0000000000587818
AUTHOR
A.v. Nesterenko
A novel integral representation for the Adler function
New integral representations for the Adler D-function and the R-ratio of the electron-positron annihilation into hadrons are derived in the general framework of the analytic approach to QCD. These representations capture the nonperturbative information encoded in the dispersion relation for the D-function, the effects due to the interrelation between spacelike and timelike domains, and the effects due to the nonvanishing pion mass. The latter plays a crucial role in this analysis, forcing the Adler function to vanish in the infrared limit. Within the developed approach the D-function is calculated by employing its perturbative approximation as the only additional input. The obtained result …
Quark gap equation within the analytic approach to QCD
The compatibility between the QCD analytic invariant charge and chiral symmetry breaking is examined in detail. The coupling in question incorporates asymptotic freedom and infrared enhancement into a single expression, and contains only one adjustable parameter with dimension of mass. When inserted into the standard form of the quark gap-equation it gives rise to solutions displaying singular confining behavior at the origin. By relating these solutions to the pion decay constant, a rough estimate of about 880 MeV is obtained for the aforementioned mass-scale.
Impact of the pion mass on nonpower expansion for QCD observables
A new set of functions, which form a basis of the massive nonpower expansion for physical observables, is presented in the framework of the analytic approach to QCD at the four-loop level. The effects due to the $\pi$ meson mass are taken into account by employing the dispersion relation for the Adler function. The nonvanishing pion mass substantially modifies the functional expansion at low energies. Specifically, the spacelike functions are affected by the mass of the $\pi$ meson in the infrared domain below few GeV, whereas the timelike functions acquire characteristic plateaulike behavior below the two-pion threshold. At the same time, all the appealing features of the massless nonpower…
The massive analytic invariant charge in QCD
The low energy behavior of a recently proposed model for the massive analytic running coupling of QCD is studied. This running coupling has no unphysical singularities, and in the absence of masses displays infrared enhancement. The inclusion of the effects due to the mass of the lightest hadron is accomplished by employing the dispersion relation for the Adler D function. The presence of the nonvanishing pion mass tames the aforementioned enhancement, giving rise to a finite value for the running coupling at the origin. In addition, the effective charge acquires a "plateau-like" behavior in the low energy region of the timelike domain. This plateau is found to be in agreement with a number…
The QCD analytic running coupling and chiral symmetry breaking
We study the dependence on the pion mass of the QCD effective charge by employing the dispersion relations for the Adler D function. This new massive analytic running coupling is compared to the effective coupling saturated by the dynamically generated gluon mass. A qualitative picture of the possible impact of the former coupling on the chiral symmetry breaking is presented.
Infrared enhanced analytic coupling and chiral symmetry breaking in QCD
We study the impact on chiral symmetry breaking of a recently developed model for the QCD analytic invariant charge. This charge contains no adjustable parameters, other than the QCD mass scale $\Lambda$, and embodies asymptotic freedom and infrared enhancement into a single expression. Its incorporation into the standard form of the quark gap equation gives rise to solutions for the dynamically generated mass that display a singular confining behaviour at the origin. Using the Pagels-Stokar method we relate the obtained solutions to the pion decay constant $f_{\pi}$, and estimate the scale parameter $\Lambda$, in the presence of four active quarks, to be about 880 MeV.