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We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial technique. A brief, historically oriented, overview of some of the results obtained over the decades for the massless 2-loop propagator-type diagram is given. Concrete examples of up to $5$-loop diagram calculations are also provided., Comment: Review article. LaTeX file with feynMF package. (v2) references added and minor typos corrected. 65 pages, 8 figures. (v1) 64 pages, 8 figures

The two-loop interaction correction coefficient to the universal ac conductivity of disorder-free intrinsic graphene is computed with the help of a field theoretic renormalization study using the BPHZ prescription. Non-standard Ward identities imply that divergent subgraphs (related to Fermi velocity renormalization) contribute to the renormalized optical conductivity. Proceeding either via density-density or via current-current correlation functions, a single well-defined value is obtained: $\mathcal{C}= (19-6\pi)/12) = 0.01$ in agreement with the result first obtained by Mishchenko and which is compatible with experimental uncertainties., Comment: LaTeX file with feynMF package. (v2) Footnotes and references added to answer referee's questions and comments. No change in results. 23 pages (JHEP format), 4 figures (v1) 12 pages, 4 figures

The field theoretic renormalization study of reduced quantum electrodynamics (QED) is performed up to two loops. In the condensed matter context, reduced QED constitutes a very natural effective relativistic field theory describing (planar) Dirac liquids, e.g., graphene and graphene-like materials, the surface states of some topological insulators and possibly half-filled fractional quantum Hall systems. From the field theory point of view, the model involves an effective (reduced) gauge field propagating with a fractional power of the d'Alembertian in marked contrast with usual QEDs. The use of the BPHZ prescription allows for a simple and clear understanding of the structure of the model. In particular, in relation with the ultra-relativistic limit of graphene, we straightforwardly recover the results for both the interaction correction to the optical conductivity: $\mathcal{C}^*=(92-9\pi^2)/(18\pi)$ and the anomalous dimension of the fermion field: $\gamma_{\psi}(\bar{\alpha},\xi) = 2 \bar{\alpha}\,(1-3\xi)/3 -16\,\left( \zeta_2 N_F + 4/27 \right)\, \bar{\alpha}^2 + O(\bar{\alpha}^3)$, where $\bar{\alpha} = e^2/(4\pi)^2$ and $\xi$ is the gauge-fixing parameter., Comment: (v2) Published in PRD. Some references added. No change in results. (v1) LaTeX file with feynMF package. 15 pages, 4 figures

We show the new relationship [1] between the anomalous dimensions, resummed through next-to-next-to-leading-logarithmic order, in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for the first Mellin moments D{q,g}(\mu2) of the quark and gluon fragmentation functions, which correspond to the average hadron multiplicities in jets initiated by quarks and gluons, respectively. This relationship, which is independent of the number of quark flavors, strongly improves previous treatments by allowing for an exact solution of the evolution equations. So far, such relationships have only been known from supersymmetric QCD., Comment: 4 pages, talk given at the International Workshop "Supersymmetries and Quantum Symmetries" (SQS'2017), July 31 - August 5, 2017 and the IVth Russian-Spanish Congress "Particle, Nuclear, Astroparticle Physics and Cosmology", September 4 - 8, 2017

We present details of study of the Bjorken polarized sum rule carried out recently in [1] within the range of energies where the data were collected by JLAB collaboration, 0.05 GeV2 < Q2 < 3 GeV2. Three approaches to QCD with analytic (holomorphic) coupling are considered: Analytic Perturbation Theory (APT), Two-delta analytic QCD, and Three-delta lattice-motivated analytic QCD in the three-loop and four-loop MiniMOM schemes. The new frameworks with respective couplings give results which agree well with the experimental data for 0.5 GeV2 < Q2 < 3GeV2 already when only one higher-twist term is taken into account., Comment: 6 pages, 2 figures, talk given at the XVIIth International Workshop on High Energy Spin Physics (DSPIN-17), September 11 - 15, 2017

We investigate the Bjorken polarized sum rule (BSR) in three approaches to QCD with analytic (holomorphic) coupling: Analytic Perturbation Theory (APT), Two-delta analytic QCD (2$\delta$anQCD), and Three-delta lattice-motivated analytic QCD in the three-loop and four-loop MOM scheme (3l3$\delta$anQCD, 4l3$\delta$anQCD). These couplings do not have unphysical (Landau) singularities, and have finite values when the transferred momentum goes to zero, which allows us to explore the infrared regime. With the exception of APT, these theories at high momenta practically coincide with the underlying perturbative QCD (pQCD) in the same scheme. We apply them in order to verify the Bjorken sum rule within the range of energies available in the data collected by the experimental JLAB collaboration, i.e., $0.05 GeV^2

