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A. L. Kataev

Publications and source records attributed to A. L. Kataev.

At least 55 records · Page 3Linked to original sources
arXiv2014

Scheme independent consequence of the NSVZ relation for N=1 SQED with N_f flavors

The exact NSVZ $β$-function is obtained for ${\cal N}=1$ SQED with $N_f$ flavors in all orders of the perturbation theory, if the renormalization group functions are defined in terms of the bare coupling constant and the theory is regularized by higher derivatives. However, if the renormalization group functions are defined in terms of the renormalized coupling constant, the NSVZ relation between the $β$-function and the anomalous dimension of the matter superfields is valid only in a certain (NSVZ) scheme. We prove that for ${\cal N}=1$ SQED with $N_f$ flavors the NSVZ relation is valid for the terms proportional to $(N_f)^1$ in an arbitrary subtraction scheme, while the terms proportional to $(N_f)^k$ with $k\ge 2$ are scheme dependent. These results are verified by an explicit calculation of a three-loop $β$-function and a two-loop anomalous dimension made with the higher derivative regularization in the NSVZ and MOM subtraction schemes. In this approximation it is verified that in the MOM subtraction scheme the renormalization group functions obtained with the higher derivative regularization and with the dimensional reduction coincide.

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arXiv2013

NSVZ scheme with the higher derivative regularization for N=1 SQED

The exact NSVZ relation between a $β$-function of ${\cal N}=1$ SQED and an anomalous dimension of the matter superfields is studied within the Slavnov higher derivative regularization approach. It is shown that if the renormalization group functions are defined in terms of the bare coupling constant, this relation is always valid. In the renormalized theory the NSVZ relation is obtained in the momentum subtraction scheme supplemented by a special finite renormalization. Unlike the dimensional reduction, the higher derivative regularization allows to fix this finite renormalization. This is made by imposing the conditions $Z_3(α,μ=Λ)=1$ and $Z(α,μ=Λ)=1$ on the renormalization constants of ${\cal N}=1$ SQED, where $Λ$ is a parameter in the higher derivative term. The results are verified by the explicit three-loop calculation. In this approximation we relate the $\bar{DR}$ scheme and the NSVZ scheme defined within the higher derivative approach by the finite renormalization.

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arXiv2012

Conformal symmetry based relation between Bjorken and Ellis-Jaffe sum rules

The identity between expressions for the coefficient functions of the Bjorken and Ellis-Jaffe sum rules is derived in the conformal invariant limit of massless U(1) theory, namely in the perturbative quenched QED model, and in the same limit of the massless $SU(N_c)$ gauge theory with fermions. The derivation is based on the comparison of results of application of the operator product expansion approach to the dressed triangle Green functions of singlet Axial vector- Vector-Vector and non-singlet Axial vector-Vector-Vector fermion currents in the limit, when the conformal symmetry is not violated. The expressions for the $O(α_s^3)$ approximation of the non-singlet coefficient function, derived in the conformal invariant limit of $SU(N_c)$ group, is reminded. Its possible application in the phenomenological analysis of the experimental data for the Bjorken polarized sum rule is outlined.

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arXiv2012

Analytical eighth-order light-by-light QED contributions from leptons with heavier masses to the anomalous magnetic moment of electron

The important consequences of the recent results of the numerical evaluations of eighth and tenth order QED contributions to the anomalous magnetic moment of electron are commented. The correctness of the results of the numerical evaluation of new eighth order QED corrections to the electron anomaly are supported by the demonstration of their consistency with the new analytical expressions for the QED contributions to $a_e$ from the diagrams with fourth-order light-by-light scattering muon and tau-lepton loops. The consistency of the similar results are demonstrated in the case of eighth order massive dependent contribution to the muon anomalous magnetic moment.

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arXiv2012

New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models

We propose a hypothesis on the detailed structure for the representation of the conformal symmetry breaking term in the basic Crewther relation generalized in the perturbation theory framework in QCD renormalized in the ${\rm \bar{MS}}$ scheme. We establish the validity of this representation in the $O(α_s^4)$ approximation. Using the variant of the generalized Crewther relation formulated here allows finding relations between specific contributions to the QCD perturbation series coefficients for the flavor nonsinglet part of the Adler function $D^{ns}_A$ for the electron-positron annihilation in hadrons and to the perturbation series coefficients for the Bjorken sum rule $S_\text{Bjp}$ for the polarized deep-inelastic lepton-nucleon scattering. We find new relations between the $α_s^4$ coefficients of $D^{ns}_A$ and $S_\text{Bjp}$. Satisfaction of one of them serves as an additional theoretical verification of the recent computer analytic calculations of the terms of order $α_s^4$ in the expressions for these two quantities.

