Structure-function measurements at HERAmusashi.phys.se.tmu.ac.jp/nufactj03/nufactj03-kuze.pdf · [email protected] 17/May/2003 NufactJ03 meeting 1 Structure-function measurements

[email protected] 17/May/2003 NufactJ03 meeting 1

Structure-function measurementsat HERA

� Introduction

� F2 measurement and PDF fit

� Low-Q2 region

� High-Q2 region

� Current status and prospects

Masahiro Kuze

Department of PhysicsTokyo Institute of Technology


HERA ep Collider at DESY/Hamburg

• Ep=920GeV ⊗ Ee=27.5GeV (e+ or e−) ⇒• 2 colliding experiments and 2 fixed-target experiments• On-tape luminosity: ~110 pb-1 e+p, ~15 pb-1 e−p (‘98-’99) for H1 or ZEUS

HERA luminosity 1992 – 2000

10

20

30

40

50

60

70

10

20

30

40

50

60

70

Inte

grat

ed L

umin

osity

(pb

-1)

Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

9293

94

95

1996

1997

98

1999 e-

1999 e+

2000

15.03.

s = 318GeV


Deep Inelastic Scattering (DIS)

• Probe the proton (our most familiar micro-cosmos)with a point-like lepton probe. ‘giant electron-microscope’

• Bjorken x: Fractional momentum of a parton in the nucleon.

• 1/Q (momentum transfer) gives the spacial resolution.

• Neutral orCharged currentin t-channelpropagator

Q2=sxy


Kinematic region probed

• > 100x larger kinematic reachcompared to fixed-target DISexperiments at CERN, DESY,FNAL, SLAC… (if proton is at rest,HERA CM energy means Ee=54TeV)

• At high Q2, probe the validity ofQCD at smallest distance →Quark structure? New particles?(Q2=40,000 GeV2 →1/Q=0.001 fm)

• At low Q2, probe the low-x region→ very soft constituents of proton;Saturation? Breakdown of standardDGLAP formalism (BFKL) ? log x

log

Q2

y =

1

y =

0.00

5

H1 + ZEUS

HERMES

E665

BCDMS

CCFR

SLAC

NMC

�

0

2

3

4

5

-6 -5 -4 -3 -2 -1

1

-1


The Detectors

• ZEUS Detector– Uranium-Scintillator calorimeter

• for electrons• for hadrons

– Central tracking detector•

• H1 Detector– Liquid-Ar calorimeter

• for electrons• for hadrons

– Central tracking detector

σ(E) /E =18%/ Eσ(E) /E = 35%/ E

σ(pT ) / pT =

0.0058pT ⊕ 0.0065⊕ 0.0014 / pT

σ(E) /E =12%/ Eσ(E) /E = 50%/ E

2 out of (Ee, θe, Eh, θh)→ Reconstruction of (x, Q2)

e→


Cross section & Structure functions

• NC differential cross section

[Y+F2(x, Q2) Y−xF3(x, Q2) − y2FL(x, Q2)]

F2 = Σ xqf+(x, Q2)[ef

2 − 2ef vf vePZ + (vf2+af

2)(ve2+ae

2)PZ2]

xF3 = Σ xqf−(x, Q2)[− 2ef af aePZ + 4vf af veaePZ

2] (f=u,d,c,s,b)

(Parton Distribution Functions)

PZ = sin−22θW⋅Q2/(Q2+MZ2) (Z-exchange & γ−Z interference)

Y± = 1 ± (1−y)2, ef: quark charge, vi/ai: EW couplings FL = F2 − 2xF1 (→0 in LO QCD, longitudinal Str. Function)

d2σ e ± p

dxdQ2 =2πα 2

xQ4

xqf± = xqf (x,Q

2) ± xq f (x,Q2)

+


Results of F2 Structure Function

• Strong rise of F2 as x decreases– Soft ‘sea’ of quarks in the proton

• Slope of rise gets steeper as Q2 ↑

softer parton smaller resol.

