This page is hopelessly out of date. I plan to fix it some day, for now please look at my Curriculum Vitae for my interests in the last decade.

You can find a list of many of my papers by querying the SPIRES HEP database at SLAC. Most of my recent physics preprints are also available from the the physics e-print server. Some of my earlier papers (not definitive versions: see the printed journals for that) are also available in my directory.

My current academic interests can be roughly divided into five research areas: phenomenology of light hadronic physics, improvement of lattice techniques to reduce discretization and perturbative errors, phenomenology of hadrons containing the b quark, understanding observed quantum systems and applying large scale computation to phylogenetic problems in biology. I end with a short description of what I have been involved with in the past. Recently, in collaboration with Csaba Csáki, Matt Martin, Yuri Shirman, and John Terning, I have also started looking into problems of defining chiral gauge theories, but I do not discuss that here yet: you can read our paper for now.

QCD, the theory of strong
interactions is the current theory explaining the formation
and many of the interactions of hadrons. Because of the extreme strength
of the coupling constant at typical hadronic scales
(10^{-15} meters, 10^{-28} kilograms,
10^{-23} seconds, or 10^{-11} Joules),
perturbative calculations cannot
provide an understanding of the hadronic physics.

Lattice QCD is a technical means of studying the property of this well
defined quantum field theory. Remembering that in QCD
perturbation theory becomes well behaved at small distances and
times (and correspondingly large energies), we discretize the
theory on a space-time lattice with points very close to each
other, a distance (10^{-16} meters or smaller, or
equivalently about 10^{-24} seconds) at which we
understand the theory. If we further make the reasonable
assumption that, as strong interactions do not have long range
forces, distance scales larger than a few times
10^{-15} meters do not affect the physics of hadrons,
the system becomes a collection of large but finite number of
interacting quantum systems, one at each point. Standard quantum
mechanical ideas based on Feynmann path integrals in Euclidean
space then allow us to calculate the properties of the
hadrons.

The gauge sector of the theory contains only one parameter which represents the `range' or `strength' (the two turn out to be related) of the QCD interactions. In addition, the weak interactions (which also couples to the matter sector of QCD) generates six `mass' parameters, three of which are almost irrelevant to light quark physics. Two of the remaining mass parameters (the so-called `up' and `down' quark current masses) can be effectively treated as being equal: the difference between them being of the same order of magnitude as the effects of the ignored electro-magnetic interactions. Thus, one expects that all properties of the spectrum of the light hadrons, as well as their strong interactions, can be explained in terms of only three parameters: a scale, a common up-down quark mass parameter, and a strange quark mass parameter.

The calculation thus proceeds by fixing these three parameters from the observed spectrum of light hadrons. It is an important consistency check on the method, and the various approximations performed, that three parameters are sufficient to match all of the masses and structure of these hadrons. After verifying this, one can use it to predict the unknown properties of the hadron, and to quantitatively estimate how the strong interactions modify the weak interactions which are responsible for many of the more interesting processes in light hadronic physics.

For the last couple of years, I have been a part of the
Lattice QCD Collaboration at LANL. In
collaboration with Rajan Gupta, Gregory
Kilcup and Stephen
Sharpe, I have been involved in a state-of-the-art evaluation
of hadron matrix elements using lattice QCD. In particular, we
used β=6 quenched Wilson 32^{3} x 64 gauge lattices
and studied the properties of mesons and baryons made of light Wilson
quarks. The final analyses of our results for the spectrum of mesons and
baryons, the decay
constants of the mesons and the weak matrix elements
B_{K}, B_{7}, B_{8}, and
B_{S} are already available. A global
analysis of the light and strange quark
masses using lattice data from various groups (including ours)
has also been completed. In Lattice '97, Rajan Gupta presented a jointly prepared
plenary talk
updating these results. In
Lattice
'95 we presented preliminary results for the form factors for
semi-leptonic and rare decays. The final analysis of these, as
well as new data from runs with tadpole improved clover action, is
currently in progress. In
Lattice '98,
Rajan Gupta presented a
short discussion
of the highlights of the clover data on spectrum, condensates and
B_{K}.

Our main qualitative result is that, as far as the spectrum and decay constants of the light hadrons is concerned, the quenched approximation provides results good to about 10-15% in most quantities. We also observed that detailed tests of the splittings between strange and ordinary hadrons provide evidence for the inadequacy of the quenched approximation. But, the largest surprise was that the quark mass parameters needed to fit the observed spectrum were in significant disagreement with the results from sum rule calculations.

To study the origin of this discrepancy, in collaboration with Rajan Gupta and Kim Maltman, I am also studying the ambiguities in the determination of light quark masses using the sum-rule techniques. Some results of our investigation are already available, and point to the large uncertainties in the existing analysis.

