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     

Quark-Antiquark states and their radiative transitions in terms of the spectral integral equation: Bottomonia

In the framework of the spectral integral equation, we consider the states and their radiative transitions. We reconstruct the interaction on the basis of data for the levels of the bottomonium states with J ^PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺ as well as the data for the radiative transitions γ (3S) → _γχbJ(2P) and γ(2S) → _γχbJ(1P) with J = 0, 1, 2. We calculate bottomonium levels with the radial quantum numbers n ≤ 6, their wave functions, and corresponding radiative transitions. The ratios Br[_χbJ(2P) → _γγ(2S)]/Br[_χbJ(2P) → _γγ(1S)] for J = 0, 1, 2 are found to be in agreement with data. We determine the component of the photon wave function using the data for the e ⁺ e ⁻ annihilation, e ⁺ e ⁻ → γ(9460), γ(10 023), γ(10 036), γ(10 580), γ(10 865), γ(11 019), and predict partial widths of the two-photon decays ηb0 → γγ, χb0 → γγ, χb2 → γγ for the radial excitation states below the threshold (n ≤ 3). The text was submitted by the authors in English.     

QCD coupling constant below 1 GeV in the poincare-covariant model

The behavior of the running coupling constant α _s (Q ²) phenomenologically parameterized in the region of Q < 1 GeV is considered within the framework of the Poincare-covariant quark model in a variety of regimes. An analysis was carried out for pseudoscalar and vector mesons with the lepton masses and decay constants (obtained by the model calculations) required to match their experimental counterparts. It shows that the constant α _s is likely to behave with α_crit = α _s (Q ² = 0) ∼ 0.667 − 0.821 in the case of a frozen regime and α_crit =0.300 − 0.692 for peaked curves, which follows from the experimental values of the leptonic decay constants and masses.     

Parton distributions in the virtual photon target up to NNLO in QCD

Parton distributions in the virtual photon target are investigated in perturbative QCD up to the next-to-next-to-leading order (NNLO). In the case Λ ²≪P ²≪Q ², where −Q ² (−P ²) is the mass squared of the probe (target) photon, parton distributions can be predicted completely up to the NNLO, but they are factorisation-scheme dependent. We analyse parton distributions in two different factorisation schemes, namely the and DIS _γ schemes, and we discuss their scheme dependence. We show that the factorisation-scheme dependence is characterised by the large-x behaviours of the quark distributions. The gluon distribution is predicted to be very small in absolute value except in the small-x region.     

Modular conformal scaling group evidenced in lepton-quark mass

Lepton-quark mass may reflect a correspondence in spacetime structure described by a modular conformal scaling group. Stemming in part from a spacetime line element correspondenceds → (expλ _n)ds in which the eight quantitiesλ ₀,λ ₁, ...,λ ₇ constitute a closed set under a modular addition, the associated formula for lepton-quark mass (yielding values at the 1 GeV scale for the leptons and lighter quarks and at the physical pole for the top) is conjectured to bem=m _fQ²(exp −λ _n), wherem _f=10.245 TeV is the progenitor fermion mass,Q is the charge number of the lepton or quark, and the modular group parameterλ _n is indexed by a fermion principal quantum numbern that depends on three mutually independent projection operators.     

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

The order α(Q²) correction to the particle multiplicity ratio in gluon and quark jets is calculated in QCD. Through α(Q²) we find , with r = <n>_{gluon jet}/<n>_{quark jet}. This ratio is independent of the opening angle chosen to define the jets.     

QCD sum rules for masses of excited heavy mesons

The masses of excited heavy mesons are studied with sum rules in the heavy quark effective theory. A set of interpolating currents creating (annihilating) excited heavy mesons with arbitrary spin and parity are proposed and their properties are discussed. Numerical results at the leading order of the O(1/m_Q) expansion are obtained for the lowest doublets (0⁺, 1⁺) and (1⁺, 2⁺).     

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     

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.     

