hera measurements for the lhc
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HERA measurements for the LHC
Katerina Lipka, DESY
for the H1 and ZEUS Collaborations
Standard Model at the LHC 2013
World-only ep collider
protons
electrons
Deep Inelastic Scattering at HERA
Central Tracker
• HERA I : 1992-2000
• HERA II: 2003-2007
• collider experiments
H1 & ZEUS,√smax= 318 GeV
• integrated Luminosity
~0.5 fb-1/ experiment
Ep=460-920 GeV Ee=27.6 GeV
HERA switched off June 2007, analyses ongoing on the way to final precisionH1 and ZEUS combine experimental data accounting for systematic correlations HERA performs the QCD analysis of (semi) inclusive DIS data (HERAPDF)H1 and ZEUS collaborations provide/support the PDF Fitting Tool (HERAFitter)
2
HERA Kinematics
E1
E2
s = τs = x1x2s
x1,2 =M√
s× exp(±y)
Q = M
Q2 =-q2 boson virtuality x=-q2/2p·q Bjorken scaling variable s=(k+p)2 center of mass energy
y transferred energy fraction Y± = 1±(1-y)2
Kinematics reconstructed from the scattered lepton (or hadronic final state)
Reconstruction of x1 and x2 not straightforward
fi(x)
DIS at HERA: clean lepton probe
Proton-proton collision at LHC
3
HERA Kinematics
fi(x)
DIS at HERA: clean lepton probe HERA covers low, medium x range of the LHCQ2 evolution via QCD
4
HERA
TEVATRON
LHC
DGLAP
HERA data: backbone for PDF determination
E1
E2
s = τs = x1x2s
x1,2 =M√
s× exp(±y)
Q = M
Proton-proton collision at LHC
4
Structure functions in DIS and proton PDFs
DIS cross sections provide an access to parton distribution functions in proton
LO : F2 ∝�
i
(qi(x) + qi(x))
LO : F3 ∝�
i
(qi(x)− qi(x))
NLO : FL ∝ x · αS · g(x,Q2)
d2σe±P
dxdQ2=
2πα2
xQ4[Y+F2 ∓ Y−xF3 − y2FL]
dominant contribution
γ/Z interference
contribution from gluon
γ, Z Exchange: Neutral Current ep → e X
σe+pCC ∝ x{(u + c) + (1− y)2(d + s)}
σe−pCC ∝ x{(u + c) + (1− y)2(d + s)}
W± Exchange: Charged Current ep → ν X
sensitive to individual quark flavours
5
HERA Inclusive DIS Measurements at highest Q2]2
[pb/
GeV
2/d
Qd
-710
-510
-310
-110
10
]2 [GeV2Q310 410
p CCH1 ep CC+H1 e
p CC HERA IIZEUS ep CC HERA II+ZEUS e
p CC (HERAPDF 1.5)SM ep CC (HERAPDF 1.5)+SM e
p NCH1 ep NC+H1 e
p NC HERA IIZEUS ep NC HERA II+ZEUS e
p NC (HERAPDF 1.5)SM ep NC (HERAPDF 1.5)+SM e
y < 0.9 = 0eP
HERA
[%] eP-100 -50 0 50 100
[pb]
CC
0
20
40
60
80
100
120p Scattering±HERA Charged Current e
2 > 400 GeV2Q y < 0.9
X p +e
X p e
HERAPDF 1.5
HERAPDF 1.5
H1 ZEUS
H1 ZEUS
NC and CC cross sections at large scales:SM: zero cross section for a RH e- or LH e+
Final HERA legacy textbook measurements in electroweak physics
Electroweak unification Good agreement with the SM
Inclusive HERA I and II dataprecision NC: ~1.5%, CC: ~4%
Charged Current
Neutral Current
arXiv:1208.6138JHEP 1209:061 (2012)EPJC 62 (2009) 625EPJC 70 (2010) 945EPJC 61 (2009) 223
6
Recent results on DIS NC Cross Sections
precision 1.5% for Q2 < 500 GeV2
arXiv:1208:6138
JHEP 1209:061 (2012)
sensitivity to valence compositiongluon distribution via scaling violations
xF γZ3 ∝ x · qval
F γZ2 ∝ q · q
JHEP 1209:061 (2012)
Q2=1500 GeV2
7
Recent results on DIS CC Cross Sections
JHEP 1209:061 (2012)
HERA II: improvement in precision: e+ (e-) p by a factor of 3 (10) luminosity wrt. HERA I
improved sensitivity to quark flavour composition 8
Combined HERA DIS Cross Sections
H1 and ZEUS
HER
A In
clus
ive
Wor
king
Gro
upA
ugus
t 201
0
x = 0.02 (x300.0)
x = 0.032 (x170.0)
x = 0.05 (x90.0)
x = 0.08 (x50.0)
x = 0.13 (x20.0)
x = 0.18 (x8.0)
x = 0.25 (x2.4)
x = 0.40 (x0.7)
x = 0.65
Q2/ GeV2
r,N
C(x
,Q2 )
HERA I+II NC e+p (prel.)HERA I+II NC e-p (prel.)