The Bessel-inspired behavior of parton densities at small Bjorken $x$ values, obtained in the case of the flat initial conditions for DGLAP evolution equations, is used along with "frozen" and analytic modifications of the strong coupling constant to study the so-called EMC effect. Among other results, this approach allowed predicting small $x$ behavior of the gluon density in nuclei., Comment: 13 pp, 4 figs

We recover in QCD an amazingly simple relationship between the anomalous dimensions, resummed through next-to-next-to-leading-logarithmic order, in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations for the first Mellin moments $D_{q,g}(\mu^2)$ of the quark and gluon fragmentation functions, which correspond to the average hadron multiplicities in jets initiated by quarks and gluons, respectively. This relationship, which is independent of the number of quark flavors, dramatically improves previous treatments by allowing for an exact solution of the evolution equations. So far, such relationships have only been known from supersymmetric QCD, where $C_F/C_A=1$. This also allows us to extend our knowledge of the ratio $D_g^-(\mu^2)/D_q^-(\mu^2)$ of the minus components by one order in $\sqrt{\alpha_s}$. Exploiting available next-to-next-to-next-to-leading-order information on the ratio $D_g^+(\mu^2)/D_q^+(\mu^2)$ of the dominant plus components, we fit the world data of $D_{q,g}(\mu^2)$ for charged hadrons measured in $e^+e^-$ annihilation to obtain $\alpha_s^{(5)}(M_Z)=0.1205\genfrac{}{}{0pt}{}{+0.016}{-0.0020}$., Comment: 8 pages, 2 figures

Deep inelastic scattering data on $F_2$ structure function obtained in the fixed-target experiments were analysed in the valence quark approximation with a next-to-next-to-leading-order accuracy. Parton distribution functions are parametrized by using information from the Gottfried sum rule. The strong coupling constant is found to be $\alpha_s(M_Z^2) = 0.1180 \pm 0.0020~\mbox(total\,exp.error)$, which coincides very well with the average world value $\alpha_s^{\rm PDG}(M_Z^2) = 0.1181 \pm 0.0013$ updated recently in a PDG report. The result for the second moment of the difference in $u$ and $d$ quark distributions $<\!\!x\!\!>_{u-d}=0.187 \pm 0.021$ is seen to be well compatible with the latest LATTICE result $<\!\!x\!\!>_{u-d}^{\rm LATTICE}=0.208 \pm 0.024$, Comment: 12 pp, 1 fig, version to be published in Phys. At. Nucl

We present a set of formulas to extract the gluon density from the Berger-Block-Tan form of the deep inelastic structure function F2 at small x in the leading order of perturbation theory., Comment: 6 pages

We consider the two-loop massless propagator-type Feynman diagram with an arbitrary (non-integer) index on the central line. We analytically prove the equality of the two well-known results existing in the literature which express this diagram in terms of ${}_3F_2$-hypergeometric functions of argument $-1$ and $1$, respectively. We also derive new representations for this diagram which may be of importance in practical calculations., Comment: 14 pages, 5 figures (v2) 2 references added

The dynamical generation of a fermion gap in graphene is studied at the infra-red Lorentz-invariant fixed point where the system is described by an effective relativistic-like field theory: reduced QED$_{4,3}$ with $N$ four component fermions ($N=2$ for graphene), where photons are $(3+1)$-dimensional and mediate a fully retarded interaction among $(2+1)$-dimensional fermions. A correspondence between reduced QED$_{4,3}$ and QED$_3$ allows us to derive an exact gap equation for QED$_{4,3}$ up to next-to-leading order. Our results show that a dynamical gap is generated for $\alpha > \alpha_c$ where $1.03 < \alpha_c < 1.08$ in the case $N=2$ or for $N < N_c$ where $N_c$ is such that $\alpha_c \to \infty$ and takes the values $3.24 < N_c < 3.36$. The striking feature of these results is that they are in good agreement with values found in models with instantaneous Coulomb interaction. At the fixed point: $\alpha = 1/137 \ll \alpha_c$, and the system is therefore in the semi-metallic regime in accordance with experiments., Comment: (v2) Accepted for publication in PRD. Short discussion and some references added at the end of Sec V (per referee's comments). No change in results. 7 pages. (v1) 7 pages

