Infrared contribution to the double-logarithmic small-x asymptotics of structure functions

The role playing by the “soft” (κ _T < 1 GeV/c) region in the small-x behaviour ofg ₁(x,Q ²) and the non-singlet structure functionf _{1, NS}(x, Q²) has been studied with the help of the effective QCD Lagrangian which takes into account the lightest degrees of freedom — the constituent quarks and the π-mesons (Goldstone bosons). It has been shown that the quark-quark interaction due to the pion exchange has a negative couplingg for the isovector component (I = 1 in thet-channel) off ₁(x,Q ²) and isosinglet component ofg ₁(x, Q²). Here the pion induced interaction changes mainly the normalization of the quark distribution (it decreasesf _1,NS ^{I = 1} (x,Q ²) two times atx < 3·10^?3) and changes slightly the effective exponents λ (?_1,NS ,g ₁ ～x ^?λ atx → 0). On the other hand due to a positive value of couplingg the value of λ increases by 15% for the isovector part ofg ₁ (x,Q ²) and up to λ ≈ 0.5 (instead of λ ≈ 0.2 without the pion contribution) for the isoscalar non-singlet structure functionf _1,NS ^{I = 0} (x,Q ²).     

Predictions for inclusive reactions based on a parton structure of hadrons

It is proposed that the asymptotic single-particle distributions f(x)=x(dσ/dx) in inclusive reactions should reflect the limiting longitudinal momentum distribution, ∼νW₂(x), of the hypothetical partons constituting a hadron. It is further argued that f(x) becomes, proportional to νW₂(x) as x → 1. Predictions are then made for a large class of inclusive reactions based on our knowledge of νW₂(x) from electroproduction data. For some of these (such as pp → π^±X), in which the predictions differ markedly from the Regge ones, present experiments distinctly favor ours.     

Spin-dependent parton distributions in polarized deep inelastic lepton nucleon scattering

We analyze the recently measured first moment Г ^p (Q ²) of the structure functiong ₁ ^p (x,Q ²) obtained in deep inelastic scattering of polarized electrons from polarized protons. It is shown that the recent experimental result Г ^p (〈Q ²〉?10 GeV²)? 0.113 implies a polarized strange quark sea whose total polarization Δs(μ²)??0.22 is comparable to Δμ(μ²)?0.74 and Δd(μ²)??0.50 already at a typically hadronic scale μ=0(1 GeV). Most remarkably, the total polarization due to quark distributions Δμ(μ²)+Δd(μ²)+Δs(μ²) practically vanishes which implies that the spin of the proton is carried by the gluons, ΔG(μ²), and/or the angular momentum of the partons. This surprising conjecture can be experimentally tested with heavy quark production in longitudinally polarized lepton-nucleon scattering. In particular the (real) photon-gluon fusion process γg→Q \(\bar Q\) provides a rather unique measure of ΔG(x,Q ²).     

SU(2N f) ⊗O(3) light diquark symmetry and current-induced heavy baryon transition form factors

We study the current-induced bottom baryon to charm baryon transitions in the Heavy Quark Symmetry limit asm _q→∞. Our discussion involvess-wave tos-wave as well ass-wave top-wave transitions. Using a constituent quark model picture for the light diquark system with an underlyingSU(2N _f)?O(3) symmetry and the heavy quark symmetry we arrive at a number of new predictions for the reduced form factors that describe these transitions.     

Solutions of Doubly and Higher Order Iterated Equations

Michael Fisher once studied the solution of the equation f(f(x))=x ²–2. We offer solutions to the general equation f(f(x))=h(x) in the form f(x)=g(ag ^–1(x)) where a is in general a complex number. This leads to solving duplication formulas for g(x). For the case h(x)=x ²–2, the solution is readily found, while the h(x)=x ²+2 case is challenging. The solution to these types of equations can be related to differential equations.     

Simple model for spin-crisis

Starting from the additive quarkSU(6) model and taking into account the pion and kaon (η) emission during the initial stage of evolution (fromq ²～m _quark ² toq ²～1 GeV²) we convert the main fraction of the proton spin into the orbital momentum of the pseudoscalar mesons. The results are in a good agreement with the experimental data. We get ∫g ₁(x)dx=0.152 for proton and +0.007 for the Λ hyperon (i.e. the quarks carry out only about 39% of the Λ spin). In the same model we explain the violation of the Gottfried sum rule ?∫(F ₂ ^p(x)?F ₂ ⁿ(x))dx=0.23 due to the charged meson exchanges at the beginning of the evolution. The Gribov-Lipatov relation between the polarized structure functions in DIS ande ⁺ e ^?-annihilation is discussed. It gives the possibility to study the spin structure of Λ hyperon produced through the decay of the jet originated by a polarized quark ine ⁺ e ^?-annihilation or in DIS.     