HERAPDF1.5 e+pHERAPDF1.5 e-p
±
10-2
10-1
1
10
10 2
10 3
10 2 10 3 10 4 10 5
0
0.5
1
1.5
2
0
0.5
1
0
0.2
0.4
0.6
0.8
H1 and ZEUS
r,C
C(x
,Q2 )
Q2 = 300 GeV2
-
Q2 = 500 GeV2 Q2 = 1000 GeV2 Q2 = 1500 GeV2
Q2 = 2000 GeV2 Q2 = 3000 GeV2
10-2 10-1
Q2 = 5000 GeV2
10-2 10-1
Q2 = 8000 GeV2
x
HER
A In
clus
ive
Wor
king
Gro
upA
ugus
t 201
0
10-2 10-1
Q2 = 15000 GeV2
10-2 10-1
Q2 = 30000 GeV2
x
HERA I+II CC e-p (prel.)HERAPDF1.5
Neutral Current Charged Current
Preliminary H1 and ZEUS measurements are combined accounting for correlationsImpressive precision up to high Q2 and high xQCD analysis of combined HERA NC and CC data: HERAPDF 9
0.2
0.4
0.6
0.8
1
-410 -310 -210 -110 1
0.2
0.4
0.6
0.8
1
HERAPDF1.5 (prel.)
exp. uncert.
model uncert. parametrization uncert.
x
xf 2 = 10 GeV2Q
vxu
vxd
0.05)×xS (
0.05)×xg (
HER
A S
truc
ture
Fun
ctio
ns W
orki
ng G
roup
July
201
0
H1 and ZEUS HERA I+II Combined PDF Fit
0.2
0.4
0.6
0.8
1
Model assumptions:
Qmin2=3.5 GeV2 , αs(MZ)=0.1176
mc=1.4 GeV; mb=4.75 GeV; fs(Q02)=0.31
HERA parton density functions
DGLAP evolution (QCDNUM, arXiv:1005.1481)
Heavy quarks: massive
Variable Flavour Number Scheme
Scales: µr = µf = Q2 , starting scale 1.9 GeV2
Experimentally uncertainty (Δχ2 =1)
Parameterization at starting scale:
HERAI +HERAII (prel.)
HERAPDF1.5: most precise DIS data, recommended HERA PDF set
10
HERA parton density functionsHERAPDF1.5 NLO and NNLO most precise DIS data, proper treatment of correlation of errors, allows for model studies
0
0.2
0.4
0.6
0.8
1
-410 -310 -210 -110 10
0.2
0.4
0.6
0.8
1
HERAPDF1.5 NNLO (prel.)
exp. uncert.
model uncert. parametrization uncert.
x
xf 2 = 10000 GeV2Q
vxu
vxd
0.05)×xS (
0.05)×xg (
HER
APD
F St
ruct
ure
Func
tion
Wor
king
Gro
upM
arch
201
1
H1 and ZEUS HERA I+II PDF Fit
0
0.2
0.4
0.6
0.8
1
NNLO
Describes LHC data very well, used in ATLAS, CMS and LHCb analyses
Available in LHAPDF with eigenvectors for uncertainties and αs variation
Final combination of HERA inclusive data and QCD analysis on the way (HERAPDF2.0)11
Precision QCD: Jets at HERA
i 1
0×
NC
/Je
t -210
1
210
410
610
810
1010
T,JetP710 20 50
DijetTP710 20 50
[GeV]TrijetTP 710 20 50
2 < 200 GeV2 150 < Q (i = 10)
2 < 270 GeV2 200 < Q (i = 8)
2 < 400 GeV2 270 < Q (i = 6)
2 < 700 GeV2 400 < Q (i = 4)
2 < 5000 GeV2 700 < Q (i = 2)
2 < 15000 GeV2 5000 < Q (i = 0)
had cNLO
= 0.118sCT10, QCDNUMNLOJet++ and fastNLO
Inclusive Jet Normalised
DijetNormalised
TrijetNormalised H1
Preliminary
(Multi)-jet production directly sensitive to the strong coupling constant
< 1% experimental error
Nuclear Physics B 864 (2012) 1
αS(MZ)=0.1206 (exp) (theory)+ 0.0023- 0.0022
+ 0.0042- 0.0035 αS(MZ)=0.1163 (exp) (theory)+ 0.0011
- 0.0011+ 0.0042- 0.0042
Measure αs running in a single experimentdifferent measurement methods agree
PhotoproductionQ2~0
DIS, 150 GeV2 < Q2 < 15000 GeV2
12
Additional Constraints on PDFs: Charm at HERA
c, b
g(x)
γe
p
c, b
stringent test of QCD, direct probe of the gluon
use different tagging methods:- meson reconstruction,- large mass and long lifetime
combination: - orthogonal uncertainties- take into account correlations
0
0.2
0
0.5
0
0.5
0
0.5
red
cc_
H1 VTX
H1 D* HERA-II
H1 D* HERA-I
ZEUS c µ X
ZEUS D* 98-00
ZEUS D* 96-97
ZEUS D0
ZEUS D+ H1 and ZEUSQ2=2.5 GeV2 Q2=5 GeV2 Q2=7 GeV2
Q2=12 GeV2 Q2=18 GeV2 Q2=32 GeV2
Q2=60 GeV2 Q2=120 GeV2 Q2=200 GeV2
Q2=350 GeV2
10-4 10-3 10-2
Q2=650 GeV2
10-4 10-3 10-2
Q2=2000 GeV2
HERA
10-4 10-3 10-2
x
Eur. Phys. J. C 73:2311 (2013), [arXiv:1211.1182]
13
Additional Constraints on PDFs: Charm at HERA
c, b
g(x)
γe
p
c, b
stringent test of QCD, direct probe of the gluon
