3,115 research outputs found
Gauge coupling renormalization in RS1
We compute the 4D low energy effective gauge coupling at one-loop order in
the compact Randall-Sundrum scenario with bulk gauge fields and charged matter,
within controlled approximations. While such computations are subtle, they can
be important for studying phenomenological issues such as grand unification.
Ultraviolet divergences are cut-off using Pauli-Villars regularization so as to
respect 5D gauge and general coordinate invariance. The structure of these
divergences on branes and in the bulk is elucidated by a 5D position-space
analysis. The remaining finite contributions are obtained by a careful analysis
of the Kaluza-Klein spectrum. We comment on the agreement between our results
and expectations based on the AdS/CFT correspondence, in particular logarithmic
sensitivity to the 4D Planck scale.Comment: 17 pages, Latex2e, uses axodraw.sty, new references added. To be
published in Nucl. Phys.
Towers of Gravitational Theories
In this essay we introduce a theoretical framework designed to describe black
hole dynamics. The difficulties in understanding such dynamics stems from the
proliferation of scales involved when one attempts to simultaneously describe
all of the relevant dynamical degrees of freedom. These range from the modes
that describe the black hole horizon, which are responsible for dissipative
effects, to the long wavelength gravitational radiation that drains mechanical
energy from macroscopic black hole bound states. We approach the problem from a
Wilsonian point of view, by building a tower of theories of gravity each of
which is valid at different scales. The methodology leads to multiple new
results in diverse topics including phase transitions of Kaluza-Klein black
holes and the interactions of spinning black hole in non-relativistic orbits.
Moreover, our methods tie together speculative ideas regarding dualities for
black hole horizons to real physical measurements in gravitational wave
detectors.Comment: Awarded second prize for 2006 Gravity Research Foundation essay
contes
Effective Field Theory and Unification in AdS Backgrounds
This work is an extension of our previous work, hep-th/0204160, which showed
how to systematically calculate the high energy evolution of gauge couplings in
compact AdS_5 backgrounds. We first directly compute the one-loop effects of
massive charged scalar fields on the low energy couplings of a gauge theory
propagating in the AdS background. It is found that scalar bulk mass scales
(which generically are of order the Planck scale) enter only logarithmically in
the corrections to the tree-level gauge couplings. As we pointed out
previously, we show that the large logarithms that appear in the AdS one-loop
calculation can be obtained within the confines of an effective field theory,
by running the Planck brane correlator from a high UV matching scale down to
the TeV scale. This result exactly reproduces our previous calculation, which
was based on AdS/CFT duality. We also calculate the effects of scalar fields
satisfying non-trivial boundary conditions (relevant for orbifold breaking of
bulk symmetries) on the running of gauge couplings.Comment: LaTeX, 27 pages; minor typos fixed, comments adde
Regge Poles in High-Energy Electron Scattering
The possibility that the photon is described by a Regge trajectory is considered, and the effect of this assumption on the analysis of electron-pion, electron-nucleon, and electron-helium scattering is examined in some detail. Partial-wave projections for the various amplitudes are made in the annihilation channel, and a multiparticle unitarity condition is formally imposed by use of the N/D matrix formulation. Since the photon does not have a fixed spin of one, the spin matrix structure is considerably more complicated than in the conventional theory. The amplitudes are written in terms of the Regge poles corresponding to the photon, Ï-Ï meson, etc., and the resulting cross sections are given in the interesting high-energy limit. In contrast to the usual analysis, where form factors depend only on the momentum transfer, we find a larger number of independent functions which depend on the energy as well, however, in a characteristic manner. That is, the essential change due to the Regge behavior of the photon is an over-all nonintegral power of the energy occurring in the cross section. The effect of this factor can be experimentally tested and this possibility is discussed
Singularities of Scattering Amplitudes on Unphysical Sheets and Their Interpretation
The analytic structure of two-particle scattering amplitudes on the unphysical sheet of the Riemann surface reached by crossing the two-particle cut is discussed. The singularities of the amplitudes there are shown to be poles and their physical interpretation is studied. The way in which bound states appear on the physical sheet in the Mandelstam representation, both as isolated poles and as cuts, is traced in detail. The properties of partial wave amplitudes and of the full amplitude as a function of energy and angle and of energy and momentum transfer are discussed. Finally, a few remarks are made in connection with unstable states
