Multiplicity Distributions in DIS at HERA Preliminary Examination Michele Sumstine University of Wisconsin Dec. 19, 2002

Outline Introduction HERA and ZEUS Kinematics Parton Shower & Hadronization Models Universality of Hadron Production Data Selection & Simulation of ZEUS Data Mean Charged Multiplicity vs. Effective Mass Summary and Plan

Particle Scattering Study structure of proton Scattering via probe exchange Wavelength Deep Inelastic Scattering – Q2 large High energy lepton transfers momentum to a nucleon via probe h : Plank’s Constant Q2: related to momentum of photon probe lepton The effective probe of proton is the virtual exchanged photon The resolving power … The degree of structure revealed increases… rp>h/2 = 6.6 E –22 MeV s Q2=40,000 GeV2 Q=200 GeV = 200e3MeV Ћc=197 MeV fm 197/200000=.000985fm Size of proton ~ 1 fm HERA Q2 Range ~ 40,000GeV2 HERA can probe to ~ 0.001 fm

Naïve Quark Parton Model Proton consists of pointlike non interacting constituents (partons) Quark Parton Model 3 families of quarks ½ spin particles In Parton Model proton consists of partons QCD tells us the partons are quarks

QCD Theory QCD Quantum Chromodynamics Strong force couples to color and is mediated by the gluon Gluon permits momentum exchange between quarks Gluons create quarks through pair production Color confinement: free partons are not observed, only colorless objects -hadrons Parton distribution function (PDF) gives probability of finding parton with given momentum within proton (experimentally determined) Experiments--NQPM isn’t whole story Quarks interact w/each other via strong force Strong force mediated by gluon Gluon carries color No naturally occurring particles have color— Only observe colorless hadrons Graphs The PDF’s are experimentally determained QCD is non-Abelian theory with SU(3) synmmetry

QCD Scale Running of aS Perturbative QCD (pQCD) Nonperturbative QCD Leading Order (LO) Next to Leading Order (NLO) A = A0 + A1aS + A2aS2 +... HERA DIS Data: Running of aS(m) Running of aS As scale m increases, aS(m) decreases (m = ET or Q) Perturbative QCD (pQCD) Small aS(m) (hard scale) Series expansion used to calculate observables Nonperturbative QCD Large aS(m) (soft scale) Series not convergent The strong coupling constant-not a constant at all… Scale= time/distance; small scale, short times, small distances, hard process large scale, long times, large distance, soft process Each vertex contributes sqrt. Cross section goes as scattering amplitude squared

From Partons to Hadrons hard scattering  parton showers  hadronization Hard scattering: large scale (short distance) perturbative process Parton showers: initial QCD radiation of partons from initial partons Hadronization: colorless hadrons produced from colored partons                           soft process (large distance) - not perturbatively calculable           phenomenological models and experimental input PS is governed by pQCD Parton Showers are QCD predictable once you have set a scale

Multiplicity and Energy Flow The hard scattering process determines the initial distribution of energy Parton Shower + Hadronization determine the number of charged particles produced Measure mean number of charged particles produced, (mean charged multiplicity, <nch>), versus the energy available for production of final state hadrons, study the mechanisms of hard scattering, parton showers and hadronization First I have a hard process that determines… Then we have the PS and Had that determine… SO I would like to measure the mean num of charged particles, and see how it depends on the energy available for hadron production. Hadronization happens at a scale where s becomes large so cannot be treated perturbatively Studies have led to phenomenological models to describe hadronization which are universal pQCD & universality of the hadronization process can be tested by comparison with data from e+e- and hadron colliders.

Unique opportunity to study hadron-lepton collisions HERA Description 920 GeV p+ (820 GeV before 1999) 27.5 GeV e- or e+ 318 GeV cms Equivalent to a 50 TeV Fixed Target Instantaneous luminosity max: 1.8 x 1031 cm-2s-1 220 bunches 96 ns crossing time IP~90mA p Ie~40mA e+ H1 ZEUS HERA Circumference: 6336 m Synchrotron radiation is lin. pol. in plane of acceleration. Mean energy loss per revolution: for Electrons: ~8MeV Fixed target: ECM=S=2E1m2 Colliding Beam: ECM = S=4E1E2 Luminosity: L =f n1 n2/4 xy N1,n2 number of particles in bunch f=frequency xy characterize beam profiles in horizontal and vertical direction ~1011 Protons/Bunch ~3.5x1010 e/Bunch Current: 1.6x10-19 q/C Vacuum Pressure: 3x10-11 Torr e+ beam: 0.165 T B field P beam: 4.65 T B field Spaces left in beam so kicker magnets can dump beam, study beamgas Sokholov-Ternov Effect: e- polarized with spin antiparallel to dir. of bending field (transverse) DESY Hamburg, Germany Unique opportunity to study hadron-lepton collisions

