S18_Search for Lightly Ionizing Particles (LIPs) with CDMS Data

M. Buss & G. Ristani

The aim of this experiment was to measure the energy deposited by the travel of hypothetical lightly ionizing particles (LIPs). The experimental data energy spectrum was observed by a germanium crystal high voltage (HV) particle detector operated within a cryogenic dilution refrigerator operated here at the U. Due to increased detector dimensions and a lower energy threshold than prior detectors, we expected an experimental sensitivity to smaller fractional charge values of LIPs (at fluxes on the order of 10^-5 cm ^-2 s ^-1 sr ^-1) than were previously accessible. In the absence of an observed LIP energy signal, an upper limit was determined on the flux from hypothetical LIPs using Poisson statistical analysis of the data energy spectrum. Our final result measured an upper limit on LIP fluxes on the order of 10^-4 cm ^-2 s ^-1 sr ^-1 with 90% confidence for the range of inverse charge (1/z) 55 to 110 in units of electron charge e.

Introduction

A lightly ionizing particle, or LIP, is a particle that would have some charge ze, where z is some fraction, rather than an integer. It is for this reason that LIPs are sometimes referred to as "fractionally charged particles". LIPs are an intriguing possibility as their detection would imply a change to the Standard Model is necessary to encompass all experimentally observed particles. Typically it is assumed that electric charge is quantized in multiples of the electron charge e, or, in the case of quarks, in multiples of e/3. However, no fundamental physical theory in fact demands that electric charge be quantized at all [1]. The question of charge quantization is long standing as a free particle with charge smaller than $e$ has never been experimentally proven to exist.

Since these particles have never been empirically observed, they have no confirmed source. This experiment attempted to look for LIPs potentially created by interactions of cosmic rays with the atmosphere using a method of direct detection, wherein the energy deposited by incident particles is measured by a detector situated on Earth. The intent of this experiment was to make progress towards identifying the existence of a LIP - and in the absence of an observed LIP energy signal, to be able to restrict new parameter space of possible LIP fluxes and charges, making an updated advance in the search taken on by the particle physics community. The main motivation for detecting LIPs was the potential extension to the Standard Model in order to further our understanding of particle physics. Additionally, LIPs may be hypothetically considered for use in medical radiation therapy.

We searched for LIPs via the comparison of the developed LIP energy model and the energy spectrum measured by the detector. The recorded data would illuminate if any LIP events were observed, and if they were not, would provide a limit on the amount of LIP flux expected for a certain range of energy and fractional charge. This experiment expected sensitivity to fluxes as small as 10 ^-5 cm ^-2 s ^-1 sr ^-1 for inverse fractional charges as small as 100, compared to a prior study, CDMSII [1], which had increased sensitivity to smaller fluxes on the order of 10 ^-8 cm ^-2 s ^-1 sr ^-1 but only from 6 to 40 inverse charge. To obtain a limit on the amount of flux due to LIPs we can expect in a detector above the rate of radioactive and cosmogenic background energy we used two methods of Poisson statistical analysis, Feldman-Cousins statistics [2] as well as maximum likelihood analysis [3]. The two different methods were used as a means to compare the conservativeness of resulting LIP flux limits.

Theory

The model of a LIP energy signal was formulated with initial assumptions about the hypothetical particle. In addition to their fractional charge, a key feature of LIPs is that they are free, rather than being in a bound state. Though quarks possess fractional charge in multiples of e/3, they are tightly bound together by the strong force into hadrons and mesons and as such have never individually been observed; their empirical confirmation comes from scattering experiments which show their existence only as components of heavier particles.[4] Considering LIPs as free charged particles implies that there are LIPs with one specific z value, whose existence would appear as an energy peak above the background spectrum. We are not assuming a range of different fractionally charged particles exist - if so, their energy signals would not be discernible from the background radiation in our detector.

During a LIP's passage through a medium energy is deposited according to the relativistic Bethe-Bloch Equation, where the 'stopping power' for a charged particle incident on given material, or change in energy per unit length:

where E is the energy, x is the path length through the target material, n is the target number density, incident particle charge number z, electron mass me, electron charge e (1.6 x 10−19C), β is the ratio v c where v is the incident particle’s velocity and c is the speed of light. Energy deposited in the detector is a small fraction of the LIP’s original energy, characteristic of particles existing in the ”minimum ionizing” region of the Bethe-Bloch curve, as seen in figure 1.