dynamics of quarks and gluons

• Good agreement with fixed-targetexperiments at middle - high x– Sea + valence quarks

HERA F2

0

1

2 Q2=2.7 GeV2 3.5 GeV2 4.5 GeV2 6.5 GeV2

0

1

2 8.5 GeV2 10 GeV2 12 GeV2 15 GeV2

0

1

2 18 GeV2

F2 em

22 GeV2 27 GeV2 35 GeV2

0

1

2 45 GeV2 60 GeV2

10-3

1

70 GeV2

10-3

1

90 GeV2

0

1

2

10-3

1

120 GeV2

10-3

1

150 GeV2

x

ZEUS NLO QCD fit

tot. error

H1 96/97ZEUS 96/97

BCDMSE665NMC


F2 for fixed x, as a function of Q2

• At low x, strong scaling violationis seen.Large gluon density + splitting→ F2 increases

• At x ~ 0.1, approximate scaling.• At higher x, F2 decreases as Q2 ↑.

• Line = result of QCD fit (next slide)

– All data points well described.

g → qq

HERA F2

0

1

2

3

4

5

1 10 102

103

104

105

F2 em

-log

10(x

)

Q2(GeV2)

ZEUS NLO QCD fit

tot. error

H1 94-00 prelim.

H1 96/97

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5 x=0.000102x=0.000161

x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65


Perturbative-QCD fit of F2 data

• Example: ZEUS NLO DGLAP analysis PRD 67 (2003) 012007

– At Q2 = Q20, input functional form of PDF (Q2

0 =7GeV2)

• xf(x) = p1xp2(1-x)p3(1+p5x) for u-valence, d-valence, sea quarks and gluons

– ‘Q2 evolution’ is predicted byDGLAP (‘Altarelli-Parisi’) Equations

• �fi/�lnQ2 = (αs/2�)�fj⊗ Pij

Pqq Pgq Pqg Pgg

– Use world’s precision DIS data + ZEUS F2• BCDMS, NMC, E665, CCFR (µ-p, µ-D, ν-Fe)

– χ2 fit to determine p1 … p5


PDFs obtained from the fitsZEUS

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10-3

10-2

10-1

1

ZEUS NLO QCD fit

αs(MZ2) = 0.118

tot. error

CTEQ 6M

MRST2001

Q2=10 GeV2

xuv

xdv

xg(× 0.05)

xS(× 0.05)

x

xf

HERA: PDF determination

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10-3

10-2

10-1

1

H1 2002 PDF Fit (prel.)�s(MZ

2) = 0.1185 fixeddata set: H1 (94/00) + BCDMS

ZEUS NLO QCD fit�s(MZ

2) = 0.1180 fixeddata set: ZEUS (96/97) + BCDMS, NMC, E665, CCFR

experimental errors only

Q2=1000 GeV2

xuv

xdv

xS( 0.05)

x

xf


Low-x sea and gluon distributions• At Q2 ~ 1GeV2, gluon becomes valence-

like (and even tends to be negative)

• Sea quark is still rising

ZEUS

-2

0

2

4

6 Q2=1 GeV2

ZEUS NLO QCD fit

xg

xS

2.5 GeV2

xS

xg

0

10

207 GeV2

tot. error(αs free)

xS

xg

xf

20 GeV2

tot. error(αs fixed)

uncorr. error(αs fixed)

xS

xg

0

10

20

30

10-4

10-3

10-2

10-1

1

200 GeV2

xS

xg

10-4

10-3

10-2

10-1

1

2000 GeV2

x

xS

xg

ZEUS

0

5

10

15

20

1 10 102

103

104

xg

Q2(GeV2)

(a)

ZEUS NLO QCD fit

tot. error (αs-free)

tot. error (αs-fixed)

x=0.0001

x=0.001

x=0.01

x=0.1


Simultaneous extraction of αs and PDF

• Scaling violation: ∂F2/∂lnQ2 ~ αs•xg(x,Q2)Data at low x allow disentanglingcorrelation of αs and xg

• αs-free fit gives:H1: (additionally ±0.0005 from renormalization scale)

ZEUS: (additionally ±0.0004 from renormalization scale)

Difference in exp. error mainly from the treatment ofsystematic error and normalization of data pointsin the fitting procedure and error propagation.