ZEUS Luminosities (pb-1) HERA Data Luminosity upgrade 5x increase in Luminosity  expect 1 fb-1 by end of 2006 For this beginning study I looked at the 96 data, which is ~12pb-1 ZEUS Luminosities (pb-1) # events (106) Year HERA ZEUS on-tape Physics e-: 93-94, 98-99 27.37 18.77 32.01 e+: 94-97, 99-00 165.87 124.54 147.55

General Purpose Detector ZEUS Detector Electron 27.5GeV Missing ET implies a  E loss by heavy charged particles Inelastic w/ e- of atoms Elastic w/ nuclei E loss by e- Collision – ionization Radiative loss – bremsstrahlung 1/(m2c4) General Purpose Detector Almost hermetic Measure ep final state particles: energy, particle type and direction

Central Tracking Detector p View Along Beam Pipe Side View Drift Chamber inside 1.43 T Solenoid Can resolve up to 500 charged tracks Average event has ~20-40 charged tracks Determine interaction vertex of the event Measure number of charged particles (tracks) R= p/qB R=mv/qB relativistic Filled with Ar(84.3%) CO2(8.4%) ethane(6.8%) ethanol(0.5%)

Uranium-Scintillator Calorimeter alternating uranium and scintillator plates (sandwich calorimeter)  = 3.0  = 5.7o  = -3.0  = 174.3o Positrons 27.5 GeV Protons 820 GeV compensating - equal signal from hadrons and electromagnetic particles of same energy - e/h = 1 Energy resolution  e/Ee= 18% / E h/Eh= 35% / E , E in GeV Rapidity important because changes in rapidity are invariant under Lorentz boosts along the beam direction. Pseudorapidity  Rapidity for m=0, =1. Rapidity. Calculate angles from the Energy and longitudinal momenta Y=1/2 log (E + pz/E – pz) Depleted Uranium, is 99.8% U238, 0.25% U235, and 0.001% U234 by Mass, Natural U has 0.72%U235 So ours is depleted of U235 e/h = 1 Important for me, don’t need a lot of corrections to get energy flow Calorimeter: EMC Depth : HAC Depth FCAL : 1 : 6 (6 nuclear interaction lengths) BCAL : 1 : 4 RCAL : 1 : 3 =1 absorption length = 25 radiation lengths for electromagnetic particles Depth of FCAL > RCAL due to Ep > Ee Used for measuring energy flow of particles. covers 99.6% of the solid angle

ZEUS Trigger First Level Second Level Third Level 107 Hz Crossing Rate,105 Hz Background Rate, 10 Hz Physics Rate First Level Dedicated custom hardware Pipelined without deadtime Global and regional energy sums Isolated m and e+ recognition Track quality information Second Level “Commodity” Transputers Calorimeter timing cuts E - pz cuts Vertex information Simple physics filters Third Level Commodity processor farm Full event info available Refined Jet and electron finding Advanced physics filters Commodity = bought from a store, as opposed to CFLT’s custom hardware Pipelined without deadtime: A perfect data acquisition system would be able to readout all the data from all the detectors w/o any deadtime due to inability to read the data from a previous event before the next event is taken. The ZEUS system buffers the data from each event in a pipeline for 5us before the level one decision. Because every event is pipelined the FLT can select events with almost no deadtime

Kinematic Variables Virtuality of exchanged photon remnant e(k) e’(k’) p(P)   (q) q’ Virtuality of exchanged photon Inelasticity: 0  y  1 Fraction of proton momentum carried by struck parton 0 x  1 = Center of mass energy of the ep system Virtuality is square of four momentum transferred from the scattered positron to the photon. Larger Q2 means more virtual photon In proton rest frame, y is fraction of energy lost by interacting positron Y=0: completely elastic, electron gives no energy to proton, final state hadrons low energy, low angle Y=1; completely inelastic X is fraction of proton momentum carried by the part of the proton that participated in the interaction s = (p + k)2 , 4 momentums, so this equals 2p dot k = 4EeEp Center of mass energy of the *P system Only two independent quantities