Figure 1: (Average) Stopping power with particle-energy: stopping power (= dE/dx) for positive muons in copper as a function of $\beta\gamma = p/Mc$ over nine orders of magnitude in momentum (twelve orders of magnitude in kinetic energy). Solid curves indicate total stopping power.

The minimum of the Bethe-Bloch curve (β = v_incident/c = 0.95) shows stopping power of a particle through a medium is constant with energy loss at these values of β.[6] Based on the geometry of the 5 cm diameter by 3.3 cm height, disk-shaped detector and a half isotropic angular distribution from 0 to 180 degrees (i.e. they do not travel through the Earth itself), one can calculate an approximate energy signal shape based on a 1/E³ result for the rate of non-normally incident particles (see the appendix section 1 for more details).

Figure 2: Model of a hypothetical LIP signal with an arbitrary flux of 1 cm ^-2 s ^-1 sr ^-1. Illustrations display different categories of particle travel through the detector as they correspond to signal features.

This hypothetical signal model was calculated based on the distribution of possible path lengths through the detector, which are dependent on the polar angle of the incident particle and vertical segment of the detector (considered from the center of the disk to the full radius distance). Energy deposition in a detector from the passage of a charged particle was measured by the total charge of electrons and holes produced by the ionization of the detector medium. The amount of ionization depends on the respective crystal structure. The ratio of ionization to energy deposited by a charged particle is well-defined for germanium and other semiconductors, so measuring the ionization gives a value proportional to the deposited energy. The average number of electron and hole pairs produced during this process can be calculated with the Bethe-Bloch formula.

The Bethe-Bloch formula implies that the rate of energy deposition for a charged particle is proportional to the charge squared, meaning that an LIP with fractional charge ze would deposit energy at a rate lower than that of a muon by a factor of z². Mathematically this can be expressed as:

Essentially, equation 2 shows a proportional relationship between the stopping power and the charge squared of the particle. Since we can approximate the minimum energy loss per surface density as equal for all particles [5], then particles traveling equal distances deposit equal amounts of energy. This indicates the energy loss of a particle is so strongly dependent on the charge squared of the particle that one may be able to identify the charge of the incident particle based on the measurement of dE/dx alone. [5]

Experimental Setup

The detector used in this experiment was operated at temperatures on the order of tens of milliKelvin. These cryogenic temperatures were reached by a Kelvinox 3He-4He Dilution Refrigerator maintained in the CDMS laboratory on campus.

Sensitivity

To understand the benefit of the improvements made in comparison to the previous CDMS II experiment [1], the current limits on LIP flux across a range of fractional charge are shown by the figure below.

Figure 3: Exclusion limits at 90% confidence level on the LIP vertical intensity versus inverse electric charge in units of 1/e, inverse charge, from the blind (pink) and improved, nonblind (blue) analyses of the CDMS II experiment compared with further past cosmogenic searches: MACRO [8] (grey), Kamiokande [9] (x), and LSD [10] (+), [1]. Our expected average flux limit for this experiment is shown by the horizontal red dashed line, and the expected range of accessible fractional charges is shown by the two vertical red dashed lines.

The prior study by CDMS II reported better sensitivity to a range of larger fractional charges with a vertical flux by utilizing a stack of multiple detectors and restricting their analysis to a vertical angular distribution [1]. In contrast we are using only one detector, but because of its larger dimensions and increased accessibility to low energies (near 1 keV) it was sensitive to LIPs with a smaller fractional charge. The expected range of energy accessible by the current HV detector was between 1.30 and 10.37 keV, with an increased sensitivity to LIP flux on the order of 10^-5 cm ^-2 s ^-1 sr ^-1, which indicated an expected improvement on CDMS II’s result [1] for smaller fractional charges. The prior experiment, CDMS II [1], used germanium and silicon crystal "Z-sensitive Ionization and Phonon (ZIP) detectors". Z here stands for the Z-axis, therefore the detectors were intended to be able to distinguish how close to a surface the event was. CDMS II analysis restricted acceptable events to solely downward LIPs that deposit energy in all of the detectors, thus eliminating most of the background from other radiation. This allowed CDMS II a sensitivity to LIP flux on the order of 10^-8 cm ^-2 s ^-1 sr ^-1, though only for the range of inverse charge 6 to 40 (in units of 1/e). Considering charges less than e/55, CDMS II's sensitivity decreased a minimum of four orders of magnitude (figure 3).

Detector

The detector used to measure the energy of incident particles was a high purity germanium crystal high voltage (HV) detector, operated at temperatures on the order of tens of millikelvin in order to minimize thermal and electronic background noise [[11]. It was set with an external voltage bias of 70 V which permeated an electric field across the detector crystal (fringing effects at the edges of the detector were also considered).

