Thomas Mehen

Space–time noncommutative field theories and unitarity

Abstract We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space–time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This can be understood from string theory, since space noncommutative field theories describe a low energy limit of string theory in a background magnetic field. On the other hand, there is no regime in which space–time noncommutative field theory is an appropriate description of string theory. Whenever space–time noncommutative field theory becomes relevant massive open string states cannot be neglected.

NNLO corrections to nucleon-nucleon scattering and perturbative pions

Abstract The 1 S 0 , 3 S 1 , and 3 D 1 nucleon–nucleon scattering phase shifts are calculated at next-to-next-to-leading order (NNLO) in an effective field theory. Predictions for the 1 P 1 , 3 P 0,1,2 , 1 D 2 , and 3 D 2,3 phase shifts at this order are also compared with data. The calculations treat pions perturbatively and include the NNLO contributions from order Q r 3 and Q r 4 radiation pion graphs. In the 3 S 1 , 3 D 1 and 3 P 0,2 channels we find large disagreement with the Nijmegen partial-wave analysis at NNLO. These spin triplet channels have large corrections from graphs with two potential pion exchange which do not vanish in the chiral limit. We compare our results to calculations within the Weinberg approach, and find that in some spin triplet channels the summation of potential pion diagrams seems to be necessary to reproduce the observed phase shifts. In the spin singlet channels the nonperturbative treatment of potential pions does not afford a significant improvement over the perturbative approach.

Conformal invariance for non-relativistic field theory

Abstract Momentum space Ward identities are derived for the amputated n-point Greens functions in 3+1 dimensional non-relativistic conformal field theory. For n=4 and 6 the implications for scattering amplitudes (i.e. on-shell amputated Greens functions) are considered. Any scale invariant 2-to-2 scattering amplitude is also conformally invariant. However, conformal invariance imposes constraints on off-shell Greens functions and the three particle scattering amplitude which are not automatically satisfied if they are scale invariant. As an explicit example of a conformally invariant theory we consider non-relativistic particles in the infinite scattering length limit.

Reparameterization Invariance for Collinear Operators

We discuss restrictions on operators in the soft-collinear effective theory (SCET) which follow from the ambiguity in the decomposition of collinear momenta and the freedom in the choice of light-like basis vectors n and n. Invariance of SCET under small changes in n and/or n implies a symmetry of the effective theory that constrains the form of allowed operators with collinear fields. The restrictions occur at a given order in the power counting as well as between different orders. As an example, we present the complete set of higher order operators that are related to the collinear quark kinetic term.

Pion interactions in the X 3872

We consider pion interactions in an effective field theory of the narrow resonance X(3872), assuming it is a weakly bound molecule of the charm mesons D{sup 0}D*{sup 0} and D*{sup 0}D{sup 0}. Since the hyperfine splitting of the D{sup 0} and D*{sup 0} is only 7 MeV greater than the neutral pion mass, pions can be produced near threshold and are nonrelativistic. We show that pion exchange can be treated in perturbation theory and calculate the next-to-leading-order correction to the partial decay width {gamma}[X{yields}D{sup 0}D{sup 0}{pi}{sup 0}].

Range corrections to doublet S-wave neutron–deuteron scattering

Abstract We calculate the range corrections to S-wave neutron–deuteron scattering in the doublet channel ( S =1/2) to first order in r / a where a is the scattering length and r the effective range. Ultraviolet divergences appearing at this order can be absorbed into a redefinition of the leading order three-body force. The corrections to the elastic scattering amplitude below the deuteron breakup threshold are computed. Inclusion of the range corrections gives good agreement with measured scattering data and potential model calculations.

Noncommutative gauge dynamics from the string worldsheet

We show how string theory can be used to reproduce the one-loop two-point photon amplitude in non-commutative U(1) gauge theory. Using a simple realization of the gauge theory in bosonic string theory, we extract from a string cylinder computation in the decoupling limit the exact one loop field theory result. The result is obtained entirely from the region of moduli space where massless open strings dominate. Our computation indicates that the unusual IR/UV singularities of non-commutative field theory do not come from closed string modes in any simple way.

Dilute Bose-Einstein condensate with large scattering length.

We study a dilute Bose gas of atoms whose scattering length a is large compared to the range of their interaction. We calculate the energy density E of a homogeneous Bose-Einstein condensate (BEC) to second order in the low-density expansion, expressing it in terms of a and a second parameter Lambda* that determines the low-energy observables in the three-body sector. The second-order correction to E has a small imaginary part that reflects the instability due to three-body recombination. In the case of a trapped BEC with large negative a, we calculate the coefficient of the three-body mean-field term in E in terms of a and Lambda*. It can be very large if there is an Efimov state near threshold.

Chiral Lagrangian with Heavy Quark-Diquark Symmetry

We construct a chiral Lagrangian for doubly heavy baryons and heavy mesons that is invariant under heavy quark-diquark symmetry at leading order and includes the leading O(1/mQ) symmetry violating operators. The theory is used to predict the electromagnetic decay width of the J = 3 member of the ground state doubly heavy baryon doublet. Numerical estimates are provided for doubly charm baryons. We also calculate chiral corrections to doubly heavy baryon masses and strong decay widths of low lying excited doubly heavy baryons.

Wigner symmetry in the limit of large scattering lengths

We note that, in the limit where the NN {sup 1}S{sub 0} and {sup 3}S{sub 1} scattering lengths, a{sup ({sup 1}S{sub 0})} and a{sup ({sup 3}S{sub 1})} , go to infinity, the leading terms in the effective field theory for strong NN interactions are invariant under Wigner`s SU(4) spin-isospin symmetry. This explains why the leading effects of radiation pions on the S -wave NN scattering amplitudes vanish as a{sup ({sup 1}S{sub 0})} and a{sup ({sup 3}S{sub 1})} go to infinity. The implications of Wigner symmetry for NN{r_arrow}NN axion and {gamma}d{r_arrow}np are also considered. {copyright} {ital 1999} {ital The American Physical Society}