139 research outputs found

### 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 $O(\beta_0^n \alpha_s^{n+1})$ 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

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