use different tagging methods:- meson reconstruction,- large mass and long lifetime
combination: - orthogonal uncertainties- take into account correlations
0
0.2
0
0.5
0
0.5
0
0.5
red
cc_
H1 VTX
H1 D* HERA-II
H1 D* HERA-I
ZEUS c µ X
ZEUS D* 98-00
ZEUS D* 96-97
ZEUS D0
ZEUS D+ H1 and ZEUSQ2=2.5 GeV2 Q2=5 GeV2 Q2=7 GeV2
Q2=12 GeV2 Q2=18 GeV2 Q2=32 GeV2
Q2=60 GeV2 Q2=120 GeV2 Q2=200 GeV2
Q2=350 GeV2
10-4 10-3 10-2
Q2=650 GeV2
10-4 10-3 10-2
Q2=2000 GeV2
HERA
10-4 10-3 10-2
x
Eur. Phys. J. C 73:2311 (2013), [arXiv:1211.1182]
Q2=18 GeV2
HERA
H1 and ZEUS
H1 VTX
H1 D* HERA-II
H1 D* HERA-I
ZEUS c µ X
ZEUS D* 98-00
ZEUS D* 96-97
ZEUS D0
ZEUS D+
x
red
cc_
10-3 10-20
0.2
0.4
0.6
Precision ~ 5% at medium Q2 reached 14
Additional Constraints on PDFs: Charm at HERA
Inclusion of charm: reduced uncertainty on gluon, charm and light sea...mostly due to better constrained charm-quark mass
Eur
. Phy
s. J
. C 7
3:23
11 (2
013)
, [ar
Xiv
:121
1.11
82]
15
Additional Constraints on PDFs: Charm at HERA
Consistent with the world averagemc(mc)wa = 1.275 ±0.025 GeV
perform PDF fit varying mc in
FFNS coefficients
Determination of mc(mc) MS at NLO Study mc -choice in variable flavor number schemes
Different schemes prefer different Mc
Eur
. Phy
s. J
. C 7
3:23
11 (2
013)
, [ar
Xiv
:121
1.11
82]
16
Additional Constraints on PDFs: Charm at HERAStudy mc -choice in
variable flavor number schemes
Different schemes prefer different Mc
Prediction for W+ (W-, Z ) production at the LHC
Uncertainty due to differences in charm treatmentin PDFs significantly reduced by using optimal Mc
Eur
. Phy
s. J
. C 7
3:23
11 (2
013)
, [ar
Xiv
:121
1.11
82]
17
HERAFitter: Open-Source Modular Tool for QCD AnalysisDeveloped at HERA, extended to LHC and theory groupsStudy the impact of different data on PDFs and test different theory approaches
experimental input
processes: NC, CC DIS, jets, diffraction, heavy quarks (c,b,t)Drell-Yan, W production
theoretical calculations/toolsHeavy quark schemes: MSTW, CTEQ, ABMJets, W, Z production: fastNLO, ApplgridTop production NNLO (Hathor)QCD Evolution DGLAP (QCDNUM) kT factorisationAlternative tools NNPDF reweightingOther models Dipole model + Different error treatment models + Tools for data combination (HERAaverager)
H1 and ZEUS
Q2 / GeV2
r,N
C(x
,Q2 )
x=0.0002x=0.002
x=0.008
x=0.032
x=0.08
x=0.25
HERA I NC e+pZEUSH1
+
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1 10 10 2 10 3 10 4
[GeV]T
p210 310
/d|y
|T
(CTE
Q 6
.6)/d
p0
2/d
|y|/d
T/d
p2 d 0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2(CL90)PDF jets. R =0.4 (0.0<|y|<0.3) tanti-k
DataCTEQ 6.6HERAPDF 1.0
HERAPDF 1.5
GJR 2008
ATLAS Preliminary
[GeV]jetT
p100 200 300 400 500 600 700
[pb/
GeV
]je
tT
dpje
t/d
y2 d
-1510
-1310
-1110
-910
-710
-510
-310
-11010
310
510
710
910
1110D0 RunII
NLOjet++ (HERAPDF1.5)
)6| < 0.4 (x 10jet|y
)3| < 0.8 (x 10jet0.4 < |y
| < 1.2 jet0.8 < |y
)-3| < 1.6 (x 10jet1.2 < |y
)-6| < 2.0 (x 10jet1.6 < |y
)-9| < 2.4 (x 10jet2.0 < |y
+ nonperturbative corr.
Tevatron inclusive jet cross sections
experiments: HERA, Tevatron, LHC, fixed target
0
0.2
0.4
0.6
0.8
1
-410 -310 -210 -110 10
0.2
0.4
0.6
0.8
1
HERAPDF1.5 NNLO (prel.)
exp. uncert.
model uncert. parametrization uncert.
x
xf 2 = 10 GeV2Q
vxu
vxd
0.05)×xS (
0.05)×xg (
HER
APD
F St
ruct
ure
Func
tion
Wor
king
Gro
upM
arch
201
1
H1 and ZEUS HERA I+II PDF Fit
0
0.2
0.4
0.6
0.8
1
PDF or DPDF,...
αS (MZ),mc,mb,mt, fs,..
Theory predictions
Benchmarking
Comparison of schemes
HER
AFi
tter
18
Open source code, available at https://www.herafitter.org/HERAFitterVersion 0.3.0 released in March 2013.