α s = 0.1150 ± 0.0017(exp)−0.0005+0.0009(model)

α s = 0.1166 ± 0.0049(exp)± 0.0018(model)

HERA αs Measurements


What if there were no HERA data?

• HERA datadeterminethe low-xgluon andsea-quarkPDF.

• HERArevealed:F2 is verysteep.

ZEUS

0

1

2 Q2=2.7 GeV2 3.5 GeV2 4.5 GeV2 6.5 GeV2

0

1

2 8.5 GeV2 10 GeV2 12 GeV2 15 GeV2

0

1

2 18 GeV2

F2 em

22 GeV2 27 GeV2 35 GeV2

0

1

2 45 GeV2 60 GeV2

10-3

1

70 GeV2

10-3

1

90 GeV2

0

1

2

10-3

1

120 GeV2

10-3

1

150 GeV2

x

ZEUSNLO-QCD fit

tot. error

WITHOUT-ZEUS fittot. error

ZEUS 96/97BCDMSE665NMC

ZEUS

0

10

20 Q2=1 GeV2

ZEUS NLO QCD fit

tot. error

2.5 GeV2

WITHOUT-ZEUS fit

tot. error

0

10

20

xg

7 GeV2 20 GeV2

0

10

20

10-4

10-3

10-2

10-1

1

200 GeV2

10-4

10-3

10-2

10-1

1x

2000 GeV2


Where is the lowest applicability of pQCD?

• Recall gluon becomes negativeat low Q2.

• It is not necessarily a problem,since PDF itself is not a physicalobservable.

• However, FL (observable)becomes also negative forQ2 < ~ 1 GeV2.

• Is this the lowest end of p-QCDapplicability?Look at the F2 data →

ZEUS

-0.2

0

0.2

0.4

0.6 Q2=0.3 GeV2 0.4 GeV2 0.5 GeV2

-0.2

0

0.2

0.4

0.6 0.585 GeV2

FL

0.65 GeV2 0.8 GeV2

-0.2

0

0.2

0.4

0.6 1.5 GeV2 2.7 GeV2

10-5

10-3

10-1

1

3.5 GeV2

-0.2

0

0.2

0.4

0.6

10-5

10-3

10-1

1

4.5 GeV2

10-5

10-3

10-1

1

6.5 GeV2

x

ZEUSNLO QCD fit

tot. error


Transition from perturbative to non-p. region

• At very low Q2, αs ↑ and non-perturbative effects important.

• ZEUS BPT data at very low Q2

available.

• Data cannot be described bypQCD fit below Q2 ~ 1 GeV2.(rather, it’s a surprise that pQCDworks as low as 1 GeV2 !)

• This is evident thanks to HERAdata at low x.

ZEUS

0

0.5

1

1.5

2 Q2=0.3 GeV2 0.4 GeV2 0.5 GeV2

0

0.5

1

1.5

2 0.585 GeV2

F2 em

0.65 GeV2 0.8 GeV2

0

0.5

1

1.5

2 1.5 GeV2 2.7 GeV2

10-5

10-3

10-1

1

3.5 GeV2

0

0.5

1

1.5

2

10-5

10-3

10-1

1

4.5 GeV2

10-5

10-3

10-1

1

6.5 GeV2

x

ZEUS NLO QCD fit

tot. error

ZEUS 96/97ZEUS BPT 97ZEUS SVX 95E665NMC


F2 slope in low-x region

• For x<0.01, F2 can be wellparameterised by c•x−λ.

• λ fairly independent of x,linearly rises with logQ2 in‘DIS’ regime.

