Electroweak/QCD Fit to NC & CC HERA Data · 2011. 7. 22. · HERA-1 HERA-2 HERA-1 operation...

Eram Rizvi

Electroweak/QCD Fit to NC & CC HERA Data

International Europhysics Conference on High Energy PhysicsGrenoble, France20th - 27th July 2011

• Introduction

• Structure Functions• H1 Measurements at High Q2 • Combined QCD / EW Fit• Results

EPS 2011 - Grenoble, FranceEram Rizvi 2

Colliders At The Electroweak Scale

e

e q

q

LHC / Tevatron

HERA

LEP/SLD

HERA data probes t-channel boson exchangeSensitive to - boson masses - EW couplings - PDFs

mtop

MWPDFs

MZ

ΓZ

etc...

σ(ep) = σ(eq) ⊗ PDFs

EW ⊗ QCD

Extraction of EW parameters requires simultaneous QCD & EW fit


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HERA NC and CC cross sections test Standard Model in region of large space-like momentum transfer, Q2

At fixed √s only two kinematic variables: x & Q2

Q2 = s.x.y

x = momentum fraction of proton carried by struck quark At HERA: 10-6 − 1

Q2 = resolving scale of the probe

Neutral and Charged Current DIS


HERA Phase-space

y=1

x

Q2 (

Ge

V 2 )

Fixed Target Experiments

HERA

10-1

1

10

10 2

10 3

10 4

10 5

10-6

10-5

10-4

10-3

10-2

10-1

1

xF3

LF

F2str

uctu

re do

minated

by gl

uon d

ynam

icsHERA data cover wide region of x,Q2

NC Measurements F2 dominates most of Q2 reachxF3 contributes in EW regimeFL contributes only at highest y

CC MeasurementsW2 and xW3 contribute equallyWL only at high y


Where Are We Going?

Log(x)

-6 -5 -4 -3 -2 -1 0

]2) [

GeV

2Lo

g(Q

0

1

2

3

4

5

6

7

8

9

HERA

ATLAS

LHCb LHCb

M = 100GeV

M = 1TeV

M = 10TeV

y = 02 24 4

y±e7TeVM = 1,2x

Q = M LHC: largest mass states at large x

For central production x=x1=x2

M=x√s

i.e. M > 1 TeV probes x>0.1

Searches for high mass states require precision

knowledge at high x

Z′ / quantum gravity / susy searches...

DGLAP evolution allows predictions to be made

High x predictions rely on

• data (DIS / fixed target)

• sum rules

• behaviour of PDFs as x→1


σ ±NC =

Q2x2απ 2

1Y+

d 2σ ±

dxdQ2

Y± = 1± (1− y)2

similarly for pure weak CC analogues:

W2± , xW3

± and WL±

Dominant contribution

Only sensitive at high Q2 ~ MZ2

Only sensitive at low Q2 and high y

F2 ∝ (xqi + xqi )∑

x F3 ∝ (xqi − xqi )∑

FL ∝α s ⋅ xg(x,Q2 )

σ NC± ~ F2

Y−

Y+

x F3

Structure Functions

The NC reduced cross section defined as:

σ ±CC =

2π xGF

2

MW2 +Q2

MW2

⎡

⎣⎢

⎤

⎦⎥

2dσCC

±

dxdQ2

dσCC±

dxdQ2 = 12Y+ W2

± Y− xW3± − y2WL

±⎡⎣ ⎤⎦

The CC reduced cross section defined as:

dσCC±

dxdQ2 = (1− Pe ) GF

2

4 π xMW

2

MW2 +Q2

⎡

⎣⎢

⎤

⎦⎥

2

Y+W2

± Y− x W3± − y2 WL

±⎡⎣ ⎤⎦

dσ NC±

dxdQ2 = 2πα 2

x 1

Q2

⎡

⎣⎢

⎤

⎦⎥

2

Y+F2 Y−x F3 − y

2 FL⎡⎣ ⎤⎦

Pe is the degree of lepton polarisation


F±2 = F2 − (ve ± Peae)κ

Q2

Q2 +M2Z

F γZ2 + (v2e + a2e ± Pe2veae)κ

2

�Q2

Q2 +M2Z

�2FZ2

xF±3 = −(ae ± Peve)κ

Q2

Q2 +M2Z

xF γZ3 + (2aeve ± Pe[v

2e + a2e])κ

2

�Q2

Q2 +M2Z

�2xFZ

3

�F2, F

γZ2 , FZ

2

�= x

�

q

[e2q, 2eqvq, v2q + a2q](q + q)

�xF γZ

3 , xFZ3

�= 2x

�

q

[eqaq, vqaq](q − q)

pure photon piece interference piece pure weak piece

interference piece pure weak pieceve is small ~0.05⇒ terms contribute little

F2ɣZ → main vq constraint

F2Z → main constraint on aq / vq correlation

xF3Z → main aq constraint

Structure Functions


W±L ≡ 0, the structure functions W±

2 and xW±3 may be expressed as the sum and difference of

the quark and anti-quark momentum distributions, xq(x, Q2) and xq(x, Q2):

W−2 = x(u + c + d + s) , W+

2 = x(u + c + d + s) , (2)xW−

3 = x(u + c − d − s) , xW+3 = x(d + s − u − c) (3)

The total cross section, σtotCC, is defined as the integrated cross section in the kinematic region

Q2 > 400 GeV2 and y < 0.9. From Eq.(1) it can be seen that the cross section has a lineardependence on the polarisation of the electron beam Pe. For a fully right handed electron beam,Pe = 1, or a fully left handed positron beam the cross section is identically zero in the StandardModel.

3 Experimental Technique

At HERA transverse polarisation of the lepton beam arises naturally through synchrotron ra-diation via the Sokolov-Ternov effect [10]. In 2000 a pair of spin rotators was installed inthe beamline on either side of the H1 detector, allowing transversely polarised leptons to berotated into longitudinally polarised states and back again. The degree of polarisation is con-stant around the HERA ring and is continuously measured using two independent polarimetersLPOL [11] and TPOL [12]. The polarimeters are situated in beamline sections in which thebeam leptons have longitudinal and transverse polarisations respectively. Both measurementsrely on an asymmetry in the energy spectrum of left and right handed circularly polarised pho-tons undergoing Compton scattering with the lepton beam. The TPOL measurement uses inaddition a spatial asymmetry. The LPOL polarimeter measurements are used when availableand TPOL measurements otherwise. The polarisation profile weighted by the luminosity valuesis shown in Fig. 1.

The H1 detector components most relevant to this analysis are the liquid argon (LAr) calorime-ter, which measures the positions and energies of charged and neutral particles over the polar1angular range 4◦ < θ < 154◦, and the inner tracking detectors, which measure the angles andmomenta of charged particles over the range 7◦ < θ < 165◦. A full description of the detectorcan be found in [13].