HERAFitter: Open-Source Modular Tool for QCD Analysis
Joined effort of experimentalists, theorists and tool-developers Successfully used by the LHC experiments
19
Summary
HERA data are unique and of particular importance for PDF determination
• HERA II inclusive DIS cross section measurements are published
• H1+ZEUS combination and analysis towards HERAPDF2.0 ongoing
• HERA jet and charm data provide additional constrains on αS and charm-quark mass
HERA Expertise in QCD analysis preserved in HERAFitter development
• developed and supported by several experiments and theory groups
• allows experimentalists to perform QCD analysis and test theory approaches
• open source program, project open for further support
20
Determination of parton density functions
x-dependence of PDFs is not calculable in perturbative QCD:
parameterize at a starting scale Q20 : f(x)=AxB(1-x)C(1+Dx+Ex2)
evolve these PDFs using DGLAP equations to Q2>Q20
construct structure functions from PDFs and coefficient functions:
predictions for every data point in (x, Q2) – plane
χ2- fit to the experimental data
Structure function factorization: for the exchange of Boson V (γ, Z, W±)
calculable in pQCDfrom measured cross sections
FV2 (x,Q2) =
�
i=q,q,g
� 1
xdz × CV,i
2 (x
z, Q2, µF , µR, αS)× fi(z, µF , µR)
µi measured value at point i
δi statistical, uncorrelated systematic error
γjj – correlated systematic error
bj – shift of correlated systematic error sources
mi _ true value (corresponds to min χ2)
Measurements performed sometimes in slightly different range of (x,Q2)
swimming to the common (x,Q2) grid via NLO QCD in massive scheme
Combination ProcedureMinimized value:
HERAPDF: Fit Improvements
0
0.2
0.4
0.6
0.8
1
-410 -310 -210 -110 10
0.2
0.4
0.6
0.8
1
HERAPDF1.5 (prel.)
exp. uncert.
model uncert. parametrization uncert.
x
xf 2 = 10 GeV2Q
vxu
vxd
0.05)×xS (
0.05)×xg (
HER
APD
F St
ruct
ure
Func
tion
Wor
king
Gro
upM
arch
201
1
H1 and ZEUS HERA I+II 10 parameter PDF Fit
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
-410 -310 -210 -110 10
0.2
0.4
0.6
0.8
1
HERAPDF1.5f (prel.) exp. uncert. model uncert. parametrization uncert.
HERAPDF1.5 (prel.)
xxf 2 = 10 GeV2Q
vxu
vxd
0.05)×xS (
0.05)×xg (
HER
APD
F St
ruct
ure
Func
tion
Wor
king
Gro
upM
arch
201
1
H1 and ZEUS HERA I+II 14 parameter PDF Fit
0
0.2
0.4
0.6
0.8
1
HERAPDF1.5f : 14-parameter fit gluon more flexible at low-x
Small difference in total uncertainty → swap between parametrisation and experimental uncertainties
1.5 1.5 flexible
HERAPDF1.5f:
Two parametrisations are studied: a 10-parameter fit which corresponds to the preliminaryPDF fit of the NC and CC combined HERA I and HERA II data, HERAPDF1.5 [3], and a 14-parameter fit, HERAPDF1.5f, which allows more flexibility, in particular for the low-x gluondistribution. At the starting scale Q2
0 = 1.9 GeV2 the PDFs are parametrized as follows:
xg(x) = AgxBg · (1− x)Cg − A′
gxB′
g(1− x)C′
g (1)xuv(x) = Auvx
Buv · (1− x)Cuv · (1 +Duvx+ Euvx2) (2)
xdv(x) = AdvxBdv · (1− x)Cdv (3)
xU(x) = AUxBU · (1− x)CU (4)
xD(x) = ADxBD · (1− x)CD (5)
The parameters Ag, Auv , Adv are constrained by the sum rules. It is assumed that BU = BD,C ′
g = 25, AU = AD(1− fs), where fs is the strangeness fraction.
In the 10-parameter fit additional four constraints are enforced: A′
g = B′
g = 0, Bdv = Buv
and Duv = 0. In both, the 10- and 14-parameter fits these choices define the central fit, whilefurther parameters are considered when evaluating the parametrization uncertainty, as describedin section 2.3.
Greater flexibility in the gluon density helps to avoid a parametrisation bias, when addingmore data that is sensitive to the gluon density, like charm or jet production. Therefore, the14-parameter fit is preferred and used for HERAPDF1.6.
1.3 Theoretical predictions
The NLO cross sections of jet production were calculated using the NLOJET++ program [13].The FastNLO [14] interface was used to efficiently convolute the matrix elements from NLO-JET++ with the fitted PDFs.
In the prediction for the normalized jet cross sections [4] QCDNUM has been used to calcu-late the corresponding inclusive cross sections. For the factorisation and renormalisation scalesthe same variables as in relevant publications are used, the combination of Q2 and transversejet energy measured in the Breit frame ET (µf = µr =
√
(Q2 + E2T )/2) for the H1 measure-
ments and transverse jet energy measured in the Breit frame (µf = µr =√
E2T ) for the ZEUS
measurements.
2 Determination of uncertainties
The total uncertainty of the parton density functions and the αsaccounts for the experimenaluncertainties of the measurements and the variations of model and parametrisation assumptions,as described in the following.
2
Two parametrisations are studied: a 10-parameter fit which corresponds to the preliminaryPDF fit of the NC and CC combined HERA I and HERA II data, HERAPDF1.5 [3], and a 14-parameter fit, HERAPDF1.5f, which allows more flexibility, in particular for the low-x gluondistribution. At the starting scale Q2
0 = 1.9 GeV2 the PDFs are parametrized as follows:
xg(x) = AgxBg · (1− x)Cg − A′
gxB′
g(1− x)C′
g (1)xuv(x) = Auvx
Buv · (1− x)Cuv · (1 +Duvx+ Euvx2) (2)
xdv(x) = AdvxBdv · (1− x)Cdv (3)
xU(x) = AUxBU · (1− x)CU (4)
xD(x) = ADxBD · (1− x)CD (5)
The parameters Ag, Auv , Adv are constrained by the sum rules. It is assumed that BU = BD,C ′
g = 25, AU = AD(1− fs), where fs is the strangeness fraction.
