Parton Distribution Functions of the Proton:
from HERA to LHC (and beyond)
Ringailė Plačakytė
Part 1:
●
Introduction to Parton Distribution Functions (PDFs)
●
PDF determination
●
●
●
Theory
Experimental input
PDFs on the market
Part 2:
●
Recent results from LHC and their impact on PDFs
●
Tools for the PDF determination
●
(new) PDF4LHC recommendations
●
Summary
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
1
Part 1:
●
●
●
Introduction to Parton Distribution Functions (PDFs)
PDF determination
●
Theory
●
Experimental input
PDFs on the market
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
2
Introduction
Proton (nucleon) is made up of point like constituents (partons)
What are partons?
→ introduced by Feynman (1969) in parton model to explain Bjorken scaling
In inelastic e.g. electron-proton scattering at sufficient high scales the proton brakes-up
→ if proton is made up from point-like particles, then the cross section becomes
approximately independent on the scale (Bjorken scaling)
Experimentally observed at SLAC in late 60s :
J.T.Friedman + H.W.Kendall,
Ann. Rev. Nucl. Sci. 22 (1972) 203
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
3
Introduction
Soon experiments (fixed target, HERA) showed that Bjorken scaling is violated:
approximate region of
SLAC measurement
According the parton model, proton is made up
from up and down quarks → the average total
momentum of the proton carried by quarks is:
... nowadays we know that gluon is responsible
for the rest of the proton momentum
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
4
Introduction
Soon experiments (fixed target, HERA) showed that Bjorken scaling is violated:
approximate region of
SLAC measurement
According the parton model, proton is made up
from up and down quarks → the average total
momentum of the proton carried by quarks is:
... nowadays we know that gluon is responsible
for the rest of the proton momentum
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
5
Parton Distribution Functions
What are Parton Distribution Functions (PDFs) of the proton and how are
they related to partons?
PDFs → probability for a parton to carry the fraction x
of proton momentum
PDFs are intrinsic property of nucleon,
i.e assumed to be process independent
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
6
Parton Distribution Functions
Parton Distribution Functions (PDFs) are of crucial for precision physics at hadron
colliders because:
→ PDFs limit the accuracy of the SM predictions (including Higgs)
→ reach of new physics searches depends on PDF knowledge at high Bjorken-x
QCD factorisation:
measured cross section =
1
PDF
hard-scattering ME
σ (α s ,μ 2R ,μ 2F )=∑ ∫ f a ( x 1 ,μ 2F )f b ( x 2 , μ 2F ) σ^ (x 1 , x 2 ; α s ,μ 2R ,μ 2F )+ ...
a, b 0
precision measurements
of HERA, LHC data
Ringailė Plačakytė
PDF determination,
heavy quark treatment,
QCD analysis tools
HEPHY Vienna, 15 – 16 October, 2015
parton cross section
(calculable in pQCD)
7
Parton Distribution Functions
x-dependence of PDFs is not calculable in perturbative QCD
→ have to be determined experimentally
Q2 dependence is calculable in perturbative QCD:
DGLAP (Dokshitzer–Gribov–Lipatov–Altarelli–Parisi) evolution equations:
Probability via splitting functions:
Pqq
Ringailė Plačakytė
Pqg
Pgq
Pgg
HEPHY Vienna, 15 – 16 October, 2015
8
PDF Determination
PDF determinations is based on QCD factorisation
Experimentally measured cross-section (observable) (x,Q2)
Q2 dependence of  is given in perturbative QCD: DGLAP evolution equations
x-dependence of PDFs is not calculable in perturbative QCD
- parametrise PDFs at the starting scale Q20
- -fit to the experimental data
- evolve PDFs using DGLAP equations to Q2 > Q20
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
9
PDF Parametrisation
PDFs are parametrised (at the starting scale Q20) using
- standard parametrisation form:
A: overall normalisation
B: small x behavior
C: x1 shape
with
HERAPDF, MSTW/MMHT
(Chebyshev polynomials), ABM, JR
or
CTEQ, CT (Bernstein polynomials)
- parametrised in x-space with the flexible neural network method
→ used by NNPDF collaboration
- MC sampling of data space (replicas)
- training and validation: fit stops when quality of
fit stops improving (determined by random
selected validation data)
advantage: unbiased parametrisation
disadvantage: requires sufficient data
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
arXiv:0808.1231
10
Heavy Quark Treatment in PDFs
QCD factorisation:
measured cross section =
1
PDF
hard-scattering ME
σ (α s ,μ R ,μ F )=∑ ∫ f a (x 1 ,μ F )f b ( x 2 , μ F ) σ^ (x 1 , x 2 ; α s ,μ R ,μ F )+ ...
