Proton elastic form factor: The JLab data

The ratio of the electric and magnetic proton form factors, G_Ep/G_Mp, has been obtained in two Hall A experiments, from measurements of the longitudinal and transverse polarization of the recoil proton, P_L and P_T, respectively, in the elastic scattering of polarized electrons, . Together these experiments cover the Q² range 0.5 to 5.6 GeV². A new experiment is currently being prepared, to extend the Q² range to 9 GeV² in Hall C.Received: 1 November 2002, Published online: 15 July 2003PACS: 13.40.Gp Specific reactions and phenomenology: Electromagnetic form factors - 14.20.Dh Properties of specific particles: Protons and neutrons - 24.70.+s Nuclear reactions: Polarization phenomena in reactions     

Dissociation of virtual photons in events with a leading proton at HERA

The ZEUS detector has been used to study dissociation of virtual photons in events with a leading proton, , in e ⁺ p collisions at HERA. The data cover photon virtualities in two ranges, 0.03 < Q ² < 0.60 GeV² and 2 < Q ² < 100 GeV², with M _X > 1.5 GeV, where M _X is the mass of the hadronic final state, X. Events were required to have a leading proton, detected in the ZEUS leading proton spectrometer, carrying at least 90% of the incoming proton energy. The cross section is presented as a function of t, the squared four-momentum transfer at the proton vertex, , the azimuthal angle between the positron scattering plane and the proton scattering plane, and Q ². The data are presented in terms of the diffractive structure function, . A next-to-leading-order QCD fit to the higher-Q ² data set and to previously published diffractive charm production data is presented.Received: 10 August 2004, Revised: 4 October 2004, Published online: 9 November 2004     

Polarized leptoproduction and dynamically generated spin-dependent parton distributions

The first moment of the polarized parton distributions of the proton is evaluated dynamically using the assumption that at some low resolution scale the proton consists of valence quarks only. The spin carried by gluons, ΔG, at the EMC resolution scaleQ ₀ ² =10 GeV² ispredicted to be ΔG/s _p ?5 withs _p=1/2 denoting the spin of the proton. This result furthermoreexplains the dynamical origin of the recent EMC measurement of the first moment of the polarized structure functiong ₁ ^P (x, Q ²).     

Double-spin asymmetries in electron-nucleon scattering in Halls B and C at JLab

Three experiments at JLab have measured the double polarization asymmetries ) in the nucleon resonance region, using polarized electron beams incident on polarized proton and deuteron targets. The analysis for the first experiment, eg1a in Hall B, is nearly finished and preliminary values of the spin structure function g₁(x, Q²) and the first moment (x) have been extracted. The other two experiments, one in Hall B and one in Hall C, are still analysing data. Some results are presented.Received: 1 November 2002, Published online: 15 July 2003PACS: 24.70.+s Polarization phenomena in reactions     

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     

Higher order differential lift equations over manifolds

LetM be a differentiable manifold modeled on a Banach space overK=R or C. LetT ^k(M) be thekth iterated tangential extension ofM, and letk ^M be thekth Bowman (=restricted tangential) extension ofM. It is shown that there is an embedding ϕ_k:k ^{→T k}(M), and that such embeddings constitute a natural transformation of functors. LetQ be a subset/submanifold inT ^k(M), and letV:Q→T(Q) be a differentiable vector field. CallV k-suitable if everyK-curveg inQ satisfyingg′=V° g has the formg=f ^[k], wheref ^[k] denotes thekth iterated differential lift of aK-curvef inM. It is shown thatV isk-suitable if and only if: (a) , where is a subset/submanifold ink ^M, and (b) , where isk-suitable relative to restricted tangentialK-curve liftsf ^(k). Interpretive consequences for motion problems are discussed.     

P T andQ 2 dependence of multijet production in γγ* collisions

In the context of a measurement recently performed by the PLUTO Collaboration at PETRA, we have computed the contribution of 2-jet, 3-jet and 4-jet production processes (each involving 2 large-p _T jets) in γγ^* collisions to the differential cross sectiondσ/(dp _T dQ ²), whereQ ² is the γ^*'s four momentum squared. It results that the total correction to the 2-jet contribution \(\left( {\gamma \gamma ^ * \to q\bar q} \right)\) , obtained forp _T andQ ² values located in the range 2 GeV<p _T <6 GeV and 0.1 GeV²<Q ²<12 GeV² varies rather slowly as a function of those two parameters; it ranges between 30% and 70%. The specific contribution of the higher twist term involving the process \(\gamma \gamma ^ * \to Mq\bar q\) appears to be insignificant. The discrepancy observed between experiment and theory atQ ²?0.3 GeV² andp _T ?2-3.5 GeV is not explained by our results.     

