arXiv subjects

Vladimir Sauli

Publications and source records attributed to Vladimir Sauli.

At least 19 recordsLinked to original sources

arXiv2026

Dispersive analysis of the $π^+ π^-$ production at the CMD3 experiment and the compatibility with muon pair production measurement by KLOE2 and the pion form factor by JLAB

The spectral function of the charged pion form factor was extracted from two data sets. The difference between the two sets is based on the presence or absence of the recent measurement of the $π^+ π^-$ production by CMD-3 . Although the CMD-3 data are largely incompatible with other recent measurements, no excess was found when the data were used for analytical continuation to the spacelike region and compared to JLaB-$π$ experiment. Instead, both data sets provide a spacelike form factor that differs from the expected behavior known from perturbative analyses of quantum chromodynamics (QCD). A precise fit of the spectral functions is provided, either based on he bare form factor and the full $e^+e^-\rightarrow π^+π^-$ as well . Furthermore, the extracted pionic spectral functions were used to obtain the QED running charge. This was then compared with the KLOE-2 measurements.

hep-ex↗

arXiv2026

Quark spectral functions from spectra of mesons and vice versa

We extract the spectral function of quarks using the QCD functional formalism.The reliability of approximations is controlled by the masses and decays of pseudoscalar mesons. For light quarks, we select the pion; for charm quarks, we choose the ground and excited states of the $η_c$ meson. To this end, we solved the ladder-rainbow approximation of the spectral Dyson-Schwinger equations for quarks coupled to the Bethe-Salpeter equation for the pion and pseudoscalar charmonia. The obtained dynamical charm mass function varies from 1 to 1.5 GeV in the timelike domain, which is significant for narrow charmonium states. This yields a notable response in the bound state spectrum. We obtained purely continuous spectral functions and discussed their connection with confinement.

hep-ph↗

arXiv2026

A Spin One Bottomonium Study in the Functional Formalism in the Feynman Gauge

The Bethe-Salpeter equation for spin-one bottomonium coupled to quark and gluon propagators is solved in a class of non-trivial linear gauges. The interaction kernel is based on a known gluon propagator extrapolated from the lattice and contains only small amount of additional phenomenology. The first numerical results are obtained in the Feynman gauge where the associated problem with infrared divergences is circumvented by by introducing a symmetry breaking regulator mass $m_L$. The presence of this mass renders the bound state vertices of vector states finite but it is also necessary to prevent inconsistent solutions of the bound state equation. For $m_L\simeq Λ_{QCD}$ it gives us good agreement with the experimental data for vector and axial vector bottomonia below the $BB$ threshold. While the primary concern pertains to the physical ramifications of the proposed concept, a potential origin for the proposed interaction is also presented.

hep-ph↗

arXiv2025

Towards the finite quantum field theory

In this study, we propose a novel regularization/renormalization scheme that utilizes an auxiliary Feynman parameterization. This approach is employed to align a specified loop diagram with a designated unit of the form $1=λ/λ$. Within the proposed regularization technique, we formulate the standard renormalization scheme and demonstrate conditions under which it yields symmetry preserving results. It is demonstrated that its minimal form yields renormalized diagrams that are equivalent to those of the dimensional renormalization scheme, with the exception of their counterterms. Furthermore, a novel procedure for taking the soft limit $λ\rightarrow 0$, where a properly defined order of computational actions provides the field theory completely finite, is presented.The qualitative and quantitative distinctions between this approach and the standard scheme are highlighted. Both schemes are elucidated in the scalar model in 3+1D for pedagogical reasons. Subsequently, the proposed schemes are applied to the Standard Model at one loop level, e.g. we calculate photon and gluon polarizations. QCD effective charge is calculated in the finite QCD, exhibiting a clear evidence that the finite QCD is not ruled out but supported by experiment. In the final section, we offer a concise discussion on the softening of anomalies and the treatment of overlapping divergences, accompanied by illustrative examples.

hep-ph↗

arXiv2022

Timelike behavior of the pion electromagnetic form factor in the functional formalism

The electromagnetic form factor of the pion is calculated within the use of functional formalism. We develop integral representation for the minimal set of Standard Model Green's functions and derive the dispersion relation for the form factor in the two flavor QCD isospin limit $m_u=m_d$. We use the dressed quark propagator as obtained form the gap equation in Minkowski space and within the Dyson-Schwinger equations formalism to derive the approximate dispersion relation for the form factor for the first time. We evaluate the form factor for the spacelike as well as for the timelike momentum in the presented formalism. A new Nakanishi-like form of integral representation is proved on the basis of the vector Bethe-Salpeter equation for the quark-photon vector with a ladder-rainbow kernel. The Gauge Technique turns out to be a part of the entire structure of the vertex. In the analytic approach presented here, it is shown that the a large amount of the $ρ$-meson peak in the cross section $e^+e^-\rightarrow π^+π^-$ is governed by the gauge invariance of QED/QCD, i.e. by Gauge Technique constructed quark-photon vertex. This approximation naturally explains the broad shape of the $ρ$-meson peak.

