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Physics at HERA
Katja Krüger KirchhoffInstitut für Physik
H1 Collaborationemail: katja.krueger@desy.de
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)
Katja Krüger Physics @ HERA 3
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)
Katja Krüger Physics @ HERA 5
HERA & its PreAccelerators
circumference: 6.3 km
e
p
bunch crossing rate: 10.4 MHz
Katja Krüger Physics @ HERA 6
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)
Katja Krüger Physics @ HERA 7
ZEUS Detector
tracking detector
calorimeter
muon system
magnet coil
p
e
Katja Krüger Physics @ HERA 10
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
Katja Krüger Physics @ HERA 18
H1 and ZEUS Combined PDF Fit
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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
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„The“ HERA Textbook Plots
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?
quarks ?
gluons ?
Katja Krüger Physics @ HERA 19
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
Katja Krüger Physics @ HERA 20
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
Katja Krüger Physics @ HERA 21
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 ]
Katja Krüger Physics @ HERA 22
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
Katja Krüger Physics @ HERA 23
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
Katja Krüger Physics @ HERA 24
Inelastic Electron Proton Scattering
● inelastic scattering: W > Mp
● ratio to Mott cross section nearly flat in Q2
Katja Krüger Physics @ HERA 25
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
Katja Krüger Physics @ HERA 26
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!
Katja Krüger Physics @ HERA 27
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 ]
Katja Krüger Physics @ HERA 28
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“
Katja Krüger Physics @ HERA 29
Scaling: F2 independent of Q2
SLAC 1972
independent of Q2, we always see the same partons (=quarks)
Katja Krüger Physics @ HERA 30
(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
Katja Krüger Physics @ HERA 33
How does F2(x) look like?
from Povh et al., „Teilchen und Kerne“
what happens at low x?
Katja Krüger Physics @ HERA 34
Scaling Violations
at smaller & larger x, the amount of quarks depends on Q2!
Katja Krüger Physics @ HERA 35
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
Katja Krüger Physics @ HERA 36
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
Katja Krüger Physics @ HERA 39
H1 and ZEUS Combined PDF Fit
HE
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Apr
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08
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
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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
Katja Krüger Physics @ HERA 40
F2 vs. Q2: example bins
H1 and ZEUS Combined PDF Fit
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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
Katja Krüger Physics @ HERA 43
DGLAP Evolution Equations
● Q2 dependence of quark densities q(x,Q2) and gluon density g(x,Q2) is predicted
Katja Krüger Physics @ HERA 44
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 ]
Katja Krüger Physics @ HERA 45
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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0.5
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1.5
x
xf
ZEUS
Katja Krüger Physics @ HERA 46
Combined H1 & ZEUS Parton Density
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combination of data from H1 and ZEUS gives big improvements!
Katja Krüger Physics @ HERA 47
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]
Katja Krüger Physics @ HERA 48
●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
Katja Krüger Physics @ HERA 49
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
Katja Krüger Physics @ HERA 51
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
Katja Krüger Physics @ HERA 52
High Q2 Neutral Current
● difference between e+p and e–p only at large
➔
Q2≈M Z2
−Z 0−interference
M Z2
Katja Krüger Physics @ HERA 53
High Q2 Neutral Current
● no significant deviation from Standard Model Fit at high Q2
● can be interpreted as limit on quark size
Katja Krüger Physics @ HERA 54
High Q2 Neutral Current
=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!
Katja Krüger Physics @ HERA 55
Charged Current Interactions
e
pq
q'
e
neutrino not visiblein detector
imbalance in transverse plane
W
Katja Krüger Physics @ HERA 56
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–
Katja Krüger Physics @ HERA 57
)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
Katja Krüger Physics @ HERA 58
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
Katja Krüger Physics @ HERA 59
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±
Katja Krüger Physics @ HERA 60
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
Katja Krüger Physics @ HERA 62
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
Katja Krüger Physics @ HERA 63
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
Katja Krüger Physics @ HERA 64
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
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