Helicity-flip Amplitudes Research Articles

Vector meson production by 4.3 GeV polarized photons on deuterium

Cross sections for γd and γn interactions and photoproduction of ϱ 0 and ω are studied at 4.3 GeV, using a linearly polarized photon beam in a deuterium bubble chamber. We find that σ T (γ n) ⋍ σ T (γ p) within about 5% and that the γn average charge multiplicity is lower than γp by 0.42±0.09. About 4000 ϱ 0 events and 70 coherent ω events are observed. We present total and differential cross sections for both xoherent and incoherent ϱ 0 production on deuterium, as well as decay angular distributions and density-matrix elements. We find that the t-channel isospin-one exchange amplitude in γN → ϱ 0N (e.g. A 2 exchange) is at most 5–13% of the dominant isoscalar amplituds. The ϱ 0 production mechanism is dominantly s-channel helicity-conserving (SHC) on both neutrons and protons. We find that relative to the SHC amplitudes, the single and double helicity-flip amplitudes at the γϱ 0 vertex are of the order of 10–15% for | t| > 0.25 GeV 2, and have the same sign on both nucleons. This shows that helicity-flip is mainly due to isoscalar exchanges. The ratio of ω to ϱ 0 coherent forward cross sections is found to be 0.16±0.04. The natural-parity exchange part of γN → ωN is strongly dominated by isoscalar exchanges, and the magnitude of the isovector-exchange is consistent with zero.

Polarization measurements in π −p, K −p and p¯p elastic scattering at 40 GeV/ c

We report final results on the polarization parameter P in elastic scattering of π −, K − and antiprotons at 40 GeV/ c incident momentum. The energy dependence of P(t) in π −p above 10 GeV/ c is well fitted by P(t) α s αR(t)-αP (t) where α R(t) are the effective Regge and Pomeron trajectories respectively. The data in K −p are compatible with exchange degeneracy. The results inp¯p show an important structure for |t|> 0.3 (GeV/c) 2 demonstrating the existence of a large helicity flip amplitude.

Amplitudes forπ−p→K0Λ0andπ−p→K0Σ0at 5 GeV/c

Using our data on $\frac{d\ensuremath{\sigma}}{dt}$ and polarization in ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}^{0}{\ensuremath{\Lambda}}^{0}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}^{0}{\ensuremath{\Sigma}}^{0}$ at 5 GeV/c, and assuming SU(3) octet dominance of the baryon couplings in $s$-channel helicity amplitudes, we determine amplitudes for these reactions up to an undetermined over-all phase. We calculate the spin rotation parameters $\stackrel{^}{A}$ and $\stackrel{^}{R}$ and compare our predictions with those from phenomenological models. Assuming a Regge phase for the helicity-flip amplitude, we find that the imaginary part of the nonflip amplitude for these reactions shows peripheral behavior but the real part does not.

The derivative rule for helicity-flip amplitudes

Consequences of the derivative relation f +- = λ∂f ++ ∂√−t , proposed empirically and also in various models for s-channel helicity amplitudes, are explored. A comparison with π −p→ π 0n charge-exchange data is made, imposing the usual Regge pole form on f +-. The assumptions are seen to conflict with the s-dependence of the cross-section dip and the polarization structure. There are also difficulties with finite energy sum rules and with-experimental data on some other reactions.

