Gluon condensate in charmonium sum rules with three-loop corrections

Charmonium sum rules are analyzed with the primary goal to obtain the restrictions on the value of the dimension 4 gluon condensate. The moments M _n (Q ² ) of the polarization operator of the vector charm currents are calculated and compared with the experimental data. The three-loop () perturbative corrections, the contribution of the gluon condensate with corrections and the contribution of the dimension 6 operator G³ are accounted. It is shown that the sum rules for the moments do not work at Q ² = 0, where the perturbation series diverges and the G³ contribution is large. The domain in the (n, Q ² ) plane where the sum rules are legitimate is found. A strong correlation of the values of gluon condensate and charm quark mass is determined. The absolute limits are found to be for the gluon condensate and for the charm quark mass in the scheme. Received: 16 July 2002 / Revised version: 6 November 2002 / Published online: 24 January 2003 RID="a" ID="a" e-mail: ioffe@vitep1.itep.ru RID="b" ID="b" e-mail: zyablyuk@heron.itep.ru     

The NLO Parton Distribution in the (x, Q 2)-Plane: A Relativistic Quark-Exchange Approach to A = 3 Mirror Nuclei

A next-to-leading order QCD analysis of polarized and unpolarized structure functions of the proton in the (x, Q²)-plane is discussed within the scheme of the radiation parton formalism. The valence quark distribution is obtained from the application of the relativistic quark-exchange model to A = 3 mirror nuclei, i.e., ³He and ³H. The sea quark and gluon distributions are calculated using the inverse Mellin technique in the NLO approximation. A comparison is made with the corresponding available experimental data. We find a good fit for F₂^p(x, Q²) to the data. It is shown that our new NLO calculation improves our previous works. We argue that the valence quark scenario at some μ₀² ≪ Q² is a reasonable assumption in the framework of the DGLAP evolution equation. In agreement with the data, it is demonstrated that the asymmetry A₁^p(x, Q²) has no significant Q²-dependence as we go to the small x, even at NLO limit. Finally we argue that for small x ≤ 0.2 it is a good approximation to consider ³He and ³H structure functions as those of neutrons and protons, respectively.     

On the perturbative stability of the QCD predictions for the ratio R=FL/FT in heavy-quark leptoproduction

We analyze the perturbative and parametric stability of the QCD predictions for the Callan–Gross ratio, R(x,Q ²)=F _L /F _T , in heavy-quark leptoproduction. We consider the radiative corrections to the dominant photon–gluon fusion mechanism. In various kinematic regions, the following contributions are investigated: exact NLO results at low and moderate Q ²≲m ², asymptotic NLO predictions at high Q ²≫m ², and both NLO and NNLO soft-gluon (or threshold) corrections at large Bjorken variable x. Our analysis shows that large radiative corrections to the structure functions F _T (x,Q ²) and F _L (x,Q ²) cancel each other in their ratio R(x,Q ²) with good accuracy. As a result, the NLO contributions to the Callan–Gross ratio are less than 10% in a wide region of the variables x and Q ². We provide compact LO predictions for R(x,Q ²) in the case of low x ≪1. A simple formula connecting the high-energy behavior of the Callan–Gross ratio and low-x asymptotics of the gluon density is derived. It is shown that the obtained hadron-level predictions for R(x→0,Q ²) are stable under the DGLAP evolution of the gluon distribution function. Our analytic results simplify the extraction of the structure functions F ₂ ^c (x,Q ²) and F ₂ ^b (x,Q ²) from measurements of the corresponding reduced cross sections, in particular at DESY HERA.     

Correlator of the quark scalar currents and Γtot(H → hadrons) at O(αs) in pQCD

We present the results of the analytical evaluation of the massless four-loop

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(α³_s) correction to the correlator of the quark scalar currents and the Higgs decay rate into hadrons. In numerical form we found (in

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scheme) that Γ (H →

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b ) = (3G_F/4

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π) M_Hm²_b (M_H) [1 + 5.667α_s/π + (35.94 − 1.359n_f) (α_s/π)² + (164.139 − 25.771n_f + 0.259n²_f) (α_s/π)³] where n_f is the number of quark flavour and α_s = α_s(M_H).     

