8,291 research outputs found
Bound-state/elementary-particle duality in the Higgs sector and the case for an excited 'Higgs' within the standard model
Though being weakly interacting, QED can support bound states. In principle,
this can be expected for the weak interactions in the Higgs sector as well. In
fact, it has been argued long ago that there should be a duality between bound
states and the elementary particles in this sector, at least in leading order
in an expansion in the Higgs condensate. Whether this remains true beyond the
leading order is investigated using lattice simulations, and support is found.
This provides a natural interpretation of peaks in cross sections as bound
states. Unambiguously, this would imply the existence of (possibly very broad)
resonances of Higgs and W and Z bound states within the standard model.Comment: 15 pages, 3 figures v2: added appendix with technical details, some
minor improvement
QCD Propagators at non-vanishing temperatures
We investigate the behaviour of the gluon and ghost propagators, especially
their infrared properties, at non-vanishing temperatures. To this end we solve
their Dyson-Schwinger equations on a torus and find an infrared enhanced ghost
propagator and an infrared vanishing gluon propagator.Comment: 2 pages, 2 figures; talk given by B.G. at the Erice summer school on
Nuclear Physics, Sept. 16 -- 24, 2003, Erice, Ital
A luminosity monitor for the A4 parity violation experiment at MAMI
A water Cherenkov luminosity monitor system with associated electronics has
been developed for the A4 parity violation experiment at MAMI. The detector
system measures the luminosity of the hydrogen target hit by the MAMI electron
beam and monitors the stability of the liquid hydrogen target. Both is required
for the precise study of the count rate asymmetries in the scattering of
longitudinally polarized electrons on unpolarized protons. Any helicity
correlated fluctuation of the target density leads to false asymmetries. The
performance of the luminosity monitor, investigated in about 2000 hours with
electron beam, and the results of its application in the A4 experiment are
presented.Comment: 22 pages, 12 figures, submitted to NIM
Exact algorithms for procurement problems under a total quantity discount structure.
In this paper, we study the procurement problem faced by a buyer who needs to purchase a variety of goods from suppliers applying a so-called total quantity discount policy. This policy implies that every supplier announces a number of volume intervals and that the volume interval in which the total amount ordered lies determines the discount. Moreover, the discounted prices apply to all goods bought from the supplier, not only to those goods exceeding the volume threshold. We refer to this cost-minimization problem as the TQD problem. We give a mathematical formulation for this problem and argue that not only it is NP-hard, but also that there exists no polynomial-time approximation algorithm with a constant ratio (unless P = NP). Apart from the basic form of the TQD problem, we describe three variants. In a first variant, the market share that one or more suppliers can obtain is constrained. Another variant allows the buyer to procure more goods than strictly needed, in order to reach a lower total cost. In a third variant, the number of winning suppliers is limited. We show that the TQD problem and its variants can be solved by solving a series of min-cost flow problems. Finally, we investigate the performance of three exact algorithms (min-cost flow based branch-and-bound, linear programming based branch-and-bound, and branch-and-cut) on randomly generated instances involving 50 suppliers and 100 goods. It turns out that even the large instances of the basic problem are solved to optimality within a limited amount of time. However, we find that different algorithms perform best in terms of computation time for different variants.Algorithms; Approximation; Branch-and-bound; Complexity; Cost; Exact algorithm; Intervals; Linear programming; Market; Min-cost flow; Order; Performance; Policy; Prices; Problems; Procurement; Reverse auction; Structure; Studies; Suppliers; Time; Volume discounts;
Color-superconductivity in the strong-coupling regime of Landau gauge QCD
The chirally unbroken and the superconducting 2SC and CFL phases are
investigated in the chiral limit within a Dyson-Schwinger approach for the
quark propagator in QCD. The hierarchy of Green's functions is truncated such
that at vanishing density known results for the vacuum and at asymptotically
high densities the corresponding weak-coupling expressions are recovered. The
anomalous dimensions of the gap functions are analytically calculated. Based on
the quark propagator the phase structure is studied, and results for the gap
functions, occupation numbers, coherence lengths and pressure differences are
given and compared with the corresponding expressions in the weak-coupling
regime. At moderate chemical potentials the quasiparticle pairing gaps are
several times larger than the extrapolated weak-coupling results.Comment: 14 pages, 9 figures; v2: one reference adde
The No-Pole Condition in Landau gauge: Properties of the Gribov Ghost Form-Factor and a Constraint on the 2d Gluon Propagator
We study the Landau-gauge Gribov ghost form-factor sigma(p^2) for SU(N)
Yang-Mills theories in the d-dimensional case. We find a qualitatively
different behavior for d=3,4 w.r.t. d=2. In particular, considering any
(sufficiently regular) gluon propagator D(p^2) and the one-loop-corrected ghost
propagator G(p^2), we prove in the 2d case that sigma(p^2) blows up in the
infrared limit p -> 0 as -D(0)\ln(p^2). Thus, for d=2, the no-pole condition
\sigma(p^2) 0) can be satisfied only if D(0) = 0. On the
contrary, in d=3 and 4, sigma(p^2) is finite also if D(0) > 0. The same results