In the 10-parameter fit additional four constraints are enforced: A′
g = B′
g = 0, Bdv = Buv
and Duv = 0. In both, the 10- and 14-parameter fits these choices define the central fit, whilefurther parameters are considered when evaluating the parametrization uncertainty, as describedin section 2.3.
Greater flexibility in the gluon density helps to avoid a parametrisation bias, when addingmore data that is sensitive to the gluon density, like charm or jet production. Therefore, the14-parameter fit is preferred and used for HERAPDF1.6.
1.3 Theoretical predictions
The NLO cross sections of jet production were calculated using the NLOJET++ program [13].The FastNLO [14] interface was used to efficiently convolute the matrix elements from NLO-JET++ with the fitted PDFs.
In the prediction for the normalized jet cross sections [4] QCDNUM has been used to calcu-late the corresponding inclusive cross sections. For the factorisation and renormalisation scalesthe same variables as in relevant publications are used, the combination of Q2 and transversejet energy measured in the Breit frame ET (µf = µr =
√
(Q2 + E2T )/2) for the H1 measure-
ments and transverse jet energy measured in the Breit frame (µf = µr =√
E2T ) for the ZEUS
measurements.
2 Determination of uncertainties
The total uncertainty of the parton density functions and the αsaccounts for the experimenaluncertainties of the measurements and the variations of model and parametrisation assumptions,as described in the following.
2
Two parametrisations are studied: a 10-parameter fit which corresponds to the preliminaryPDF fit of the NC and CC combined HERA I and HERA II data, HERAPDF1.5 [3], and a 14-parameter fit, HERAPDF1.5f, which allows more flexibility, in particular for the low-x gluondistribution. At the starting scale Q2
0 = 1.9 GeV2 the PDFs are parametrized as follows:
xg(x) = AgxBg · (1− x)Cg − A′
gxB′
g(1− x)C′
g (1)xuv(x) = Auvx
Buv · (1− x)Cuv · (1 +Duvx+ Euvx2) (2)
xdv(x) = AdvxBdv · (1− x)Cdv (3)
xU(x) = AUxBU · (1− x)CU (4)
xD(x) = ADxBD · (1− x)CD (5)
The parameters Ag, Auv , Adv are constrained by the sum rules. It is assumed that BU = BD,C ′
g = 25, AU = AD(1− fs), where fs is the strangeness fraction.
In the 10-parameter fit additional four constraints are enforced: A′
g = B′
g = 0, Bdv = Buv
and Duv = 0. In both, the 10- and 14-parameter fits these choices define the central fit, whilefurther parameters are considered when evaluating the parametrization uncertainty, as describedin section 2.3.
Greater flexibility in the gluon density helps to avoid a parametrisation bias, when addingmore data that is sensitive to the gluon density, like charm or jet production. Therefore, the14-parameter fit is preferred and used for HERAPDF1.6.
1.3 Theoretical predictions
The NLO cross sections of jet production were calculated using the NLOJET++ program [13].The FastNLO [14] interface was used to efficiently convolute the matrix elements from NLO-JET++ with the fitted PDFs.
In the prediction for the normalized jet cross sections [4] QCDNUM has been used to calcu-late the corresponding inclusive cross sections. For the factorisation and renormalisation scalesthe same variables as in relevant publications are used, the combination of Q2 and transversejet energy measured in the Breit frame ET (µf = µr =
√
(Q2 + E2T )/2) for the H1 measure-
ments and transverse jet energy measured in the Breit frame (µf = µr =√
E2T ) for the ZEUS
measurements.
2 Determination of uncertainties
The total uncertainty of the parton density functions and the αsaccounts for the experimenaluncertainties of the measurements and the variations of model and parametrisation assumptions,as described in the following.
2
Two parametrisations are studied: a 10-parameter fit which corresponds to the preliminaryPDF fit of the NC and CC combined HERA I and HERA II data, HERAPDF1.5 [3], and a 14-parameter fit, HERAPDF1.5f, which allows more flexibility, in particular for the low-x gluondistribution. At the starting scale Q2
0 = 1.9 GeV2 the PDFs are parametrized as follows:
xg(x) = AgxBg · (1− x)Cg − A′
gxB′
g(1− x)C′
g (1)xuv(x) = Auvx
Buv · (1− x)Cuv · (1 +Duvx+ Euvx2) (2)
xdv(x) = AdvxBdv · (1− x)Cdv (3)
xU(x) = AUxBU · (1− x)CU (4)
xD(x) = ADxBD · (1− x)CD (5)
The parameters Ag, Auv , Adv are constrained by the sum rules. It is assumed that BU = BD,C ′
g = 25, AU = AD(1− fs), where fs is the strangeness fraction.
In the 10-parameter fit additional four constraints are enforced: A′
g = B′
g = 0, Bdv = Buv
and Duv = 0. In both, the 10- and 14-parameter fits these choices define the central fit, whilefurther parameters are considered when evaluating the parametrization uncertainty, as describedin section 2.3.
Greater flexibility in the gluon density helps to avoid a parametrisation bias, when addingmore data that is sensitive to the gluon density, like charm or jet production. Therefore, the14-parameter fit is preferred and used for HERAPDF1.6.