A significantly lower value of the quark mass is phenomenologically very interesting. A sector of the weak interactions which is very poorly understood shows up in the almost imperceptible violation of a proposed symmetry of nature: the CP symmetry. It has so far been observed only in the decays of K mesons. Strong interactions dictate the mass and the structure of these mesons, and so understanding them is essential to predicting the expected experimental rates. Recent experiments show a significantly higher rate for a certain kind of CP violating processes, those parameterized by the direct CP violation parameter ε'/ε, than was previously expected. Our results indicate very strongly that this is due mainly to the use of incorrect values of the quark mass parameters, and also, to a certain extent, not properly incorporating the strong corrections to the process. A talk presented by my collaborator Rajan Gupta at the Lattice '96 discusses this issue, though the actual results there have been superceded by our later papers. Currently, we are engaged in calculations to make the lattice estimates, both of the quark masses and of QCD corrections to these CP violating processes, more precise and reliable.

Since the phenomenon of CP violation is so important to understanding the
nature of the standard model, we have now begun a detailed study of this
process. Preliminary analyses of some of the matrix elements relevant
to direct CP violation were
presented at Lattice 2001. Recently, we
have started a project to estimate the quenching uncertainty in
B_{K} and other four-fermi weak matrix
elements relevant to ε' and ε. Progress in this enterprise
was presented at
Lattice 2002, and
again at
Lattice 2003.
Preliminary results indicate that the perturbative uncertainty in the
analysis is small if an improved staggerred formulation called HYP is
used to discretize the fermions on the space-time lattice, and quenching
uncertainties are rather large, as previously anticipated in theoretical
work by Golterman and
Pallante.

One of the important steps in reducing these uncertainties is to reduce the effect of the discretization. Even though at the scale we are working, the QCD interactions are quite perturbative, the uncertainty in the extrapolation and matching to the `continuum' theory result in a significant part of our final errors.

Currently, in collaboration with Shailesh Chandrasekharan, Rajan Gupta, Weonjong Lee and Stephen Sharpe, I am involved in the non-perturbative calculation of the renormalization constants (and improvement coefficients) necessary to relate the lattice quantities to the continuum. A vast majority of these quantities can be calculated solely from the imposition of axial and vector Ward identities; a paper describing this method for the quenched theory, and some preliminary calculations is available (a preliminary analysis was presented at Lattice '98). A discussion of the efficacy of this method and comparison between the results from various groups, and with perturbation theory, was presented at Lattice '99; a detailed paper describing these issues supplemented with a scaling study was published, and later work by other authors was briefly commented on in Lattice 2000. In Lattice 2001, this was supplemented with a semi-quantitative analysis.

Rajan Gupta, Weonjong Lee, Stephen Sharpe, and I have managed to extend this method to the fully unquenched case for more than two flavours: a preliminary account was first presented at Lattice '99. Subsequent work updating and correcting this was carried out, with Jackson M.S. Wu joining our team, and presented at Lattice 2003. Details will be forthcoming.

For the quantites whose definition depends on the renormalization scheme and scale, the Ward identity method is not sufficient. These quantities can be evaluated by studying the behaviour of the matrix elements of the operators between quark states at high momenta in a fixed gauge. Preliminary results from calculations using this method were presented at Lattice 2000. In Lattice 2001, we demonstrated that all but one of these quantities can be obtained by this method. A paper describing the details is in preparation.

In collaboration with Rajan Gupta and Weonjong Lee I am studying a new gauge action. This work follows previous work by others aimed at determining the asymptotic form of the renormalization group trajectory (called classically perfect action). We study a sqrt(3) renormalization group transformation which has been studied numerically before, and determine the classical perfect action following from it. Preliminary results for this were presented at Lattice '99.

The other area of active experimental work is studying hadrons
containing the b quark. Such hadrons are five
to ten times heavier than the light hadrons, and due to the mass energy
equivalence of relativity and the quantum mechanical
uncertainty principles, cannot be studied on lattices as coarse as
ours. As the size of the heavy light hadrons are still typically
about 10^{-15} meters, we do need to study them in a box
a few times that size wide. Reducing the lattice spacing to make
these hadrons accessible then increases the number of degrees of
freedom to far beyond what we can currently handle.

