Pr

1

ISMD2005. Kromeriz.
Multiplicity structure of inclusive and
diffractive scattering at HERA.

Benoît DELCOURT, L.A.L. Orsay (Fr.), on
behalf of H1 and Zeus collaborations.
Comparison of H1 and Zeus results on
multiplicities.
A study by Zeus on multiplicities in ep vs ee-
and pp.
Dependence of multiplicities upon various
variables in DIS and diffractive DIS (DDIS).
Does KNO scaling hold for DIS and Diffractive DIS?
2

Comparison of H1 and Zeus results on
multiplicities.

• Requirements of H1 and Zeus analysis.
• H1 1994(1.3 pb-1) H1
  2000(41pb-1) Zeus 96-97(38.6pb-1)
• For events
• Ee gt12GeV
  gt12GeV
• Z of vertex lt30cms
  lt30cms
• y 0,05ltylt0.65
  0.04ltylt0.95
• Q2 gt10GeV2 gt5GeV2
  gt25GeV2
• For tracks
• Pt gt100 MeV/c
  gt150MeV/c
• q 15ltqlt165
  deg. 20ltqlt160 deg.
• Corresp. hlab -2lt hlab lt2.
  -1.75lt hlab lt1.75

3

Photon region in the hadronic center of mass
frame. W total energy in this frame.
ltnchgt

ZEUS, 96_97,Preliminary.
Ariadne
Lepto

Good agreement

4

• A study of Zeus of multiplicity on ep vs pp and
  ee-.

1. Study in the HCM frame high total energy.
2. Study in the Breit frame low total energy.

5

1.Hadronic center of mass frame, HCM.
W2Q2(1-x)/xmp2.

p
g
Photon region
Proton region
Zeus
M.C. Ariadne
6

2.Breit frame2xPprotonq0.
Current region
Target region
N

For comparison to ee-, replace Q2 by s and
multiply ltnchgt by 2 only one final quark instead
of 2. Also gluon radiation -? many hadrons lost
into the target region instead of Q, better use
the total energy seen in current region Ecurrent
.
Zeus
7
Differences of HCM and Breit frames.

• The energy scale in HCM frame W,
• in Breit frame Q.
  
• Q ltW.
• Why this difference?
• In Breit frame, many hadrons are rejected
  because in target region these are taken into
  account in HCM frame.

8

Multiplicities vs energy scale for ee-,ep,pp

9

Conclusions of this study (Zeus)
-- Measurement in current region of Breit frame
and photon region of HCM frame have to be
multiplied by 2. --There is agreement with ee-
at low and high energy and with the pp results
which are plotted vs Qhad (with the leading
particles removed). --All data agree with the
same M.C.(Ariadne).
10
Dependence of multiplicities upon various
variables in DIS and diffractive DIS (DDIS).

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Do the multiplicities depend upon x and Q2 at
fixed invariant mass, in the lab., of the had.
final state,Meff?

Meff is measured with the calorimeter, restricted
to the Central tracker acceptance.
ARIADNE.
Answerno.
Meff
100
10
12

Q2 150- 1200 GeV2 50- 150 GeV2 25-50 GeV2
X Bj 6-12. 10-4 1.2-2.4 10-3 2.4-10 10-3
10-2-10-1
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Diffractive DIS (DDIS).


Q2/(Q2Mx2)
xBj/b
Regge factorisation
Reggeon model Pomeron is replaced by mesons.
14

H1 2000 data, 46.6 pb-1.

Acceptance vs h hgt1,which restricts the photon
region (hgt0) , both in DIS and DDIS
15

Do the multiplicities depend upon Q2 when W is
fixed?

Answer neither in DIS nor in DDIS. There is an
(expected) dependence on MX in DDIS.
16

Do the DDIS multiplicities depend upon b when Mx
is fixed? No!

p
p
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ltngt dependence on W at fixed Mx in DDIS.

The Pomeron alone does not describe the reality.
One has to consider also a Reggeon, which is
most important at large Mx.
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Does KNO scaling hold for DIS and DDIS?

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KNO scaling in ee-.

20

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Approximate (non KNO) models when ltngt does not
vary much.

• Poisson law large number independent parton
  emitters in fragmentation chain. Moments Fq like
  F2ltn.(n-1)gt/ltngt2 should be 1 they are known not
  to be 1 in DIS, but no new analysis in DIS, and
  no analysis ready in DDIS.
• Negative binomial distribution, NBD. Parameter k
  number of identical independent parton emitters.

For k large -gt back to Poisson.
22

Comparison with Poisson law with ltngt4 (black
squares)

ltnneggt3.6
ltnneggt3.8
ltnneggt4.2
ltnneggt4.5
Poisson large number of independent emitters in
the hadronisation chain.
23


Comparison with Poisson ltngt5.0(black squares)

24

Comparison with NBD law with ltngt4.0, k10 (red
squares)

ltnneggt3.6
ltnneggt3.8
ltnneggt4.2
ltnneggt4.5
25

Comparison with NBD law with ltngt4.0, k100 (blue
squares)

ltnneggt3.6
ltnneggt3.8
ltnneggt4.2
ltnneggt4.5
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Conclusion of this study of KNO scaling.

• Distribution of ltngtPn
• -- in DIS, not so far from Poisson, even if
  we know it is not exactly Poisson-like (moments)
  for NBD, there is a need of a large number of
  independent parton sources .
• -- DIS and DDIS seem to have similar
  behaviours.

27

ISMD2005. Kromeriz.
Conclusions.
Comparison of H1 and Zeus results on
multiplicities. Agreement.

A study by Zeus on multiplicities in ep vs ee-
and pp.Agreement, in a large energy range, if
one uses W in HCM frame and Ecurrent in Breit
frame .
Dependence of multiplicities upon various
variables in DIS and diffractive DIS (DDIS). At
fixed W or Meff, no dependence of ltngt on x (b)
and Q2. Confirmation that the Pomeron is not
enough to describe all DDIS, need something else
(Reggeon?) at large Mx.
28

Does KNO scaling hold for DIS and DDIS? Yes.
But the Poisson law, which does not obey KNO
scaling, is not very far from reality.

29

Moments Fq


(should all be 1 for Poisson law, and Energy
independent for KNO scaling.)

Zeus, P.L.B 510(2001)
F2
1
10
Pt,Gev
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H1, 1994 DIS data,DESY96-160

F2
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H1 Diff. DESY 98-044 Eur.Phys.J. Hadronic system
X. Left both hemisph. Right separate
hemisph. For H1, the abscissa is Mx.


ltngt

D
F2