1,526 research outputs found
Fluctuations, Saturation, and Diffractive Excitation in High Energy Collisions
Diffractive excitation is usually described by the Good--Walker formalism for
low masses, and by the triple-Regge formalism for high masses. In the
Good--Walker formalism the cross section is determined by the fluctuations in
the interaction. In this paper we show that by taking the fluctuations in the
BFKL ladder into account, it is possible to describe both low and high mass
excitation by the Good--Walker mechanism. In high energy collisions the
fluctuations are strongly suppressed by saturation, which implies that pomeron
exchange does not factorise between DIS and collisions. The Dipole Cascade
Model reproduces the expected triple-Regge form for the bare pomeron, and the
triple-pomeron coupling is estimated.Comment: 20 pages, 12 figure
Deep Inelastic Scattering in Conformal QCD
We consider the Regge limit of a CFT correlation function of two vector and
two scalar operators, as appropriate to study small-x deep inelastic scattering
in N=4 SYM or in QCD assuming approximate conformal symmetry. After clarifying
the nature of the Regge limit for a CFT correlator, we use its conformal
partial wave expansion to obtain an impact parameter representation encoding
the exchange of a spin j Reggeon for any value of the coupling constant. The
CFT impact parameter space is the three-dimensional hyperbolic space H3, which
is the impact parameter space for high energy scattering in the dual AdS space.
We determine the small-x structure functions associated to the exchange of a
Reggeon. We discuss unitarization from the point of view of scattering in AdS
and comment on the validity of the eikonal approximation.
We then focus on the weak coupling limit of the theory where the amplitude is
dominated by the exchange of the BFKL pomeron. Conformal invariance fixes the
form of the vector impact factor and its decomposition in transverse spin 0 and
spin 2 components. Our formalism reproduces exactly the general results predict
by the Regge theory, both for a scalar target and for gamma*-gamma* scattering.
We compute current impact factors for the specific examples of N=4 SYM and QCD,
obtaining very simple results. In the case of the R-current of N=4 SYM, we show
that the transverse spin 2 component vanishes. We conjecture that the impact
factors of all chiral primary operators of N=4 SYM only have components with 0
transverse spin.Comment: 44+16 pages, 7 figures. Some correction
The Regge Limit for Green Functions in Conformal Field Theory
We define a Regge limit for off-shell Green functions in quantum field
theory, and study it in the particular case of conformal field theories (CFT).
Our limit differs from that defined in arXiv:0801.3002, the latter being only a
particular corner of the Regge regime. By studying the limit for free CFTs, we
are able to reproduce the Low-Nussinov, BFKL approach to the pomeron at weak
coupling. The dominance of Feynman graphs where only two high momentum lines
are exchanged in the t-channel, follows simply from the free field analysis. We
can then define the BFKL kernel in terms of the two point function of a simple
light-like bilocal operator. We also include a brief discussion of the gravity
dual predictions for the Regge limit at strong coupling.Comment: 23 pages 2 figures, v2: Clarification of relation of the Regge limit
defined here and previous work in CFT. Clarification of causal orderings in
the limit. References adde
On the Energy Dependence of the Dipole-Proton Cross Section in Deep Inelastic Scattering
We study the dipole picture of high-energy virtual-photon-proton scattering.
