283 research outputs found
Exclusive and inclusive muon pair production in collisions of relativistic nuclei
The exclusive production of one pair in collisions of two
ultra-relativistic nuclei is considered. We present a simple method for the
calculation of the Born cross section for this process based on an improved
equivalent photon approximation. We find that the Coulomb corrections to this
cross section (corresponding to multi-photon exchange of the produced
with the nuclei) are small while the unitarity corrections
(corresponding to the exchange of light-by-light blocks between nuclei) are
large. This is in sharp contrast to the exclusive pair production
where the Coulomb corrections to the Born cross section are large while the
unitarity corrections are small. We calculate also the cross section for the
production of one pair and several pairs in the leading
logarithmic approximation. Using this cross section we find that the inclusive
production of pair coincides in this approximation with its Born
value.Comment: 16 pages, 4 figure
A search for double beta decays of tin isotopes with enhanced sensitivity
A search for the various double beta decay modes of 124Sn and 112Sn has been
performed on 75 kg.days of data. New half-life limits for excited states in
124Sn have been obtained including a lower limit for the decay into the first
excited 2+ state of 124Te of T_half > 0.87e20 yrs (90% CL) and into the first
excited 0+ state of T_half > 1.08e20 yrs (90% CL). Ground state and excited
state transitions of 112Sn have also been experimentally explored. A limit for
the 2 neutrino double electron capture of T_half > 1.8e19 yrs (90% CL) is
obtained. The non-observation of de-excitation gammas from the 0+ at 1888.5keV
results in a lower half-life limit on the 0 neutrino double electron capture
decay of 112Sn of T_half > 0.8e19 yrs (90% CL), despite a possible resonant
enhancement of the decay rate due to degenerated states.Comment: 6 pages, 7 figures, updated analysis and tex
Process 3 -> 3 and crossing symmetry violation
Using the Sudakov technique we sum the perturbation series for the process
and obtain the compact analytical expression for the amplitude of this
process, which takes into account all possible Coulomb interactions between
colliding particles. Compare it with the amplitude of the lepton pair
production in heavy ion collision i.e. in the process , we show that
crossing symmetry between this processes holds only if one neglects the
interaction of produced pair with ions (i.e. in the approximation
).Comment: LaTeX2e, 10 pages, 5 eps figure
Contact symmetry of time-dependent Schr\"odinger equation for a two-particle system: symmetry classification of two-body central potentials
Symmetry classification of two-body central potentials in a two-particle
Schr\"{o}dinger equation in terms of contact transformations of the equation
has been investigated. Explicit calculation has shown that they are of the same
four different classes as for the point transformations. Thus in this problem
contact transformations are not essentially different from point
transformations. We have also obtained the detailed algebraic structures of the
corresponding Lie algebras and the functional bases of invariants for the
transformation groups in all the four classes
SU(5) grand unification on a domain-wall brane from an E_6-invariant action
An SU(5) grand unification scheme for effective 3+1-dimensional fields
dynamically localised on a domain-wall brane is constructed. This is achieved
through the confluence of the clash-of-symmetries mechanism for symmetry
breaking through domain-wall formation, and the Dvali-Shifman gauge-boson
localisation idea. It requires an E_6 gauge-invariant action, yielding a
domain-wall solution that has E_6 broken to differently embedded SO(10) x U(1)
subgroups in the two bulk regions on opposite sides of the wall. On the wall
itself, the unbroken symmetry is the intersection of the two bulk subgroups,
and contains SU(5). A 4+1-dimensional fermion family in the 27 of E_6 gives
rise to localised left-handed zero-modes in the 5^* + 10 + 1 + 1 representation
of SU(5). The remaining ten fermion components of the 27 are delocalised exotic
states, not appearing in the effective 3+1-dimensional theory on the
domain-wall brane. The scheme is compatible with the type-2 Randall-Sundrum
mechanism for graviton localisation; the single extra dimension is infinite.Comment: 21 pages, 9 figures. Minor changes to text and references. To appear
in Phys. Rev.
Implications of non-feasible transformations among icosahedral orbitals
The symmetric group that permutes the six five-fold axes of an
icosahedron is introduced to go beyond the simple rotations that constitute the
icosahedral group . Owing to the correspondence , the
calculation of the Coulomb energies for the icosahedral configurations
based on the sequence can be brought
to bear on Racah's classic theory for the atomic d shell based on . Among the elements of is the kaleidoscope
operator that rotates the weight space of SO(5) by . Its use
explains some puzzling degeneracies in d^3 involving the spectroscopic terms
^2P, ^2F, ^2G and ^2H.Comment: Tentatively scheduled to appear in Physical Preview Letters Apr 5,
99. Revtex, 1 ps figur
Fundamental Weights, Permutation Weights and Weyl Character Formula
For a finite Lie algebra of rank N, the Weyl orbits
of strictly dominant weights contain number of
weights where is the dimension of its Weyl group . For any
, there is a very peculiar subset for
which we always have For
any dominant weight , the elements of are called
{\bf Permutation Weights}.
It is shown that there is a one-to-one correspondence between elements of
and where is the Weyl vector of .
The concept of signature factor which enters in Weyl character formula can be
relaxed in such a way that signatures are preserved under this one-to-one
correspondence in the sense that corresponding permutation weights have the
same signature. Once the permutation weights and their signatures are specified
for a dominant , calculation of the character for
irreducible representation will then be provided by
multiplicity rules governing generalized Schur functions. The main idea is
again to express everything in terms of the so-called {\bf Fundamental Weights}
with which we obtain a quite relevant specialization in applications of Weyl
character formula.Comment: 6 pages, no figures, TeX, as will appear in Journal of Physics
A:Mathematical and Genera
Conditional probabilities in Ponzano-Regge minisuperspace
We examine the Hartle-Hawking no-boundary initial state for the Ponzano-Regge
formulation of gravity in three dimensions. We consider the behavior of
conditional probabilities and expectation values for geometrical quantities in
this initial state for a simple minisuperspace model consisting of a
two-parameter set of anisotropic geometries on a 2-sphere boundary. We find
dependence on the cutoff used in the construction of Ponzano-Regge amplitudes
for expectation values of edge lengths. However, these expectation values are
cutoff independent when computed in certain, but not all, conditional
probability distributions. Conditions that yield cutoff independent expectation
values are those that constrain the boundary geometry to a finite range of edge
lengths. We argue that such conditions have a correspondence to fixing a range
of local time, as classically associated with the area of a surface for
spatially closed cosmologies. Thus these results may hint at how classical
spacetime emerges from quantum amplitudes.Comment: 26 pages including 10 figures, some reorganization in the
presentation of results, expanded discussion of results in the context of 2+1
gravity in the Witten variables, 3 new reference
Invariants of solvable rigid Lie algebras up to dimension 8
The invariants of all complex solvable rigid Lie algebras up to dimension
eight are computed. Moreover we show, for rank one solvable algebras, some
criteria to deduce to non-existence of non-trivial invariants or the existence
of fundamental sets of invariants formed by rational functions of the Casimir
invariants of the associated nilradical.Comment: 16 pages, 7 table
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