A borel-weil-bott approach to representations of sl q (2, ℂ)

We use a quite concrete and simple realization of sl _q (2, ) involving finite difference operators. We interpret them as derivations (in the noncommutative sense) on a suitable graded algebra, which gives rise to the noncommutative scheme ¹ II ^1* as the counterpart of the standard ¹ = Sl(2, )/B.     

The geometry of the quantum correction for topological σ-models

The ring (Frobenius algebra) of local observables for topological -models on ¹ with values in the grassmannianG(s, n) is known to be the same as the quotient of the homology ring of the target space by the (inhomogeneous) ideal generated by the so-called quantum correction. While the need for a quantum correction comes from algebraic motivations in field theory, the aim of this paper is to understand its geometric meaning. The simple examples of ^{1 n} models tell us that the quantum correction comes by restriction on the boundary of the moduli spaces which allows to compute intersections on moduli spaces of lower degrees. We will check this point of view for the case of ¹ G(s,n) models, yielding a proof of the algebraic result from physics in terms of the geometry of the -model itself.Work partially supported by National Project 40% Probabilistic and geometrical methods in Mathematical Physics and by CNR-Gruppo Nazionale di Fisica Matematica.     

Diffractive production of ρ-mesons and of ρπ-systems by neutrinos and antineutrinos on protons

Evidence is presented for diffractive production of -mesons and of -systems invp and chargedcurrent interactions. In the (anti-)neutrino energy range 10 GeVE _v <60 gev=" the=" cross=" sections=" for=" diffractive="> and diffractive production are found to be (0.64±0.14 (stat.)±0.08 (syst.))% and (0.28±0.08 (stat.)±0.04 (syst.))% of the charged-current cross section. The diffractive signal is consistent with being entirely due to diffractivea ₁ production. However, the data cannot distinguish between diffractivea ₁ and diffractive nonresonant production. The experimental distributions ofW, Q ²,x _Bj andy _Bj for diffractive and events are consistent with model predictions.     

Discrete Dynamical Systems Associated with the Configuration Space of 8 Points in ℙ<Superscript>3</Superscript>(ℂ)

A 3 dimensional analogue of Sakais theory concerning the relation between rational surfaces and discrete Painlevé equations is studied. For a family of rational varieties obtained by blow-ups at 8 points in general position in ³, we define its symmetry group using the inner product that is associated with the intersection numbers and show that the group is isomorphic to the Weyl group of type E₇⁽¹⁾. By parametrizing the configuration space by means of elliptic curves, the action of the Weyl group and the dynamical system associated with a translation are explicitly described. As a result, it is found that the action of the Weyl group on ³ preserves a one parameter family of quadratic surfaces and that it can therefore be reduced to the action on ¹×¹.     

Noncommutative Geometry and the Regularization Problem of 4D Quantum Field Theory

We give a noncommutative version of the complex projective space ² and show that scalar QFT on this space is free of UV divergencies. The tools necessary to investigate quantum fields on this fuzzy ² are developed and several possibilities to introduce spinors and Dirac operators are discussed.     

Conformational completion of Lorentz symmetric spaces

Every simply connected Lorentz symmetric space of dimensionn3 has a symmetric quotient which can be conformally imbedded in a quadric of the projective space ⁿ⁺¹ (R).     

Photon-deuteron diffractive scattering

One expects a similarity of the energy dependence of the difference _tot(*p)– _tot(*n) for virtual (deep inelastic scatteringQ ²m ²) and real (Q ²=0) photons. Previous analysis of D structure functions with allowence for nuclear shadowing (NS) in the deuteron has led to conclusion that _tot(*p)– _tot(*n)<0>x<0.015. the=" early=" evidence=" from=" the=" real=" photoproduction=" data="> _tot(p)– _tot(n)<0. we=" critically=" reexamine=" determinations=" of=" the="> _tot(p)– _tot(n), using more accurate calculations of NS correction to _tot(D), and discuss a possibility of _tot(n) _tot(p) at moderately high energies.     

Projective quantum spaces

Associated to the standard SU _q (n) R-matrices, we introduce quantum spheresS _q ^2n-1 , projective quantum spaces _q ^n-1 , and quantum Grassmann manifoldsG _k( _q ⁿ ). These algebras are shown to be homogeneous spaces of standard quantum groups and are also quantum principle bundles in the sense of T. Brzeziski and S. Majid.     

The structure of28Si above 10 MeV excitation energy I: gamma-decay modes and radiative widths of levels

The systematics of-decay modes and radiative widths of highly excited states in²⁸Si has been extended by taking-ray spectra on 60 resonances of the²⁷Al(p,) reaction in the range 1097 keVE _p 4492 keV (12643 keVE _x 15915 keV) and on the²⁴Mg(,) resonances atE =3355, 3431, 4003 keV (E _x =12860, 12925, 13 415 keV). The-decay modes of levels in the sub-resonance region (E _x =10–12.5 MeV) were studied with both the²⁷ A1(p, ) reaction and the²⁷ A1(d, n) reaction at E_d=4,5,6 MeV. Information on radiative widths of levels was obtained by measuring the resonance strengthsS =(2I+1) _p / for 52 resonances of the²⁷Al(p, ) reaction with an emphasis on prospective T=1 states.     

AssociateJ/ψ+γ production: a clean probe of gluon densities

Production of strange and charm particles by hadron-proton collisions is analyzed in terms of a fire-ball (FB) model assuming the multiplicity of secondaries of a given massm, to be proportional to the FB mass: n(m)M ^*, the FB kinematics being determined by the Feynman-Yang scaling, as in the case of production. It is found that (m)1/m ² and that, using this property together with the scaling, no-free-parameter fits to currently available data of strange and charm particles frompp and p collisions are satisfactory, as well as for the photoproduction of charm mesonD and charm hyperon _c .     