Simulated DIS events are used in order to determine acceptance corrections. DIS processes aregenerated using the DJANGO [14] Monte Carlo (MC) simulation program, which is based onLEPTO [15] for the hard interaction and HERACLES [16] for single photon emission and vir-tual EW corrections. LEPTO combines O(αs) matrix elements with higher order QCD effectsusing the colour dipole model as implemented in ARIADNE [17]. The JETSET program [18]is used to simulate the hadronisation process. In the event generation the DIS cross section iscalculated using the H1 PDF 2009 [8] parametrisation for the proton PDFs.

The dominant ep background contribution arises from photoproduction processes. These aresimulated using the PYTHIA [19] MC with leading order PDFs for the proton taken fromCTEQ [20] and for the photon from GRV [21]. Further backgrounds from NC DIS, QED-Compton scattering, lepton pair production, prompt photon production and heavy gauge boson

1The polar angle θ is defined with respect to the positive z axis, the direction of the incident proton beam.

2

NC data constrain: - singlet quarks / gluon PDFs- non-singlet valence quark PDFs at high Q2

But, flavour sensitivity is weak

CC data enable flavour decomposition of proton:

Requires e+ and e- scattering data

d 2σCC−

dxdQ2 =GF

2

2πMW

2

MW2 + Q2

⎛

⎝⎜

⎞

⎠⎟

2

(u + c) + (1− y)2(d + s )⎡⎣ ⎤⎦

d 2σCC+

dxdQ2 =GF

2

2πMW

2

MW2 + Q2

⎛

⎝⎜

⎞

⎠⎟

2

(u + c ) + (1− y)2(d + s)⎡⎣ ⎤⎦

CC e+ data provide strong dv constraint at high x(y ~ 0)

Structure Functions

For polarised lepton beams CC cross sectionscales linearly with P


Neutral current event selection:

High PT isolated scattered leptonSuppress huge photo-production background by imposing longitudinal energy-momentumconservation

Kinematics may be reconstructed in many ways:energy/angle of hadrons & scattered leptonprovides excellent tools for sys cross checks

Removal of scattered lepton provides a high stats “pseudo-charged current sample”Excellent tool to cross check CC analysis

Final selection: ~105 events per sample at high Q2

~107 events for 10 < Q2 < 100 GeV2

Charged current event selection:

Large missing transverse momentum (neutrino)

Suppress huge photo-production background

Topological finders to remove cosmic muons

Kinematics reconstructed from hadrons

Final selection: ~103 events per sample

H1 - Neutral and Charged Current Selections

Q**2 = 21475 y = 0.55 M = 198

Q**2 = 21475 y = 0.55 M = 198

820 GeV920 GeV

27.6 GeV


Days of running

H1

Inte

grat

ed L

umin

osity

/ pb

-1

Status: 1-July-2007

0 500 1000 15000

100

200

300

400electronspositronslow E

HERA-1

HERA-2

HERA-1 operation 1993-2000Ee = 27.6 GeVEp = 820 / 920 GeV∫L ~ 110 pb-1 per experiment

HERA-II operation 2003-2007Ee = 27.6 GeVEp = 920 GeV ∫L ~ 330 pb-1 per experimentLongitudinally polarised leptons

Low Energy Run 2007Ee = 27.6 GeVEp = 575 & 460 GeVDedicated FL measurement

HERA Operation

unpolarised

polar

ised

lept

on b

eam


1 Introduction

Precision measurements of proton structure in neutral current (NC) and charged current (CC)

deep inelastic scattering (DIS) with polarised lepton beams provide a critical stress-test of

our understanding of parton dynamics and QCD as well as allowing the chiral structure of

electroweak (EW) interactions to be simultaneously probed at the highest energies and four-

momentum transfers, Q. Previously published measurements [1–7] have already provided

unique constraints [3, 8–10] on the parton density functions (PDFs) of the proton as well as

the axial and vector couplings of the light quarks to the Z0boson [11].

In this paper we present the final H1 measurements of inclusive charged and neutral current

cross sections at high Q2. The precision measurements utilise the complete HERA-II data set

of 329.1 pb−1delivered with longitudinally polarised electron and positron beams. Inclusive

neutral current interactions are defined as the process ep → eX mediated via γ/Z0exchange,

whereas inclusive charged current interactions are defined as ep → νX and are purely weak

processes mediated via W exchange only and yield complementary information on the QCD

and EW parts of the Standard Model.

The data reach a precision of ∼ 2% in the NC channel and cover the Q2range from 100 to

30 000 GeV2. Together with previous H1 measurements at lower Q2

down to ∼ 1 GeV2

[5, 7]

the data cover an impressive 4 orders of magnitude in kinematic reach: from the transition re-

gion between phenomenological models and pertubatively stable fixed order QCD calculations,

through the heavy quark production threshold region, to the kinematic domain of scattering me-

diated by the electroweak bosons. In particular the high Q2NC and CC data presented here give

stringent constraints on the proton PDFs for Bjorken x in the range 0.001 < x < 0.65 which

is of direct relevance to all predicitions for pp scattering at centre-of-mass energy of 7 TeV and

higher at the LHC [12]. Production cross sections of new high mass states in the LHC kinematic

domain are very sensitive to the high x PDFs constrained by the HERA DIS data.

The inclusive NC and CC single differential cross sections, dσ/dQ2and the reduced cross

sections σ(x,Q2) are presented for e+p and e−p scattering. The data were taken with an incident

lepton beam energy of 27.5GeV, whilst the unpolarised proton beam energy was 920GeV,

yielding a centre-of-mass energy of√s = 318GeV. Both data sets are further subdivided into

samples of left handed and right handed longitudinal polarisation, Pe = (NR−NL)/(NR+NL),where NR (NL) is the number of right (left) handed leptons in the beam. The corresponding

data sets are termed the R and L data sets respectively. The luminosity and longitudinal lepton

beam polarisation for each data set is given in Tab. 1 below.

R L

e−pL = 45.9 pb

−1 L = 103.2 pb−1

Pe = (+36.9± 2.3)% Pe = (−26.1± 1.0)%

e+pL = 98.1 pb

−1 L = 81.9 pb−1

Pe = (+32.5± 1.2)% Pe = (−37.6± 1.4)%

Table 1: Table of integrated luminosities, L, and luminosity weighted longitudinal lepton beam

polarisation, Pe for the data sets presented here.

