Searcharxiv⌕ Search

arXiv subjects

V. Sauli

Publications and source records attributed to V. Sauli.

At least 19 recordsLinked to original sources
arXiv2025

The effective charm mass from the excited charmonium leptonic decays

We use the covariant four-dimensional Bethe-Salpeter (BS) equation to determine the effective charm quark mass. The scale dependence of the effective charm quark mass is determined using experimentally known spin-one charmonium spectra and leptonic decay constants. The infrared finite, massive-like effective QCD running charge is used to solve the Bethe-Salpeter equation to achieve this. The obtained effective charm quark mass values run from 1.1 GeV for the $J/Psi$ meson to 1.5 GeV for its higher radial excitations. These values are substantially smaller than those extracted in the perturbative MS renormalization scheme, but they agree with the semi-perturbative solution of the quark Schwinger-Dyson equation in the momentum subtraction scheme. Within the interaction entirely governed by QCD running coupling, the sliding scale charm quark mass is crucial for the correct determination of leptonic decays. Notably, for leptonic decay constants of excited states, this is the first time the theory based on Bethe-Salpeter equation has met the precision of the experimental data.

hep-ph↗
arXiv2025

Excited s-wave $1^{--}$ vector mesons, their leptonic decays and (in-)complete absence of abnormal states as seen from the constituent quark BSE

Within a lattice inspired interaction between quark and antiquark, we obtain a hierarchy of solutions to the Bethe-Salpeter equation (BSE) for vector quarkonia excited states in the constituent quark mass approximation. As a toy model, we apply the similar to calculate ground and excited states of $\phi$ and $\omega/\rho$ meson. Through detailed numerical searches, our study provides evidence that the single-valued constant mass quark propagator does not yield known meson spectra without the simultaneous presence of abnormal (unphysical) solutions. We classify normal and abnormal solutions and discuss necessary changes in the calculation scheme to avoid the spectrum of inconsistent solutions. While all experimental narrow vector mesons are identified with a normal state of the BSE, the occurrence of mutually cancelled normal-abnormal states are reported. The results are slightly different for the heavy and light mesons, but in both cases they seem to result from the inconsistent use of the hmogeneous BSE to describe broad resonances.

hep-ph↗
arXiv2020

Gauge Technique approximation to the $πγ$ production and the pion transition form factor

The pion transition form factor $G(q^2)$ is computed on the entire domain of spacelike and timelike momenta using a quantum field theory continuum approach. In analytical continuation of the function $G(Q^2)$ we utilized the Gauge Technique with the quark propagator determined from Minkowski space solution of QCD Dyson-Schwinger equations. The scale is set up by the phenomena of dynamical chiral symmetry breaking, which is a striking feature of low energy QCD.

hep-ph↗
arXiv2019

Electromagnetic production of pions and quark dynamical mass in Minkowski space

Mechanism for generation of vector meson resonances is studied in the framework of QCD Dyson-Schwinger equations, which are defined and actually solved in Minkowski space. It is suggested that the timelike pion form factor is generated by the interference of the background quark loops together with the resonant structure predominantly created in the photon-quark-antiquark vertex. It is suggested that QCD Green's functions involving quark fields are oscillating for timelike arguments, which makes the interference effect among various QCD Green's functions quite strong and important for the correct description of production processes. A further peculiarities of dynamical chiral symmetry breaking and confinement phenomena as viewed in Minkowski space are discussed.

hep-ph↗
arXiv2016

Analytical solution for the correlator with Gribov propagators

Propagators approximated by a meromorphic functions with complex conjugated poles are widely used to model infrared behavior of QCD Green's functions. In this paper, analytical solutions for two point correlator made out of functions with complex conjugated poles or branch points have been obtained in the Minkowski space for the first time. As a special case the Gribov propagator has been considered as well. The result is different from the naive analytical continuation of the correlator primarily defined in the Euclidean space. It is free of ultraviolet divergences, and instead of Lehmann it rather satisfies Gribov integral representation.

hep-th↗
arXiv2014

Pions and excited scalars in Minkowski space DSBSE formalism

We present the solution of Schwinger-Dyson and Bethe-Salpeter equation (BSE) for a light flawour non-singlet spinless meson in Minkowski space. The equations are solved in momentum space without the use of the auxiliary Euclidean space. To exhibit that Minkowski space non perturbative calculations are actually possible is the main purpose of presented paper. According to confinement, the quark propagator is regular in momentum space, which allows us to look for the BSE solution directly in the Minkowski momentum space. We find the Minkowski space solution for confining theories is not only numerically accessible, but also provides a reasonable description of the pseudoscalar meson system. However, in the case of scalar mesons, the model is less reliable and we get more extra light states then observed experimentally.

hep-ph↗
arXiv2010

Chiral Symmetry Breaking and confinement in Minkowski space QED2+1

Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Obtained complex fermion propagator exhibits confinement in the sense that it has no pole. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. Obvious invalidity of Wick rotation is briefly discussed. The infrared value of the dynamical mass is compared with other known approaches, e.g. with the standard Euclidean calculation.