Dynamical chiral symmetry breaking (D$\chi$SB) is studied within ($2+1$)-dimensional QED with $N$ four-component fermions. The leading and next-to-leading orders of the $1/N$ expansion are computed exactly. The analysis is carried out in an arbitrary non-local gauge. Resumming the wave-function renormalization constant at the level of the gap equation yields a strong suppression of the gauge dependence of the critical fermion flavour number, $N_c(\xi)$ where $\xi$ is the gauge fixing parameter, which is such that D$\chi$SB takes place for $N

The Bessel-inspired behavior of parton densities at small x, obtained in the case of the flat initial conditions for DGLAP evolution equations, is used in the fixed flavor scheme to analyze precise H1+ZEUS combined data on the structure function F2., Comment: 4 pages, 1 figure, talk given at the International Session-Conference SNP PSD RAS "Physics of Fundamental Interactions", April 12 - 15, 2016

The dynamical generation of a fermion mass is studied within ($2+1$)-dimensional QED with $N$ four-component fermions in the leading and next-to-leading orders of the 1/N expansion. The analysis is carried out in the Landau gauge which is supposed to insure the gauge independence of the critical fermion flavour number, N_c. It is found that the dynamical fermion mass appears for N

We review the method of uniqueness which is a powerful technique for multi-loop calculations in higher dimensional theories with conformal symmetry. We use the method in momentum space and show that it allows a very transparent evaluation of a two-loop massless propagator Feynman diagram with a non-integer index on the central line. The result is applied to the computation of the optical conductivity of graphene at the infra-red Lorentz invariant fixed point. The effect of counter-terms is analysed. A brief comparison with the non-relativistic case is included., Comment: Prepared for the Vth International Conference "Models in Quantum Field Theory" dedicated to Prof. Aleksandr Nikolaevich Vasiliev. LaTeX file with feynMF package. 15 pages, 4 figures (v2) Minor modifications (some per referee's comments)

We review some results of calculations, having the property of maximal transcendentality., Comment: 15 pages, 3 figures, talk given at the V International Conference "Models in Quantum Field Theory" (MQFT-2015), September 21-25, 2015, V.A. Fock Physical Research Institute, Petergof, Russia. arXiv admin note: substantial text overlap with arXiv:1212.3732

We review the result for the BFKL Pomeron intercept at N=4 Supersymmetric Yang-Mills model in the form of the inverse coupling expansion $j_0=2-2\lambda^{-1/2}-\lambda^{-1} + 1/4 \, \lambda^{-3/2} + 2(3\zeta_3+1) \, \lambda^{-2} +(18\zeta_3+361/64) \, \lambda^{-5/2} + (39\zeta_3+447/32) \, \lambda^{-3} + O(\lambda^{-7/2})$ which has been calculated in [1]-[5] with the use of the AdS/CFT correspondence., Comment: 5 pages, 1 figure, talk given on the international Workshop "Hadron Structure and QCD" (HSQCD'2014), June 30 - July 4, Gatchina, 2014; one reference was added in the second version

We show the results in [1,2] for computing the QCD contributions to the scale evolution of average gluon and quark jet multiplicities. The new results came due a recent progress in timelike small-x resummation obtained in the MSbar factorization scheme. They depend on two nonperturbative parameters with clear and simple physical interpretations. A global fit of these two quantities to all available experimental data sets demonstrates by its goodness how our results solve a longstandig problem of QCD. Including all the available theoretical input within our approach, alphas(Mz)=0.1199 +- 0.0026 has been obtained in the MSbar scheme in an approximation equivalent to next-to-next-to-leading order enhanced by the resummations of ln x terms through the NNLL level and of ln Q2 terms by the renormalization group. This result is in excellent agreement with the present world average., Comment: 14 pages, 3 figures, talk given on the conference "Quark Confinement and Hadron Spectrum XI", September 7-12, St. Petersburg, Russia