AdS-QCD quark–antiquark potential,meson spectrum and tetraquarks

The AdS/QCD correspondence predicts the structure of the quark–antiquark potential in the static limit. We use this piece of information together with the Salpeter equation (Schrödinger equation with relativistic kinematics) and a short range hyperfine splitting potential to determine quark masses and the quark potential parameters from the meson spectrum. The agreement between theory and experimental data is satisfactory, provided one considers only mesons comprising at least one heavy quark. We use the same potential (in the one-gluon-exchange approximation) and these data to estimate the constituent diquark masses. Using these results as input we compute tetraquark masses using a diquark–antidiquark model. The masses of the states X(3872) or Y(3940) are predicted rather accurately. We also compute tetraquark masses with open charm and strangeness. Our result is that tetraquark candidates such as D _s (2317), D _s (2457) or X(2632) can hardly be interpreted as diquark–antidiquark states within the present approach.     

Vehicular traffic through a self-similar sequence of traffic lights

We study the dynamical behavior of vehicular traffic through a sequence of traffic lights positioned self-similarly on a highway, where all traffic lights turn on and off simultaneously with cycle time T_s. The signals are positioned self-similarly by Cantor set. The nonlinear-map model of vehicular traffic controlled by self-similar signals is presented. The vehicle exhibits the complex behavior with varying cycle time. The tour time is much lower such that signals are positioned periodically with the same interval. The arrival time T(x) at position x scales as (T(x)-x)∝x^d_f, where d_f is the fractal dimension of Cantor set. The landscape in the plot of T(x)−x against cycle time T_s shows a self-affine fractal with roughness exponent α=1−d_f.     

Electromagnetic N-Δ transition form factors in a covariant quark-diquark model

The electromagnetic N-Δ transition form factors are calculated in the framework of a formally covariant constituent diquark model. As a spin- $tfrac {3}{2}$ particle the Δ is assumed to be a bound state of a quark and an axial-vector diquark. The wave function is obtained from a diquark-quark Salpeter equation with an instantaneous quark exchange potential. The three transition form factors are calculated for momentum transfers squared from the pseudothreshold (M_Δ ?M _N )² up to ?2 (GeV/c)². The magnetic form factor is in qualitative agreement with experiment. We find very interesting results for the ratios E2/M1 and C2/M1.     

Dual analytic model of generalized parton distributions

A model for generalized parton distributions (GPDs) in the form of ∼(x/g ₀)^{(1−x)ᾶ(t)}, where ᾶ(t) = α(t) − α(0) is the nonlinear part of the Regge trajectory and g ₀ is a parameter, g ₀ > 1, is presented. For linear trajectories, it reduces to earlier proposals. We compare the calculated moments of these GPDs with the experimental data on form factors and find that the effects from the nonlinearity of Regge trajectories are large. By Fourier transforming the obtained GPDs, we access the spatial distribution of protons in the transverse plane. The relation between dual amplitudes with Mandelstam analyticity and composite models in the infinite-momentum frame is discussed, the integration variable in dual models being associated with the quark longitudinal-momentum fraction x in the nucleon. The text was submitted by the authors in English.     

SU (2N f) ⊗ O(3) light diquark symmetry and current-induced heavy baryon transition form factors

We study the current-induced bottom baryon to charm baryon transitions in the Heavy Quark Symmetry limit as m_q → ∞. Our discussion involves s-wave to s-wave as well as s-wave to p-wave transitions. Using a constituent quark model picture for the light diquark system with an underlying SU (2N_f) ? O(3) symmetry and the heavy quark symmetry we arrive at a number of new predictions for the reduced form factors that describe these transitions.     

Period doubling in maps with a maximum of order z

We consider the scaling behaviour in period-doubling systems, exemplified by the one-dimensional map χ_n+1 = 1 − λ|χ_n|^z, which has a maximum of order z (z > 1). The Feigenbaum scaling factors α and δ are studied as functions of z, and more generally the scaling functions 1/σ and ƒ(a). In particular, using the universal functions g(x) and h(x) we establish the inequality δ < α^z, which implies that δ remains finite (≲ 30) in the limit z → ∞.     

Analytical solution of the double-logarithmic integral equation with QCD running coupling

The analytical solution of the double-logarithmic integral equation with QCD running coupling describing small-x behaviour of the non-singlet structure function ? _NS(x,Q ²) has been found for any cut-off parameter μ. Analytical properties of the solution and a position of the right-most singularity in the complex ρ-plane which determines the asymptotics of ? _NS(x,Q ²) at small x have been studied. The asymptotical formula ? _NS(x,Q ²) = C ₁ x ^-λ1{ln^κ1(Q ²/Λ²) —ln^κ1 (μ ²/Λ²) + κ ₁ ln^κ1-1(Q ²/Λ²)[ψ(1) - ψ(λ₁)]} valid if x ? 1 and ln(Q ²/Λ²) ? 1 has been obtained where C ₁, λ₁ are constants, κ ₁ = g/λ₁, λ₁ < g = 8/(33 - 2gh _f), gh _f is a number of active flavours and ψ(ξ) denotes the digamma function.     