Resonance ambiguities, Barrelet zeros, and duality in K −p→ Λπ0

The method of Barrelet zeros has been used to study the ambiguities of our partial wave solutions for the reactions K −p→ Λπ 0 from 1550 to 2170 MeV. Details of this two-body analysis technique are presented and ambigous sets of partial waves corresponding to the same d σ/d ω and (d σ/d ω) P are analysed. Seven ambigous solutions have been found which maintain the dominant ∑ resonant structure [D3(1660), D5(1765), F5(1920), F7(2040)] but differ in the resonant couplings (t = Γ e Γ r /Γ ) for these states, as well as in the resonant structure in the lower partial waves. Evidence is given for the possible existence of new resonant states in the F5, D5 and F7 partial waves and for additional resonances in lower waves. The resonant structure suggested by the additional solutions is more prolific than the structure previously indicated for this reaction. Several solutions contain resonant “daughter” states at the same mass but with different J P in qualitative agreement with Veneziano models and suggestive of the Harari-Freund conjecture of purely resonant scattering in non-diffractive, inelastic channels. The ambiguities are experimentally distinguishable only by measurement of R and A, which are predicted from the solutions. Each solution has been shown to be consistent with semi-local duality from observed averaging about zero exhibited by Im A′( s, t), the invariant, t-channel helicity non-flip amplitude calculated at t = 0 and at t = m K ∗ 2 . Local averaging was not seen in B ( s, t), the t-channel helicity flip amplitude. The variation of resonant coupling among these solutions for the dominant resonances suggests that SU(3) tests involving the Λπ channel should be reconsidered. The results indicate that partial wave ambiguities should be more carefully studied and that the possible ∑ resonances should be looked for in other KN reactions.

Tensor exchange in meson-baryon scattering

Amplitudes for A 2 quantum number exchange in K ±N scattering are determined at p L = 3, 4 and 6 GeV using new K ±N CEX differential cross-section data supplemented by sum rule estimates of polarizations. Amplitudes for ϱ quantum number exchange are calculated from πN scattering by SU(3) octet symmetry. This is justified by K ±N FESR, which furthermore are used to resolve ambiguities in the analysis. Comparison with other reactions involving charge and hyperchange exchange shows reasonable overall consistency between data, SU(3), and the tensor amplitudes. The phase of the A 2 s-channel helicity flip amplitude is well described by a Regge pole term with trajectory displaced downwards relative to that appropriate for the ϱ flip amplitude. This is shown to be the main mechanism contributing to the difference between differential cross sections for the K ±N CEX processes, connected by line reversal. It is suggested that this mechanism may persist at higher energies. The A 2 non-flip amplitude does not have the standard peripheral form.

Analysis of π N → K Λ and [formula omitted] using fixed- t dispersion relations, fesr and duality

A simultaneous analysis of low-energy ( W ⩽ 2 GeV) data for the reactions π −p→ K O Λ and K −p → π O Λ has been made using the hypothesis of two-component duality combined with fixed- t dispersion relations. Results are presented for the ϵ ∗ Λπ and N ∗ Λ K couplings. The low-energy amplitudes are used to evaluate FESR integrals and lead to large EXD breaking for the K V ∗ − K T ∗ helicity flip amplitudes.

Amplitude analysis of Kaon-nucleon scattering data

The KN scattering amplitudes have been extracted from experimental data in the energy range 3 ≲ k ⩽ 14 GeV/ c and for transfer values between −0.05 and −0.6 GeV 2. The ω and P+f helicity-flip amplitudes and the A 2 helicity non-flip amplitude have been neglected; it is shown, that these simplifications are compatible with the data and have no significant influence on our results. One needs to assume the approximate validity of SU(3) symmetry for the ϱ and A 2 couplings. A very important constraint for this analysis comes from recent experimental data for the reaction K L 0p → K S 0p. The results for A 2 and ω exchanges are analysed as functions of momentum transfer and energy and we test several current theoretical ideas. Information about f-exchange is also obtained when some further assumptions are made concerning SU(3) symmetry and duality at t = 0. Extrapolating the amplitudes to t = 0 a comparison is made with dispersion relation calculations; at other t-values we compare with results obtained from finite energy sum rules and other analyses based on fixed f analyticity. The predictions for KN data which have not been considered in this analysis are shown to be in good agreement. One of our results is that the ϱ-ω universality rule is approximately satisfied; we also find a strong indication for a peripheral behaviour of the imaginary part of the non-flip f-exchange amplitude.

