**ABOUT RESEARCH-INTERESTS TEACHING PUBLICATIONS OUTREACH AWARDS PAST-STUDENTS**

Research Interests

My theoretical research is on extensions of the standard model of particle physics. Here, I will describe two programs that I have been involved with as illustrations.

The Standard Model of particle physics has been developed over the past couple of decades to address the fundamental questions: what is our universe made of and what holds its constituents together? Within this model, the basic building blocks of nature (the elementary particles) are of two kinds: (1) matter particles called quarks (which make up protons and neutrons and hence most of the ordinary matter) and leptons (such as the electron) and (2) force carriers which mediate interactions between the matter particles, namely, the electromagnetic force (ordinary light); the weak force (which appears in radioactivity); and the strong force (which is involved in nuclear reactions). In addition, there is the force of gravity which is responsible for holding us to the earth and, in turn, the earth to the Sun.

However, in spite of its success in describing the observed interactions of elementary particles, the Standard Model is an incomplete theory since it leaves many questions unanswered. For example, why is there such a big hierarchy of quark and lepton masses (the electron is a million times lighter than the top quark, which is the heaviest known quark)? Or, why are the strengths of the various forces so disparate?

Specifically, the mass of carriers of the weak force is about 10,000 trillion times smaller than the mass scale of gravity (which is known as the Planck scale). Such a huge hierarchy in mass scales is required in order to account for the feebleness of gravity compared with the other forces. Another mystery is that most of matter in the universe seems to be ``dark'', i.e., it is not made of ordinary matter.

In 1999, Lisa Randall and Raman Sundrum proposed a novel extension of the Standard Model to solve the Planck-weak mass scale hierarchy problem. Their set-up is based on warped 5th dimension, where the mass scales at the two ends of the extra dimension are vastly different due to the presence of the curvature in the extra dimension. So, if the gravitational physics resides at one end of the extra dimension, whereas the physics of weak force occupies the other end, then it is natural for the mass scales of gravity and the weak force to be hierarchical. It was also realized that profiles for quarks and leptons in the same extra dimension can account for the hierarchies in their masses. Thus, the upshot is that there is a geometrical origin for all hierarchies of Standard Model: the Planck-weak mass scales and that of quark and lepton masses.

Over the past decade, I have been involved in detailed studies of various aspects of this Randall-Sundrum model. In this model, there are excitations of the Standard Model particles in the 5th dimension which are called Kaluza-Klein particles.

I have discovered mechanisms (within this framework) whereby masses of these Kaluza-Klein particles as small as a 1000 times the mass of the proton can satisfy the constraints from their indirect effects on currently measured properties of standard model particles, whereas previous models required these masses to be much larger for this consistency. I also showed that these particles might then be directly accessible to an ongoing high energy experiment known as the large hadron collider in Europe. Moreover, indirect effects of these new particles will be seen in ongoing/planned experiments probing further the properties of the quarks and leptons.

One of the holy grails of particle physics is grand unification which is the idea that the 3 forces (other than gravity) are different aspects of the same interaction. As mentioned above, the strengths of the 3 forces are observed to be quite different when measured at low energies, but these strengths evolve as we go to higher energies so that it is possible that the strengths are the same at some very high energy scale. However, in the Standard Model, such a unification of the 3 forces does not occur.

We demonstrated that in the Randall-Sundrum model the evolution of the strengths of these forces is modified relative to that in the Standard Model due to profiles for quarks and leptons in the 5th dimension, resulting in a precise meeting of the strengths of the forces (see Figure below). In addition, the above grand unified model has a particle which can play the role of dark matter of the universe, with good prospects to be seen in ongoing direct searches for dark matter. Thus, my work has shown that the framework of a warped extra dimension solves all the above-mentioned puzzles of the Standard Model. Moreover, these ideas will soon be tested.

Evolution of the strengths of the 3 forces in the (non-supersymmetric) warped extra dimensional model with energy.

Last, but not the least, a fascinating aspect of this research program is that these warped extra dimensional models provide a weakly-coupled dual description of some new (purely) four-dimensional strongly-coupled dynamics, of which the standard model Higgs boson is a composite. In fact, the tower of KK particles arising from the warped extra dimension (which was alluded to above) corresponds to a similar one of composite/bound states in the four-dimensional theory. This general idea of a composite Higgs boson (in four dimensions) has been around since the 1908’s, but the newer, warped realizations are in a sense more compelling. Thus, my work here has led to a resurgence of interest in this older paradigm.

More recently, I am engaged (as follows) in studying collider signals of particle physics candidates for dark matter (DM). Part of my work is an example of thinking "outside the box" (in this area of research) and thus has the potential to significantly impact the development of strategies for searching for DM at colliders.

As alluded to above, by now there is ample evidence for the presence of a DM component in the energy/mass budget of the universe. A stable weakly interacting massive particle (WIMP) – with a mass also of order the weak scale – is a well-motivated candidate for this DM since it approximately has the correct relic density upon thermal freeze-out. Such a particle also often arises in extensions of the standard model (SM) of particle physics, especially those motivated by solutions to the Planck-weak hierarchy problem of the SM. Finally, if the WIMP is a part of an extension of the SM, then it is likely to have (weak) interactions with SM particles. Hence, the WIMP paradigm can be tested via non-gravitational methods, for example, direct/indirect detection of cosmic DM or production of the DM at colliders. In particular, the collider searches of the DM paradigm typically involves producing a heavier particle charged under the same symmetry which stabilizes the DM. Such a “mother” particle must decay to DM, manifesting as missing energy, along with a SM final state. A tremendous amount of effort has been put-in into such a research program, especially at the LHC. Most of this work has been for models in which a Z_2/parity symmetry stabilizes the DM (henceforth called Z_2 models). This is partly because there are several models with such a symmetry. However, while Z_2 might be the simplest possibility for such a symmetry, it is by no means the only one. So, my collaborators and I have initiated the program of instead determining the DM stabilization symmetry from collider data. For simplicity and definiteness, we focused on how to distinguish a Z_3 DM stabilization symmetry from a Z_2 model. The basic idea behind distinguishing Z_3 from Z_2 models is that a single mother charged under a Z_3 symmetry can decay into one or two DM candidates. This is to be contrasted with the fact that mother particles charged under a Z_2 symmetry have only one DM candidate in the final state. Our work has involved showing (in general) how this new aspect of Z_3 models modifies (relative to the "standard" paradigm of Z_2 symmetry) various features of (standard) collider observables that are used in this program of piecing together the elements of the DM model.

Our group is also developing new techniques for measurement of masses of new particles which decay into DM, plus SM, in fact exhibiting a remarkable twist in this paradigm. Instead of the usual approach of employing Lorentz-invariant observables for this purpose, the idea is to use distribution of energy (i.e., a Lorentz-variant quantity) of the SM particles: the crucial point being that the location of the peak in such a distribution can be invariant under boost distributions of the decaying particle. Consequently, in these techniques, there is no need to measure the missing energy in an event (unlike some techniques proposed previously). Thus, such ideas can be very complementary to existing methods.