Physics at HERA - DESY · Physics at HERA Katja Krüger ... H1 Collaboration email:...

Physics at HERA

Katja Krüger KirchhoffInstitut für Physik

H1 Collaborationemail: [email protected]

Summer Student Lectures18 + 19 August 2008

Katja Krüger Physics @ HERA 2

Overview● Introduction to HERA● Inclusive DIS & Structure Functions

– formalism

– HERA results

● High Q2 & Electroweak Physics● QCD: Jet Physics, Heavy Flavour Production● Beyond the Standard Model● (Diffraction)


Collider Types

e+e

+ clean initial and final state

+ small background

– limited energy

● LEP (200 GeV) ILC (1 TeV)

p±p±

+ high energy

– complicated final state

– large background

● Tevatron (2 TeV) LHC (14 TeV)

ep+ unique initial state

+ electron as probe of proton structure

– two accelerators

● HERA (300 GeV)


HERAHERA

eepp27.6 GeV27.6 GeV920 GeV920 GeV

H1

ZEUS


HERA & its PreAccelerators

circumference: 6.3 km

e

p

bunch crossing rate: 10.4 MHz


Collected Luminosity● HERA operated 19922007

● lumi upgrade in 2001– higher luminosity

– e polarization

– detector upgrades

● in total ~500 pb1 of high energy data collected per experiment

● last months devoted to low p energy (460, 575 GeV)


ZEUS Detector

tracking detector

calorimeter

muon system

magnet coil

p

e


H1 Detector

tracking detector

calorimeter

muon system

magnet coil

p

e


Schematic View of the H1 Detector


Physics Topics at HERA

● proton structure– structure functions

– parton densities

– s

● photon structure

● perturbative QCD– jets

– heavy quarks

● electroweak

● exotics (beyond the standard modell)– SUSY

– leptoquarks

– ...

● diffraction

expected not (so) expected


Some Events...


Event Rates

some Hz

some kHz

some min1

some hour1


ep Scattering & Structure Functions


H1 and ZEUS Combined PDF Fit

HE

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x = 0.000032, i=22x = 0.00005, i=21

x = 0.00008, i=20x = 0.00013, i=19

x = 0.00020, i=18x = 0.00032, i=17

x = 0.0005, i=16x = 0.0008, i=15

x = 0.0013, i=14x = 0.0020, i=13

x = 0.0032, i=12x = 0.005, i=11

x = 0.008, i=10x = 0.013, i=9

x = 0.02, i=8

x = 0.032, i=7

x = 0.05, i=6

x = 0.08, i=5

x = 0.13, i=4

x = 0.18, i=3

x = 0.25, i=2

x = 0.40, i=1

x = 0.65, i=0

Q2/ GeV2

σ r(x,Q

2 ) x 2

i

HERA I e+p (prel.)Fixed TargetHERA I PDF (prel.)

103

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„The“ HERA Textbook Plots

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quarks ?

gluons ?


Rutherford Scattering

● first scattering experiment

➔ existence of the nucleus from HyperPhysics

dd

= 140

Z 1 Z 2 e2

4 E kin

2

1

sin4 2

assumes– Coulomb potential– no spins– no recoil


Elastic Electron Scatteringvariables:● q = k – k'● Q2 = – q2

=

●

➔ only one independent!

dd Q2=

42 z2

Q4 E 'E

2

cos2 2

e (k) e' (k')

q

q=k−k '4 E E ' sin2 /2

E '=E

12 E /M sin2 /2particles

staysintact

mass M, charge z,spin 0Coulomb

Potential ~1/rrecoil


Elastic Electron Scattering: Cross Section● Mott Scattering: electron on a pointlike

charged particle with spin 0

● Dirac Sacttering: electron on a pointlike charged particle with spin ½

● electron on proton: „form factors“ needed:

➔ protons are not pointlike!

dd Q2

Mott

=42

Q4 E 'E

2

cos2 2

dd Q2

Dirac

= dd Q2

Mott[12 tan2

2 ] with =Q2

4 M 2

dd Q2

ep

= dd Q2

Mott[GE

2 Q2GM2 Q2

12 G M

2 Q2 tan2 2 ]


Electric Form Factor of the Proton

● describes the charge distribution in the proton (Fourier transform)

● measured:

