100 research outputs found
Amplitude Bootstrap in (Anti) de Sitter Space And The Four-Point Graviton from Double Copy
We propose studying a new representation of amputated Anti de Sitter (AdS)
amplitude in Mellin Momentum space, where it encodes all the dynamical
information in Cosmological Correlators. At tree level, we demonstrate that
this amplitude has a similar analytic structure as the S-matrix, with residues
of poles made up of on-shell lower-point amplitudes. We use this structure to
bootstrap 4-point scalar amplitudes with spin-1 and spin-2 exchange. In the
second part of the paper, we use double copy to construct the 4-point graviton
amplitude in general dimension. This leads us to a novel, concise formula that
exhibits the flat space structure. We also verified this formula for the case
when d=3 with literature.Comment: v3: the double copy proposal improved, with new graviton dilaton
interaction predicte
Bootstrapping Witten diagrams via differential representation in Mellin space
We explore the use of the differential representation of AdS amplitudes to compute Witten diagrams. The differential representation expresses AdS amplitudes in terms of conformal generators acting on contact Witten diagrams, which allows us to construct differential equations for Witten diagrams. These differential equations can then be transformed into difference equations in Mellin space, which can be solved recursively. Using this method, we efficiently re-computed scalar four-point amplitudes and obtained new results for scalar six-point amplitudes mediated by gluons and scalars, as well as two examples of scalar eight-point amplitudes from gluon exchange
Color/kinematics duality in AdS4
In flat space, the color/kinematics duality states that perturbative Yang-Mills amplitudes can be written in such a way that kinematic numerators obey the same Jacobi relations as their color factors. This remarkable duality implies BCJ relations for Yang-Mills amplitudes and underlies the double copy to gravitational amplitudes. In this paper, we find analogous relations for Yang-Mills amplitudes in AdS4. In particular we show that the kinematic numerators of 4-point Yang-Mills amplitudes computed via Witten diagrams in momentum space enjoy a generalised gauge symmetry which can be used to enforce the kinematic Jacobi relation away from the flat space limit, and we derive deformed BCJ relations which reduce to the standard ones in the flat space limit. We illustrate these results using compact new expressions for 4-point Yang-Mills amplitudes in AdS4 and their kinematic numerators in terms of spinors. We also spell out the relation to 3d conformal correlators in momentum space, and speculate on the double copy to graviton amplitudes in AdS4
Stability analysis of the Eulerian-Lagrangian finite volume methods for nonlinear hyperbolic equations in one space dimension
In this paper, we construct a novel Eulerian-Lagrangian finite volume (ELFV)
method for nonlinear scalar hyperbolic equations in one space dimension. It is
well known that the exact solutions to such problems may contain shocks though
the initial conditions are smooth, and direct numerical methods may suffer from
restricted time step sizes. To relieve the restriction, we propose an ELFV
method, where the space-time domain was separated by the partition lines
originated from the cell interfaces whose slopes are obtained following the
Rakine-Hugoniot junmp condition. Unfortunately, to avoid the intersection of
the partition lines, the time step sizes are still limited. To fix this gap, we
detect effective troubled cells (ETCs) and carefully design the influence
region of each ETC, within which the partitioned space-time regions are merged
together to form a new one. Then with the new partition of the space-time
domain, we theoretically prove that the proposed first-order scheme with Euler
forward time discretization is total-variation-diminishing and
maximum-principle-preserving with {at least twice} larger time step constraints
than the classical first order Eulerian method for Burgers' equation. Numerical
experiments verify the optimality of the designed time step sizes.Comment: Submitted to Mathematics of Computatio
Graviton Trispectrum from Gluons
The tree-level wavefunction coefficient for four gravitons in de Sitter space
was recently bootstrapped using the Cosmological Optical Theorem, flat space
limit, and Manifestly Local Test \cite{Bonifacio:2022vwa}. Inspired by the
double copy for scattering amplitudes, we derive a compact new expression for
this quantity starting from the wavefunction coefficient for gluons.Comment: 29 page
The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe
The preponderance of matter over antimatter in the early Universe, the
dynamics of the supernova bursts that produced the heavy elements necessary for
life and whether protons eventually decay --- these mysteries at the forefront
of particle physics and astrophysics are key to understanding the early
evolution of our Universe, its current state and its eventual fate. The
Long-Baseline Neutrino Experiment (LBNE) represents an extensively developed
plan for a world-class experiment dedicated to addressing these questions. LBNE
is conceived around three central components: (1) a new, high-intensity
neutrino source generated from a megawatt-class proton accelerator at Fermi
National Accelerator Laboratory, (2) a near neutrino detector just downstream
of the source, and (3) a massive liquid argon time-projection chamber deployed
as a far detector deep underground at the Sanford Underground Research
Facility. This facility, located at the site of the former Homestake Mine in
Lead, South Dakota, is approximately 1,300 km from the neutrino source at
Fermilab -- a distance (baseline) that delivers optimal sensitivity to neutrino
charge-parity symmetry violation and mass ordering effects. This ambitious yet
cost-effective design incorporates scalability and flexibility and can
accommodate a variety of upgrades and contributions. With its exceptional
combination of experimental configuration, technical capabilities, and
potential for transformative discoveries, LBNE promises to be a vital facility
for the field of particle physics worldwide, providing physicists from around
the globe with opportunities to collaborate in a twenty to thirty year program
of exciting science. In this document we provide a comprehensive overview of
LBNE's scientific objectives, its place in the landscape of neutrino physics
worldwide, the technologies it will incorporate and the capabilities it will
possess.Comment: Major update of previous version. This is the reference document for
LBNE science program and current status. Chapters 1, 3, and 9 provide a
comprehensive overview of LBNE's scientific objectives, its place in the
landscape of neutrino physics worldwide, the technologies it will incorporate
and the capabilities it will possess. 288 pages, 116 figure
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