Constraints on the phases of helicity amplitudes due to positivity

From the positivity of the expansion coefficients of the absorptive part of a helicity non-flip, elastic scattering amplitude we get bounds on the phase of the corresponding helicity non-flip amplitude such as | Arg F λ.λ(s,cos ΘM)|<a+b Max 0<Θ<Θ M Im F λ,λ(s,cosΘ=1) F λ,λ(s,cosΘ) 2 , a and b being bounded real positive constants which can be computed. For helicity-flip amplitudes we get bounds on the local variation of the phase between two positive scattering angles, | Arg F λ.λ(s,cos Θ 1)- Arg F λ,μ(s,cos Θ c)|<c+d Max Θ 1<Θ<Θ 0 Im F λ,λ(s,cosΘ=1)+Im F μ,μ(s,cosΘ=1) F λ,λ(s,cosΘ) 2 , c and d being also bounded, real, positive, computable constants.

Universality of Urbaryon Rearrangement Amplitudes

The concept of universality of urbaryon rearrangement amplitudes is introduced, in which the amplitudes of the same type of urbaryon rearrangement for meson-meson, meson-baryon and baryon- (anti) baryon scattering are described as common with each other and the ampli­ tudes of each type are counted even in the presence of the U (6) symmetry breaking, i.e., not pure f-type coupling. Relations for helicity non-flip and flip amplitudes are obtained on the basis of the concept of universality. Above all, it should be noticed that the following results are derived: (i) The relations which comprise the Johnson-Treiman relations and the Freund relations as special cases are obtained and in good agreement with experiments if one takes D/F ratio of helicity non-flip part as F+ =f+/ Cf+ +d+) =1.5. (ii) Universality relations for t-channel iso-scalar part in helicity non-flip and flip amplitudes hold independ­ ently of D/F ratios. (iii) Universality relations for t-channel iso-vector part depend on D/F ratios. (iv) The experimental ratio of polarizations for K+p-elastic scattering to that for pp­ one can be explained reasonably. These results give support to the view that the countable nature of constituent urbaryons reflects on the scattering amplitudes for hadronic reactions. Furthermore, the validity of the universality of urbaryon rearrangement amplitudes suggests that urbaryon rearrangement interaction shares a coupling strength independent of the num­ ber of spectator urbaryons (the universality of urbaryon rearrangement interaction). From the viewpoint of the urbaryon rearrangement (hereafter referred to as UR) it has been found that various characteristic features of hadronic reactions could be interpreted as a consequence of several properties of each UR amplitude. Presumptive evidence in support of the composite model of hadrons and UR model seems to be exhibited in the examination of hadronic reactions in terms of UR. 1 l~s) Especially the validity of the additivity of UR amplitudes seems to be closely related to existence of urbaryon and its dynamics. In view of the elucidation of dynamical properties of urbaryon, it is an interesting problem to ascertain more definitely whether the countable nature of constituent urbaryon reflects on the scattering amplitudes of hadronic reactions. The quark counting 7l in 1965 has been one of the first attempts on the above problem. In this model, however, the scattering amplitudes have not been classified according to the UR diagrams contributing to each process, and furthermore the countable nature of constituent urbaryons is indelibly associated with pure f-type coupling for baryon vertex which is also required by U(6) symmetry. As a result of quark count­ ing, for example, the following relations for total cross sections of high energy meson-baryon and baryon- (anti) baryon scattering have been obtained:

πN amplitudes at large momentum transfer

The πN amplitudes are estimated from data in the region 0.8 ⩽ | t| ⩽ 1.4 (GeV/ c) 2 for incident momentum between 3.7 and 14 GeV/ c, under the assumption of ϱ-Regge-pole phase for the I t = 1 s-channel helicity flip amplitude. The main conclusions are: (i) the real part of the I t = 0 non-flip amplitude is substantial and its non-asymptotic variation with energy has not died out, (ii) the I t = 1 non-flip amplitude shows a large degree of shrinkage as energy increases out to t = −1.4 (GeV/ c) 2, (iii) the I t = 1 non-flip amplitude has a second cross-over zero at t ≊ −1.2 ( GeV/c) 2 in its imaginary part.