• Qualitative change happensaround Q2 < ~1GeV2, then λflattens in non-pert. region.

H1

Col

labo

ratio

n


DIS in the hadronic picture

• At very low Q2, quasi-real photon acts likea hadron (vector-meson dominance)

• Plot shows F2 for fixed y, i.e.at fixed γ*-p CM energy W (W2~sy= Q2/x)

• σtot(γ*p)=(4π2α/Q2)F2(x=Q2/W2, Q2)so F2 must vanish as F2∝Q2 as Q2 → 0.

• Data show this behaviour (25<W<270 GeV)

and successfully fitted by a Regge-type fit.(consitent with Pomeron and Reggeon trajectoriesdetermined from hadron-hadron scattering)


Attempts to describe both regions

• γ dissociates into a qq pair (dipole) ofradius r=1/Q upstream of the proton.

• Its cross section with proton (σdipole)rises as r2 for small r (pQCD region).

• It saturates at large r, for r >~ R0.

• The critical radius R0 is characterisedby the parton density: R0~1/gluon~xλ

(low x = high-density environment).

• DIS cross section is a convolution ofσdipole and photon wave function Ψ.

Dipole models: a class of phenomenological modelsexample: Golec-Biernat & Wuesthoff DGLAP-like saturation

_

ˆ

ˆCartoon: R.Yoshida


Does it describe the data?• This simple model gives a good

description of x<0.01 F2 data for both Q2

regions.

• Amazing thing is that the single modeldescribes F2, diffractive cross section andvector-meson production at the sametime (not discussed here).

Red:original GB&W

Blue:modified one (includesDGLAP evolution)Bartels, GB, KowalskiPRD66(2002)014001

Transition to low Q2

Q2 (GeV2)

F2(

x=Q

2 /sy,

Q2 )

y=0.007(x 1)

y=0.015(x 2)

y=0.025(x 4)

y=0.05(x 8)

y=0.12(x 16)

y=0.20(x 32)

y=0.26(x 64)

y=0.33(x 128)

y=0.4(x 256)

y=0.5(x 512)

y=0.6(x 1024)

y=0.7(x 2048)

y=0.8(x 4096)

10-1

1

10

10 2

10 3

10-2

10-1

1 10 102

Effective slopes

Q2(GeV2)

λ

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

10-2

10-1

1 10 102


High-Q2 region − Electroweak effects• Pz = Q2/(Q2+MZ

2)At Q2 > ~5000 GeV2, effect ofZ-exchange clearly visible.

• σ(e−p) > σ(e+p) due to ±xF3

sensitive to valence quarks

• Statistically limited: more luminosity helps(esp. e−p)

ZEUS

0

0.5

1

1.5 Q2=200 GeV2 250 GeV2 350 GeV2 450 GeV2

0

0.25

0.5

0.75

1650 GeV2

σ∼ NC

800 GeV2 1200 GeV2 1500 GeV2

0

0.2

0.4

0.6

0.82000 GeV2 3000 GeV2 5000 GeV2

10-2

1

8000 GeV2

0

0.2

0.4

0.6

10-2

1

12000 GeV2

10-2

1

20000 GeV2

10-2

1

30000 GeV2

x

ZEUSNLO QCD fit

tot. error

ZEUS NC e- p98/99

ZEUS NC e+ p96/97

xF 3∝q(x,Q2) − q(x,Q2)

-0.2

0

0.2

0.4xF~

3

Q2 = 1500 GeV2 Q2 = 3000 GeV2 Q2 = 5000 GeV2

0

0.2

0.4

10-1

1

Q2 = 8000 GeV2

10-1

1

Q2 = 12000 GeV2

10-1

1x

Q2 = 30000 GeV2

ZEUSH1

SM


Charged current − flavour decomposition

• e+p: only negative-charge quarks take part.

At high x, mainly d(x, Q2) probed.

• e−p: only positive-charge quarks take part.

