# Presentation: 648396

## Regge poles  fight back

**Enrico Predazzi**

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## II. Historical Interlude 

**In the Sixties**  (operating the proton accelerators at Berkeley and CERN at pl~30 GeV and Serpukhov at pl~50 GeV), a blend of:
- i) Rigorous theorems by Froissart, Martin, Khuri, Bessis, Auberson, Kinoshita, Cornille, Pomeranchuk and Russian  school.
- ii) Approximations and empirism

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## iii) S-Matrix theory, Dispersion relations (analyticity), crossing and unitarity, 
iv) Complex angular momenta (WSR representation)
v) Eikonal approximation
vi) Mandelstam representation
vii) Veneziano model 
Clean and clever mathematics, muddy physics, 
growing multiplicities and increasing 
complication of exclusive reactions (3n-4 
variables for n-body final states)

- iv) Complex angular momenta (WSR representation)
- v) Eikonal approximation
- vi) Mandelstam representation
- vii) Veneziano model
- Clean and clever mathematics, muddy physics,
- growing multiplicities and increasing
- complication of exclusive reactions (3n-4
- variables for n-body final states)

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## In the Seventies   (ISR, FNAL, CERN) attention turns to inclusive reactions
                      A +  B  →  C  +  X
where X denotes a bunch of unresolved particles 
(3 variables instead of 3n-4). 
This can be diffractive according to the general prescription that no quantum numbers be exchanged

-                       A +  B  →  C  +  X
- where X denotes a bunch of unresolved particles
- (3 variables instead of 3n-4).
- This can be diffractive according to the general prescription that no quantum numbers be exchanged

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## i) Mueller generalized optical theorem
ii) Decline of interest in standard diffractive physics
iii) Rise of interest in DIS (Bjorken)
iv) First proposal od QCD

**ii) Decline of interest in standard diffractive physics**
**iii) Rise of interest in DIS (Bjorken)**
**iv) First proposal od QCD**

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## In the Eighties  (CERN SppS, HERA, Tevatron planned) 
Begins the resurgence of interest in diffractive physics
Perturbative picture of the Pomeron as made of gluon ladders (Lipatov, Fadin etc.)
Ingelman & Schlein suggest that seminclusive ep physics (at HERA) is relevant for diffraction 

**Begins the resurgence of interest in diffractive physics**
**Perturbative picture of the Pomeron as made of gluon ladders (Lipatov, Fadin etc.)**
**Ingelman & Schlein suggest that seminclusive ep physics (at HERA) is relevant for diffraction**

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## In the Nineties  (HERA, Tevatron, LEP, LHC planned)
Full come back of diffraction through small x physics (rise of F2(x, Q2) at low x values)
Pomeron (BFKL etc. in agreement with the data)
Donnachie & Landshoff   
            σtot ~ A sε+1 + O(s), 
   in principle violates Froissart’s theorem not in practice and very economical. 

    BFKL corrections 

- Full come back of diffraction through small x physics (rise of F2(x, Q2) at low x values)
- Pomeron (BFKL etc. in agreement with the data)
**Donnachie & Landshoff   **
**            ****σ****tot**** ~ A s****ε+1**** + *****O*****(s), **
**   ****in principle violates Froissart’s theorem not in practice and very economical. **
**    ****BFKL corrections **

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## In the first decade of the third millennium  (RHIC, Tevatron and great expectations waiting for LHC)
Today’s diffractive physics (take a look  at the program of the school)

- Today’s diffractive physics (take a look  at the program of the school)

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

##  III. Regge poles resurrected 

**1. Diffraction in Deep Inelastic Scattering**
**Regge theory has made a full come back. Together with DL somewhat unexpectedly, this comes from a brilliant twist in a topic, DIS (Deep Inelastic Scattering) that had received little attention from the point of view of diffraction since it had been devoted mostly to unravel the structure of the hadrons**

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## Classical DIS is the inclusive production in lepton proton (see figure ...)
(1.1)    l(k)  +  h(p)  → l'(k')  +  X
   where, as already mentioned, X is a system of particles which are left unresolved (“summed over”). 
This process was very popular since it provided conclusive evidence that hadrons are made of seemingly pointlike constituents called quarks (or partons) and it became extremely interesting since it provided a direct clue to measuring the so-called structure functions of the proton. 

