Constituent Interchange Model Research Articles

Phenomenology of high-momentum-transfer elastic processes

An analysis is carried out to extract the leading effective trajectories and residues in $\mathrm{pp}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}p$ elastic scattering. The results are compared with the predictions of the constituent-interchange model and the logarithmic dual model, which are shown to be the only two types of theory capable of providing a uniform link between backward and forward Regge regions and the fixed-angle region. The hypothesis of a smooth connection between forward and backward Regge regions puts strong contraints on a priori unrelated trajectories and residues. The possibility of a connection between the two models is discussed. As expected from interchange theory the extracted ${\ensuremath{\pi}}^{\ensuremath{-}}p$ trajectory and residue behave quite differently than those for $\mathrm{pp}$. The dual model seems to give the best overall description of the $\mathrm{pp}$ trajectory and residue functions while the $\ensuremath{\pi}p$ results agree completely with the interchange predictions. The two model fits to $\mathrm{pp}$ elastic scattering at moderate energies (12-24 GeV) are used to extract an expected Pomeron term. The shape of the extracted diffractive contribution is strikingly similar to the recent CERN ISR differential cross sections which exhibit a dip at $t = \ensuremath{-}1.4$ ${\mathrm{GeV}}^{2}$ and a slow falloff in the large-$t$ region.

Forward inclusive production spectrum ofKS,Λ0,Λ¯0, andnin the collision of 200-GeV/cπ−,K−,p¯, andpon Be

We have measured the forward production spectra of various neutral particles produced by ..pi../sup -/, K/sup -/, p-bar, and p at 200 GeV/c, and by ..pi../sup -/ at 290 GeV/c incident on a Be target. The salient features of these measurements are (1) copious production of K/sup 0//sub S/ at large Feynman x/sub L/ for incident ..pi../sup -/ and K/sup -/, (2) production of roughly equal fluxes of ..lambda../sup 0/ and ..lambda..-bar/sup 0/ for incident ..pi../sup -/, and (3) close similarity of the following spectra: ..pi../sup -/ ..-->.. n and K/sup -/ ..-->.. ..lambda../sup 0/; ..pi../sup -/ ..-->.. ..lambda../sup 0/, ..pi../sup -/ ..-->.. ..lambda..-bar/sup 0/; and p ..-->.. K/sup 0//sub S/; ..pi../sup 0/- ..-->.. K/sub s//sup 0/ and p ..-->.. ..lambda../sup 0/. The overall features of the various distributions seem to agree with the ideas of dimensional counting presented in the constituent-interchange model of quark collisions. Results are presented in terms of the invariant cross section Ed/sup 3/sigma (x/sub L/, P/sub perpendicular/ = 0)/dp/sup 3/ per Be nucleus for each inclusive reaction.

Jet structure ine+e−annihilation as a test of quantum chromodynamics and the quark-confining string

We examine the jet structure in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation from two processes: (a) the bremsstrahlung of a hard gluon and (b) the emission of a meson at wide angle via the constituent-interchange model (CIM). At center-of-mass energies from 12 to 25 GeV, both processes, if present, are found to broaden the sharp transverse-momentum damping of jets observed at SPEAR. At lower energies and large transverse momentum we find that the CIM process prevails. But by center-of-mass energies greater than 30 GeV the gluonic process should be dominant. We also examine the jet structure generated by the decay of a bound state of new heavy quarks into three gluons. Should such quarks (${m}_{q}\ensuremath{\gtrsim}5$ GeV) exist, this bound state would provide an ideal place to look for gluon-induced jets. Other topics we have studied include (i) jet structure via the production of four quarks and (ii) different possible gluonic fragmentation functions. Jet structure in deep-inelastic lepton-hadron scattering processes is also briefly considered. We conclude that ${e}^{+}{e}^{\ensuremath{-}}$ annihilation is probably the cleanest place to search for gluonic structure, whose existence would be striking evidence in favor of quantum chromodynamics (QCD). On the other hand, the absence of such structure would necessitate a reexaminat on of our intuitive understanding of QCD and a serious consideration of other field-theoretical hadronic models, e.g., the quark-confining string, which, unlike QCD, does not possess gluonic degrees of freedom.