Deep inelastic scattering data on $F_2$ structure function obtained by BCDMS, SLAC and NMC collaborations in fixed-target experiments were analyzed in the non-singlet approximation with next-to-next-to-leading-order accuracy. The strong coupling constant is found to be $\alpha_s(M_Z^2) = 0.1157 \pm 0.0022 (total\,\,\,exp.error) + \biggl\{\begin{array}{l} +0.0028 \\ -0.0016 \end{array} (theor)$, which is seen to be well compatible with the average world value. Results obtained in the present paper by carrying out fits similar to those done in our earlier study, with the exception for systematic errors in BCDMS data taken into account in a different way, confirm those which were derived in that same paper., Comment: 19 pages, 11 figs, 8 tables, published in JPG42. arXiv admin note: text overlap with arXiv:0912.4672

We compute the two-loop interaction correction to the minimal conductivity of disorder-free intrinsic graphene with the help of dimensional regularization. The calculation is done in two different ways: via density-density and via current-current correlation functions. Upon properly renormalizing the perturbation theory, in both cases, we find that: $\sigma = \sigma_0\,( 1 + \al\,(19-6\pi)/12) \approx \sigma_0 \,(1 + 0.01\, \al)$, where $\al = e^2 / (4 \pi \hbar v)$ is the renormalized fine structure constant and $\sigma_0 = e^2 / (4 \hbar)$. Our results are consistent with experimental uncertainties and resolve a theoretical dispute., Comment: (v2) 5 pages, 2 figures, ref [19] added, minor typos corrected, no change in results. (v1) 5 pages, 2 figures

We use the Bessel-inspired behavior of the structure function F2 at small x, obtained for a flat initial condition in the DGLAP evolution equations. We fix the scale of the coupling constant, which eliminates the singular part of anomalous dimesnions at the next-to-leading order of approximation. The approach together with the "frozen" and analytic modifications of the strong coupling constant is used to study the precise combined H1 and ZEUS data for the structure function F2 published recently., Comment: 5 pages, 1 figure, talk given at International Workshop "Physics of Fundamental Interactions", Protvino, November 5-8, 2013

It is shown that in the leading twist approximation of the Wilson operator product expansion with "frozen" and analytic strong coupling constants, considering the Bessel-inspired behavior of the structure functions F2 and the derivative d ln F2/(d ln(1/x)) at small x values, obtained for a flat initial condition in the DGLAP evolution equations,leads to a good agreement with the deep inelastic scattering H1 and ZEUS experimental data from HERA, Comment: 9 pages, 4 figures, talk given at II Russian-Spanish Congress "Particle and Nuclear Physics at all scales, Astroparticle Physics and Cosmology", Saint-Petersburg, October 1-4, 2013

We show the result for the BFKL Pomeron intercept at N=4 Supersymmetric Yang-Mills model in the form of the inverse coupling expansion j0=2-2 lambda**(-1/2)- lambda**(-1) + 1/4 lambda**(-3/2) + 2(1+3zeta3) lambda**(-2) + O(lambda**(-5/2)), which has been calculated recently in [1] with the use of the AdS/CFT correspondence., Comment: 5 pages, talk given at International Moscow Phenomenology Workshop (devoted to the memory of Prof. Alexei Kaidalov), July 21-25, 2013, Moscow, Russia

We compute the two-loop fermion self-energy in massless reduced quantum electrodynamics for an arbitrary gauge using the method of integration by parts. Focusing on the limit where the photon field is four-dimensional, our formula involves only recursively one-loop integrals and can therefore be evaluated exactly. From this formula, we deduce the anomalous scaling dimension of the fermion field as well as the renormalized fermion propagator up to two loops. The results are then applied to the ultra-relativistic limit of graphene and compared with similar results obtained for four-dimensional and three-dimensional quantum electrodynamics., Comment: (v2) Accepted for publication in PRD. Footnote with reference added per referee's comment, other minor modifications. No change in results. 23 pages, 4 figures. (v1) LaTeX file with feynMF package. 23 pages, 4 figures

