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a new dark force that influences primarily dark matter par- ticles, and to a much ... rise in the fractional flux of positrons at energies ranging from several GeV to ...





ecades of progress in fundamental physics have resulted in a deep understanding of the nature of atoms, nuclei, elementary particles, and the forces that govern their interaction. It is precisely this understanding, combined with unprecedented progress in observational cosmology, that has led to the “missing energy” problem: 95% of the total energy density of the Universe does not consist of the atomic matter with which we are familiar, but rather a new form of matter and energy. We are aware of this missing energy only through its gravitational effects and its participation in the cosmological evolution. Understanding the nature of “dark matter”, responsible for the formation of cosmological structures such as galaxies, is one of the primary goals of particle physicists, astrophysicists and cosmologists today [1]. Although a wide variety of evidence for the gravitational interaction of dark matter exists, its connection to the micro-world of particle physics remains a mystery, and a subject of intensive experimental, observational, and theoretical research. One must keep in mind that this may be an open-ended journey, with no guarantee that the nongravitational interactions of dark matter will ever be detected. In light of this, several recent results from cosmic ray astrophysics experiments have generated considerable excitement in the physics community, as they can be interpreted as a combined effect of dark matter and dark forces. Theorists at the Perimeter Institute have pio-

SUMMARY The idea of dark forces - new gauge interactions with small couplings to the Standard Model particles and interaction ranges accessible in medium energy collisions - has remained on the back burner of particle physics for almost three decades. During the last two years, however, this subject has become a focal point due to the new exciting developments that tie the combination of dark forces and particle dark matter to the newly discovered cosmic ray anomalies. Here we review this new motivation for studying dark forces, and give an account of the contribution of Perimeter Institute to the development of new search strategies of dark forces in particle physics experiments.

neered many crucial ideas in this exciting new direction in dark matter research. What do we mean by dark forces? The standard model of elementary particles dictates that besides gravity, there are three fundamental forces that describe all known interactions of ordinary matter: the electromagnetic, weak, and strong forces. These forces are transmitted by the so-called gauge bosons which are elementary particles with unit spin, and can be schematically described by the Yukawa potential between point-like particles,

V (r ) = ±

α exp ( − r / λ ) , r


where α is the strength of the force and λ is its range, with a positive sign for repulsion and negative sign for attraction. For example, the photon is the gauge boson which communicates the electromagnetic force between charged matter with α ≅ 1/137 and infinite range. Analogous to these forces familiar from particle physics, it has been postulated that dark matter may be accompanied by new gauge bosons, or “dark photons”, which carry a new dark force that influences primarily dark matter particles, and to a much lesser degree ordinary particles such as electrons and protons [2,3]. The existence of dark forces can explain in a natural way the recent anomalies observed in experiments studying cosmic rays, energetic particles coming from space. The most striking result comes from PAMELA, a satelliteborne experiment that investigates charged particles in the cosmic rays and has the capacity to distinguish between types of particles and their charge, e.g. electron vs. positron. There are two important results that PAMELA has published. The first result is the observation of a stark rise in the fractional flux of positrons at energies ranging from several GeV to about 100 GeV [6], shown in Fig. 1. This suggests a new primary source of cosmic ray positrons at high energies. One possible new primary source is the annihilation of dark matter particles in the galactic halo into electron-positron pairs. However, a standard particle dark matter candidate has a characteristic annihilation cross section which is too small to obtain the measured flux. The second observation from PAMELA is the cosmic ray anti-proton fractional flux, which agrees very nicely with the predicted flux due to standard astrophysical sources [7]. Thus, if one takes seriously the possibility that dark matter annihilation is responsible for the



B. Batell , Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 and M. Pospelov , University of Victoria and Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5

CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 111


enhancement of the annihilation cross section, a well-known effect in the annihilation of electron-positron pairs. To summarize, the presence of a GeV-scale dark force naturally provides an overall enhancement of the dark matter annihilation cross section, and thus a new primary source of high energy positrons which may explain the PAMELA positron flux [6]. While the notion of dark matter is somewhat exotic, even if well-accepted, the idea of dark forces may seem completely far-fetched. Nevertheless, models of dark forces make a number of concrete and striking predictions that can be tested in ongoing and upcoming particle physics and dark matter experiments, and much of the groundwork in exploring the phenomenology in this area has been carried out by researchers at Perimeter Institute [8,9].

Fig. 1

The PAMELA positron flux. The red data points indicate a rising fractional positron flux at energies above 10 GeV. The solid line is the predicted result based on known astrophysical sources.

PAMELA positron anomaly, one must explain 1) the large annihilation cross section into electrons and positrons, and 2) the small annihilation cross section into protons and antiprotons. These two requirements can be naturally satisfied given the existence of a new dark force[4,5]. Let us call the dark matter particle χ and the “dark photon” (or more precisely the “massive dark force gauge boson”) V. The dominant dark matter annihilation process is

χ + χ →V +V.


Once a dark photon V is produced, it can decay back into ordinary particles, such as electrons and protons:

V → e+ + e− ;

V → p+ + p− .

While there exists a variety of models of dark forces, a basic framework may be characterized by two parameters. The first is the mass of the dark photon mV, which is of course one-toone related to the range of the force, mV = 1/λ. While the interaction of two dark matter particles via the dark force may have strength similar to the regular interactions, the coupling of the dark matter particles to electrons and protons is given by the coupling strength κα, where κ can be interpreted as a small mixing angle between the ordinary photon and the dark photon. How can we test the idea of dark forces experimentally? The most direct and convincing evidence would be to produce and detect dark photons directly in the laboratory, and this is the opportunity afforded by fixed-target and collider experiments. Let us first discuss fixed-target experiments, focusing on the neutrino experiments LSND [13], MiniBooNe [14], and NuMi/ MINOS [15]. The basic experimental setup is as follows: a highintensity proton beam strikes a target of material, producing particles through the strong interactions, e.g. πnmesons, ρnmesons, protons, etc. Some of these particles decay electromagnetically, e.g. π0  γγ, where γ indicates a photon. Because the dark photon V may have a small mixing angle κ with the ordinary photon, particles like the neutral pion may, very rarely, decay to a final state containing a dark photon. For example, one particular production channel may be summarized as

p + A  π0 + X  V + γ + X.


However, if the dark photon is rather light, with a mass less than twice the mass of the proton, mV < 2mp , conservation of energy forbids the decay of V  p+ + pn. Thus, the production of cosmic ray protons and antiprotons via dark matter annihilation is negligible provided the dark force carrier is light, mV