hep-ph↗

arXiv2022

Confinement within the use of Minkowski space integral representation

We determine the gluonic spectral function $SU(3)$ Yang-Mills theory as well as we found fermionic spectral functions in the strong quenched QED where we found new solutions. Our novel technique provides solutions with the usual branch cut for propagators while not showing any pole structure at the first Riemann sheet (identical with entire complex plane) of complex square of momentum. Implications and further utilizations are briefly adressed for QCD and Standard model calculations.

hep-lat↗

arXiv2021

Muon pair production with hadronic vacuum polarization re-evaluated using precise data fits

Using optical theorem within sophisticated fits for exclusive hadronic productions in $e^+e^-$ collisions the interference between leptonic and hadronic vacuum polarization functions is considered and applied for calculation of $μ-$pair productions below 3 GeV. Particularly, the dispersion relation for the pion production form factor was obtained, confirming a possible evidence for the light $ρ(1250)$ resonance. The inflated error was introduced and used to discriminate the quality of various phenomenological fits. Resulting hadronic vacuum polarization was compared with other conventional sources and compared with KLOE experiment for $μ^{-}μ^{+}$ production at $ϕ$ meson energy. Furthermore, the obtained running fine structure coupling is compared with KLOE2 experiment for radiative return $μ^{-}μ^{+}$ production at $ ω/ρ$ meson energy and careful analysis of the error stemming form various fits of combined data was made and discussed.

hep-ph↗

arXiv2019

The quark spectral functions and the Hadron Vacuum Polarization from application of DSEs in Minkowski space

The hadronic vacuum polarization function $Π_h$ for two light flavors is computed on the entire domain of spacelike and timelike momenta using a framework of Dyson-Schwinger equations. The analytical continuation of the function $Π_h$ is based on the utilization of the Gauge Technique with the entry of QCD Green's functions determined from generalized quark spectral functions. For the first time, the light quark spectral functions are extracted from the solution of the gap equation for the quark propagator. 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

Nakanishi integral representation for the quark-photon vertex

Using a nonperturbative framework of Dyson-Schwinger equations a class of Nakanishi's like integral representations for the transverse part of the quark-photon vertex is derived. For this but also for its own purpose the two and single variable integral representations for untruncated quark-antiquark-photon vertex is proposed as well. To exhibit the adequacy of proposed representation, the Dyson-Schwinger equation for the vertex is transformed into the equivalent set of coupled integro-differential equations for Nakanishi weight functions: functions that appear linearly in the numerator of given integral representation. Their knowledge then provide self-consistent nonperturbative solution for the vertex in the entire Minkowski space.

hep-ph↗

arXiv2017

Hadronic vacuum polarization in $e^{+}e^{-}\to μ^{+}μ^{-}$ process bellow 3 GeV

The interference effect between leptonic radiative corrections and hadronic polarization functions is calculated via optical theorem for $μ-$pair productions. It is achieved within the use of the last data for $σ_h(e^+e^-\rightarrow hadrons)$ from SND,CMD,CMD-2,BABAR and BESSIII experimental Collaborations. The paper takes into account specific experimental conditions and the result is compared with KLOE experiment for $μ^{-}μ^{+}$ production at $ϕ$ meson energy. Small, but non-negligible tension between theory and experiment is discussed.

hep-ph↗

arXiv2014

Intriguing solutions of the Bethe-Salpeter equation for radially excited pseudoscalar charmonia

The purpose of this paper is twofold. The first purpose is to find a fully Poincare invariant solution of the Bethe-Salpeter equation for excited quarkonia, however, the second, in fact, major focus is on the relevance of the space-time metric choice and its imapact on the correct description of the ground and all excited states. For the first time, we compare BSE solutions defined independently with Euclidean and Minkowski metric. For this purpose, the BSE is conventionally defined and solved in Euclidean space with two versions of the propagator : the bare propagator and the confined form of the quark propagator with complex conjugated poles. In both considered cases, there is unexpected doubling of the spectrum, when comparing to the experiments as well as to the solutions of the Schrodinger equation. The quark propagator with complex conjugated singularities allows us to find the BSE solution directly in Minkowski momentum space as well. We find the Minkowski space solution for confining theories is not only numerically accessible, but provides a reliable, albeit not yet completely satisfactory, description of the ground and excited meson states.

hep-ph↗

arXiv2014

Lattice data inspired but Minkowski space calculated QCD fundamental propagator

We study the Dyson-Schwinger equation for the quark propagator in Minkowski space. In order to have analytical behaviour at the timelike axis of momenta under control, we use the Stieltjes and the Hilbert transformation for the interaction kernels and discuss the solution from the perspective of these transformations. In addition, a lattice fit for the gluon propagator and approximation for quark-gluon vertex are employed, and within the model the quark propagator is obtained through the solution of Dyson-Schwinger equation in Minkowski space. The resulting propagators in all studied cases do not show up particle like pole and production thresholds. Instead of, the quark propagator satisfies Hilbert transformation and the associated dynamical mass function becomes complex without a presence of particle like branch point.