Bounds for Kℓ3 decay parameters

The extremum of the integral ∫^∞f(x) ‖F (x)‖² dx is determined for the case when the values taken by the function F (x)¹ at three points are known. The result is applied to the K_?3 problem, the function F (x) being replaced by the form factor f₊(q²)+f₋(q²)q²(m_K²−m_π²) of the divergence of the strangeness changing vector current.     

Effects of nickel doping on structural and optical properties of spinel lithium manganate thin films

Spinel LiNi_xMn_2−xO₄ (x≤0.9) thin films were synthesized by a sol-gel method employing spin-coating. The Ni-doped films were found to maintain cubic structure at low x but to exhibit a phase transition to tetragonal structure for x≥0.6. Such cubic-tetragonal phase transition can be explained in terms of Ni³⁺(d⁷) ions with low-spin (t_2g⁶,e_g¹) configuration occupying the octahedral sites of the compound, thus being subject to the Jahn-Teller effect. By X-ray photoelectron spectroscopy both Ni³⁺ and Ni²⁺ ions were detected where Ni²⁺ is more populated than Ni³⁺. Optical properties of the LiNi_xMn_2−xO₄ films were investigated by spectroscopic ellipsometry in the visible-ultraviolet range. The measured dielectric function spectra mainly consist of broad absorption structures attributed to charge-transfer transitions, O²⁻(2p)→Mn⁴⁺(3d) for 1.9 (t_2g) and 2.8-3.0 eV (e_g) structures and O²⁻(2p)→Mn³⁺(3d) for 2.3 (t_2g) and 3.4-3.6 eV (e_g) structures. Also, sharp absorption structures were observed at about 1.6, 1.7, and 1.9 eV, interpreted as being due to d-d crystal-field transitions within the octahedral Mn³⁺ ion. In terms of these transitions, the evolution of the optical absorption spectrum of LiMn₂O₄ by Ni doping could be explained and the related electronic structure parameters were obtained.     

Phase Transition and Level-Set Percolation for the Gaussian Free Field

We consider level-set percolation for the Gaussian free field on ${\mathbb{Z}^{d}}$ , d ≥ 3, and prove that, as h varies, there is a non-trivial percolation phase transition of the excursion set above level h for all dimensions d ≥ 3. So far, it was known that the corresponding critical level h _*(d) satisfies h _*(d) ≥ 0 for all d ≥ 3 and that h _*(3) is finite, see Bricmont et al. (J Stat Phys 48(5/6):1249–1268, 1987). We prove here that h _*(d) is finite for all d ≥ 3. In fact, we introduce a second critical parameter h _** ≥ h _*, show that h _**(d) is finite for all d ≥ 3, and that the connectivity function of the excursion set above level h has stretched exponential decay for all h > h _**. Finally, we prove that h _* is strictly positive in high dimension. It remains open whether h _* and h _** actually coincide and whether h _* > 0 for all d ≥ 3.     

Asymptotics of Self-similar Solutions to Coagulation Equations with Product Kernel

We consider mass-conserving self-similar solutions for Smoluchowski’s coagulation equation with kernel K(ξ,η)=(ξη) ^λ with λ∈(0,1/2). It is known that such self-similar solutions g(x) satisfy that x ^?1+2λ g(x) is bounded above and below as x→0. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function h(x)=h _λ x ^?1+2λ g(x) in the limit λ→0. It turns out that \(h \sim 1+ C x^{\lambda/2} \cos(\sqrt{\lambda} \log x)\) as x→0. As x becomes larger h develops peaks of height 1/λ that are separated by large regions where h is small. Finally, h converges to zero exponentially fast as x→∞. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE.     

The effect of an external field on an interface,entropic repulsion

We consider the effects of an external potential -h∑f(S _x ) withh>0,f increasing, on the equilibrium state of a system with a Hamiltonian of the form $$H^0 (S) = \sum\limits_{\left\langle {xy} \right\rangle } {\Phi (S_x - S_y )} ,S_x \in R,x \in Z^d ,d \geqslant 3$$ Φ even and convex, e.g.,Φ(t)=1/2t ² andf(t)=signt. This can be thought of as a model of the interactions between a random interface S _x and a “soft” wall. We show that the random surface is (entropically) repelled to infinity for allh>0, i.e., with probability one,S _x ≥K, for anyK ε R.     

Investigation of inclusive production ofK 0 andK * (892)0 mesons inK + A interactions at 11.2 GeV

Inclusive production ofK ⁰ andK ^* (892)⁰ mesons inK ⁺ A-interactions (A=Be, Cu, Pb) at the energy 11.2 GeV has been investigated to study hadronisation of the leading \(\bar s\) -quark; the results are presented. Double differential cross sections d²σ/dx _f dp _t ² were measured in the region of incident particle fragmentation (0.4≦x _f ≦1,p _t ≦0.5 GeV/c). The experimental data obtained were analysed on the basis of the Lund model FRITIOF and a quark-gluon model that takes into account colour screening and hadron formation length effects. The experimental data confirm the picture of hadronisation of the leading \(\bar s\) -quark developed in the latter model.