Pomeron Pole Research Articles

Proton‐Proton Interaction in a Dual Model

AbstractThe “background‐pomeron” component of the amplitude is studied in the framework of a dual model with square‐root trajectories. Double pomeron poles are used as vacuum exchanges in various channels, with exotic Regge poles dual to them. The expressions obtained are applied to describe total and differential cross sections of proton‐proton interaction in wid eenergy regions.

Dynamics of froissarons in high-energy physics

It is shown that a small shift of the pomeron pole position from unity to α(0) = 1 + Δ changes slightly the Regge scheme in accordance with experimental data in a modern energy region. At asymptotic energies Δ 1n ( s/ s 0) ⪢ 1, however, the theory is changed drastically. A new object, a “froissaron”, which is a multi-pomeron stream, dominates in the scattering amplitude. After summing over all pomeron Griboy-Cardy graphs, we find that the total cross section in asymptotics increases as 8 πΔ 0 α′ 1n 2( s/ s 0) and the mean multiplicity 〈 n〉 ∼ ( s/ s 0) Δ 0/1n( s/ s 0). Here Δ 0 is a new renormalized value of the pomeron position shift, which emerges after the enhanced graphs are taken into account.

Зависимость и систематика полных поперечных сечений адронов

It is shown that all the qualitative and quantitative features of the total cross-sections for π±p, K±p, $$\bar pp$$ and pp scatterings from low energies up to ISR energies can be explained in terms of three universal components contributing to the hadron-proton amplitude. Besides the well-known pomeron pole and exchange-degenerate reggeon, there is a third universal crossing-symmetric component, whose contribution to pp, πp and Kp scatterings, respectively, scales in the ratio 1∶5/4∶2. This empirical regularity is interpreted as being a consequence of the fact that the coupling of the third comonent to any hadron-nucleon scattering is given by the mean value of the hypercharge squared of the consitituent quarks. Our approach leads to a classification of all hadron-nucleon total cross-sections in terms of the number of strange quarks involved in the scattering. In particular, we obtain an equal-spacing law for the total cross-sections of exotic reactions. The ϕp total cross-section is predicted to have the fastest rise of all hadron-proton reactions. We also predict the values and the rates of increase of hyperon-proton cross-sections, which can be tested by the hyperon beam experiments now planned at Fermilab.

Comments on Geometrical Features of the Shielded Fixed Pole Pomeron at Very High Energies. II

Comments on Geometrical Features of the Shielded Fixed Pole Pomeron at Very High Energies. II

Fdominance and final-state counting in multiperipheral cluster models

We discuss several problems associated with the formulation and use of multiperipheral cluster models and the closely related Reggeon-loop expansion in dual models. We present a method which unambiguously and uniquely counts final states, and combine it with conventional factorization to obtain a t-channel integral equation with Regge-pole solutions. These correctly counted solutions are used to estimate the error induced by various incorrect counting schemes. We then consider the relation between Reggeon and Pomeron poles, assuming the latter originate from crossed-loop or cylinder diagrams, and emphasize the tacit assumptions needed to obtain f-dominated Pomeron couplings. We find a Pomeron intercept of about 0.8. (AIP)

Comments on Geometrical Features of the Real Part of the Shielded Fixed Pole Pomeron

Comments on Geometrical Features of the Real Part of the Shielded Fixed Pole Pomeron

Regge cuts inγγscattering

It is shown that the Pomeron-Pomeron cut in $\ensuremath{\gamma}\ensuremath{\gamma}$ scattering has natural $C$ parity and conspires, in contrast to the Pomeron pole which is evasive, and has natural parity and $C$ parity. The constraints this places upon the invariant amplitudes are analyzed.

How strong are the Pomeron decoupling theorems?

An investigation is made of how close to one a Pomeron pole can be before the decoupling mechanisms make the total pion-pion cross section too small to be consistent with that deduced from experiment by means of factorization. Our method employs energy-momentum sum rules for singly and doubly inclusive cross sections. Assuming pion pole dominance in the forward direction, enables elimination of the triple-Pomeron coupling which leaves an inequality involving only the Pomeron pole location and the pion-Pomeron coupling. From this it is concluded that the decoupling mechanism is exceedingly weak. (AIP)

J-plane structure of the “cylinder”; slope and intercept of the bare pomeron

We derive and investigate an integral equation for the “cylinder” with full t-dependence. In contrast to the pure pole planar model, the “cylinder” contains, in addition to the bare pomeron pole, also a Reggeon-Reggeon cut. The strongly correlated slope and intercept of the bare pomeron have the correct observed values. We also briefly comment on the concept of “asymptotic planarity”.