Kinematic Reconstruction Four Measured Quantities: Ee’, e, Eh, h. (p,E) conservation   DIS Event Variable Electron Method (Ee’,) Jacquet-Blondel (Eh,) Double Angle (,) Q2 X y Electron Method: Angles can be measured precisely E’ can’t be measured so precisely due to detector resolution, and dead material --Q2el --good at high Q2 (higher E’s which don’t rely so much on resolution) --yel—good at higher y --not good for x anywhere Hadron Method --Q2—not as good due to indirect measurement of E --y --good at lower y’s (opposite of el) --x—slightly better DA method All are better because this uses only angles Separate page for Reconstruction calculations

Deep Inelastic Scattering Proton remnant missed Scattered quark is manifested as a jet in detector The electron is scattered out and is manifested as an Em shower in the det. In low Q2 the positron is scattered much more towards the rear calorimeter.

50 TeV Fixed Target Experiment HERA Kinematic Range Q2 = sxy 0.1 < Q2 < 20000 GeV2 10-6 < x < 0.9 Equivalent to a 50 TeV Fixed Target Experiment SVX- shifted vertex: shift vtx toward FCAL,a lower angle track will still hit the RCAL so can go into lower Q2 BPT-Beam Pipe Tracker: Cal behind the RCAL, if e scatters at low angle & misses the RCAL can still go into the beam pipe calorimeter, so can go to lower Q2 Also added Beam Rotators Curved portions follow a line of constant scatterd electron angle 170-175 for yellow green: follow a line of constant E (27.5)

Modeling Multi-parton Production Model multiple parton emissions from partons produced in hard scattering Not possible to perform exact matrix element calculations Two approaches: Parton Shower and Color Dipole Model Parton Shower Model successive splitting process cascade of partons with decreasing virtuality cascade continues until a cut-off ~ 1 GeV2 How do we model emissions from partons produced in hard scattering? Two approaches: Radiations can also produce additional partons

Color Dipole Model Chain of independently radiating color dipoles ep: first dipole between struck quark and proton remnant gluon induced processes are added in "by hand“ Subsequent gluon radiation eminates from dipoles spanned btwn the newly created color charges … Gluon induced hard scale processes are added in by hand DON’T SAY THIS: (just notes) or the gluon induced processes, half the time they assume q half time qbar. In contrast to the PS model it is not possible to distinguish from initial and state radiation, i.e. can’t reconstruct an evolution path

Hadronization Models Use phenomenological models because these processes aren’t calculable in pQCD – low scale Lund String Model and Cluster Fragmentation Models Start at low cut-off scale – set of partons from parton shower transformed into colorless hadrons Local parton-hadron duality Long distance process involving small momentum transfers Hadron level flow of momentum and quantum numbers follows parton level Flavor of quark initiating a jet found in a hadron near jet axis The hadronization process must be phe-nom–en-o-locically modeled due to the low scale of these processes, i.e. as is large and so they are not calculable in pQCD. Hadronization starts at low cut off scale… The models follow Local hadron parton duality, Proposes that the observed hadron distributions are proportional to the calculated parton distributions If your leading parton is a strange quark, then after the long distance hadronization process you will find a strange hadron within some small angular region in the direction on the original strange quark.

Lund String Fragmentation color "string" stretched between q and q moving apart confinement with linearly increasing potential (1GeV/fm) string breaks to form 2 color singlet strings, and so on., until    only on-mass-shell hadrons. Hadrons are formed when the string energy is too small to create further qqbar pairs

Cluster Fragmentation Model preconfinement of color (after parton shower) non-perturbative splitting after parton shower color-singlet clusters of neighboring partons formed We group colored partons ion to colorless clusters, then these clusters decay into hadrons. Gluons are split non perturbatively into qqbar pairs, color neutral clusters are formed which decay into hadrons clusters decay into hadrons

Universality of Hadron Production Can look at just part of the string: assumed to give final state particles proportional to logarithm of mass Similarity of particle production at ee, ep and pp colliders If you look at hadron production in e+e-, ep and ppbar, what you see is there is a section of the process where the hadrons get produced through a similar process. If you compare e+e- and ep, you see the difference is that in ep I have the proton remnant to contend with. I can test hpw similar the process is by studying the universality. This can be done by measuring… Aim: Test the universality of hadronization in QCD nch ~ length of the string(s) ~ ln of energy available for hadron production

e+e- & ep : Breit Frame Phase space for e+e- annihilation evolves with Q/2 = s/2 Current hemisphere of Breit frame evolves as Q/2 For testing the universality, I need a frame where I can compare e+e- and ep directly So move to Breit frame… Z=0 separates current from target region, Longitudinal momentum = 0 ZEUS data must be multiplied by 2 when comparing to e+e-, because in e+e- there are two quarks hadronizing, in ep just 1. So my current region in BF is same as either hemisphere for e+e-. (in e+e- both hemispheres are same) Current region  e+e- annihilation

