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^{0} \bar D^{*0} and D^{*0} \bar D^{0}. Since the hyperfine splitting of the D^{0} and D^{*0} is only 7 MeV greater than the neutral pion mass, pions can be produced near threshold and are non-relativistic. 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 \to D^0 \bar D^{0} \pi^0].Comment: 26 pages, 11 figures, revtex4, to appear in Phys. Rev.

The NN scattering 3S1-3D1 mixing angle at NNLO

The 3S1-3D1 mixing angle for nucleon-nucleon scattering, epsilon_1, is calculated to next-to-next-to-leading order in an effective field theory with perturbative pions. Without pions, the low energy theory fits the observed epsilon_1 well for momenta less than $\sim 50$ MeV. Including pions perturbatively significantly improves the agreement with data for momenta up to $\sim 150$ MeV with one less parameter. Furthermore, for these momenta the accuracy of our calculation is similar to an effective field theory calculation in which the pion is treated non-perturbatively. This gives phenomenological support for a perturbative treatment of pions in low energy two-nucleon processes. We explain why it is necessary to perform spin and isospin traces in d dimensions when regulating divergences with dimensional regularization in higher partial wave amplitudes.Comment: 17 pages, journal versio

Towards an explicit expression of the Seiberg-Witten map at all orders

The Seiberg-Witten map links noncommutative gauge theories to ordinary gauge theories, and allows to express the noncommutative variables in terms of the commutative ones. Its explicit form can be found order by order in the noncommutative parameter theta and the gauge potential A by the requirement that gauge orbits are mapped on gauge orbits. This of course leaves ambiguities, corresponding to gauge transformations, and there is an infinity of solutions. Is there one better, clearer than the others ? In the abelian case, we were able to find a solution, linked by a gauge transformation to already known formulas, which has the property of admitting a recursive formulation, uncovering some pattern in the map. In the special case of a pure gauge, both abelian and non-abelian, these expressions can be summed up, and the transformation is expressed using the parametrisation in terms of the gauge group.Comment: 17 pages. Latex, 1 figure. v2: minor changes, published versio

Hadronic Atoms and Effective Interactions

We examine the problem of hadronic atom energy shifts using the technique of effective interactions and demonstrate equivalence with the conventional quantum mechanical approach.Comment: 22 page latex file with 2 figure

Scheming in Dimensional Regularization

We consider the most general loop integral that appears in non-relativistic effective field theories with no light particles. The divergences of this integral are in correspondence with simple poles in the space of complex space-time dimensions. Integrals related to the original integral by subtraction of one or more poles in dimensions other than D=4 lead to nonminimal subtraction schemes. Subtraction of all poles in correspondence with ultraviolet divergences of the loop integral leads naturally to a regularization scheme which is precisely equivalent to cutoff regularization. We therefore recover cutoff regularization from dimensional regularization with a nonminimal subtraction scheme. We then discuss the power-counting for non-relativistic effective field theories which arises in these alternative schemes.Comment: 12 pages, additional text in opening section, version to be published in J. Phys.

Renormalization schemes and the range of two-nucleon effective field theory

The OS and PDS renormalization schemes for the effective field theory with nucleons and pions are investigated. We explain in detail how the renormalization is implemented using local counterterms. Fits to the NN scattering data are performed in the 1S0 and 3S1 channels for different values of mu_R. An error analysis indicates that the range of the theory with perturbative pions is consistent with 500 MeV.Comment: 40 pages, typos corrected, journal version. Discussion of the range in section VII clarified, conclusions unchange

Branes as Stable Holomorphic Line Bundles On the Non-Commutative Torus

It was recently suggested by A. Kapustin that turning on a $B$-field, and allowing some discrepancy between the left and and right-moving complex structures, must induce an identification of B-branes with holomorphic line bundles on a non-commutative complex torus. We translate the stability condition for the branes into this language and identify the stable topological branes with previously proposed non-commutative instanton equations. This involves certain topological identities whose derivation has become familiar in non-commutative field theory. It is crucial for these identities that the instantons are localized. We therefore explore the case of non-constant field strength, whose non-linearities are dealt with thanks to the rank-one Seiberg--Witten map.Comment: 12 pages, LaTe

AdS/CFT duality for non-relativistic field theory

We formulate a correspondence between non-relativistic conformal field theories (NRCFTs) in d-1 spatial dimensions and gravitational theories in AdS_{d+2} backgrounds with one compactified lightlike direction. The breaking of the maximal SO(2,d+1) symmetry of AdS_{d+2} to the non-relativistic conformal group arises from boundary conditions on bulk fields, without the need to introduce non-vacuum sources of energy-momentum. As a check of the proposal, we use the gravitational theory to reproduce the NRCFT state-operator correspondence between scaling dimensions of primary operators and energy eigenstates of the non-relativistic system placed in an external harmonic potential.Comment: 19 pages LaTeX, no figure

Renormalization of the one-pion-exchange interaction

A renormalization scheme for the nucleon-nucleon (NN) interaction based on a subtracted T-matrix equation is proposed and applied to the one-pion-exchange potential supplemented by contact interactions. The singlet and triplet scattering lengths are given to fix the renormalized strengths of the contact interactions. With only one scaling parameter ($\mu$), the results show an overall very good agreement with neutron-proton data, particularly for the observables related to the triplet channel. The agreement is qualitative in the $^1S_0$ channel. Between the low-energy NN observables we have examined, the mixing parameter of the $^3S_1-^3D_1$ states is the most sensible to the scale. The scheme is renormalization group invariant for $\mu\to\infty$.Comment: 16 pages, 4 eps figures, to appear in Nuclear Physics