Optimal Jet Finder

We describe a FORTRAN 77 implementation of the optimal jet definition for identification of jets in hadronic final states of particle collisions. We discuss details of the implementation, explain interface subroutines and provide a usage example. The source code is available from http://www.inr.ac.ru/~ftkachov/projects/jets/Comment: version to appear in Comp. Phys. Commun., 36 page

Pouzyry: a novel class of algorithms for restoring a function from a random sample

A novel class of algorithms for restoring a function from a random sample is based on the concept of weak convergence, borrows algorithmic solutions from the Optimal Jet Finder (hep-ph/0301185), offers a considerable algorithmic flexibility, is applicable to non-positive functions, is insensitive to the choice of coordinate axes. A first implementation demonstrates feasibility of the approach.Comment: 4p PS; talk at ACAT'03; see also http://www.inr.ac.ru/~ftkachov/projects/pouzyry/; v.3: refs. adde

Threshold expansion for heavy-light systems and flavor off-diagonal current-current correlators

An expansion scheme is developed for Feynman diagrams describing the production of one massive and one massless particle near the threshold. As an example application, we compute the correlators of heavy-light quark currents, (\bar b gamma_mu u) and (\bar b gamma_5 u), through O(alpha_s^2).Comment: 4 pages, revtex

The Asymptotic Expansion of Lattice Loop Integrals Around the Continuum Limit

We present a method of computing any one-loop integral in lattice perturbation theory by systematically expanding around its continuum limit. At any order in the expansion in the lattice spacing, the result can be written as a sum of continuum loop integrals in analytic regularization and a few genuine lattice integrals (``master integrals''). These lattice master integrals are independent of external momenta and masses and can be computed numerically. At the one-loop level, there are four master integrals in a theory with only bosonic fields, seven in HQET and sixteen in QED or QCD with Wilson fermions.Comment: 9 pages, 2 figure

Dispersive calculation of the massless multi-loop sunrise diagram

The massless sunrise diagram with an arbitrary number of loops is calculated in a simple but formal manner. The result is then verified by rigorous mathematical treatment. Pitfalls in the calculation with distributions are highlighted and explained. The result displays the high energy behaviour of the massive sunrise diagrams, whose calculation is involved already for the two-loop case.Comment: 10 pages, 1 figure, LATEX, uses kluwer.cls, some references adde

Energy Flow in Interjet Radiation

We study the distribution of transverse energy, Q_Omega, radiated into an arbitrary interjet angular region, Omega, in high-p_T two-jet events. Using an approximation that emphasizes radiation directly from the partons that undergo the hard scattering, we find a distribution that can be extrapolated smoothly to Q_Omega=Lambda_QCD, where it vanishes. This method, which we apply numerically in a valence quark approximation, provides a class of predictions on transverse energy radiated between jets, as a function of jet energy and rapidity, and of the choice of the region Omega in which the energy is measured. We discuss the relation of our approximation to the radiation from unobserved partons of intermediate energy, whose importance was identified by Dasgupta and Salam.Comment: 26 pages, 8 eps figures. Revised to include a discussion of non-global logarithm

Explicit results for all orders of the epsilon-expansion of certain massive and massless diagrams

An arbitrary term of the epsilon-expansion of dimensionally regulated off-shell massless one-loop three-point Feynman diagram is expressed in terms of log-sine integrals related to the polylogarithms. Using magic connection between these diagrams and two-loop massive vacuum diagrams, the epsilon-expansion of the latter is also obtained, for arbitrary values of the masses. The problem of analytic continuation is also discussed.Comment: 8 pages, late

Current correlators to all orders in the quark masses

The contributions to the coefficient functions of the quark and the mixed quark-gluon condensate to mesonic correlators are calculated for the first time to all orders in the quark masses, and to lowest order in the strong coupling constant. Existing results on the coefficient functions of the unit operator and the gluon condensate are reviewed. The proper factorization of short- and long-distance contributions in the operator product expansion is discussed in detail. It is found that to accomplish this task rigorously the operator product expansion has to be performed in terms of non-normal-ordered condensates. The resulting coefficient functions are improved with the help of the renormalization group. The scale invariant combination of dimension 5 operators, including mixing with the mass operator, which is needed for the renormalization group improvement, is calculated in the leading order.Comment: 24 pages, LateX file, TUM-T31-21/92, 1 postscript file include

Two-loop corrections to the Isgur-Wise function in QCD sum rules

We complete the QCD sum rule analysis of the Isgur Wise form factor $\xi(v\cdot v')$ at next-to-leading order in renormalization-group improved perturbation theory. To this end, the exact result for the two-loop corrections to the perturbative contribution is derived using the heavy quark effective theory. Several techniques for the evaluation of two-loop integrals involving two different types of heavy quark propagators are discussed in detail, among them the methods of integration by parts and differential equations. The order-$\alpha_s$ corrections to the Isgur-Wise function turn out to be small and well under control. At large recoil, they tend to decrease the form factor by $5-10\%$.Comment: 24 pages (REVTEX), 2 figures available upon request, SLAC-PUB-599

Two-loop Anomalous Dimensions of Heavy Baryon Currents in Heavy Quark Effective Theory

We present results on the two-loop anomalous dimensions of the heavy baryon HQET currents $J=(q^TC\Gamma\tau q)\Gamma'Q$ with arbitrary Dirac matrices $\Gamma$ and $\Gamma'$. From our general result we obtain the two-loop anomalous dimensions for currents with quantum numbers of the ground state heavy baryons $\Lambda_Q$, $\Sigma_Q$ and $\Sigma_Q^*$. As a by-product of our calculation and as an additional check we rederive the known two-loop anomalous dimensions of mesonic scalar, pseudoscalar, vector, axial vector and tensor currents $(J=\bar q\Gamma q)$ in massless QCD as well as in HQET.Comment: 21 pages, LaTeX, 2 figures are included in PostScript forma