Beauty,charm, and <Emphasis Type="Italic">F</Emphasis><Subscript><Emphasis Type="Italic">L</Emphasis></Subscript> at HERA: New data vs. Early predictions

One of the well-known effects of the asymptotic freedom is splitting of the leading-log BFKL pomeron into a series of isolated poles in complex angular momentum plane. Following our earlier works we explore the phenomenological consequences of the emerging BFKL-Regge factorized expansion for the small-x charm (F ₂ ^c ) and beauty (F ₂ ^b ) structure functions of the proton. As we found earlier, the colordipole approach to the BFKL dynamics predicts uniquely decoupling of subleading hard BFKL exchanges from F ₂ ^c at moderately large Q ². We predicted precocious BFKL asymptotics of F ₂ ^c (x,Q ²) with intercept of the rightmost BFKL pole α _P(0) − 1 = Δ_P ≈ 0.4. High-energy open beauty photo- and electroproduction probes the vacuum exchange at much smaller distances and detects significant corrections to the BFKL asymptotics coming from the subleading vacuum poles. In view of the accumulation of the experimental data on small −x F ₂ ^c and F ₂ ^b we extended our early predictions to the kinematical domain covered by new HERA measurements. Our structure functions obtained in 1999 agree well with the determination of both F ₂ ^c and F ₂ ^b by the H1 published in 2006 but contradict very recent (2008, preliminary)H1 results on F ₂ ^b . We present also comparison of our early predictions for the longitudinal structure function F _L with recent H1 data (2008) taken at very low Bjorken x. We comment on the electromagnetic corrections to the Okun-Pomeranchuk theorem.     

The BFKL-Regge phenomenology of deep inelastic scattering

We calculate the Regge trajectories of the subleading BFKL singularities and eigenfunctions for the running BFKL pomeron in the color dipole representation. We obtain a viable BFKL-Regge expansion of the proton structure function F _2p (x,Q ²) in terms of several rightmost BFKL singularities. We find large subleading contributions to F _2p (x,Q ²) in the HERA kinematical region which explain the lack of predictive power of GLDAP extrapolations of F _2p (x,Q ²) to the region of small x. We point out the relation of our early finding of precocious BFKL asymptotic behavior to the nodal structure of subleading BFKL eigenfunctions. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 134–138 (10 August 1997) Published in English in the original Russian journal. Edited by Steve Torstveit     

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.     

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.     

A measurement of the photon structure function F 2γ at an average Q 2 of 12 GeV2/ c 4

The hadronic photon structure functionF ₂ ^γ has been measured in theQ ² range from 4 to 30 GeV²/c ⁴ and down tox values of order 0.001, using data taken with the DELPHI detector at LEP between 1991 and 1993. A comparison is made with severalF ₂ ^γ parameterizations with special emphasis on their lowx behaviour. A result on theQ ² evolution ofF ₂ ^γ is presented.     

Measurement of the proton structure function F 2 at low x and low Q 2 at HERA

We report on a measurement of the proton structure functionF ₂ in the range 3.5×10⁻⁵≤x≤4×10⁻³ and 1.5 GeV²≤Q ²≤15GeV² at theep collider HERA operating at a centre-of-mass energy of √s=300GeV. The rise ofF ₂ with decreasingx observed in the previous HERA measurements persists in this lowerx andQ ² range. TheQ ² evolution ofF ₂, even at the lowestQ ² andx measured, is consistent with perturbative QCD. supported by EU HCM contract ERB-CHRX-CT93-0376     

The exponent λ (x, Q2) of the proton structure functionF2(x, Q2) at lowx

The exponent λ of the structure function F₂ ∼x ^−λ is calculated using the solution of the DGLAP equation for gluon at lowx reported recently by the present authors. The quantity λ is calculated both as a function ofx at fixedQ ² and as a function ofQ ² at fixedx and compared with the most recent data from H1     