hep-ph↗
arXiv2009

Confinement, Chiral Symmetry Breaking and complex mass in QED2+1 in Minkowski and Euclidean spaces

Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. The obtained complex fermion propagator exhibits confinement because of the lack of the pole at the real timelike $q^2$ axis.

hep-ph↗
arXiv2009

Behaviour of propagator and quark confinement

The propagator of confined quarks is calculated for timelike momenta by transforming Minkowski Greens functions to the Temporal Euclidean space. Based on the framework of the Schwinger-Dyson equations the QCD quark propagator is obtained in two approximations which differ by assuming behaviour of gluon propagator. In both studied cases we get universal result for the light quarks: The quark mass function becomes complex bellow expected perturbative threshold, the obtained absolute value of the infrared mass is $M\simeq Λ_{QCD} $ with the infrared phase $\simeq {π\over 2}$. Permanent confinement of quarks is maintained by generation of the complex mass function which prevents a real pole in the propagator. We will show that timelike dynamical Chiral Symmetry Breaking (CSB) solution is approximately, but non-trivially determined by the solution of gap equation in the standard Euclidean space.

hep-ph↗
arXiv2008

Quark Schwinger-Dyson equation in temporal Euclidean space

We present an elementary nonperturbative method to obtain Green's functions (GFs) for timelike momenta. We assume there are no singularities in the first and third quadrants of the complex plane of space momentum components and perform a 3d analogue of Wick rotation. This procedure defines Greens functions in a timelike Euclidean space. As an example we consider the quark propagator in QCD. While for weak coupling, this method is obviously equivalent to perturbation theory, for a realistic QCD coupling a complex part of the quark mass and renormalization wave function has been spontaneously generated even below the standard perturbative threshold. Therefore, our method favors a confinement mechanism based on the lack of real poles.

hep-ph↗
arXiv2008

Running Top quark mass in the presence of light SM Higgs

The running of the Top quark mass is considered in the nonperturbative framework of the Schwinger-Dyson equation. Based on the input of physical pole mass meassured at the Tevatron the method provides the resulting mass function which is almost constant at low spacelike and timelike scales. The skeleton loops including Standard Model Higgs and gluons are taken into account. The dominant two-loop skeleton contribution with triplet Higgs interaction is considered in addition to one loop dressed approximation of the top quark self-energy.

hep-ph↗
arXiv2008

Spectrum of Higgsonium in the SM and beyond

Using the formalism of Bethe-Salpeter equation (BSE) the Higgsonium bound state is studied. The condition for formation of Higgsonium bound states are discussed in SM and in the simple extension of.

hep-ph↗
arXiv2008

Solving the Bethe-Salpeter equation for a pseudoscalar meson in Minkowski space

A new method of solution of the Bethe-Salpeter equation for a pseudoscalar quark-antiquark bound state is proposed. With the help of an integral representation, the results are directly obtained in Minkowski space. Dressing of Green's functions is naturally taken into account, thus providing the possible inclusion of a running coupling constant as well as quark propagators. First numerical results are presented for a simplified ladder approximation.

hep-ph↗
arXiv2007

On the quark propagator singularity

Using the method of Fukuda and Kugo \cite{FUKKUG} the continuation of Euclidean solution is performed to the timelike axis of fourmomenta. It is shown that assumed presence of the real simple pole in quark propagator is not in agreement with the solution. The simple pole disappears because of the discontinuity in the resulting quark mass function.

hep-ph↗
arXiv2007

On the absence and presence of pole(s) in fermion propagator in the simple model with mass generation

Within the Pauli-Villars regularization technique the fermion propagator is studied in the framework of Schwinger-Dyson equations in the Euclidean space. Making the generalization of Fukuda and Kugo proposals, the analytical continuation is performed into the timelike region of fourmomenta. The massive gauge boson kernel is considered and the fermion propagator pole structure is discussed in detail.

hep-ph↗
arXiv2007

Dynamical chiral symmetry breaking with Minkowski space integral representations

The fermion propagator is studied in the whole Minkowski space with the help of the Schwinger-Dyson equations. Various integral representations are employed to get solutions for the dynamical breaking of chiral symmetry in different regimes of the coupling constant. In particular, in the case of massive boson, we extend the singularity structure of the fermion propagator to the two real pole Ansatz.

hep-ph↗
arXiv2007

Solving the Bethe-Salpeter equation for fermion-antifermion pseudoscalar bound state in Minkowski space

The new method of solution of the Bethe-Salpeter equation for quark-antiquark pseudoscalar bound state is proposed. With the help of integral representation the results are directly obtained in Minkowski space. Dressing of Greens functions is naturally considered providing thus the correct inclusion of the running coupling constant and the quark propagators as well as. The first numerical results are presented for a simplified ladder approximation.

hep-ph↗