Deep Inelastic Scattering José Repond Argonne National Laboratory CTEQ Summer School 2002, Madison,...

Deep Inelastic Scattering

José RepondArgonne National Laboratory

CTEQ Summer School 2002, Madison, Wisconsin, June 2- 20, 2002

June 2, 2002 J Repond - DIS 2

Introduction: What is Deep Inelastic Scattering?

γ*

Q2 = -q2 … mass of exchanged γ* squared ~ energy of photon in p rest mass Probing the proton with a wavelength or resolving power λ = ħ/√Q2

e.g. Q2 = 10 5 GeV2: λ ~ 10-18 m or 10-3 ·Rp

Consider electron – proton scattering

Deep ≡ high resolving power ≡ high Q2

W2 = (P+q)2 … mass of scattering γ* and p mass of hadronic final state X

Inelastic ≡ proton breaks up ≡ high W


More variables…

Consider elastic e – q scattering with x the momentum fraction of the proton carried by the struck q

4- momentum of outgoing quark xP+q mass of outgoing quark 0 = (xP + q)2 ~ q2 + 2xP·q

x = Q2/2P·q … Bjorken x

s = (k + p)2 ~ 4EeEp …total center of mass energy squared

y = P·q/P·k …Inelasticity Fraction of k carried by the γ*

Related to scattering angle of e, q in their center of mass system


Relations between variables…

Q2 = sxy

W2 ≈ Q2(1-x)/x

Easy to show that…

only 2 independent Q2, x variables needed x, y W2, Q2

….

At fixed center of mass energy s

to describe inclusive deep inelastic scattering

ee’(θ,E)


Introduction: History of Deep Inelastic Scattering

1911 Rutherford Elastic scattering of α – particles on atoms Discovery of atomic nucleus Size of nucleus 10-5 size of atom

1968 SLAC-MIT

Deep inelastic scattering of e- of p, d Observation of ~flat Q2 dependence of R= σinel/σMott

R can be interpreted as form factor (describing form of scatterer)

R~const → pointlike scatterers inside proton

Partons later identified with quarks


1973 Gargamelle (Bubble chamber at CERN)

Observation of ÷ö + N ! ÷ö + hadrons

With no outgoing μ!!!

Discovery of neutral current interactions (mediated by Z0 boson)

Distance in detector

ν ν

p

hadrons

Z0


1988 European Muon Collaboration at CERN

Scattering of

Study of spin asymmetries

Integral of spin structure function g_1 related to contributions of quarks to p spin

(Expected Σ =1 from valence quarks) Contribution of quarks to p spin small

ö~+ N~! ö + X

Rgp1(x)dx = 0:123æ0:013æ0:019

Î = É u + É d + É s = 0:12æ0:16


Introduction: The HERA Collider

First and only ep collider e± p

27.5 GeV 920 GeV√s = 318 GeV

Equivalent to fixed target experiment with 50.6 TeV e±

Located in Hamburg (Germany)


World’s most complicated collider

ZEUS

HERA-B

HERMES

H1H1 – ZEUS

Colliding beam experiments

HERA-B

Uses p beam on wire target Goal: B - physics

HERMES

Uses e± beam on gas jet target Both lepton and target polarized Measurement of polarized structure functions

Two independent storage rings


HERA Performance and Future

Commissioned in 1992Ran almost continuously until 2000Performance improved over yearsDelivered

RLdt = 27pbà1(electrons)RLdt = 166pbà1(positrons)

Total RLdt = 193pbà1

Shutdown in September 2000Insertion of quadropoles close to IR → Increase of Luminosity by a factor of 5Insertion of spin rotators around H1-ZEUS → Longitudinally polarized e±

HERA II Program

To be completed by 2006/7Expect RLdt ø 1fbà1


Introduction: The Collider Experiments

H1 DetectorComplete 4π detector with

Tracking Si-μVTX Central drift chamber

Liquid Ar calorimeter

Rear Pb-scintillator calorimeter

î E=E = 12%= E[GeV ]p

(e:m:)î E=E = 50%= E[GeV ]

p(had)

