158 research outputs found
Symmetry of Anomalous Dimension Matrices for Colour Evolution of Hard Scattering Processes
In a recent paper, Dokshitzer and Marchesini rederived the anomalous
dimension matrix for colour evolution of scattering, first derived
by Kidonakis, Oderda and Sterman. They noted a weird symmetry that it possesses
under interchange of internal (colour group) and external (scattering angle)
degrees of freedom and speculated that this may be related to an embedding into
a context that correlates internal and external variables such as string
theory.
In this short note, I point out another symmetry possessed by all the colour
evolution anomalous dimension matrices calculated to date. It is more prosaic,
but equally unexpected, and may also point to the fact that colour evolution
might be understood in some deeper theoretical framework. To my knowledge it
has not been pointed out elsewhere, or anticipated by any of the authors
calculating these matrices. It is simply that, in a suitably chosen colour
basis, they are complex symmetric matrices.Comment: 3 page
Symmetry of anomalous dimension matrices explained
In a previous paper, one of us pointed out that the anomalous dimension
matrices for all physical processes that have been calculated to date are
complex symmetric, if stated in an orthonormal basis. In this paper we prove
this fact and show that it is only true in a subset of all possible orthonormal
bases, but that this subset is the natural one to use for physical
calculations.Comment: 4 page
Color evolution of 2 -> 3 processes
The color structure needed for resummation of all colored 2 -> 3 processes is
calculated using multiplet inspired s-channel bases. In this way the resulting
matrices, describing the color structure, are guaranteed to obey simplifying
symmetries.Comment: 25 page
Color structure for soft gluon resummation - a general recipe
A strategy for calculating the color structure needed for soft gluon
resummation for processes with any number of colored partons is introduced
using a N_c --> infinity inspired basis. In this basis a general formalism can
be found at the same time as the calculations are simplified.
The advantages are illustrated by recalculating the soft anomalous dimension
matrix for the processes gg --> gg, q\qbar --> q \qbar g and q\qbar --> ggg.Comment: 16 page
Soft gluons and superleading logarithms in QCD
After a brief introduction to the physics of soft gluons in QCD we present a
surprising prediction. Dijet production in hadron-hadron collisions provides
the paradigm, i.e. h_1 +h_2 \to jj+X. In particular, we look at the case where
there is a restriction placed on the emission of any further jets in the region
in between the primary (highest p_T) dijets. Logarithms in the ratio of the jet
scale to the veto scale can be summed to all orders in the strong coupling.
Surprisingly, factorization of collinear emissions fails at scales above the
veto scale and triggers the appearance of double logarithms in the hard
sub-process. The effect appears first at fourth order relative to the leading
order prediction and is subleading in the number of colours.Comment: Talk presented at the workshop "New Trends in HERA Physics", Ringberg
Castle, Tegernsee, 5-10 October 200
Altered functional brain network connectivity and glutamate system function in transgenic mice expressing truncated Disrupted-in-Schizophrenia 1
Considerable evidence implicates DISC1 as a susceptibility gene for multiple psychiatric diseases. DISC1 has been intensively studied at the molecular, cellular and behavioral level, but its role in regulating brain connectivity and brain network function remains unknown. Here, we utilize a set of complementary approaches to assess the functional brain network abnormalities present in mice expressing a truncated Disc1 gene (Disc1tr Hemi mice). Disc1tr Hemi mice exhibited hypometabolism in the prefrontal cortex (PFC) and reticular thalamus along with a reorganization of functional brain network connectivity that included compromised hippocampal–PFC connectivity. Altered hippocampal–PFC connectivity in Disc1tr Hemi mice was confirmed by electrophysiological analysis, with Disc1tr Hemi mice showing a reduced probability of presynaptic neurotransmitter release in the monosynaptic glutamatergic hippocampal CA1–PFC projection. Glutamate system dysfunction in Disc1tr Hemi mice was further supported by the attenuated cerebral metabolic response to the NMDA receptor (NMDAR) antagonist ketamine and decreased hippocampal expression of NMDAR subunits 2A and 2B in these animals. These data show that the Disc1 truncation in Disc1tr Hemi mice induces a range of translationally relevant endophenotypes underpinned by glutamate system dysfunction and altered brain connectivity
Multiparton Interactions in Photoproduction at HERA
The high energy photoproduction of jets is being observed at the ep collider,
HERA. It may be that the HERA centre-of-mass energy is sufficiently large that
the production of more than one pair of jets per ep collision becomes possible,
owing to the large number density of the probed gluons. We construct a Monte
Carlo model of such multiparton interactions and study their effects on a wide
range of physical observables. The conclusion is that multiple interactions
could have very significant effects upon the photoproduction final state and
that this would for example make extractions of the gluon density in the photon
rather difficult. Total rates for the production of many (i.e. > 2) jets could
provide direct evidence for the presence of multiple interactions, although
parton showering and hadronization significantly affect low transverse energy
jets.Comment: 21 pages, 8 figures include
Soft gluons in Higgs plus two jet production
We investigate the effects of an all order QCD resummation of soft gluon
emissions for Higgs boson production in association with two hard jets. We
consider both the gluon-gluon fusion and weak boson fusion processes and show
how to resum a large part of the leading logarithms in the jet veto scale. Our
resummation improves on previous analyses which also aim to include the effects
of multiple soft gluon radiation. In addition we calculate the interference
between weak boson fusion and gluon-gluon fusion and find that it is small.Comment: 15 pages and 5 figure
Unitary designs and codes
A unitary design is a collection of unitary matrices that approximate the
entire unitary group, much like a spherical design approximates the entire unit
sphere. In this paper, we use irreducible representations of the unitary group
to find a general lower bound on the size of a unitary t-design in U(d), for
any d and t. We also introduce the notion of a unitary code - a subset of U(d)
in which the trace inner product of any pair of matrices is restricted to only
a small number of distinct values - and give an upper bound for the size of a
code of degree s in U(d) for any d and s. These bounds can be strengthened when
the particular inner product values that occur in the code or design are known.
Finally, we describe some constructions of designs: we give an upper bound on
the size of the smallest weighted unitary t-design in U(d), and we catalogue
some t-designs that arise from finite groups.Comment: 25 pages, no figure
Jet vetoing at the LHC
We study the effect of a veto on additional jets in the rapidity region
between a pair of high transverse momentum jets at the LHC. We aim to sum the
most important logarithms in the ratio of the jet transverse momentum to the
veto scale and to that end we attempt to assess the significance of the
super-leading logarithms that appear at high orders in the perturbative
expansion. We also compare our results to those of HERWIG++, in an attempt to
ascertain the accuracy of the angular ordered parton shower. We find that there
are large corrections that arise for large enough jet transverse momenta as a
consequence of Coulomb gluon exchanges.Comment: 25 page
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