– GE(0) = 1

– GM(0) = 2.79

–

➔ elastic scattering only import at low Q2

GE Q2 , GM Q

2 ∝ 1 Q2

0.71 GeV2 −2

fromJ.J. Murphy et al., „Proton form factor from 0.15 to 0.79 fm2


Inelastic Electron Scattering

variables:● q = k – k'● Q2 = – q2 ● s = (P + k)2

● W2 = (P + q)2

= M2 + 2q∙P – Q2

● y = q∙P / k∙P

➔ two independent!

e (k)

e' (k')

q

q=k−k '

p (P)W

inelastic: W > Melastic: W = M


Inelastic Electron Proton Scattering

● inelastic scattering: W > Mp

● ratio to Mott cross section nearly flat in Q2


Deep Inelastic Scattering (DIS)● deep: Q2 > Mp

● inelastic: W > Mp

● for HERA: me, Mp << W neglect me, Mp – s = 4 Ep Ee

–

–

– W = y √s – Q2

● one more variable: x = Q2 / (2 P∙q) = Q2 / ys

k=(Ee,0,0,Ee)

P=(Ep,0,0,Ep)

k '=E 'e ,0 , E 'e sine , E 'e cose

attentione=−

Q2=2 Ee E 'e1cose

y=1−E'eEe

sin2 e

2


DIS: What is x?

k

k'

P

xP

P'q

q

P 'q=qxP

qxP2 =−Q22x q⋅PxP2

qxP2 = xP2 = mq2

x =Q2

2 q⋅P=

Q2

ys

x can be interpreted as the momentum fraction of the struck parton of the proton:

inelastic proton scattering is scattering on a parton of the proton!


Structure Functions F1 & F2

● the DIS cross section can be written as

● comparison with Dirac formula

➔ F2 corresponds to electric field of the parton

➔ F1 corresponds to spin of the parton

d2dx dQ2=

42

Q4

1x [1−y F2 x ,Q2

y2

22 x F1x ,Q2]

=42

Q4

1x

E 'E [F 2 x ,Q2 cos2

2

Q2

2 x2 M p2 2 x F 1 x ,Q2 sin2

2 ]

dd Q2

Dirac

=42 z2

Q4 E 'E

2

[cos2 2

Q2

2 M2 sin2 2 ]


Parton Spin● parton spin ½: 2 x F1 = F2 (Callan Gross)

● parton spin 0: 2 x F1 = 0

partons have spin ½

from P. Schmüser, „FeynmanGraphen und Eichtheorien für Experimentalphysiker“


Scaling: F2 independent of Q2

SLAC 1972

independent of Q2, we always see the same partons (=quarks)


(Naive) Quark Parton Model

● proton consists of 3 partons, identified with the QCD quarks

● during the interaction proton is „frozen“

● electron proton scattering is sum of incoherent electron quark scatterings

● proton structure is defined by parton distributions F2 x , Q2=x∑ eq

2 q x


How does F2(x) look like?



from Povh et al., „Teilchen und Kerne“

what happens at low x?


Scaling Violations

at smaller & larger x, the amount of quarks depends on Q2!


Parton Evolution● number of partons changes with Q2

● Q2 can be interpreted as resolving power: Q2∝ℏ/2

small Q2:● many partons with large x● (nearly) no partons at low x

large Q2:● less partons with large x● more partons at low x


DGLAP Evolution Equations

● Q2 dependence of quark densities q(x,Q2) and gluon density g(x,Q2) is predicted

● no prediction for the x dependence initial condition needed


HERA Kinematic Range

beforeHERAnew


Events in Different Regions



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x = 0.000032, i=22x = 0.00005, i=21

x = 0.00008, i=20x = 0.00013, i=19

x = 0.00020, i=18x = 0.00032, i=17

x = 0.0005, i=16x = 0.0008, i=15

x = 0.0013, i=14x = 0.0020, i=13

x = 0.0032, i=12x = 0.005, i=11

x = 0.008, i=10x = 0.013, i=9

x = 0.02, i=8

x = 0.032, i=7

x = 0.05, i=6

x = 0.08, i=5

x = 0.13, i=4

x = 0.18, i=3

x = 0.25, i=2

x = 0.40, i=1

x = 0.65, i=0

Q2/ GeV2

σ r(x,Q

2 ) x 2

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F2 vs. Q2

● HERA data cover huge range: 5 orders in Q2 and 4 orders in x

● approximate scaling at large x

● clear scaling violations at small x fixed target


F2 vs. Q2: example bins


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HERA I e+p (prel.)

