Fig. 1).
We point out that depending on the energy bins and histogramming routine, the spectral structure may vary slightly ~ O(bin-width). To match our plot we recommend counting events in energy bins [(0.1,0.11), (0.11,0.12) ,...] in keVee. For example Fig. 2 was generated with MATLAB via,
bt=[0.1:0.01:1.6]; % bins in keVee
stairs(bt,histc(event_vec,bt)); % here event_vec is the vector of events from CDMSliteRun1_EnergyinkeVee.txt
ylabel('Raw Counts');xlabel('Energy [keVee]');
The plots above are histograms of raw counts. The exposure weighted efficiency is provided. Thus one can convert these spectra into traditional rate units by weighting it with 1/Efficiency(energy)/exposure/bin-width. Since above threshold the efficiency is fairly constant, a rough conversion factor may be applied. Multiplying the bin content of the major plot (Fig.1 main spectrum going up to 12 keVee) by 2.1655 [1/kg/day/keVee], and the bin content of the zoomed plot (inset of Fig.1 or Fig. 2) by 16.2410 [1/kg/day/keVee] converts the units from raw counts to counts/kg/day/keVee. The next section will show the spectrum in the cannonical nuclear recoil units.
To set limits on the WIMP-nucleon cross section, one needs to convert the above data in electron equivalent energies (keVee) to nuclear recoil energies. Thus one needs to measure or have a theoretical model of theionization yield (also known as quenching factor or ionization efficiency), since electron recoils and nuclear recoils create electron-hole pairs in germanium with different efficiencies. To make this conversion using a yield model Y, one has to use the following formula :
As described in our paper the yield model used for this analysis follows from the theoretical formulation by Lindhard et.al. The yield is defined by the following formulae:
For germanium, k=0.157 (Z=32, A=72.64).
One can choose other yield models to study effective nuclear recoil spectra. Refer to our paper for details on yield models we considered and further details and references.
Details on all cuts may be found in the paper. The major contributors to less than 100% efficiency are:
The exposure for CDMSlite Run 1 was 6.2561 kg-days. The text file CDMSliteRun1_EffinkeVee.txt has the experiment's total efficiency weighted by this exposure. Note that the function given in the text file is evaluated at energies in keVee.
The following is the inferred nuclear recoil spectrum, taken from our paper. We use the standard Lindhard yield to convert from ionization to nuclear recoil energy scale. Also shown are some examples of expected WIMP rates in Ge.
Here we show the 90 % C.L. calculated using a version of the optimal interval method ( the routine as used in this article ). This Fortran routine is present in the OI_code directory. The main file is LiteUpper.f which takes the WIMP spectrum and list of event energies in ULinput and computes the optimum interval limit cross section which is saved in ULoutput. Instructions to compile LiteUpper.f are given at the top of the file.
Please note that depending on the routine used to calculate the limit the results may slightly disagree with this plot and the numbers in the related text file, CDMSliteRun1_limits.txt.
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