î E=E = 7:5%= E[GeV ]p

(e:m:)

μ chambers

and much more…


ZEUS Detector

Complete 4π detector with

Tracking Si-μVTX Central drift chamber

Uranium-Scintillator calorimeter

î E=E = 18%= E[GeV ]p

(e:m:)î E=E = 35%= E[GeV ]

p(had)

μ chambers

and much more…Both detectors asymmetric


Introduction: Physics Processes

Neutral Current Interactions e’e

γ, Z0

qq’

Photoproduction

Q2 ~ 0 GeV2 (real γ)

e p

Deep Inelastic Scattering

Q2 ≥ 4 GeV2 (virtual γ*, Z0)

pT of events balanced

e pe’

e’


Charged Current Interactions

e p

pT of events not balanced

e

W±

qq’

ν

Inclusive scattering described by 2 variables e.g. x, Q2

Details of hadronic final state ignored Charged current kinematics reconstructed with hadronic final state

ν

ee’(θ,E)


Studies of Hadronic Final State in DISMulti-jet Production in NC events

Processes in Leading – Order in αS

e

γ, Z0

g

e’e

γ, Z0

g

e’

αS

Boson-gluon Fusion QCD Compton

Need additional variables to describe events e.g. NJet, ηJet, pT

Jet… Thrust, Sphericity… Ncharged tracks, Nπ…


Diffractive eventse

e p

Gap in rapidity η

e’

γ, Z0

p p

Color neutral exchange: P or 2 gluons

Proton stays intactApproximately 10% of the events

Additional variables: xP, ηmax, β…


Kinematic Regions of DIS

Previous fixed target experiments

Reaching values of x < 10-6

Reaching values of Q2 > 104 GeV2

HERA: extension by several orders of magnitude

Kinematic limit defined by Q2 = sxysHERA = 100000 GeV2


Outline of Lectures

Inclusive measurementsExclusive measurements

Total γp cross sectionNeutral current scattering Structure function F2

Interpretations Extraction of parton densities Measurements of FL

Measurement of xF3

Valence quarks Contributions of charm to F2

Charged current scattering

Jet production Jets in DIS Extraction of αS

Jets in photoproductionHeavy flavor production Charm production cross sections Interpretations Charm fragmentation Beauty production cross sections J/ψ production cross sectionsDiffraction Rate of inclusive diffraction Interpretations Vector-meson production

Exotic searches Leptoquarks, SUSY signatures, Contact Interactions…

Outlook and conclusionsPolarized structure functions


Total γP cross section

Most fundamental measurement at HERAConsider e± as source of (real ) photons Inclusive measurement with only 1 variable

WγP … center of mass of γ and proton

or

… Inelasticity

= E eE pyp

y = 1à E e0=E e


Measurement

dydûep

tot(y) = LA eN e(y)

Tag events at low Q2 < 0.02 GeV2

with e± tagger at 35 m from IP

35 m

Require O(1GeV) in calorimeter

Count events Ne(y)

Bethe-Heitler Bremsstrahlungs process ep → eγp

105 m

e’

γ

Count events Nγ

(syst) nb-

1

L = ûB HáA íN í = 49:26æ0:54

Can be calculated with high accuracyAcceptance: real challenge!

Reconstruct W from Ee’

γ tagger


Reliably calculable for 12 < Ee’ < 16 GeV corresponds to

0.56 > y > 0.42 or 225 > W > 194 GeV

Acceptance Ae = A35m ACAL

Requires simulation of all physics processes

Fraction determined

in separate measurements in fits to detector observables

Major uncertainty of measurement!


Extraction of γP Cross SectionMeasurement of How to extract σγP(W) ???

