49 research outputs found
Algebraic connections on parallel universes
For any manifold , we introduce a \ZZ -graded differential algebra
, which, in particular, is a bi-module over the associative algebra
. We then introduce the corresponding covariant differentials and
show how this construction can be interpreted in terms of Yang-Mills and Higgs
fields. This is a particular example of noncommutative geometry. It differs
from the prescription of Connes in the following way: The definition of
does not rely on a given Dirac-Yukawa operator acting on a space of spinors.Comment: 10 pages, CPT-93/PE 294
COMMENTS ABOUT HIGGS FIELDS, NONCOMMUTATIVE GEOMETRY AND THE STANDARD MODEL
We make a short review of the formalism that describes Higgs and Yang Mills
fields as two particular cases of an appropriate generalization of the notion
of connection. We also comment about the several variants of this formalism,
their interest, the relations with noncommutative geometry, the existence (or
lack of existence) of phenomenological predictions, the relation with Lie
super-algebras etc.Comment: pp 20, LaTeX file, no figures, also available via anonymous ftp at
ftp://cpt.univ-mrs.fr/ or via gopher gopher://cpt.univ-mrs.fr
Triangular Textures for Quark Mass Matrices
The hierarchical quark masses and small mixing angles are shown to lead to a
simple triangular form for the U- and D-type quark mass matrices. In the basis
where one of the matrices is diagonal, each matrix element of the other is, to
a good approximation, the product of a quark mass and a CKM matrix element. The
physical content of a general mass matrix can be easily deciphered in its
triangular form. This parameterization could serve as a useful starting point
for model building. Examples of mass textures are analyzed using this method.Comment: 10 pages, no figure
The Nielsen Identities of the SM and the definition of mass
In a generic gauge theory the gauge parameter dependence of individual Green
functions is controlled by the Nielsen identities, which originate from an
enlarged BRST symmetry. We give a practical introduction to the Nielsen
identities of the Standard Model (SM) and to their renormalization and
illustrate the power of this elegant formalism in the case of the problem of
the definition of mass.We prove to all orders in perturbation theory the
gauge-independence of the complex pole of the propagator for all physical
fields of the SM, in the most general case with mixing and CP violation. At the
amplitude level, the formalism provides an intuitive and general understanding
of the gauge recombinations which makes it particularly useful at higher
orders. We also include in an appendix the explicit expressions for the
fermionic two-point functions in a generic R_\xi gauge.Comment: 28 pages, LaTeX2e, 4 Postscript Figures, final version to appear on
PRD, extensive revision
Testing quark mass matrices with right-handed mixings
In the standard model, several forms of quark mass matrices which correspond
to the choice of weak bases lead to the same left-handed mixings ,
while the right-handed mixings are not observable quantities. Instead, in
a left-right extension of the standard model, such forms are ansatze and give
different right-handed mixings which are now observable quantities. We
partially select the reliable forms of quark mass matrices by means of
constraints on right-handed mixings in some left-right models, in particular on
. Hermitian matrices are easily excluded.Comment: 12 pages RevTex, no figures. Minor corrections. Comment on SO(10)
changed and one reference adde
Pinch Technique and the Batalin-Vilkovisky formalism
In this paper we take the first step towards a non-diagrammatic formulation
of the Pinch Technique. In particular we proceed into a systematic
identification of the parts of the one-loop and two-loop Feynman diagrams that
are exchanged during the pinching process in terms of unphysical ghost Green's
functions; the latter appear in the standard Slavnov-Taylor identity satisfied
by the tree-level and one-loop three-gluon vertex. This identification allows
for the consistent generalization of the intrinsic pinch technique to two
loops, through the collective treatment of entire sets of diagrams, instead of
the laborious algebraic manipulation of individual graphs, and sets up the
stage for the generalization of the method to all orders. We show that the task
of comparing the effective Green's functions obtained by the Pinch Technique
with those computed in the background field method Feynman gauge is
significantly facilitated when employing the powerful quantization framework of
Batalin and Vilkovisky. This formalism allows for the derivation of a set of
useful non-linear identities, which express the Background Field Method Green's
functions in terms of the conventional (quantum) ones and auxiliary Green's
functions involving the background source and the gluonic anti-field; these
latter Green's functions are subsequently related by means of a Schwinger-Dyson
type of equation to the ghost Green's functions appearing in the aforementioned
Slavnov-Taylor identity.Comment: 45 pages, uses axodraw; typos corrected, one figure changed, final
version to appear in Phys.Rev.
The pinch technique at two-loops: The case of mass-less Yang-Mills theories
The generalization of the pinch technique beyond one loop is presented. It is
shown that the crucial physical principles of gauge-invariance, unitarity, and
gauge-fixing-parameter independence single out at two loops exactly the same
algorithm which has been used to define the pinch technique at one loop,
without any additional assumptions. The two-loop construction of the pinch
technique gluon self-energy, and quark-gluon vertex are carried out in detail
for the case of mass-less Yang-Mills theories, such as perturbative QCD. We
present two different but complementary derivations. First we carry out the
construction by directly rearranging two-loop diagrams. The analysis reveals
that, quite interestingly, the well-known one-loop correspondence between the
pinch technique and the background field method in the Feynman gauge persists
also at two-loops. The renormalization is discussed in detail, and is shown to
respect the aforementioned correspondence. Second, we present an absorptive
derivation, exploiting the unitarity of the -matrix and the underlying BRS
symmetry; at this stage we deal only with tree-level and one-loop physical
amplitudes. The gauge-invariant sub-amplitudes defined by means of this
absorptive construction correspond precisely to the imaginary parts of the
-point functions defined in the full two-loop derivation, thus furnishing a
highly non-trivial self-consistency check for the entire method. Various future
applications are briefly discussed.Comment: 29 pages, uses Revtex, 22 Figures in a separate ps fil