1.3 Theoretical predictions
The NLO cross sections of jet production were calculated using the NLOJET++ program [13].The FastNLO [14] interface was used to efficiently convolute the matrix elements from NLO-JET++ with the fitted PDFs.
In the prediction for the normalized jet cross sections [4] QCDNUM has been used to calcu-late the corresponding inclusive cross sections. For the factorisation and renormalisation scalesthe same variables as in relevant publications are used, the combination of Q2 and transversejet energy measured in the Breit frame ET (µf = µr =
√
(Q2 + E2T )/2) for the H1 measure-
ments and transverse jet energy measured in the Breit frame (µf = µr =√
E2T ) for the ZEUS
measurements.
2 Determination of uncertainties
The total uncertainty of the parton density functions and the αsaccounts for the experimenaluncertainties of the measurements and the variations of model and parametrisation assumptions,as described in the following.
2
HERAPDF1.5 (10 parameter fit)
Two parametrisations are studied: a 10-parameter fit which corresponds to the preliminaryPDF fit of the NC and CC combined HERA I and HERA II data, HERAPDF1.5 [3], and a 14-parameter fit, HERAPDF1.5f, which allows more flexibility, in particular for the low-x gluondistribution. At the starting scale Q2
0 = 1.9 GeV2 the PDFs are parametrized as follows:
xg(x) = AgxBg · (1− x)Cg − A′
gxB′
g(1− x)C′
g (1)xuv(x) = Auvx
Buv · (1− x)Cuv · (1 +Duvx+ Euvx2) (2)
xdv(x) = AdvxBdv · (1− x)Cdv (3)
xU(x) = AUxBU · (1− x)CU (4)
xD(x) = ADxBD · (1− x)CD (5)
The parameters Ag, Auv , Adv are constrained by the sum rules. It is assumed that BU = BD,C ′
g = 25, AU = AD(1− fs), where fs is the strangeness fraction.
In the 10-parameter fit additional four constraints are enforced: A′
g = B′
g = 0, Bdv = Buv
and Duv = 0. In both, the 10- and 14-parameter fits these choices define the central fit, whilefurther parameters are considered when evaluating the parametrization uncertainty, as describedin section 2.3.
Greater flexibility in the gluon density helps to avoid a parametrisation bias, when addingmore data that is sensitive to the gluon density, like charm or jet production. Therefore, the14-parameter fit is preferred and used for HERAPDF1.6.
1.3 Theoretical predictions
The NLO cross sections of jet production were calculated using the NLOJET++ program [13].The FastNLO [14] interface was used to efficiently convolute the matrix elements from NLO-JET++ with the fitted PDFs.
In the prediction for the normalized jet cross sections [4] QCDNUM has been used to calcu-late the corresponding inclusive cross sections. For the factorisation and renormalisation scalesthe same variables as in relevant publications are used, the combination of Q2 and transversejet energy measured in the Breit frame ET (µf = µr =
√
(Q2 + E2T )/2) for the H1 measure-
ments and transverse jet energy measured in the Breit frame (µf = µr =√
E2T ) for the ZEUS
measurements.
2 Determination of uncertainties
The total uncertainty of the parton density functions and the αsaccounts for the experimenaluncertainties of the measurements and the variations of model and parametrisation assumptions,as described in the following.
2
Two parametrisations are studied: a 10-parameter fit which corresponds to the preliminaryPDF fit of the NC and CC combined HERA I and HERA II data, HERAPDF1.5 [3], and a 14-parameter fit, HERAPDF1.5f, which allows more flexibility, in particular for the low-x gluondistribution. At the starting scale Q2
0 = 1.9 GeV2 the PDFs are parametrized as follows:
xg(x) = AgxBg · (1− x)Cg − A′
gxB′
g(1− x)C′
g (1)xuv(x) = Auvx
Buv · (1− x)Cuv · (1 +Duvx+ Euvx2) (2)
xdv(x) = AdvxBdv · (1− x)Cdv (3)
xU(x) = AUxBU · (1− x)CU (4)
xD(x) = ADxBD · (1− x)CD (5)
The parameters Ag, Auv , Adv are constrained by the sum rules. It is assumed that BU = BD,C ′
g = 25, AU = AD(1− fs), where fs is the strangeness fraction.
In the 10-parameter fit additional four constraints are enforced: A′
g = B′
g = 0, Bdv = Buv
and Duv = 0. In both, the 10- and 14-parameter fits these choices define the central fit, whilefurther parameters are considered when evaluating the parametrization uncertainty, as describedin section 2.3.
Greater flexibility in the gluon density helps to avoid a parametrisation bias, when addingmore data that is sensitive to the gluon density, like charm or jet production. Therefore, the14-parameter fit is preferred and used for HERAPDF1.6.
1.3 Theoretical predictions
The NLO cross sections of jet production were calculated using the NLOJET++ program [13].The FastNLO [14] interface was used to efficiently convolute the matrix elements from NLO-JET++ with the fitted PDFs.
In the prediction for the normalized jet cross sections [4] QCDNUM has been used to calcu-late the corresponding inclusive cross sections. For the factorisation and renormalisation scalesthe same variables as in relevant publications are used, the combination of Q2 and transversejet energy measured in the Breit frame ET (µf = µr =
√
(Q2 + E2T )/2) for the H1 measure-
ments and transverse jet energy measured in the Breit frame (µf = µr =√
E2T ) for the ZEUS
measurements.
2 Determination of uncertainties
The total uncertainty of the parton density functions and the αsaccounts for the experimenaluncertainties of the measurements and the variations of model and parametrisation assumptions,as described in the following.
