446 research outputs found
Poisson-Lie group of pseudodifferential symbols
We introduce a Lie bialgebra structure on the central extension of the Lie
algebra of differential operators on the line and the circle (with scalar or
matrix coefficients). This defines a Poisson--Lie structure on the dual group
of pseudodifferential symbols of an arbitrary real (or complex) order. We show
that the usual (second) Benney, KdV (or GL_n--Adler--Gelfand--Dickey) and KP
Poisson structures are naturally realized as restrictions of this Poisson
structure to submanifolds of this ``universal'' Poisson--Lie group.
Moreover, the reduced (=SL_n) versions of these manifolds (W_n-algebras in
physical terminology) can be viewed as subspaces of the quotient (or Poisson
reduction) of this Poisson--Lie group by the dressing action of the group of
functions.
Finally, we define an infinite set of functions in involution on the
Poisson--Lie group that give the standard families of Hamiltonians when
restricted to the submanifolds mentioned above. The Poisson structure and
Hamiltonians on the whole group interpolate between the Poisson structures and
Hamiltonians of Benney, KP and KdV flows. We also discuss the geometrical
meaning of W_\infty as a limit of Poisson algebras W_\epsilon as \epsilon goes
to 0.Comment: 64 pages, no figure
Composition of processes and related partial differential equations
In this paper different types of compositions involving independent
fractional Brownian motions B^j_{H_j}(t), t>0, j=1,$ are examined. The partial
differential equations governing the distributions of
I_F(t)=B^1_{H_1}(|B^2_{H_2}(t)|), t>0 and
J_F(t)=B^1_{H_1}(|B^2_{H_2}(t)|^{1/H_1}), t>0 are derived by different methods
and compared with those existing in the literature and with those related to
B^1(|B^2_{H_2}(t)|), t>0. The process of iterated Brownian motion I^n_F(t), t>0
is examined in detail and its moments are calculated. Furthermore for
J^{n-1}_F(t)=B^1_{H}(|B^2_H(...|B^n_H(t)|^{1/H}...)|^{1/H}), t>0 the following
factorization is proved J^{n-1}_F(t)=\prod_{j=1}^{n} B^j_{\frac{H}{n}}(t), t>0.
A series of compositions involving Cauchy processes and fractional Brownian
motions are also studied and the corresponding non-homogeneous wave equations
are derived.Comment: 32 page
Non-Local Matrix Generalizations of W-Algebras
There is a standard way to define two symplectic (hamiltonian) structures,
the first and second Gelfand-Dikii brackets, on the space of ordinary linear
differential operators of order , . In this paper, I consider in detail the case where the are
-matrix-valued functions, with particular emphasis on the (more
interesting) second Gelfand-Dikii bracket. Of particular interest is the
reduction to the symplectic submanifold . This reduction gives rise to
matrix generalizations of (the classical version of) the {\it non-linear}
-algebras, called -algebras. The non-commutativity of the
matrices leads to {\it non-local} terms in these -algebras. I show
that these algebras contain a conformal Virasoro subalgebra and that
combinations of the can be formed that are -matrices of
conformally primary fields of spin , in analogy with the scalar case .
In general however, the -algebras have a much richer structure than
the -algebras as can be seen on the examples of the {\it non-linear} and
{\it non-local} Poisson brackets of any two matrix elements of or
which I work out explicitly for all and . A matrix Miura transformation
is derived, mapping these complicated second Gelfand-Dikii brackets of the
to a set of much simpler Poisson brackets, providing the analogue of the
free-field realization of the -algebras.Comment: 43 pages, a reference and a remark on the conformal properties for
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Single Spin Asymmetry in Polarized Proton-Proton Elastic Scattering at GeV
We report a high precision measurement of the transverse single spin
asymmetry at the center of mass energy GeV in elastic
proton-proton scattering by the STAR experiment at RHIC. The was measured
in the four-momentum transfer squared range \GeVcSq, the region of a significant interference between the
electromagnetic and hadronic scattering amplitudes. The measured values of
and its -dependence are consistent with a vanishing hadronic spin-flip
amplitude, thus providing strong constraints on the ratio of the single
spin-flip to the non-flip amplitudes. Since the hadronic amplitude is dominated
by the Pomeron amplitude at this , we conclude that this measurement
addresses the question about the presence of a hadronic spin flip due to the
Pomeron exchange in polarized proton-proton elastic scattering.Comment: 12 pages, 6 figure
Longitudinal double-spin asymmetry and cross section for inclusive neutral pion production at midrapidity in polarized proton collisions at sqrt(s) = 200 GeV
We report a measurement of the longitudinal double-spin asymmetry A_LL and
the differential cross section for inclusive Pi0 production at midrapidity in
polarized proton collisions at sqrt(s) = 200 GeV. The cross section was
measured over a transverse momentum range of 1 < p_T < 17 GeV/c and found to be
in good agreement with a next-to-leading order perturbative QCD calculation.