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arXiv2011

The analytical singlet $α_s^4$ QCD contributions into the $e^+e^-$-annihilation Adler function and the generalized Crewther relations

The generalized Crewther relations in the channels of the non-singlet and vector quark currents are considered. They follow from the double application of the operator product expansion approach to the same axial vector-vector-vector triangle amplitude in two regions, adjoining to the angle sides $(x,y)$ (or $p^2,q^2$). We assume that the generalized Crewther relations in these two kinematic regimes result in the existence of the same perturbation expression for two products of the coefficient functions of annihilation and deep-inelastic scattering processes in the non-singlet and vector channels. Taking into account the 4-th order result for $S_{GLS}$ and the perturbative effects of the violation of the conformal symmetry in the generalized Crewther relation, we obtain the analytical contribution to the singlet $α_s^4$ correction to the $D_A^{V}$-function. Its a-posteriori comparison with the recent result of direct diagram-by-diagram evaluation of the singlet 4-th order corrections to $D_A^{V}$- function demonstrates the coincidence of the predicted and obtained $ζ_3^2$-contributions to the singlet term. They can be obtained in the conformal invariant limit from the original Crewther relation. On the contrary to previous belief, the appearance of $zeta_3$-terms in perturbative series in gauge models does not contradict to the property of conformal symmetry and can be considered as ragular feature. The Banks-Zaks motivated relation between our predicted and obtained 4-th order corrections is mentioned. This confirms Baikov-Chetyrkin-Kuhn expectation that the generalized Crewther relation in the channel of vector currents receives additional singlet contribution, which in this order of perturbation theory is proportional to the first coefficient of the QCD $β$-function.

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arXiv2011

The absence of QCD $β$-function factorization property of the generalized Crewther relation in the 't Hooft $\bar{MS}$-based scheme

We apply the 't Hooft $\bar{MS}$-based scheme to study the scheme-dependence of the QCD generalization of Crewther relation for the product of the normalised non-singlet perturbative contributions to the $e^+e^-$-annihilation Adler function and to the Bjorken sum rule of the polarized lepton-nucleon deep-inelastic scattering process. We prove that after the transformations from the pure $\bar{MS}$-scheme to the 't Hooft scheme the characteristic $\bar{MS}$-scheme theoretical property of this relation, namely the factorization of the $β$-function in its conformal symmetry breaking part, disappears. Another "non-comfortable" theoretical consequence of the application of this prescription in $\mathcal{N}=1$ SUSY QED model is mentioned. It is shown, that within the 't Hooft scheme the expansions of Green functions in terms of the Lambert function is simplified in high orders of perturbation theory. This may be considered as the attractive feature of the 't Hooft scheme, which manifest itself in high-order perturbative phenomenological applications.

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arXiv2011

New extended Crewther-type relation and the consequences of multiloop perturbative results

We discuss the current status of the investigations of the conformal symmetry breaking contributions to three forms for the QCD generalizations of the Crewther relation. The new third form of the extension of this relation is considered in more detail. Particular attention is paid to the discussions of the applications of the $β$-expansion formalism proposed previously by one of us (SVM). Several relations between 5-loop contributions to the Adler D-function $D^{NS}_{A}$ and to the polarized Bjorken sum rule $S_\text{Bjp}$ are presented. One of them gives the additional confirmation of the correctness of the advanced analytical computer calculations of order $α_s^4$ contributions to $D^{NS}_{A}$ and $S_\text{Bjp}$ in the general $SU(N_c)$ gauge group.

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arXiv2010

Riemann $ζ(3)$- terms in perturbative QED series, conformal symmetry and the analogies with structures of multiloop effects in N=4 supersymmetric Yang-Mills theory

As was discovered recently, 5-loop perturbative quenched QED approximation to the QED $β$-function consist from the rational term and the term proportional to $ζ(3)$-function. It is stressed, that this feature is also manifesting itself in the conformal invariant pqQED series for the 4-loop approximation to the anomalous mass dimension. The 4-loop pqQED expression for the singlet contribution into the Ellis-Jaffe polarized sum rule is obtained. It coincides with the similar approximation for the non-singlet coefficient function of Ellis-Jaffe sum rule and of Bjorken polarized sum rule. It is stressed that this property is valid in all orders of perturbation theory thanks to the conformal symmetry of pqQED series and to Crewther relation, which relates non-singlet and singlet coefficient functions of Ellis-Jaffe sum rule with the coefficient functions of non-singlet and singlet Adler D-functions. The basic steps of derivation of Crewther relation in the singlet channel from the AVV triangle diagram are outlined. The similarities between analytical structure of asymptotic series for the coefficient functions in pqQED and for the anomalous dimensions in N=4 conformal invariant supersymmetric Yang-Mills theory are observed. The guess is proposed that the appearance of $ζ(3)$-terms in the pqQED expressions and the absence of $ζ(5)$-terms at the same level is the indication of absence of "wrapping" interactions in pqQED.

