[PPT] - Structure functions and Structure functions and electroweak studies PowerPoint Presentation

SLIDE 1

Structure functions and electroweak studies at HERA Structure functions and electroweak studies at HERA

Alexey Petrukhin

(On behalf of H1 and ZEUS collaborations)

LISHEP 2006, Workshop on Collider Physics

SLIDE 2

Content Content

Introduction to HERA Deep Inelastic Scattering Structure functions Electroweak studies Polarised physics Summary and outlook

SLIDE 3

H1 and ZEUS at HERA H1 and ZEUS at HERA

HERA collider at DESY, Hamburg ep accelerator ring, 27.5 x 920 GeV, GeV circumference: 6.3km 4 experimental halls, 2 collider experiments:

319 sep =

ZEUS H1

WM’06 Arena

SLIDE 4

H1 and ZEUS experiments H1 and ZEUS experiments

Nearly 4π detector coverage Delivering data since 1992 HERA 2: higher luminosity since 2004

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HERA luminosity and status HERA luminosity and status

Luminosity upgrade: mid 2000 – end 2001
Longitudinal polarisation of e-beam for HERA 2
Improvement in machine performance

HERA delivered

50 100 150 200 250 300 200 400 600 800 1000 1200 1400

days of running Integrated Luminosity (pb-1)

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Inclusive Deep Inelastic Scattering at HERA Inclusive Deep Inelastic Scattering at HERA

Neutral current Charged current

e p(P) neutrino

2 2

) ' ( k k Q =

four momentum transfer squared in the reaction
fraction of the proton momentum carried by the parton

e(k) e(k‘) p(P) γ/Z°(Q )

2

X

p eE

E s 4 = sx Q y

2

=

fraction of the lepton’s energy loss,
center-of-mass energy squared

) ' ( 2

2

k k P Q x =

W(Q )

2

X

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Dominant contribution Sizeable only at high y (y>~0.6) Contribution only important at high Q2 (from γZ interference)

] [

3 2 2 2 2 2 4 2 2 2

2 1 ) ( 1 2 ) (

± − ± ± + ±

− + = xW Y W y W Y M Q x M G Q dxd p e d

L W W F CC

m π σ

NC Cross Section: CC Cross Section:

CC Reduced cross section:

] [

~ ~ ~ 2 ) (

3 2 2 4 2 2 2

F x Y Y F Y y F Y Q x Q dxd p e d

L NC + − + + ±

= m α π σ

NC Reduced cross section:

) , ( ~

2

Q x

NC

σ

Cross sections and structure functions Cross sections and structure functions

) , ( ~

2

Q x

CC

σ

2

) 1 ( 1 y Y ± =

±

SLIDE 8

Structure functions Structure functions

The proton structure function in QPM:
Structure function ~gluon density g(x) in NLO QCD and 0 in QPM
determines the valence quark

distributions

Combinations of structure functions allow to unfold PDF and check

QCD as well as electroweak theory

∑

+ =

i i i i

x q x q x e F )] ( ) ( [

2 2

sum of the (anti)quarks density

distributions weighted with their electric charge squared

L

F

∑

−

i i i i i

x q x q x a e xF )] ( ) ( [ 2 ~

3

) (

2

c u s d x W + + + =

+

) , (

2

Q x xqv

) (

2

s d c u x W + + + =

−

flavour separation at high x

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Kinematic plane coverage Kinematic plane coverage

HERA extends

kinematic plane coverage to lower x and higher Q by 2

rders of magnitude

H1 and ZEUS overlap

with fixed target results in wide range of x and Q

x Q2 / GeV2

y = 1 y = . 4 HERA Experiments:

H1 1994-2000 H1 ISR 2000 (Prel.) ZEUS 1994-2000

Fixed Target Experiments:

NMC BCDMS E665 SLAC

10

1

1 10 10 2 10 3 10 4 10

6

10

5

10

4

10

3

10

2

10

1

1

2 2

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Low Q Low Q -

x physics

x physics

2 2

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Structure function F2 Structure function F2

Precision measuremens at

low Q : F2 ~2-3%

F2 rises towards low x

for all measured Q bins

H1 and ZEUS results are

in a good agreement with fixed target data in the overlapping regions

2 2

HERA F2

1 2

Q2=2.7 GeV2 3.5 GeV2 4.5 GeV2 6.5 GeV2

1 2

8.5 GeV2 10 GeV2 12 GeV2 15 GeV2

1 2

18 GeV2

F2

em

22 GeV2 27 GeV2 35 GeV2

1 2

45 GeV2 60 GeV2

10

3

1

70 GeV2

10

3

1

90 GeV2

1 2 10

3

1

120 GeV2

10

3

1

150 GeV2

x

ZEUS NLO QCD fit H1 PDF 2000 fit H1 96/97 ZEUS 96/97 BCDMS E665 NMC

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Rise of F2 towards low x Rise of F2 towards low x

2

Q

) λ(Q 2 2

2

x ) c(Q F

−

⋅ =

F2 used to fit x-dependences in bins for x<0.01 and W>12 GeV:

) /Λ ln(Q ~ λ

2 2

) c(Q2

2 2

GeV 3.5 Q >

2 2

GeV 1 Q = 0.08 λ → Q 2→

and ~const. for Around λ deviates from log-dependence From soft hadronic interactions

it is expected that

for

BPT

SLIDE 13

FL at low Q – ‘shape’ method FL at low Q – ‘shape’ method

2 2

H1 Collaboration

Difference in the shape

between σ and extrapolated F2 vs x is driven by y /Y mostly

+ 2

Fit in Q bins:

λ

σ

− +

⋅ = − = x c F F Y y F

L fit 2 2 2

,

One FL bin per Q

Model dependent determination

Assume

λ −

⋅ = x c F2

2 2

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FL extraction FL extraction

Extracted FL is greater than 0 for all bins in

2

Q

H1 Collaboration

SLIDE 15

FL extraction FL extraction

2

Q

MRST and ZEUS NLO fits tend to be low at low H1 NLO QCD fit is consistent with the data for wide range Alekhin fit is in agreement with the data

2

Q

H1 Collaboration

SLIDE 16

Future Future

Direct measurement of FL can be performed only by measuring

cross section for the same Q -x but with different proton beam energies (different y):

2

L r

F y f F ) (

2 −

= σ

F2-FL

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Expected precision of F Expected precision of FL

L

MRST CTEQ

ZEUS and H1 expressed interest to perform low energy run

460GeV E , 10pb 920GeV E , 30pb

p 1 p 1

= =

− −

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NC and CC unpolarised cross NC and CC unpolarised cross sections, high Q sections, high Q

2 2

SLIDE 19

F2 measurements F2 measurements

F2 across the whole kinematic plane
Extend low Q measurements consistent

with them

Negative scaling violation for x>0.18:

running of αs

Positive scaling violation for x<0.1:

effect of high gluon density

Scaling violations are well described over

4 orders of magnitude in x and Q by QCD fit

2 2

10

3

10

2

10

1

1 10 10 2 10 3 10 4 10 5 10 6 1 10 10

2

10

3

10

4

10

5

Q2 / GeV2 F2 ⋅ 2i

x = 0.65, i = 0 x = 0.40, i = 1 x = 0.25, i = 2 x = 0.18, i = 3 x = 0.13, i = 4 x = 0.080, i = 5 x = 0.050, i = 6 x = 0.032, i = 7 x = 0.020, i = 8 x = 0.013, i = 9 x = 0.0080, i = 10 x = 0.0050, i = 11 x = 0.0032, i = 12 x = 0.0020, i = 13 x = 0.0013, i = 14 x = 0.00080, i = 15 x = 0.00050, i = 16 x = 0.00032, i = 17 x = 0.00020, i = 18 x = 0.00013, i = 19 x = 0.000080, i = 20 x = 0.000050, i = 21

H1 e+p ZEUS e+p BCDMS NMC H1 PDF 2000 extrapolation H1 Collaboration

SLIDE 20

NC cross section and xF3 NC cross section and xF3

At high Q the NC cross

sections in e p and e p scattering are different

The results of measured

cross sections and structure function xF3 are comparable with corresponding SM expectations (γZ interference)

0.25 0.5 0.75 1 0.1 0.2 10

1

1 10

1

1 10

1

1

σ

∼ NC Q2 = 1500 GeV2 Q2 = 5000 GeV2 Q2 = 12000 GeV2 H1 PDF 2000: e+p e−p √s = 319 GeV e+p H1 94-00 e−p H1 98-99

xF

∼ 3 H1 H1 PDF 2000

x

H1 Collaboration

2

+

]

~ ~ [ 2 1 ~ ~

3 + − −

−

NC NC

Y F x σ σ

SLIDE 21

CC and NC cross section measurements CC and NC cross section measurements

Unification of EM and weak

interactions in DIS for

NC cross section exceeds CC

cross section at low Q

Agreement between H1, ZEUS

and QCD fit over seven orders

f magnitude in cross section

2 2 W

M Q >

2 W

M

2 Z

M

γZ interf.

diff. u,d

distribut.

2

γ dominant

SLIDE 22

CC cross section CC cross section

CC e p e p allow to disantangle contributions of u and d quarks:

+

1

2 0.5 1 0.25 0.5 0.75 1 10

2

10

1

10

2

10

1

10

2

10

1

HERA Charged Current

Q2 = 280 GeV2

σ

∼ H1 e-p ZEUS e-p 98-99 H1 e+p 94-00 ZEUS e+p 99-00 SM e-p (CTEQ6D) SM e+p (CTEQ6D)

Q2 = 530 GeV2 Q2 = 950 GeV2 Q2 = 1700 GeV2 Q2 = 3000 GeV2 Q2 = 5300 GeV2 Q2 = 9500 GeV2 Q2 = 17000 GeV2 Q2 = 30000 GeV2

x

σ

) ( ) 1 ( ~ ~ ) ( ) 1 ( ~ ~

2 2

s d y c u s d y c u

CC CC

+ − + + + − + +

− +

σ σ

most sensitive to
most sensitive to
valence quarks suppressed

by factor

p e+ p e− ) , (

2

Q x d ) , (

2

Q x u p e+

2

) 1 ( y −

SLIDE 23

Parton density functions (PDFs) Parton density functions (PDFs)