At high x, mainly u(x, Q2) probed.

• In addition to u(x, Q2) > d(x, Q2), e+p getshelicity suppression (1-y)2. (y=Q2/sx)⇒ σ(e−p) >> σ(e+p) at large Q2.

• Data (not used in the fit) well described byQCD prediction.

ZEUS

0.5

1

1.5

2Q2=280 GeV2 530 GeV2 950 GeV2

ZEUSNLO QCD fit

tot. error

0.25

0.5

0.75

1 1700 GeV2

σ∼ CC

3000 GeV2 5300 GeV2

0.2

0.4

0.6

0.8

10-1

1

9500 GeV2

10-1

1

17000 GeV2

10-1

1

30000 GeV2

x

ZEUS CC e- p98/99

ZEUS CC e+ p94-97

d2σ e + p

dxdQ2 =GF

2πMW

2

MW2 +Q2

2

u + c + (1− y)2(d + s)[ ]

d2σ e − p

dxdQ2 =GF

2πMW

2

MW2 +Q2

2

u + c + (1− y)2(d + s)[ ]


Can valence be determined by HERA only?

• ZEUS-only fit (all HERA-I NC/CC data, prel.) still a bit less precise thanglobal fit, but looks promising with future HERA-II data (e.g. d/u at high x).

• Using only ep data: no uncertainty from nuclear corrections (D, Fe, …).

ZEUS

10-2

10-1

1

0 0.2 0.4 0.6 0.8 1

xqV

Q2=1 GeV2

0 0.2 0.4 0.6 0.8 1

20 GeV2

ZEUS ONLY fit (prel.)

(94-00 data)

10-2

10-1

1

0 0.2 0.4 0.6 0.8 1

200 GeV2

tot. error

xuV

xdV

0 0.2 0.4 0.6 0.8 1

x

2000 GeV2

uncorr. error

ZEUS

10-2

10-1

1

0 0.2 0.4 0.6 0.8 1

xqV

Q2=1 GeV2

0 0.2 0.4 0.6 0.8 1

20 GeV2

ZEUS NLO QCD fit

10-2

10-1

1

0 0.2 0.4 0.6 0.8 1

200 GeV2

tot. error

xuV

xdV

0 0.2 0.4 0.6 0.8 1

x

2000 GeV2

uncorr. error


Evidence of Electro-Weak Unification

• At low Q2:NC ~ 1/Q4 (EM current)CC ~ GF

2 (Weak current)

• At high Q2 (> Mz2, MW

2):Both NC and CC mediated by unifiedEW current. σNC~σCC

• Dumping of σCC at high Q2

comes from Mw. Fit gives: (Z. e−p)

Mw = 80 ±2(stat)±1(syst)±1(PDF) GeV

• Space-like: q2(boson) << 0Completely different phase-space fromtime-like bosonsat LEP and Tevatron (q2 > 0).Complementary evidence/measurement. 10

-7

10-6

10-5

10-4

10-3

10-2

10-1

1

10

103

104

H1 e+p CC 94-00 prelim.

H1 e-p CCZEUS e+p CC 99-00 prelim.

ZEUS e-p CC 98-99 prelim.

SM e+p CC (CTEQ5D)

SM e-p CC (CTEQ5D)

H1 e+p NC 94-00 prelim.H1 e-p NC

ZEUS e+p NC 99-00 prelim.

ZEUS e-p NC 98-99 prelim.