The longitudinal double-spin asymmetry was measured in the range of 3.7 < p_T <
11 GeV/c and excludes a maximal positive gluon polarization in the proton. The
mean transverse momentum fraction of Pi0's in their parent jets was found to be
around 0.7 for electromagnetically triggered events.Comment: 6 pages, 3 figures, submitted to Phys. Rev. D (RC
High non-photonic electron production in + collisions at = 200 GeV
We present the measurement of non-photonic electron production at high
transverse momentum ( 2.5 GeV/) in + collisions at
= 200 GeV using data recorded during 2005 and 2008 by the STAR
experiment at the Relativistic Heavy Ion Collider (RHIC). The measured
cross-sections from the two runs are consistent with each other despite a large
difference in photonic background levels due to different detector
configurations. We compare the measured non-photonic electron cross-sections
with previously published RHIC data and pQCD calculations. Using the relative
contributions of B and D mesons to non-photonic electrons, we determine the
integrated cross sections of electrons () at 3 GeV/10 GeV/ from bottom and charm meson decays to be = 4.0({\rm
stat.})({\rm syst.}) nb and =
6.2({\rm stat.})({\rm syst.}) nb, respectively.Comment: 17 pages, 17 figure
Evolution of the differential transverse momentum correlation function with centrality in Au+Au collisions at GeV
We present first measurements of the evolution of the differential transverse
momentum correlation function, {\it C}, with collision centrality in Au+Au
interactions at GeV. {\it C} exhibits a strong dependence
on collision centrality that is qualitatively similar to that of number
correlations previously reported. We use the observed longitudinal broadening
of the near-side peak of {\it C} with increasing centrality to estimate the
ratio of the shear viscosity to entropy density, , of the matter formed
in central Au+Au interactions. We obtain an upper limit estimate of
that suggests that the produced medium has a small viscosity per unit entropy.Comment: 7 pages, 4 figures, STAR paper published in Phys. Lett.
Longitudinal scaling property of the charge balance function in Au + Au collisions at 200 GeV
We present measurements of the charge balance function, from the charged
particles, for diverse pseudorapidity and transverse momentum ranges in Au + Au
collisions at 200 GeV using the STAR detector at RHIC. We observe that the
balance function is boost-invariant within the pseudorapidity coverage [-1.3,
1.3]. The balance function properly scaled by the width of the observed
pseudorapidity window does not depend on the position or size of the
pseudorapidity window. This scaling property also holds for particles in
different transverse momentum ranges. In addition, we find that the width of
the balance function decreases monotonically with increasing transverse
momentum for all centrality classes.Comment: 6 pages, 3 figure
Energy and system size dependence of \phi meson production in Cu+Cu and Au+Au collisions
We study the beam-energy and system-size dependence of \phi meson production
(using the hadronic decay mode \phi -- K+K-) by comparing the new results from
Cu+Cu collisions and previously reported Au+Au collisions at \sqrt{s_NN} = 62.4
and 200 GeV measured in the STAR experiment at RHIC. Data presented are from
mid-rapidity (|y|<0.5) for 0.4 < pT < 5 GeV/c. At a given beam energy, the
transverse momentum distributions for \phi mesons are observed to be similar in
yield and shape for Cu+Cu and Au+Au colliding systems with similar average
numbers of participating nucleons. The \phi meson yields in nucleus-nucleus
collisions, normalised by the average number of participating nucleons, are
found to be enhanced relative to those from p+p collisions with a different
trend compared to strange baryons. The enhancement for \phi mesons is observed
to be higher at \sqrt{s_NN} = 200 GeV compared to 62.4 GeV. These observations
for the produced \phi(s\bar{s}) mesons clearly suggest that, at these collision
energies, the source of enhancement of strange hadrons is related to the
formation of a dense partonic medium in high energy nucleus-nucleus collisions
and cannot be alone due to canonical suppression of their production in smaller
systems.Comment: 20 pages and 5 figure
Measurement of the Bottom contribution to non-photonic electron production in collisions at =200 GeV
The contribution of meson decays to non-photonic electrons, which are
mainly produced by the semi-leptonic decays of heavy flavor mesons, in
collisions at 200 GeV has been measured using azimuthal
correlations between non-photonic electrons and hadrons. The extracted
decay contribution is approximately 50% at a transverse momentum of GeV/. These measurements constrain the nuclear modification factor for
electrons from and meson decays. The result indicates that meson
production in heavy ion collisions is also suppressed at high .Comment: 6 pages, 4 figures, accepted by PR
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