124 research outputs found
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 MeV. Including pions
perturbatively significantly improves the agreement with data for momenta up to
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 -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 (), 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
channel. Between the low-energy NN observables we have examined, the
mixing parameter of the states is the most sensible to the scale.
The scheme is renormalization group invariant for .Comment: 16 pages, 4 eps figures, to appear in Nuclear Physics
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