1

Polarisation / % -60 -40 -20 0 20 40 60

-1Lu

min

osity

/ nb

0

2000

4000

6000

8000

10000

p-e

Polarisation / % -60 -40 -20 0 20 40 60

-1Lu

min

osity

/ nb

0

2000

4000

6000

8000

10000

p+e

Luminosity & Polarisation

HERA-II Luminosity


Summary of HERA-I datasets

H1 Structure Function Data

Data Set x Range Q2 Range L e+/e− √s x,Q2 Reconstruction ReferenceGeV2 pb−1 GeV Method Equation

H1 svx-mb 95-00 5 × 10−6 0.02 0.2 12 2.1 e+ p 301-319 10,14,16 [1]H1 low Q2 96-00 2 × 10−4 0.1 12 150 22 e+ p 301-319 10,14,16 [2]H1 NC 94-97 0.0032 0.65 150 30000 35.6 e+ p 301 15 [3]H1 CC 94-97 0.013 0.40 300 15000 35.6 e+ p 301 11 [3]H1 NC 98-99 0.0032 0.65 150 30000 16.4 e− p 319 15 [4]H1 CC 98-99 0.013 0.40 300 15000 16.4 e− p 319 11 [4]H1 NC HY 98-99 0.0013 0.01 100 800 16.4 e− p 319 10 [5]H1 NC 99-00 0.0013 0.65 100 30000 65.2 e+ p 319 15 [5]H1 CC 99-00 0.013 0.40 300 15000 65.2 e+ p 319 11 [5]ZEUS BPC 95 2 × 10−6 6 × 10−5 0.11 0.65 1.65 e+ p 301 10 [6]ZEUS BPT 97 6 × 10−7 0.001 0.045 0.65 3.9 e+ p 301 10, 15 [7]ZEUS SVX 95 1.2 × 10−5 0.0019 0.6 17 0.2 e+ p 301 10 [8]ZEUS NC 96-97 6 × 10−5 0.65 2.7 30000 30.0 e+ p 301 18 [9]ZEUS CC 94-97 0.015 0.42 280 17000 47.7 e+ p 301 11 [10]ZEUS NC 98-99 0.005 0.65 200 30000 15.9 e− p 319 17 [11]ZEUS CC 98-99 0.015 0.42 280 30000 16.4 e− p 319 11 [12]ZEUS NC 99-00 0.005 0.65 200 30000 63.2 e+ p 319 17 [13]ZEUS CC 99-00 0.008 0.42 280 17000 60.9 e+ p 319 11 [14]

Table 1: H1 and ZEUS data sets used for the combination. The H1 svx-mb [1] andH1 low Q2 [2] data sets comprise averages including data collected at E p = 820 GeV [35,36]and Ep = 920 GeV. The formulae for x,Q2 reconstruction are given in section 2.2.

at z = −294 cm close to the beam axis, and a silicon microstrip tracking device (BPT) installedin front of the BPC.

Both H1 and ZEUS were also equipped with photon taggers, positioned at " 100m downthe e beam line, for a determination of the luminosity from Bethe-Heitler scattering, ep→ epγ.The measurement accuracy of the luminosity was about 1 − 2% for each of the experiments.

2.4 Data Samples

A summary of the data used in this analysis is given in Table 1. In the first years until 1997, theproton beam energy Ep was set to 820GeV. In 1998 it was increased to 920GeV. The NC datacover a wide range in x and Q2. The lowestQ2 ≥ 0.045 GeV2 data come from the measurementsof ZEUS using the BPC and BPT [6,7]. The Q2 range from 0.2 GeV2 to 1.5 GeV2 is coveredusing special HERA runs, in which the interaction vertex position was shifted forward allowingfor larger angles of the backward scattered electron to be accepted [1,8,35]. The lowest Q2 forthe shifted vertex data was reached using events, in which the effective electron beam energywas reduced by initial state radiation [1]. Values of Q2 ≥ 1.5 GeV2 were measured using thenominal vertex settings. For Q2 ≤ 10 GeV2, the cross section is very high and the data werecollected using dedicated trigger setups [1,9,36]. The highest accuracy of the cross-sectionmeasurement is achieved for 10 ≤ Q2 ≤ 100 GeV2 [2,9,36]. For Q2 ≥ 100 GeV2, the statisticaluncertainty of the data becomes relatively large. The high Q2 data included here were collectedwith positron [3,5,9,13] and with electron [4,11] beams. The CC data for e+p and e−p scatteringcover the range 300 ≤ Q2 ≤ 30000 GeV2 [3,5,10,12,14].

12

H1 CC e−p 149 pb-1 H1prelim-09-043

H1 CC e+p 180 pb-1 H1prelim-09-043

H1 NC e−p 149 pb-1 H1prelim-09-042

H1 NC e+p 180 pb-1 H1prelim-09-042

Summary of HERA-II datasets


H1PDF 2009H1 Data

2H1 Low Q2H1 High Q

x - 410 - 310 - 210 - 110

0

0.5

1

1.5

2 = 150 GeV2Q

- 410 - 310 - 210 - 1100

0.5

1

1.52 = 120 GeV2Q

x - 410 - 310 - 210 - 110

0

0.5

1

1.5

2 = 90 GeV2Q

- 410 - 310 - 210 - 1100

0.5

1

1.5

2 = 60 GeV2Q

- 410

- 310

- 210

- 110

0

0.5

1

1.5

2 = 45 GeV2Q

- 410

- 310

- 210

- 1100

0.5

1

1.52 = 35 GeV2Q

- 410

- 310

- 210

- 110

0

0.5

1

1.5

2 = 25 GeV2Q

- 410

- 310

- 210

- 110

0

0.5

1

1.5

2 = 20 GeV2Q

- 410

- 310

- 210

- 110

0

0.5

1

1.5

2 = 15 GeV2Q

- 410

- 310

- 210

- 1100

0.5

1

1.52 = 12 GeV2Q

H1 Collaboration

2F

Figure 5: Measurement of the structure function F2 at fixed Q2 as a function of x. The data ofthis measurement (closed circles) are complemented by the previously published data at low Q2(open circles) [2] and high Q2 (open boxes) [9]. The error bars represent the total measurementuncertainties. The curve represents the QCD fit described in this paper.

30

Precision data from H1 for Q2 < 150 GeV2

Typical uncertainty of 1.3 - 2 %Provides strong constraints on PDFs - gluon and singlet quarks

DESY-09-005H1 Collab, Eur.Phys.J.C64 (2009) 561

Precision F2 at Medium Q2


10 20 30 40 500

10

20

30

[GeV]elecE’

eve

nts

310

0

20

40

210 310 410]2 [GeV2Q

eve

nts

310

50 100 1501

10

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510

610p-H1 NC Data e

NC MC + Bkg MCBkg MC

H1 Preliminary

]o [ elec!

Even

ts

0.5 1 1.5 20

20

40

HER

A II

elecT/Phad

TP

eve

nts

310

10 20 30 40 500

10

20

30

40

[GeV]elecE’

eve

nts

310

0

20

40

60

210 310 410]2 [GeV2Q

eve

nts

310

50 100 1501

10

210

310

410

510

610p+H1 NC Data e


H1 Preliminary

]o [ elec!

Even

ts

0.5 1 1.5 20

20

40

60

HER

A II

elecT/Phad

TP

eve

nts

310

(a) (b)

(c) (d)

(e) (f)

(g) (h)

Figure 2: Distributions of (a,e) E ′e, (b,f) θe, (c,g) Q2

e and (d,h) PT,h/PT,e shown in upper andlower plots for the selected events in the (a-d) e−p and (e-h) e+p data sets. The Monte Carlo(MC) contributions from the neutral current (NC) process and the ep background (bkg) pro-cesses are shown as open histograms with the latter contribution alone being shown as shadedhistograms. In these plots the left and right handed samples are combined for each leptoncharge.

