arXiv subjects
Publications and source records attributed to S. I. Troyan.
The non-radiative scattering amplitudes for electron-positron annihilation into quark and lepton pairs in the TeV energy range are calculated in the double-logarithmic approximation. The expressions for the amplitudes are obtained using infrared evolution equations with different cut-offs for virtual photons and for W and Z bosons, and compared with previous results obtained with an universal cut-off.
The running of the QCD coupling is incorporated into the infrared evolution equations for the flavour structure function g_1. The explicit expressions for g_1 including the total resummation of the double-logarithmic contributions and accounting for the running coupling are obtained. We predict that asymptotically g_1 ~ x^{- Δ_S}, with the intercept Δ_S = 0.86, which is more than twice larger than the non-singlet intercept. The impact of the initial quark (δq) and gluon (δg) densities on the sign of g_1 at x << 1 is discussed and explicit expressions relating δq and δg are obtained.
The running QCD coupling effects for $g_1$ singlet are studied. We predict that asymptotically $g_1^S \sim x^{- Δ_S}$, with the singlet intercept $Δ_S \approx 0.85$.
The impact of the electroweak radiative corrections on the value of the forward-backward asymmetry in e^+ e^- annihilation into a quark-antiquark pair is considered in the double-logarithmic approximation at energies much higher than the masses of the weak bosons.
Accounting for double-logarithmic contributions to high-energy (>> 100 GeV) e^+ e^- annihilation into a quark or a lepton pair in the kinematics where the final particles are colinear to the e^+e^- beams leading to a sizable difference between the forward and backward scattering amplitudes, i.e. to the forward-backward asymmetry. When the annihilation is accompanied by emission of n electroweak bosons in the multi-Regge kinematics, it turns out that the cross sections of the photon and Z production have the identical energy dependence and asymptotically their ratio depends only on the Weinberg angle (is equal to tan^{2n} theta_W) whereas the energy dependence of the cross section of the W production is suppressed by factor s^{-0.4} compared to them.
The forward-backward asymmetry in e+ e- annihilation into a quark-antiquark pair is considered in the double-logarithmic approximation at energies much higher than the masses of the weak bosons. It is shown that after accounting to all orders for the exchange of virtual photons and W, Z -bosons one is lead to the following effect (asymmetry): quarks with positive electric charge (e.g. u, \bar{d}) tend to move in the e+ - direction whereas quarks with negative charges (e.g. d, \bar{u}) tend to move in the e- - direction. The value of the asymmetry grows with increasing energy when the produced quarks are within a cone with opening angle, in the cmf, θ_0\sim 2M_Z/\sqrt{s} around the e+e- -beam. Outside this cone, at θ_0 << θ<< 1, the asymmetry is inversely proportional to θ.
Production of electroweak bosons in e+e- annihilation into quarks and into leptons at energies much greater than 100 Gev is considered. We account for double-logarithmic contributions to all orders in electroweak couplings. It is assumed that the bosons are emitted in the multi-Regge kinematics. The explicit expressions for the scattering amplitudes of the process are obtained. It is shown that the cross sections of the photon and Z production have the identical energy dependence and asymptotically their ratio depends only on the Weinberg angle whereas the energy dependence of the cross section of the W production is suppressed by factor s^{-0.4} compared to them.
The treatment of the running QCD coupling in evolution equations is discussed. It is shown that the use of the virtuality of ladder (vertical) partons as the scale for QCD coupling in every rung of ladder graphs is an approximation that holds for DIS at large x only. On the contrary, in the small x region the coupling depends on the virtuality of s -channel (horizontal) gluons. This observation leads to different results for the Regge-like processes and DIS structure functions at small x.
Talk given at 9th Workshop DIS 2001, Bologna, April,27 -May,1, 2001.
The asymptotic behaviour of the electromagnetic form factors of the electron and quark is obtained in the double-logarithmic approximation for Sudakov kinematics, i.e. for the case that the value of the momentum transfer is much greater than the mass of the particle.
Infrared evolution equations for small-$x$ behaviour of the non-singlet structure functions $f_1^{NS}$ and $g_1^{NS}$ are obtained and solved in the next-to-leading approximation, to all orders in $α_s$, and including running $α_s$ effects. The intercepts of these structure functions, i.e. the exponents of the power-like small-$x$ behaviour, are calculated. A detailed comparison with the leading logarithmic approximation (LLA) and DGLAP is made. We explain why the LLA predictions for the small-$x$ dependence of the structure functions may be more reliable than the prediction for the $Q^2$ dependence in the range of $Q^2$ explored at HERA.
A generalization of the leading-order DGLAP evolution at small x is performed for the non-singlet structure function by resumming the leading-order DGLAP anomalous dimension to all orders in the QCD coupling. Explicit expressions are obtained for the non-singlet structure function of the deep inelastic scattering, taking into account both the double-logarithmic and the single-logarithmic contributions, including the running alpha_s effects. It is shown that when these contributions are included, the asymptotic small-x behaviour is power-like, with an exponent of about 0.4.
The asymptotical behaviour of the magnetic form factor for electron and quark is obtained in the double-logarithmic approximation for the Sudakov kinematics, i.e. for the case when the value of the transfer momentum is much greater than the mass of the particle.
We show that for small x and in the double logarithmic approximation (DLA) g_2 can be expressed through derivative of g_1 with respect to logarithm of the QCD coupling. Therefore the small-x behavior of the both structure functions is similar. The analytical expression for flavor nonsinglet structure function g_1 is presented and its asymptotical behaviour is calculated.
Nonsinglet structure function g_2(x) for deep inelastic scattering of a lepton on a constituent quark is calculated in the double logarithmic approximation at x<<1. Small-x asymptotics of g_2 is shown to have the same singular behaviour as asymptotics of the nonsinglet structure function g_1.
Perturbative QCD formula for inclusive energy spectra of heavy quarks from heavy quark initiated jets which takes into account collinear and/or soft logarithms in all orders, the exact first order result and two-loop effects is applied to distributions of heavy flavoured hadrons in the framework of the LPHD concept. Fits to experimentally measured charm and bottom mean energy losses result in $α_{\MSbar}(M_Z)=0.125\pm 0.003\pm 0.004$ and $(2\GeV)^{-1}\int_0^{2\GeV} dk α_s^{eff}(k)= 0.18\pm 0.01\pm 0.02$ with $α_s^{eff}$ an infrared finite effective QCD coupling.