Equivalent Photon Approximation relates the two

Qmax … maximum Q defined by experimental conditions

Qmin … minimum Q given by finite e± massσT … cross section for transversely polarized γσL … cross section for longitudinally polarized γ → expected to be very small

Integration over Q2

Photon flux factor fγ(y)


Resultûí p(W = 209GeV ) = 174æ1(stat) æ13(syst)öb

Rise parameterized as sα

with

α = 0.08

Same value as in pp, pp, πp, Kp

γp scattering behaves like hadron-hadron scattering

At low Q2: γ is just a hadron


Proton Structure Function from NC DIS

Cross section calculated as convolution of Lμν Lepton tensor calculable in QED

Wμν Hadron tensor contains 3 ‘a priori’ unknown structure functions Fi

Helicity structure: Jz= 0 → 1 1 → (1 - y)2

F2 … Parity conserving structure function (γ and Z0 exchange plus interference)FL … Longitudinal structure function (exchange of longitudinally polarized γ/Z0)xF3 … Parity violating structure function (pure Z0 exchange and interference)

Coupling

Propagator


For Q2 « MZ2 → xF3 negligible

FL only important at high y

Both FL and xF3 ~ calculable in QCD

Correct for higher order QED radiation

Extract F2(x,Q2) from measurement of

Measurement of F2(x,Q2)

dxdQ2d2ûep

Difficult measurements:

Nevertheless high precision: errors of 2-3%


Scaling and its violations

Elastic scattering off pointlike and free partons → does not depend on Q2

‘a point is a point’

Scaling

Scaling violations

Scaling violations

Result of emission of gluons from partons inside proton

(non) – dependence on Q2

Depletion at high x → quarks emit gluonsIncrease at low x → quarks having emitted gluons

Effect increases with αslog Q2


Interpretation: DGLAP evolutionF2(x,Q2) can in principle be calculated on the Lattice → Some results emerged in the last few years

Standard analysis assumes that F2(x,Q2) not calculable

However: evolution with Q2 calculable in pQCDDokshitzer, Gribov, Lipatov, Altarelli, Parisi (DGLAP):

Parton Density Functions (PDFs) qi(x,Q2) … Density of quark i at given x, Q2 g(x,Q2) … Density of gluons at given x, Q2

Pij(x/z) … Splitting functions

Quark-Parton Model (QPM)

…in DIS scheme


Probability of parton i going into parton j with momentum fraction z

Calculable in pQCD as expansions in αS

In Leading Order Pij(z) take simple forms

Pqq Pqg Pgq Pgg

Splitting Functions Pij(z)


b) Sum i) over q and q separately

Fit to DGLAP equations

c) Define: Valence quark density

Singlet quark density

I) Rewrite DGLAP equations

a) Simplify notation

Nf … number of flavors

i)

ii)

ia)

ib)

← u,u,d


II) DGLAP equations govern evolution with Q2

Do not predict x dependence: Parameterize x-dependence at a given Q2 = Q2

0 = 4 – 7 GeV2

d) Rewrite DGLAP equations

Valence quark density decouples from g(x,Q2) Only evolves via gluon emission depending on Pqq

55 parameters

Low x behaviour High x behaviour: valence quarks


III) Sum rules and simplifying assumptions

Valence distributions 2 valence up-quarks

1 valence down quarks

Symmetric sea

Treatment of heavy flavors (different treatments available…) Below mHF:

Above mHF: generate dynamically via DGLAP evolution

Momentum sum rule: proton momentum conserved

Effect number of parameters: 55 (parameters) – 3 (sum rules) – 13 (symmetric sea) – 22(heavy flavors) = 17

Difficult fits, involving different data sets with systematic errors…


Results of fits I

Several groups perform global fits CTEQ: currently CTEQ6 MRS: currently MRST2001 GRV: currently GRV98 Experiments: H1, ZEUSOverall good agreement between fitsDespite some differenent assumptions

Fit quality: excellent everywhere! → no significant deviationsEvolution with Q2: 5 orders of magnitude QCDs greatest success!!!No deviations at high Q2: → no new physics: no contact interactions no leptoquarks Fit includes data with low Q2: αS(Q2) large → surprise → expected to work only for Q2 ≥ 10 GeV2