12

10 20 30 40 500

10

20

30

[GeV]elecE’

eve

nts

310

0

20

40

210 310 410]2 [GeV2Q

eve

nts

310

50 100 1501

10

210

310

410

510

610p-H1 NC Data e


H1 Preliminary

]o [ elec!

Even

ts

0.5 1 1.5 20

20

40

HER

A II

elecT/Phad

TP

eve

nts

310

10 20 30 40 500

10

20

30

40

[GeV]elecE’

eve

nts

310

0

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60

210 310 410]2 [GeV2Q

eve

nts

310

50 100 1501

10

210

310

410

510

610p+H1 NC Data e


H1 Preliminary

]o [ elec!

Even

ts

0.5 1 1.5 20

20

40

60

HER

A II

elecT/Phad

TP

eve

nts

310

(a) (b)

(c) (d)

(e) (f)

(g) (h)

Figure 2: Distributions of (a,e) E ′e, (b,f) θe, (c,g) Q2

e and (d,h) PT,h/PT,e shown in upper andlower plots for the selected events in the (a-d) e−p and (e-h) e+p data sets. The Monte Carlo(MC) contributions from the neutral current (NC) process and the ep background (bkg) pro-cesses are shown as open histograms with the latter contribution alone being shown as shadedhistograms. In these plots the left and right handed samples are combined for each leptoncharge.

12

Neutral Current Control Distributions

HERA-II e−p HERA-II e+p

Kinematic distributions are well described by MC~3% normalisation shiftwithin preliminary luminosity uncertainty ±2.1%


])2[GeVh2(Q

10log

2.0 2.5 3.0 3.5 4.0 4.5 5.0

Even

ts

20406080

100120140160180200

[GeV]T,hP0 10 20 30 40 50 60 70 80 90 100

Even

ts

50

100

150

200

250

300

H1 Preliminaryp CC Data+H1 e

MC (CC + Bkg)MC (Bkg)

= -37.6%eP

[GeV]zE-P0 10 20 30 40 50 60

Even

ts

20

40

60

80

100

120

140

160

)h

(x10

log-2.0 -1.5 -1.0 -0.5 0.0

Even

ts

20

40

60

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140

HER

A II

])2[GeVh2(Q

10log

2.0 2.5 3.0 3.5 4.0 4.5 5.0

Even

ts

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500

[GeV]T,hP0 10 20 30 40 50 60 70 80 90 100

Even

ts

100

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500

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700H1 Preliminary

p CC Data+H1 eMC (CC + Bkg)MC (Bkg)

= 32.5%eP

[GeV]zE-P0 10 20 30 40 50 60

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ts

50

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350

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)h

(x10

log-2.0 -1.5 -1.0 -0.5 0.0

Even

ts

50

100

150

200

250

300

350

HER

A II

(a) (b)

(c) (d)

(e) (f)

(g) (h)

Figure 3: Distributions of (a,e) log10 Q2h, (b,f) PT,h, (c,g) E − PZ and (d,h) log10 xh shown in

upper and lower plots for the selected events in the (a-d) e−p L and (e-h) e+p R data sets. TheMonte Carlo (MC) contributions from the charged current (CC) process and the ep background(bkg) processes are shown as the full line, the total uncertainty is represented by the shadedband. The contribution from the ep background is shown as the lower shaded histogram.

12

])2[GeVh2(Q

10log

2.0 2.5 3.0 3.5 4.0 4.5 5.0

Even

ts

20406080

100120140160180200

[GeV]T,hP0 10 20 30 40 50 60 70 80 90 100

Even

ts

50

100

150

200

250

300

H1 Preliminaryp CC Data+H1 e

MC (CC + Bkg)MC (Bkg)

= -37.6%eP

[GeV]zE-P0 10 20 30 40 50 60

Even

ts

20

40

60

80

100

120

140

160

)h

(x10

log-2.0 -1.5 -1.0 -0.5 0.0

Even

ts

20

40

60

80

100

120

140

HER

A II

])2[GeVh2(Q

10log

2.0 2.5 3.0 3.5 4.0 4.5 5.0

Even

ts

100

200

300

400

500

[GeV]T,hP0 10 20 30 40 50 60 70 80 90 100

Even

ts

100

200

300

400

500

600

700H1 Preliminary

p CC Data+H1 eMC (CC + Bkg)MC (Bkg)

= 32.5%eP

[GeV]zE-P0 10 20 30 40 50 60

Even

ts50

100

150

200

250

300

350

400

)h

(x10

log-2.0 -1.5 -1.0 -0.5 0.0

Even

ts

50

100

150

200

250

300

350

HER

A II

(a) (b)

(c) (d)

(e) (f)

(g) (h)

Figure 3: Distributions of (a,e) log10 Q2h, (b,f) PT,h, (c,g) E − PZ and (d,h) log10 xh shown in

upper and lower plots for the selected events in the (a-d) e−p L and (e-h) e+p R data sets. TheMonte Carlo (MC) contributions from the charged current (CC) process and the ep background(bkg) processes are shown as the full line, the total uncertainty is represented by the shadedband. The contribution from the ep background is shown as the lower shaded histogram.

12

Charged Current Control Distributions

HERA-II e−p HERA-II e+p

Kinematic distributions are well described by MCWithin errors normalisation is fine


-1100

0.2

0.4

0.6

0.8

1

HER

A I

+ II

2 = 1500 GeV2transformed to Q Z!3xF

x

H1 Preliminary

H1 (prel.)HERAPDF 1.0H1PDF 2009

Figure 21: The structure function xF γZ3 extracted from all HERA-I and HERA-II data (solid

points) and transformed to Q2 = 1 500GeV2 is shown together with the Standard Model expec-tation from H1 PDF 2009 (solid curve) and HERAPDF 1.0 (shaded band). The inner error barsrepresent the statistical uncertainties and the outer error bars represent the total errors whichincludes the normalisation uncertainty.

31

0

0.5

12 = 1200 GeV2Q 2 = 1200 GeV2Q 2 = 1200 GeV2Q 2 = 1200 GeV2Q

0

0.5


0

0.5


0

0.5


0

0.5


0

0.5


0

0.5


0

0.5


0

0.5


p NC (prel.)-H1 eH1PDF 2009

p NC (prel.)+H1 eH1PDF 2009

HER

A I

+ II

NC!"H1 Preliminary

x

0

0.5

1

0

0.5

1

0

0.5

1

-110 1 -110 1 -110 1

Figure 18: The reduced cross section σNC in unpolarised e±p scattering using the completeHERA I+II dataset for Q2 above 1 000 GeV2. The data are compared to the Standard Modelprediction from H1 PDF 2009. The inner error bars represent the statistical uncertainties andthe outer error bars represent the total errors. The normali sation uncertainty is not included inthe error bars.