Connection between fixed-angle and fixed-momentum-transfer scattering in the framework of the double phase representation

The double phase representation of Sugawara and Nambu, which assumes some simple analytical properties with respect to momentum transfer for the phase of the amplitude, is applied to the discussion of large-angle scattering. From the assumptions of Regge behavior and finite asymptotic Regge trajectories, one derives the fixed-angle scaling laws $F(s,\ensuremath{\theta})\ensuremath{\simeq}{s}^{\ensuremath{\Delta}}F(\ensuremath{\theta})$, and the extrapolation to the large-angle region of the Regge formula; the high-momentum-transfer behavior of Regge residues is thereby obtained. As a byproduct, we get the general form of the amplitude (including its phase) in the large-angle region for given values of $\ensuremath{\Delta}$ and of the three asymptotic leading Regge trajectories in the $s$, $t$, and $u$ channels. The angular dependence of various scattering processes is determined, using as input the values of $\ensuremath{\Delta}$ and of the asymptotic trajectories given by the constituent-interchange model. A strong correlation between the forward-backward asymmetry of the angular distribution in a given channel and the ratio of the 90\ifmmode^\circ\else\textdegree\fi{} cross sections in the other two channels is shown to be present in a simple case. Applied to ${\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ scattering the double phase representation shows, together with positivity and the Froissart bound, that the angular distribution can take only two possible forms for each choice of the fixed-angle power $\ensuremath{\Delta}$; in this case one also finds, using the Kinoshita-Loeffel-Martin upper bound, that the asymptotic Pomeron trajectory is bounded from above either by 0 or by 2/3.

Problems with the normalization of cross sections in the constituent-interchange model

It is in principle straightforward to estimate the size of differential cross sections at wide angle in parton models. We show in this note that such estimations in the framework of the constituent-interchange model disagree completely with experimental data.

Electroproduction of forward protons up toQ2=9.5GeV2

We report new measurements of inclusive proton electroproduction. Data were taken with a hydrogen target at the (W,Q/sup 2/) points (2.2 GeV, 1.2 GeV/sup 2/), (2.7, 2.0), (2.7, 3.3), (2.7, 6.2), and (2.7, 9.5) and with a deuterium target at (2.2, 1.2), (2.7, 2.0), (2.7, 6.2), and (2.7, 9.5). The invariant structure function is studied as a function of W, Q/sup 2/, ..omega.., and x'. The data are compared with the predictions of the constituent-interchange model.

Antiproton-proton annihilation into π+π− and K +K − at 6.2 GeV/ c

The angular distributions for the two annihilation channels p ̄ p →π +π − and p ̄ p → K +K − have been measured at 6.2 GeV/ c. The two-pion channel shows peripheral peaks for π + and π − going forward, and the two-kaon channel shows a peripheral peak for the K − going forward. The results have been compared with the line-reversed elastic backward scattering reactions and also with a constituent interchange model.

Hadronic production of large-p⊥leptons and of large-Q2lepton pairs

We study, within the framework of the constituent-interchange model, the contribution of the subprocess meson + quark \ensuremath{\rightarrow} massive photon + quark to the production of massive lepton paris and of large-${p}_{\ensuremath{\perp}}$ leptons. Special attention is paid to the problem of gauge invariance. Our numerical results indicate that this subprocess may give, for the massive-pair production, a greater contribution than that coming from the Drell-Yan mechanism in the range $1\ensuremath{\lesssim}{Q}^{2}\ensuremath{\lesssim}9$ Ge${\mathrm{V}}^{2}$. Its contribution to the large-${p}_{\ensuremath{\perp}}$ lepton production may become observable for ${p}_{\ensuremath{\perp}}\ensuremath{\gtrsim}3\ensuremath{-}4$ GeV/c. We also argue that the best way to study the origin of lepton pairs of momentum $Q$ consists in looking at $\frac{d\ensuremath{\sigma}}{d{Q}^{2}d\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}}$; a calculation of $\frac{d\ensuremath{\sigma}}{d{Q}_{\ensuremath{\perp}}}$ within our model agrees well with the available data.

