1,076 research outputs found
Solvable non-Markovian dynamic network
Non-Markovian processes are widespread in natural and human-made systems, yet explicit modeling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy-tailed Mittag-Leffler distribution for the interevent times. We derive an analytically and computationally tractable system of Kolmogorov-like forward equations utilizing the Caputo derivative for the probability of having a given number of active links in the network and solve them. Simulations for the RLAD are also studied for power-law interevent times and we show excellent agreement with the Mittag-Leffler model. This agreement holds even when the RLAD network dynamics is coupled with the susceptible-infected-susceptible spreading dynamics. Thus, the analytically solvable Mittag-Leffler model provides an excellent approximation to the case when the network dynamics is characterized by power-law-distributed interevent times. We further discuss possible generalizations of our result
Loops in Twistor Space
We elucidate the one-loop twistor-space structure corresponding to
momentum-space MHV diagrams. We also discuss the infrared divergences, and
argue that only a limited set of MHV diagrams contain them. We show how to
introduce a twistor-space regulator corresponding to dimensional regularization
for the infrared-divergent diagrams. We also evaluate explicitly the
`holomorphic anomaly' pointed out by Cachazo, Svrcek, and Witten, and use the
result to define modified differential operators which can be used to probe the
twistor-space structure of one-loop amplitudes.Comment: 21 pages, TeX. v3. missing citations added. v4. subtlety with the i
\epsilon prescription clarifie
Scattering amplitudes with massive fermions using BCFW recursion
We study the QCD scattering amplitudes for \bar{q}q \to gg and \bar{q}q \to
ggg where q is a massive fermion. Using a particular choice of massive fermion
spinor we are able to derive very compact expressions for the partial spin
amplitudes for the 2 \to 2 process. We then investigate the corresponding 2 \to
3 amplitudes using the BCFW recursion technique. For the helicity conserving
partial amplitudes we again derive very compact expressions, but were unable to
treat the helicity-flip amplitudes recursively, except for the case where all
the gluon helicities are the same. We therefore evaluate the remaining partial
amplitudes using standard Feynman diagram techniques.Comment: 21 page
Gluon Scattering Amplitudes in Finite Temperature Gauge/Gravity Dualities
We examine the gluon scattering amplitude in N=4 super Yang-Mills at finite
temperature with nonzero R-charge densities, and in Non-Commutative gauge
theory at finite temperature. The gluon scattering amplitude is defined as a
light-like Wilson loop which lives at the horizon of the T-dual black holes of
the backgrounds we consider. We study in detail a special amplitude, which
corresponds to forward scattering of a low energy gluon off a high energy one.
For this kinematic configuration in the considered backgrounds, we find the
corresponding minimal surface which is directly related to the gluon scattering
amplitude. We find that for increasing the chemical potential or the
non-commutative parameter, the on-shell action corresponding to our Wilson loop
in the T-dual space decreases. For all of our solutions the length of the short
side of the Wilson loop is constrained by an upper bound which depends on the
temperature, the R-charge density and the non-commutative parameter. Due to
this constraint, in the limit of zeroth temperature our approach breaks down
since the upper bound goes to zero, while by keeping the temperature finite and
letting the chemical potential or the non-commutative parameter to approach to
zero the limit is smooth.Comment: 30 pages, 16 figures, minor corrections (plus improved numerical
computation for the non-commutative case
Comments on MHV Tree Amplitudes for Conformal Supergravitons from Topological B-Model
We use the twistor-string theory on the B-model of CP^{3|4} to compute the
maximally helicity violating(MHV) tree amplitudes for conformal supergravitons.
The correlator of a bilinear in the affine Kac-Moody current(Sugawara
stress-energy tensor) can generate these amplitudes. We compare with previous
results from open string version of twistor-string theory. We also compute the
MHV tree amplitudes for both gravitons and gluons from the correlators between
stress-energy tensor and current.Comment: 27p
Recommended from our members
Seismic retrofitting and health monitoring of school buildings of Cyprus
The vulnerability of existing buildings to seismic forces and their retrofitting is an international problem. The majority of structures in seismic-prone areas worldwide are structures that have been designed either without the consideration of seismic forces, or with previous codes of practice specifying lower levels of seismic forces. In Cyprus, after the three earthquakes that occurred in 1995, 1996, and 1999, the Cyprus State, acting in a pioneering way internationally, has decided the seismic retrofitting of all school buildings, taking into account the sensitivity of the society towards these structures, which house the future generation of the society. In this paper the overall assessment methodology is presented, along with details of the over 10 year ongoing retrofitting program of the school buildings of Cyprus, with emphasis on the description of the program and the development of a wireless monitoring system. In addition, mathematical models of selected school buildings are presented and comparison is made with in-situ measurement
MHV-Vertices for Gravity Amplitudes
We obtain a CSW-style formalism for calculating graviton scattering
amplitudes and prove its validity through the use of a special type of
BCFW-like parameter shift. The procedure is illustrated with explicit examples.Comment: 21 pages, minor typos corrected, proof added in section
Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory
We present the two-loop QCD helicity amplitudes for quark-quark and
quark-antiquark scattering. These amplitudes are relevant for
next-to-next-to-leading order corrections to (polarized) jet production at
hadron colliders. We give the results in the `t Hooft-Veltman and
four-dimensional helicity (FDH) variants of dimensional regularization and
present the scheme dependence of the results. We verify that the finite
remainder, after subtracting the divergences using Catani's formula, are in
agreement with previous results. We also provide the amplitudes for
gluino-gluino scattering in pure N=1 supersymmetric Yang-Mills theory. We
describe ambiguities in continuing the Dirac algebra to D dimensions, including
ones which violate fermion helicity conservation. The finite remainders after
subtracting the divergences using Catani's formula, which enter into physical
quantities, are free of these ambiguities. We show that in the FDH scheme, for
gluino-gluino scattering, the finite remainders satisfy the expected
supersymmetry Ward identities.Comment: arXiv admin note: substantial text overlap with arXiv:hep-ph/030416
MHV Vertices and Scattering Amplitudes in Gauge Theory
The generic googly amplitudes in gauge theory are computed by using the
Cachazo-Svrcek-Witten approach to perturbative calculation in gauge theory and
the results are in agreement with the previously well-known ones. Within this
approach we also discuss the parity transformation, charge conjugation and the
dual Ward identity. We also extend this calculation to include fermions and the
googly amplitudes with a single quark-anti-quark pair are obtained correctly
from fermionic MHV vertices. At the end we briefly discuss the possible
extension of this approach to gravity.Comment: Latex file, 38 pages, 15 figures; v2, minor changes, references
added; v2, minor changes, 2 references adde
MHV Vertices and Fermionic Scattering Amplitudes in Gauge Theory with Quarks and Gluinos
The Cachazo-Svrcek-Witten approach to perturbative gauge theory is extended
to gauge theories with quarks and gluinos. All googly amplitudes with
quark-antiquark pairs and gluinos are computed and shown to agree with the
previously known results. The computations of the non-MHV or non-googly
amplitudes are also briefly discussed, in particular the purely fermionic
amplitude with 3 quark-antiquark pairs.Comment: 41 pages, 21 figures; v2, minor changes, references added;v3, 2
important additions, references adde
- …