The Lorentz integral transform (LIT) method
The LIT approach is reviewed both for inclusive and exclusive reactions. It
is shown that the method reduces a continuum state problem to a
bound-state-like problem, which then can be solved with typical bound-state
techniques. The LIT approach opens up the possibility to perform ab initio
calculations of reactions also for those particle systems which presently are
out of reach in conventional approaches with explicit calculations of many-body
continuum wave functions. Various LIT applications are discussed ranging from
particle systems with two nucleons up to particle systems with seven nucleons.Comment: Lectures delivered at the 4th DAE-BRNS Workshop on Hadron Physics,
AMU, Aligarh, India, Feb. 18-23, 2008; 23 pages, 16 figure
Systematics of Coupling Flows in AdS Backgrounds
We give an effective field theory derivation, based on the running of Planck
brane gauge correlators, of the large logarithms that arise in the predictions
for low energy gauge couplings in compactified AdS}_5 backgrounds, including
the one-loop effects of bulk scalars, fermions, and gauge bosons. In contrast
to the case of charged scalars coupled to Abelian gauge fields that has been
considered previously in the literature, the one-loop corrections are not
dominated by a single 4D Kaluza-Klein mode. Nevertheless, in the case of gauge
field loops, the amplitudes can be reorganized into a leading logarithmic
contribution that is identical to the running in 4D non-Abelian gauge theory,
and a term which is not logarithmically enhanced and is analogous to a two-loop
effect in 4D. In a warped GUT model broken by the Higgs mechanism in the
bulk,we show that the matching scale that appears in the large logarithms
induced by the non-Abelian gauge fields is m_{XY}^2/k where m_{XY} is the bulk
mass of the XY bosons and k is the AdS curvature. This is in contrast to the UV
scale in the logarithmic contributions of scalars, which is simply the bulk
mass m. Our results are summarized in a set of simple rules that can be applied
to compute the leading logarithmic predictions for coupling constant relations
within a given warped GUT model. We present results for both bulk Higgs and
boundary breaking of the GUT gauge group.Comment: 22 pages, LaTeX, 3 figures. Comments and references adde
Studying High Energy Final State Interactions by N/D Method
We discuss the final state interaction effects at high energies via a
multi-channel N/D method. We find that the 2 by 2 charge--exchange final state
interactions typically contribute an enhancement factor of a few times
in the meson decay amplitudes, both for the real and the
imaginary part. We also make some discussions on the elastic rescattering
effects.Comment: 10 pages, revte
Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory
The leading-order nucleon-nucleon (NN) potential derived from chiral
perturbation theory consists of one-pion exchange plus a short-distance contact
interaction. We show that in the 1S0 and 3S1-3D1 channels renormalization of
the Lippmann-Schwinger equation for this potential can be achieved by
performing one subtraction. This subtraction requires as its only input
knowledge of the NN scattering lengths. This procedure leads to a set of
integral equations for the partial-wave NN t-matrix which give
cutoff-independent results for the corresponding NN phase shifts. This
reformulation of the NN scattering equation offers practical advantages,
because only observable quantities appear in the integral equation. The
scattering equation may then be analytically continued to negative energies,
where information on bound-state energies and wave functions can be extracted.Comment: 16 pages, 11 figure
Phenomenological analysis of the double pion production in nucleon-nucleon collisions up to 2.2 GeV
With an effective Lagrangian approach, we analyze several NN \to NN\pi\pi
channels by including various resonances with mass up to 1.72 GeV. For the
channels with the pion pair of isospin zero, we confirm the dominance of
N*(1440)\to N\sigma in the near threshold region. At higher energies and for
channels with the final pion pair of isospin one, we find large contributions
from N*(1440)\to \Delta\pi, double-Delta, \Delta(1600) \to N*(1440)\pi,
\Delta(1600) \to \Delta\pi and \Delta(1620) \to \Delta\pi. There are also
sizeable contributions from \Delta \to \Delta\pi, \Delta \to N\pi, N \to
\Delta\pi and nucleon pole at energies close to the threshold. We well
reproduce the total cross sections up to beam energies of 2.2 GeV except for
the pp\to pp\pi^0\pi^0 channel at energies around 1.1 GeV and our results agree
with the existing data of differential cross sections of pp \to pp\pi^+\pi^-,
pp \to nn\pi^+\pi^+ and pp \to pp\pi^0\pi^0 which are measured at CELSIUS and
COSY.Comment: 36 pages, 18 figure
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