Proton-proton and antiproton-proton elastic scattering and the constituent-interchange model

i.e. a fixed-angle (0) power-law dependence. The exponent ~V, which gives the energy dependence, varies from 6 to 12, depending on the specific reaction and on the model (1). However, for the scattering on protons of particle and antiparticle, respectively, the energy dependence is the same. In the specific constituent-interchange model of GvNIo~, BRODSKY and BLA~K~NBECLER (2), where the baryon is primarily considered as a bound state of a quark and a spin-one core-thus favouring quark-interchange processes--, the exponent N takes the value 7 for photoproduction on nucleons, 8 for T:p and Kp elastic scattering and 12 for pp and ~p elastic scattering. The absolute value of the cross-section is, however, not predicted. The same result for the exponent 2V is given by MATV~EV, MURADYAN and TAVKH~LIDZE (~). Furthermore, the angular dependence, given by ](0) in (1) is described as a simple and well-defined function of z ~ cos 0 .... . The model has been rather successfully tested on experimental results on pp, ::• and K~p elastic scattering (1,4), and also on some two-body hadronic reactions involving K~ (5).

Phenomenological analysis of high-pTspectra and angular multiplicity correlations inppcollisions

We analyze the high-energy and high-${p}_{T}$ proton-proton 90\ifmmode^\circ\else\textdegree\fi{} inclusive spectra in the framework of the constituent-interchange model. We perform both single- and few-term fits to find out whether a small number of hard-collision subprocesses can describe the data. We also consider constraints to the fits due to particle ratios. We conclude that the single-particle spectra together with particle ratios can be understood within factors of two in the model with a few hard subprocesses and with simple structure functions. The main problems occurring in our analysis include omission of some leading hard-subprocess diagrams without justification and inaccurate determination of the power of $\ensuremath{\epsilon}=\frac{{(\mathrm{missing}\mathrm{mass})}^{2}}{s}$ using the counting rules. Using the above results the quantum-number content of particles balancing the high-${p}_{T}$ trigger is predicted in the different cases. Next we analyze the data on proton-proton angular multiplicity correlations. We first discuss measurements of the opposite-side multiplicity distributions as a function of angle or rapidity. Using a simplifying assumption we calculate these angular multiplicity distributions in the various cases using the dominant subprocesses found in the single-particle fits described above. Qualitative agreement is found with mildly peripheral amplitudes except for the pion triggers.

Inclusive photoproduction of charged particles in the forward hemisphere

We report measurements of the invariant cross section in the forward hemisphere for inclusive photoproduction of ..pi../sup + -/, K/sup + -/, p, and p-bar from hydrogen and deuterium with an incident photon energy of 18 GeV. A small amount of data was also taken at incident energies of 9 and 13 GeV. The measurements were made using the SLAC 20-GeV/c spectrometer, and a bremsstrahlung-subtraction technique was used to obtain the cross sections at the specified incident energy. The data are compared with those from lower-energy experiments and interpreted within the context of the Mueller--Regge model and the constituent-interchange model. (AIP)

Angular dependence of the differential cross section of hadronic exclusive processes at asymptotic energies

The angular dependence of the differential cross section is derived for meson-baryon and baryon-baryon elastic scattering and for some related processes, in the framework of the constituent interchange model, assuming the validity of dimensional scaling laws and using the Mandelstam representation of the amplitude.

Parity violation in pp collisions at high momentum transfer

Estimates are given for the parity-violating asymmetry A( π ±) for the inclusive reaction p + p → π ± + X at high momentum transfer, p T, using longitudinally polarized protons. The most reliable estimate is derived from a weak amplitude calculated by inserting a weak interaction in place of a hard scattering in the constituent interchange model of high p T events. For values of p T as large as 8 GeV/ c, asymmetries A( π) are expected to be of the order 10 −4 or less.

