39,834 research outputs found
Susceptibility of a two-level atom near an isotropic photonic band edge: transparency and band edge profile reconstruction
We discuss the necessary conditions for a two-level system in the presence of
an isotropic band edge to be transparent to a probe laser field. The two-level
atom is transparent whenever it is coupled to a reservoir constituted of two
parts - a flat and a non-flat density of modes representing a PBG structure. A
proposal on the reconstruction of the band edge profile from the experimentally
measured susceptibility is also presented.Comment: 15 pages, 3 figure
Treatment of the infrared contribution: NLO QED evolution as a pedagogic example
We show that the conventional prescription used for DGLAP parton evolution at
NLO has an inconsistent treatment of the contribution from the infrared (IR)
region. We illustrate the problem by studying the simple example of QED
evolution, treating the electron and photon as partons. The deficiency is not
present in a physical approach which removes the IR divergency and allows
calculation in the normal 4-dimensional space.Comment: 15 pages, 2 figures, erratum at the end of the articl
Improving the Drell-Yan probe of small x partons at the LHC via a k_t cut
We show that the observation of the Drell-Yan production of low-mass
lepton-pairs (M 3) at the LHC can make a
direct measurement of parton distribution functions (PDFs) in the low x region,
x < 10^{-4}. We describe a procedure that greatly reduces the sensitivity of
the predictions to the choice of the factorization scale and, in particular,
show how, by imposing a cutoff on the transverse momentum of the lepton-pair,
the data are able to probe PDFs in the important low scale, low x domain. We
include the effects of the Sudakov suppression factor.Comment: 14 pages, 5 figures, version to be published in EPJC, with expanded
explanatio
The LHC can probe small x PDFs; the treatment of the infrared region
First, we show how to reduce the sensitivity of the NLO predictions of the
Drell-Yan production of low-mass, lepton-pairs, at high rapidity, to the choice
of factorization scale. In this way, observations of this process at the LHC
can make direct measurements of parton distribution functions in the low x
domain; x < 10^{-4}. Second, we find an inconsistency in the conventional NLO
treatment of the infrared region. We illustrate the problem using the NLO
coefficient function of Drell-Yan production.Comment: 5 pages, 1 figure, contribution to the Proceedings of
"Diffraction2012", Puerto del Carmen, Lanzarote, Spain, Sept. 10-15th, 201
Physical factorisation scheme for PDFs for non-inclusive applications
We introduce the physical factorisation scheme, which is necessary to
describe observables which are `not completely inclusive'. We derive the
formulae for NLO DGLAP evolution in this scheme, and also for the `rotation' of
the conventional MSbar PDFs into the physical representation. Unlike, the MSbar
prescription, where, for example, the gluon PDF at NLO obtains an admixture of
the quark-singlet PDF, and vice-versa, the physical approach does not mix
parton PDFs of different types. That is, the physical approach retains the
precise quantum numbers of each PDF. The NLO corrections to DGLAP evolution in
the physical scheme are less than those in the MSbar case, indicating a better
convergence of the perturbative series
Treatment of heavy quarks in QCD
We show that to correctly describe the effects of the heavy-quark mass, m_h,
in DGLAP evolution, it is necessary to work in the so-called `physical' scheme.
In this way, we automatically obtain a smooth transition through the
heavy-quark thresholds. Moreover, we show that to obtain NLO accuracy, it is
sufficient to account for the heavy-quark mass, m_h, just in the LO (one-loop)
splitting function. The use of the MS-bar factorisation scheme is not
appropriate, since at NLO we deal with a mixture of quarks and gluon (that is,
the mass of the heavy parton is not well-defined). The formulae for the
explicit m_h dependence of the splitting functions, and for alpha_s, are
presented.Comment: 14 pages, 3 figures, references updated, version to be published in
EPJ
Hermitian Dirac Hamiltonian in time dependent gravitational field
It is shown by a straightforward argument that the Hamiltonian generating the
time evolution of the Dirac wave function in relativistic quantum mechanics is
not hermitian with respect to the covariantly defined inner product whenever
the background metric is time dependent. An alternative, hermitian, Hamiltonian
is found and is shown to be directly related to the canonical field Hamiltonian
used in quantum field theory.Comment: 9 pages, final version, to appear in Class. Quant. Gra
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