Dual Unitarization Scheme Research Articles

8702269 Process for simultaneous extraction of SO〉2〈 and NO〉x〈 contained in waste gases

The splitting of trajectories with non-vacuum quantum numbers is discussed within the dual unitarisation scheme. The estimated difference in intercepts between vector-tensor trajectories of opposite signatures, such as ϱ − A2 and K∗ − K∗∗, agrees both in sign and magnitude with that deduced from phenomenological analyses.

Jet variable distributions in antiproton- proton interactions

The event shape in momentum space of pp interactions at 22.4 GeV/c has been investigated by means of the variables thrust, triplicity and dithrust. Events with clear multijet shape corresponding to the dual topological unitarization scheme predictions are not observed. The events have mainly collinear shape. A fast algorithm for the calculation of the event shape variables is proposed.

LargeN behaviour of perturbative QCD coupling

A correspondence between perturbative QCD in an axial gauge and dual topological unitarization (DTU) scheme is expressed by linking the QCD scale Λ toN, the number of flavors or colors supposed to be large through a relation which involves a typical hadronic scale.

Charge distributions in hadronic collisions

The distribution of charge versus rapidity is examined in the framework of available parton models for multiparticle production in hadron-hadron collisions. Fragmentation models with a twochain Pomeron contribution (based on the dual topological unitarization scheme) are shown to describe rather well the recently measured data on charge distributions in high energypp and πp collisions (140 GeV/c≦pLAB≦360 GeV/c). Carefully measured charge distributions at still higher energies which will be accessible in the near future offer a possibility of distinguishing between some of the current theoretical approaches.

Dual model foru, d, s andc quark fragmentation functions

In the dual topological unitarization scheme, we derive a model for theu, d, ands quark fragmentation into mesons by considering the parton interpretation of planar one particle inclusive cross sections. A good agreement with experiment is obtained. Relying on these results, we generalize the model in order to include the charm fragmentation functions into any meson and again get a nice agreement with data.

Parton Description of Softp¯pAnnihilation

A parton description of soft, high-energy $\overline{p}p$ annihilation is presented in a three-chain model based on the dual topological unitarization scheme. With this model, full, quantitative, zero-parameter predictions are made for inclusive single-particle rapidity distributions and their energy dependence, which are testable in forthcoming $\overline{p}p$ experiments.

Perturbative and non-perturbative two component model of deep inelastic scattering

We propose a two-component model for describing deep inelastic scattering, based on nonperturbative and perturbative mechanisms. The nonperturbative dynamics obey the usualS-matrix constraints, as realized by the Dual Topological Unitarization Scheme, whereas the perturbative component stems from the underlying field theory. However, these two components arenot independent.

Experimental verification of the dual unitarization scheme

The connection between particle production in antiproton-proton annihilation and non-diffractive proton-proton processes is discussed in the framework of the dual unitarization scheme. We calculate relative multiplicity moments for antiproton-proton annihilation using the moments of non-diffractive proton-proton interactions and find good agreement with experimental annihilation data.

Dual unitarization scheme with several trajectories

Consequences of bootstrap with several input Regge trajectories are investigated. We find that in a general (without the duality-diagrams constraints) treatment of bootstrap, consistency requires the intercept of the output Pomeron pole in the one-dimensional case to be larger than one: ${\ensuremath{\alpha}}_{P}(0)>1$, a situation reminiscent of the one in Reggeon field theory. Symmetry breakings of the Pomeron couplings are discussed. These couplings coincide with those of the $f$-dominated Pomeron model of Carlitz, Green, and Zee (CGZ). The case when in the unitarity loops all possible trajectories are exchanged is also considered. Predictions of the dual unitary model for the slopes of differential cross sections for diffractive scattering are made which differ from those of the CGZ model. A comparison with the experimentally available data is performed.

Flavour symmetry breaking and production processes in dual unitarisation

The effects of SU(3) and SU(4) symmetry breaking upon the dual unitarisation scheme are considered, at the planar and cylinder levels. When the effect of cluster threshold masses is considered, it becomes difficult to explain the observed rise in the proton-proton cross section in terms of pomeron flavouring. Estimates are obtained of strange and of charmed production cross sections. The associated production of the phi and psi mesons is also considered.