Modelling the quark propagator

We are interested in developing covariant, confining, and asymptotically free models of hadrons. With this goal in mind we have carried out a study of dynamical chiral symmetry breaking without imposing the frequently used approximation α_s(−(p−k)²) α₅(−p_>²), where p_>² ≡ max(p², k²) for the running coupling constant in the quark Schwinger-Dyson equation. We present numerical results in Landau gauge and compare these with earlier results obtained when using this approximation. We see in this context that a gluon propagator which has the form 1/q⁴ in the infrared is too singular and must be regulated. We derive a suitably generalized expression for the pion decay constant f_π. With essentially one free parameter we are able to reproduce reasonable results for various physical quantities of interest including , and Λ_QCD.     

α(Q2) corrections to particle multiplicity ratios in gluon and quark jets

The order $\text{α(Q}{}^2\text{)}$ correction to the particle multiplicity ratio in gluon and quark jets is calculated in QCD. We find

$\text{r=}\text{9}\text{4}\text{1?}\text{αC}{}_{\mathrm{<mtext>A</mtext>}}\text{2π}\text{1}\text{3}\text{+}\text{N}{}_{\mathrm{?}}\text{3C}{}_{\mathrm{<mtext>A</mtext>}}\text{?}\text{2N}{}_{\mathrm{?}}\text{C}{}_{\mathrm{<mtext>F</mtext>}}\text{3C}{}^2{}_{\mathrm{<mtext>A</mtext>}}$

with r=〈n〉_{gluon jet}/〈n〉_{quark jet}. The method used is systematic and could be used for an order α(Q²) calculation.     

On the rise of the proton structure function F2 towards low x

A measurement of the derivative (∂ lnF₂/∂ lnx)_Q²≡−λ(x,Q²) of the proton structure function F₂ is presented in the low x domain of deeply inelastic positron–proton scattering. For 5×10⁻⁵x0.01 and Q²1.5 GeV², λ(x,Q²) is found to be independent of x and to increase linearly with lnQ².     

Energy dependence of the differences between the quark and gluon jet fragmentation

Three jet events arising from decays of the Z boson, collected by the DELPHI detector, were used to measure differences in quark and gluon fragmentation. Gluon jets were anti-tagged by identifying b quark jets. Unbiased quark jets came from events with two jets plus one photon. Quark and gluon jet properties in different energy ranges were compared for the first time within the same detector. Quark and gluon jets of nearly the same energy in symmetric three jet event topologies were also compared. Using three independent methods, the average value of the ratio of the mean charged multiplicities of gluon and quark jets is $$< r >=1.241 pm 0.015 (stat.)pm 0.025 (syst.).$$ Gluon jets are broader and produce fragments with a softer energy spectrum than quark jets of equivalent energy. The string effect has been observed in fully symmetric three jet events. The measured ratio R_γ of the charged particle flow in the qq? inter-jet region of the qq?g and qq?γ samples agrees with the perturbative QCD expectation. The dependence of the mean charged multiplicity on the hadronic center-of-mass energy was analysed in photon plus n-jet events. The value for α_s(M _Z) determined from these data using a QCD prediction with corrections at leading and next-to-leading order is $$←pha_s(M_Z)=0.116pm 0.003 (stat.)pm 03009 (syst.).$$     

Comment on Vub from exclusive semileptonic B and D decays

The prospects for determining |V_ub| from exclusive B semileptonic decay are discussed. The double ratio of form factors (f^(B→ρ)/f^(B→K*))/(f^(D→ρ)/f^(D→K*)) is calculated using chiral perturbation theory. Its deviation from unity due to contributions that are non-analytic in the symmetry breaking parameters is very small. Combining experimental data obtainable from , and can lead to a model independent determination of |V_ub| with an uncertainty from theory of about 10%.     

