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: E e >12GeV >12GeV |Z| of vertex <30cms <30cms y 0,05<y< <y<0.95 Q 2 >10GeV2 >5GeV 2 >25GeV 2 For tracks: P t >100 MeV/c >150MeV/c  deg.  deg. Corresp.  lab -2<  lab < <  lab <1.75

Ariadne Lepto (prelim.) Photon region in the hadronic center of mass frame. W: total energy in this frame. 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 W 2 =Q 2 (1-x)/x+m p 2. Proton region M.C.: Ariadne

2.Breit frame:2xP proton +q=0. N Zeus For comparison to e+e-, replace Q 2 by s and multiply 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 E current. Current region Target region

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 Q had (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 Q 2 at fixed invariant mass, in the lab., of the had. final state,M eff ? M eff is measured with the calorimeter, restricted to the Central tracker acceptance. Answer:no. ARIADNE M eff

Q GeV GeV GeV 2 X Bj

Reggeon model: Pomeron is replaced by mesons. =Q 2 /(Q 2 +M x 2 ) =x Bj /  Diffractive DIS (DDIS). Regge factorisation

H data, 46.6 pb -1. Acceptance vs  *:  *>1,which restricts the photon region (  *>0), both in DIS and DDIS

Do the multiplicities depend upon Q 2 when W is fixed? Answer: neither in DIS nor in DDIS. There is an (expected) dependence on M X in DDIS.

Do the DDIS multiplicities depend upon  when M x is fixed? No! p p

dependence on W at fixed M x 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 does not vary much. Poisson law: large number independent parton emitters in fragmentation chain. Moments F q like F 2 = / 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 =4 (black squares) =3.6 =3.8 =4.2 =4.5 Poisson: large number of independent emitters in the hadronisation chain.

Comparison with Poisson =5.0 (black squares)

Comparison with NBD law with =4.0, k=10 (red squares) =3.6 =3.8 =4.2 =4.5

Comparison with NBD law with =4.0, k=100 (blue squares) =3.6 =3.8 =4.2 =4.5

Conclusion of this study of KNO scaling. Distribution of P n : -- 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 on x  and Q 2. 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 E current 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 F q F2F2 P t,Gev 110

H1, 1994 DIS data, DESY F2F2

H1 Diff. DESY Eur.Phys.J. Hadronic system X. Left: both hemisph. Right: separate hemisph. For H1, the abscissa is M x. D F2F2