Download Nominal versus Effective Energy

OPENING LECTURE
THE EFFECTIVE ENERGY AND QCD
Antonino Zichichi
ABSTRACT
The Effective Energy allows to discover the existence of universality
features in the multihadronic systems produced in strong, electromagnetic and
weak interactions. These features manifest themselves in the: fractional
momentum distribution d ⁄ dx, average number of charged particles nch,
ratio of the “charged” over the total energy, transverse momentum distribution
d ⁄ dp2t , normalized transverse momentum distribution, event planarity, two–
particle correlations, scale–breaking effects, forward–backward correlation. It is
thanks to the Effective Energy that a difference between “gluon” and “quark”
hadronization processes has been established.
The Effective Energy allows to discover the “quantum number flow”,
from an initial to a final state, no matter if the interaction is strong,
electromagnetic or weak and to put on the same basis high and low transverse
momentum physics.
The Effective Energy is a QCD non–perturbative effect whose
theoretical explanation is still to be found.
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OPENING LECTURE
THE EFFECTIVE ENERGY AND QCD
Antonino Zichichi
TABLE OF CONTENTS
Introduction 
1 Nominal versus Effective Energy 
1.1 The QCD Effective Energy 
1.2 The “QCD light” 
2 The Hidden Side of QCD and the Effective Energy 
3 The Universality Features 
3.1 The fractional momentum distribution d ⁄ dx 
3.2 The average number of charged particles nch 
3.3 The ratio of the “charged” over the total energy 
3.4 The transverse momentum distribution d ⁄ dp2t 
3.5 The normalized transverse momentum distribution 
3.6 The event planarity 
3.7 The two–particle correlations 
3.8 The scale–breaking effects 
3.9 The forward–backward correlation 
3.10 Where the difference is 
4 The Quantum Number Flow 
4.1 Basics on the quantum number flow 
4.2 Flow of quantum numbers in strong interactions 
4.3 Flow of quantum numbers in electromagnetic and weak
interactions 
4.4 The quantum numbers flow in (e+e) annihilation 
4.5 Flow of quantum numbers. Conclusions 
5 The End of a Myth: HighpT Physics 
5.1 Compare high and lowpT (pp) physics with DIS 
6 Conclusions and Future 
References 
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OPENING LECTURE
THE EFFECTIVE ENERGY AND QCD
Antonino Zichichi
INFN and University of Bologna, Italy
CERN, Geneva, Switzerland
Introduction.
It is with gratitude that I take part in this special Session in honour of
Professor Vladimir N. Gribov. It was the year 1980 when for the first time I
interacted with Gribov. He is the theorist who first emphasized the importance
of the “Effective Energy” in the study of the multihadronic systems produced at
ISR at the “nominal energy” ( s )pp = 62 Gev. This “nominal energy” produces
in fact a wide spectrum of “Effective Energies” as shown in Fig. 1.
Fig. 1: Ranges of Effective hadronic Energy available for particle production (2Ehad) for a
given ISR incident energy Einc. These ranges depend on the proton xF range selected
as shown in Fig. 2. The values of ( s )pp are also shown.
The first paper on the use of the Effective Energy for the analyses of the
multihadronic systems produced at ISR [1] allowed to put on the same basis
the differential cross sections for particle production in purely hadronic
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interactions (pp) and in purely electromagnetic interactions (ee), as reported
in Fig. 5 of § 1.2.
Let me recall that, before the discovery of the Effective Energy, the only
candidates to establish a link between (ee) annihilations, (DIS) processes and
purely hadronic processes were highpT (pp) interactions.
A systematic study at the ISR of the final states produced in lowpT (pp)
interactions in terms of the Effective Energy has allowed to compare the
multihadronic final states produced with the results obtained in the processes
mentioned above and listed below:
(ee) annihilations
(DIS) processes
highpT (pp) interactions.
Thus the multihadronic systems produced in lowpT (pp) interactions
compare well with those produced in the processes studied at the various
laboratories facilities and collaborations indicated below:
Laboratories
CERN
Process
SLAC, DORIS, PETRA
(ee) – Standard
SPS/EMC
(DIS)
ISR (AFS)
(pp)
SPS Collider (UA1)
( p p)
PETRA/TASSO
(ee) – Effective Energy .
The structure of my lecture will be as follows:
1 – Nominal versus Effective Energy
2 – The Hidden Side of QCD
3 – The Universality Features
4 – The Quantum Number Flow
5 – The End of a Myth: HighpT Physics
6 – Conclusions and Future.
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Transverse physics
1 –
1.1 –
Nominal versus Effective Energy.
The QCD Effective Energy.
When there are two protons colliding with energy
E1 and E2 , with E1 = E2 = Einc ,
the total “nominal” c.m. energy available in this collision is generally taken to
be
s pp = 2Einc .
However, we say that this is not the right energy to use in analysing the
process. As shown in Fig. 2, after the collision, the two incoming protons keep,
on the average, a large fraction of the available energy and play a privileged role
in the energy–momentum sharing among the particles in the final state.
Fig. 2: Protons and pions xF distributions in (pp) interactions. The range of physics of the
Effective Energy is shown. Central and diffractive regions are also shown.
Our statement is that you have to subtract the energy carried by each
proton in the final state in order to obtain, on each hemisphere, the Effective
Energy available for particle production. We call it E1,had2 . The reason for this
splitting into two terms will soon be clear.
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The range of hadronic Effective Energies varies according to:
i) the xF cut one applies to the leading proton;
ii) the total energy ( s ) available in the pp collision.
For example, one can select the leading proton in the range
0.35 ≤ xF ≤ 0.86 .
In this case, the Effective hadronic Energy available for various values of s
in the proton–proton centre–of–mass system is as follows:
 s  30 GeV : 4.2  19 GeV 


