IPPP/18/60 Statistical challenges in the search for dark matter Sara Algeri,1 Melissa van Beekveld,2 Nassim Bozorgnia,3 Alyson Brooks,4 J. Alberto Casas,5 Jessi 6 7 8, 9 Cisewski-Kehe, Francis-Yan Cyr-Racine, Thomas D. P. Edwards, ∗ Fabio Iocco, Bradley J. 8, 10 11 12 Kavanagh, ∗ Judita Mamuˇzi´c, Siddharth Mishra-Sharma, Wolfgang Rau, Roberto Ruiz de 10 13 14, 15 16 Austri, Benjamin R. Safdi, Pat Scott, ∗ Tracy R. Slatyer, Yue-Lin Sming Tsai, Aaron 12, 17, 8 18 19 C. Vincent, ∗ Christoph Weniger, Jennifer Rittenhouse West, and Robert L. Wolpert 1Department of Mathematics, Imperial College London, SW72AZ, United Kingdom 2Theoretical High Energy Physics, IMAPP, Faculty of Science, Mailbox 79, Radboud University, The Netherlands 3Institute for Particle Physics Phenomenology, Department of Physics, Durham University, Durham, DH1 3LE, United Kingdom 4Department of Physics & Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854 U.S.A. 5Instituto de F´ısica Te´orica, IFT-UAM/CSIC, Universidad Aut´onomade Madrid, 28049 Madrid, Spain 6Department of Statistics and Data Science, Yale University, New Haven, CT 06520 U.S.A. 7Department of Physics, Harvard University, Cambridge, MA 02138 U.S.A. 8Gravitation Astroparticle Physics Amsterdam (GRAPPA), Institute of Physics, University of Amsterdam, 1090 GL Amsterdam, The Netherlands 9ICTP South American Institute for Fundamental Research, and Instituto de Fısica Teorica - Universidade Estadual Paulista (UNESP), Rua Dr. Bento Teobaldo Ferraz 271, 01140-070 Sao Paulo, SP Brazil 10Instituto de F´ısica Corpuscular (IFIC) / Consejo Superior de Investigaciones Cient´ıficas (CSIC) - Universidad de Valencia (UV), Spain 11Department of Physics, Princeton University, Princeton, NJ 08544 U.S.A. 12Arthur B. McDonald Canadian Astroparticle Physics Research Institute, Department of Physics, Engineering Physics and Astronomy, Queen's University, Kingston ON K7L 3N6, Canada 13Leinweber Center for Theoretical Physics, Department of Physics, University of Michigan, Ann Arbor, MI 48109 U.S.A. 14Department of Physics, Imperial College London, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, United Kingdom 15Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 U.S.A. 16Institute of Physics, Academia Sinica, Taipei 11529, Taiwan 17Visiting Fellow, Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, Ontario N2L 2Y5, Canada 18Department of Physics & Astronmy, University of California, Irvine, CA 92697 U.S.A. 19Department of Statistical Science, Duke University, Durham, NC 27708 U.S.A (Dated: August 4, 2020) The search for the particle nature of dark matter has given rise to a number of experimental, theoretical and statistical challenges. Here, we report on a number of these statistical challenges and new techniques to address them, as discussed in the DMStat workshop held Feb 26 { Mar 3 2018 at the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Alberta.a CONTENTS 1. WIMP Signatures4 2. Detection Channels4 I. Introduction2 3. Statistical methods in direct detection5 A. Disambiguation3 B. Indirect searches5 C. Collider searches6 II. The dark matter problem3 1. Collider signatures7 2. Statistical approaches at the LHC7 III. Contemporary challenges in Dark Matter4 A. Direct searches4 D. Gravitational probes and structure formation8 IV. Statistical challenges and approaches9 ∗ Editors A. Novel Techniques 10 a http://www.birs.ca/events/2018/5-day-workshops/18w5095 1. Selecting between non-nested models 10 2 2. Exploiting the count statistics of the Following several decades of searches, it has become signal 11 increasingly clear that discovery is less likely to happen 3. Euclideanized signals 12 via a single \smoking gun" signal, but rather by scru- 4. ABC: when you can't actually afford a tinizing data from many experiments in many disparate likelihood 13 fields. The main searches for dark matter are broadly B. Progress and Challenges 15 categorized into direct detection, indirect detection, and 1. Quantifying nuisances 15 production at colliders. 2. Global fits: let's just do everything (and The next decade will present us with major advances worry later about trying to afford it) 16 in experiments designed to search for dark matter, as 3. Machine Learning in DM Physics 17 well as experiments with a broader focus on searches for 4. The statistical interpretation of BSM physics. Even though current and past searches fine-tuning 17 have thus far come up empty, the parameter space that 5. Global significance for overlapping signal has been explored pales in comparison with what will regions 18 become available in years to come. This includes an un- paralleled quantity of astrophysical data, from e.g. the V. Examples and toy models 19 Square Kilometre Array (SKA) radio telescope [2] that A. Parameter limits with non-compact support 19 will map the distribution of matter in the dark ages be- B. Combining two experiments 20 fore the formation of the first galaxies via the 21 cm spin C. Presenting the p-value and the probability of