Analytic fields on Riemann surfaces. II

The properties of analytic fields on a Riemann surface represented by a branch covering of ¹ are investigated in detail. Branch points are shown to correspond to the vertex operators with simple conformal properties. As applications we compute determinants of operators forZ _n -symmetric surfaces and obtain various representations for the two-loop measure in the bosonic string theory together with various identities for theta-functions of hyperelliptic surfaces. We also present an integral representation for the quantum part of the twist field correlation functions, which describe propagation of the string on the orbifold background. We also calculate the quantum part of the structure constants of the twist-field operator algebra, generalizing the results of Dixon, Friedan, Martinec, and Shenker.     

Soft photons in hadron-hadron collisions: synchrotron radiation from the QCD vacuum?

We discuss the production of soft photons in high energy hadron-hadron collisions. We present a model where quarks and antiquarks in the hadrons emit synchrotron light when being deflected by the chromomagnetic fields of the QCD vacuum, which we assume to have a nonperturbative structure. This gives a source of prompt soft photons with frequencies <~300 mev=" in=" the=" c.m.=" system=" of=" the=" collision=" in=" addition=" to=" hadronic=" bremsstrahlung.=" in=" comparing=" the=" frequency=" spectrum=" and=" rate=" of=">synchrotron photons to experimental results we find some supporting evidence for their existence. We make an exclusive-inclusive connection argument to deduce from the synchrotron effect a behaviour of the neutron electric formfactorG _E ⁿ (G ²) proportional to (Q ²)^1/6 forQ ²20 fm^–2. We find this to be consistent with available data. In our view, soft photon production in high energy hadron-hadron and lepton-hadron collisions as well as the behaviour of electromagnetic hadron formafactors for lowQ ² are thus sensitive probles of the nonperturbative structure of the QCD vacuum.     

Experimental study of hard photon radiation processes at HERA

We present an experimental study of theepe+p andepe+X processes using data recorded by the H1 detector in 1993 at the electron-proton collider HERA. These processes are employed to measure the luminosity with an accuracy of 4.5 %. A subsample of theepe+X events in which the hard photon is detected at angles 0.45 mrad with respect to the incident electron direction is used to verify experimentally the size of radiative corrections to theepeX inclusive cross section and to investigate the structure of the proton in theQ ² domain down to 2 GeV², lower than previously attained at HERA.Supported by the Bundesministerium für Forschung und Technologie, FRG under contract numbers 6AC17P, 6AC47P, 6DO57I, 6HH17P, 6HH27I, 6HD17I, 6HD27I, 6KI17P, 6MP17I, and 6WT87P     

Search forN ϕ (1960) baryon

In the experiments at the SPHINX facility in the 70 GeV proton beam of the IHEP accelerator the diffractive production reactionsp+N[(1385)⁰ K ⁺] +N andp+N[(1385)⁰ K ⁺]+N+ (neutral particles) were studied. In the effective mass spectra of the [(1385)⁰ K ⁺] system in these processes there were no signals from the anomalously narrow baryon stateN (1960) which had been observed earlier in the measurement at the BIS-2 setup.SPHINX Collaboration (IHEP-ITEP)     

Study of theπ + π − γ system centrally produced in the reactionpp→p f (π + π − γ)p s at 300 GeV/c

The reactionppp _f ( ^{+ –} )p _s , where the ^{+ –} system is centrally produced, has been studied at 300 GeV/c. The ^{+ –} mass spectrum shows evidence for a ⁰ decay mode of the (958) andf ₁ (1285). The branching ratio (f ₁(1285) ^{+ +})/(f ₁(1285) ⁰ ) is found to be 5.0±0.7. No evidence is found for a ⁰(770) decay mode of theE/f ₁ (1420) for which an upper limit BR (E/f ₁(1420) ⁰ )<0.08 at=" 95%=" cl=" is=">     

Computation of quantum fluctuations around multi-instanton fields from exact Green's functions: TheCP n−1 Case

We calculate exactly the contribution of instanton fields to the partition function of ^n–1 models in two dimensions. Forn=2, the pure instanton gas is infrared finite, infinitely dense and generates a mass dynamically. Forn3, the gas corresponds to a system with complicatedn-body interactions, whose properties are yet to be explored.     

LargeP T P−P collisions to probe the gluonic and sea spin distribution in the proton

We parametrise the polarised gluon and sea distribution functions incorporating the interpretation of the EMC experiment that, due to the axial anomaly the observed quark contribution to proton spin at Q ²>=10.7 GeV². Typical processes to isolate the gluonic and sea content of the proton studied here are the largeP _T direct photon production processes (a) using single polarized protonPPX and (b) polarized beam and target protonPPX. In both the above process the dominant contribution comes from the Compton subprocess and so can be used as a clean probe of the gluonic content of the proton. LargeP _T muon pair production PP(^+–)X are also studied and we find that the annihilation subprocess dominates, but not much larger than the Compton subprocess and so may not be a clean probe of the sea content of the proton. The effect of two loop corrections to the parametrisation and asymmetries are also considered, and are found to be negligible.     

The decays of theρ′1 andω′1 mesons

New measurements of the reactione ⁺ e ^– confirm previous evidence for the decay₁ and provide a strong constraint on the mass of the₁. The results from a detailed analysis of these data are compared with those from a corresponding analysis of new data on the reactione ⁺ e ^–. It is shown that in accord with expectation. This identification of a strong₁ decay supports a previous claim that the₁ and theC(1480), observed in the channel, cannot be different manifestations of the same particle.