Dedication to Nathan Isgur

Nathan passed away in July after a lengthy illness. I am sure most of you are familiar with his many contributions to heavy quark physics and it is certainly fitting that we take a few minutes to honor him at the beginning of this meeting. Actually Nathan's main physics interest was the strong interactions rather than heavy quark physics per se. He was already very well known for work he did with Gabriel Karl and others on the nonrelativistic quark model before the work that he did on heavy quark symmetry and its applications. However, Nathan understood the limitations of the nonrelativistic quark model, and was thrilled that the methods he helped develop allowed one to derive systematically from the theory of the strong interactions many properties of hadrons that contain a heavy quark

Fourth generation bound states

We investigate the spectrum and wave functions of q̅ ′q′ bound states for heavy fourth generation quarks (q′) that have a very small mixing with the three observed generations of standard model quarks. Such bound states come with different color, spin and flavor quantum numbers. Since the fourth generation Yukawa coupling, λ_q′, is large we include all perturbative corrections to the potential between the heavy quark and antiquark of order λ_(q′)^(2)N_c/16π^2 where N_c is the number of colors, as well as relativistic corrections suppressed by (v/c)^2. We find that the lightest fourth generation quark masses for which a bound state exists for color octet states. For the color singlet states, which always have a bound state, we analyze the influence that the Higgs couplings have on the size and binding energy of the bound states

Generalized *-Products, Wilson Lines and the Solution of the Seiberg-Witten Equations

Higher order terms in the effective action of noncommutative gauge theories exhibit generalizations of the *-product (e.g. *' and *-3). These terms do not manifestly respect the noncommutative gauge invariance of the tree level action. In U(1) gauge theories, we note that these generalized *-products occur in the expansion of some quantities that are invariant under noncommutative gauge transformations, but contain an infinite number of powers of the noncommutative gauge field. One example is an open Wilson line. Another is the expression for a commutative field strength tensor in terms of the noncommutative gauge field. Seiberg and Witten derived differential equations that relate commutative and noncommutative gauge transformations, gauge fields and field strengths. In the U(1) case we solve these equations neglecting terms of fourth order in the gauge field but keeping all orders in the noncommutative parameter.Comment: 10 pages, minor changes to text, references adde

Effective Theory and Simple Completions for Neutrino Interactions

We consider all the dimension 6 operators as well as some simple extensions of the standard model that give new contributions to neutrino interactions with matter. Such interactions are usually parametrized by $\epsilon_{\alpha \beta}$, where $\alpha$ and $\beta$ are neutrino flavor indices taking the values $e$, $\mu$ and $\tau$. In the simple models we consider the $\epsilon_{\alpha \beta}$'s are much more constrained than in the operator-based model-independent approach. Typically the $\epsilon_{\alpha \beta}$'s are restricted to be smaller in magnitude than around $10^{-3}$. In some of the leptoquark models, a specific pattern for the leptoquark Yukawa couplings allows the diagonal element $\epsilon_{\tau\tau}$ to be as large as $\sim0.1$, or one of $\epsilon_{ee}$, $\epsilon_{\mu\mu}\sim0.01$. We discuss the interplay between neutrino physics and leptoquark searches at the LHC.Comment: 12 pages, 2 figure