hep-ph↗

arXiv2013

Vertical mass hierarchy in the case study of a hybrid model

We study a hybrid model in which the Technicolor and fundamental heavy scalars live together. We concern extreme case, where electroweak symmetry breaking (EWSB) comes almost entirely from the strong dynamics of Technicolor, but the masses of the light fermions, e.g. leptons arises due to the weakly interacting scalars with one universal Yukawa interaction. We have found that SU(2) scalar two doublets, which are private but universal for each generation, offer a natural explanation of the vertical mass hierarchy. There is no large Yukawa coupling in the theory and the scalar masses are expected to be quite universal and large. The lepton mass hierarchy arises radiatively from the quark mass hierarchy, which is affected by the scalar sector as well. Lepton and down quark masses are calculated in a simplified case of neglected mixing.

hep-ph↗

arXiv2012

Bethe-Salpeter study of radially excited vector quarkonia

We solve the Bethe-Salpeter equation (BSE) for a system of a heavy quark-antiquark pair interacting with a Poincare invariant generalization of screened linear confining potential. In order to get reliable description the Lorentz scalar confining interaction is complemented by the effective one gluon exchange. Within presented model we reasonably reproduce all known radial excitations of the vector charmonia. We have found that $J/Ψ$ is the only charmonium left bellow naive quark-antiquark threshold $2m_c$, while the all excited states are situated above this threshold. We develop a method which is enable to provide solution of full four dimensional BSE for the all excited states. We discuss the consequences of the use of the free propagators for calculation of excited states above the threshold. The Bethe-Salpeter string breaking scale $μ\simeq 350MeV$ appears to be relatively larger then the one defined in various potential models $μ\simeq 150MeV$.

hep-ph↗

arXiv2012

Confined gluon from Minkowski space continuation of PT-BFM SDE solution

Recent lattice studies exhibit infrared finite effective QCD charges. Corresponding gluon propagator in Landau gauge is finite and nonzero, suggesting a mechanism of dynamical gluon mass generation is in the operation. In this paper, the analytical continuation of the Euclidean (spacelike) Pinch Technique-Background Field Method (PT-BFM) solution of Schwinger-Dyson equation for gluon propagator to the timelike region of $q^2$ is found. We found the continuation numerically showing good agreement with a generalized Lehman representation for small Schwinger coupling. The associate non-positive spectral function has an unexpected behavior. Albeit infrared Euclidean space solution naively suggests like single scale "massive" propagator, the obtained spectrum of gluon propagator does not correspond to the delta function at single scale $q=m$, instead more possible singularities are generated. The pattern depends on the details of assumed Schwinger mechanism: for stronger coupling there are few maxima and minima which appear at the scale $Λ$, while for perturbatively small Schwinger coupling the spectral function shows up two narrow peaks: particle and ghost excitation, which have mutually opposite signs.

hep-lat↗

arXiv2011

Excited charmonium states from Bethe-Salpeter equation

We solve the Bethe-Salpeter equation for a system of a heavy quark-antiquark pair interacting with a screened linear confining potential. First we show the spinless QFT model is inadequate and fail to describe even gross feature of the quarkonia spectrum. In order to get reliable description the spine degrees of freedom has to be considered. Within the approximation employed we reasonably reproduce known radial excitation of vector charmonium. The BSE favors relatively large string breaking scale $μ\simeq 350MeV$ . Using free charm quark propagators we observe that $J/Ψ$ is the only charmonium left bellow naive quark-antiquark threshold $2m_c$, while the all excited states are situated above this threshold. Within the numerical method we overcome obstacles related with threshold singularity and discuss the consequences of the use of free propagators for calculation of excited states above the threshold.

hep-ph↗

arXiv2010

On the decoupling solution for pinch technique gluon propagator

Within a simple Ansatz for renormalized gluon propagator and using gauge invariant pinch-technique for Schwinger-Dyson equation, the limits on the effective gluon mass is derived. We calculated scheme invariant running coupling, which in order to be well defined, gives the lower limit on the gluon mass. We conclude mass should be larger as $m>0.4Λ$ in order to avoid Landau ghost. The upper limit is estimated from assumed quark mass generation which requires gauge coupling must be large enough to trigger chiral symmetry breaking. It allows only small range of $m$, which lead to a reasonably large infrared coupling. Already for $m\simeq Λ$ we get no chiral symmetry breaking at all. Further, we observe that sometimes assumed or postulated Khallen-Lehmann representation for running coupling is not achieved for any value of $m$.

hep-ph↗

arXiv2009

Higgsonium in singlet extension of Standard Model

A possible formation of bound state is predicted in the Standard Model extension with with additional scalar singlet. A suitable method of solution of the Bethe-Salpeter equation for a Higgsonium bound state is proposed. With the help of an integral representation the results are directly obtained in Minkowski space. The appearance of Higgsonia is shown to be quite natural for considered extension of Standard model and the calculations are presented for the bound state composed from two scalars which result from the large mixture of electroweak doublet and singlet eigenstate.

hep-ph↗