Results of fits II

Quark and gluon densities

Valence quarks

Gluon density

Inferred from QCD fit not probed directly by γErrors of order 4% at Q2 = 200 GeV2

Strong coupling constant

Based on NLO pQCD including terms of αS

2

Scale error reduced with NNLO not yet available

CTEQ6


Universality of Parton Density Functions

Determined with DIS data and pQCD fitsCan now be used to calculate any process involving protons

Higgs production at LHC

W± Production at the Tevatron

Jet production at HERAAnd yetanother success

of pQCD…


Other interpretationsDGLAP formalism

Standard approach: Equations to NLO Include all terms O(αS

2) Calculation of NNLO corrections First results by the MRST group Effects seem small, but will reduce uncertainties

Collinear Factorization DGLAP also resums terms proportional (αS log Q2)n

corresponds to gluon ladder with kT ordered gluons kT,n >> kT,n-1 … >> kT,0

struck parton collinear with incoming proton Does not resum terms proportional to (αS log 1/x)n

→ Is this ok at small x?


BFKL formalism

Resums terms proportional to (αs log 1/x)n

gluons in ladder not kT ordered, but ordered in x x1 >> x2 … >> xn

Predicts x, but not Q2 dependence

kT Factorization results in kT unintegrated gluon distributions g(x,kT

2,Q2)

Y Balitskii, V Fadin, L Lipatov, E Kuraev

CCFM formalism

S Catani, M Ciafaloni, F Fiorani, G Marchesini

Resums terms proportional to (αs log 1/x)n and (αs log 1/(1-x))n

gluons in ladder now ordered in angle

kT Factorization results in kT unintegrated gluon distributions g(x,kT

2,Q2)

Easier to implement in MC programs, e.g. CASCADE

Low x: approaches BFKL

High x: approaches DGLAP

x

Q2

DGLAPCCFM

BFKL


Asymmetric sea

Measurement of Drell-Yan production with H2 and D2 targets p N →μ+ μ- X

FNAL fixed target experiment E-866

…with x = x1 – x2

Sea not flavor symmetric!!! Explanations: Meson clouds Chiral model Instantons More data to come: P-906 at the Main Injector


Longitudinal Structure Function FL from NC DIS

Need to vary y, keeping x, Q2 fixed

→ vary s lower Ep to say 920 → 450 GeV

Involves large effort - Machine tuning - Detector acceptance for lower Ee’

- Large statistics needed

Not yet done at HERA

Disentangle F2(x,Q2) and FL(x,Q2)

…ignore xF3 at lower Q2


H1 Analysis

Determine PDFs using only low y data contribution from FL negligibleEvolve PDFs to high y region according to DGLAP equationsSubtract prediction of F2 from measurements at high y → FL

Yellow line: Result of DGLAP fit including FL

Points: Subtraction technique

ZEUS: No comparable analysis Circularity?

At small x:

Fit at low y already determines FL


Low Energy Results

Data from SLAC and CERN Electron/μ scattering on fixed targets with different beam energies

Measurement of R(x,Q2) Ratio of longitudinal and transverse cross section


Measurements at high x > 0.1 but low Q2 < 80 GeV2

Curves

Rfit … fit to empirical function

RQCD … prediction based on PDFs from F2data

RQCD+TM … same as above, corrected for target mass effects

Differences between data and QCD

higher twist effects?

gdecrease as 1/Q2

Important to measure at HERA!!!


xF3 Structure Function from NC DIS

FL(x,Q^2) … ignored (small at high Q2)

Cross section for scattering of Left, Right – handed electrons

Parity conserving

Parity violating

… sum over all q and q …sum over the 2 valence distributions

At high Q2: weak terms non-negligible

electromagneticinterference

pure weak interference pure weak


Up to now: no longitudinal polarization for H1/ZEUS

→ How to measure xF3(x,Q2) ???

