707 research outputs found
Renormalization Mass Scale and Scheme Dependence in the Perturbative Contribution to Inclusive Semileptonic Decays
We examine the perturbative calculation of the inclusive semi-leptonic decay
rate for the -quark, using mass-independent renormalization. To
finite order of perturbation theory the series for will depend on the
unphysical renormalization scale parameter and on the particular choice
of mass-independent renormalization scheme; these dependencies will only be
removed after summing the series to all orders. In this paper we show that all
explicit -dependence of , through powers of ln, can be
summed by using the renormalization group equation. We then find that this
explicit -dependence can be combined together with the implicit
-dependence of (through powers of both the running coupling
and the running -quark mass ) to yield a -independent
perturbative expansion for in terms of and both
evaluated at a renormalization scheme independent mass scale which is
fixed in terms of either the " mass" of the
quark or its pole mass . At finite order the resulting perturbative
expansion retains a degree of arbitrariness associated with the particular
choice of mass-independent renormalization scheme. We use the coefficients
and of the perturbative expansions of the renormalization group
functions and , associated with and
respectively, to characterize the remaining renormalization scheme
arbitrariness of . We further show that all terms in the expansion of
can be written in terms of the and coefficients and a set
of renormalization scheme independent parameters .Comment: 26 pages, 4 figures, typo correcte
Off-Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral
The DeWitt expansion of the matrix element M_{xy} = \left\langle x \right|
\exp -[\case{1}{2} (p-A)^2 + V]t \left| y \right\rangle, in
powers of can be made in a number of ways. For (the case of interest
when doing one-loop calculations) numerous approaches have been employed to
determine this expansion to very high order; when (relevant for
doing calculations beyond one-loop) there appear to be but two examples of
performing the DeWitt expansion. In this paper we compute the off-diagonal
elements of the DeWitt expansion coefficients using the Fock-Schwinger gauge.
Our technique is based on representing by a quantum mechanical path
integral. We also generalize our method to the case of curved space, allowing
us to determine the DeWitt expansion of \tilde M_{xy} = \langle x| \exp
\case{1}{2} [\case{1}{\sqrt {g}} (\partial_\mu - i
A_\mu)g^{\mu\nu}{\sqrt{g}}(\partial_\nu - i A_\nu) ] t| y \rangle by use of
normal coordinates. By comparison with results for the DeWitt expansion of this
matrix element obtained by the iterative solution of the diffusion equation,
the relative merit of different approaches to the representation of as a quantum mechanical path integral can be assessed. Furthermore, the
exact dependence of on some geometric scalars can be
determined. In two appendices, we discuss boundary effects in the
one-dimensional quantum mechanical path integral, and the curved space
generalization of the Fock-Schwinger gauge.Comment: 16pp, REVTeX. One additional appendix concerning end-point effects
for finite proper-time intervals; inclusion of these effects seem to make our
results consistent with those from explicit heat-kernel method
On the Standard Approach to Renormalization Group Improvement
Two approaches to renormalization-group improvement are examined: the
substitution of the solutions of running couplings, masses and fields into
perturbatively computed quantities is compared with the systematic sum of all
the leading log (LL), next-to-leading log (NLL) etc. contributions to
radiatively corrected processes, with n-loop expressions for the running
quantities being responsible for summing N^{n}LL contributions. A detailed
comparison of these procedures is made in the context of the effective
potential V in the 4-dimensional O(4) massless model,
showing the distinction between these procedures at two-loop order when
considering the NLL contributions to the effective potential V.Comment: 6 page
Supersymmetry on AdS3 and AdS4
We consider a supersymmetric extension of the algebra associated with three
and four dimensional Anti de Sitter space. A representation of the
supersymmetry operators in superspace is given. Supersymmetry invariant models
are constructed for the superspace associated with AdS3.Comment: 14 pages, no figures. Final published version. Now includes a
discussion of the relation of our approach to previous work on supersymmetry
in AdS space
- …