28

xF3

At high Q2 xF3 arises due to Z0 effectsenhanced e- cross section wrt e+

Difference is xF3

Sensitive to valence PDFs

x F3 =

Y+

2Y−

( σ NC− − σ NC

+ ) ≈ aeχZ xF3γ Z

xF3 ∝ (xqi − xqi )∑

desy-10-228


0 0.5 10

0.2

0.4

0.6

0.8

1

X!"p+ H1 eH1PDF 2009

)s+d(x2)y(1-)c+u(x

= 0.0%eP

x-210 -110

0.05

0.1

0.15

0.2 2 = 15000 GeV2Q

x-210 -110

0.05

0.1

0.15

0.2 2 = 8000 GeV2Q-2 -1

0.2

0.4

0.6

HER

A I+

II

2 = 5000 GeV2Q

0.2

0.4

0.6

2 = 3000 GeV2Q

-2 -1

0.2

0.4

0.6

2 = 2000 GeV2Q-2 -1

0.5

1

1.5

H1 Preliminary2 = 1000 GeV2Q

0.5

1

1.5

2 = 500 GeV2Q

-2 -1

0.5

1

1.5CC#$ 2 = 300 GeV2Q

Figure 18: The reduced cross section σCC in unpolarised e+p scattering using the completeHERA-I+II data sets. The data are compared to the Standard Model prediction from H1 PDF2009. The inner error bars represent the statistical uncertainties and the outer error bars rep-resent the total errors. The normalisation uncertainty is not included in the error bars. Theseparate contributions from quarks and anti-quarks are shown as the dashed and dashed-dottedcurves.

27

0 0.5 10

0.2

0.4

0.6

0.8

1

X!"p_ H1 eH1PDF 2009

)c+u(x)s+d(x2)y(1-

= 0.0%eP

x-210 -110

0.5

1 2 = 15000 GeV2Q

x-210 -110

0.5

1 2 = 8000 GeV2Q-2 -1

0.5

1

HER

A I+

II

2 = 5000 GeV2Q

0.5

1 2 = 3000 GeV2Q

-2 -1

0.5

1 2 = 2000 GeV2Q-2 -1

0.5

1

1.5

H1 Preliminary2 = 1000 GeV2Q

0.5

1

1.5

2 = 500 GeV2Q

-2 -1

0.5

1

1.5CC#$ 2 = 300 GeV2Q

Figure 17: The reduced cross section σCC in unpolarised e−p scattering using the completeHERA-I+II data sets. The data are compared to the Standard Model prediction from H1 PDF2009. The inner error bars represent the statistical uncertainties and the outer error bars rep-resent the total errors. The normalisation uncertainty is not included in the error bars. Theseparate contributions from quarks and anti-quarks are shown as the dashed and dashed-dottedcurves.

26

CC Flavour Sensitivity

HERA-I+II e+p HERA-I+II e−p

Dashed lines show quark flavour compositionHigh x dv is not well constrained by NC dataGood constraints from CC e+ data


eP-1 -0.5 0 0.5 1

[pb]

CC

!

0

20

40

60

80

100

120 H1 Preliminary

2 > 400 GeV2Q y < 0.9

X" #p +e

X" #p -e

HERAPDF 1.0

H1 HERA IH1 HERA II (prel.)

H1 HERA IH1 HERA II (prel.)

eP-1 -0.5 0 0.5 1

[pb]

CC

!

0

20

40

60

80

100

120

Figure 5: The dependence of the e±p CC cross section on the lepton beam polarisation Pe. Theinner and outer error bars represent respectively the statistical and total errors. The uncertaintieson the polarisation measurement are smaller than the symbol size. The data are compared tothe Standard Model prediction based on the HERAPDF 1.0 parametrisation (dark shaded band).The light shaded band corresponds to the resulting one-sigma contour of a linear fit to the datashown as the central line.

14

Clear linear scaling of CC cross sectionVerifies absence of weak right-handed currents

CC Polarisation Dependence


]2 [GeV2Q310 410

-1

-0.5

0

0.5

1

p+A eH1PDF 2009

p-A eH1PDF 2009

H1 Preliminary

HER

A II

A

Figure 13: The Q2 dependence of the polarisation asymmetry A, for e+p (red circles) ande−p (blue squares). The data (solid points) are compared to the Standard Model prediction(full lines). The inner error bars represent the statistical uncertainties and the outer error barsrepresent the total errors. The normalisation uncertainty is not included in the error bars.

23

A =2

PR − PL· σ

±(PR)− σ±(PL)

σ±(PR) + σ±(PL)

NC Polarisation Dependence

NC parity violating effects are more subtle Measure NC polarisation asymmetry


xf (x,Q02 ) = A ⋅ xB ⋅ (1− x)C ⋅ (1+ Dx + Ex2 + Fx3)

Apply momentum/counting sum rules:

dx ⋅uv = 20

1

∫ dx ⋅dv = 10

1

∫

dx ⋅ (xuv + xdv + xU + xD + xg) = 10

1

∫Parameter constraints:Buv = Bdv

BUbar = BDbar

sea = 2 x (Ubar +Dbar)Ubar = Dbar at x=0

Combined QCD & EW FitCombined NC and CC HERA-I data from H1No usage of other experimental data (e.g. non-DIS)Complete MSbar NLO fitNLO: standard parameterisation with14 parametersFit PDFs and light quark axial/vector couplings

QCD & EW Fit

xgxuv xdvxU xD

xgxU = xu + xcxD = xd + xsxU = xu + xcxD = xd + xs

Q02 = 4 GeV2

Q2 > 3.5 GeV2

2 x 10-4 < x < 0.65Fits performed in massless HQ scheme

xs = fsxD strange sea is a fixed fraction fs of D at Q02

The fit to the H1 data uses the following functional forms

xg(x) = AgxBg(1 − x)Cg · [1 + Dgx]

xU(x) = AUxBU (1 − x)CU · [1 + DUx + FUx3]

xD(x) = ADxBD(1 − x)CD · [1 + DDx] (17)xU(x) = AUxBU (1 − x)CU

xD(x) = ADxBD(1 − x)CD ,

in which the number of free parameters are further reduced using the constraints and assump-tions detailed below.

The number of parameters required by the fit for the different parton distributions follows theexpectation. A high x term Egx2 is not needed in the gluon distribution, since at large x thescaling violations are due to gluon bremsstrahlung, i.e. are independent of the gluon distribution.The xU and xD distributions require more parameters than the anti-quark distributions xUand xD because the former are a superposition of valence and sea quarks, in contrast to thelatter. Due to the different electric charges, e2

u = 4e2d, and the y dependence of the charged

current cross section, the data are much more sensitive to the up quark than to the down quarkdistributions. Thus less parameters are needed for xD than for xU .

A number of relations between parameters can be introduced naturally in this ansatz. At lowx the valence quark distributions are expected to vanish and the sea quark and the anti-quarkdistributions can be assumed to be equal. Thus the low x parameters Aq and Bq are required tobe the same for xU, xU and for xD, xD. In the absence of deuteron data from HERA there isno distinction possible of the rise towards low x between xU and xD. Thus the correspondingB parameters are required to be equal, i.e. BU = BD = BU = BD ≡ Bq. Further constraintsare the conventional momentum sum rule and the valence quark counting rules.

