587 research outputs found
From bubbles to foam: dilute to dense evolution of hadronic wave function at high energy
We derive the evolution of a hadronic light cone wave function with energy at
weak coupling. Our derivation is valid both in the high and the low partonic
density limit, and thus encompasses both the JIMWLK and the KLWMIJ evolution.
The hadronic wave function is shown to evolve by the action of the
Bogoliubov-type operator, which diagonalizes on the soft gluon sector the
light-cone hamiltonian in the presence of an arbitrary valence charge density.
We find explicitly the action of this operator on the soft as well as the
valence degrees of freedom of the theory.Comment: 30 page
The Higgs field and the ultraviolet behaviour of the vortex operator in 2+1 dimensions
We calculate the change in the ultraviolet behaviour of the vortex operator
due to the presence of dynamical Higgs field in both 2+1 dimensional QED and
the 2+1 dimensional Georgi-Glashow model. We find that in the QED case the
presence of the Higgs field leads at the one loop level to power like
correction to the propagator of the vortex operator. On the other hand, in the
Georgi-Glashow model, the adjoint Higgs at one loop has no affect on the vortex
propagator. Thus, as long as the mass of the Higgs field is much larger than
the gauge coupling constant, the ultraviolet behaviour of the vortex operator
in the Georgi-Glashow model is independent of the Higgs mass.Comment: 14 page
The Yin and Yang of High Energy Chromodynamics: Scattering in Black and White
We further discuss the QCD Reggeon field theory (RFT) as it emerges from the
JIMWLK/KLWMIJ evolution equation and beyond. We give an explicit expression for
the calculation of scattering amplitude in terms of the eigenstates of the RFT
Hamiltonian. We point out that the spectrum of RFT is doubly degenerate, the
degeneracy being related to the spontaneous breaking of the Dense-Dilute
Duality symmetry of RFT. The degeneracy is between the "almost white" states
(the Yang sector) which contain a small number of gluons, and "almost black"
states (the Yin sector). The excitations above the Yang vacuum have natural
interpretation in terms of gluons. Analogously the excitations above the Yin
vacuum have natural interpretation as "holes" in the black disk - points at
which an incoming gluon does not scatter with unit probability. We discuss in
detail the spectrum of the "parton model approximation" to the KLWMIJ evolution
introduced in our previous paper, and prove that it is explicitly selfdual.
This allows us to find explicitly the counterpart hole states in this
approximation. We also present an argument to the effect that the end point of
the evolution for any physical state cannot be a "grey disk" but must
necessarily be the "black disk" Yin vacuum state. Finally, we suggest an
approximation scheme for including the Pomeron loop contribution to the
evolution which requires only the solution of the JIMWLK/KLWMIJ Hamiltonian.Comment: 25 pages, 1 figur
More Remarks on High Energy Evolution
We discuss several issues related to recent work on high energy evolution. In
particular we show that the Hilbert space for action of the operator of the
evolution can be conveniently defined by the space of weight functional
introduced recently in \cite{kl4}. These weight functionals automatically
implement the correct properties of the charge density correlators, thus
eliminating the need in explicit introduction of the Wess Zumino term. We also
discuss various aspects of Dense Dilute Duality in the toy dipole model.Comment: 20 pages, 1 figur
Critical Exponents of the Superconducting Phase Transition
We study the critical exponents of the superconducting phase transition in
the context of renormalization group theory starting from a dual formulation of
the Ginzburg-Landau theory. The dual formulation describes a loop gas of
Abrikosov flux tubes which proliferate when the critical temperature is
approached from below. In contrast to the Ginzburg-Landau theory, it has a
spontaneously broken global symmetry and possesses an infrared stable fixed
point. The exponents coincide with those of a superfluid with reversed
temperature axis.Comment: Postscript file. For related work see www adress
http://www.physik.fu-berlin.de/kleiner_re.html in our homepage
http://www.physik.fu-berlin.de/kleinert.htm
Treading on the cut: Semi inclusive observables at high energy
We develop the formalizm for calculating semi inclusive observables at high
energy in the JIMWLK/KLWMIJ approach. We consider several examples including
diffractive processes, elastic and inclusive over the target degrees of
freedom, scattering with fixed total transverse momentum transfer and inclusive
gluon production. We discuss evolution of these observables with respect to
various rapidity variables involved in their definitions (total rapidity,
rapidity gap, width of diffractive interval etc.). We also discuss the dipole
model limit of these observables and derive closed simple (as opposed to
functional) differential equations in this approximation. We point out that
there are some interesting differences between the full JIMWLK/KLWMIJ evolution
and the dipole model evolution of diffractive cross section. In particular we
show that in the dipole approximation the target does not diffract beyond the
valence rapidity interval, consistently with the intuition suggested by the
Pomeron fan diagramms. On the other hand such diffractive processes do exist in
the full JIMWLK/KLWMIJ approach, albeit suppressed by the factor 1/N_c^2.Comment: 37 pages, 3 figures. A few remarks added. To appear in PR
Hanbury-Brown-Twiss measurements at large rapidity separations, or can we measure the proton radius in p-A collisions?
We point out that current calculations of inclusive two-particle correlations
in p-A collisions based on the Color Glass Condensate approach exhibit a
contribution from Hanbury-Brown-Twiss correlations. These HBT correlations are
quite distinct from the standard ones, in that they are apparent for particles
widely separated in rapidity. The transverse size of the emitter which is
reflected in these correlations is the gluonic size of the proton. This raises
an interesting possibility of measuring the proton size directly by the HBT
effect of particle pairs produced in p-A collisions.Comment: 11 pages, 3 eps figures; v2: comments, discussions, references and
acknowledgements added, conclusions unchanged, final versio
The Dipole Picture and Saturation in Soft Processes
We attempt to describe soft hadron interactions in the framework of
saturation models, one based upon the Balitsky-Kovchegov non-linear equation
and another one due to Golec-Biernat and W\"{u}sthoff. For , , and scattering the relevant hadronic wave functions are formulated, and total,
elastic cross-sections, and the forward elastic slope are calculated and
compared to experimental data. The saturation mechanism leads to reasonable
reproduction of the data for the quantities analyzed, except for the forward
elastic slope, where the predicted increase with energy is too moderate.Comment: 12 pages, 4 figures. One figure and several explanations are added.
The version is to appear in PL
Magnetic Z(N) symmetry in 2+1 dimensions
This review describes the role of magnetic symmetry in 2+1 dimensional gauge
theories. In confining theories without matter fields in fundamental
representation the magnetic symmetry is spontaneously broken. Under some mild
assumptions, the low-energy dynamics is determined universally by this
spontaneous breaking phenomenon. The degrees of freedom in the effective theory
are magnetic vortices. Their role in confining dynamics is similar to that
played by pions and sigma in the chiral symmetry breaking dynamics.
I give an explicit derivation of the effective theory in (2+1)-dimensional
weakly coupled confining models and argue that it remains qualitatively the
same in strongly coupled (2+1)-dimensional gluodynamics. Confinement in this
effective theory is a very simple classical statement about the long range
interaction between topological solitons, which follows (as a result of a
simple direct classical calculation) from the structure of the effective
Lagrangian. I show that if fundamentally charged dynamical fields are present
the magnetic symmetry becomes local rather than global. The modifications to
the effective low energy description in the case of heavy dynamical fundamental
matter are discussed. This effective lagrangian naturally yields a bag like
description of baryonic excitations. I also discuss the fate of the magnetic
symmetry in gauge theories with the Chern-Simons term
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