are obtained by evaluating G(p^2) explicitly at one loop, using fitting forms
for D(p^2) that describe well the numerical data of D(p^2) in d=2,3,4 in the
SU(2) case. These evaluations also show that, if one considers the coupling
constant g^2 as a free parameter, G(p^2) admits a one-parameter family of
behaviors (labelled by g^2), in agreement with Boucaud et al. In this case the
condition sigma(0) <= 1 implies g^2 <= g^2_c, where g^2_c is a 'critical'
value. Moreover, a free-like G(p^2) in the infrared limit is obtained for any
value of g^2 < g^2_c, while for g^2 = g^2_c one finds an infrared-enhanced
G(p^2). Finally, we analyze the Dyson-Schwinger equation (DSE) for sigma(p^2)
and show that, for infrared-finite ghost-gluon vertices, one can bound
sigma(p^2). Using these bounds we find again that only in the d=2 case does one
need to impose D(0) = 0 in order to satisfy the no-pole condition. The d=2
result is also supported by an analysis of the DSE using a spectral
representation for G(p^2). Thus, if the no-pole condition is imposed, solving
the d=2 DSE cannot lead to a massive behavior for D(p^2). These results apply
to any Gribov copy inside the so-called first Gribov horizon, i.e. the 2d
result D(0) = 0 is not affected by Gribov noise. These findings are also in
agreement with lattice data.Comment: 40 pages, 2 .eps figure
Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)
We study a gauge invariant order parameter for deconfinement and the chiral
condensate in SU(2) and SU(3) Yang-Mills theory in the vicinity of the
deconfinement phase transition using the Landau gauge quark and gluon
propagators. We determine the gluon propagator from lattice calculations and
the quark propagator from its Dyson-Schwinger equation, using the gluon
propagator as input. The critical temperature and a deconfinement order
parameter are extracted from the gluon propagator and from the dependency of
the quark propagator on the temporal boundary conditions. The chiral transition
is determined using the quark condensate as order parameter. We investigate
whether and how a difference in the chiral and deconfinement transition between
SU(2) and SU(3) is manifest.Comment: 15 pages, 9 figures. For clarification one paragraph and two
references added in the introduction and two sentences at the end of the
first and last paragraph of the summary. Appeared in EPJ
Temperature Dependence of Gluon and Ghost Propagators in Landau-Gauge Yang-Mills Theory below the Phase Transition
The Dyson-Schwinger equations of Landau-gauge Yang-Mills theory for the gluon
and ghost propagators are investigated. Numerical results are obtained within a
truncation scheme which has proven to be successful at vanishing temperature.
For temperatures up to 250 MeV we find only minor quantitative changes in the
infrared behaviour of the gluon and ghost propagators. The effective action
calculated from these propagators is temperature-independent within the
numerical uncertainty.Comment: 9 pages, 14 figures, submitted to EPJ C, typos corrected, reference
and 2 minor clarifications added, in v3: one paragraph extended, some
references added, version to appear in EPJ
What the Infrared Behaviour of QCD Vertex Functions in Landau gauge can tell us about Confinement
The infrared behaviour of Landau gauge QCD vertex functions is investigated
employing a skeleton expansion of the Dyson-Schwinger and Renormalization Group
equations. Results for the ghost-gluon, three-gluon, four-gluon and quark-gluon
vertex functions are presented. Positivity violation of the gluon propagator,
and thus gluon confinement, is demonstrated. Results of the Dyson-Schwinger
equations for a finite volume are compared to corresponding lattice data. It is
analytically demonstrated that a linear rising potential between heavy quarks
can be generated by infrared singularities in the dressed quark-gluon vertex.
The selfconsistent mechanism that generates these singularities necessarily
entails the scalar Dirac amplitudes of the full vertex and the quark
propagator. These can only be present when chiral symmetry is broken, either
explicitly or dynamically.Comment: 13 pages, 13 figures; to appear in the Proceedings of ``X Hadron
Physics 2007'', Florianopolis, Brazil, March 26 - 31, 200
Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism
Three decades of work on the quantum field equations of pure Yang-Mills
theory have distilled two families of solutions in Landau gauge. Both coincide
for high (Euclidean) momentum with known perturbation theory, and both predict
an infrared suppressed transverse gluon propagator, but whereas the solution
known as "scaling" features an infrared power law for the gluon and ghost
propagators, the "massive" solution rather describes the gluon as a vector
boson that features a finite Debye screening mass.
In this work we examine the gauge dependence of these solutions by adopting
stochastic quantization. What we find, in four dimensions and in a rainbow
approximation, is that stochastic quantization supports both solutions in
Landau gauge but the scaling solution abruptly disappears when the parameter
controlling the drift force is separated from zero (soft gauge-fixing),
recovering only the perturbative propagators; the massive solution seems to
survive the extension outside Landau gauge. These results are consistent with
the scaling solution being related to the existence of a Gribov horizon, with
the massive one being more general.
We also examine the effective action in Faddeev-Popov quantization that
generates the rainbow and we find, for a bare vertex approximation, that the
the massive-type solutions minimise the quantum effective action.Comment: 13 pages, 7 figures. Change of title to reflect version accepted for
publicatio
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