2
HERAPDF1.7: DIS+ low energy+jets+charm
0.2
0.4
0.6
0.8
1
-410 -310 -210 -110 1
0.2
0.4
0.6
0.8
1
HERAPDF1.7 (prel.) exp. uncert. model uncert. parametrization uncert.
HERAPDF1.6 (prel.)
x
xf 2 = 10 GeV2Q
vxu
vxd
0.05)×xS (
0.05)×xg (
HER
APD
F St
ruct
ure
Func
tion
Wor
king
Gro
upJu
ne 2
011
HERA I+II inclusive, jets, charm PDF Fit
0.2
0.4
0.6
0.8
1Flexible parametrization
heavy flavours:
mc=1.5±0.15 GeV
αS (MZ)=0.119
steeper gluon as HERAPDF1.6
Including the jet and the charm data: decouple the gluon from αS and mc
FV2 (x,Q2) =
�
i=q,q,g
� 1
xdz × CV,i
2 (x
z, Q2, µF , µR, αS)× fi(z, µF , µR)
Heavy Quarks and PDF Fits
Factorization:
i - number of active flavours in the proton: defines the factorization (HQ) scheme
• i fixed : Fixed Flavour Number Scheme (FFNS)
only light flavours in the proton: i = 3 (4)
c- (b-) quarks massive, produced in boson-gluon fusion
Q2 » mHQ2 : can be less precise, NLO coefficients contain terms ~
• i variable: Variable Flavour Number Scheme (VFNS)
- Zero Mass VFNS: all flavours massless. Breaks down at Q2 ~mHQ2
- Generalized Mass VFNS: different implementations provided by PDF groups smooth matching with FFNS for Q2 →mHQ
2 must be assured
ln� Q
mHQ
�
QCD analysis of the proton structure: treatment of heavy quarks essential
HQ contributions to the proton structure function F2 : (e.g. charm)
Direct test of HQ schemes in PDF fits
Heavy Quark Production at HERAHeavy quarks in ep scattering produced in boson-gluon fusion
Contribution to total DIS cross section:
charm: ~ 30% at large Q2
beauty: at most few %
Gluon directly involved: cross-check of g(x) from NC and CC DIS cross sections
c (b)
c (b)
g(x)
γe
p
/ GeVmodelcm
1.2 1.3 1.4 1.5 1.6 1.7 1.8
2
600
700
800
900
1000
flexible param standard param
/ndf
2
1
1.2
1.4
1.6
H1 and ZEUS (prel.)
(prel.)cc2HERAPDF1.0 + F
RT standard
0.018 GeV±(opt)=1.572 modelcm
/ GeVmodelcm
1.2 1.3 1.4 1.5 1.6 1.7 1.8
2
520
540
560
580
600
620
640
660
680
flexible param standard param
/ndf
2
0.9
0.95
1
1.05
1.1
1.15
H1 and ZEUS (prel.)
HERAPDF1.0 RT standard
0.100 GeV±(opt)=1.308 modelcm
Charm Mass as a Model Parameter in PDF
F2+charmF2
Strong dependence on mc Weak dependence on mc
Study the sensitivity of the PDF fit to the value of mc
PDF fit to inclusive DIS PDF fit to inclusive DIS + charm data
Prediction using mc=1.4 GeV
Error band: PDF uncertainty
Experimental error
Parametrization variation
Model assumptions
including mc variation
Heavy Quarks in PDFs and W/Z at LHC
√s=14 TeV
rapidity
NLO ⊗ HERAPDF1.0
Prediction of W± cross section @ LHC: dominant uncertainty due to PDF
mc variation in PDF: significant uncertainty on W@LHC in central region
/ GeV modelcm
1.2 1.4 1.6 1.8
/ nb
+W
52
54
56
58
60
62
64
RT standard
) = 7 TeVs (+W(prel.)cc
2HERAPDF1.0 + F
HER
A In
clus
ive
Wor
king
Gro
up
Aug
ust 2
010
Vary the charm mass in the PDF. Use resulting PDFs for LHC predictions
Larger mc → more gluons, less charm → more light quarks → larger σW
Charm at HERA and W/Z at LHC
/ GeV modelcm
1.2 1.4 1.6 1.8
/ nb
+W
52
54
56
58
60
62
64
RT standard
) = 7 TeVs (+W(prel.)cc
2HERAPDF1.0 + F
HER
A In
clus
ive
Wor
king
Gro
up
Aug
ust 2
010
Vary the charm mass in the PDF. Use resulting PDFs for LHC predictions
Only one HQ scheme mc variation in PDF
1.4 < mc < 1.65 GeV
3% uncertainty on W prediction
Charm at HERA and W/Z at LHC
/ GeV modelcm
1.2 1.4 1.6 1.8
/ nb
+W
52
54
56
58
60
62
64
RT standard RT optimised ACOT-full S-ACOT- ZMVFNS
) = 7 TeVs (+W(prel.)cc
2HERAPDF1.0 + F
HER
A In
clus
ive
Wor
king
Gro
up
Aug
ust 2
010
Vary the charm mass in the PDF. Use resulting PDFs for LHC predictions
Several HQ schemes mc variation in PDF
1.4 < mc < 1.65 GeV
3% uncertainty on W prediction
Using different HQ schemes:
+ 7% uncertainty
Large uncertainty on σW prediction due to HQ treatment in PDFs
Charm at HERA and W/Z at LHC
(HERA)PDF and top quark at the LHC Top quark at CMS: cross section @ approx. NNLO
mtpole (GeV)
t t_
(pb)
approx. NNLO (Langenfeld et al.) × HERAPDF15NNLO
only PDF uncertainties (68% CL):experimentalparametrizationmodel variations: Q2 > 5 GeV2
CMS (Prel.) CMS-PAS-TOP-11-005 (2011)
0
200
400
600
140 150 160 170 180 190
Dominant uncertainty: variation of Q2min imposed on data used in the fit
top quark production at the LHC has potential to constrain the high-x gluon
Q2=4mt2
thanks A. Cooper-Sarkar
HERAPDF1.5NNLO
PDF fits using HERA jet data: fixed αS
0
0.2
0.4
0.6
0.8
12 =10 GeV2Q
vxu
0
0.2
0.4
0.6
0.8
1
-0.4-0.2
00.20.4
-410 -310 -210 -110 1x-0.4-0.2
00.20.4
-0.4-0.2
00.20.4
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
12 =10 GeV2Q
vxd
HERAPDF1.6 (prel.) Exp. uncert. Model uncert. Param uncert. HERAPDF1.5f (prel.)
