2. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS Instanton production at ZEUS Ioannis Gialas University of Aegean Member institute of ZEUS April 20 th 2003 EESFYE, NTUA o An introduction o Implications on HERA physics o Instanton induced events at ZEUS o Events reconstruction and selection o Sample enhamcement o Results

3. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS Instantons in QCD Instantons have a well defined size The tunneling process proceeds almost instantaneously. A naïve picture is that of bubbles in boiling water. In order to understand the nucleonic properties we have to understand: How to reproduce the full spectrum, including the excited states The structure of the QCD vacuum.  Instantons are classical solutions to the Euclidean equations of motion.  They are fluctuations of the gluonic fields in non-abelian gauge theories.  They can be interpreted as tunneling processes between degenerate vacua.

4. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS …some implications to HERA physics Except of being novelle and interesting on their own sake, instantons could play a role in understanding other processes studied at HERA. Diffraction Instantons represent non-perturbative gluons that naturally bring in an intrinsic size scale of hadronic dimension. The instanton size happens to be close to the corresponding diffractive size scale. There is work under way on the possibility that larger size intantons may be associated with a dominant part or even make up diffractive scattering. Low-x. HERA experiments show a strong growth of the gluon density at small x Bj. A mechanism is needed which would eventually lead to saturation. Instanton background can be considered to cause such an effect. (Shrempp, Utermann)

5. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS Instanton events at HERA ZEUS H1 820 GeV protons 27 GeV electrons γ*,W ±, Z 0 (q) e(k) P(p) e,ν (k’) X(p’) Two collider experiments, ZEUS and H1 A sizeable event rate is predicted for HERA 1996/1997 data: 820 GeV p on 27.5 GeV e + Integrated luminosity: 38.3 pb -1 Thesis by Sonja Hillert Neutral current DIS events were used with Q 2 = -q 2 = -(k-k’) 2 > 120 GeV 2

6. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS Instanton event A photon emitted by the incoming electron converts to a qqbar pair. One of the quarks hadronizes and forms the current jet. The other one fuses with a gluon from the proton.

7. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS Instanton induced event shape I uLuL uRuR dRdR d- R sRsR s- R gluons (Ringwald and Shrempp) Flavour democracy One pair of each flavour High multiplicity and high E T Hard subprocess produces 2n f -1 plus 3 gluons on average Isotropic distribution of final state particles in instanton CMS Chirality violation of quarks.

8. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS Monte Carlo Instantons: QCDINS Simulation of the hard subprocess using instanton perturbation theory Fragmentation and hadronization are described by HERWIG Normal DIS events: DJANGO: Interface to ARIADNE (Color Dipole Model of QCD cascade) JETSET Lund String model of hadronization HERACLES: Radiative corrections +12% admixture of diffractive events (from RAPGAP) HERWIG : Matrix element and parton shower.

9. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS A QCD INS event as seen in ZEUS

10. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS Event shape variables Circularity C=2(1-λ 2 ) where λ 1, λ 2, λ 1 >λ 2, are eigenvalues of the two-dimensional momentum tensor Sphericity S=3/2(Q 1 +Q 2 ) where Q 1, Q 2, Q 3, 0  Q 1  Q 2  Q 3, are eigenvalues of the three-dimensional momentum tensor N efo : Multiplicity of “Energy Flow Objects” assigned to the instanton N efo : Multiplicity of tracks use din constructing these efo’s. Shape parameter ε’

11. Distribution of event shape variables

12. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS Event shape variables (2) Shape parameter ε’ Measure of the average distance in η hcms between the efo’s assigned to the instanton part of the hadronic final state Corrected for multiplicity dependence to achieve better separation power.

13. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS Instanton enhancement methods Cuts are placed on: Combination of one-dimensional cuts Combination of two-dimensional cuts Cuts on linear combinations of variables from the Fisher Algorithm QCDINS efficiency r I = I E /I O I E, I O : Number of QCDINS events in the enhanced and inclusive samples N E, N O : Number of normal DIS MC events in the enhanced and inclusive sample Normal DIS MC efficiency r N = N E /N O

14. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS Combination of one-dimensional cuts Applied Cutsyielding Instanton efficiency: r I =23% Normal DIS efficiency: r N = 1.6 % (Django/Rapgap) r N = 0.92 % (Herwig) Predicted I fraction: f I,th =8.8%

15. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS How to get to the instanton numbers Fit: Extract information on contribution of instanton events from shape of distributions of S and C in enhanced samples Very sensitive to exact description of nDIS Monte Carlo Cut: Apply hard cuts, find the most conservative limit on number of Instanton induced events assuming the nDIS background to be zero f I,th : Predicted fraction of instanton-induced events σ I : Cross section of I-events predicted by QCDINS σ D : Cross section of the data Σ g : QCDINS generated cross section N D : Number of data events N c : Number of QCDINS events within the cuts constraining the sample N g : Number of events generated

16. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS Fitting of the S and C distributions n iD σ iD : Number of data events and error n iI σ iI : Number of normal DIS events and error n iN σ iN : Number of QCDINS events and error The asterisk indicates that each of the distributions has been normalized to 1 within the cuts considered. A fit to the S and C distributions is used to extract the fraction of instanton events in the samples.

17. Max. Likelihood Approach χ 2 Approach Predicted fraction Results of the S fit Good fit according to χ 2 Fit favours f I  0 Difference between nDIS MC’s ~ predicted signal 2σ limits from both MC are below prediction (No systematic effects taken into account)

18. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS Systematic studies 2σ limit on instanton contribution in the enhanced sample from one-dimensional cuts From Herwig: 12% Django/Rapgap: 8.1% Predicted: 8.8%

19. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS A conservative estimate The fit results are compatible with both the QCDINS predicted value and with zero There are indications that the normal DIS Monte Carlos are not reliable in the Instanton rich regions. So, alternatively….. Make stricter cuts: S > 0.5 and C > 0.5 For the one-dimensional cut method: r I  9% Inclusive sample contains 252  16 events QCDINS predicts 54.6  0.9 instanton induced events Assuming that normal DIS background is zero, we get a 2σ conservative estimate of 252+2*16=284 events

20. EESFYE, April 20, 2003I. Gialas Instantons at ZEUS Conclusion The existence of instantons is an important prediction of QCD Many people believe that instantons should be there If there are instantons, HERA is a good place to look for them. A first analysis by both ZEUS and H1 has not found a definite signal. However, it has shown the limits of the followed methods. To go forward we need: More data. We already have three times the data that was used in the analysis and more will start coming in starting in summer 2003. New analysis strategies ( we are pursuing new ideas) Enthusiasm (no problem) We need manpower (we don’t have it). Instanton search in ZEUS is a good project for a young physicist (either as a phd thesis or a postdoc).