# Presentation: 035217

## The Present Situation of the Odderon Intercept -Experiment, Theory and Phenomenology

*Basarab Nicolescu*
*LPNHE, CNRS and University of Paris 6, France*

- September 27-29, 2005

- BNL, Odderon Searches at RHIC

- Basarab Nicolescu

## I will not make make an historical review.I already presented such reviews in the past:EDS 1991, Vancouver 1998, EDS 1999

- Just a reference:
- Basarab Nicolescu, « The Odderon - past, Present and Future », *Nucl. Phys.* (Proc. Suppl.) **25B** (1992) 142
- « Future » for me, in 1992, was RHIC and LHC.
- RHIC is now « the present », while LHC is still « the future ».
- Here : a review on the odderon intercept, a crucially important information for RHIC experiments.

## In fact, the situation of the Odderon was already nicely summarized in 1881 by Odilon Redon (Kazunori Itakura, private communication, 2005)

## My own contribution: « Odderon » is just an anagram of « Od. Redon ».

- (1840 - 1916)

## Question: how many analytic forms of the Odderon are allowed by the general principles - analyticity, unitarity and positivity ?

- Answer: an infinite number, but in a restricted class of functions

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## The most pedagogical way of visualising the restrictions introduced by general principles is, I think, to consider the following toy model for the even-under-crossing amplitude F+(s,t) and for the odd-under-crossing amplitude F-(s,t), valid at t = 0 and high s:

- and

- (an overall scale factor is, of course, assumed)

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## Cornille showed in 1973 that analyticity, unitarity and positivity of the total cross-sections imply

- The restrictions induced by the general principles are visualized in the Cornille plot (+, -)

## Slide 8

- Basarab Nicolescu

- BNL, Odderon Searches at RHIC

## Interesting particular cases:

- Odderon as simple Regge pole

- The minimal Odderon

**N.B.**

- Basarab Nicolescu

- BNL, Odderon Searches at RHIC

## I love, of course, the LN point (b+ = 2, b- = 2) and I hope that Leszek, Elliot and maybe Lev also love this point in the graph.

- My preference is, first of all, based on esthetics:

- The maximal Odderon embodies the old maximality principle of strong interactions: strong interactions are as strong as possible
- The maximal Odderon corresponds to a nice symmetry of the analytic behaviour of *F**+* and *F**-*

## The maximal Odderon is in agreement with a nice philosophical theorem of Leibniz (Hans Guenter Dosch, private communication, 2003)

*« I have reasons to believe that any arbitrary event will not be embodied in the great Universe... But I am convinced that any event, compatible with the perfect harmony of the Universe, will be embodied. »*
*Leibniz, New Essays 3, IV,12*

- So, I keep being convinced, from 32 years now, that experimentalists will find the maximal Odderon. But I will be not totally unhappy if they will find another type of Odderon.

## EXPERIMENTAL EVIDENCE FOR THE ODDERON

**EXPERIMENTAL EVIDENCE FOR THE ODDERON**

- a.  Strong evidence for the non-perturbative Odderon

- A. Breakstone et al., *Phys. Rev. Lett.* **54** (1985) 2180.
- S. Erhan et al., *Phys. Lett.* **B152** (1985) 131.
- Data obtained in one week, just before ISR was closed.

- 1985: Experimental discovery at ISR of a difference between
- in the dip-shoulder region

## in the region

- 1.1 < | t | < 1.5 GeV2

**99.9 % confidence level**
- for this Odderon effect

- Basarab Nicolescu

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## Phenomenology:

- P. Gauron, E. Leader and B. Nicolescu, *Phys. Lett.* **B238** (1990) 406 ; *Nucl. Phys.* **B299** (1988) 640

- Result: very good fit of all existing       and *pp* data

- + = 2 ± 0.005, - = 2 ± 0.05

- GLN model:

- Basarab Nicolescu

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## This is evidence for the non-perturbative Odderon

- N.B.: The region in t where the Odderon effect appears  t quite small  Regge approach is valid

- Basarab Nicolescu

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## A. Donnachie and P.V. Landshoff, Nucl. Phys. B244 (1984) 322

- The evolution of *(d****/dt)* with *s* favours the maximal Odderon.