The ansatz presented above allows the quark distributions xU, xD, xU, xD to be determined.Further disentangling the individual quark flavour contributions to the sea is possible only withadditional experimental information and/or assumptions. Assuming that the strange and charmsea quark distributions xs and xc can be expressed as x-independent fractions fs and fc of xDand xU at the starting scale of Q2

0 = 4 GeV2 (see table 5), a further constraint is used in the fit:AU = AD · (1 − fs)/(1 − fc), which imposes that d/u → 1 as x → 0.

The total number of free parameters of the five parton distributions is thus equal to 10 in the fitto the H1 data. The χ2 value is hardly improved by including any half integer power of x. Theparametric form of eq. 17 is also found starting from an alternative polynomial in xk, whichincludes half integer powers up to x5/2. The addition of the large x BCDMS µp and µD dataleads to two additional terms, GUx4 and FDx3, in the polynomials.

5 Results

5.1 NC and CC Cross Sections dσ/dQ2, dσ/dx and σtotCC

The e+p single differential neutral current cross section dσ/dQ2 measured for y < 0.9 isshown in fig. 5(a). The data are compared with previous H1 e+p measurements made at

19

EW parameters from PDF2009:Mtop = 171.3 GeVMW = 80.398 GeVαS = 0.1176

PDFs parameterised at starting scale Q02


HERAPDF1.0Combine NC and CC HERA-I data from H1 & ZEUS Complete MSbar NLO fitNLO: standard parameterisation with10 parametersαs = 0.1176 (fixed in fit)

xgxuv xdvxU xD

xgxU = xu + xcxD = xd + xsxU = xu + xcxD = xd + xs

uncertainties in quadrature the χ2 is 532 and for a fit treating all 113 by the Hessian methodthe χ2 is 579. The resulting experimental uncertainties on the PDFs are small. Therefore, athorough consideration of further uncertainties due to model assumptions and parametrisationdependence is necessary.

4.2 Theoretical Formalism and Assumptions

The QCD predictions for the structure functions are obtained by solving the DGLAP evolutionequations [21–25] at NLO in the MS scheme with the renormalisation and factorization scaleschosen to be Q2. The programme QCDNUM [48] is used and checked against the programmeQCDfit [49]. The DGLAP equations yield the PDFs at all values of Q2 if they are providedas functions of x at some input scale Q20. This scale is chosen to be Q20 = 1.9 GeV2 such thatthe starting scale is below the charm mass threshold, Q20 < m2c . The light quark coefficientfunctions are calculated in QCDNUM. The heavy quark coefficient functions are calculated inthe general-mass variable-flavour-number scheme of [50], with recent modifications [51,52].The heavy quark masses mc = 1.4 GeV and mb = 4.75 GeV are chosen following [45]. Thestrong coupling constant is fixed to αs(M2Z) = 0.1176 [19].The HERA data have a minimum invariant mass of the hadronic system,W, of 15GeV and

a maximum x of 0.65, such that they are in a kinematic region where there is no sensitivity totarget mass and large-x higher-twist contributions. A minimum Q2 cut of Q2min = 3.5 GeV2 isimposed to remain in the kinematic region where perturbative QCD should be applicable.PDFs are parametrised at the input scale by the generic form

x f (x) = AxB(1 − x)C(1 + ε√x + Dx + Ex2). (26)

The parametrised PDFs are the gluon distribution xg, the valence quark distributions xuv, xdv,and the u-type and d-type anti-quark distributions xU, xD. Here xU = xu, xD = xd + xs atthe chosen starting scale. The central fit is found by first setting the ε, D and E parametersto zero (this leaves 9 parameters free) and then introducing them in the fit procedure, one ata time, to determine the best fit. The best 10 parameter fit has Euv ! 0. The other ε, D andE parameters are then added, one at a time, to determine the best 11 parameter fit. The 11parameter fits do not represent a significant improvement in fit quality compared to the best10 parameter fit4. The 10 parameter fit, selected as the central fit, has a good χ2 per degreeof freedom, 574/582, and satisfies the criteria that all the PDFs are positive and they obey thevalence quark approximation that xdv > xd at large x. The resulting parametrisations are

xg(x) = AgxBg(1 − x)Cg , (27)xuv(x) = Auv xBuv (1 − x)Cuv

(

1 + Euv x2)

, (28)xdv(x) = Adv xBdv (1 − x)Cdv , (29)xU(x) = AU xBU (1 − x)CU , (30)xD(x) = ADxBD(1 − x)CD . (31)

The normalisation parameters, Ag, Auv , Adv , are constrained by the quark number sum-rules andmomentum sum-rule. The B parameters BU and BD are set equal, BU = BD, such that there is4The largest decrease in χ2 is ∆χ2 = −5, for a fit which has xdv < xd at large x.

19

QCD & EW Fit

xf (x,Q02 ) = A ⋅ xB ⋅ (1− x)C ⋅ (1+ Dx + Ex2 + Fx3)

Alternative parametric form included as uncertaintyTaken from HERAPDF1.0 QCD fit


Excellent consistency of input data allow standardstatistical error definition:Δχ2 = 1

A B C Exg 6.8 0.22 9.0xuv 3.7 0.67 4.7 9.7xdv 2.2 0.67 4.3xU 0.113 −0.165 2.6xD 0.163 −0.165 2.4

Table 3: Central values of the HERAPDF1.0 parameters.

Variation Standard Value Lower Limit Upper Limitfs 0.31 0.23 0.38mc [GeV] 1.4 1.35(a) 1.65mb [GeV] 4.75 4.3 5.0Q2min [GeV2] 3.5 2.5 5.0Q20 [GeV2] 1.9 1.5(b) 2.5(c,d)

(a)Q20 = 1.8 (c)mc = 1.6(b) fs = 0.29 (d) fs = 0.34

Table 4: Standard values of input parameters and the variations considered.