We develop a new formalism for computing and including both the perturbative and nonperturbative QCD contributions to the scale evolution of average gluon and quark jet multiplicities. The new method is motivated by recent progress in timelike small-x resummation obtained in the MS-bar factorization scheme. We obtain next-to-next-to-leading-logarithmic (NNLL) resummed expressions, which represent generalizations of previous analytic results. Our expressions depend on two nonperturbative parameters with clear and simple physical interpretations. A global fit of these two quantities to all available experimental data sets that are compatible with regard to the jet algorithms demonstrates by its goodness how our results solve a longstandig problem of QCD. We show that the statistical and theoretical uncertainties both do not exceed 5% for scales above 10 GeV. We finally propose to use the jet multiplicity data as a new way to extract the strong-coupling constant. Including all the available theoretical input within our approach, we obtain alpha_s^(5)(M_Z)=0.1199 +- 0.0026 in the MS-bar scheme in an approximation equivalent to next-to-next-to-leading order enhanced by the resummations of ln(x) terms through the NNLL level and of ln(Q^2) terms by the renormalization group, in excellent agreement with the present world average., Comment: 33 pages, 11 figures; two more experimental data sets included; accepted for publication in Nucl. Phys. B

In this note we evaluate Wilson coefficients for "deep inelastic scattering" (DIS) in N=4 SYM theory at NLO in perturbation theory, using as a probe an R-symmetry conserved current. They exhibit uniform transcendentality and coincide with the piece of highest transcendentality in the corresponding QCD Wilson coefficients. We extract from the QCD result a NNLO prediction for the N=4 SYM Wilson coefficient, and comment on the features of its Regge limit asymptotics., Comment: 11 pages; v2: corrected eqq. (3.12) and (3.13), paragraph on large j exponentiation added, corrected misprint in eq. (3.22), references added

Using the method of uniqueness a two-loop massless propagator Feynman diagram with a non-integer index on the central line is evaluated in a very transparent way. The result is applied to the computation of the two-loop polarization operator in reduced quantum electrodynamics., Comment: (v2) 4 pages, 2 figures; references added, footnote added before Eq.(20), other minor modifications, no change in results; to appear in PRD (v1) LaTeX file with feynMF package. 4 pages, no figure

We find the BFKL Pomeron intercept at N=4 supersymmetric gauge theory in the form of the inverse coupling expansion j0=2-2/lambda**(1/2)-1/lambda + 1/4 1/lambda**(3/2) + 2(1+3zeta3)/lambda**(2) + O(1/lambda**(5/2)) with the use of the AdS/CFT correspondence in terms of string energies calculated recently. The corresponding slope gamma'(2) of the anomalous dimension calculated directly up to the fifth order of perturbation theory turns out to be in an agreement with the closed expression obtained from the recent Basso results., Comment: 18 pages, 1 figure, fixed some typos

We study the polarized Bjorken sum rule at low momentum transfer squared Q2<3GeV2 in the twist-two approximation and to the next-to-next-to-leading order accuracy., Comment: 6 pages, 3 figures, talk given at 20th International Symposium on Spin Physics (SPIN2012), September 16-23, 2012, JINR, Dubna, Russia

We use the Bessel-inspired behavior of the structure function F2 at small x, obtained for a flat initial condition in the DGLAP evolution equations, with "frozen" and analytic modifications of the strong coupling constant to study precise combined H1 and ZEUS data for the structure function F2 published recently., Comment: 5 pages, 1 figure, will appear in Phys.Part.Nucl.(2013)

We review the results having the property of maximal transcendentality., Comment: 12 pages, 3 figures, talk given at the IV International Conference "Models in Quantum Field Theory" (MQFT-2012), September 24-27, 2012, V.A. Fock Physical Research Institute, Petergof, Russia

It is shown that in the leading twist approximation of the Wilson operator product expansion with "frozen" and analytic strong coupling constants, Bessel-inspired behavior of the structure functions F2 and F2cc and also the derivative d(ln F2)/d(ln(1/x)) at small x values, obtained for a flat initial condition in the DGLAP evolution equations, leads to good agreement with the deep inelastic scattering experimental data from HERA., Comment: 26 pages, 8 figures, talk given at the XXI International Baldin Seminar on High Energy Physics Problems,September 10-15, 2012, JINR, Dubna, Russia

We present a new approach to consider and include both the perturbative and the non-perturbative contributions to the multiplicities of gluon and quark jets. Thanks to this new method, we have included for the first time new contributions to these quantities obtaining next-to-next-to-leading-logarithmic resummed formulas. Our analytic expressions depend on two non-perturbative parameters with a clear and simple physical interpretation. A global fit of these two quantities shows how our results solve a longstanding discrepancy in the theoretical description of the data., Comment: 4pages, 2 figures; final published version