New short-range electromagnetic current in the deuteron

A new model for short-range isoscalar current in the deuteron and NN system is developed and tested on a variety of isoscalar magnetic observables such as the deuteron magnetic moment, magnetic form factor, and the circular polarization of photons at radiative capture at thermal neutron energies. The model for electromagnetic two-nucleon current proposed in the paper is based on generation of an intermediate dibaryon in the short-range NN interaction. This intermediate dibaryon, in turn, is treated within the new model for intermediate and short-range NN interaction recently proposed by the present authors. The transition current model developed here satisfies the current conservation relation by the construction. Our calculations have demonstrated that the new current model, using only one parameter (with a clear physical meaning), is able to describe, in very good agreement with the experimental data, three basic deuteron observables of magnetic type, viz., the magnetic moment, the photon circular polarization in the process, and the structure function B(Q ²) up to Q ² ≃ 60 fm⁻². The text was submitted by the authors in English.     

Quark-hadron duality and Q<Superscript>2</Superscript> evolution of the GDH integral in the HERMES experiment

First results on quark-hadron duality in the spin sector from the HERMES experiment are reported in the range GeV² and GeV². A complete set of measurements of the generalised GDH integrals for the deuteron, proton and neutron is also shown in the same Q² range and in the full W² range.Received: 1 November 2002, Published online: 15 July 2003PACS: 13.60.Hb Total and inclusive cross-sections (including deep-inelastic processes) - 12.38.Qk Experimental tests - 13.88.+e Polarization in interactions and scattering - 25.20.Dc Photon absorption and scatteringA. Fantoni: On behalf of the HERMES Collaboration     

Morse and Melnikov functions for NLS Pde's

The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat linear operator , is developed in sufficient detail for later use in studies of perturbations of the NLS equation. Counting lemmas for the non-selfadjoint operator , are established which control its spectrum and show that all of its eccentricities are finite in number and must reside within a finite discD in the complex eigenvalue plane. The radius of the discD is controlled by theH ¹ norm of the potential . For this integrable NLS Hamiltonian system, unstable tori are identified, and Backlund transformations are then used to construct global representations of their stable and unstable manifolds-whiskered tori for the NLS pde.The Floquet discriminant is used to introduce a natural sequence of NLS constants of motion, [ , where _c ^j denotes thej ^th critical point of the Floquet discriminant ()]. A Taylor series expansion of the constants , with explicit representations of the first and second variations, is then used to study neighborhoods of the whiskered tori. In particular, critical tori with hyperbolic structure are identified through the first and second variations of , which themselves are expressed in terms of quadratic products of eigenfunctions of . The second variation permits identification, within the disc D, of important bifurcations in the spectral configurations of the operator . The constant , as the height of the Floquet discriminant over the critical point _c ^j , admits a natural interpretation as a Morse function for NLS isospectral level sets. This Morse interpretation is studied in some detail. It is valid globally for the infinite tail, , which is associated with critical points outside the discD. Within this disc, the interpretation is only valid locally, with the same obstruction to its global validity as to a global ordering of the spectrum. Nevertheless, this local Morse theory, together with the Backlund representations of the whiskered tori, produces extremely clear pictures of the stratification of NLS invariant sets near these whiskered tori-pictures which are useful in the study of perturbations of NLS. Finally, a natural connection is noted between the constants of the integrable theory and Melnikov functions for the theory of perturbations of the NLS equation. This connection generates a simple, but general, representations of the Melnikov functions.Funded in part by AFOSR-90-0161 and by NSF DMS 8922717 A01     