Unitarity and Analyticity Bounds on Pion-Nucleon Helicity Amplitudes

Unitarity and analyticity bounds on the absorptive parts of ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ $s$-channel helicity amplitudes are compared with the results of a recent amplitude analysis. It is found that in particular the helicity-flip amplitude is severely restricted in the forward region.

Vector-Meson Production by Polarized Photons at 2.8, 4.7, and 9.3 GeV

We present results on vector-meson photoproduction via $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{Vp}$ in the LBL-SLAC 82-in. hydrogen bubble chamber exposed to a linearly polarized photon beam at 2.8, 4.7, and 9.3 GeV. We find ${\ensuremath{\rho}}^{0}$ production to have the characteristics of a diffractive process, i.e., a cross section decreasing slowly with energy and a differential cross section with slope of \ensuremath{\sim} 6.5 ${\mathrm{GeV}}^{\ensuremath{-}2}$. Within errors the ${\ensuremath{\rho}}^{0}$ production amplitudes are entirely due to natural-parity exchange. $s$-channel helicity is conserved to a high degree in the $\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}$ transition. We find evidence for small helicity-flip amplitudes for $\ensuremath{\pi}\ensuremath{\pi}$ pairs in the ${\ensuremath{\rho}}^{0}$ region. Photoproduction of $\ensuremath{\omega}$ mesons is separated into its natural- (${\ensuremath{\sigma}}^{N}$) and unnatural- (${\ensuremath{\sigma}}^{U}$) parity-exchange contributions. The ${E}_{\ensuremath{\gamma}}$ and $t$ dependence and the spin density matrix of the unnatural-parity-exchange contribution are consistent with a one-pion-exchange process. The natural-parity-exchange part has characteristics similar to ${\ensuremath{\rho}}^{0}$ production. At 9.3 GeV the ratio of $\ensuremath{\sigma}({\ensuremath{\rho}}^{0})$ to ${\ensuremath{\sigma}}^{N}(\ensuremath{\omega})$ is \ensuremath{\sim} 7. The slope of the $\ensuremath{\varphi}$ differential cross section is \ensuremath{\sim} 4.5 ${\mathrm{GeV}}^{\ensuremath{-}2}$, smaller than that of ${\ensuremath{\rho}}^{0}$ and $\ensuremath{\omega}$ production. Natural-parity exchange is the main contributor to $\ensuremath{\varphi}$ production. No evidence for higher-mass vector mesons is found in $\ensuremath{\pi}\ensuremath{\pi}$, $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\pi}$, or $K\overline{K}$ final states. The $s$ and $t$ dependences of Compton scattering as calculated from $\ensuremath{\rho}$, $\ensuremath{\omega}$, and $\ensuremath{\varphi}$ photoproduction using vector-meson dominance agree with experiment, but the predicted Compton cross section is too small by a factor of 2.

Conspiracy and Regge Cuts in Pion-Nucleon Amplitudes

The pion-nucleon amplitudes are analyzed in terms of the conspiracy and strong- and weak-cut Regge-pole models. The weak-cut model has serious difficulty, in that it predicts the wrong sign of the helicity-flip amplitude. The strong-cut model appears to have the correct form for the amplitudes, but has the wrong energy dependence for differential cross sections and polarizations. The conspiracy model is found not to suffer from any serious difficulty.

Crossing invariant solution of baryon exchange degeneracy and reggeon [formula omitted] ratios

A crossing invariant solution of baryon exchange degeneracy is found within the framework of SU(3) and no exotics in all channels. Reggeon F D rations are predicted to be ( F D ) ++ = − 7 3 and ( F D ) +− = 1 3 for s- channel helicity non-flip and flip amplitudes respectively which are in good agreement with data.