It is shown that a Bessel-like behaviour of the structure function F2 at small x, obtained for a flat initial condition in the DGLAP evolution equations, leads to good agreement with the deep inelastic scattering experimental data from HERA., Comment: 8 pages, 3 figures, in Proc. of the third International Workshop on Multiple Partonic Interactions at the LHC (21-25 November 2011, DESY, Hamburg)

We show that the new relation between master integrals recently obtained in Ref. [1] can be reproduced using the integration-by-parts technique implemented with an effective mass. In fact, this relation is recovered as a special case of a whole family of new relations between master integrals., Comment: 4 pages, more general formula and figure are included, accepted for publication in Phys.Lett.B

We give a short review of our recent analysis [1] of the deep inelastic scattering data (provided by BCDMS, SLAC, NMC) on F2 structure function in the non-singlet approximation with up to next-to-next-to-leading-order accuracy and analytic and frozen modifications of the strong coupling constant featuring no unphysical singularity (the Landau pole). Improvement of agreement between theory and experiment, with respect to the case of the standard perturbative definition of the strong coupling constant considered recently in [2], was observed., Comment: 28pp, 7 figs, contribution to the Proceedings of XLV PNPI Winter School held in Roschino (Russia) on 28 feb - 5 March, 2011

We calculate the single logarithmic contributions to the quark singlet and gluon matrix of timelike splitting functions at all orders in the modified minimal-subtraction (MSbar) scheme. We fix two of the degrees of freedom of this matrix from the analogous results in the massive-gluon regularization scheme by using the relation between that scheme and the MSbar scheme. We determine this scheme transformation from the double logarithmic contributions to the timelike splitting functions and the coefficient functions of inclusive particle production in e+ e- annihilation now available in both schemes. The remaining two degrees of freedom are fixed by reasonable physical assumptions. The results agree with the fixed-order results at next-to-next-to-leading order in the literature., Comment: Minor changes to the text, accepted for publication in Nucl. Phys. B

In contrast to the coupling parameter in the usual perturbative QCD (pQCD), the coupling parameter in the analytic QCD models has cuts only on the negative semiaxis of the Q^2-plane (where q^2 = -Q^2 is the momentum squared), thus reflecting correctly the analytic structure of the spacelike observables. The Minimal Analytic model (MA, named also APT) of Shirkov and Solovtsov removes the nonphysical cut (at positive Q^2) of the usual pQCD coupling and keeps the pQCD cut discontinuity of the coupling at negative Q^2 unchanged. In order to evaluate in MA the physical QCD quantities whose perturbation expansion involves noninteger powers of the pQCD coupling, a specific method of construction of MA analogs of noninteger pQCD powers was developed by Bakulev, Mikhailov and Stefanis (BMS). We present a construction, applicable now in any analytic QCD model, of analytic analogs of noninteger pQCD powers; this method generalizes the BMS approach obtained in the framework of MA. We need to know only the discontinuity function of the analytic coupling (the analog of the pQCD coupling) along its cut in order to obtain the analytic analogs of the noninteger powers of the pQCD coupling, as well as their timelike (Minkowskian) counterparts. As an illustration, we apply the method to the evaluation of the width for the Higgs decay into b+(bar b) pair., Comment: 29 pages, 5 figures; sections II and III extended, appendix B is new

The one-loop HQET heavy-heavy vertex diagram with arbitrary powers of all three denominators and arbitrary residual energies is investigated. Various particular cases in which the result becomes simpler are considered., Comment: 4 pages

We present a simple formula for the total cross section sigma^{nu N} of neutral- and charged-current deep-inelastic scattering of ultrahigh-energy neutrinos on isoscalar nuclear targets, which is proportional to the structure function F_2^{nu N}(M_V^2/s, M_V^2), where M_V is the intermediate-boson mass and s is the square of the center-of-mass energy. The coefficient in the front of F_2^{nu N}(x, Q^2) depends on the asymptotic low-x behavior of F_2^{nu N}. It contains an additional ln(s) term if F_2^{nu N} scales with a power of ln(1/x). Hence, an asymptotic low-x behavior F_2^{nu N} propto ln^2(1/x), which is frequently assumed in the literature, already leads to a violation of the Froissart bound on sigma^{nu N}., Comment: 5 pages, 2 figures, to appear in Physical Review Letters