It is shown that different choices for the energy variable in the dipole cross
section used in the literature are not related to each other by simple
arguments equating the typical dipole size and the inverse photon virtuality,
contrary to what is often stated. We argue that the good quality of fits to
structure functions that use Bjorken-x as the energy variable - which is
strictly speaking not justified in the dipole picture - can instead be
understood as a consequence of the sign of scaling violations that occur for
increasing Q^2 at fixed small x. We show that the dipole formula for massless
quarks has the structure of a convolution. From this we obtain derivative
relations between the structure function F_2 at large and small Q^2 and the
dipole-proton cross section at small and large dipole size r, respectively.Comment: 27 page
Non-linear evolution in CCFM: The interplay between coherence and saturation
We solve the CCFM equation numerically in the presence of a boundary
condition which effectively incorporates the non-linear dynamics. We retain the
full dependence of the unintegrated gluon distribution on the coherence scale,
and extract the saturation momentum. The resulting saturation scale is a
function of both rapidity and the coherence momentum. In Deep Inelastic
Scattering this will lead to a dependence of the saturation scale on the photon
virtuality in addition to the usual x-Bjorken dependence. At asymptotic
energies the interplay between the perturbative non-linear physics, and that of
the QCD coherence, leads to an interesting and novel dynamics where the
saturation momentum itself eventually saturates. We also investigate various
implementations of the "non-Sudakov" form factor. It is shown that the
non-linear dynamics leads to almost identical results for different form
factors. Finally, different choices of the scale of the running coupling are
analyzed and implications for the phenomenology are discussed.Comment: 37 pages, 21 figure
Prompt atmospheric neutrino fluxes: perturbative QCD models and nuclear effects
We evaluate the prompt atmospheric neutrino flux at high energies using three
different frameworks for calculating the heavy quark production cross section
in QCD: NLO perturbative QCD, factorization including low-
resummation, and the dipole model including parton saturation. We use QCD
parameters, the value for the charm quark mass and the range for the
factorization and renormalization scales that provide the best description of
the total charm cross section measured at fixed target experiments, at RHIC and
at LHC. Using these parameters we calculate differential cross sections for
charm and bottom production and compare with the latest data on forward charm
meson production from LHCb at TeV and at TeV, finding good agreement
with the data. In addition, we investigate the role of nuclear shadowing by
including nuclear parton distribution functions (PDF) for the target air
nucleus using two different nuclear PDF schemes. Depending on the scheme used,
we find the reduction of the flux due to nuclear effects varies from to
at the highest energies. Finally, we compare our results with the
IceCube limit on the prompt neutrino flux, which is already providing valuable
information about some of the QCD models.Comment: 61 pages, 25 figures, 11 table
Inferring transient dynamics of human populations from matrix non-normality
This is the final version of the article. Available from Springer Verlag via the DOI in this record.In our increasingly unstable and unpredictable world, population dynamics rarely settle uniformly to long-term behaviour. However, projecting period-by-period through the preceding fluctuations is more data-intensive and analytically involved than evaluating at equilibrium. To efficiently model populations and best inform policy, we require pragmatic suggestions as to when it is necessary to incorporate short-term transient dynamics and their effect on eventual projected population size. To estimate this need for matrix population modelling, we adopt a linear algebraic quantity known as non-normality. Matrix non-normality is distinct from normality in the Gaussian sense, and indicates the amplificatory potential of the population projection matrix given a particular population vector. In this paper, we compare and contrast three well-regarded metrics of non-normality, which were calculated for over 1000 age-structured human population projection matrices from 42 European countries in the period 1960 to 2014. Non-normality increased over time, mirroring the indices of transient dynamics that peaked around the millennium. By standardising the matrices to focus on transient dynamics and not changes in the asymptotic growth rate, we show that the damping ratio is an uninformative predictor of whether a population is prone to transient booms or busts in its size. These analyses suggest that population ecology approaches to inferring transient dynamics have too often relied on suboptimal analytical tools focussed on an initial population vector rather than the capacity of the life cycle to amplify or dampen transient fluctuations. Finally, we introduce the engineering technique of pseudospectra analysis to population ecology, which, like matrix non-normality, provides a more complete description of the transient fluctuations than the damping ratio. Pseudospectra analysis could further support non-normality assessment to enable a greater understanding of when we might expect transient phases to impact eventual population dynamics.This work was funded by Wellcome Trust New Investigator 103780 to TE, who is also funded by NERC Fellowship NE/J018163/1. JB gratefully acknowledges the ESRC Centre for Population Change ES/K007394/1
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