SM e+p NC (CTEQ5D)

SM e-p NC (CTEQ5D)

y < 0.9

Q2 (GeV2)

dσ/d

Q2 (

pb/G

eV2 )

Interplay of EW and QCD physics


Limits on quark radius

• Repeat ‘form-factor measurement’ as we did for protons, butat Q2 ~ 40,000 GeV2 instead of 1 GeV2.– Resolution = 1/Q ~ 10-16cm = 0.001 proton radius

• If quark has a finite radius, cross section will decrease as theprobe ‘penetrates’ into it (sees less EW charge). σ = σSM(1−<Rq

2>Q2/6)2

• Limits on quark size(assuming electron is pointlike)ZEUS: Rq < 0.73*10-16 cm H1: Rq < 0.82*10-16 cm(95% CL)

Q2 [GeV2]

N/N

CT

EQ

5D

ZEUSZEUS (prel.) 94-00 e±p

Quark Radius Limit

Rq=0.73 ⋅10-16cm

1

10

103

104

103

104

0.8

1

1.2

High-Q2 NC data


Large Extra Dimensions?• Arkani-Hamed, Dimopoulos and Dvali:

Assume n extra dimensions compactified to scale R,where only gravity propagates.Real GUT scale could be as low as TeV(RnMs

n+2 ~ M2Planck)

• Collider consequence: exchange of Kaluza-Kleinexcitations of gravitons would modify SM-particlescattering at high energy.

• HERA: eeqq CI formalism with λ/Ms4 as a parameter

• λ=+1: Ms > 0.83 TeV (H1), 0.81 TeV (ZEUS)λ=−1: Ms > 0.79 TeV (H1), 0.82 TeV (ZEUS)

• LEP, Tevatron limits ~ 1 TeV

0

1

2

3

103

104

��H1 data��

e−pNeutral Current√s¬=318 GeV

HERA I H1 preliminary

Q2 (GeV2)

dσ

/dQ

2 / dσ

SM

/dQ

2

Large Extra Dimension

Ms=580 GeV�� λ=+1Ms=610 GeV�� λ=−1

0

1

2

3

103

104

��H1 data��

e+pNeutral Current√s¬=318 GeV

HERA I H1 preliminary

Q2 (GeV2)

dσ

/dQ

2 / dσ

SM

/dQ

2

Large Extra Dimension

Ms=770 GeV�� λ=+1Ms=730 GeV�� λ=−1


HERA luminosity upgrade

• 2000-2001: shutdown for lumi upgrade.– Final focussing magnets inside detector→ 5x luminosity than 2000 values

– Goal: Accumulate ~1 fb-1 in HERA-II run (till 2006)

– Longitudinal e± polarization for H1/ZEUS by spin rotators(was available only for HERMES)

• Also detector upgrades (ZEUS example)– Micro-vertex detector (b,c-tagging)

– Straw-tube tracker (forward tracking)

– New luminosity counters (calorimeter + spectrometer)


Current status

• New detector components successfully commissioned.

• New machine optics fine, achieved design specific luminosity

(luminosity per beam currents).

• 2002-03 run: with commissioning (modest) beam currents.

• Beam currents limited by backgrounds at detectors (chamber currents).

– Unexpectedly high double-scattered synchrotron radiation

– Vacuum conditioning of the new ring slower than expected

→ high proton beam-gas background in the detector

• Remedies will be taken in the shutdown March to June 2003.

• Achieved before shutdown: L=2.7*1031cm-2s-1 (design 7.0)

• Max 50% e+ polarization achieved with H1/HERMES/ZEUS rotators.


Summary

• Probing the proton with very high-energy probe showed us:– Precise measurement of sea-quark and gluon distributions

at low x → Crucial inputs for current and future experiments.

– Point of transition from perturbative to non-perturbative picture ofthe proton in QCD: Q2~1GeV2

– At high Q2, EW effects clearly visible and QCD evolution is validup to ~10,000GeV2.

• HERA-2 has started. High-luminosity run expected this fall.– Very precise determination of F2 and gluon distribution.

– Flavour decomposition using various tools.

– Polarized e±p to probe EW structure of DIS.

• Exciting future ahead with 10x more data and polarization.

Documents

Structure-function measurements at HERAmusashi.phys.se.tmu.ac.jp/nufactj03/nufactj03-kuze.pdf · [email protected] 17/May/2003 NufactJ03 meeting 1 Structure-function measurements