Cross section measurements

in ep interactions at HERA allow PDF fits

H1 and ZEUS PDFs are in

reasonable agreement though there are differences in the shape of xg

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10

4

10

3

10

2

10

1

x xf(x,Q2)

H1 PDF 2000 H1 ZEUS-S PDF ZEUS-S PDF

Q2=10 GeV2

xuV xdV xg(×0.05) xS(×0.05) xS(x0.05) xg(x0.05)

Sea and gluon distributions are divided by a factor of 20

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Electroweak physics Electroweak physics

Derived from NC DIS (high Q and

high x)

Combined fit to determine PDFs and

Z couplings to u and d quarks

2 H1

68% CL

vu-au-vd-ad-PDF vu-au-PDF Standard Model CDF

au vu

1

1

1

1

Result consistent with SM, comparative

with determination at Tevatron

H1

68% CL

H1 vu-au-vd-ad-PDF H1 vd-ad-PDF Standard Model CDF

ad vd

1

1

1

1

First HERA results on

EW parameters

SLIDE 25

Polarised physics at HERA II Polarised physics at HERA II

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Polarised CC cross section Polarised CC cross section

Linear dependence of CC cross section on

polarisation:

The degree of longitudinal polarisation:

) , ( ~ ) ( 1 2 ) (

2 2 2 2 4 2 2 2

Q x M Q P x M G Q dxd p e d

CC W e W F CC ± ±

+ ± = σ π σ

Vanishing cross section for e and e

RH

+

LH

) /( ) (

L R L R e

N N N N P + =

NR(NL) – number of right(left) handed polarised leptons in the beam

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CC total cross section CC total cross section

Data exhibit linear

dependence with P and are compatible with vanishing cross sections for left(right)-handed positrons(electrons)

Measurements of CC cross

section at HERA1 and HERA2 consistent with Standard Model

e

P

1
0.5

0.5 1

(pb)

CC

σ

10 20 30 40 50 60 70 80 90 100

2

> 400 GeV

2

Q y < 0.9

X ν → p

+

e

H1 (prel.) H1 ZEUS (prel.) ZEUS SM (MRST)

X ν → p e

H1 (prel.) H1 ZEUS (prel.) ZEUS SM (MRST)

Charged Current ep Scattering (HERA II)

SLIDE 28

Polarised NC cross section Polarised NC cross section

ZEUS

10

5

10

4

10

3

10

2

10

1

1 10 10

3

10

4

ZEUS NC 04 e+ (12.3 pb-1) SM (ZEUS-JETS) Pe = +0.32 (a)

Q2 (GeV2) dσ/dQ2 (pb / GeV2) 10

5

10

4

10

3

10

2

10

1

1 10 10

3

10

4

ZEUS NC 04 e+ (11.5 pb-1) SM (ZEUS-JETS) Pe = −0.41 (b)

Q2 (GeV2) dσ/dQ2 (pb / GeV2) 0.5 1 1.5 10

3

10

4

σ (Pe=+0.32) / σ (Pe=−0.41)

Q2 (GeV2) 0.5 1 1.5 10

3

10

4 SM (ZEUS-JETS) ZEUS NC 04 e+ Pe=+0.32 / Pe=−0.41

(c)

2 2

1000GeV Q >

) 41 . ( / ) 32 . ( − = + =

e e

P P σ σ Above ratio of is above 1. Well consistent with SM prediction

ZEUS

)

2

(GeV

2

Q

3

10

4

10 )

2

(pb/GeV

2

/dQ σ d

6

10

5

10

4

10

3

10

2

10

1

10 1 10

)

1

p (8.4pb

ZEUS NC (prel.) 04-05 e

SM (ZEUS-S) P=+29.2%

(a) )

2

(GeV

2

Q

3

10

4

10 )

2

(pb/GeV

2

/dQ σ d

6

10

5

10

4

10

3

10

2

10

1

10 1 10

)

1

p (45.1pb

ZEUS NC (prel.) 05 e

SM (ZEUS-S) P=-25.9%

(b) )

2

(GeV

2

Q

3

10

4

10

(P=-25.9%)

2

/dQ σ (P=+29.2%) / d

2

/dQ σ d

0.5 1 1.5 2 2.5 3

p

ZEUS NC (prel.) 04-05 e

SM (ZEUS-S) P=+29.2% / P=-25.9%

(c)

SLIDE 29

Conclusions Conclusions

HERA continues to deliver many interesting results
Precision of ~2−3 % achieved for F2
H1 and ZEUS want to measure FL at low EP
The electroweak results provide consistency check of SM
The measured NC and CC cross sections (also for longitudinally

polarised lepton beam) are consistent with the Standard Model