1,157 research outputs found

### Regularization and renormalization in effective field theories of the nucleon-nucleon interaction

Some form of nonperturbative regularization is necessary if effective field
theory treatments of the NN interaction are to yield finite answers. We discuss
various regularization schemes used in the literature. Two of these methods
involve formally iterating the divergent interaction and then regularizing and
renormalizing the resultant amplitude. Either a (sharp or smooth) cutoff can be
introduced, or dimensional regularization can be applied. We show that these
two methods yield different results after renormalization. Furthermore, if a
cutoff is used, the NN phase shift data cannot be reproduced if the cutoff is
taken to infinity. We also argue that the assumptions which allow the use of
dimensional regularization in perturbative EFT calculations are violated in
this problem. Another possibility is to introduce a regulator into the
potential before iteration and then keep the cutoff parameter finite. We argue
that this does not lead to a systematically-improvable NN interaction.Comment: 5 pages, LaTeX, uses espcrc1.sty, summary of talk given at the 15th
International Conference on Few-Body Problems in Physic

### Electric properties of the Beryllium-11 system in Halo EFT

We compute E1 transitions and electric radii in the Beryllium-11 nucleus
using an effective field theory that exploits the separation of scales in this
halo system. We fix the leading-order parameters of the EFT from measured data
on the 1/2+ and 1/2- levels in Be-11 and the B(E1) strength for the transition
between them. We then obtain predictions for the B(E1) strength for Coulomb
dissociation of the Be-11 nucleus to the continuum. We also compute the charge
radii of the 1/2+ and 1/2- states. Agreement with experiment within the
expected accuracy of a leading-order computation in this EFT is obtained. We
also discuss how next-to-leading-order (NLO) corrections involving both s-wave
and p-wave neutron-Be-10 interactions affect our results, and display the NLO
predictions for quantities which are free of additional short-distance
operators at this order. Information on neutron-Be-10 scattering in the
relevant channels is inferred.Comment: 27 pages, 8 figures, final versio

### The potential of effective field theory in NN scattering

We study an effective field theory of interacting nucleons at distances much
greater than the pion's Compton wavelength. In this regime the NN potential is
conjectured to be the sum of a delta function and its derivatives. The question
we address is whether this sum can be consistently truncated at a given order
in the derivative expansion, and systematically improved by going to higher
orders. Regularizing the Lippmann-Schwinger equation using a cutoff we find
that the cutoff can be taken to infinity only if the effective range is
negative. A positive effective range---which occurs in nature---requires that
the cutoff be kept finite and below the scale of the physics which has been
integrated out, i.e. O(m_\pi). Comparison of cutoff schemes and dimensional
regularization reveals that the physical scattering amplitude is sensitive to
the choice of regulator. Moreover, we show that the presence of some regulator
scale, a feature absent in dimensional regularization, is essential if the
effective field theory of NN scattering is to be useful. We also show that one
can define a procedure where finite cutoff dependence in the scattering
amplitude is removed order by order in the effective potential. However, the
characteristic momentum in the problem is given by the cutoff, and not by the
external momentum. It follows that in the presence of a finite cutoff there is
no small parameter in the effective potential, and consequently no systematic
truncation of the derivative expansion can be made. We conclude that there is
no effective field theory of NN scattering with nucleons alone.Comment: 25 pages LaTeX, 3 figures (uses epsf

### Gauge invariant reduction to the light-front

The problem of constructing gauge invariant currents in terms of light-cone
bound-state wave functions is solved by utilising the gauging of equations
method. In particular, it is shown how to construct perturbative expansions of
the electromagnetic current in the light-cone formalism, such that current
conservation is satisfied at each order of the perturbation theory.Comment: 12 pages, revtex

### Deuteron Matrix Elements in Chiral Effective Theory at Leading Order

We consider matrix elements of two-nucleon operators that arise in chiral
effective theories of the two-nucleon system. Generically, the short-distance
piece of these operators scales as 1/r^n, with r the relative separation of the
two nucleons. We show that, when evaluated between the leading-order wave
functions obtained in this effective theory, these two-nucleon operators are
independent of the cutoff used to renormalize the two-body problem for n=1 and
2. However, for n greater than or equal to 3 general arguments about the
short-distance behavior of the leading-order deuteron wave function show that
the matrix element will diverge.Comment: 7 pages, 5 .eps figure

### Relativistic effects and quasipotential equations

We compare the scattering amplitude resulting from the several quasipotential
equations for scalar particles. We consider the Blankenbecler-Sugar, Spectator,
Thompson, Erkelenz-Holinde and Equal-Time equations, which were solved
numerically without decomposition into partial waves. We analyze both
negative-energy state components of the propagators and retardation effects. We
found that the scattering solutions of the Spectator and the Equal-Time
equations are very close to the nonrelativistic solution even at high energies.
The overall relativistic effect increases with the energy. The width of the
band for the relative uncertainty in the real part of the scattering $T$
matrix, due to different dynamical equations, is largest for
backward-scattering angles where it can be as large as 40%.Comment: Accepted for publication in Phys. Rev.

### Unitarity and the Bethe-Salpeter Equation

We investigate the relation between different three-dimensional reductions of
the Bethe-Salpeter equation and the analytic structure of the resultant
amplitudes in the energy plane. This correlation is studied for both the
$\phi^2\sigma$ interaction Lagrangian and the $\pi N$ system with $s$-, $u$-,
and $t$-channel pole diagrams as driving terms. We observe that the equal-time
equation, which includes some of the three-body unitarity cuts, gives the best
agreement with the Bethe-Salpeter result. This is followed by other 3-D
approximations that have less of the analytic structure.Comment: 17 pages, 8 figures; RevTeX. Version accepted for publication in
Phys. Rev.

### Two-body correlations in Bose condensates

We formulate a method to study two-body correlations in a condensate of N
identical bosons. We use the adiabatic hyperspheric approach and assume a
Faddeev like decomposition of the wave function. We derive for a fixed
hyperradius an integro-differential equation for the angular eigenvalue and
wave function. We discuss properties of the solutions and illustrate with
numerical results. The interaction energy is for N~20 five times smaller than
that of the Gross-Pitaevskii equation

### Parity-violating asymmetry in $\gamma d \to \vec{n}p$ with a pionless effective theory

Nuclear parity violation is studied with polarized neutrons in the
photodisintegration of the deuteron at low energies. A pionless effective field
theory with di-baryon fields is used for the investigation. Hadronic weak
interactions are treated by parity-violating di-baryon-nucleon-nucleon
vertices, which have undetermined coupling contants. A parity-violating
asymmetry in the process is calculated for the incident photon energy up to 30
MeV. If experimental data for the parity-violating asymmetry become available
in the future, we will be able to determine the unknown coupling contants in
the parity-violating vertices.Comment: 4 pages. A contribution to APFB2011, August 22-26, 2011, Seoul, Kore

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