2
2
2
2
2
2
a, b 0
a, b - partons in the proton (g, q ,qbar) of different flavours
• if #flavours 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 ~ ln(Q/mHQ )
• if #flavours 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 →mHQ2 must be assured
→ mC is a parameter (MC)
treatment of heavy quarks is essential in PDFs
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
11
Parton Distribution Functions: from HERA to LHC
QCD factorisation:
PDF
1
hard-scattering ME
σ (α s ,μ R ,μ F )=∑ ∫ f a (x 1 ,μ F ) f b ( x 2 , μ F ) σ^ ( x 1 , x 2 ; α s ,μ R ,μ F )+ ...
2
2
2
2
2
2
a, b 0
Deep Inelastic Scattering (DIS):
unique opportunity to study PDFs
e, e
Q2
LHC
TEVATRON
/Z, W
DGLAP
x
HERA
Fixed
target
same PDFs can be used to predict
pp collisions
evolution in Q2 via DGLAP
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
12
Deep Inelastic Scattering as Probe of the Proton
Deep Inelastic Scattering (DIS) provides unique opportunity to study
the structure of the proton
e , e

Neutral Current (NC): epeX
Charged Current (CC): epX
Kinematics:
Q2
/Z, W
Q2 - virtuality of exchanged boson
x – Bjorken scaling variable
x
y – inelasticity
Q2 = sxy (s centre-of-mass energy)
HERA - worlds only e±p collider (1994-2007)
e(27.5 GeV), p(460-920 GeV) s= 225-318 GeV
Two collider experiments: H1 and ZEUS
~0.5 fb-1 of luminosity recorded by each experiment
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
13
ep scattering at HERA: Neutral Currents
Neutral current DIS cross section:
e
Q2
/Z(q)
x
Cross section is decomposed in terms of structure functions:
dominant contribution
important at high Q2
sizable at high y

 x
2e a (q-q)
2
LO: F2  x e q(q+q) (in NLO (s g) appear)
xF3
Ringailė Plačakytė
q
q
PDFs
HEPHY Vienna, 15 – 16 October, 2015
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ep scattering at HERA: Charged Currents
Charged current DIS cross section:
e
Q2
W(q)
x
P - electron(positron) polarisation
In SM weak interaction acts only
on left-handed particles
(right-handed anti-particles)
at LO e+/e- sensitive to different quark densities:
eCC  x[u+c] + (1-y)2x[d+s]
eCC  x[u+c] + (1-y)2x[d+s]
PDFs
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
15
ep scattering at HERA
Final word from HERA:
arXiv:1506.06042
→ inclusive data combination
→ in the combination 7 data sets with
162 sources of uncertainties used
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
16
PDFs from HERA
Final word from HERA:
arXiv:1506.06042
→ HERAPDF2.0 from the combined inclusive data
HERA provides a clean determination of proton PDFs (from ep data only)
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
17
PDFs from HERA
arXiv:1506.06042
HERA heavy quark and jet data bring additional sensitivity to PDFs
LO jet production in DIS:
→ direct sensitivity to gluon and strong
coupling constant
s(MZ)=0.1183  0.0009(exp)
0.0005(mod)0.0012(had) +0.0037
- 0.0030 (th)
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
18
PDFs from HERA
Eur.Phys. J. C73 (2012), 2311
HERA heavy quark and jet data bring additional sensitivity to PDFs
LO charm (boson-gluon-fusion)
production in DIS:
→ direct sensitivity to gluon
HERA charm and beauty data provide
→ stringent tests of heavy quark
treatment in PDFs
→ significant constrain on heavy
quark mass
Ringailė Plačakytė
Different schemes prefer
different MC
HEPHY Vienna, 15 – 16 October, 2015
19
QCD Analysis of HERA Charm Data
Eur.Phys. J. C73 (2012), 2311
In VFN schemes the charm quark mass parameter MC does not correspond
directly to a physical mass
→ not the case for Fixed-Flavour Number Scheme (FFNS)
An NLO QCD analysis in the FFNS
(FFNS of ABM, arXiv:1011.5790)
performed to determine the MSbar
running charm quark mass mc(mc)
consistent with the world average of
mc(mc) = 1.275 ± 0.025 GeV
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
20
PDFs on the Market
MMHT/MSTW
→ global PDF set (includes all type of data) with 25 eigenvector pairs (VFNS-TR').