The running BFKL: Resolution of Caldwell’s puzzle

The HERA data on the proton structure function F ₂(x,Q ²) at very small x and Q ₂ show a dramatic departure of the logarithmic slope ∂F ₂/∂log Q ² from theoretical predictions based on the DGLAP evolution. We show that the running BFKL approach provides a quantitative explanation for the observed x and/or Q ² dependence of ∂F ₂/∂log Q ². Pis’ma Zh. éksp. Teor. Fiz. 69, No. 2, 92–97 (25 January 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The structure of mixed fluorides Ca1?xSrxF2 and Sr1?xBaxF2 and the luminescence of Eu2+ in these crystals

The structure of the mixed fluorites Ca_1−x Sr_xF₂ and Sr_1−x Ba_xF₂, as well as the structure of the Eu²⁺ impurity center in these crystals, is calculated within the framework of the virtual-crystal method realized in the shell model and pair-potential approximation. The phenomenological dependence of the position of the lower level of the 4f ⁶5d configuration of the Eu²⁺ ion on distance to the Eu²⁺-ligand is derived. The dependences of the Stokes shift and the Huang-Rhys factor on x are calculated for the yellow luminescence in Sr_1−x Ba_xF₂:Eu²⁺. The value of x at which the lower level of the 4f ⁶5d configuration of the Eu²⁺ ion in Sr_1−x Ba_xF₂:Eu²⁺ falls within the conduction band is found. __________ Translated from Fizika Tverdogo Tela, Vol. 45, No. 5, 2003, pp. 823–826. Original Russian Text Copyright ? 2003 by Nikiforov, Zakharov, Chernyshev, Ugryumov, Kotomanov.     

Observation of a resonance in the KSp decay channel at a mass of 1765?MeV/c2

We report on the observation of a K_Sp resonance signal at a mass of 1765 ± 5 MeV/c ², with intrinsic width Γ = 108 ± 22 MeV/c ², produced inclusively in Σ^--nucleus interactions at 340 GeV/c in the hyperon beam experiment WA89 at CERN. The signal was observed in the kinematic region x_F>0.7, in this region its production cross section rises approximately linearly with (1-x_F), reaching BR(X→K_Sp)dσ/dx_F=(5.2±2.3)μb per nucleon at x_F=0.8. The hard x_F spectrum suggests the presence of a strong leading particle effect in the production and hence the identification as a Σ^*+ state. No corresponding peaks were observed in the K^-p and Λπ^± mass spectra. PACS 25.80.-e; 13.60.Rj; 14.20.Jn     

Azimuthal asymmetry and ratio R = FL/FT as probes of the charm content of the proton

We study two experimental ways to measure the heavy-quark content of the proton: using the Callan-Gross ratio R(x,Q ²) = F _L /F _T = and/or azimuthal cos(2φ) -asymmetry in deep inelastic lepton-nucleon scattering. Our approach is based on the perturbative stability of the QCD predictions for these two quantities. We resume the mass logarithms of the type α _s ln(Q ²/m ²) and conclude that heavy-quark densities in the nucleon can, in principle, be determined from data on the Callan-Gross ratio and/or azimuthal asymmetry. In particular, the charm content of the proton can be measured in future studies at the proposed Large Hadron-Electron (LHeC) and Electron-Ion (EIC) Colliders.     

The longitudinal structure function F L(x, Q 2) and the gluon distribution G(x, Q 2) at low x

We obtain a relation between the longitudinal structure function F _L(x, Q ²), F ₂(x, Q ²) and G(x, Q ²) at small x, using the formalism recently reported by one of the authors [2]. We also obtain a relation between F _L(x, Q ²), F ₂(x, Q ²) and its slope (dF ₂(x, Q ²))/(dlnQ ²). This provides us with the determination of the longitudinal structure function F _L(x, Q ²) from F ₂(x, Q ²) data and hence extract the gluon distribution G(x, Q ²).     

