Helicity Non-flip Amplitudes Research Articles

Study of the Reaction K-p → πoΛ

It is shown that at high energy all available data for differential and integrated cross sections and the Λ-polarization in the reaction K-p → πoΛ can be fitted by using a simple Regge pole model with phenomenological residue functions. The characteristics of helicity and helicity non-flip amplitudes are also examined.

Structure of the I=1 nucleon-nucleon amplitudes at 6 GeV/c

By utilising a dispersion-theoretic calculation of the isospin-zero helicity non-flip amplitude to supplement the experimental data, and by making physically reasonable assumptions about isospin-one dominance of certain helicity flip amplitudes, the authors have been able to obtain a unique, stable set of amplitudes in the region -0.7<or=t<or=-0.1 (GeV/c)2 at pL=6 GeV/c. They demonstrate how the qualitative structure of the amplitudes is determined by the data, and use their amplitudes to predict the values of observables not yet measured.

Pion-nucleon charge-exchange polarization by gribov reggeon calculus and the derivative rule

Polarization measurements in u + p + u ~ indicate the presence of a relative phase between the nonflip and the flip helicity amplitudes. Corrections to the single Reggeon exchange can, in principle, generate such a relative phase. These corrections are cuts in the complex j-plane whose strength can be calculated by means of the absorption model. This model (1) describes the polarization data for very small momentum transfers but for larger values it fails entirely giving a tremendous negative peak where the experimental data are consistent with zero. The polarization obtained from the absorption model changes sign at t -~ _~ 0.20 (GeV/c) 2 as a direct consequence of the fact that the relative phase between the absorption cut and the pole of the nonfiip helicity amplitude reaches 180 ~ I t is an inevitable feature of the tradit ional absorption model tha t this relative phase can never be much larger than 180 ~ at t = 0 (GeV/c) 2. Since the cut rotates very slowly in comparison with the pole, any modification of the model has to considerably increase the starting point of the cut. The phase-modified absorption model (2) is the most extreme version of a successful modification. This model pushes the cut right into the fourth quadrant by multiplying the nourotat ing part of the cut by a factor of i and therefore absorbs the imaginary part of the amplitude total ly at the expense of the real part. The zero of the imaginary part of the helicity nonflip amplitude has to occur before the zero of the real part of this amplitude. Unless the cut is modified, the relative positions of these zeros are interchanged and the amplitude therefore rotates incorrectly in a counterclockwise manner around the origin of the Argand diagram (3). In order to achieve the needed modification in a less arbitrary way, one can do the traditional absorption model convolution, but with a pomeron which has a real and a more detailed structure (4).

Proportionality Relations in Charge-Exchange Reactions

except for the forward spikes of the differential cross-sections of the so-called /;-exchange reactions. 3l In the Regge pole model the factorization relation of the differential sections is satisfied if the exchanges of only one Regge pole dominate the ential cross-sections, each of which is dominated by one helicity amplitude. it is well known that helicity non-flip amplitudes are inconsistent with the crossdiffer­ Ncnv, simple Regge pole model. Though helicity-flip amplitudes are consistent with the Regge pole model, they are also consistent with peripheral interaction models') and it is not clear i£ the factorization of the experimental differential cross-sections imli­ cates the factorization of underlying mechanism. In all cases where the relation (1) has been checked by experimental data the targets b and e are nucleons and the final baryons d and f arc the nucleon

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.

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.

Helicity-independent structure hypothesis, peripherality and πN charge exchange amplitude

A new constraint on s-channel helicity amplitudes in the impact parameter representation called the helicity-independent structure hypothesis (HISH) is proposed. This is a less restrictive constraint on helicity amplitudes than that of the dual absorptive model in the sense that pheripherality is not required explicitly in the proposed model. It is shown that the HISH plays a central role in the approach used, just as the peripherality does inthe dual absorptive model, and that the peripherality of the helicitynonflip amplitude is not the consequence of absorption effects but is due to the peripheral structure of the Regge-pole residue itself. The helicity amplitudes of pi /sup -/ + p yields pi /sup o/ + n interactio ns are successfully explained in the proposed model. (JFP)

Analysis of data for hypercharge-exchange reactions

The properties of the experimental data on the hypercharge-exchange reactions πN→KΣ, KΛ and $$\bar K$$ N→πΣ, πΛ in the region (4÷16) GeV/c are surveyed, with attention to line-reversal inequalities, reaction energy dependences in terms of effective trajectories, phase-energy properties, andSU 3 for exchanges. We determine thes-channel helicity nonflip amplitudes at 4 and 14 GeV/c, assuming an exchange degenerate $$K_V^* - K_T^* $$ Regge-pole approximation for the flip amplitudes. In the impact-parameter representation only the imaginary parts of the πN→KY nonflip amplitudes (or in terms of exchanges Im $$K_V^* $$ ) are found to be peripheral. All other nonflip amplitude components are central. AnSU 3 comparison is made with K−p→νΛ, ν'Λ data.