Diffractive deep-inelastic scattering with a leading proton at HERA

The cross section for the diffractive deep-inelastic scattering process ep→eXp is measured, with the leading final state proton detected in the H1 Forward Proton Spectrometer. The data analysed cover the range x_IP<0.1 in fractional proton longitudinal momentum loss, 0.08<|t|<0.5 GeV^-2 in squared four-momentum transfer at the proton vertex, 2<Q²<50 GeV² in photon virtuality and 0.004<β=x/x_IP<1, where x is the Bjorken scaling variable. For , the differential cross section has a dependence of approximately dσ/dt∝e^6t, independently of x_IP, β and Q² within uncertainties. The cross section is also measured triple differentially in x_IP, β and Q². The x_IP dependence is interpreted in terms of an effective pomeron trajectory with intercept α_IP(0)=1.114±0.018(stat.)±0.012(syst.)^+0.040 _-0.020(model) and a sub-leading exchange. The data are in good agreement with an H1 measurement for which the event selection is based on a large gap in the rapidity distribution of the final state hadrons, after accounting for proton dissociation contributions in the latter. Within uncertainties, the dependence of the cross section on x and Q² can thus be factorised from the dependences on all studied variables which characterise the proton vertex, for both the pomeron and the sub-leading exchange.     

Dynamics of low-energy nuclear forces for electromagnetic and weak reactions with the deuteron in the Nambu-Jona-Lasinio model of light nuclei

A dynamics of low-energy nuclear forces is investigated for low-energy electromagnetic and weak nuclear reactions with the deuteron in the Nambu-Jona-Lasinio model of light nuclei by example of the neutron-proton radiative capture (M1-capture) n + p → D + γ, the photomagnetic disintegration of the deuteron γ + D → n + p and weak reactions of astrophysical interest. These are the solar proton burning p + p → D + e⁺ + ν _e, the pep-process p + e⁻ + p → D + ν _e and the neutrino and antineutrino disintegration of the deuteron caused by charged ν _e + D → e⁻ + p + p, + D → e⁺ + n + n and neutral ν _e() + D → ν _e() + n + p weak currents.     

Measurement of the photon structure functionF2γ in the reactione+e?→e+e?+hadrons at LEP

We present measurements of the hadronic photon structure functionF ₂ (x), in twoQ ² ranges with mean values of 5.9 GeV² and 14.7 GeV². The data were taken by the OPAL experiment at LEP, with close to theZ ⁰ mass and correspond to an integratede ⁺ e ^– luminosity of 44.8 pb^–1. In the context of a QCD-based model we find the quark transverse momentum cutoff separating the vector meson dominance (VMD) and perturbative QCD regions to be 0.27±0.10 GeV. We confirm that there is a significant pointlike component of the photon when the probe photon hasQ ²>4 GeV². Our measurements extend to lower values ofx than any previous experiment, and no increase ofF ₂ (x) is observed.     

$\mbox{Log}(1/x)$ gluon distribution and structure functionsin the loop-loop correlation model

We consider the interaction of the partonic fluctuation of a scalar photon with an external color field to calculate the leading and next-to-leading order gluon distribution of the proton following the work done by Dosch-Hebecker-Metz-Pirner. We relate these gluon distributions to the short and long distance behavior of the cross section of an adjoint dipole scattering off a proton. The leading order result is a constant, while the next-to-leading order result shows a enhancement at small x. To get numerical results for the gluon distributions at the initial scale Q²₀ = 1.8 GeV², we compute the adjoint dipole-proton cross section in the loop-loop correlation model. Quark distributions at the same initial scale are parameterized according to Regge theory. We evolve quark and gluon distributions to higher Q² values using the DGLAP equation and compute charm and proton structure functions in the small-x region for different Q² values.Received: 13 September 2003, Revised: 22 November 2003, Published online: 15 January 2003     

Exact monopole solutions in gauge theories for an arbitrary semisimple compact group

We construct an exact n-parametric monopole and dyon solutions for an arbitrary compact gauge group G of rank n by using the symmetry between cylindrically symmetric instanton equations in Euclidean space R ₄ and monopole equations in Minkowski space R _3,1 (with Higgs scalar field in adjoint representation). The solutions are spherically symmetric with respect to the total momentum operator represents the minimal embedding of SU(2) in G. Explicit expressions for the monopole magnetic charge and mass matrices are obtained. The remarkable aspect of our results is the existence of discrete series of the monopole solutions, which are labelled by n quantum numbers and degenerated in the latter ones at a fixed monopole mass matrix.     