Flavor symmetry breaking in DTU

The implications of the breaking of SU (N) flavor symmetry are studied at the planar and cylinder levels of the Dual Topological Unitarization scheme. It is shown that the ρ intercept is constrained to lie between 0.51 and 0.54, and that SU (4) symmetry is necessarily more strongly broken that SU (3). The matrix structure of the cylinder bootstrap equations is shown to suppress many of the problems of the “cylinder extinction of the planar poles”, and to lead to a sensible singularity spectrum.

S-channel discontinuities of the torus insertion in the dual unitarisation scheme

The refined analysis of the s-channel discontinuities of the torus insertion in the topological expansion is performed. Assuming the dependence on reggeon masses of the fixed-pole residue similar to that given by the Veneziano model we obtain almost exact cancellations of the discontinuities which in the one-dimensional approximation were argued to be responsible for the exchange degeneracy breaking between ϱ and A 2 trajectories. Implications on different f-IP schemes are discussed.

Baryons in dual unitarization and dynamical thresholds

Baryon exchange and baryon resonance production is introduced in the dual unitarisation scheme. The dynamical threshold for the production of meson and baryon resonances is incorporated. It is shown that the intercepts of the ω and the f, which are generated by baryons, are suppressed by the above dynamical threshold effects to α ω(0) ⋍ 0 and α f(0) < 0. The pomeron is shifted slightly upwards by baryon production. An upper limit is determined for the ratio of the crossed and uncrossed produced baryon lines. The breaking of the Freund-Rosner-Walz rule is discussed.

Baryon and Baryonium States with String-Junctions in the Dual Unitarization Scheme

\'Ve consider a baryon and a family of baryonium states m the dual unitarization scheme taking account of topological structures; a baryon has a Y shaped structure with a string­ junction at the center and baryonium states denoted by iJ,, M, and }IJ, have a pair of junction and antijunction. Coupled channel bootstrap equations are given for the baryonic and meeoonic reggeons and for the pomeron. The breaking of the exchange degeneracy between the iJ and /3 trajectories of baryons is given through a non-planar diagram with a twisted meson bridge between two membranes swept by strings; we have a.;,-aNp~O.l. The intercepts of the family of baryonium states are that aM.(±)<aM,(±)<a.,,,( +)<aM,(-), where (±) denote charge conjugation parity, and the triple-reggeon couplings iJnNI1\Il are shown to be g' (iJ,<±l 1\IIM) <g'(fVI,<±l N£1\4.) <o' (.A/f,<+J },11\ll) <o' (fVJ,<-l j'vJ.f'vf), where lvf denotes an ordinary natural parity meson: The ratio g (iVJ, <-l 1\111\11) : (} (lVJ, H BE) =1: 2 is encouraging to the idea that the difficulty of the 'o extinction can be remedied by the existence of the ]\1, (-).

On the Regge-cut cancellation in planar amplitudes of the dual unitarisation scheme

The problem of the Regge-cut cancellation in equations for planar reggeons is considered by using the j-plane methods in treating the underlying integral equations. It is shown that the kernel should have the zero which cancels the reggeon-loop singularity in order to eliminate the cut in the reggeon-reggeon scattering amplitude besides amplitudes involving external particles. This zero (nonsense zero) implies that the finite size cluster is incompatible with the cut cancellation. Two alternative no-double-counting conditions of the “reggeon bootstrap” (the Oxford-Rutherford model and the Finkelstein-Koplik model) are examined and it is found that the Regge cut cannot be cancelled because of the finite size of the cluster. Substantial modifications of the “reggeon bootstrap” model may be necessary if the Regge cut is to be cancelled.

