RIKEN Accel. Prog. Rep. 50 (2017)

Ⅱ-6. Particle Physics

New insights on dark matter using lattice gauge theories
E. Rinaldi∗1
Dark matter is thought to be the dominant formof matter in our universe today. Its energy density is
about ﬁve times larger than common visible matter according to recent cosmological observations. However,dark matter is very elusive and it has not yet been
detected despite large experimental eﬀorts. Moreover,the particle dark matter candidate generally used as atemplate for all the experimental analysis, the so-called
WIMP (weakly interacting massive particle) dark matter, is a product of supersymmetric theories and these
theoris have not been discovered yet.
From the theoretical point of view, it is interesting
to start exploring dark matter models where the candidates are more exotic than the usual WIMPs and thatcan naturally explain why all the experimental searches
have turned out empty handed. This research program
focuses on composite dark matter, a framework fordark matter models where the candidate new particle
is a bound state of a new strong interaction. Composite dark matter has a non-trivial internal structure andits main properties are dictated by non-perturbativestrong dynamics, which naturally include self interactions.
This type of picture is familiar to everyone working
in Quantum Chromodynamics (QCD), the theory ofquarks and gluons that explains how composite particles like protons and neutrons are created. Moreover, methods that are succesfull in exploring nonperturbative QCD properties can be applied to composite dark matter theories. This is the case for latticegauge theory simulations. They provide a systematicway of solving the strong dynamics of the theory withimprovable and controllable errors.
Applying lattice ﬁeld theory methods to models ofcomposite dark matter has been very fruitful. In particular, for the case of Stealth Dark Matter, they havehelped determining the strength of the dominant interactions with the photon1) and the Higgs boson2) .
Stealth Dark matter is a model with a SU(4) gauge
group and dark fermions that have electric charges andare bound together into a heavy neutral four-fermion
object that constitutes dark matter. Since this objecthas constituents with electric charge and mass, it willinteract with Standard Model particles through the exchange of the corresponding gauge bosons, the photon
and the Higgs. While the dominant interaction withthe Higgs boson depends on unknown parameters ofthe model at high energy and can only be bound using existing experimental results, the electro-magnetic
interaction between the dark matter and the nuclear
matter in detectors like LUX or XENON1T can be∗1RIKEN Nishina Center- 138 -Fig. 1. The DM spin-independent scattering cross section
per nucleon evaluated for xenon is shown as the purple
band obtained from the SU(4) polarizability, where thewidth of the band corresponds to 1/3 < MFA < 3 from
low to high. The blue curve and the light blue region
above it is excluded by the LUX constraints. The vertical, darker shaded region is excluded by the LEP II
bound on charged mesons1) .

directly calculated with lattice simulations.
The operator
OF = CF B ∗ B F μα Fαν vμ vν ,(1)where CF is the EM polarizability, corresponds to across section with a nucleon ofσnucleon (Z, A) =Z 4 144πα2 μ2nB (MFA )2[αm̃3B C̃F ]2 ,(2)
6R2A2MDM

where Z and A are the usual atomic number and mass,
while MDM is the unknown dark matter mass. Thecross section per nucleus scales as Z 4 and not A2 , andso the cross section per nucleon must be calculated
for each nucleus separately in order to compare withexperiments.
Comparing to LUX gives the cross section in Figure 1 as a function of the dark matter mass. StealthDark matter of mass 500 GeV is not excluded by experiments.
These results have been presented at the BNL EarlyCareer Researcher Symposium in December 2016 andthe presentation won an award for its originality3) .
References
1) Lattice Strong Dynamics (LSD) Collaboration,
Phys. Rev. Lett. 115, 171803 (2015), Editors’ Suggestion.
2) Lattice Strong Dynamics (LSD) Collaboration,
Phys. Rev. D92, 075030 (2015), Editors’ Suggestion.
3) Outstanding oral presentation award,
Early Career Researcher Symposium 2016, Brookhaven
National Laboratory.