- (1.1)    l(k)  +  h(p)  → l'(k')  +  X
-    where, as already mentioned, X is a system of particles which are left unresolved (“summed over”).
- This process was very popular since it provided conclusive evidence that hadrons are made of seemingly pointlike constituents called quarks (or partons) and it became extremely interesting since it provided a direct clue to measuring the so-called *structure functions *of the proton.

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## It was, however, observed by Ingelman and Schlein that, if we look at the semi inclusive reaction (see figure ...)
 (1,2) l(k)+N(p) → l'(k')+N'(p')+ X(JPC =1 ̄  ̄)
in which the two hadrons in the initial and final state are the same (i.e. have the same quantum numbers), in accord with our general definition of a diffractive process, this is one and Pomeron dominance is therefore expected.

-  (1,2) l(k)+N(p) → l'(k')+N'(p')+ X(JPC =1 ̄  ̄)
- in which the two hadrons in the initial and final state are the same (i.e. have the same quantum numbers), in accord with our general definition of a diffractive process, this is one and Pomeron dominance is therefore expected.

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## A somewhat different semi inclusive diffractive reactions could also be chosen like vector production
(1.3) l(k)  +  N(p)  → l'(k')  +  V(1 ̄  ̄)  + X
or quasi-elastic                
(1.4) l(k) + N(p)  → l'(k') + N'(p') + V(1 ̄  ̄)
All these reactions have been studied using a different diffractive signature tool proposed by Bjorken i.e., as we have already commented) large rapidity gaps.

- (1.3) l(k)  +  N(p)  → l'(k')  +  V(1 ̄  ̄)  + X
- or quasi-elastic
- (1.4) l(k) + N(p)  → l'(k') + N'(p') + V(1 ̄  ̄)
- All these reactions have been studied using a different diffractive signature tool proposed by Bjorken i.e., as we have already commented) *large rapidity gaps*.

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## Slide 13

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## Slide 14

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## Slide 15

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## We will not dig further on this topic which has been widely covered in previous lectures and seminars. Perhaps, it is just worth recalling how one of the shocking “discoveries” of HERA related to this huge chapter, came from the comparison of the “new” low-x data with the then prediction of the models (see figure). Of this shocking discovery (which had been anticipated by some authors) we are still under the spell today, as we have heard.

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## Slide 17

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## 4. Hard diffraction (just few words)

- Hard diffraction has been the queen of the school so that it would be senseless for me to spend more than few worlds on it. Let me just remind a key ingredient which has received little asttention (probably for its being too well known to everybody). This is Mueller generalized optical theorem which, graphically

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## Mueller generalized optical theorem

**Mueller generalized optical theorem**

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## One of the reasons to mention Mueller theorem is the role it has had in promoting the understanding of one of the key ingredients in the resurrection of Regge poles, the so called triple Regge coupling which, again, in graphical terms, reads

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## Triple Regge Couplings

**Triple Regge Couplings**

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## It’s easy to show using the full machinery recalled in these days, that the inclusive M2 dependence predicted from triple pomeron for the inclusive cross section behaves like 1/M2 and, once again, this prediction is met by the data (see figure) but, once more, we will not elaborate on this point which would require more time and a much larger digression than we can give it

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## Slide 23

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## Slide 24

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## For a comprehensive and self contained account of all the major developments that have occurred in the field of hadronic diffraction, let me refer once more to 

V. BARONE and E. PREDAZZI
   High energy particle diffraction (Springer Texts and monographs in physics) ISBN 3-540-42107-6 (2002)

**V. BARONE and E. PREDAZZI**
*   **High energy particle diffraction* (Springer Texts and monographs in physics) ISBN 3-540-42107-6 (2002)

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## 5. b-Unitarity

- Again jus a few words on an issue which is seldom taken up by some people who claim that power law increase of cross sections are a long way from leading to the violation of unitarity. This is true when comparing the energy growth in the usual energy variable but the situation is entirely different when we translate this in the language of the impact parameter repr.

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## Slide 27

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007

## 6. Conclusions...

- No clonclusions for such a lively, exciting and ever selfrenovating field.
- See you to the next school.

- QCD, lowx, Saturation and Diffraction; Copanello

- 1-13 July 2007