Summing pomeron trees

It is argued that multi-pomeron exchange diagrams not involving pomeron loops play a dominant role in the presently accessible energy range. These diagrams are explicitly summed for a pomeron pole with intercept larger than one (in the limit α′ = 0). s-channel unitarity is automatically satisfied (but not saturated). For particle-particle scattering we obtain phenomenological features in agreement with the data (σ T , σ el , ( d log σ el dt )∣ t=0 increase to a finite limit and σ el σ T can be made arbitrarily small). Our results are also applied to nucleus-nucleus scattering.

Non-regge and hyper-regge effects in pion-nucleon charge exchange scattering at high energies

The experimental data on the charge exchange differential cross-section and on the difference of the π+p and π−p total cross-sections in the rangep L =5 GeV/c to 200 GeV/c are shown to be incompatible with conventional Regge asymptotic behaviour. It is shown that an additional term is required which grows in importance with energy. The precise form of the new term cannot be ascertained, but it is shown that it corresponds to a singularity atJ =1 in the complex-angular-momentum plane. Amongst the possible types of additional term there are two which are aesthetically favoured and which have been closely analysed. These correspond to i) a non-Regge behaviour associated with the maximal growth permitted in axiomatic field theory; ii) a «hyper-Regge» term,i.e. an odd-signatured Regge pole, the analogue of the pomeron pole, with interceptα =1 att =0. Very striking predictions, in particular for the charge exchange polarization, follow as a consequence of the non-Regge or hyper-Regge asymptotic behaviour of the crossing-odd amplitude.

Pp Total Cross Section Rise with a Renormalized Romeron

The single-loop Pomeron diagram connected through the generalized optical theorem to two-cluster production is used to construct an integral equation. The infinite class . of Pomeron loop diagrams taken into account by this equation effectively renormalizes the Pomeron singularity. A simple pole Pomeron·at IXo=l is renormalized by this procedure into a j-plane pole-doublet and leads to a rising pp total cross section. Single or double-particle diffrac:tive dissociation has been one of several mechanisms proposed to account for the observed proton-proton total cross section rise above PL=50 Ge V / c.u- 4> It is found, however, that quantitative predictions from either one are insufficient5'- 7' to explain this experimental feature, although numerical results vary according to the chosen functional form and strength at t=O of the triple Pomeron coupling.8'· 9' In this work we start from a bare Pomeron trajectory a ( t) = a 0 +a' t ex­ changed between two diffractively produced fireballs, and assumed to control the triple-Regge region. 10' An integral equ~tion is then constructed to sum the class of (bare) Pomeron loop-diagrams that correspond to diffractive production of an unrestricted number of fireballs. This equation is (approximately) solved and the contribution to the elastic amplitude of the resulting renormalized Pomeron is obtained and compared to pp total cross section data. One secondary term rvs- 1/ 2 is added to extend the description of data down to PL=10GeV/c. Proton-proton scattering may produce an event with at least one large repidity gap separating groups of particles. If the energy is larger than some certain threshold, a minimum separation in rapidity is ensured between the fireballs. The cross section for two fireballs with masses squared s1 and s2 is given in the Regge asymptotic limit by1n' 12'

Direct-channel tests of the strong-coupling Pomeron

We discuss how the strong-coupling renormalization-group solution of Reggeon field theory satisfies some of the simplest constraints of direct-channel unitarity, including those which lead to the decoupling theorems for the simple Pomeron pole.

A topological expansion for high-energy hadronic collisions: (I). General properties and connection with the reggeon calculus

In this and in a companion paper a “topological expansion” for high-energy hadronic processes is proposed and discussed. In this first paper the general properties of the expansion and its connection with Gribov's reggeon calculus are presented. The topological expansion is first defined mathematically for a large class of theories and is shown to be equivalent to a “large N expansion” in some theories which include planar dual models and non-Abelian gauge theories. Next, the definition of the bare parameters is given in terms of graphs on a sphere. The bare pomeron pole and its couplings are thus introduced. The (inclusive) form of s-channel unitarity and its consequences fo the above couplings are recalled. It is then shown how the expansion in the number of “handles” of the graph can be related to Gribov's reggeon calculus and how, with the aid of discontinuity equations in the J-plane, scaling solutions can be obtained and critical indices can be computed to yield known results. Our main new results, including the study of s-channel discontinuities and of positivity constraints as well as the definition of a new fireball expansion, and the discussion of the relevance of this theory at finite (present) energies are presented in the second paper.