Correlations at large transverse momenta

After a brief discussion of the failure of the constituent-interchange model (CIM) to account for recent experimental data on large-${q}_{T}$ correlations, a hadronic-bremsstrahlung model is introduced. We analyze the structure of the large-${q}_{T}$ events, we present calculations of the correlation coefficients for $p+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}+X$ when the two ${\ensuremath{\pi}}^{0}'\mathrm{s}$ are produced at 90\ifmmode^\circ\else\textdegree\fi{} with respect to the colliding proton either in opposite directions or in the same direction, and we compare with the data and with the predictions of the CIM. Further predictions of the models and simple experimental tests are pointed out.

Large transverse momentum processes

We present a comprehensive survey of experimental and theoretical work on large transverse momentum processes. Exclusive data and single particle inclusive measurements are summarized and some discussion of multiparticle inclusive data is included. We review many of the predictions of nonparton models including the geometrical, statistical, eikonal and bootstrap approaches. A more detailed discussion is given of the structure of models based on the hard scattering of constituents. The predictions for hadronic and electromagnetic processes based on quark counting rules and the constituent interchange model (CIM) are summarized. We present numerous comparisons with experiment and indicate the framework for the comparison with new experimental data. Recent theoretical progress in the problem of relating short distance structure of hadrons with the asymptotic behavior of form factors and fixed angle amplitudes is also reviewed. We include a brief discussion of the possible influence of new hadronic degrees of freedom on large- pT phenomena. Finally, we attempt to anticipate the type of experiments which will prove decisive in the understanding of this subject.

Constituent theory of large-mass production

It is argued that the study of the production of a pair of particles with large invariant mass can provide information on the dynamics of hadronic constituents in a similar way to the study of large-transverse-momentum reactions. A general framework for the analysis and interpretation of these reactions is developed in terms of hadron-irreducible subprocesses and the constituent-interchange model. Counting rules are developed that predict the energy and mass dependence of the cross section. In particular, the production of a massive lepton pair or hadron pair in reactions with photon or hadron beams is discussed. A particularly interesting process that is discussed involves the production of a massive hadron pair in electron-positron annihilation. Its importance in measuring properties of generalized structure functions is emphasized.

Granddaughter trajectories in $$\bar pp$$ annihilations

We have fitted the differential cross-section data for pp annihilations to π−π+ and K−K+ with a model consisting of resonances together with a constituent interchange model background. We find strong evidence for meson resonances of mass 2.11, 2.3 and 2.48 GeV/c2 with spins of 3, 4 and 5 respectively. We also have weaker evidence for a J=2 resonance near threshold. Together with the ρ′(1600) these resonances from a « granddaughter » Regge trajectory approximately two units of angular momentum below ther> A2 trajectory.

Correlation coefficients in the constituent interchange model

Correlation coefficients (CC) for two large transverse momentum hadrons are studied in the constituent interchange model. For p+p→ π°+ π°+X when the two π°'s are produced in opposite directions with momenta p TC, p TD the model predicts significant structure of the CC at p TC ≃ p TD; and when the two π°'s are produced in the same direction it predicts a very small CC. Comparison with existing data is also given.

Elastic proton-proton scattering at large momentum transfer in parton field theory

The constituent interchange model is investigated by means of the DGSIN (Deser-Gilbert-Sudarshan-Ida-Nakanishi) integral representation for the Bethe-Salpeter wave function. It is shown that this model gives a consistent picture (i.e. magnitude and dependence on energy and angle) of proton-proton elastic large-angle scattering when the constituent mass is around 30 MeV.

Unified description of inclusive and exclusive reactions at all momentum transfers

The constituent-interchange model is used to relate large- and small-momentum-transfer reactions, to relate inclusive and exclusive processes, and to predict the form of the inclusive cross section throughout the Peyrou plot. Two important corrections to the triple-Regge formula are derived. The first, important at a small missing mass, allows a smooth connection to exclusive processes. The second, important at large missing mass, allows a smooth connection to the central region and to the large-transverse-momentum regime. Simple quark-counting rules are given which predict the limiting behavior of Regge trajectories and residue functions, and also the powers of ${{P}_{T}}^{2}$ and the missing-mass dependence of inclusive cross sections. Many experimental consequences of the model are given.