Figure 4: Left: Germanium high purity crystal detector with 5 cm radius and 3.3 cm height. Right: illustration of an incident particle interacting electromagnetically with a Ge nucleus in a HV crystal detector and producing phonons.

If a charged particle travels through the detector, it interacts with the electrons in the germanium crystal via the electromagnetic force, ionizing them and produces electron-hole pairs. The bias voltage set across the detector propagates these electron-hole pairs, and their travel creates tiny vibrations called phonons [12], measured by devices called transition edge sensors (TES) [11], patterned to the crystal surface. The recorded energy of the phonons correspond to the energy of the incident particle and imply detection. A transition edge sensor operates at a transition temperature of 60 mK, below which its resistance is basically zero. At a certain transition temperature, very small variations in temperature of the sensor correspond to large changes in its measured resistance.

Figure 5: Temperature as a function of resistance for a transition edge sensor. The transition temperature for the TES in the HV detector was near 60 mK and maintained with a negative feedback loop.

The increase in temperature of the sensor is due to the energy of a phonon reaching the detector surface, and the increase in resistance of the sensor indicates the amount of energy of the phonon. It was critical to the quality of data obtained from the experiment that the bias voltage be as high as possible, as a strong electric field serves to increase the signal to noise ratio. The increase in temperature of the sensor is due to the energy of a phonon reaching the detector surface, and the increase in resistance of the sensor indicates the amount of energy of the phonon. Data was recorded in the detector when an 'event', or measure of phonon energy in a specific detector channel, was greater than the threshold energy value set by a DCRC for the specific channel being triggered on [11]. The data used in this experiment was taken while separately triggering on either channel C or E, see below.

Figure 6: Diagram of phonon channel arrangement on surface of detector.

The detector tower containing the detector itself and its copper housing was connected to side coaxial cables and extender plugs that allow the signals measured by the detector to be read out with hardware. This process was accomplished with custom detector control and readout cards (DCRCs). The DCRCs provide the electronic communication with the detector as well as digitize the phonon signals. Standard telnet protocols are used to communicate with DCRCs in order to read information and store raw data. Because of the large amount of raw data produced by CDMS detectors, a set of streamlined processing code had been developed to automatically calculate meaningful quantities from each recorded event. These quantities, such as amplitudes and timing of pulses, were used to determine the position and energy of events [11].

K100 Kelvinox 3He-4He Dilution Refrigerator

The housing tower was installed within the internal equipment of the fridge at room temperature, and then the temperature was decreased to the desired range after installation. Operating the detector at tens of milliKelvin ensured that the electron-hole pairs created by the incident particle do not become trapped in the crystal before their collection. The cryogenic temperatures increased the detector's response to phonons and decreased electronic noise sources, as mentioned previously. However, the signals were still not exposed to any internal amplification, and as such low-noise amplifiers were used external to the detector. The detector and dilution refrigerator were encased in lead and polyethylene shielding during operation in order to mitigate background gamma and neutron radiation signals [16].

Figure 7: Left: 3He-4He dilution refrigerator and external polyethylene shielding with overlay of illustrated internal equipment. Right: Internal arrangement of fridge components and cooling equipment with external shielding and container de-installed.

Data was recorded over 34.06 hours in 70 series of 30 minute data sequences for a total of 34.06 hours. Each series had a 30 second LED "flash" sequence applied to the detector surface in between series. A flash of LED light, in the UV range, served to remove any trapped charge in the crystal lattice of the detector and thus ensure that it was neutralized with respect to charge before applying a voltage bias. This had an effect of warming the fridge to a temperature not optimal for data collection. Thus the flashing sequence included an additional 30 minutes of time post-flash before starting a new series of data to allow the cryostat to cool to the optimum temperature.

Analysis

Analysis was accomplished with code written in C/C++ using the ROOT library to plot data.

Calibration

The detector is calibrated via two signal peaks from neutron activation processes at 1.30 keV and 10.37 keV. This neutron activation occurs due to detector exposure to neutron source, plutonium beryllium (PuBe). Pu emits alpha particles, and Be emits neutrons when bombarded with alphas, therefore the combination PuBe serves as a neutron source [17]. Though any neutron source could be used to activate the detector, what is relevant is the resulting decay of ⁷¹Ge to ⁷¹Ga by electron capture, a form of beta decay [14]. ⁷¹Ga has a half-life of of 11.4 days and its decay produces energies in measured peaks corresponding to different shells in the daughter isotope's electron structure [13].