HERA I PDF (prel.)

H1 2000 PDFZEUSJETS

● clear scaling violations at small x

● approximate scaling at large x


F2 vs. x

strong rise towards low x, steepness rising with Q2


DGLAP Evolution Equations

● Q2 dependence of quark densities q(x,Q2) and gluon density g(x,Q2) is predicted


Parton Density FitsDGLAP predicts only Q2 dependence➔ assume parametrisation of the parton density functions

(PDFs) as a function of x at a starting scale Q02 (typically

around 4 7 GeV2):

➔ evolve the PDFs to all measured Q2, calculate F2, and fit

the parameters to match the data

some freedom in the procedure!– how many parameters, which Q

02 ?

– how to combine quark and antiquark densities?

x q x ,Q02=A xB 1−x C [1D xE x2F x3 ]


Parton Density Fitsquark and antiquark densities:● most general:

● distinguish valence and sea quarks (ZEUS):

● distinguish uptype and downtype quarks (H1):

u ,u ,d , d ,s ,s ,c ,c ,b ,b

uv , d v , sea ,d−u

U=uc , D=ds b U=uc , D=ds buv=U−U , d v=D−D

xU

vxu

Ux

xD

vxd

Dx

xg

2 = 10 GeV2 Q

ZEUSJETS fit tot. uncert.

H1 PDF 2000 tot. exp. uncert. model uncert.

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ZEUS


Combined H1 & ZEUS Parton Density

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Longitudinal Structure Function FL

● CallanGross relation 2 x F1 = F2 only true in naive QuarkPartonModel

● the longitudinal structure function FL is defined as FL = F2 – 2 x F1

● FL is directly proportional to the gluon density● for a measurement of FL one needs data at the same x

and Q2, but different y

● only possible with different s because Q2 = xys➔ measure at different beam energies!

d 2dx dQ2=

42

Q4

1x1−y

y2

2[ F 2 x ,Q2 −

y2/21−yy2 /2

F L x ,Q2]


●Longitudinal Structure Function FL

r=x Q4

22

1Y

d2dx dQ2

=F 2 x ,Q2 −y2

Y

F L x ,Q2

with Y=11−y2

● linear expression in y2/Y+

➔ use linear fits in y2/Y+ and determine FL from slope


Longitudinal Structure Function FL

ZEUS

LF

x

0

1

2= 24 GeV2Q

310 210

0

1

2= 60 GeV2Q

2= 32 GeV2Q

310 210

2= 80 GeV2Q

2= 45 GeV2QZEUS (prel.)ZEUSJETS

310 210

2= 110 GeV2Q)1 = 225 GeV (14.0pbs)1 = 252 GeV ( 6.0pbs)1 = 318 GeV (32.8pbs

● consistent with PDF fit to F2

● most precise information on gluon still from scaling violations


High Q2 & Electroweak Physics


More Structure Functions

d 2NC±

dx dQ2 =22

Q4

1x

Y [F 2 x ,Q2 −y2

Y

F L x ,Q2 ∓Y−

Y

x F3 x ,Q2]

/Z 0

FL = F

2 – 2xF

1 = 0 in the QPM

F 3:−Z 0−interference

● FL relevant only at large y

● F3 relevant only at large Q2,

different sign for e+ and e–

e e

p

Y± = 1±1−y2


High Q2 Neutral Current

● difference between e+p and e–p only at large

➔

Q2≈M Z2

−Z 0−interference

M Z2



● no significant deviation from Standard Model Fit at high Q2

● can be interpreted as limit on quark size



=x Q4

22

1Y

d 2NC±

dx dQ2

e– positive interference

e+ negative interference

x F 3∝ x∑ eq2 q−q

direct handle on valence quark distribution!