Measurement of the proton structure functionF2 from the 1993 HERA data

The ZEUS detector has been used to measure the proton structure functionF ₂. During 1993 HERA collided 26.7 GeV electrons on 820 GeV protons. The data sample corresponds to an integrated luminosity of 0.54 pb^–1, representing a twenty fold increase in statistics compared to that of 1992. Results are presented for 7Q ²<>⁴ GeV² andx values as low as 3×10^–4. The rapid rise inF ₂ asx decreases observed previously is now studied in greater detail and persists forQ ² values up to 500 GeV².supported by Worldlab, Lausanne, Switzerland     

Diffractive photoproduction of D*±(2010) at HERA

Diffractive photoproduction of D^*±(2010) mesons was measured with the ZEUS detector at the ep collider HERA, using an integrated luminosity of 78.6 pb^-1. The D^* mesons were reconstructed in the kinematic range: transverse momentum p_T(D^*) > 1.9 GeV and pseudorapidity |η(D^*)|<1.6, using the decay D^*+→D⁰π⁺ _s followed by D⁰→K^-π⁺(+c.c.). Diffractive events were identified by a large gap in pseudorapidity between the produced hadronic state and the outgoing proton. Cross sections are reported for photon–proton centre-of-mass energies in the range 130 < W < 300 GeV and for photon virtualities Q² < 1 GeV², in two ranges of the Pomeron fractional momentum x_IP<0.035 and x_IP<0.01. The relative contribution of diffractive events to the inclusive D^*±(2010) photoproduction cross section is about 6%. The data are in agreement with perturbative QCD calculations based on various parameterisations of diffractive parton distribution functions. The results are consistent with diffractive QCD factorisation.     

Absolute cross sections of electron attachment to molecular clusters. Part II: Formation of (H2O) N? , (N2O) N? , and (N2) N?

Absolute cross sections σ⁻(E, N) of electron attachment to clusters (H₂O) _N , (N₂O) _N , and (N₂) _N for varying electron energy E and cluster size N are measured by using crossed electron and cluster beams in a vacuum. Continua of σ⁻(E) are found that correlate well with the functions of electron impact excitation of molecules’ internal degrees of freedom. The electron is attached through its solvation in a cluster. In the formation of (H₂O) _N ⁻ , (N₂O) _N ⁻ , and (N₂) _N ⁻ , the curves σ⁻(N) have a well-defined threshold because of a rise in the electron thermalization and solvation probability with N. For (H₂O)₉₀₀, (N₂O)₃₅₀, and (N₂)₂₆₀ clusters at E = 0.2 eV, the energy losses by the slow electron in the cluster are estimated as 3.0 × 10⁷, 2.7 × 10⁷, and 6.0 × 10⁵ eV/m, respectively. It is found that the growth of σ⁻ with N is the fastest for (H₂O) _N and (N₂) _N clusters at E → 0 as a result of polarization capture of the s-electron. Specifically, at E = 0.1 eV and N = 260, σ⁻ = 3.0 × 10⁻¹³ cm² for H₂O clusters, 8.0 × 10⁻¹⁴ cm² for N₂O clusters, and 1.4 × 10⁻¹⁵ cm² for N₂ clusters; at E = 11 eV, σ⁻ = 9.0 × 10⁻¹⁶ cm² for (H₂O)₂₀₀ clusters, 2.4 × 10⁻¹⁴ cm² for (N₂O)₃₅₀ clusters, and 5.0 × 10⁻¹⁷ cm² for (N₂)₂₆₀ clusters; finally, at E = 30 eV, σ⁻ = 3.6 × 10⁻¹⁷ cm² for (N₂O)₁₀ clusters and 3.0 × 10⁻¹⁷ cm² for (N₂)₁₂₅ clusters. Original Russian Text ? A.A. Vostrikov, D.Yu. Dubov, 2006, published in Zhurnal Tekhnicheskoĭ Fiziki, 2006, Vol. 76, No. 12, pp. 1–15.     