During electron capture, an electron close to the nucleus combines with a proton in the nucleus. In this decay process a neutrino is emitted, and the nucleus recoils slightly - these are not measured by this experiment. The daughter nucleus is in an electronically excited state because one of its inner shells is missing an electron [17]. Outer electrons fall in to fill this empty state, and that energy transfers in some form (x-rays, Auger electrons). The recoil of the nucleus produces a small but measurable amount of energy, around 0.3 keV. When the decay occurs we observe the nuclear recoil energy plus the binding energy corresponding to the empty electron state. Majority of the time the electron capture is from the innermost K-shell, relating to an energy of 10.37 keV. Less frequently, this occurs in the following shell, L,which corresponds to energy of 1.30 keV. Least likely this occurs in M-shell, an energy of 0.1 keV [17]. These resulting energy peaks in the spectrum, apart from simply characterizing the observable range of energies observable by the detector, allow the calibration of number of incident events as a function of the deposited energy.

Figure 8: Gaussian fitting of the two neutron activation peaks in the full energy spectrum of the detector. The values of sigma as a function of energy indicate the effects of the energy resolution.

These calibration peaks also served to characterize the energy resolution of the detector in the form of a linear convolution function, which must also be taken into account for the LIP signal model. The detector does not have a 100% energy resolution, due to effects such as electronic background noise. This detector dependent energy resolution must be applied to any model being compared to the experimental data spectrum. Indeed, in order to make the hypothetical LIP signal model as representative of what would be seen in the detector, it needs to be convolved against the resolution function of the detector.

Figure 9: Original LIP signal compared to the post-convolution LIP signal. The blue peak shows obvious 'smearing' or decrease in energy resolution taking into account detector effects.

Trigger Efficiency

In order to search for LIPs in the range of energies between the calibration peaks, an estimation of the amount of background radiation measured in the energy spectrum was needed. This experiment assumed a flat energy spectrum as a background model between the calibration energy peaks. It was verified if the expected ratio of events at 1.30 and 10.37 keV due to ⁷¹Ge decay [13] was the same as what is observed in the data at these energies. It was found that, for the 1.30 keV peak, the amount of events recorded compared to the expected number was dependent on the distance of the event from the triggering channel, either C or E. Trigger efficiency refers to the fraction of recorded events that occur below a critical energy. Some events are eliminated as they do not meet the trigger threshold energy when measured in a channel far from the trigger channel. The experimental data showed a decrease in trigger efficiency at low energies.

To characterize the trigger efficiency as a function of energy we compared data in which Channel C was the triggering channel to data in which Channel E was the triggering channel. Comparing the position dependence of events based on start times or relative amplitudes indicated which channel, C or E, events were recorded in. For events in the 10.37 keV calibration peak, it was found that the relative amounts of energy in Channels C and E did not depend on which channel was the triggering channel. This suggests 100% trigger efficiency. By calculating this efficiency at 1.30 and 10.37 keV we were able to estimate the minimum energy at which the trigger efficiency was 100%, 4.95 keV. From this value of trigger efficiency, we interpolated the function with the value of efficiency at 1.30 keV. This assumes the efficiency rises linearly with energy (relating to our assumption of a flat background) to the critical energy 4.95 keV.

Figure 10: Trigger efficiency function and flat background superimposed on experimental energy spectrum.

Visually, the trigger efficiency function seems to match the experimental energy spectrum between the calibration peaks well. This implies that the flat background combined with the trigger efficiency function gives a reasonable estimation of the background radiation recorded by the detector.

Data Selection: Fiducial Radius

Once the function of our background radiation was deemed to appropriately fit the energy spectrum, other adjustments to the data were considered to improve quality of data. A physical effect on recorded data is the behavior of the applied electric field near the edges of the detector. Electric field fringing at high radius values causes an inefficiency in measurement of events occurring far from the center of the detector. Another consideration included the desire to avoid excess noise in the data. The initial cut necessary to calculate was a physical fiducial (reduced) radius 'cut' to reject events that occur at a high radius, which can be seen as the red peak in figure \ref{fig:model} below, contrasted with the signal's appearance when including the detector's full radius. Also a motivation for a fiducial radius cut is to remove the events occurring near the edges of the detector, where the electric field fringes (recall Appendix 2.iii). This must be taken into account when analyzing our model and data.