Diffraction at HERA, Color Opacity and Nuclear Shadowing in DIS off nuclei

The QCD factorization theorem for diffractive processes in DIS is used to derive formulae for the leading twist contribution to the nuclear shadowing of parton distributions in the low thickness limit (due to the coherent projectile (photon) interactions with two nucleons). Based on the current analyzes of diffraction at HERA we find that the average strength of the interactions which govern diffraction in the gluon sector at x≤ 10⁻³, Q ₀= 2 GeV is ∼50mb. This is three times larger than in the quark sector and suggests that applicability of DGLAP approximation requires significantly larger Q ₀ in the gluon sector. We use this information on diffraction to estimate the higher order shadowing terms due to the photon interactions with N≥ 3 nucleons which are important for the scattering of heavy nuclei and to calculate nuclear shadowing and Q ² dependence of gluon densities. For the heavy nuclei the amount of the gluon shadowing: G _A(x,Q ₀ ²) /AG _N(x,Q ₀ ²)_{|x ≤ 10−3}∼ 0.25–0.4 is sensitive to the probability of the small size configurations within wave function of the gluon “partonometer” at the Q ₀ scale. At this scale for A∼ 200 the nonperturbative contribution to the gluon density is reduced by a factor of 4–5 at x≤ 10⁻³ unmasking PQCD physics in the gluon distribution of heavy nuclei. We point out that the shadowing of this magnitude would strongly modify the first stage of the heavy ion collisions at the LHC energies, and also would lead to large color opacity effects in eA collisions at HERA energies. In particular, the leading twist contribution to the cross section of the coherent J/ψ production off A≥ 12 nuclei at s ⁻²≥ 70 GeV is strongly reduced as compared to the naive color transparency expectations. The Gribov black body limit for F _2A(x,Q ²) is extended to the case of the gluon distributions in nuclei and shown to be relevant for the HERA kinematics of eA collisions. Properties of the final states are also briefly discussed. Received: 12 March 1999     

On Meson Masses

It is shown that in the framework of an analytical confinement, when quark and gluon propagators are induced by a vacuum self-dual gluon field with constant strength, the masses of mesons with quantum numbers Q = (J ^P ,n), where n is the radial quantum number, and quark constituents m ₁, m ₂ are described with reasonable accuracy by the formula The positive parameter A _Q is unique for all mesons with a fixed quantum number Q. Sets of mesons J ^P = 1⁻, 0⁺, 1⁺, 2⁺, 3⁻ for n = 0 and 1⁻ , 2⁺ for n > 0 and different flavor constituent quarks (u = d, s, c, b) are considered.     

Determination of the effective strong coupling constant from CLAS spin structure function data

We present a new extraction of the effective strong coupling constant α_s,g1(Q²). The result agrees with a previous determination and extends the measurement of the low and high Q² behavior of α_s,g1(Q²) that was previously deduced from sum rules. In particular, it experimentally verifies the lack of Q²-dependence of α_s,g1(Q²) in the low Q² limit. This fact is necessary for application of the AdS/CFT correspondence to QCD calculations. We provide a parameterization of α_s,g1(Q²) that can equivalently be used to parameterize the Q²-dependence of the generalized Gerasimov–Drell–Hearn and Bjorken sums.     

The Q<Superscript>2</Superscript> dependence of polarized and unpolarized proton structure functions in the relativistic quark exchange framework

In this article we intend to discuss the evolution of polarized and unpolarized structure functions in the (x,Q²) plane. We analyze the proton data on the spin dependence asymmetry A₁(x,Q²), by making the dynamical assumption that at low resolution energies, the hadrons consist only of valence quarks and the scaling violation of F₂(x,Q²) at low x comes only from the gluons density. While the sea quark and the gluon distributions are calculated using the inverse Mellin technique and the various moments of the valence quarks, the valence quark distribution itself is obtained from the relativistic quark-exchange model. A comparison is made with the corresponding available experimental data. Finally in agreement with the data, it is demonstrated that there is no significant Q²-dependence of asymmetry A₁(x,Q²) for x ranging 0.014 ≤ x ≤ 0.25. Received: 11 September 1999 / Revised version: 8 December 1999     