The estimates of periodic potentials in terms of effective masses

LetG _n=(A _n ⁻ , A _n ⁺ ),n≧1, denote the gaps,M _n ^± be the effective masses and Σn=[A _n−1 ⁺ ,A _n ^- ],A ₀ ⁺ =0, be the spectral bands of the Hill operatorT=−d ²/dx ²+V(x) inL ² (R), whereV is a 1-periodic real potential fromL ²(0,1). Let the length gapL _n=|G_n|, h_n be the height of the corresponding slit on the quasimomentum domain and Δ_n=π²(2n−1)−∣Σ_n∣>0 be the band reduction. Let ,n≧1, denote the gap length for the operator . Introduce the sequencesL={L_n}, h={h_n}, l={l_n}, Δ={Δ_n},M ^±={M _n ^± } and the norms ,m≧0. The following results are obtained: i) The estimates of‖V‖, ‖L‖, ‖h‖ ₁, ‖l‖₁, ‖δ‖ in terms of ‖M^±‖₂, ii) identities for the Dirichlet integral of quasimomentum and integral of potentials and so on, iii) the generation of i), ii) for more general potentials. The research described in this publication was made possible in part by grant from the Russian Fund of Fundamental Research and INTAS.     

Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique in the case of different quark masses

The Bethe-Salpeter equations for quark-antiquark composite systems with different quark masses, such as \(q\bar s(with q = u,d),q\bar Q\), and \(s\bar Q\) (with Q = c, b), are written in terms of spectral integrals. For mesons characterized by the mass M, spin J, and radial quantum number n, the equations are written for the (n, M²) trajectories with fixed J. The mixing between states with different quark spin S and angular momentum L is also discussed.     

Search for and study of low-mass scalar mesons in reaction np → npπ+π? at neutron beam momentum Pn = (5.20 ± 0.12) GeV/c

We present the results of a search for and study of the resonance effects in the system of π⁺π⁻ from the reaction np → npπ⁺π⁻ at the momentum of quasi-monochromatic neutrons P _n = (5.20 ± 0.12) GeV/c from the data obtained in an exposure of the 1-m hydrogen bubble chamber of Veksler and Baldin Laboratory of High Energies, Joint Institute for Nuclear Research (VBLHE JINR). After the supplementary selection of the events where a secondary proton was emitted in the forward hemisphere in the general c.m.s. of the reaction (cosθ* _p > 0) in the effective mass spectrum of π⁺π⁻ combinations, we found nine peculiarities at the masses (350 ± 3), (408 ± 3), (489 ± 3), (579 ± 5), (676 ± 7), (762 ± 11), (878 ± 7), (1036 ±13), and (1170 ± 11) MeV/c ² with experimental widths of no more than several tens of MeV/c ². We carried out a direct measurement of the spins of resonances and also obtained other quantum numbers. All of these peculiarities have a similar set of quantum numbers I ^G (J ^PC ) = 0⁺ (0⁺⁺). We investigated a sequence of scalar-isoscalar resonances f ₀(σ₀) with masses in the range M ≤ 1200 MeV/c ². We found a phenomenological dependence of the resonance mass on its number. This dependence covered not only the resonances shown in this paper, but also those present in PDG tables with quantum numbers of f ₀(σ₀) mesons.     

Search for and study of low-mass scalar mesons in reactions np → npπ+π? at neutron beam momentum Pn = (3.83 ± 0.12) GeV/c

The results of a search for and study of the scalar 0⁺ [0⁺⁺] σ₀ mesons in a π⁺π⁻ system produced in the reaction np → npπ⁺π⁻ at the quasi-monochromatic neutron beam momentum P _n = (3.83 ± 0.12) GeV/c are presented as derived from analyzing the data obtained during the exposure of a 1-meter hydrogen bubble chamber at the Laboratory of High Energy, Joint Institute for Nuclear Research (LHE JINR). It is found that there is a significant bump in the effective mass distribution at M_{p⁺ p^-} = (404 ±5)MeV/c²M_{\pi ^ + \pi ^ - } = (404 \pm 5)MeV/c^2 and Γ_res^exp = (14±5.4) MeV/c ², which is observed with more than four standard deviations from the background. The spin of this resonance is estimated to be most likely equal to zero. Its quantum numbers are found to be 0⁺ [0⁺⁺].     

