Does KNO scaling hold for DIS and Diffractive DIS?

Dependence of multiplicities upon various variables in DIS and diffractive DIS (DDIS).

Comparison of H1 and Zeus results on multiplicities.

A study by Zeus on multiplicities in ep vs e+e- and pp.

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.

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 >12GeV >12GeV|Z| of vertex <30cms <30cmsy 0,05<y<0.65 0.04<y<0.95Q2 >10GeV2 >5GeV2 >25GeV2

For tracks:

Pt >100 MeV/c >150MeV/c

deg.deg.Corresp. lab -2<lab <2. -1.75<lab <1.75

•

AriadneLepto

(prelim.)

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

<nch>

ZEUS, 96_97,Preliminary.

Good agreement

A study of Zeus of multiplicity on ep vs pp and e+e-.

1. Study in the HCM frame: high total energy.

2. Study in the Breit frame: low total energy.

1.Hadronic center of mass frame, HCM.

*

p

Photon region Zeus

W2=Q2(1-x)/x+mp2.

Proton region

M.C.: Ariadne

2.Breit frame:2xPproton+q=0.

N

Zeus

For comparison to e+e-, replace Q2 by s and multiply <nch> 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 .

Currentregion

Targetregion

Differences of HCM and Breit frames.

The energy scale: in HCM frame: W, in Breit frame Q.

Q <W.

Why this difference? In Breit frame, many hadrons are rejected

because in target region; these are taken into account in HCM frame.

Multiplicities vs energy scale for e+e-,ep,pp

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 e+e- 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).

Dependence of multiplicities upon various

variables in DIS and diffractive DIS (DDIS).

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.

Answer:no.

ARIADNE.

10 100Meff

Q2

150-1200 GeV2

50-150GeV2

25-50GeV2

X Bj 6-12. 10-4 1.2-2.4 10-3 2.4-10 10-3 10-2-10-1

Reggeon model: Pomeron is replaced by mesons.

=Q2/(Q2+Mx2)

=xBj/

Diffractive DIS (DDIS).

Regge factorisation

H1 2000 data, 46.6 pb-1.

Acceptance vs *: *>1,which restricts the photon region (*>0) , both in DIS and DDIS

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.

Do the DDIS multiplicities

depend upon when Mx is fixed? No!

p

p

<n> 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.

Does KNO scaling hold for DIS and DDIS?

KNO scaling in e+e-.

Approximate (non KNO) models when <n> does not vary much.

• Poisson law: large number independent parton emitters in fragmentation chain. Moments Fq like F2=<n.(n-1)>/<n>2 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 -> back to Poisson.

Comparison with Poisson law with <n>=4 (black squares)

<nneg>=3.6<nneg>=3.8<nneg>=4.2<nneg>=4.5

Poisson: large number of independent emitters in the hadronisation chain.

Comparison with Poisson <n>=5.0(black squares)

•

Comparison with NBD law with <n>=4.0, k=10 (red squares)

<nneg>=3.6<nneg>=3.8<nneg>=4.2<nneg>=4.5

•

Comparison with NBD law with <n>=4.0, k=100 (blue squares)

<nneg>=3.6<nneg>=3.8<nneg>=4.2<nneg>=4.5

Conclusion of this study of KNO scaling.

• Distribution of <n>Pn:

-- 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.

Dependence of multiplicities upon various variables in DIS and diffractive DIS (DDIS). At fixed W or Meff, no dependence of <n> on x and Q2. Confirmation that the Pomeron is not enough to describe all DDIS, need something else (Reggeon?) at large Mx.

Comparison of H1 and Zeus results on multiplicities.Agreement.

A study by Zeus on multiplicities in ep vs e+e- and pp.Agreement, in a large energy range, if one uses W in HCM frame and Ecurrent in Breit frame .

ISMD2005. Kromeriz.Conclusions.

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.

•

Zeus, P.L.B 510(2001)

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

Moments Fq

F2

Pt,Gev1 10

H1, 1994 DIS data,DESY96-160

F2

H1 Diff.DESY 98-044Eur.Phys.J.Hadronicsystem X.Left: bothhemisph. Right: separate hemisph. For H1, theabscissa isMx.

<n>

D

F2