55,393 research outputs found
Adler Function, DIS sum rules and Crewther Relations
The current status of the Adler function and two closely related Deep
Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for
polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A
new result is presented: an analytical calculation of the coefficient function
of the latter sum rule in a generic gauge theory in order O(alpha_s^4). It is
demonstrated that the corresponding Crewther relation allows to fix two of
three colour structures in the O(alpha_s^4) contribution to the singlet part of
the Adler function.Comment: Talk presented at 10-th DESY Workshop on Elementary Particle Theory:
Loops and Legs in Quantum Field Theory, W\"orlitz, Germany, 25-30 April 201
Higher Resonance Contributions to the Adler-Weisberger Sum Rule in the Large N_c Limit
We determine the --dependence of the resonance contributions to the
Adler--Weisberger sum rule for the inverse square of the axial charge
coupling constant and show that in the large limit the contributions of
the Roper-like excitations scale as . Consistency with the
scaling of the term in the sum rule requires these contributions to
cancel against each other.Comment: 10 pages, LaTeX, TH Darmstadt preprint IKDA 93/47, REVISE
Evaluation of the Axial Vector Commutator Sum Rule for Pion-Pion Scattering
We consider the sum rule proposed by one of us (SLA), obtained by taking the
expectation value of an axial vector commutator in a state with one pion. The
sum rule relates the pion decay constant to integrals of pion-pion cross
sections, with one pion off the mass shell. We remark that recent data on
pion-pion scattering allow a precise evaluation of the sum rule. We also
discuss the related Adler--Weisberger sum rule (obtained by taking the
expectation value of the same commutator in a state with one nucleon),
especially in connection with the problem of extrapolation of the pion momentum
off its mass shell. We find, with current data, that both the pion-pion and
pion-nucleon sum rules are satisfied to better than six percent, and we give
detailed estimates of the experimental and extrapolation errors in the closure
discrepancies.Comment: Plain TeX file;minor changes; version to be published in Pys. Rev. D;
corrected refs.12,1
Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
The analytic result for the singlet part of the Adler function of the vector
current in a general gauge theory is presented in five-loop approximation.
Comparing this result with the corresponding singlet part of the
Gross-Llewellyn Smith sum rule [1], we successfully demonstrate the validity of
the generalized Crewther relation for the singlet part. This provides a
non-trivial test of both our calculations and the generalized Crewther
relation. Combining the result with the already available non-singlet part of
the Adler function [2,3] we arrive at the complete
expression for the Adler function and, as a direct consequence, at the complete
correction to the annihilation into hadrons in
a general gauge theory.Comment: 4 pages, 1 figure. Final published versio
Sum Rules for Radiative and Strong Decays of Heavy Mesons
We derive two model-independent sum rules relating the transition matrix
elements for radiative and strong decays of excited heavy mesons to properties
of the lowest-lying heavy mesons. The sum rule for the radiative decays is an
analog of the Cabibbo-Radicati sum rule and expresses the sum of the radiative
widths in terms of the isovector charge radius of the ground state heavy meson.
Using model-dependent estimates and heavy hadron chiral perturbation theory
calculations, we show that this sum rule is close to saturation with states of
excitation energies less than 1 GeV. An analog of the Adler-Weisberger sum rule
gives an useful sum rule for the pionic widths of heavy excited mesons, which
is used to set a model-independent upper bound on the coupling of the P-wave
heavy mesons.Comment: 12 pages, REVTe
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