Nominal (pp) Energy  s  44 GeV : 6.2  28 GeV  Effective Energy ranges.
 s  62 GeV : 8.7  40 GeV 


The QCD Effective Energy is based on the following conjectures:
1) There exists a relativistic invariant quantity:
qinc
tot 
2
this
q 
in c 2
to t

 q1inc  q inc
2

2
;
 is an effective initial total (mass)2.
2) This initial
qinc
tot 
2
splits into two effective hadronic systems, described by
q 1had  q1inc  q1lead
q 2had 

qinc
2


q lead
2 
where q lead
and q lead
are the quadrimomenta of the two protons in each final
1
2
state (lead stands for leading) and q 1had , q 2had are the two quadrimomenta
associated with the two multihadronic systems produced in each hemisphere
(1, 2). The two q 1had and q 2had are totally uncorrelated (see Fig. 3).
3) The two hadronic systems described by q 1had and q 2had are
projected into the total quadrimomentum
;
q inc
tot
 
this is how E 1had and E 2had come out:
q 1had  q inc
tot
q inc
tot 
2
and
c
q 2had  q in
tot
q intotc 
2
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 E1had
 E had
.
2
The physics of each multihadronic system, associated with each
quadrimomentum q 1had and q 2had , allows the validity of the following formulae:
had
 E1
had
 E2
E1
E2
inc
 E1
lead
inc
 E2
lead
.
These are the key quantities for the Universality Features of the
multihadronic states produced. As mentioned above, we have proved that these
two quantities are totally uncorrelated. The data are reported in Fig. 3.
The proof that q1had
and q had
are totally uncorrelated
2
Fig. 3: Scatter plot of the fractional energies of the two leading
lead
lead
in c
lead
protons, x1 , 2  E 1 , 2 E1 , 2 , in the range 0.4  x1, 2 < 0.9, at the (pp) c.m. energy
s pp = 62 GeV.
 
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From what precedes it is clear how, in (pp) interactions, you can work
out the right quantities to conform with DIS or (ee):
(ee) (like) quantities
q had
tot 
2

q 1had

had 2
 q2

 s ehad
 e
2q had  q had
had
tot
x R pp  had
had
q tot  q tot
(1)
(2)
DIS (like) quantities
W 2 pp
had

 q1had  q inc
2

2
q had
 q inc
had
i
2
Z pp  had
q 1  q inc
2
(3)
(4)
where q had
is the quadrimomentum of the ith particle in the q 1had multihadronic
i
final state. Notice that in the ee system, the total energy available in the
centre of mass system is