transition line of the hydrogen atom [3]; gamma ray tele- the null 21 scopes such as the Cherenkov Telescope Array (CTA) [4] that will yield important information about the high- VI. Conclusions 22 est energies in the universe; and the next generation of galaxy surveys (eBOSS [5], DESI [6]) which will map the Acknowledgments 23 distribution of structure in the universe. Starting in 2022, the Large Synoptic Survey Telescope (LSST) [7] will sur- References 23 vey the southern sky to unprecedented depth, allowing for the discovery of new ultra-faint dwarf galaxies [8] and increasing the sample of known galaxy-scale strong gravi- I. INTRODUCTION tational lenses by a factor of 10 [9]. Taken together, these new observations will dramatically improve our knowl- The nature of dark matter (DM) is one of the most edge of dark matter structure on kiloparsec scales and pressing puzzles in modern particle physics and astron- below, hence stress-testing the standard cold dark mat- omy. Overwhelming evidence from galactic dynamics to ter paradigm in a new regime. Concurrently, space based cosmology tells us that 85% of the matter content of missions such as Gaia [10, 11] will map the distribution the Universe is in a very∼ different form from the famil- of dark matter in our own neighbourhood for the first iar \baryonic" matter described by the Standard Model time, with the promise of sub-milliarcsecond astrometry. (SM) of particle physics. Precision measurements of the The PINGU upgrade to the IceCube neutrino detector cosmic microwave background (CMB) suggest the exis- at the South Pole [12] will be able to detect light DM tence of a new particle that is cold (i.e. non-relativistic candidates, as we embark on the first decade of neutrino at sufficiently early cosmic times), dark (very weakly- astronomy. interacting with quarks, electrons and photons), and be- Meanwhile, DM-specific searches such as XENONnT haved like matter (a pressureless fluid) in the Early Uni- [13], LUX-ZEPLIN [14] and ADMX [15] (along with DM- verse [1]. focused analyses of collider data) will provide the best Evidence for dark matter comes to us entirely via its sensitivity for testing a large variety of hypotheses re- gravitational influence; however, there are many good garding the particle properties of DM. reasons to believe in a particle physics portal to the dark Reconciling the vast landscape of theoretical models sector. In fact, many theories of physics beyond the stan- and the many disparate data sets is not an easy task, and dard model (BSM) such as supersymmetry naturally pre- it inevitably leads to a number of statistical challenges dict a nonzero relic abundance of \dark" particles. on scales that range from the interpretation of a single In the absence of a definitive non-gravitational sig- experiment, all the way to combination of models and nal of DM, the space of possible models of particle large datasets with one another. dark matter has also thrived. Theoretical motivations Our aim in this short review is to outline major sta- such as the \WIMP miracle," the \baryon disaster," the tistical challenges that came up over the course of the 1 Peccei-Quinn solution to the strong CP problem, and the DMStat workshop , along with proposed approaches and neutrino mass problem motivate such candidates as the WIMP, asymmetric dark matter, the axion or the sterile neutrino. The full list of DM candidates is as varied as it is extensive. 1 Held Feb 26 { Mar 3 2018 at the Banff International Re- 3 solutions including software developed by the commu- fraction of repeated experiments in which the true nity. We begin with a brief review of the problem of value of a quantity actually appears inside a con- dark matter (Sec. II), followed in Sec. III by a descrip- fidence interval/region. A 90% confidence inter- tion of current strategies for experimental dark matter val/contour is said to undercover if the true value searches and some challenges those searches have encoun- would actually appear inside the interval in less tered. We then outline and discuss several statistical ap- than 90% of repeated experiments, or to overcover proaches (Sec.IV), including some novel techniques, and if the true value would appear within the interval present some simple examples in SecV. in more than 90% of repeats. Overcoverage is in- efficient but relatively benign, as it increases the probability of a type II error (failure to reject a A. Disambiguation false null hypothesis, a \false negative" finding); undercoverage leads to an increase in the rate of Although statistics acts in some sense as a lingua type I error (rejection of a true null hypothesis, a franca across the sciences, there are certain \regional di- \false positive" finding), so is generally considered alects" that should be noted: we have identified a few more serious. terms in particular that have very different meanings when used by the astroparticle physics community versus Machine learning: A field that grew out of computer statisticians.