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Regge poles fight backRegge poles fight back

Enrico PredazziEnrico Predazzi

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II. Historical InterludeII. Historical Interlude

• In the SixtiesIn the Sixties (operating the (operating the proton accelerators at Berkeley and proton accelerators at Berkeley and CERN at pCERN at pℓℓ~30 GeV and Serpukhov ~30 GeV and Serpukhov at pat pℓℓ~50 GeV), a blend of:~50 GeV), a blend of:

• i) Rigorous theorems by Froissart, i) Rigorous theorems by Froissart, Martin, Khuri, Bessis, Auberson, Martin, Khuri, Bessis, Auberson, Kinoshita, Cornille, Pomeranchuk Kinoshita, Cornille, Pomeranchuk and Russian school.and Russian school.

• ii) Approximations and empirismii) Approximations and empirism

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• iii) S-Matrix theory, Dispersion relations iii) S-Matrix theory, Dispersion relations (analyticity), crossing and unitarity, (analyticity), crossing and unitarity,

• iv) Complex angular momenta (WSR iv) Complex angular momenta (WSR representation)representation)

• v) Eikonal approximationv) Eikonal approximation

• vi) Mandelstam representationvi) Mandelstam representation

• vii) Veneziano model vii) Veneziano model

Clean and clever mathematics, muddy Clean and clever mathematics, muddy physics, physics,

growing multiplicities and increasing growing multiplicities and increasing

complication of exclusive reactions (3n-4 complication of exclusive reactions (3n-4

variables for n-body final states)variables for n-body final states)

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• In the SeventiesIn the Seventies (ISR, FNAL, (ISR, FNAL, CERN) attention turns to inclusive CERN) attention turns to inclusive reactionsreactions

A + B → C + XA + B → C + X

• where X denotes a bunch of where X denotes a bunch of unresolved particles unresolved particles

• (3 variables instead of 3n-4). (3 variables instead of 3n-4).

• This can be diffractive according to This can be diffractive according to the general prescription that no the general prescription that no quantum numbers be exchangedquantum numbers be exchanged

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• i) Mueller generalized i) Mueller generalized optical theoremoptical theorem

• ii) Decline of interest in ii) Decline of interest in standard diffractive physicsstandard diffractive physics

• iii) Rise of interest in DIS iii) Rise of interest in DIS (Bjorken)(Bjorken)

• iv) First proposal od QCDiv) First proposal od QCD

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• In the Eighties In the Eighties (CERN S(CERN SpppS, pS, HERA, Tevatron planned) HERA, Tevatron planned)

• Begins the resurgence of Begins the resurgence of interest in diffractive physicsinterest in diffractive physics

• Perturbative picture of the Perturbative picture of the Pomeron as made of gluon Pomeron as made of gluon ladders (Lipatov, Fadin etc.)ladders (Lipatov, Fadin etc.)

• Ingelman & Schlein suggest that Ingelman & Schlein suggest that seminclusive ep physics (at seminclusive ep physics (at HERA) is relevant for diffractionHERA) is relevant for diffraction

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• In the NinetiesIn the Nineties (HERA, Tevatron, LEP, LHC (HERA, Tevatron, LEP, LHC planned)planned)

• Full come back of diffraction through small x Full come back of diffraction through small x physics (rise of Fphysics (rise of F22(x, Q(x, Q22) at low x values)) at low x values)

• Pomeron (BFKL etc. in agreement with the Pomeron (BFKL etc. in agreement with the data)data)

• Donnachie & Landshoff Donnachie & Landshoff

σσtottot ~ A s ~ A sε+1ε+1 + + OO(s), (s),

in principle violates Froissart’s theorem in principle violates Froissart’s theorem not in practice and very economical. not in practice and very economical.