Early Experimental Evidence for Universality Mean charged multiplicity vs. Q in e+e- and current region of Breit frame at HERA Linear dependence vs. ln Q observed Data in e+e- and ep agree universality of hadronization process observed Also look at <nch> as a function of energy available for particle production (slide to follow) e+e- ep Here we have EARLY measurement of mean charged multiplicity vs. Q for e+e- and current region of BF at HERA.

96-97 Data Sample Event Selection Track Selection Scattered positron found with E > 12 GeV longitudinal vertex cut: |Zvtx| < 50 cm scattered positron position cut: |x| > 15 cm or |y| > 15cm (in RCAL) “Box cut” 40 GeV < E-pz < 60 GeV Track Selection Tracks associated with primary vertex || < 1.75 pT > 150 MeV Physics and Kinematic Requirement Q2 (from double angle) > 12 GeV2 y (from scattered positron) < 0.95 y (from hadrons) > 0.04 For this initial study, I have looked at part of the 1996 data, And I used the following criteria to select my events. EVENT SELECTION: To ensure that the kinematic variables can be reconstructed with sufficient accuracy, I required a good positron be found coming from the vertex, I used a box cut to ensure that the positron is fully contained in the detector, And required the total E-pz to be near 55 Gev TRACK SELECTION: Trks associated with primary vtx, <1.75, ensure tracks are in a region of high CTD acceptance, where detector response & systematics are well understood Pt>150, to ensure the track makes it thru the layers of the CTD KINEMATIC: Yel<.95 removes photoproduction Yjb>0.04 to guarentee accuracy for DA method (which is used to reconstruct Q2) The hadron angle depends on yjb, and the measurement of yjb is distorted bu Uranium noise in the cal for low yjb NOTES: E-pz. For e+ E=27.5, pz = -27.5 since E2-p2=m2 and m=0, so 27.5- - 27.5 = 55, for the proton, Ep=920, p=920, 920-920 =0 Total e-pz = 55 GeV E-pz removes photoproduction (scattered e is missing, q2 is low=0, electron goes in beam pipe, Ee=0.) removes evnts w/ large radiative corrections (electron looses energy by radiating a big photon, so Ee is less than 27.5) 95842 events before cuts 4798 events after all cuts

Event Simulation Ariadne ’96 v2.0 Q2 > 10 GeV2 Matrix elements at LO pQCD O(s) Parton showers: CDM Hadronization: String Model Proton PDF’s: GRV94 HO parameterization of experimental data* Q2 > 10 GeV2 Detector Simulation: software package based on GEANT Proton PDF’s are parameterized from experimental data Detector simulation besed on JAY-AUNT 19990 events before cuts 7058 events after all cuts *M.Glück, E.Reya and A.Vogt, Phys. Lett. B306 (1993) 391

Work done by M.Sumstine Summer 2002 Zeus ’96 Data vs. Ariadne Vertex Position X & Y vertex MC simulates transverse vertex well Z vertex Here I am comparing only a small part of the 1996 data, to the simulation of the Zvtx which is averaged over the full year, Because the event vertex can shift over time, the Zvtx appears shifted here, this will come into better agreement when I increase statistics. Longitudinal vertex is shifted due to partial data Work done by M.Sumstine Summer 2002

Energy & Theta of Scattered Positron Scattered Positron Energy Polar Angle of Scattered Positron Ariadne ’96-’97 Data Energy Corrections for dead material (the uranium) material through which particles travel before they reach our detector, for example: magnets, cables (as far as the uranium calorimeter is concerned, also CTD is dead material . . .).  While travelling through this materialthe particles loose some energy, so the one we measure in the CAL is less than we would expect. This has to be corrected for. for non-uniformities in the calorimeter (there is the beampipe, etc) - the detector is not perfect, there are gaps betwee modules and other different boundaries between different sections/parts/etc. of the CAL. These caus the detector response not to be uniform all over the (spatial) angle. That's why the correction for them is called non-uniformities correction. Positron energy corrections needed – under study.