Pomeron decoupling theorems

We investigate the hypothesis that diffractive scattering is dominated (as $s\ensuremath{\rightarrow}\ensuremath{\infty}$) by a Pomeron Regge pole [${\ensuremath{\alpha}}_{P}(t)$]. This hypothesis is particularly attractive since a Regge pole and its attendant cuts satisfy $t$-channel unitarity. For a complete theory the constraints of $s$-channel unitarity must also be satisfied. In addition to Froissart's bound and its wellknown consequence, ${\ensuremath{\alpha}}_{P}(0)\ensuremath{\le}1$, $s$-channel unitarity implies a large number of decoupling for an isolated Pomeron pole with ${\ensuremath{\alpha}}_{P}(0)=1$. Here we systematically review these decoupling theorems. The are treated in order of increasing strength so as to clearly distinguish the strong theorems which can be used to prove the complete decoupling of the Pomeron (e.g., ${\ensuremath{\sigma}}_{\mathrm{Tot}}\ensuremath{\rightarrow}0$) from the weak theorems which cannot. This review is undertaken with two goals in view: (1) To focus attention on possible points of departure for more realistic treatments of diffractive scattering, and (2) to emphasize the importance of $s$-channel unitarity which is expected to strongly constrain diffractive production in certain regions of phase space regardless of the exact nature of the Pomeron singularity.

A new interpretation of the absorption mechanism for high energy scattering

We propose a new s-channel absorption mechanism for high energy processes. A possible small dimensionless physical quantity naturally emerges. Consequently, the proposed s-channel equation can accommodate, at present energies, an elastic amplitude dominated by a simple factorizable bare pomeron pole, as in the t-channel perturbative expansion of the Gribov's Reggeon calculus in the strong coupling limit.

Comments on Geometrical Features of the Shielded Fixed Pole Pomeron at Very High Energies

Comments on Geometrical Features of the Shielded Fixed Pole Pomeron at Very High Energies

Are constant asymptotic total cross sections ruled out by high-energy measurements?

It is a common belief that the conventional contributions of the Pomeron pole and the two-Pomeron cut in the Gribov Reggeon calculus cannot give enough rise of the $pp$ total cross section at CERN ISR energies. However, we find from a detailed analysis of $\frac{d\ensuremath{\sigma}}{dt}$ at small $t$ that one can, in fact, get a reasonable rise of the $pp$ total cross section at CERN ISR energies. The ${K}^{+}p$ total cross sections are also fitted; however, their consistency with $\frac{d\ensuremath{\sigma}}{dt}$ has to be checked out when the data are available.

Regge parameters from duality and unitarity

From s-channel unitarity, two coupled integral equations are derived for the reggeon and pomeron propagators using a method developed in an earlier work. The first (R) is a consistency equation constraining the reggeon parameters, while the second (P) gives the pomeron trajectory in terms of the solutions of the first. Starting then from the empirical information on the reggeon intercept ( α R∼0.5) and the t-dependence of the triple-reggeon vertex obtained in inclusive reactions, one is able to calculate the strength of reggeon couplings g and the parameters of the pomeron by solving these equations. Two approximate solutions are given, one asymptotically and one at finite energies. The first gives g = 8.6, α P(0) = 1.12 and α′ P(0) = 0.1 GeV −2 while the second gives g = 7.0, α P(0) = 0.95 and α′ P(0) = 0.5 GeV −2. These are to be compared with the empirical values g∼6.3, α P(0)∼1.0 and α′ P(0)∼0.25 GeV −2. In addition, one predicts the relative normalisation of the pomeron and reggeon propagators at t = 0 to be P R = 1.0 which is quite close to the values between 0.9 and 1.2 obtained from phenomenological fits to σ T. The pomeron pole is generated here as the shadow of amplitudes which are dominated by the multiperipheral production of resonant clusters. A crude estimate with our solution yields at NAL-ISR energies an average charge multiplicity of about 2.3 per cluster as compared with the value of 2.2±0.2 obtained from a recent experiment.

Scaling in pp elastic scattering

Abstract Various scaling laws such as d σ d t ∼ s −n ƒ(z) are tested against the large |t| pp elastic scattering data including that from ISR. We draw the following tentative conclusions. (a) The ISR data are not incompatible with scaling for |t| > 2.4 GeV2. (b) This scaling seems to be aroperty of the P ⊗ P cut not the P (pomeron) pole. (c) But the power n seems to decrease from about 11.5 at z = 0 to 9 or less at z = 0.99 (at large s) which could be due to the Landshoff diagram or eikonalisation becoming important, making scaling just a low energy phenomenon. (d) Though ƒ(z) has a fairly simple structure it does not seem to be directly related to the proton's electromagnetic form factor.