a single B parameter for the sea distributions. The strange quark distribution is expressed asx-independent fraction, fs, of the d-type sea, xs = fsxD at Q20. The central value fs = 0.31is chosen to be consistent with determinations of this fraction using neutrino-induced di-muonproduction [45,53]. The further constraint AU = AD(1 − fs), together with the requirementBU = BD, ensures that xu → xd as x → 0. For the central fit, the valence B parameters, Buvand Bdv are also set equal, but this assumption is dropped when parametrisation variations areconsidered. The central values of the parameters are given in Table 3.Model uncertainties and parametrisation uncertainties of the central fit solution are evaluated

by varying the input assumptions. The variation of numerical values chosen for the central fitis specified in Table 4. The variation of fs is chosen to span the ranges determined in [45,53].The variations of Q20 and fs are not independent, since QCD evolution will ensure that thestrangeness fraction increases as Q20 increases. The value fs = 0.29 is used for Q20 = 1.5 GeV2and the value fs = 0.34 is used for Q20 = 2.5 GeV2 in order to be consistent with the choicefs = 0.31 at Q20 = 1.9 GeV2. The variations of Q20 and mc are also not independent, sinceQ0 < mc is required in the fit programme. Thus when mc = 1.35GeV, the starting scale usedis Q20 = 1.8GeV2. Similarly, when Q20 = 2.5 GeV2 the charm mass used is mc = 1.6 GeV.In practice, the variations of fs, mc, mb, mostly affect the model uncertainty of the xs, xc, xb,quark distributions, respectively, and have little effect on other parton flavours. The differencebetween the central fit and the fits corresponding to model variations of mc, mb, fs, Q2min areadded in quadrature, separately for positive and negative deviations, and represent the modeluncertainty of the HERAPDF1.0 set.The variation in Q20 is regarded as a parametrisation uncertainty, rather than a model un-

certainty. At the starting scale the gluon parametrisation is valence-like. For the downwardvariation of the starting scale, Q20 = 1.5 GeV2, a parametrisation which explicitly allows for anegative gluon contribution at low x is considered: a term of the form A′gxB

′g(1 − x)C′g is sub-

tracted from the gluon of the standard parametrisation, where C′g = 25 is fixed5 and A′g and B′g5The fit is not sensitive to this value provided it is high enough (C′g > 15) that the term does not contribute at

20

Experimental systematic sources of uncertainty allowed to float in fitInclude model assumptions into uncertainty:fs , mc , mb , Q20, Q2min

QCD & EW Fit

au vu ad vd

Model

SM

Param.

Total Sys.

Exp.

±0.02 ±0.01 ±0.03 ±0.01

±0.02 ±0.01 ±0.03 ±0.02

±0.03 ±0.02 ±0.06 ±0.06

±0.04 ±0.02 ±0.07 ±0.06

±0.06 ±0.08 ±0.19 ±0.27

Uncertainties

New combined QCD & EW fit performedTakes into account full correlation of uncertaintiesχ2/ndf = 1184 / 1230 = 0.96


0.5

1

1.5! NC

0.5

1

1.5! NC

0.5

1

1.5! NC

0.5

1

1.5! NC

0.5

1

1.5! NC

0.5

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1.5! NC

0.5

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1.5! NC

0.5

1

1.5! NC

0.5

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Q2=3.5GeV2 Q2=5GeV2 Q2=6.5GeV2 Q2=8.5GeV2 Q2=12GeV2

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1.5! NC

0.5

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Q2=15GeV2 Q2=20GeV2 Q2=25GeV2 Q2=35GeV2

10-3

1x

Q2=45GeV2

10-3

1x

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Q2=60GeV2

10-3

1x

Q2=90GeV2

10-3

1x

Q2=120GeV2

10-3

1x

Q2=150GeV2

Ep=920GeV

PDF a laHERAPDF1.0

PDF a laH1PDF2000

0.5

1

1.5! NC

0.5

1

1.5! NC

Q2=3.5GeV2 Q2=5GeV2 Q2=6.5GeV2 Q2=8.5GeV2

0.5

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Q2=12GeV2 Q2=15GeV2

10-3

1x

Q2=20GeV2

10-3

1x

Q2=25GeV2

10-3

1x

0.5

1

1.5! NC

0.5

1

1.5! NC

Q2=35GeV2

10-3

1x

Q2=45GeV2

Ep=820GeV

PDF a la HERAPDF1.0

PDF a la H1PDF2000

(a)

(b)

Figure 4: Low and medium Q2cross section data at Q2 ≥ 3.5 GeV2

measured at HERA-

1 with proton beam energy Ep = 920 GeV (a) and Ep = 820 GeV (b) in comparison with

predictions based on the fitted PDFs using parameterisation forms either as HERAPDF1.0 [5]

or as H1PDF2000 [6].

5

QCD/EW Fit gives good description of precision F2 data

Results

H1 Collaboration


0.5

1

1.5! N

C

0.5

1

1.5! N

C

0.5

1

1.5! N

C Q2=150GeV2 Q2=200GeV2 Q2=250GeV2 Q2=300GeV2 Q2=400GeV2

0.5

1! NC

0.5

1! NC

0.5

1! NC

0.5

1! NC

0.5

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0.5

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1! NC Q2=500GeV2 Q2=650GeV2 Q2=800GeV2 Q2=1000GeV2 Q2=1200GeV2

0.250.5

0.751

! NC

0.250.5

0.751

! NC

0.250.5

0.751

! NC

0.250.5

0.751

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0.250.5

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0.250.5

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0.250.5

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! NC

0.250.5

0.751

! NC Q2=1500GeV2 Q2=2000GeV2 Q2=3000GeV2

10-2

1x

Q2=5000GeV2

10-2

1x

Q2=8000GeV2

10-2

1x

0.20.40.60.8

! NC

0.20.40.60.8

! NC

0.20.40.60.8

! NC

0.20.40.60.8

! NC Q2=12000GeV2

10-2

1x

Q2=20000GeV2

10-2

1x

Q2=30000GeV2

e"p, Pe="0.2603e"p, Pe=+0.3690PDF a la HERAPDF1.0PDF a la H1PDF2000

0.5

1

1.5

! NC

0.5

1

1.5

! NC

0.5

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1.5

! NC Q2=150GeV2 Q2=200GeV2 Q2=250GeV2 Q2=300GeV2 Q2=400GeV2

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1! NC Q2=500GeV2 Q2=650GeV2 Q2=800GeV2 Q2=1000GeV2 Q2=1200GeV2

0.20.40.60.8! N

C

0.20.40.60.8! N

C

0.20.40.60.8! N

C

0.20.40.60.8! N

C

0.20.40.60.8! N

C

0.20.40.60.8! N

C

0.20.40.60.8! N

C

0.20.40.60.8! N

C Q2=1500GeV2 Q2=2000GeV2 Q2=3000GeV2

10-2

1x

Q2=5000GeV2

10-2

1x

Q2=8000GeV2

10-2

1x

0.10.20.3! N

C

0.10.20.3! N

C

0.10.20.3! N

C

0.10.20.3! N

C Q2=12000GeV2

10-2

1x

Q2=20000GeV2

10-2

1x

Q2=30000GeV2

e+p, Pe="0.3762e+p, Pe=+0.3252PDF a la HERAPDF1.0PDF a la H1PDF2000

(a)

(b)

Figure 7: High Q2NC e−p (a) and e+p (b) cross section data measured at HERA-2 in compar-

ison with predictions based on the fitted PDFs using parameterisation forms either as HERA-

PDF1.0 [5] or as H1PDF2000 [6].