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## b. Moderate evidence for the non-perturbative Odderon 

- D. Hill et al., Phys. *Rev. Lett.* **30** (1973) 239
- P. Bonamy et al., *Nucl. Phys.* **52B** (1973) 392

- to pL = 40 GeV/c

- D. Apokin et al., *Z. Phys.* **C15** (1982) 293

## Namely, the polarization goes from positive values at small t (0 < | t | < 0.5 GeV2) at pL = 5 GeV/c to negative values at pL = 40 GeV/c (a new zero appears in the polarization. This is compatible with the maximal Odderon.

- D. Joynson, E. Leader, C. Lopez and B. Nicolescu, *Nuovo Cimento Lett.* **15** (1976) 397
- P. Gauron, E. Leader and B. Nicolescu, *Phys. Rev. Lett.* **52** (1984) 1952

- Namely, the polarization goes from positive values at small t (0 < | t | < 0.5 GeV2) at pL = 5 GeV/c to negative values at pL = 40 GeV/c (a **new zero** appears in the polarization. This is compatible with the maximal Odderon.

- Basarab Nicolescu

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## Remarks:

-  the phase of the maximal Odderon is radically different from those of Regge poles  strong interference effects
-   + ' can not explain the change in shape of the polarization
-  new dynamical zero: cancellation between   ' and   Odderon terms
-  the position of this zero moves towards t = 0 when energy increases and the polarization becomes more and more negative (dominance of   Odderon term).
-  This Odderon **is not** the perturbative QCD Odderon, whose quantum numbers are those of the vacuum (except C)
- This Odderon has the  quantum numbers IG(JPC)=1+(1- -)

- Basarab Nicolescu

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## c. Weak evidence for the non-perturbative Odderon

- A strange effect is seen in the UA4/2 *dN/dt* data at      = 541 GeV, namely **bump** at

- UA4/2 Coll. C. Augier et al., *Phys. Lett.* **B316** (1993) 448

- Maurice Haguenauer agrees that this bump is significantly present in the data (private communication, 1997).
- Strangely enough, nobody remarked this strange effect, except us (P. Gauron, B. Nicolescu and O. Selyugin).

## Slide 21

- Basarab Nicolescu

- BNL, Odderon Searches at RHIC

## Theoretical interpretation of the « bump »:

- P. Gauron, B. Nicolescu and O. Selyugin, Phys. Lett. **B397** (1997) 305

**Oscillations** of a very small period due to the Auberson-Kinoshita-Martin (AKM) theorem (for the *F**+* amplitude) :
- G. Auberson, T. Kinoshita and A. Martin, *Phys. Rev.* **D3** (1971) 3185
- Generalization for the *F**-* amplitude:
- P. Gauron, E. Leader and B. Nicolescu, *Nucl. Phys.* **B299** (1988) 640

## d. Negative evidence for the Heidelberg Odderon

- Heidelberg BDBN Odderon:

- E. R. Berger, A. Donnachie, H. G. Dosch and O. Nachtmann, *Eur. Phys. J.* **C14** (2000) 673
- A. Donnachie, H. G. Dosch and O. Nachtmann, hep-ph/0508196

- in the Stochastic Vacuum Model (SVM) of Dosch and Simonov.
- Search for photoproduction of C = +  mesons (0, f2, a2)

- Data : H1 Coll., C. Adloff et al., Phys. Lett. **B544** (2002) 35

## N.B. : The Heidelberg Odderon is a simple Regge pole

**N.B. : The Heidelberg Odderon is a ****simple Regge pole**

- GLN, *Phys. Lett.* **B238** (1990) 406

-  The coupling of the Odderon pole is compatible with 0. Why ? Contribution only to Re F  shifts  - values by a constant amount from the best fit.

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## Conclusion of this section on experiment vs. phenomenology

- Conclusion of this section on **experiment vs. phenomenology**

- only few experimental evidences for the non-perturbative Odderon: this is not a paradox, because experimentalists looked till now only in channels where the Odderon is hidden by the huge Pomeron contribution
- no (yet) experimental evidence for the perturbative Odderon, which nevertheless has a much firmer - perturba-tive QCD - status ! This situation is quite paradoxical, but it will certainly change in the future
- many proposals already made for looking for both non-perturbative and perturbative Odderon in the appropriate channels. In this context, the RHIC polarization will certainly bring major (good) surprises.