Consider Parity and CP Operations

Operation on e-L on xF3

P e-R -xF3

CP e+R xF3

P(CP) e+L -xF3

CP conserved in DIS

xF3(x,Q2) can be measured using difference of

Clear difference at high Q2


First measurement on proton No nuclear corrections

Agrees with expectations based on PDFs from F2 fits

Clearly needs more statistics → HERA II program


Charm contribution to F2

Events with charm identified through

Mass plot of Δm = m(Kππ) – m(Kπ)Sharp peak at Δm = mD

* - mD = 145 MeV

Identify e± with dE/dx of central drift chamber


Charm production mechanisms

Variable Flavor Number Scheme VFNS

- Charm treated as extra flavor c(x,Q2) in proton (mass ignored) - c(x,Q2) assumed to be zero for scales μ < mc

- c(x,Q2) evolved to higher scales using DGLAP → this also resums (log(Q/mc)2)n

- Expect good description at large Q2 where log’s might be large - Expect problems at Q ~ mc

Fixed Flavor Number Scheme FFNS

- no heavy quarks inside proton, only u, d, s quarks - Charm produced via Boson-gluon fusion process (including masses) - Expect good description for μ ~ mc

- Expect problems at large Q2, since log’s not resummed

Mixed Flavor Scheme MFS

- Uses best of both

γ, Z0

c

γ, Z0

g

c

c


Determination of Fc(x,Q2)

Charmed production measured in limited phase space e.g. 1.5 < pT(D*) < 15 GeV |η(D*)| < 1.5Extrapolation to full (pT,η) phase space model dependent!

2

ignored

Nice agreement with FFNS based on xg(x) from F2 fits


Comparison of Schemes

FFNS VFNSVFNS

Some differences at 3 < Q2 < 32 GeV2

Data can not distinguish → HERA II

Agreement between schemes at large Q2

→ (log(Q/mc)2)n not important?

Plots from A Chuvakin, B Harris and J Smith


Charm Fraction of Inclusive F2

Fraction increases with increasing Q2

→ as large as 30% !!!

Reproduced by FFNS calculations based on xg(x,Q2) from fits to inclusive F2


Propagator

NC

CC

Suppression at low Q2

Coupling

NC

CC

Approximately the same Unification of Electromagnetic and weak forces!!!

Charged Current DIS

…ignore FL and xF3

λ = ± 1 for left/right handed e-

For Q2 > MW:

Same propagator!!!

e

W±

qq’

ν


Structure Function F2(x,Q2)

NC

CC e- p W- couples to

e+p W+ couples to

Dominated by flavor symmetric sea

Difference due to valence quarks 2u quarks versus 1d quark (1-y)2 suppression


Flavor decomposition of proton

Use different angular dependence of valence and sea quarks both electron and positron data

Clearly need more data

→ HERA II

F2CC


Outlook

HERA I Program

Shutdown period

Completed in September 2000

RLdt = 193pbà1

September 2001 – September 2001

New quadrupoles close to interaction region → increase of luminosity by factor ~5

Spin rotators around H1/ZEUS → rotate transverse spin into longitudinal

ZEUS upgrades → new μVTX detector → new forward tracker

Sokolov-Ternow Effect → Polarization build-up through emission of synchrotron radiation


HERA II Program

Completed by 2006/7

RLdt = 1000pbà1 = 1fbà1

High precision F2(x,Q2) data → up to x = 0.65 → up to Q2 of 40000 GeV2

Further constraints on PDFs Δ[xg]/xg ≤ 3% Determination of αs(MZ) to < 2% (with NNLO formalism)

Charged current interactions Disentangle flavor content of p

Search for deviations Discovery or stringent limits Leptoquarks SUSY Contact Interactions Flavor changing NC Excited fermions …..


Conclusions

Historically DIS has been a powerful for new discoveries

HERA has extended the reach in x, Q2

Precision measurements available from HERA I

Strong constraints on parton density functions Tests of QCD over large kinematic range Confrontation with different theoretical approaches

HERA II to start anytime now

Improved precision at very high Q2

Deep Inelastic Scattering José Repond Argonne National Laboratory CTEQ Summer School 2002, Madison,...

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