Latest MMHT14 sets in LO, NLO and NNLO EPJC75 (2015) 204, arXiv:1412.3989
CT/CTEQ/CJ
→ global PDF set with 28 eigenvector pairs (VFNS-ACOT).
Latest CT14 sets in LO, NLO and NNLO (90% CL) arXiv:1506.07443
NNPDFs
→ global PDF set with 100 and 1000 MC replicas (VFNS FONLL-B and FFNS) .
Latest NNPDF3.0 sets in LO, NLO and NNLO JHEP 04 (2015) 040, arXiv:1410.8849
HERAPDF
→ HERA (combined) data (VFNS-TR').
Latest HERAPDF2.0 sets in LO, NLO and NNLO
arXiv:1506.06042
ABM/ABKM
→ global PDF set (FFNS).
Latest ABM12 sets in NLO and NNLO
PRD89 (2014) 054028, arXiv:1310.3059
JR/GJR
→ global PDF set (no LHC data) with dynamical approach (FFNS+VFNS).
Latest JR14 sets in NLO and NNLO Phys.Rev. D89 (2014), no. 7 074049, arXiv:1403.1852
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
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Data in PDF fits
Deep Inelastic Scattering:
ep (HERA) data: quarks and gluon at small x (FL), jets (moderate x),
CC → flavour separation, heavy quark structure functions
heavy flavour → gluons, tests of heavy quark schemes, mass determination
fixed target data: higher x
neutrino DIS: flavour decomposition, x>0.01
Drell-Yan production:
quark-antiquark annihilation – high x sea quarks, deuterium target –
u/d asymmetry
W/Z ratio, asymmetries → quark flavour separation
V+ heavy flavour → sensitivity to s quark
Inclusive jets, dijets and ratios:
high x gluon, alphas
Isolated photon → gluon at medium and high x
ttbar, single top:
gluon at high x, u and d
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
22
Data used in PDFs
PDF groups use different experimental data in the fits
→ changes in time for CT, MMHT and NNPDF PDFs
S. Forte
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
23
PDF Fitting Groups
Main sources of difference between different PDFs:
- inclusion of different data
- methods of determining 'best fit'
- uncertainty treatment/sources
- assumptions in procedure (parametrisation)
- heavy flavour treatment
- PDF and s correlation
... lead to differences in the cross section predictions
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
24
PDF Fit Groups: Benchmarking (PDF4LHC)
Different PDF lead to differences in cross section predictions
G.Watt
arXiv:1301.6754
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
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PDF Fit Groups: Benchmarking (PDF4LHC)
Different PDF lead to differences in cross section predictions
(plots from PDF4LHC recommendations – released this morning)
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
26
Why PDFs are Important? (pre-LHC)
PDFs are crucial for precision physics at hadron colliders
QCD factorisation:

 =  PDF
→ PDFs are one of main uncertainties in Higgs production, MW measurement,
BSM searches, etc
Deep Inelastic Scattering:
e, e
Q2
/Z, W
x
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
27
Why PDFs are Important? (post-LHC)
PDFs are crucial for precision physics at hadron colliders
QCD factorisation:

 =  PDF
→ PDFs are one of main uncertainties in Higgs production, MW measurement,
BSM searches, etc
E1
x1


E2
LHC
TEVATRON
x2
DGLAP

 – perturbative QCD cross section
HERA Fixed
target
LHC data can improve PDFs further
evolution in Q2 via DGLAP
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
28
Summary (of Part 1)
Parton Distribution Functions of the proton (PDFs)
crucial for precision physics at hadron colliders because:
→ PDFs limit the accuracy of the SM predictions (including Higgs)
→ reach of new physics searches depends on PDF knowledge at high Bjorken-x
DIS provides unique opportunity to study the structure of the proton
→ final HERA inclusive data andHERAPDF2.0 are published
Several available PDFs on the market
→ differences due to methodology, data, parametrisation, EW parameters, etc...