A Re‐Examination of the Arguments for Baryon Parity Doublets

AbstractThe arguments for baryon parity doubling are re‐examined by use of a spin formalism developed by the author together with B. E. LAURENT. It is shown that the transformation between good parity amplitudes and helicity flip and non‐flip amplitudes in πN scattering is ambiguous. It is further shown that the unitary condition for boson‐fermion scattering gives no information of the parity of intermediate states contributing to a good parity amplitude. These ambiguities follow from the fact that for boson‐fermion scattering the CPT transformation of an amplitude does not commute with the projection on a definite parity. It is finally shown how a Regge pole model with linear trajectories without parity doubling can be constructed without any specific dynamical assumptions or artifices. The constraints on the residues needed in this case do not violate any general principles.

Transient phenomena at intermediate energies

Considering the experimental energy behaviours of elastic K +p, pp, πp, polarizations, we show that in helicity-flip amplitudes non-leading contributions, non-identifiable with absorptive corrections, Regge-Regge cuts or resonance tails, remain non-negligible up to ∼ 10 GeV/ c. The interpretation of such contributions appears uncertain.

Fixed poles in the t-channel helicity-flip amplitude in charge- and hypercharge-exchange reactions

We try to find evidence for fixed poles in two-body meson-baryon scattering. The contribution of wrong-signature fixed poles occur in wrong-signature sum rules. We evaluate the first wrong-signature sum rule for the t-channel helicity flip amplitude in π N, KN charge-exchange and in hypercharge-exchange scatterings. According to recent theoretical analysis the J = 0 KN charge-exchange wrong-signature fixed pole is generated, via t-channel unitarity, from the πN one. Its existence implies a J = 0 KN charge-exchange right-signature fixed pole. Evidence for the existence of a J = 0 wrong-signature fixed pole is found in all of them. It is also found that the non-peripheral resonances are mainly responsible for all these fixed poles.

Amplitude Analysis of Charge-Exchange and Strangeness-Exchange Processes in Pseudoscalar-Meson-Baryon Scattering Using the Dual Absorptive Model

An amplitude analysis of charge-exchange and strangeness-exchange reactions in pseudoscalar-meson-baryon scattering is presented for the momentum interval \ensuremath{\sim} 4 to \ensuremath{\sim} 16 GeV/c. The imaginary parts of the $s$-channel helicity-nonflip and helicity-flip amplitudes are assumed to have "${J}_{0}$" and "${J}_{1}$" structures, respectively, as specified by the dual absorptive model of Harari. This model has been successful previously in explaining the main features of elastic scattering data. The present analysis applies this model to inelastic scattering reactions and determines empirically the real part of the $s$-channel nonflip amplitude from the data. The resulting amplitudes reproduce well the existing differential cross section and polarization data for charge-exchange and strangeness-exchange reactions. The $\ensuremath{\rho}$ and ${A}_{2}$ amplitudes in $\mathrm{KN}$ charge exchange are found to be in approximate agreement with strong exchange degeneracy. In contrast, the ${K}^{*}$ and ${K}^{**}$ amplitudes in $\ensuremath{\Sigma}$ and $\ensuremath{\Lambda}$ reactions are not strongly exchange-degenerate, even though equal forward differential cross sections are observed for the line-reversed pairs of reactions $\ensuremath{\pi}N\ensuremath{\rightarrow}\mathrm{KY}$ and $\overline{K}N\ensuremath{\rightarrow}\ensuremath{\pi}Y$.

Successes and failures of dual absorption models

The peripherality assumption of dual absorption models is examined in the case of elastic scattering. Data on differential cross sections sums dσ dt ( A B) + dσ dt ( AB) exclude a peripheral character for the energy dependent part, casting serious doubts on the validity of the two component theory of the Pomeron. Analysis of the differences dσ dt ( A B)− dσ dt ( AB) as a function of both t and s are consistent with a peripheral J O( R√− t) s n−1 structure for the imaginary parts of the helicity non-flip ϱ exchange in πN and ω-exchange in KN. The non-flip ω-amplitude in NN has a different structure than that expected from simple peripherality. A relation between K +p and K −p polarization derived from exchange degeneracy for the helicity flip amplitude is in qualitative accord with data. Regge - Regge interference terms are porposed as possible explanation of the double zero around t ≌-0.8 in pp polarization.