2
inc
inc
q1  q 2
e e 

 ,
had
q tot
2
(5)
but for DIS the total available energy in the centre of mass is
(W)DIS
as defined above (3).
The Effective Energies put all reactions, be they of the (hadron–hadron)
type such as (pp), or (hadron–lepton) such as DIS, or (lepton–antilepton) such as
(ee), on the same mathematical basis.
This allows Universality Features to show up, as we will see in § 3.
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1.2 –
The “QCD light”.
Let us take pp   + X at the nominal energy ( s )pp = 62 GeV. The
–spectrum is shown in Fig. 4.
p+p   + X
( s ) = 62 GeV
Fig. 4.
This is what Gribov called the “QCD light”. In fact this –spectrum,
when analyzed in terms of Effective Energies, splits up into many spectra, as
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shown in Fig. 5. The reason for this is that in QCD we have quarks and gluons
interacting and producing jets made of many pions.
Fig. 5:
The data are from (pp) interactions using the Effective
Energies indicated as 2Ehad. The lines are best fits to (e+e) data at equivalent energies.
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This is the root of the Universality Features to be discussed in § 3.
And now an important detail of technical nature. In the low–pT range of
proton–proton collisions at the ISR, it was not possible to have C erenkov
counters nor any other system such as time of flight, in order to discriminate
pions from high energy protons. We could only rely on Nature. Nature has
been kind enough to give us a very powerful tool in terms of the behaviour of
the proton in this kind of interaction. In fact, the ratio p/ in pp collisions at ISR
behaves exponentially (see Fig. 6) as a function of x F. If you take, for example,
particles with xF = 0.5, you will have a sample consisting of ~ 85% protons
and ~ 15%  contamination. The ratio p/ scales with . The full errors are
statistical and systematic combined in quadrature. The inner error bars indicate the
statistical uncertainties. The points with the arrows  indicate how the data are
corrected by the introduction of the “Effective Energy”. The black and  points
correspond to our analysis using the Effective Energy. The correction allows all
points to agree with expectations.
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6
–
Conclusions and Future.
The Universality Features are a QCD non–perturbative effect. It will be
interesting to study how the Effective Energy is related to the non–Abelian
nature of the interaction describing quarks and gluon. References and other
details on this topic can be found in the volume edited by Lipatov [5].
Let me say a few words on the future. As you know, I am engaged in the
ALICE experiment where the future of non–perturbative QCD can be
investigated. The experiments with ALICE will allow to study the physics of
open colour without the “colour neutral” conditions imposed by confinement.
The quark gluon plasma will contain not only the “light” proton and the “heavy”
 but also all the states of SU(3)rgb , i.e. the complete QCD world. It will also
be possible to study if other forms of subnuclear matter can be there, in addition
to the plasma of quarks and gluons. Another sector of extreme interest is the
coherent effects in the nuclei–nuclei collisions. Here again the existence of the
Effective Energy in the multihadronic final states could be investigated.
No one is able to make the transition from QCD: the colour–full world
of quarks and gluons to Nuclear Physics: the colour neutral world of mesons
and baryons. The lattice–QCD calculations are at present the only attempt. But
these computations are difficult and have big uncertainties.
Let me close by recalling my question to Gribov and his answer: «Why
is QCD not able to “predict” the Universality Features?» V. Gribov: «I first
need to understand confinement».
Yuri Dokshitzer will report the last attempt of our great friend and leader
in trying to finally understand confinement.
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References.
[1]
Evidence of the Same Multiparticle Production Mechanism in p–p Collisions
as in ee Annihilation
M. Basile, G. Cara Romeo, L. Cifarelli, A. Contin, G. D'Alì, P. Di Cesare,
B. Esposito, P. Giusti, T. Massam, F. Palmonari, G. Sartorelli, G. Valenti and
A. Zichichi
Physics Letters 92B, 367 (1980).
[2]
(UA)5 Collaboration, K. Alpgard et al., Physics Lett. 121B (1983) 209.
[3]
The "Leading"-Particle Effect in Hadron Physics
M. Basile, G. Cara Romeo, L. Cifarelli, A. Contin, G. D'Alì, P. Di Cesare,
B. Esposito, P. Giusti, T. Massam, R. Nania, F. Palmonari, V. Rossi,
G. Sartorelli, M. Spinetti, G. Susinno, G. Valenti, L. Votano and A. Zichichi
Nuovo Cimento 66A, 129 (1981).
[4]
The "Leading"-Baryon Effect in Strong, Weak, and Electromagnetic
Interactions
M. Basile, G. Cara Romeo, L. Cifarelli, A. Contin, G. D'Alì, P. Di Cesare,
B. Esposito, P. Giusti, T. Massam, R. Nania, F. Palmonari, V. Rossi,
G. Sartorelli, M. Spinetti, G. Susinno, G. Valenti, L. Votano and A. Zichichi
Lettere al Nuovo Cimento 32, 321 (1981).
[5]
The Creation of Quantum ChromoDynamics and the Effective Energy
V.N. Gribov, G. 't Hooft, G. Veneziano and V.F. Weisskopf; N.L. Lipatov
(ed), Academy of Sciences and University of Bologna, INFN, SIF; published
by World Scientific Series in 20th Century Physics, Vol. 25, 2000.
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