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H. F. Jones

Publications and source records attributed to H. F. Jones.

43 records · Page 3Linked to original sources
arXiv1997

Non-perturbative Expansion, Renormalons, and $τ$ Decay

We analyze inclusive $τ$ decay using a modified version of the $a$ expansion, a non-perturbative technique in which the effective coupling is analytic in the infrared region. The modification involves renormalization group improvement of the integrand in a spectral representation for the D-function prior to implementing the $a$ expansion. The advantage of this approach is that it enables us to monitor the structure of the induced power corrections and to ensure that these are consistent with the operator product expansion. Numerically the method agrees well with experiment: the comparison is made with the physical quantity $R_Z$ using $R_τ$ as input.

hep-ph↗
arXiv1996

A New Approach to QCD Sum Rules and Inclusive $τ$ Decay

We show that renormalization group improvement, making use of analyticity and the structure of the operator product expansion, combined with a non-perturbative expansion method allows one to describe quarkonium states via QCD sum rules without the need for explicit power corrections. This technique also allows an accurate determination of parameters related to the inclusive decay of the $τ$ lepton.

hep-ph↗
arXiv1995

Analytic Properties of the QCD Running Coupling Constant and $τ$ Decay

A non-perturbative expansion method which gives a well-defined analytic continuation of the running coupling constant from the spacelike to the timelike region is applied to the inclusive semileptonic decay of the $τ$--lepton. The method allows us to evaluate $R_τ$ by integration over the non-perturbative physical region, rather than by using Cauchy's theorem, and hence to incorporate threshold effects in a very direct way. Within our framework the difference between the effective coupling constants in the timelike and spacelike domains can be substantial and is not simply a matter of the standard $π^2$ terms.

hep-ph↗
arXiv1993

Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude: Zero Dimensions

Recent proofs of the convergence of the linear delta expansion in zero and in one dimensions have been limited to the analogue of the vacuum generating functional in field theory. In zero dimensions it was shown that with an appropriate, $N$-dependent, choice of an optimizing parameter $ł$, which is an important feature of the method, the sequence of approximants $Z_N$ tends to $Z$ with an error proportional to ${\rm e}^{-cN}$. In the present paper we establish the convergence of the linear delta expansion for the connected vacuum function $W=\ln Z$. We show that with the same choice of $ł$ the corresponding sequence $W_N$ tends to $W$ with an error proportional to ${\rm e}^{-c\sqrt N}$. The rate of convergence of the latter sequence is governed by the positions of the zeros of $Z_N$.

hep-th↗