The particle's travel is expected to leave an energy signal in the form of the characteristics seen in the image of our hypothetical LIP model, related to the three different illustrated categories of a particle's possible travel through the detector. The effects of different fiducial radii on the signal model can be seen below.

Figure 11: Model of a hypothetical LIP signal based on the geometry of the HV detector with a fiducial radius cut applied for comparison of signal appearance as fiducial radius is decreased.

This cut served to remove events from our data that were measured in the outer region of the detector, based on comparing the ratio of energy in the outer ring channel (Channel A) to the total energy in all channels. In order to eliminate this inefficiently measured signal from the data, a fiducial radius cut is applied not only to the signal model as discussed previously, but to the detector itself as well which removes all data from particles incident upon the detector that are more than a given distance from the center.

The above figure shows a decrease in number of events measured across the full energy spectrum. An optimum fiducial radius cut would allow the maximization of the signal peak to background noise ratio.

It can be seen in the figure that the fiducial radius cut served to improve the shape of the peak. This makes intuitive sense because events with reduced phonon energy were removed. It also reduced more of the background radiation than it reduced LIP detection efficiency. It was decided that a fiducial radius of 2.5 cm, effectively half of the original detector radius, was the appropriate fiducial cut. This fiducial radius corresponds to a 25% efficiency, so we tuned the cut to be 25% efficient when applied to the 10.37 keV peak.

Figure 12: Comparison of the experimental energy spectra with and without a fiducial radius cut applied. The blue spectrum shows the data when the fiducial radius is not applied. The red spectrum shows the data with the fiducial radius cut applied.

Data Selection: Quality Cuts

The next adjustments applied to the selected data were cuts based on the quality of events recorded by the detector. The energy reconstruction of an event performed by the data processing code can be unreliable if the event occurs too close in time to another event. Each series begins with 500 randomly-triggered events which are monitored in real time as a data quality measure. The only condition imposed on a randomly-triggered pulse (a “random” for short) is that no hardware triggers are issued during the readout time window [18]. The first cut applied to the data to remove such events from consideration is aimed at these random events. Another consideration is events that 'pile-up', as seen in the 'bad' event illustrated in the inset of the below figure.

Figure 13: Comparison of the experimental energy spectra with and without quality cuts applied. The blue spectrum shows the data when randoms are removed and the fiducial radius cut applied. The red spectrum shows the data with removed randoms and the fiducial radius cut applied, as well as the quality cut to reduce pile-ups. The top left illustration shows the contrast between what a 'good' vs. 'bad' peak is visually.

There are two categories of these events: events in which two pulses overlap, and events in which the pulse occurs on a long tail of a previous, very high energy event. The former type can be identified by comparing the maximum pulse height to the integral over the peak. The latter type can be identified by comparing the level of the trace just before the pulse to the average level. The applied quality cuts reduce the amount of background radiation in the search region and makes it more uniform. Because these cuts will also remove some potential LIP events, an efficiency factor was applied to the LIP signal model. The efficiency of the quality cuts was calculated by observing how many events in the 10.37 keV peak are removed by the cuts, giving an efficiency of 74%.

Maximum-Likelihood

After the above modifications were made to the model and the data, the aforementioned Poisson statistical analysis processes were utilized to place an upper limit on the LIP flux through the detector for various fractional charges. A Poisson process can be characterized as a stochastic process satisfying three principal requirements. First of all, in a given time interval, the probability of observing at least one ”event” must be directly proportional to the length of that interval. Second, in a sufficiently small time interval, the probability of observing two or more events must be negligible. And finally, the numbers of event occurrences in disjoint intervals must be mutually independent. If a process fits these requirements (which, indeed, ours does), Poisson statistics prescribes that the random variable Y of this process will assume values y with a probability given by:

The mean and variance of this distribution are equal and given by µ = λt, where λ is the rate of events occurring and t indicates the length of the time interval of observation. Using the theoretical model of the energy spectrum that was created, the product of the Poisson probabilities can be calculated for each energy bin. If this procedure is done for a pair of separate models it yields the relative likelihood between the two that the observed spectrum of data would actually occur. The numbers yielded by such an analysis for a large number of events are quite small, however, and as such it is easier from a mathematical perspective to work with the logarithm of this likelihood than the likelihood itself.

This naturally leads to the creation of a ”log-likelihood” function for a fractional charge z and corresponding flux Φ:

Here i is the bin index, Ni is the number of background events in bin i, mi is the expected event count in bin i, and L(z, Φ) is the likelihood function of a flux Φ for particles of charge fraction z.