Charged Current Interactions

e

pq

q'

e

neutrino not visiblein detector

imbalance in transverse plane

W


Charged Current Cross Section

● W bosons couple differently to up and downtype quarks

● in the QPM:

➔

d2CC±

dx dQ2 =GF

2

4 x M W2

M W2 Q2

2

Y[W 2± −

y2

Y

W L±∓

Y−

Y

x W 3±]

W 2=x UD , x W 3

=x D−U W 2

−=x UD , x W 3−=x U−D

W L±=0

CC− ∝ x [U 1−y2 D ]

CC ∝ x [U 1−y2 D ]

e+

e–


)2 (p

b/G

eV2

/dQ

σd

710

510

310

110

10

)2 (GeV2Q

310 410

p CC 0304 (prel.)+H1 e

p CC 2005 (prel.)H1 e

p CC 2004+ZEUS e

p CC 0405 (prel.)ZEUS e

p CC (CTEQ6M)+SM e

p CC (CTEQ6M)SM e

p NC 0304 (prel.)+H1 ep NC 2005 (prel.)H1 e

p NC 2004+ZEUS ep NC 0405 (prel.)ZEUS e

p NC (CTEQ6M)+SM ep NC (CTEQ6M)SM e

y < 0.9 = 0eP

HERA II

Comparison NC vs. CC● at low Q2: different

dependences because of photon in NC

● at high Q2: „electroweak unification“ but:

∝1

Q4

∝1

M W2 Q22

d2CC±

dx dQ2≈

GF2

4 x⋅ M W

2

M W2 Q2

2

⋅YW 2±

d2 NC±

dx dQ2 ≈22

x⋅

1Q4 ⋅Y F2

GF≈4

2 MW2

similar because


Electroweak Parameters: W Mass

● G = GF determined by normalization of the CC cross section

● Mprop = MW determined by the Q2 dependence of the CC cross section

82.87±1.82exp 0.30−0.16model GeV


CC & Polarization

● CC cross section depends on longitudinal electron/positron polarization Pe

● reason: W boson couples only to lefthanded (LH) particles and righthanded (RH) antiparticles:

d 2CC±

dx dQ2 Pe ≈ 1±PeGF

2

4 x⋅ MW

2

MW2 Q2

2

⋅YW 2±


Polarization @ HERA

● transverse polarization builds up in ~40 minutes through synchrotron radiation (SokolovTernov effect)

● spin rotators flip transverse longitudinal before experiments and back after

Pe =N RH−N LH

N RHN LH


Polarization @ HERA

spin rotator


eP1 0.5 0 0.5 1

(p

b)

CC

σ

0

20

40

60

80

100

120p Scattering±Charged Current e

Xν→p e

Xν→p +e

2 > 400 GeV2Q

y < 0.9

MRST 2004

CTEQ6D

H1 2005 (prel.)H1 9899ZEUS 0405 (prel.)ZEUS 9899

H1 9904ZEUS 0607 (prel.)ZEUS 9900

eP1 0.5 0 0.5 1

(p

b)

CC

σ

0

20

40

60

80

100

120

CC: Polarization Dependence

● Standard Modell expectation:

● experimental result: (H1)

CC− Pe=1 = 0

CC Pe=−1 = 0

CC− 1 =−0.9±2.9stat

±1.9syst±1.9pol pb

CC −1 =−3.9±2.3stat

±0.7syst±0.8pol pb


Electroweak Parameters: Z0 Couplings

1 0.5 0 0.5 1

1

0.5

0

0.5

1PDF (prel.)uv

u ZEUSpola total uncert. uncorr. uncert.

H1 prel. (HERA I+II 9505)

SM CDF LEP

1 0.5 0 0.5 1

1

0.5

0

0.5

1

ua

uv

68% CL

ZEUS

1 0.5 0 0.5 1

1

0.5

0

0.5

1PDF (prel.)dv

d ZEUSpola total uncert. uncorr. uncert.

H1 prel. (HERA I+II 9505)

SM CDF LEP

1 0.5 0 0.5 1

1

0.5

0

0.5

1

da

dv

68% CL

ZEUS

polarization also allows better sensitivity to vector and axialvector couplings of up and downtype quarks to the Z0


Summary

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● inclusive ep scattering reveales structure of the proton● large amount of gluons in the proton

● Standard Modell can be cross checked


Hadrons vs. Partons

x<0.01F

2

F 2∝x−

0.08 correponds tohadronhadron scattering

transition from hadronic to partonic bahaviour

Physics at HERA - DESY · Physics at HERA Katja Krüger ... H1 Collaboration email:...

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