July 15, 2008 1Structure of hadrons and nuclei at an electron-ion collider

Small-x Physics and Diffraction: HERA Results

Allen Caldwell, Max Planck Institute for PhysicsMunich, Germany

Topics:1.Inclusive measurements (structure functions, photon-proton cross sections)2.Fits to inclusive cross sections3.Diffraction (‘inclusive’, VM production, DVCS)4.Factorization in diffraction5.Forward jets

July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider 2

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d2σ (emp)

dxdQ2 =2πα 2

xQ4 (1+ (1− y)2)F2 − y2FL ± xF3[ ]

Structure Functions

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Q2 = −q2 = −(k − ′ k )2

k

k’

Transverse resolution

Momentum fraction

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0 ≤ x ≤ 1

0 ≤ y ≤ 1 Inelasticity

Not relevant at small xNew resultsNew resultsNew

Results/fitsNew

Results/fits

July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider 3

HERA Discovery!

The rise of the parton densities (and of F2) with decreasing x is strongly dependent on Q2. Implies very large density of partons in the proton when probe at high energies !

Small-xF2 x-

Small fraction of HERA dataTypically define small x as x<0.01

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Below Q2 0.5 GeV2, see same x (energy) dependence as observed in hadronic interactions. Start to resolve the (constituent) quarks and see the partons at larger Q2.

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F2 = C(Q2)x−λ x < 0.01

Parametrize:

I will show an update of this plot laterI will show an update of this plot later

A classic HERA plot: the dependence of the rise of F2 on Q2

A classic HERA plot: the dependence of the rise of F2 on Q2

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Recent development: combined ZEUS and H1 Data sets/fits

Recent development: combined ZEUS and H1 Data sets/fits

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There are signs that DGLAP (Q2 evolution) may be in trouble at small x (negative gluons, high 2 for fits).

Need better data to test whether our parton densities are reasonable. The structure function FL will provide an important test.

all is not well …

Range of validity of DGLAP not clearRange of validity of DGLAP not clear

July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider 7

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FL =α S

4πx2 dz

z3

16

3F2 + 8 eq

2(1− xz∑ )zg ⎡

⎣ ⎢ ⎤ ⎦ ⎥

x

1

∫

Expected to dominate at small-x

LO pQCD€

d2σ

dxdQ2 =2πα 2

xQ4 Y+F2(x,Q2) − y2FL (x,Q2)[ ] Need to measure differential cross section at two beam energies (at least).

y2/Y+

r

10

F2

F2-FL

small Q2

Available luminosity (pb-1)HER EHER Epp=920 GeV e=920 GeV e++p >300p >300 ee--p >200 MER Ep=575 GeV e+p 8LER ELER Epp=460 GeV e+p 14

Brand New : FL from HERABrand New : FL from HERA

July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider 8

Reduced Cross SectionsReduced Cross Sections

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˜ σ = Y+F2(x,Q2) − y 2FL (x,Q2)[ ]

FL expected to produce turnover at small-x (assuming F2 continues as x-λ)

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Preliminary results just out …

H1 results consistent with NLO pQCD expectations from H1 fits, ZEUS data somewhat lower. H1 results now published, ZEUS still preliminary.

July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider 10

s0.08

HERA: total photoproduction cross section

ZEUS prel.€

sγP = W 2 ≈Q2

x

(W2)

Hadron-Hadron Cross SectionHadron-Hadron Cross Section

e

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The rise at small x revisitedThe rise at small x revisited

Look in proton rest frame

Parameterize:

D

2P

BH

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Data Sets for FittingData Sets for Fitting

Bayesian analysis based on Markov Chain Monte Carlo

Hep-ph 0802.0769

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Fixed TargetFixed Target

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H1H1

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ZEUSZEUS

Summary:2P gives best fitsD also OKBH does not fit

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Slope of the cross section with l increases with Q

Extrapolation of the cross section with the D parameterization:

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Data extrapolated with this form indicates a merging of cross sections.

Crossing is unphysical, eventually expect all cross sections to behave similarly at large l, independent of the starting scale.

Is the distance scale meaningful ?

July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider 18

Look at the effective slope with all available data. See indications of a turnover at the highest Q.

The data prefers the 2P parameterization. In this case, there is a saturation of the growth of the cross section with Q (so there would not be a unique l for crossing as could happen in the D parameterization).

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The second HERA surpriseThe second HERA surprise

E

rapidity

Color-neutral object

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10% of events have large rapidity gap !Implies scattering on color neutral cluster: at least two gluons.