A study of the reactions [formula omitted] and [formula omitted] at 8.25 GeV/ c

A variation of the model proposed by Plahte and Roberts is used to fit data from the reaction K − p → K 0π − p at 8.25 GeV/ c. The channel K − p → K ∗− p is also studied in some detail and the energy dependence of the cross section is discussed. The behaviour of the differential cross sections and of the density matrix elements of K ∗ in the G-J frame as function of t' suggests dominance of vector exchange with a small π-exchange contribution. The density matrix elements are also given in the helicity fram and a fit to the Harari model supports the dominance of natural-parity exchange and of the helicity non-flip amplitude at the nucleon vertex.

Amplitude analysis for hypercharge exchange reactions

The s channel helicity non-flip amplitudes for the line reversed reactions π N → K [ Σ, Λ] and KN → π [Σ, Λ] are determined directly from cross-section and polarization data at 4 GeV/ c. Rigorous bounds are obtained on the magnetudes of the flip amplitudes, whose phases are assumed to be given by an exchange degenerate K ∗ - K ∗∗ Regge trajectory. Our solution for the non-flip amplitude is unique and shows the following characteristics: i) Im K ∗ (Δλ = 0) has a “cross-over” zero at t ≈ −0.15 in both Σ and Λ reactions, ii) Im K ∗∗ (Δλ = 0) has an approximate double zero near t ≈ −0.6 in Σ reactions and a positive minimum there in Λ reactions, iii) Re K ∗ (Δλ = 0) and Re K ∗∗ (Δλ =0) are less peripheral in characters than their imaginary counter-part and have similar behavior at α = 0 to simple Regge poles.

Duality in [formula omitted

We have tested the duality diagram predictions for the reactions KN →πΣ andKN→πΣ in the energy region 1500MeV <Ecm < 1900MeV. The πΛ amplitudes are consistent with the predictions, but the exotic It=32 amplitudes in K−p → π+Σ− do not show local averaging to zero. Within the limited size of our energy interval the It = 12 and the helicity non-flip amplitudes show better local averaging than the It = 32 and the flip amplitudes.

Rho-dominant sum rules for kaon-nucleon scattering

We present here a new set of sum rules for the helicity non-flip amplitude, the helicity-flip amplitude B, and the amplitude A for kaon-nucleon scattering corresponding to t-channel isospin and G-parity I G = 1 +. These sum rules are derived assuming unsubtracted dispersion relations for these amplitudes both in the forward as well as in the backward directions and that the ϱ-meson dominates in the I G = 1 + channel. The sum rules are in excellent agreement with the available experimental data. Our analysis vindicates the hypothesis of universal ϱ-coupling to hadrons.

O(3,1) symmetry and the charge exchange reaction [formula omitted

The high-energy behaviour of the charge exchange reaction p ̄ p → n ̄ n is analysed within the context of the O(3,1) symmetry formalism. A good fit to the experimental data is obtained if the exchangedparticles are chosen to be ϱ, ϱ′ and A 2. It is found that the dominant contribution of ϱ and A 2 is from the helicity non-flip amplitudes while the contribution of ϱ′ is purely from the helicity flip amplitude.

Regge-Pole Model for the Secondary Maxima inπNandNNScattering and the No-Compensation Mechanism

The dip-bump structure in the low-energy ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ elastic differential cross section has been studied. We find that a zero in the helicity nonflip amplitude of the ${P}^{\ensuremath{'}}$ trajectory gives a natural explanation of this structure. At the same time we have consistently fitted the high-energy ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ total and differential cross sections, the ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ polarizations, and the ${\ensuremath{\pi}}^{\ensuremath{-}}p$ charge-exchange differential cross-section data. The helicity nonflip amplitude of the ${P}^{\ensuremath{'}}$ trajectory will vanish at ${\ensuremath{\alpha}}_{{P}^{\ensuremath{'}}}=0$ if the ${P}^{\ensuremath{'}}$ trajectory chooses what we call the no-compensation mechanism. Consistent with our ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ solution, the $\mathrm{pp}$ and $\overline{p}p$ total and differential cross sections can also be well fitted. The secondary maximum in the low-energy $\overline{p}p$ differential cross section is reproduced.