A way out of this impasse is provided by treating the heavy
quarks as nonrelativistic systems, which turns out to be a very
good approximation. In collaboration with Arifa Ali
Khan, Sara
Collins, Christine
Davies, Rajan Gupta, Greg
Kilcup, Colin Morningstar, Junko
Shigemitsu, and John Sloan, I am involved in the calculation
of the properties of these heavy-light mesons and baryons. The
data from the first exploratory phase using tadpole improved
clover light fermions and 1/M^{2}
tree-level tadpole-improved NRQCD heavy fermions on 16^{3} x 48
quenched Wilson β=6 gauge lattices is being analyzed right
now. Results on the pseudoscalar decay
constants of heavy light mesons is available. The analysis
of the spectrum of the heavy-light hadrons (B,
B_{s}, S and
P states as well as the baryons containing
one or two heavy quarks) along with a determination of the
b quark mass and HQET parameters is also complete. The
analyses of the heavy-heavy mesons, b quark mass
from these systems, the strong coupling constant, and the spectrum of
hadrons containing both b and c quarks are ongoing. An extremely preliminary
analysis of the B_{c} system was presented at Lattice '96 and updated at Lattice '98.
The extension to other values of the scale (possibly β =
5.8, 6.1) are now needed to demonstrate scaling. Calculation of
matrix elements (e.g. B_{B}) would also
be interesting.

I strongly believe that the underlying dynamics of our world is
quantum in nature: the classical behaviour emerges as such systems get
complicated (An article
written in collaboration with Nikki Cooper
explains my views on quantum mechanics in non-technical terms).
In collaboration
with Salman Habib and Kurt Jacobs, I am
working on understanding the
emergence of these classical properties of a quantum system.
Basically, the problem is that some of the classical properties
are defined in terms of the trajectories of the system. Thus,
for example, the Lyapunov exponents of a system are defined as the
rate of divergence of the nearby trajectories in the long time
limit. The presence of well defined trajectories is however a
classical property: the corresponding quantum system delocalizes
under time evolution. We show how, even in systems which are not
otherwise interacting with their environment, the very process of
continuous observation manages to localize the system
continuously, and we find trajectories emerging in the measurement
record. In fact, if the measurement strength satisfies certain
inequalities, the measurement record is indistinguishable from that
predicted for the corresponding classical system, but driven by a small
amount of noise. We derive these inequalities explicitly for a simple
system: a particle moving in an one-dimensional potential, and find that
these are difficult to violate when the system action is large in
comparision to the quantum scale of 10^{-34} Js. By explicit
simulation, we demonstrate that the Lyapunov exponents measured on the
quantum trajectories are the same as the Lyapunov exponents defined for
the corresponding classical system. An overview of our
results and a detailed
paper are now available; as is a largely non-technical
version.
A related work provides
an example where a `large action' system coupled to a
`small action' one fails to reach classicality; essentially, the large
system gets entangled with, and hence `measures', the small one and, for
some parameter values, even a weak measurement of the large system
ensures a strong measurement of the small one; the analysis was also
extended to a slightly
more interesting domain.

Current atomic optics experiments can study some driven systems whose quantum behaviour is very different from its classical behaviour. One such system called the delta kicked rotor is essentially a free particle which is kicked by turning on an instantaneous sinusoidal potential at regular intervals. Classically, for almost all initial conditions, on average, the kicks feed in energy into the system at a constant rate depending only on the mass and the nature of the kicks. Quantum mechanically, however, this system displays `dynamical localization': asymptotically at large times, the energy approaches a constant. In our recent work, we study how the quantum to classical transition occurs in this case, and point out that the transition is not always a smooth interpolation between the classical and quantum behaviour.

In collaboration with Dan Steck and Hideo Mabuchi, we have also studied how a system in the deep quantum regime can be controlled by manipulating its Hamiltonian based on continuous classical observations. In particular, our preliminary work shows that in idealized simulations it should be possible to cool an atom in an optical cavity to its ground state by this method. Further work is in progress.

The AIDS epidemic is one of the most serious problems of the current times. However, the early history of the causative virus HIV is obscured by the fact that the disease takes about 10 years to manifest itself and the virus was late to be diagnosed. The earliest clear evidence of this virus is from tissue samples of a patient in 1959.

In collaboration with B. Korber of the T-10 group, M. Muldoon of UMIST, Manchester, J. Theiler of the NIS-2 group, A. Lapedes of the T-13 group, R. Gupta of our group, B.H. Hahn and F. Gao of the University of Alabama, Birmingham, and S. Wolinsky of the Northwestern University, Chicago, we did a phylogenetic study on the available genetic data on this virus. Using a maximum likelihood method, we reconstructed the evolutionary history of this virus and tested how well the evolution of this virus has been constant in time. Armed with this evidence, we then proceeded to evaulate the most likely time of the last common ancestor (whether before or after it made its way into humans) to the diverse forms of HIV-1 M group circulating in the human population today. The entire methodology was tested by succesfully reproducing the few historically known points in the tree (the 1959 sequence and the CRF01-AE epidemic in Thailand), so we consider the results reliable. The paper (the link needs subscription) appears in the June 9, 2000 issue (volume 288, number 5472) of Science. The central result is that the last common ancestor of the HIV-1 M group arose around 1931 with a 95% confidence interval that spans 1915 to 1941. An addendum to the paper explaining the technical details is available on the web. In collaboration with Una Smith and Carla Kuiken, I have used the same methods to the Subtype C Epidemic in Ethiopia: this work contains a slightly more detailed explanation of the error model used in the analyses.