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arXiv2010

New extended Crewther-type relation

We propose a conjecture about the detailed structure of the conformal symmetry breaking term in the generalized Crewther relation. We conclude that this conjecture leads to new relations between the QCD expansion coefficients of the Adler D-function and the polarized Bjorken sum rule B$_{jp}$

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arXiv2009

Uncertainties of QCD predictions for Higgs boson decay into bottom quarks at NNLO and beyond

An importance of the detailed studies of the theoretical QCD predictions for the decay width of Standard Model Higgs boson into bottom quarks, in the case when $\rm{M_H\leq 2M_W}$, is emphasized. The effects of higher order perturbative QCD corrections up to order $α_s^4$-terms are considered. The resummations of the $π^2$ terms resulting from analytical continuation, typical of Minkowskian quantities, is undertaken for the $Γ(H\to\bar{b}b)$ decay width. The uncertainties in the calculation of this decay width are analyzed.

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arXiv2009

Higgs boson decay into bottom quarks and uncertainties of perturbative QCD predictions

Different methods for treating the results of higher-order perturbative QCD calculations of the decay width of the Standard Model Higgs boson into bottom quarks are discusssed. Special attention is paid to the analysis of the $M_H$ dependence of the decay width $Γ(H\to \bar{b}b})$ in the cases when the mass of b-quark is defined as the running parameter in the $\bar{MS}$-scheme and as the quark pole mass. The relation between running and pole masses is taken into account in the order $α_s^4$-approximation. Some special features of applications of Analytical Perturbation Theory (APT) are commented.

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arXiv2008

Conformal invariance and the expressions for $C_F^4α_s^4$ contributions to the Bjorken polarized and the Gross-Llewellyn Smith sum rules

Considering massless axial-vector-vector triangle diagram in the conformal invariant limit and the the results of recent distinguished analytical calculations of the 5-loop single-fermion loop corrections to the QED $β$-function, we derive the analytical expressions for the $C_F^4α_s^4$-contributions to the Bjorken polarized and Gross-Llewellyn Smith sum rule. This visible in future evaluation can shed extra light on the reliability of the appearance of $ζ_3$-term in the explicitly known part of 5-loop corrections to the QED $β$-function which are proportional to the conformal invariant set of $C_F^4α_s^4$ -contributions into to the $e^+e^-$- annihilation Adler function.

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arXiv2008

Is it possible to check urgently the 5-loop analytical results for the $e^+e^-$-annihilation Adler function ?

Considering the results of recent distinguished analytical calculations of the 5-loop single-fermion loop corrections to the QED $β$-function we emphasize that to our point of view it is important to perform their independent cross-checks. We propose one of the ways of these cross-check. It is based on the application of the original Crewther relation. We derive the new analytical expressions for the $C_F^4α_s^4$-contributions to the Bjorken polarized sum rule. If results of possible direct calculations will agree with the presented expression, then the appearance of $ζ_3$-term in the 5-loop correction to the QED $β$-function and in the $C_F^4α_s^4$ contribution into the $e^+e^-$ annihilation Adler function will get independent support and may be analysed within the framework of the recently introduced concept of "maximal transcendentality".

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arXiv2007

Higgs Decay To \bar{b}b: Different Approaches To Resummation Of QCD Effects

The comparison between parameterisations of the perturbation results for the decay width of the Standard Model Higgs boson to \bar{b}b-quarks pairs, based on application of \bar{MS}-scheme running quark mass and pole b-quark mass, are presented. In the case of the latter parameterisation taking into account of order O(α_s^3) term is rather important. It is minimising deviations of the results obtained at the O(α_s^2) level from the results, which follow from the running quark mass approach

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arXiv2007

Non-planar structure of analytical QCD predictions for the Gottfried sum rule

It is stressed that within large N_c-expansion {\bf analytical calculations} of the $(α_s/π)^2$ QCD contributions to the valence part of the Gottfried sum rule for F_2 structure function of charged leptons-nucleon deep-inelastic scattering reveals the existence of the $O(1/N_c^2)$ {\bf non-planar} corrections only and the disappearance of the {\bf planar} O(N_c^0) perturbative terms. The relation between Gottfried and Adler sum rule for neutino-nucleon DIS is established and the proposal that the differebce between corresponding QCD corrections to higher non-singlet moments in charged-lepton and neutrino DIS are {\bf suppressed by 1/N_c^2} is made. The possible consequence of the cancellation of {\bf perturbative planar} graphs in the considered perturbative series, namely the existence of light-quark flavour asymmetry $\bar{u}(x)<\bar{d}(x)$, is mentioned. The effect of the similar origin, i.e. the relation of {\bf ``light-by-light-type''-type structure} in DIS characteristics at the $α_s^3$-level to the generation of light quark-antiquark asymmetry, is also commented.

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