A key feature of maximum likelihood analysis is that it gives more weight to data points near peaks in the data. This is a strength it has over the Feldman-Cousins method, described after the following figure. Figure 14 shows a sample result of the maximum likelihood analysis for an LIP of charge e/80.

Figure 14: Maximum likelihood analysis for a fractional charge e/80, chosen because it was close to the middle of the searched range of fractional charges.

Feldman-Cousins

Feldman-Cousins analysis is a method based upon the principles of Poisson statistics. As with the maximum likelihood analysis, a model of the data was constructed as a sum of the signal model and background model. The method relies upon a chosen signal energy window, as well as a background rate calculated based on events outside of the energy window. Then the number of signal events in that window is determined through a simple subtraction of the background count from the raw data count. [2]

Feldman-Cousins analysis differs from maximum likelihood analysis in that it does not endow points with varying weights based upon their location (near or far away from a peak). Because of this it was expected that it would give a more conservative upper limit for LIP fluxes through the detector. The figure below shows the result of Feldman-Cousins analysis for a charge e/80.

Figure 15: Feldman-Cousins analysis for a fractional charge e/80.

Results

Figure 16: The result of both maximum-likelihood and Feldman-Cousins analyses as compared to the CDMS II [1] limiting flux result.

The above figure shows the limiting curves for flux values obtained by applying the two different analyses for a range of inverse charge 55 to 110 (in units of 1/e). This experiment achieved sensitivity to limiting flux values of more than 10^-4 cm ^-2 s ^-1 sr ^-1 for inverse charges 55 to 110, over both types of analyses. The strongest value of limiting LIP flux measured by CDMS II [1] was on the order of 10^-4 cm ^-2 s ^-1 sr ^-1 for charges smaller than e/55. These improved values are an obvious indication that our detector was indeed sensitive to particles with lower energies.

Previously it was stated that the maximum-likelihood method was expected to produce a stronger, less conservative limiting flux value. Maximum-likelihood's appropriate consideration of the signal shape and scan over all possible background levels would include possible LIP models with less LIP signal and a higher background. The Feldman-Cousins analysis, as it assumes a specific background value, gave an expectation of a weaker, more conservative limit on LIP flux. As seen in the above figure, the Feldman-Cousins method produced stronger limits for larger inverse fractional charges, contrary to expectation. It was considered that are cases where the signal spectrum is more strongly peaked at lower energies. Thus when the signal is strongly peaked, Feldman-Cousins' lack of incorporating the full signal shape, has a decreased relevance in the calculation of the limit. At smaller inverse charges, the maximum-likelihood analysis gave stronger limiting flux values, as initially expected. Overall, our results show a clear improvement in the sensitivity of the limiting flux value for LIPs compared to the previous experiment CDMS II [1] in the region of fractional charge e/110 to e/55.

Outlook

This experiment will intend to improve upon this paper's result during the summer and fall of 2018 through further additions to the analysis. The most prominent consideration may be in our initial assumption of the quantity dE/dx from the Bethe-Bloch equation as constant for identical charged particles with the same incident energy and traveled path length. There is evidence that dE/dx is only an average value for the stopping power of a particle in a material [7] - and our result must be adjusted for the resulting effect of this on our LIP signal model.

Perhaps the most difficult refinement to the investigation would be the creation of a simulation for the background environment in the laboratory-the practicality of this has been called into question, however, as an accurate simulation of this nature would require extensive knowledge of all background radiation sources. If, however, it were to be created, this simulation would of course be an invaluable asset, allowing for observation of the agreement between theory and data or lack thereof with minimal obfuscation from the background. Looking at the applied quality cuts as a function of time and energy would indicate if there is an energy or time dependent quality efficiency function, rather than an average value as currently assumed. Finally, another type of analysis that could be compared to the maximum-likelihood and Feldman-Cousins analyses is the optimum interval method. This method is a way to estimate an upper limit in the presence of an unknown background [15], which would perhaps eliminate the need to simulate the background radiation.

Even without these future considerations taken into account, the results on the limiting flux for a range of LIPs with charges e/110 to e/55 clearly improved over orders of magnitude compared to the previous results from CDMS II. [1] This experiment successfully excluded a previously unexplored region of LIP parameter space, a marked advance towards the detection or exclusion of LIPs and a benefit to the ongoing search for these hypothetical particles.

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Acknowledgements

This experiment was accomplished with the assistance of Matthew Fritts and Vuk Mandic. Advising was also appreciated from Ke Wang, Kurt Wick, and Dan Dahlberg.