The phylogenetic analyses were carried out using a locally developed version of G. Olsen's fastDNAml and DNArates programs. The modifications allowed one to use the REV model instead of the simpler F84 model of base-pair evolution and exploited the power of parallel supercomputers. These modified codes will be made available after they are cleaned up and properly documented, if you want them before that, look at the web site which serves as an addendum to our science paper mentioned above. A paper describing the efficacy of the more complicated model and the program is being prepared.

The same phylogenetic methods will also be used to study other issues dealing with the evolution of HIV and possibly the influenza virus. Plans are also under way to adapt the program to deal with amino acid sequences in proteins rather than base-pairs in nucleic acids.

In addition, along with Karina Yusim and Bette Korber of the T-10 group, Martine Peeters, Éric Delaporte, and Claire Mulanga of the Laboratoire rétrovirus parasites, IRD, Montpellier, Oliver G. Pybus of the Evolutionary Biology Group, Oxford University, Mark Muldoon of UMIST, Manchester, and James Theiler of the NIS-2 group, I have started looking at coalescence theory to understand the growth in HIV infections. The method works on the assumption that the surviving strains of HIV are descendants of a random selection of the strains present at any earlier time, all of which had equal reproductive fitness. Under these assumptions, one can relate the probability of finding descendants of two daughters of the same parent in a random sample from a later time to the history of the population size in the various generations. As our phylogenetic trees, coupled with a molecular clock, give us information about the likely times of the parents of the sequences sampled, we can infer the history of the epidemic. Results from our preliminary analysis (using the program called Genie) were reported by Bette Korber at a Royal Society Meeting and indicate that, at least in the Democratic Republic of Congo, the epidemic did not follow a steady exponential growth; rather there seems to have been an early phase of slow spread and the exponential growth took off later. More work in this direction is in progress.

Along with Brian Gaschen, Karina Yusim, Brian Foley, and Bette Korber of the T-10 group, Jesse Taylor of the mathematics department of University of Arizona, Feng Gao and Beatrice Hahn of the University of Alabama at Birmingham, Barton Haynes of the Duke University AIDS center, and Vladimir Novitsky of Department of Immunology and Infectios Diseases of the Harvard School of Public Health, I have been involved in understanding the implications of the immense diversity of HIV for designing vaccines. In a recent report we argue that evolutionary relationships between viruses may be more important than geographical considerations in designing vaccines. Furthermore, since the virus has been rapidly diversifying for about half of its evolutionary existence, there may be some advantage in considering consensus or reconstructed `best-guess' ancestral sequences as the strain against which immunity would be useful.

In collaboration with Carla Kuiken, Kevin Kunstman, Jennifer Kunstman, Kristina Kommander, Benjamin Good, Satish Pillai, and Steve Wolinsky, I have also investigated the succession of strains that appear in an infected person undergoing anti-retroviral therapy. I shall continue such studies because of their importance in vaccine design: most available strains are from late in infection, whereas vaccines are likely to be most efficacious against early strains. It would also help to know if escape mutants under therapy have reduced fitness so that they tend to revert to ancestral forms.

In the past, I have worked on the Clebsch-Gordon problem in SL(2R) (with D. Basu, as part of my M. Sc. thesis), the phenomenological implications of a micro electron Volt gravitino (the superpartner of the quantum of gravity) (my Ph.D. thesis under P. Roy), the definition of masses and widths of particles near decay threshold (with S. Willenbrock), perturbative calculations in high temperature QCD (with A. Gocksch, C.P. Korthals-Altes, and R.D. Pisarski), the large q expansion of q-state Pott's model (with R. Lacaze and A. Morel) and anti-ferromagnetic Heisenberg model on a stacked triangular lattice (with A. Billoire, R. Lacaze, and Th. Jolicœur). I, along with E. Mottola and S. Catterall, am also interested in studying gravity using dynamical triangulations; and along with S. Habib, in quantum chaotic dynamics. With S. Habib and E. Mottola, I have also studied how neutrino clocks run in curved space times. For amusement, I follow work on the fundamentals of quantum mechanics, entanglement and quantum computation. The links here are to the last long paper in each of these field, you may get more details on me from my Curriculum Vitae. It is also available in postscript, dvi or PDF versions. Only the html version is likely to be up to date.

At a cultural level, I am interested in a variety of topics: but, as my knowledge wouldn't qualify me as even a student of those fields, they do not belong to this page.

Tanmoy Bhattacharya [March 10, 2005]