- Basarab Nicolescu

- BNL, Odderon Searches at RHIC

## THEORY

- Odderon - major object of QCD.
- It was (theoretically) rediscovered both in QCD and in CGC (Color Glass Condensate).
- So, it has to be found.
- If not, QCD might be wrong:

- Odderon is a crucial test of QCD.

**THEORY**

- Basarab Nicolescu

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## There are two Odderon solutions found in QCD(two different classes of functions):

**There are two Odderon solutions found in QCD****(two different classes of functions):**

- 1. R. A. Janik and J. Wosiek, *Phys. Rev. Lett.* **82** (1999) 1092

- The same solution found, in a different formalism by M. A. Braun, P. Gauron and B. Nicolescu, *Nucl. Phys.* **B542** (1999) 329

**Odd(0) = 0.94

**Odd(0) = 0.96

*** *= 0.22269 

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## Solution corresponding to an intercept exactly equal to 1

- 2. J. Bartels, L. N. Lipatov and G. P. Vacca, *Phys. Lett.* **B477** (2000) 178.

**Odd(0) = 1

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## BLV solution is, of course, more spectacular, because it persists at very high energies, while the JW solution vanishes at very high energies.

- However, the JW and BLV Odderons are coupled in a different way to external particles - e.g. BLV couples to the impact factor *  c, while JW does not couple.

- N.B. Both JW and BLV Odderons ARE NOT simple poles: cuts in the complex angular momentum plane. « Intercept » means here the beginning of the cut.

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## THE ODDERON INTERCEPT FROM SPECTROSCOPY

**THE ODDERON INTERCEPT FROM SPECTROSCOPY**

- There are several calculations, all indicating a **low** intercept.

- However, the way in which this intercept is identified in lattice calculations is questionable.

- H. B. Meyer and M. J. Teper, *Phys. Lett.* **B605** (2005) 344
- H. B. Meyer, PhD thesis at Oxford, hep-lat/0508002

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## The authors get a 1- - state with mass

- The authors get a 1- - state with mass
- m1 = 3.24 GeV
- and a 3- - state with mass
- m3 = 4.33 GeV

- By drawing a straight line
- (t) = (0) + 't
- through these states, they get
- and
*** *'Odd = 0.24 (GeV)-2
- (near the value of 'Pom)

**Odd(0) = -1.54

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## However, the problem is the following: if Odd = 1, then obviously the state 1- - can not belong to the leading trajectory - the first state is 3- - 

- However, the problem is the following: if **Odd = 1, then obviously the state 1- - **can not** belong to the leading trajectory - the first state is 3- -

- In this case
- and therefore, the 1- - state belongs to a trajectory with intercept **-0.12**  i.e. it is on the first **daughter** trajectory.

**Odd = 1

** ' = 0.11

- Check of all this: calculation of the mass of 5- - (not yet done)

**Odd = -1.54, 	*** *'Odd = 0.24 	 	m5 = 5.22 GeV
**Odd = 1, 	*** *'Odd = 0.11	 	m5 = 6.03 GeV

- Basarab Nicolescu

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## TWO REMARKS :

- I do not see why the slope of the Odderon trajectory has to be the same as the slope of the Pomeron trajectory : **string tension is different**, in principle, in the 2 constituent-gluons case (Pomeron) as compared with the 3 constituent-gluons case (Odderon). The argument of Kaidalov and Simonov (2000) - analogy between diquarks and digluons - does not seem convincing.
- One intriguing theoretical possibility:
- 	**If the maximal Odderon is the final answer,** the problem of high or low intercept of the oddball trajectory is **irrelevant** : the maximal Odderon is anyway dominant at high energies.

- Basarab Nicolescu

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## CONCLUSION

**CONCLUSION**

**THE ODDERON**
- The Odderon, the Odderon,
- one has heard of it.
- It likes to be shy,
- when one wants to detect it.
- Nebulous are all signs,
- a kink in σ must suffice.
- But that data bend here
- Can not convince everybody.
- An η, diffractively appearing
- would most lovely serve us.
- Yet, the search remains very simple,
- one simply does not find it.
- And even if we hope so much,
- in the end as always things are open.
- Carlo Ewerz
- (translation from the original in German)

- OMNE POSSIBILE
- EXISTERE EXIGIT

- RHIC is our hope

- Basarab Nicolescu

- BNL, Odderon Searches at RHIC