arXiv subjects
Publications and source records attributed to M. L. Nekrasov.
The method of the top quark mass measurement from $M_{b l}$ distribution in $t \to b l ν$ decays can be considerably improved if applying the technique of moments and proceeding to moments of high degree. At the LHC this allows one to reduce the systematic and statistical errors of the top mass by more than a factor of two.
We explore a possibility of optimization of the method of determination of the top quark mass from $M_{b\ell}$ distribution in semi-leptonic decays $t \to b \ellν$ at LHC and a future linear collider (LC). We discover that the systematic and statistical errors of $M_t$ determination can be diminished if considering the high moments over the distribution. In the case of LHC this allows one to reduce more than in twice the errors, and in the case of LC to approach to the precision expected at studying the threshold scan of the total cross-section $e^+e^- \to t\bar t$.
An integral in the sense of principal value of a singular function or of product of singular functions can appear itself as a singular function in some range of values of integration parameters. In this case, if necessary subsequently to integrate with respect to parameters, the problem arises about interpretation of the initial integral as a distribution over the integration parameters. A solution to this problem is offered, which is initiated by actual applications in quantum field theory.
The modified perturbation theory (MPT), based on direct expansion of probabilities instead of amplitudes, allows one to avoid divergences in the phase-space integrals resulting from production and decay of unstable particles. In the present paper the range of applicability of MPT is determined numerically in the case of the process $e^+e^- \to (γ,Z) \to t\bar t \to W^{+}b:W^{-}\bar b$. It is shown that with the complete expansion in powers of the coupling constant (without Dyson resummation) MPT operates best at the energies located near the maximum of the cross-section and slightly above the maximum. In this region the MPT expansion within the next-to-leading order considerably exceeds in accuracy well-known DPA approach.
A generalization of the on-mass-shell scheme of UV renormalization (the OMS-bar scheme) to the case of presence of unstable fundamental particles (like W and Z bosons) is proposed. Its basic ingredients are as follows: (i) the renormalized mass coincides with a real part of the position of the complex pole of the corresponding propagator, (ii) the imaginary part of the on-shell self-energy coincides with the imaginary part of the complex pole position. The latter property implies the gauge-invariance of the imaginary part of the on-shell self-energy in the OMS-bar scheme and its connection with the lifetime of an unstable particle. Starting with the three-loops this connection becomes nontrivial.
The processes of production and subsequent decay of W- and Z-bosons in $e^+ e^-$ collisions are considered in a recently proposed modified perturbation theory (PT), based on a direct expansion of probabilities instead of amplitudes. In such an approach the non-integrable singularities in the phase space, which are intrinsic in the conventional PT, appear as singularities in the coupling constant (with subsequent compensation by the decay factors of unstable particles). In the present paper the systematic investigation of the modified PT is carried out. The results are compared with the results of the conventional approach, based on calculation of the amplitude with Dyson resummation. A solution to the problem of the loss of one-loop PT order in the resonance region is found. On the basis of this solution the proof of gauge cancellations in any order of the modified PT is given. A simple generalization of the fermion-loop scheme is proposed which provides a complete description of W-pair production in next-to-leading order approximation.
The processes $e^{+}e^{-} \to 4f(γ)$ mediated by W-pair (and single) production are considered in the framework of the modified perturbation theory, based on the expansion of probability in powers of the coupling constant instead of amplitude. A full set of one-loop corrections to cross-section, and two-loop corrections to self-energy of unstable particles are completely taken into consideration. It is shown that the manifestly non-factorizable corrections do not make contributions into the next-to-leading-order approximation. Moreover, the colour reconnection does not make contributions within this precision, either. The rest of the corrections together with the leading-order contribution provide the gauge-invariant description of the processes.
The nature of $ι/η(1440)$ is analysed in the framework of the hypothesis that it represents a single pseudoscalar resonance. Assuming that it arises due to the mixing between the glueball and the $q\bar q$ nearby states ($η$, $η'$, and their radial excitations) two upper estimates are obtained for the partial width $Γ(ι/η(1440) \to K^* K)$ --- one for the case when $ι/η(1440)$ is mainly a glueball and another one when it is mainly a radial excitation of the $s\bar s$ state. Both estimates are obtained in the chiral perturbation theory approach taking into account the available data on the vector mesons and the pseudoscalar state K(1460), which is interpreted as a radial excitation of the $K$ meson. The same partial width is independently estimated on the basis of the combined OBELIX and Crystal Barrel data on the production of $ι/η(1440)$ in $p\bar p$ annihilation. Comparing the results we show that the glueball content of $ι/η(1440)$ is suppressed while its $s\bar s$ radial-excitation interpretation is favoured by the data.
A generalization of the chiral effective lagrangian of order $p^2$ is proposed which involves the $η'$-meson, its excitation, and the pseudoscalar (PS) glueball. Model-independent constraints are found for the contributions to the lagrangian of the above singlet states. Those allow one to independently identify the nature of these singlet states in the framework of the approach. The mixing among the iso-singlet states (including $η^8$-state) is analysed, and the hierarchy of the mixing angles is described which is defined by the chiral and large-$N_c$ expansions. The recent PCAC results are reproduced, which are related to the problem of the renormalization-group invariant description of the $η'$ and the PS glueball, and a further analysis of this problem is performed.
An effective chiral lagrangian of order $p^2$, describing the interaction of light pseudoscalar (PS) mesons with $η'$-meson and PS-glueball, has been determined taking into consideration the renorm-group requirements imposed by QCD renormalization. It is shown that the interpolating fields for the lowest singlet quarkic and gluonic states, $η^0$ and $η^G$, may be involved into the effective theory to be renorm-invariant objects not mixing due to QCD renormalization. It is established that the potential describing the ``mass'' term of the lagrangian does not depend on $η^0$. The dependence on $η^G$ is permitted only when there is not direct interaction between $η^0$ and $η^G$ out of the ``mass'' term without the octet fields contribution. The peculiarities distinguishing the glueball from excitation over $η^0$ have been considered.