Unnatural Parity Mesons in the Dual Unitarization Scheme

The spectrum of parity mesons is studied in the dual unitarization scheme extended to a two-channel problem. It is shown that the pion trajectory lies higher than the B meson trajectory at t=O and that the cylinder coupling of parity has the negative sign, i.e., the unnatural parity pomeron has odd charge conjugation parity. It is also shown that there are consistent solutions satisfying the bootstrap eq nations for both un­ natural and natural parity reggeons. )~?) In this paper we discuss parity reggeons in the dual unitarization scheme extended to a multi-channel problem. Our as­ sumptions are as follows: (1) Three-meson (reggeon) vertices are types of NNN and of UUN, where N denotes vector ( V) and tensor (T) mesons (reggeons), while U denotes pseudoscalar (P) and axial vector (B, JPc = 1 +-) mesons (reg­ geons). The coupling constant of the NNN(UUN) vertex is gN(gu). (2) 1>aN -au> 1/2, where the exchange degenerate input trajectories of N and U are denoted by aN and au. (3) The ratio of the produced N line with twist to that without twist is given by eN and that of the U case by eu. The mass spectrum of the pseudoscalar mesons is strongly deviated from that of the ideal nonet owing to too light pion and probably kaon masses. On the other hand, the mass of the B meson is close to those of the A 2 and f mesons, that is, the difference between the B trajectory and the A 2 is approximately unity for t>l.5 GeV 2 • This means that the SU(6) mass spectrum of the 3P 2 and 1P 1 states holds in the first approximation, though the masses of other SU(3) partners of the B meson are not yet known. Therefore it is intriguing to consider some dynamical mechanism that can shift the pseudoscalar meson trajectories upwards from the expected SU(6) spectrum and then break the exchange degeneracy be­ tween P and B. Here we mean by the SU(6) spectrum aN-au=l. In this paper we shall search such a mechanism in the dual unitarization scheme. We shall often use the SU(6) spectrum to get explicit expressions, because the use

Reggeon, pomeron and annihilation production processes in the dual unitarization scheme

In the framework of the dual unitarization scheme we discuss the connection between particle production in processes dominated by reggeon, pomeron and annihilation diagrams and suggest critical tests of the scheme. The simple relation for average multiplicities n R = 1 2 n P = 1 3 n A and other relations for inclusive cross sections and higher moments of the particle distribution are shown to be in reasonable agreement with data.

Dynamical thresholds in the dual unitarization scheme

Mass differences of particles produced in high-energy collisions lead to dynamical thresholds in unitarity integrals for two-body scattering. These thresholds are understood as being responsible for the rapid energy dependence of exotic-exchange and Zweig-rule-violating amplitudes. Processes involving twisted intermediate states, and consequently cancellations, in the unitarity sum are expected to be particularly sensitive to these thresholds. In the J-plane, the corresponding amplitudes are characterized by a weak leading singularity accompanied by strong non-leading effective singularities associated with threshold effects. The requirement that states of even and odd C-conjugation be produced with equal strength in order to keep exotic amplitudes small at high energies can also be relaxed as a consequence of the said threshold phenomena. The SU(3) structure of exotic states generated by multiperipheral duality diagrams is also discussed.

Baryon exchange effects in dual unitarisation

The effects of baryon exchanges in the renormalisation of Regge trajectories are studied in the dual unitarisation scheme. The main results are that: (i) the pomeron is boosted above α = 1, giving rising total cross sections beyond baryon-antibaryon thresholds, and (ii) the ω trajectory remains approximately at α = 0.5 but acquires a sizeable admixture of the exotic q qqq state, which enhances its coupling to baryons. There are in addition a number of other interesting predictions.

S-channel discontinuities of reggeon diagrams with planar vertices

The mutual relations between s-channel discontinuities of reggeon diagrams with planar triple-Regge vertices are discussed. It is shown that, in general, contributions coming from different cuttings are not simply related to each other as certain vertices acquire non-trivial phase factors depending on the nature of the cutting. For diagrams with only triple-Regge vertices this phase may be related to the triple-Regge phase. The complete four-reggeon vertices are not known in general. An approximation is considered which amounts to preserving only the absorptive part of triple- or four-reggeon amplitudes in certain parts of the diagrams. This approximation turns out to be equivalent to a simple absorbed multiperipheral model. The problem of exchange degeneracy breaking within the dual unitarisation Scheme is briefly discussed as an example.