From the Theory Group: Measuring the Masses of Invisible Particles
Astrophysical observations indicate that 80 percent of the mass in the universe is made of a neutral, very weakly interacting type of matter called "dark matter." Dark matter is composed of elementary particles, but these must be of a new type, not found in the Standard Model of particle physics. Many models of dark matter have been proposed. In most of these, dark matter is composed of a heavy, neutral, stable particle that can be produced at colliders of sufficiently high energy. Now the Large Hadron Collider is running at CERN, and this accelerator could well be capable of producing dark matter particles. If researchers can identify the events with dark matter production, we will have a unique opportunity to study the elementary quanta of dark matter in the laboratory.
However, the essential property of dark matter—its weak interaction with ordinary matter—makes its particles difficult to study. Dark matter particles are expected to leave no signals or energy deposits in the detectors at the LHC. If theory holds true, they will be visible only as a missing element in the aftermath of LHC collisions, for example, as events in which the observed particle tracks have unbalanced momentum. Still, we will want to know what the LHC observations can tell us about the missing particles. Is the invisible particle produced in the laboratory the same as that in the dark matter in space? To answer this question, scientists need to measure the properties of the dark matter particle, such as its mass, spin and interaction strengths.
Recently, there has been a great deal of theoretical effort developing tests to explore the nature of dark matter particles at the LHC and at a future linear collider, such as the proposed International Linear Collider. Most of these studies have been performed in the context of a particular model of dark matter (for example, supersymmetry). The methods and results depend on the parameters of the assumed model and its specific particle content. Rarely is it asked how events from the LHC can be analyzed in a generic and model-independent way to give us information on invisible particles.
At first sight, it looks impossible to make generic statements about events at proton colliders such as the LHC. At these colliders, not only do we not observe dark matter particles in the final state, but also we do not know the total momentum of the initial state. The reason for this is that the proton is a composite state—a bag of quarks and gluons—and new particles are produced in the collision of individual quarks and gluons that carry only a fraction of the momentum of the proton. Even worse, most models predict that dark matter particles are produced in pairs, so that each event has two invisible final particles. Typically, the original collision of quarks or gluons is predicted to produce two new heavy particles, also of unknown mass, each of which decays to a dark matter particle plus observable quarks, gluons and leptons.
Nevertheless, it is possible to measure the masses of some particles with invisible decay products very accurately at proton colliders. The CDF and D0 experiments at the Fermilab Tevatron measure the mass of the W boson to an accuracy of 0.05 percent, even though the W boson decays to an electron or muon plus an invisible neutrino. The trick used was to construct an estimate of the mass using only the components of momentum perpendicular, or transverse, to the axis of the incoming proton beams. This quantity, called the "transverse mass," must be less than the W mass. The distribution of values for the transverse mass has a sharp cutoff at the W mass. The precision measurement is made by observing the position of this sharp endpoint of the distribution.
To account for two invisible particles, it is necessary to be even more clever. About ten years ago, Chris Lester and David Summers of Cambridge University suggested a new variable, similar to transverse mass, called MT2. To form this variable, one measures the missing transverse momentum and then considers all possible ways to divide it between the two invisible particles. With the correct definition, one again finds a variable with a sharp endpoint related to the mass of the invisible particle. In the past few years, MT2 has been studied extensively by groups at Cambridge, in Korea, and by me in collaboration with Konstantin Matchev, at the University of Florida, and his student and post doc, Myeonghun Park and Partha Konar. Many wonderful new properties of this variable have been discovered. We have found methods for mass measurement that are model-independent and can be applied to any new physics model.
One of our new ideas is to build two MT2 distributions in the same event. In any proton collider event, there are two directions transverse to the beam axis. We found a way to choose, for each event, a reference direction in this two-dimensional space. With our choice, the distributions of MT2 using momenta parallel and perpedicular to the reference direction have different endpoints. From these two constraints, it is possible to solve for both the mass of the dark matter particle and the mass of the heavier particle of which it is a decay product. This method can always provide an absolute determination of the dark matter particle mass regardless of the complexity of the decay chain that leads to the invisible particle.
Further exploration with MT2 gives a way to measure whether or not the two missing particles in an event are identical. All previous studies have assumed that there is only one dark matter particle, or a particle and antiparticle with identical masses. However, we found that this assumption is unnecessary. By suitable modifications of the existing analysis techniques with MT2 one can test both the number and the type of the missing particles in the observed events.
MT2 can be used for discovery of new physics as well as just for mass determination, just as, for the W boson, the original transverse mass is used not only to measure the mass but to enhance the W signal. Once the LHC indicates the presence of events with missing transverse momentum, we will need to attack these events with all of our tools to understand whether the new invisible particles are particles of dark matter. MT2 can play a crucial role in that investigation.
—K. C. Kong
Dark Matter Particle Spectroscopy at the LHC: Generalizing MT2 to Asymmetric Event Topologies, JHEP 1004:086,2010.
Superpartner mass measurement technique using 1D orthogonal decompositions of the Cambridge transverse mass variable MT2, to be published in Physical Review Letters.