On Non-Relativistic Conformal Field Theory and Trapped Atoms: Virial Theorems and the State-Operator Correspondence in Three Dimensions

The field theory of nonrelativistic fermions interacting via contact interactions can be used to calculate the properties of few-body systems of cold atoms confined in harmonic traps. The state-operator correspondence of Non-Relativistic Conformal Field Theory (NRCFT) shows that the energy eigenvalues (in oscillator units) of N harmonically trapped fermions can be calculated from the scaling dimensions of N-fermion operators in the NRCFT. They are also in one-to-one correspondence with zero-energy, scale-invariant solutions to the N-body problem in free space. We show that these two mappings of the trapped fermion problem to free space problems are related by an automorphism of the SL(2,R) algebra of the conformal symmetry of fermions at the unitary limit. This automorphism exchanges the internal Hamiltonian of the gas with the trapping potential and hence provides a novel method for deriving virial theorems for trapped Fermi gases at the unitary limit. We also show that the state-operator correspondence can be applied directly in three spatial dimensions by calculating the scaling dimensions of two- and three-fermion operators and finding agreement with known exact results for energy levels of two and three trapped fermions at the unitary limit.Comment: 23 pages, 3 .ps figure

Summing O(β0nαsn+1)O(\beta_0^n \alpha_s^{n+1}) Corrections to Top Quark Decays

Order $\beta_0^n \alpha_s^{n+1}$ QCD corrections to top quark decays into $W^+$ and $H^+$ bosons are computed to all orders in perturbation theory. Predictions for the radiative corrections to the top quark width are compared with the estimates from BLM scale setting procedures. The results of the summation are shown to greatly improve understanding of higher order corrections in the limit $m_W,~m_H \to m_t$, where the BLM scale setting method is known to fail. Attempts to reduce nonperturbative error by substituting the running mass for the pole mass in the expression for the decay are shown to fail in the limit $m_W,~m_H \to m_t$ because of subtleties in the treatment of phase space.Comment: 12 pages, Latex, 5 figures. Uses revtex and epsf macro

Charm production asymmetries from heavy-quark recombination

Charm asymmetries in fixed-target hadroproduction experiments are sensitive to power corrections to the QCD factorization theorem for heavy quark production. A power correction called heavy-quark recombination has recently been proposed to explain these asymmetries. In heavy-quark recombination, a light quark or antiquark participates in a hard scattering which produces a charm-anticharm quark pair. The light quark or antiquark emerges from the scattering with small momentum in the rest frame of the charm quark, and together they hadronize into a charm particle. The cross section for this process can be calculated within perturbative QCD up to an overall normalization. Heavy-quark recombination explains the observed D meson and \Lambda_c asymmetries with a minimal set of universal nonperturbative parameters.Comment: 10 pages, LaTeX, 8 figures, talk given at Strange Quark Matter 2003 Conference, Atlantic Beach, North Carolina, Mar 12-17, to be published in J. Phys.

The decay of the X(3872) into \chi_{cJ} and the Operator Product Expansion in XEFT

XEFT is a low energy effective theory for the X(3872) that can be used to systematically analyze the decay and production of the X(3872) meson, assuming that it is a weakly bound state of charmed mesons. In a previous paper, we calculated the decays of X(3872) into \chi_{cJ} plus pions using a two-step procedure in which Heavy Hadron Chiral Perturbation Theory (HH\chiPT) amplitudes are matched onto XEFT operators and then X(3872) decay rates are then calculated using these operators. The procedure leads to IR divergences in the three-body decay X(3872) \to \chi_{cJ} \pi \pi when virtual D mesons can go on-shell in tree level HH\chiPT diagrams. In previous work, we regulated these IR divergences with the $D^{*0}$ width. In this work, we carefully analyze X(3872) \to \chi_{cJ} \pi^0 and X(3872) \to \chi_{cJ} \pi \pi using the operator product expansion (OPE) in XEFT. Forward scattering amplitudes in HH\chiPT are matched onto local operators in XEFT, the imaginary parts of which are responsible for the decay of the X(3872). Here we show that the IR divergences are regulated by the binding momentum of the X(3872) rather than the width of the D^{*0} meson. In the OPE, these IR divergences cancel in the calculation of the matching coefficients so the correct predictions for the X(3872) \to \chi_{c1} \pi \pi do not receive enhancements due to the width of the D^{*0}. We give updated predictions for the decay X(3872) \to \chi_{c1} \pi \pi at leading order in XEFT.Comment: 20 pages, 10 figure