BFKL corrections BFKL corrections

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• In the first decade of the third In the first decade of the third millenniummillennium (RHIC, Tevatron and (RHIC, Tevatron and great expectations waiting for LHC)great expectations waiting for LHC)

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

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III. Regge poles III. Regge poles resurrectedresurrected

• 1. Diffraction in Deep Inelastic 1. Diffraction in Deep Inelastic ScatteringScattering

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

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• Classical DIS is the inclusive production in Classical DIS is the inclusive production in lepton proton (see figure …)lepton proton (see figure …)

(1.1) ℓ(k) + h(p) → ℓ'(k') + X(1.1) ℓ(k) + h(p) → ℓ'(k') + X

where, as already mentioned, X is a where, as already mentioned, X is a system of particles which are left system of particles which are left unresolved (“summed over”). unresolved (“summed over”).

This process was very popular since it This process was very popular since it provided conclusive evidence that hadrons provided conclusive evidence that hadrons are made of seemingly pointlike are made of seemingly pointlike constituents called constituents called quarks quarks (or (or partonspartons) and ) and it became extremely interesting since it it became extremely interesting since it provided a direct clue to measuring the so-provided a direct clue to measuring the so-called called structure functions structure functions of the proton.of the proton.

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• It was, however, observed by Ingelman It was, however, observed by Ingelman and Schlein that, if we look at the semi and Schlein that, if we look at the semi inclusive reaction (see figure …)inclusive reaction (see figure …)

(1,2) (1,2) ℓ(k)+N(p) → ℓ'(k')+N'(p')+ X(Jℓ(k)+N(p) → ℓ'(k')+N'(p')+ X(JPCPC =1¯ =1¯ ¯)¯)

• in which the two hadrons in the initial in which the two hadrons in the initial and final state are the same (i.e. have and final state are the same (i.e. have the same quantum numbers), in accord the same quantum numbers), in accord with our general definition of a with our general definition of a diffractive process, this is one and diffractive process, this is one and Pomeron dominance is therefore Pomeron dominance is therefore expected.expected.

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• A somewhat different semi inclusive A somewhat different semi inclusive diffractive reactions could also be diffractive reactions could also be chosen like vector productionchosen like vector production

(1.3) (1.3) ℓ(k) + N(p) → ℓ'(k') + V(1¯ ¯) + Xℓ(k) + N(p) → ℓ'(k') + V(1¯ ¯) + X

• or quasi-elastic or quasi-elastic

(1.4) (1.4) ℓ(k) + N(p) → ℓ'(k') + N'(p') + V(1¯ ℓ(k) + N(p) → ℓ'(k') + N'(p') + V(1¯ ¯)¯)

• All these reactions have been studied All these reactions have been studied using a different diffractive signature using a different diffractive signature tool proposed by Bjorken i.e., as we tool proposed by Bjorken i.e., as we have already commented) have already commented) large rapidity large rapidity gapsgaps..

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

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4. Hard diffraction (just few 4. Hard diffraction (just few words)words)

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

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Mueller generalized optical theorem

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

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Triple Regge Couplings

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• It’s easy to show using the full It’s easy to show using the full machinery recalled in these days, machinery recalled in these days, that the inclusive Mthat the inclusive M2 2 dependence dependence predicted from triple pomeron for the predicted from triple pomeron for the inclusive cross section behaves like inclusive cross section behaves like 1/M1/M2 2 and, once again, this prediction and, once again, this prediction is met by the data (see figure) but, is met by the data (see figure) but, once more, we will not elaborate on once more, we will not elaborate on this point which would require more this point which would require more time and a much larger digression time and a much larger digression than we can give itthan we can give it

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

• V. BARONE and E. PREDAZZIV. BARONE and E. PREDAZZI

High energy particle diffractionHigh energy particle diffraction (Springer Texts and monographs in (Springer Texts and monographs in physics) ISBN 3-540-42107-6 (2002)physics) ISBN 3-540-42107-6 (2002)

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5. b-Unitarity5. b-Unitarity• Again jus a few words on an issue which Again jus a few words on an issue which

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

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6. Conclusions…6. Conclusions…

• No clonclusions for such a lively, No clonclusions for such a lively, exciting and ever selfrenovating exciting and ever selfrenovating field.field.

• See you to the next school.See you to the next school.