8

Polarised LH / RH neutral current cross sections in e−p scattering

Results

H1 Preliminary


0.51

1.52

2.5! C

C

0.51

1.52

2.5! C

C

0.51

1.52

2.5! C

CQ2=300GeV2 Q2=500GeV2 Q2=1000GeV2

0.5

1

1.5

! CC

0.5

1

1.5

! CC

0.5

1

1.5

! CC

0.5

1

1.5

! CC

Q2=2000GeV2 Q2=3000GeV2

10-2

10-1

x

Q2=5000GeV2

10-2

10-1

x

0.25

0.5

0.75

1! CC

0.25

0.5

0.75

1! CC

0.25

0.5

0.75

1! CC

Q2=8000GeV2

10-2

10-1

x

Q2=15000GeV2

PDF a laHERAPDF1.0PDF a laH1PDF2000e"p, Pe="0.2603

0.5

1

1.5

! CC

0.5

1

1.5

! CC

0.5

1

1.5

! CC

Q2=300GeV2 Q2=500GeV2 Q2=1000GeV2

0.2

0.4

0.6! CC

0.2

0.4

0.6! CC

0.2

0.4

0.6! CC

0.2

0.4

0.6! CC

Q2=2000GeV2 Q2=3000GeV2

10-2

10-1

x

Q2=5000GeV2

10-2

10-1

x

0.2

0.4

! CC

0.2

0.4

! CC

0.2

0.4

! CC

Q2=8000GeV2

10-2

10-1

x

Q2=15000GeV2

PDF a laHERAPDF1.0PDF a laH1PDF2000e"p, Pe=+0.369

(a)

(b)

Figure 8: High Q2CC e−p cross section data measured at HERA-2 with left- (a) and right-

handed (b) polarised electron beam in comparison with predictions based on the fitted PDFs

using parameterisation forms either as HERAPDF1.0 [5] or as H1PDF2000 [6].

9

Polarised LH charged current cross sections in e−p scattering

Results

H1 Preliminary


Table 1: Datasets used in the combined electroweak and QCD fit. The low and medium Q2

datasets are combined data samples from all the measurements published by H1. For each

dataset, the corresponding center-of-mass energy√

s, the integrated luminosity value and the

average polarisation value (for HERA-2 data samples) are given.

Dataset√

s (GeV) L (pb−1) Pe (%)Low Q2

(e+p) 301 0.114 + 1.8 −Low Q2

(e+p) 319 0.505 −Medium Q2

(e+p) 301 17.9 −Medium Q2

(e+p) 319 2.1 + 22 −NC High Q2

(e+p) 301 35.6 −CC High Q2

(e+p) 301 35.6 −NC High Q2

(e−p) 319 16.4 −CC High Q2

(e−p) 319 16.4 −NC High Q2

(e+p) 319 65.2 −CC High Q2

(e+p) 319 65.2 −NC High Q2

(e+p) 319 81.9 −37.6± 1.4CC High Q2

(e+p) 319 81.9 −37.6± 1.4NC High Q2

(e+p) 319 98.1 32.5± 1.2CC High Q2

(e+p) 319 98.1 32.5± 1.2NC High Q2

(e−p) 319 103.2 −26.0± 1.0CC High Q2

(e−p) 319 103.2 −26.0± 1.0NC High Q2

(e−p) 319 45.9 36.9± 2.3CC High Q2

(e−p) 319 45.9 36.9± 2.3

Table 2: The results of the fits to weak neutral current couplings in comparison with their

SM values. The first errors correspond to experimental uncertainties and the second ones to

systematic uncertainties covering variations of the strange fraction fs, the charm and bottom

masses mc and mb, the minimum Q2selection cut Q2

min, the top mass mt, the Z0and W boson

masses and the strong coupling αs as well as variations of PDF parameterisation forms and the

initial Q20 value.

Fit vu-au-vd-ad-PDF vu-au-PDF vd-ad-PDF SM

au 0.49± 0.06± 0.04 0.53± 0.04 − 0.5vu 0.23± 0.08± 0.02 0.23± 0.04 − 0.191ad −0.67± 0.19± 0.07 − −0.61± 0.15 −0.5vd −0.31± 0.27± 0.06 − −0.44± 0.13 −0.346

χ2/dof 1183.8/1230 1184.5/1232 1184.2/1232 −

1

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

HERA-1+2 (prel)

Published (94-00)

H168% CL

Standard ModelLEP EWWGCDF

au

v u

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

HERA-1+2 (prel)

Published (94-00)

H168% CL


ad

v d

(a)

(b)

Figure 1: Results at 68% confidence level (CL) on the weak neutral current couplings of u (a)

and d (b) quarks to teh Z0boson determined in this analysis using the full HERA-1+2 H1 data

(shaded contours) in comparison with the corresponding results publised previously using the

HERA-1 data [1]. These results can be compared with those determined by the LEP EWWG [2]

and the CDF experiment [3]. The stars show the expected SM values.

2

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

HERA-1+2 (prel)

Published (94-00)

H168% CL


au

v u

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

HERA-1+2 (prel)

Published (94-00)

H168% CL


ad

v d

(a)

(b)

Figure 1: Results at 68% confidence level (CL) on the weak neutral current couplings of u (a)

and d (b) quarks to teh Z0boson determined in this analysis using the full HERA-1+2 H1 data

(shaded contours) in comparison with the corresponding results publised previously using the

HERA-1 data [1]. These results can be compared with those determined by the LEP EWWG [2]

and the CDF experiment [3]. The stars show the expected SM values.

2

Fits with new polarised HERA-I data shown in 68% CL blue contourImproved sensitivity to vector couplings compared to HERA-I unpolarised data (blue shaded area)Competitive determinations to CDF and LEPHERA data resolves LEP sign ambiguity

Results


Conclusions

•HERA data provide some of the most stringent constraints on PDFs

• Stress-test of QCD over 4 orders of mag. in Q2

•HERA data provide a self-consistent data set for complete flavour decomposition of the proton

•Combined QCD & EW analysis performed gives improved precision on axial & vector couplings

Soon to publish final HERA-II data

3

10 10

-7

-5

-3

-1

10

]2 [p

b/G

eV2

/dQ

!d

-710

-510

-310

-110

10

]2 [GeV2Q310 410

p CC (prel.)+H1 ep CC (prel.)-H1 e

p CC 06-07 (prel.)+ZEUS ep CC 04-06-ZEUS e

p CC (HERAPDF 1.0)+SM ep CC (HERAPDF 1.0)-SM e

p NC (prel.)+H1 ep NC (prel.)-H1 e

p NC 06-07 (prel.)+ZEUS ep NC 05-06-ZEUS e

p NC (HERAPDF 1.0)+SM ep NC (HERAPDF 1.0)-SM e

y < 0.9 = 0eP

HERA

Figure 19: The Q2 dependence of the unpolarised NC and CC cross sections dσ/dQ2, shownfor the e+p (open points) and e−p (solid points) scattering data from the H1 and ZEUS col-laborations. The results are compared with the corresponding Standard Model expectationsdetermined from the HERAPDF 1.0 fit. The inner and outer error bars represent respectivelythe statistical and total errors.

28

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Electroweak/QCD Fit to NC & CC HERA Data · 2011. 7. 22. · HERA-1 HERA-2 HERA-1 operation...

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