23,831 research outputs found
Relativity of representations in quantum mechanics
Only the position representation is used in introductory quantum mechanics
and the momentum representation is not usually presented until advanced
undergraduate courses. To emphasize the relativity of the representations of
the abstract formulation of quantum mechanics, two examples of representations
related to the operators aX+(1-a)P and (XP+PX)/2 are presented.Comment: 10 pages, no figures, accepted in Am.J.Phy
Transverse-momentum resummation for heavy-quark hadroproduction
We consider the production of a pair of heavy quarks () in
hadronic collisions. When the transverse momentum of the heavy-quark pair
is much smaller than its invariant mass, the QCD perturbative expansion is
affected by large logarithmic terms that must be resummed to all-orders. This
behavior is well known from the simpler case of hadroproduction of colourless
high-mass systems, such as vector or Higgs boson(s). In the case of
production, the final-state heavy quarks carry colour charge and are
responsible for additional soft radiation (through direct emission and
interferences with initial-state radiation) that complicates the evaluation of
the logarithmically-enhanced terms in the small- region. We present the
all-order resummation structure of the logarithmic contributions, which
includes colour flow evolution factors due to soft wide-angle radiation.
Resummation is performed at the completely differential level with respect to
the kinematical variables of the produced heavy quarks. Soft-parton radiation
produces azimuthal correlations that are fully taken into account by the
resummation formalism. These azimuthal correlations are entangled with those
that are produced by initial-state collinear radiation. We present explicit
analytical results up to next-to-leading order and next-to-next-to-leading
logarithmic accuracy.Comment: Some comments expanded and references added. Version published on NP
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