Magnetic monopole interactions: Shell structure of meson and baryon states

It is suggested that a low-mass magnetic monopole of Dirac chargeg=(137/2)e may be interacting with ac-quark's magnetic dipole moment to produce Zeeman splitting of meson states. The massM ₀=2397 MeV of the monopole is in contrast to the 10¹⁶-GeV monopoles of grand unification theories (GUT). It is shown that shell structure of energyE _n =M ₀+1/4nM ₀+ exists for meson states. The presence of symmetric meson states leads to the identification of the shell structure. The possible existence of the 2397-MeV magnetic monopole is shown to quantize quark masses in agreement with calculations of quantum chromodynamics (QCD). From the shell structure of meson states, the existence of two new mesons is predicted:(1814±50 MeV) withI ^G(J ^PC =0⁺(0^–+) and _c (3907±100 MeV) withJ ^PC =0^–+. The presence of shell structure for baryon states is shown.     

Colour effects in Drell-Yan process

We examine the predictions of gauge theories with colour excitation for the processpp →μ ⁺ μ ⁻ X. Relative to the predictions of quark parton model (with three colours) we find enhancements as large as a factor 3 – 4 for the cross-sectionM ³ d ² σ/dMdy|_y=0 in the region 0·03 ≲M/√s ≲ 0·2 at √s=62 GeV,M being the invariant mass andy the rapidity of the muon pair. We study the sensitivity of this result to the colour gluon mass and the underlying parametrisation of the quark and gluon distribution functions.     

Confrontation of nucleus deformation and multipole mixture parameters in (2+0 n ?2+01) transitions with rotational band structure for K π = 0 2+ and 0 3+

The difference of the energies of levels Δ _n = E _lev(2⁺0 _n ) − E _lev(0⁺0 _n ) at n = 1, 2, and 3 and the multipole-mixture parameter δ for (2⁺0₂−2⁺0₁) and (2⁺0₃−2⁺0₁) transitions are contrasted against the structure of the K ^π = 0₂⁺ and 0₃⁺ rotational bands that was calculated on the basis of the quasiparticle-phonon model. The values of (Δ₂ − Δ₁), (Δ₃ − Δ₁), and (Δ₂ − Δ₃) are found to correlate with the sign of the parameter δ and with the calculated structure of the K ^π = 0₂⁺ and 0₃⁺ bands. Original Russian Text ? A.M. Demidov, L.I. Govor, V.A. Kurkin, I.V. Mikhailov, 2009, published in Yadernaya Fizika, 2009, Vol. 72, No. 2, pp. 236–240.     

Soft end-point and mass corrections to the η′g*g* vertex function

Power-suppressed corrections arising from end-point integration regions to the space-like vertex function of the massive η^′-meson virtual gluon transition are computed. Calculations are performed within the standard hard-scattering approach (HSA) and the running coupling method supplemented by the infrared renormalon calculus. Contributions to the vertex function from the quark and gluon contents of the η^′-meson are taken into account and the Borel resummed expressions for (Q²,ω,η), as well as for (Q²,ω=±1,η) and (Q²,ω=0,η) are obtained. It is demonstrated that the power-suppressed corrections ∼(Λ²/Q²)ⁿ, in the explored range of the total gluon virtuality 1≤Q²≤25 GeV², considerably enhance the vertex function relative to the results found in the framework of the standard HSA with a fixed coupling. Modifications generated by the η^′-meson mass effects are discussed. PACS 12.38.Bx; 14.40.Aq; 11.10.Hi