704 research outputs found
Effective Field Theory Dimensional Regularization
A Lorentz-covariant regularization scheme for effective field theories with
an arbitrary number of propagating heavy and light particles is given. This
regularization scheme leaves the low-energy analytic structure of Greens
functions intact and preserves all the symmetries of the underlying Lagrangian.
The power divergences of regularized loop integrals are controlled by the
low-energy kinematic variables. Simple diagrammatic rules are derived for the
regularization of arbitrary one-loop graphs and the generalization to higher
loops is discussed.Comment: 22 pages, 11 figures and 1 tabl
Some distance bounds of branching processes and their diffusion limits
We compute exact values respectively bounds of "distances" - in the sense of
(transforms of) power divergences and relative entropy - between two
discrete-time Galton-Watson branching processes with immigration GWI for which
the offspring as well as the immigration is arbitrarily Poisson-distributed
(leading to arbitrary type of criticality). Implications for asymptotic
distinguishability behaviour in terms of contiguity and entire separation of
the involved GWI are given, too. Furthermore, we determine the corresponding
limit quantities for the context in which the two GWI converge to Feller-type
branching diffusion processes, as the time-lags between observations tend to
zero. Some applications to (static random environment like) Bayesian decision
making and Neyman-Pearson testing are presented as well.Comment: 45 page
A modified naturalness principle and its experimental tests
Motivated by LHC results, we modify the usual criterion for naturalness by
ignoring the uncomputable power divergences. The Standard Model satisfies the
modified criterion ('finite naturalness') for the measured values of its
parameters. Extensions of the SM motivated by observations (Dark Matter,
neutrino masses, the strong CP problem, vacuum instability, inflation) satisfy
finite naturalness in special ranges of their parameter spaces which often
imply new particles below a few TeV. Finite naturalness bounds are weaker than
usual naturalness bounds because any new particle with SM gauge interactions
gives a finite contribution to the Higgs mass at two loop order.Comment: 17 pages, 3 figures. v3: final version uploaded, references added,
numerical error in the last column of table 1 fixe
Renormalization group, trace anomaly and Feynman-Hellmann theorem
We show that the logarithmic derivative of the gauge coupling on the hadronic mass and the cosmological constant term of a gauge theory are related to the gluon condensate of the hadron and the vacuum respectively. These relations are akin to FeynmanâHellmann relations whose derivation for the case at hand is complicated by the construction of the gauge theory Hamiltonian. We bypass this problem by using a renormalisation group equation for composite operators and the trace anomaly. The relations serve as possible definitions of the gluon condensates themselves which are plagued in direct approaches by power divergences. In turn these results might help to determine the contribution of the QCD phase transition to the cosmological constant and test speculative ideas
Divergences Test Statistics for Discretely Observed Diffusion Processes
In this paper we propose the use of -divergences as test statistics to
verify simple hypotheses about a one-dimensional parametric diffusion process
\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t, from discrete
observations with , , under the asymptotic scheme , and
. The class of -divergences is wide and includes
several special members like Kullback-Leibler, R\'enyi, power and
-divergences. We derive the asymptotic distribution of the test
statistics based on -divergences. The limiting law takes different forms
depending on the regularity of . These convergence differ from the
classical results for independent and identically distributed random variables.
Numerical analysis is used to show the small sample properties of the test
statistics in terms of estimated level and power of the test
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