0
0.2
0.4
0.6
0.8
1
-0.4-0.2
00.20.4
-410 -310 -210 -110 1x-0.4-0.2
00.20.4
-0.4-0.2
00.20.40
0.2
0.4
0.6
0.8
1
012345678
2 =10 GeV2QxS
012345678
-0.4-0.2
00.20.4
-410 -310 -210 -110 1x-0.4-0.2
00.20.4
-0.4-0.2
00.20.4
012345678
02468
10121416
2 =10 GeV2Qxg
02468
10121416
-0.4-0.2
00.20.4
-410 -310 -210 -110 1x-0.4-0.2
00.20.4
-0.4-0.2
00.20.402468
10121416
H1 and ZEUS HERA I+II PDF Fit with Jets
HER
APD
F St
ruct
ure
Func
tion
Wor
king
Gro
upM
arch
201
1
Inclusion of jet data into the PDF fit using fixed αS does not have large impact
Inclusive DIS data: combined HERAI+HERAII
Jet data:H1 high Q2 , EPJ C65 (2010) low Q2, EPJ C67 (2010)
ZEUS incl. jets PLB547 (2002) incl.+2jets NP B765 (2007)
PDF Fit: - flexible parametrisation- αs(MZ) fixed
13
PDF fits with free αS (MZ)
0
0.2
0.4
0.6
0.8
1
-410 -310 -210 -110 10
0.2
0.4
0.6
0.8
1
HERAPDF1.5f (prel.) )
Z(Ms free
exp. uncert. model uncert. parametrization uncert.
x
xf 2 = 10 GeV2Q
vxu
vxd
0.05)×xS (
0.05)×xg (
HER
APD
F St
ruct
ure
Func
tion
Wor
king
Gro
upM
arch
201
1
H1 and ZEUS HERA I+II PDF Fit
0
0.2
0.4
0.6
0.8
1
no jet data
14
0
0.2
0.4
0.6
0.8
1
-410 -310 -210 -110 10
0.2
0.4
0.6
0.8
1
HERAPDF1.5f (prel.) )
Z(Ms free
exp. uncert. model uncert. parametrization uncert.
x
xf 2 = 10 GeV2Q
vxu
vxd
0.05)×xS (
0.05)×xg (
HER
APD
F St
ruct
ure
Func
tion
Wor
king
Gro
upM
arch
201
1
H1 and ZEUS HERA I+II PDF Fit
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
-410 -310 -210 -110 10
0.2
0.4
0.6
0.8
1
HERAPDF1.6 (prel.) )
Z(Ms free
exp. uncert. model uncert. parametrization uncert.
x
xf 2 = 10 GeV2Q
vxu
vxd
0.05)×xS (
0.05)×xg (
vxu
vxd
0.05)×xS (
0.05)×xg (
HER
APD
F St
ruct
ure
Func
tion
Wor
king
Gro
upM
arch
201
1
H1 and ZEUS HERA I+II PDF Fit with Jets
0
0.2
0.4
0.6
0.8
1
no jet data + jet data
PDF fits with free αS (MZ)
Inclusion of jet data into the PDF fit decouples the gluon and αS (MZ)
14
αS (MZ) from PDF fits including HERA jet data
)Z
(MS
0.114 0.116 0.118 0.12 0.122 0.124 0.126
m
in2
- 2
0
5
10
15
20H1 and ZEUS (prel.)
HERAPDF1.5fHERAPDF1.6
HER
APD
F St
ruct
ure
Func
tion
Wor
king
Gro
up
Mar
ch 2
011
)Z
(Ms
0.11 0.12 0.13)
Z(Ms
0.11 0.12 0.13
exp. uncert.th. uncert.
World averageS. Bethke, Eur. Phys. J. C64, 689 (2009)
jets 98-00TZEUS incl. kPhys. Lett. B 649, 12 (2007)
jets 96-97TZEUS incl. kPhys. Lett. B 547, 164 (2002)
multijetsT k2H1 low QEur. Phys. J. C67, 1 (2010)
multijetsT norm. k2H1 high QEur. Phys. J. C65, 363 (2010)
HERAPDF1.6Preliminary
H
ERA
Stru
ctur
e Fu
nctio
n W
orki
ng G
roup
Mar
ch 2
011
H1 and ZEUS (prel.)Scan of the αS (MZ) in the PDF fit
+ jet data
no jet data
PDF and αS (MZ) determined in the common fit:αS (MZ)= 0.1202 ± 0.0013exp ± 0.0007model/param ± 0.0012had+0.0045scale
From including the Jet data in the PDF fit: determine gluon and αS (MZ) 15
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