Evidence of Hard Diffraction at HERAEvidence of Hard Diffraction at HERA

Nearly constant ratio of diffraction to total as a function of W for fixed MX,Q2

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Diffractive PDF’s

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d3σ (emp)

dβdQ2dxP

=2πα 2

β 2Q4 1 + (1− y)2[ ]σ r

D(3)

where

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rD(3) = F2

D(3) −y2

1+ (1− y)2( )

FLD(3)

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The ‘inclusive’ diffractive cross section has the same x dependence as the total cross section. There is an indication of universal behavior:

Similar at small x

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Forward neutron production - electron - pion scatteringForward neutron production - electron - pion scattering

Same x dependence as inclusive

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Message: at small-x, data suggests that source of partons (photon, pion, proton, pomeron) is not critical – the gluon density is a universal quantity. Fundamental aspect of matter at small distances.

Small x partonsSmall x partons

July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider 25

Ratio of diffractive to total cross section versus scaleRatio of diffractive to total cross section versus scale

Logarithmic decrease of diffractive cross section at fixed W, MX

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Factorization in Diffractive ScatteringFactorization in Diffractive Scattering

Factorization has been proven for Diffractive DIS and exclusive hard diffraction (Collins, Berera&Soper, Trentadue&Veneziano).

However, factorization is not expected to hold for diffractive hadron-hadron scattering. The cross sections for large rapidity gap events at the Tevatron are well below expectations based on HERA diffractive pdfs.

What about diffractive photoproduction ? The photon can behave both as a point particle and as a composite (hadronic) particle.

The ratio of dijet measurement to NLO prediction is photoproduction is a factor 0.5+-0.1 smaller than the same ratio in DIS. However, no dependence on xgamma found.

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Factorization in Diffractive ScatteringFactorization in Diffractive Scattering

ZEUS also sees some evidence of suppression of dijets in diffractive photoproduction, but less than H1. Could be related to higher ET.

Summary:• Diffractive charm – no hint of factorization breaking observed• Diffractive dijets – in photoproduction, data favor a global suppression relative to NLO QCD diff pdfs. Factorization breaking observed at low ET but no xgamma dependence.

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Exclusive ProcessesExclusive Processese

p

€

γ*

γ,VM

A long list of processes have been measured:

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eP → ePV V = ρ,ω,ϕ ,J /ψ ,Υ

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eP → eNV V = ρ,ω,ϕ ,J /ψN is low mass system

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eP → ePγand QCD

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Data can be parameterized as smooth function of

July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider 30

The dependence of R on W is not the expected one (much less W dependence than initially expected). Maybe due to wavefunction effects.

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The Upsilon is now seen with 5 sigma with the full HERA data.

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DVCS has also been measured – consistent interpretation withing the CDM (see talk by H. Kowalski)

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Forward Jet Production in DISForward Jet Production in DIS

Forward Jet High x

Small x

Idea (A. Mueller): selection of events with large rapidity interval visible in the detector – laboratory for studying QCD radiation.

NLOJET++: Fixed order QCD partonic cross section, on mass shell ME + DGLAP , (collinear factorisation)

July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider 34

MC ModelsMC Models

LEPTO: LO ME on mass shell + PS in DGLAPLEPTO: LO ME on mass shell + PS in DGLAP

Strong ordering in kTStrong ordering in kT

CASCADE: LO off mass shell ME + PS based on kT factorized CCFM evolutionCASCADE: LO off mass shell ME + PS based on kT factorized CCFM evolution

At small xBj no ordering in kTAt small xBj no ordering in kT

ARIADNE: implementation of Color Dipole Model (CDM)ARIADNE: implementation of Color Dipole Model (CDM)

Random walk in kT like in BFKLRandom walk in kT like in BFKL

July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider 35

• Lepto too low

• Ariadne “default “ too high

• Ariadne “tuned”(by H1) is fine

CASCADE has problem with shape of distributions

Inclusive Forward JetInclusive Forward Jet

July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider 36

Trijet with Forward JetTrijet with Forward Jet

NLOJET++ is below the data – more partons needed. LEPTO also too low, default ARIADNE too high, tuned ARIADNE OK.

Summary: Only CDM (ARIADNE MC), with BFKL-like kT parton cascade, can describe all data on forward jets. However, parameter tuning was necessary.

NLOJET++ is below the data – more partons needed. LEPTO also too low, default ARIADNE too high, tuned ARIADNE OK.

Summary: Only CDM (ARIADNE MC), with BFKL-like kT parton cascade, can describe all data on forward jets. However, parameter tuning was necessary.

July 15, 2008 Structure of hadrons and nuclei at an electron-ion collider 37

SummarySummary

Understanding the small-x physics is still a work in progress, but:

• new data from HERA still coming in (FL, VM updates, total photoproduction cross section)

• The data has simple features• indications of universality in small-x behavior• at small enough x, forget the source – gluons are fundamental aspect of nature

• Phenomenological studies can give insight• need for new round of experiments, e.g., EIC. What will it bring for the small-x aspects of QCD ?