Event Shapes, Jet Substructure and S at HERA Adam Everett University of Wisconsin On Behalf of the ZEUS and H1 Collaborations

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+ 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

HERA Kinematic Variables Center of Mass Energy of ep system squared: s = (p+k)2 ~ 4EpEe Photon Virtuality (4-momentum transfer squared at electron vertex): q2 = -Q2 = (k-k’)2 Fraction of Proton’s Momentum carried by struck quark: x = Q2/(2p·q) Fraction of e’s energy transferred to Proton in Proton’s rest frame: y = (p·q)/(p·k) Variables are related: Q2 = sxy W: invariant mass of the system recoiling against the scattered lepton y: measures inelasticity of interaction. y=1 – E’_e/E_e in proton rest frame Related to scattering angle ************** y=0: totally elastic x=0 when y=1. y=0 when x=1.

Methods to Study QCD QCD Effects – Gluons Jets Event Shapes Direct – gluons observed as jets Complexity of jet reconstruction and identification Jet cross sections and substructure Event Shapes Energy and particle flow Direct – gluon radiation changes event shapes Reduce dependence on hadronization We have already briefly discussed 1 and 2. Now we will focus on 3.

Jets Colored partons evolve to a roughly collinear “spray” of colorless hadrons  JETS Partons => Hadrons => Detector: schematically: As produced As observed

Jet Finding: Longitudinally Invariant KT Algorithm In ep: kT is transverse momentum with respect to beamline For every object i and every pair of objects i, j compute d2i = E2T,i (distance to beamline in momentum space) d2ij = min{E2T,i,E2T,j}[Dh2 + Df2]1/2 (distance between objects) Calculate min{ d2i , d2ij } for all objects If d2ij is the smallest, combine objects i and j into a new object If d2i is the smallest, then object i is a jet Inclusive in title? Divide by R^2? JADE algorithm: dij = 2EiEj[1-cos(thetaij)] invariant mass of 2 particles 2 gluons can be combined into “phantom” jet kT algorithm: dij2 = 2min{Ei2,Ej2}[1-cos(thetaij)] minimum relative transverse momentum of two particles designed to reduce higher order contributions compared to JADE Longitudinally invariant kT: d2ij = min{E2T,i,E2T,j}[Dh2 + Df2]1/2 Combinations: ET,ij = ET,i + ET,j hij = (ET,I * hi + ET,j *hJ)/ ET,ij fij = (ET,I * fi + ET,j *fJ)/ ET,ij JADE: Disadvantages: Large recombination scheme dependence kT: Advantages: No seed requirements Same application to cells, hadrons, partons No overlapping jets Infrared safe to all orders Good in ZEUS forward region Relatively independent of MC recombination scheme Longitudinally invariant kT: Infrared and collinear safe to all orders in pQCD Invariant under longitudinal boosts (along beam axis) Small experimental and theoretical uncertainities

Event Shapes Axis Dependent: Axis Independent: Multi-Jet: Thrust Broadening Axis Independent: C Parameter Jet Mass Multi-Jet: yn_kt: disstance scale at which an event changes from n+1 to n jets using the KT algorithm Momentum out of plane Jet Rate

Event Plane Energy flow out of event plane defined by proton direction and thrust major axis Sensitive to perturbative & non-perturbative contributions Dijet event: Perturbative physics takes place in the plane Non-perturbative physics give rise to out-of-plane momentum

Approach to Non-perturbative Calculations pQCD prediction → measured distribution Correction factors for non-perturbative (soft) QCD effects Proposed theory* reduces corrections for any infrared safe event shape variable, F: Power correction Independent of any fragmentation assumptions “Non-perturbative parameter” * – (Dokshitzer, Webber, phys. Lett. B 352(1995)451) Used to determine the hadronization corrections Two realms: pQCD and npQCD. pQCD is calculable: uses alpha-s. npQCD is not. Recent theoretical work [2], involving power corrections to event shape variables, provides a new approach to determine the hadronisation corrections compared to monte carlo event generators. The new work involves a phenomenological model based around an effective strong coupling which comes in at low Q. This model conveniently reduces the hadronisation corrections to be of a form containing alpha-s and a new phenomenological variable alpha-0. Define power correction….. Why do we care? –> because we can’t calculate features of npQCD hadronization Future plans involve the fitting of parton level next to leading order curves with power corrections to the mean distributions. This will then yield a value for not only alpha-s but also the new phenomenological variable alpha-0 and allow tests on its universality. Relate hadronization effects to power corrections. Q dependence of the means of the event shape parameters is presented, from which both the power corrections and the strong coupling constant are determined without any assumption on fragmentation models.

Shape Means 2-parameter fit Simultaneous fit for s and 0 Each shape fit separately Bins of x and q2 High-x data points are not fit. Fits use Hessian method for statistical and systematic errors. All variables with a good 2

Mean Parameters Extracted parameters for each shape Fitted s values consistent to within 5% Fitted 00.45 to within 10% Theory errors dominate, except for  axis shapes.

Shape Distributions  = 1-T Fit differential distributions over a limited range. Bins for which theoretical calculations are expected to be questionable are omitted from fit. Resummation is applied with DISRESUM.

Distribution Parameters Fits use Hessian method for statistical and systematic errors. All variables with a good 2 Fits are sensitive to matching method. 0  0.5

Jet Rate Event Shape No fits performed up to now. NLOJET++ gives a good description of the data for higher values of Q. Waiting on generalized resummation program.

3-jet Event Shape Variable No fits performed up to now. First comparison with LO+NLL+PC is shown. Waiting on generalized resummation program.

Jet Substructure Jet substructure depends mainly on type of primary parton and to lesser extent on the particular hard scattering process pQCD: gluon initiated jets are broader than quark initiated jets Jet substructure studied with the jet shape: (r): fraction of the jet ET inside a cone in the - plane of radius r Jet dependence: DIS: none P: jets broader as jet increases Etjet dependence: DIS and p: jets become narrower as ETjet increases At sufficiently high jet transverse energy, where fragmentation effects become negligible, the jet substructure is expected to be calcculable in pQCD pQCD predicts that gluon-initiated jets are broader than quark-initiated jets due to the large color charge of the gluon (seen by LEP) Jets searched with kt in LAB frame At least one jet with Et>17 and –1 < eta < 2.5 Q^2 < 1 and 0.2 < y < 0.85 Eta dependence: Comp to QCD PYTHIA with ISR and FSR Good desc of data –1..1.5 Data broader than prediction 1.5..2.5 Thus, quark like –1..0, increasingly gluon like as eta increases Et dependence

Jet Substructure 2 Put something here

Multijet Production Jets ordered in ETBRT Jets ordered in LAB Et Measurement down to low Et Scale dependence Good agreement NLOJET over large range of scales Eta Angular distribution NLOJET over whole eta range Jets ordered in ETBRT Jets ordered in LAB

Multijet Production 2 R3/2 = trijet/dijet Dijet: alphas_s^2 Trijet: alpha_s^3 Scale dependence R3/2 = trijet/dijet Systematic uncertainties substatially reduced Very sensitive test of QCD calculation

s Values

Summary Mean and differential event shapes have been measured in eP collisions Power correction fits performed for data for most event shapes Waiting on resummation terms Measurement of jet shape and subjet multiplicities demonstrate the validity of the description of the internal structure of jets by pQCD R3/2 cross section ratio is sensitive to s Some sensitivity to PDF is also observed