Measurement and QCD analysis of the diffractive deep-inelastic scattering cross section at HERA

A detailed analysis is presented of the diffractive deep-inelastic scattering process ep→eXY, where Y is a proton or a low mass proton excitation carrying a fraction 1-x_IP>0.95 of the incident proton longitudinal momentum and the squared four-momentum transfer at the proton vertex satisfies |t|<1 GeV². Using data taken by the H1 experiment, the cross section is measured for photon virtualities in the range 3.5≤Q²≤1600 GeV², triple differentially in x_IP, Q² and β=x/x_IP, where x is the Bjorken scaling variable. At low x_IP, the data are consistent with a factorisable x_IP dependence, which can be described by the exchange of an effective pomeron trajectory with intercept α_IP(0)=1.118±0.008(exp.)^+0.029 _-0.010(model). Diffractive parton distribution functions and their uncertainties are determined from a next-to-leading order DGLAP QCD analysis of the Q² and β dependences of the cross section. The resulting gluon distribution carries an integrated fraction of around 70% of the exchanged momentum in the Q² range studied. Total and differential cross sections are also measured for the diffractive charged current process e⁺p→ν̄_eXY and are found to be well described by predictions based on the diffractive parton distributions. The ratio of the diffractive to the inclusive neutral current ep cross sections is studied. Over most of the kinematic range, this ratio shows no significant dependence on Q² at fixed x_IP and x or on x at fixed Q² and β.     

The next-to-leading order (NLO) gluon distribution from DGLAP equation and the logarithmic derivatives of the proton structure functionF 2(x, Q 2) at lowx

At lowx, an analytic solution of the DGLAP equation for gluon in the next-to-leading order (NLO) is obtained by applying the method of characteristics. Its compatibility with double leading logarithmic approximation (DLLA) asymptotics is discussed and comparison with the exact ones like GRV98NLO is made. The solution is then utilized to calculate the derivatives∂F ₂ (x,Q ²)/∂ lnQ ² and ∂ lnF ₂(x,Q ²)/∂ ln (1/x) and compared with the recent HERA data. Our solution is found to reproduce most of the essential features of the data on the derivatives.     

Electron-vibrational energy exchange in collisions of Ar atoms in the 3P2 metastable state with N2(X1S g+ ) molecules

Rate constants for electron-vibrational energy exchange Ar(³ P ₂) + N₂(X ¹Σ _g ⁺, ν = 0) → Ar(¹ S ₀) + N₂(C ³Π _u , ν′), where ν′ = 0, 1, 2, were calculated. Calculations were performed taking into account the presence of a resonance in electron scattering by N₂(X ¹Σ _g ⁺). As a result, the interaction of Ar(³ P ₂) with N₂(X ¹Σ _g ⁺, ν = 0) was characterized by attraction and, in the end, intersection of electron-vibrational potential surfaces correlating with Ar(³ P ₂) + N₂(X ¹Σ _g ⁺, ν = 0) and Ar(¹ S ₀) + N₂(C ³Π _u , ν′) at interparticle distances of 2.5–3.5 ?. Exchange interaction at which electron-vibrational transitions in the region of intersection of electron-vibrational transitions in the region of intersection of electron-vibrational potential surfaces accompanied by spin exchange were induced was calculated by the asymptotic method. The rate constants determined at 300–600 K were on the order of 10⁻¹¹−10⁻¹² cm³/s and weakly increased as the temperature grew. Mainly the C ³Π _u , ν′ = 0 state of the N₂ molecule was populated. The calculation results were in satisfactory agreement with the experimental data obtained at 300 K.     

Production of V0 pairs in the hyperon experiment WA89

We present a comprehensive study of the inclusive production of V⁰V⁰ pairs (V⁰=Λ, Λ̄ or K_S ) by Σ^- and π^- of 340 GeV/c momentum and neutrons of 260 GeV/c mean momentum in copper and carbon targets. In particular, the dependence of the x_F spectra on the combination of beam-particle and produced V⁰V⁰ pair is investigated and compared to predictions obtained from PYTHIA and QSGM calculations. The data and these predictions differ in many details, the agreement can at best be termed as qualitative. A signal from decays of the tensor meson f’₂(1525) was observed in the K_S K_S mass distribution and inclusive production cross sections were measured. No signal was found from the double-strange H-dibaryon decaying to ΛΛ.