→ new PDF4LHC recommendations are underway (overview in Part 2)
LHC data can improve PDFs further
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
29
Part 2:
●
●
●
●
Recent results from LHC and their impact on PDFs
Tools for the PDF determination
(new) PDF4LHC recommendations
Summary
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
30
LHC Processes Sensitive to PDFs
LHC data
→ can help to discriminate between PDF sets
→ can help to improve PDFs
process
sensitivity to PDFs
W asymmetry
W and Z production (differential)
W+c production
Drell-Yan (DY): high invariant mass
Drell-Yan (DY): low invariant mass
W,Z +jets
→ quark flavour separation
→ valence quarks
→ strange quark
→ sea quarks, high-x
→ low-x
→ gluon medium-x
Inclusive jet and di-jet production
→ gluon and αs(MZ)
Direct photon
→ gluon medium, high-x
ttbar, single top
→ gluon and αs(MZ)
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
31
Back-Up Slides
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
32
High Q2 Neutral Current Cross Sections
Structure function xF3
dominant
contribution
from xF3Z
xF3γZ~xqval
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
33
High Q2 Neutral Current Cross Sections
Measuring the difference in NC polarised cross sections F 2Z can be accessed:
F2Z measurement is only
possible because of
+
e and e-, L and R data
First measurement of F2γZ
F2γZ ~ q+q
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
34
Polarisation Asymmetry in NC
The charge dependent polarisation asymmetries in neutral currents
→ direct measure of EW effects
neglecting Z term generalised structure function F2 is expressed:
Polarisation asymmetry A
at LO:
is proportional to aevq combination:
→ direct measurement of the parity violation
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
35
High Q2 Charged Current Data
e p
ep
HERA CC e+/e- measurements:
→ sensitivity to quark flavour
→ improvement in precision: e+(e-)p factor of 3(10) luminosity vs HERA I
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
36
Electroweak Unification
arXiv:1208:6138
Inclusive HERA I and II data
JHEP 1209:061 (2012)
with typical precision:
NC: ~1.5%
CC: ~4%
EPJC 70 (2010) 945
EPJC 62 (2009) 625
EPJC 61 (2009) 223
neutral (/Z)
charged (W±)
currents cross sections
2
at Q2 >
 M Z/W scale
are similar:
EW unification
good agreement with
the SM (HERAPDF 1.5)
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
37
HERAPDF Fit
QCD fit to combined HERA I+II data (H1 and ZEUS)
uncertainties:
https://www.desy.de/h1zeus/combined_results/index.php
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
741 data points
experimental
model
parametrisation
38
Constraints on PDFs from HERA Jet Data
LO jet production in DIS:
Direct sensitivity to gluon and strong coupling constant
Reduce correlation of gluon and s in PDF fit
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
39
HERA PDFs with Jet Data
Free s (no jets)
Free s (with jets)
+ jets
HERA jet data allow to constrain
simultaneously s and gluon
(+jets)
s(MZ)=0.1202  0.0013(exp)
0.0007(mod)0.0012(had)
Ringailė Plačakytė
+0.0045
- 0.0036
(th)
HEPHY Vienna, 15 – 16 October, 2015
40
HERA Charm Data
Eur.Phys. J. C73 (2012), 2311
LO charm production at
DIS (boson-gluon-fusion):
Direct access to the gluon
Heavy quark (HQ) treatment in PDFs
is important
Different HQ schemes exist
(different treatment of mass terms
in perturbative calculation)
Ringailė Plačakytė
Theory (HERAPDF1.5) uncertainty
dominated by mC variation
Data are within theory uncertainty
→ provide significant constrain on mC
HEPHY Vienna, 15 – 16 October, 2015
41
QCD Analysis of HERA Charm Data
Eur.Phys. J. C73 (2012), 2311
W+ cross section@LHC
1.5%
Different schemes prefer
different mCmodel
Variation between schemes ~6%
Significantly reduced at mcmodel (opt) (★)
HERA charm measurements help to reduce uncertainties
of predictions for the LHC
Ringailė Plačakytė
HEPHY Vienna, 15 – 16 October, 2015
42