Last Update:

Oct 2014

Copyright © 2014 Howard Trottier

**Trottier's Research Interests Page**

My research has been centered on studies of lattice Quantum Chromodynamics (QCD), including high precision determinations of the parameters of the standard model, and the spectra and matrix elements of hadrons with one or more heavy quarks. I am also trying to climb the equally technical learning curve on QCD corrections in jet physics and standard model processes at the LHC.

QCD is the theory of the strong interactions between quarks and gluons, the constituents of the proton and other hadronic (strongly-interacting) particles. The lattice formulation of QCD due to Wilson provides a discrete approximation to the theory, defined on a finite grid of space-time points, which is suitable for numerical simulations. However, lattice QCD is far more than a numerical trick: it is an explicit (and gauge-invariant!) realization of Wilson's general concept of an effective field theory, which allows one to systematically account for physics that lies beyond a necessary (or convenient) cutoff.

In the case of lattice QCD, Wilson's approach allows one to systematically account for the effects of high-energy states which are excluded by the lattice grid. Lattice QCD simulations thereby provide a first-principles approach to the determination of many hadronic quantities, where one has control over all of the systematic uncertainties. An effective field theory analysis is crucial to obtaining accurate results on lattices with an affordable grid spacing.

Much of the work that I do is as a member of the HPQCD Collaboration, and I have co-authored papers with Christine Davies (Glasgow), Ron Horgan (Cambridge), Kent Hornbostel (SMU), Peter Lepage (Cornell), Junko Shigemitsu (Ohio State), Richard Woloshyn (TRIUMF), and with members of the Fermilab Lattice Collaboration (Aida El-Khadra, Andreas Kronfeld, and Paul Mackenzie).

A principal goal of the HPQCD and Fermilab collaborations is the determination of hadronic matrix elements that are required as input in order to extract values of the so-called CKM quark-mixing matrix from experimental measurements. We are also calculating the spectra and transition rates of many hadronic states, to an unprecedented precision of a few percent, in order to demonstrate the reliability of this approach by comparison with a wealth of existing experimental data.

The work of our collaboration was featured as the *New Scientist* cover story for the Aug. 13 2005 edition, and I am quoted a couple of times in the article. Click the image to go to the on-line listing for this edition (click here to jump directly to the on-line listing for the article). The article was about a key period in the work by the HPQCD, Fermilab and MILC collaborations, in which we were racing to predict the decay constant of the D meson before the CLEOc experiment released the results of its measurement: our prediction came out just days ahead, and was subsequently confirmed by the experiment.

My most important contributions to this program have been in the development and use of aggressive analytical techniques for the higher-order perturbative matching calculations that are needed in the Wilsonian effective field theory framework. This work has resulted in recent high-precision determinations of fundamental parameters of the standard model, including the strong coupling and quark masses, which have the smallest quoted errors of any approach.

I have worked on both analytical and numerical aspects of lattice QCD. My analytical work (with computer algebra assist) includes next-to-next-to leading order (NNLO, or two-loop) perturbation theory on both the lattice and the continuum sides of the effective field theory matching. I have also done alot of Monte Carlo simulations of various aspects of QCD, including simulations of physical quantities in heavy quark systems, qualitative studies of confinement, and the use of non-perturbative simulations in the weakly coupled phase of the theory to extract short-distance expansions relevant to the perturbative matching program.