Gluon distributions in real and virtual photon and the photon structure function

Gluon distributions in real and virtual photons are calculated using evolution equations in the NLO approximation. The quark distributions in the photon determined on the basis of the QCD sum rule approach in [1] are taken as an input. It is shown that gluon distribution in the photon can be reliably determined up tox=0.03÷0.05, much lower than the corresponding values in the case of quark distributions. Two variants of the calculations are considered: (1) it is assumed that there are no intrinsic gluons in the photon at some low normalization pointQ ²=Q ₀ ² ∼1GeV²; (2) it is assumed that gluonic content of the photon at lowQ ₀ ² is described by gluonic content of vector mesonsρ, ω, ϕ. The gluon distributions in these two variants appear to be different. This fact permits one to clarify the origin of nonperturbative gluonic content of the photon by comparing the results with experiment. Structure functionsF ₂(x) for real and virtual photon are calculated and it is shown that in the regionx≥0.2 where QCD approach is valid, there is a good agreement with experiment.     

Elastic double diffractive production of axial-vector mesons and the Landau–Yang theorem

We discuss exclusive elastic double diffractive axial-vector χ_c(1⁺) meson production in proton–antiproton collisions at the Tevatron. The amplitude for the process is derived within the k_t-factorization approach with unintegrated gluon distribution functions (UGDFs). We show that the famous Landau–Yang theorem is not applicable in the case of off-shell gluons. Differential cross sections for different UGDFs are calculated. We compare exclusive production of χ_c(1⁺) and χ_c(0⁺). The contribution of χ_c(1⁺) to the J/Ψ+γ channel is smaller than that of the χ_c(0⁺) decay, but not negligible and can be measured. The numerical value of the ratio of the both contributions is much less dependent on the UGDFs modeling than the cross sections themselves.     

Photoproduction of D mesons associated with a leading neutron

The photoproduction of D^*±(2010) mesons associated with a leading neutron has been observed with the ZEUS detector in ep collisions at HERA using an integrated luminosity of 80 pb⁻¹. The neutron carries a large fraction, x_L>0.2, of the incoming proton beam energy and is detected at very small production angles, θ_n<0.8 mrad, an indication of peripheral scattering. The D^* meson is centrally produced with pseudorapidity |η|<1.5, and has a transverse momentum p_T>1.9 GeV, which is large compared to the average transverse momentum of the neutron of 0.22 GeV. The ratio of neutron-tagged to inclusive D^* production is 8.85±0.93(stat.)^+0.48_−0.61(syst.)% in the photon–proton center-of-mass energy range 130<W<280 GeV. The data suggest that the presence of a hard scale enhances the fraction of events with a leading neutron in the final state.     

Resonances in at rest

Data on at rest show two resonant processes: (a) f₀(1370)η,f₀(1370)→σσ and ρρ, (b) η(1440)σ, η(1440)→ηπ⁺π⁻. The branching ratio BR[f₀(1370)→ρρ]/BR[f₀(1370)→σσ]=0.98±0.25 in the mass range available here. Using data on , the ratio Γ_4π/Γ_2π5 for f₀(1370). The effects of the strongly s-dependent width of f₀(1370) are discussed in some detail.The η(1440) is observed decaying to ησ and a₀(980)π, with strong destructive interference between them. In its decay to a₀(980)π, a narrow peak appears in the ηπ mass spectrum, but 30–50 MeV above that usually attributed to a₀(980) and significantly above the KK threshold. This effect is explained naturally by a two-step process: η(1440)→K^*(890)K followed by rescattering of the two kaons through a₀(980) to ηπ above the KK threshold.     

On integrability of generalized Veronese curves of distributions

Given a 1-parameter family of 1-forms γ(t) = γ₀+tγ₁+ ···+tⁿψ_n, consider the condition dγ(t)γ(t) = 0 (of integrability for the annihilated by γ(t) distribution w(t)). We prove that in order that this condition is satisfied for any t it is sufficient that it is satisfied for N = n + 3 different values of t (the corresponding implication for N = 2n + 1 is obvious). In fact we give a stronger result dealing with distributions of higher codimension. This result is related to the so-called Veronese webs and can be applied in the theory of bihamiltonian structures.