Possible method for measuring the proton form factors in processes with and without proton spin flip

The ratio of the squares of the electric and magnetic proton form factors is shown to be proportional to the ratio of the cross sections for the elastic scattering of an unpolarized electron on a partially polarized proton with and without proton spin flip. The initial proton at rest should be polarized along the direction of the motion of the final proton. Similar results are valid for both radiative ep scattering and the photoproduction of pairs on a proton in the Bethe-Heitler kinematics. When the initial proton is fully polarized in the direction of the motion of the final proton, the cross section for the ep → ep process, as well as for the ep → epγ and γp → $ e\bar ep $ e\bar ep processes, without (with) proton spin flip is expressed only in terms of the square of the electric (magnetic) proton form factor. Such an experiment on the measurement of the cross sections without and with proton spin flip would make it possible to acquire new independent data on the behavior of G _E ²(Q ²) and G _M ²(Q ²), which are necessary for resolving the contradictions appearing after the experiment of the JLab collaboration on the measurement of the proton form factors with the method of polarization transfer from the initial electron to the final proton.     

The proton form factor measurements at Jefferson Lab, past and future

Use of the double-polarization technique to obtain the elastic nucleon form factors has resulted in a dramatic improvement of the quality of two of the four nucleon electromagnetic form factors, G _Ep and G _En . It has also changed our understanding of the proton structure, having resulted in a distinctly different Q ²-dependence for both G _Ep and G _Mp , contradicting the prevailing wisdom of the 1990’s based on cross section measurements, namely that G _Ep and G _Mp obey a “scaling” relation μG _Ep ～ G _Mp . A related consequence of the faster decrease of G _Ep revealed by the Jefferson Lab (JLab) polarization results was the disappearance of the early scaling F ₂/F ₁ ～ 1/Q ² predicted by perturbative QCD. In three experiments, GEp(1), GEp(2) and GEp(3), in Halls A and C at JLab, the ratio of the proton’s electromagnetic elastic form factors, G _Ep /G _Mp , was measured up to four momentum transfer Q ² of 8.5 GeV² with high precision, using the recoil polarization technique. The initial discovery that the proton form factor ratio measured in these three experiments decreases approximately linearly with four-momentum transfer, Q ², for values above ～ 1 GeV², was modified by the GEp(3) results, which suggests a slowing down of this decrease. There is an approved experiment, GEp(5), to continue these measurements to 15 GeV². A dedicated experimental setup, the super bigbite spectrometer (SBS), will be built for this purpose. It will be equipped with a new focal plane polarimeter to measure the polarization of the recoil protons. In this presentation, I will review the status of the proton elastic electromagnetic form factors, mention succinctly a number of theoretical approaches to describe results and show some features required for the future GEp(5) experiment.     

Links between neutrino oscillations,leptogenesis, and proton decay within supersymmetric grand unification

Evidence in favor of supersymmetric grand unification including that based on the observed family multiplet-structure, gauge coupling unification, neutrino oscillations, baryogenesis, and certain intriguing features of quark-lepton masses and mixings is noted. It is argued that attempts to understand (a) the tiny neutrino masses (especially Δm ²(v ₂ – v₃)), (b) the baryon asymmetry of the Universe (which seems to need leptogenesis), and (c) the observed features of fermion masses such as the ratiom _b/m_τ, the smallness ofV _cb and the maximality of seem to select out the route to higher unification based on an effective string-unifiedG(224) =SU(2)_L ×SU(2)_R ×SU(2)^c orSO(10)-symmetry that should be operative in 4D, as opposed to other alternatives. A predictiveSO(10)/G(224)-framework possessing supersymmetry is presented that successfully describes the masses and mixings of all fermions including neutrinos. It also accounts for the observed baryon asymmetry of the Universe by utilizing the process of leptogenesis, which is natural to this framework. It is argued that a conservative upper limit on the proton lifetime within thisSO(10)/G(224)-framework, which is so far most successful, is given by x 10³⁴ years. This in turn strongly suggests that an improvement in the current sensitivity by a factor of five to ten (compared to SuperK) ought to reveal proton decay. Implications of this prediction for the next-generation nucleon decay and neutrino-detector are noted.