Position of Scattered Positron at RCAL x position y position Important for reconstruction of Q2 Cut: |x| or |y| > 15cm : Eliminates events close to beam pipe

Kinematics: Virtuality Q2 electron method Energy corrections not yet applied Good agreement on 2 orders of magnitude

Kinematics: Inelasticity Y electron method Y hadron method needs electron energy corrections uses hadronic system variables

Tracking: # of Charged Tracks Number of tracks well described by Ariadne model over two orders of magnitude Validation of model & CTD tracking simulation Pause: OK I have showed the kinematic variables associated with the calorimeter, Now I need to look at tracking. Here we have….

Tracking:  & pT First look at tracking, acceptable for use to correct for detector effects

Effective Mass Study: <nch> vs. Meff CAL within the CDT acceptance Study: <nch> vs. Meff CTD Hadronic final state within  Charged part seen as tracks Energy measured by calorimeter Ok I need a variable that describes the energy available for hadron production, but in order to campare to e+e-, I need to remove the proton remnant. The variable I need is Meff. It is calculated form the square of the energy of the hadrons minus the square of their momentum. It measures the hadronic final state within some eta region, Charged Tracks are counted in CTD while effective mass of this part is determined within the same opening angle in the calorimeter

Mean Charged Multiplicity vs. Meff Average number of charged particles vs. effective mass Reasonable agreement for first look at partial data sample, statistics limited at high Meff Uncorrected ZEUS ’96 data compared to Ariadne proportional to ln (Meff) Here is my first measurement of mean charged multiplicity with Meff:

ZEUS Measurement Investigation of degree of universality in particle production <nch> consistent with linear dependence vs. Meff <nch> 15% above corresponding e+e- Understand color dynamics at the pre- hadronization stage at HERA Now we look at a previous ZEUS investigation of the degree…, A possible explanation is initial gluon radiation at HERA . Further study in this area could lead to better understanding… NOTES: The obtained results can be considered as possible evidence that in the inclusive production about 85% of final state hadrons are produced by non-perturbative mechanism (confinement) while about 15% of the mean charged multiplicity is contributed by the hard perturbative mechanism of color charge radiation

Summary First look at Multiplicity Distributions in DIS at HERA   using 1996 data DIS data sample compared to pQCD + parton showers + hadronization models predictions Event kinematics and tracking well understood and simulated Plan Increase statistics of data and simulation events include all 96 and 97 data Investigate diffractive effects Measure multiplicities vs. Q^2 in the current and target region of the Breit frame Measure momentum spectra Compare different models for parton showers and hadronization to data Evaluate systematic uncertainties Including all 96 Data will increase my statistics an order of magnitude Total luminosity for my study 0.06 pb-1; total for 1996 ~12pb-1 Diffraction: Events with low momentum transferred to the hadron.

Diffractive events expected at large angles (low max) Diffraction & max Diagram Event Display DIS Diffraction 5-10% of events Not modeled by Ariadne Dynamics different for these events Will distribution be same? Eta max, eta of most forward energy in the calorimeter Diffractive events expected at large angles (low max)

Look for Diffractive Events Only max>3.2 is described by Ariadne ~500 events out of total data sample (4798 events) These are diffractive events that are not simulated by the Ariadne Monte Carlo Note: Log Scale Solutions: (fast) Cut out diffractive events (better) Use mixture of diffractive & non-diffractive monte carlo. will do both Move this to later, say I didn’t put the cut, add it to Plans Describe what is eta max, eta of most forward hadron Normalized above max = 3.2

Mix Diffractive & Non-Diffractive Models RapGap contains diffraction; Ariadne does not A fit to a superposition of RapGap and Ariadne max distributions, determines relative contribution of each Data & fitted MC mixture 16% RAPGAP+ 84% Ariadne # of events RapGap + Ariadne 10<Q2<1200 Plans 70<W<260 Correct for detector effects Understand purities/efficiencies To give the best description of the inclusive events, a superposition of the corresponding distributions from non-diffractive and DIS diffractive MC event samples should be used. The relative contribution of each to be determined by fitting the measured inclusive etamax distributions to the combination of the etamax distributions from the diffractive & non-diffractive MC event samples

pQCD series Perturbative QCD (pQCD) series: A = A0 + A1aS + A2aS2 +...  photon quark lepton gluon QCD studies strong interactions Coupling : leads to two regimes of QCD What does expand with alpha_s mean? A = A0 + A1aS + A2aS2 +... Leading Order (LO) Next to Leading Order (NLO)