Phenomenology of top-quark pair
production at the LHC: studies with DiffTop
Marco Guzzi, Katerina Lipka and Sven-Olaf Moch
“TOP LHC WG meeting”, CERN, January 12-13, 2015
Outline and motivations
◮
Top-quark pair production at the LHC is crucial for many
phenomenological applications/investigations:
-Physics beyond the SM (⇒ distortions/bumps in
distributions like Mt t̄ ),
-extent of QCD factorization,
-PDFs determination in global QCD analyses:
Clean constraints on the gluon at large x,
Correlation between αs , top-quark mass mt , and the gluon.
◮
New data available: the CMS and ATLAS collaborations
published measurements
of differential cross sections for t t̄
√
pair production ( S = 7 and 8 TeV) as a function of different
observables of interest with unprecedented accuracy:
9
8
T
-1
1 dσ
σ dpt GeV
e/µ + Jets Combined
7
Data
MadGraph
MC@NLO
POWHEG
Approx. NNLO
CMS, 5.0 fb-1 at s = 7 TeV
1 dσ
σ dyt
CMS, 5.0 fb-1 at s = 7 TeV
×10
-3
10
0.7
e/µ + Jets Combined
Data
MadGraph
MC@NLO
POWHEG
Approx. NNLO
0.6
0.5
(arXiv:1009.4935)
6
(arXiv:1105.5167)
0.4
5
0.3
4
3
0.2
2
0.1
1
0
0
50
0
-2.5 -2 -1.5 -1 -0.5 0
100 150 200 250 300 350 400
0.5
1
1.5
2
pt GeV
T
10-2
Data
MadGraph
MC@NLO
POWHEG
10-3
25
e/µ + Jets Combined
20
Data
MadGraph
MC@NLO
POWHEG
15
10-4
10
-5
10
10-6
CMS, 5.0 fb-1 at s = 7 TeV
×10
-3
-1
1 dσ
σ tt GeV
dp
1 dσ GeV-1
σ
dmtt
CMS, 5.0 fb-1 at s = 7 TeV
e/µ + Jets Combined
2.5
yt
T
5
400
600
800
1000
1200
1400
1600
mtt GeV
0
0
50
100
150
200
250
300
ptt GeV
T
√
R
The CMS Collaboration EPJC 2013, Ldt = 5.0[fb]−1 , S = 7 TeV,
√
R
TOP-12-028 → Ldt ≈ 12[fb]−1 , S = 8 TeV
-1
1 dσ
σ dm GeV
Data
ALPGEN+HERWIG
10-3
tt
ALPGEN+HERWIG
T
-1
1 dσ
σ dpt GeV
Data
MC@NLO+HERWIG
10-3
MC@NLO+HERWIG
POWHEG+HERWIG
POWHEG+HERWIG
ATLAS Preliminary
∫ L dt = 4.6 fb
∫ L dt = 4.6 fb
10
-1
10-4
ATLAS Preliminary
-4
-1
s = 7 TeV
s = 7 TeV
-5
10
100
200
300
400
500
600
700
1
0.5
0
1.50
800
MC
Data
MC
Data
1.50
100
200
300
400
500
600
500
1000
1500
2000
2500
500
1000
1500
2000
2500
mtt [GeV]
1
0.5
0
700 800
pt [GeV]
tt
1 dσ
σ dy
10-2
Data
ATLAS Preliminary
Data
∫ L dt = 4.6 fb
ALPGEN+HERWIG
-1
ALPGEN+HERWIG
T
-1
1 dσ
σ tt GeV
dp
T
MC@NLO+HERWIG
s = 7 TeV
1
-3
10
MC@NLO+HERWIG
POWHEG+HERWIG
POWHEG+HERWIG
ATLAS Preliminary
∫ L dt = 4.6 fb
-1
10-4
s = 7 TeV
10-1
-5
10
100
200
300
400
500
600
700
800
900 1000
MC
Data
MC
Data
1.50
1
0.5
0
100 200 300 400 500 600 700 800 900 1000
ptt [GeV]
T
-2.5
1.2
1
0.8
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
y
tt
The ATLAS Collaboration ATLAS-CONF-2013-099, lepton+jets,
√
R
Ldt = 4.6[fb]−1 , S = 7 TeV
Main focus: exploit the full potential of these new (and
forthcoming) data in QCD analyses of PDFs.
◮
◮
◮
◮
◮
We need tools incorporating the current state-of-the-art of
QCD calculations:
some of them are already on the market,
for some others work is still in progress.
Global QCD analyses of the current measurements set specific
requirements to the representation of the experimental data
and availability of fast computing tools.
We tried to address these requirements in the context of
differential t t̄ production cross sections by using approximate
calculations.
DiffTop calculates t t̄ differential cross sections in 1PI
kinematics at approximate NLO (O(αs3 )), and NNLO O(αs4 ).
Exploratory work for future PDF fits using the exact NNLO
theory when available and usable.
Available calculations
NLO exact computations available since many years:
◮ Nason, Dawson, Ellis (1988); Beenakker, Kuijif, Van Neerven, Smith
(1989); Meng, Schuler, Smith, Van Neerven (1990); Beenakker, Van
Neerven, Schuler, Smith (1991); Mangano, Nason, Rodolfi (1992).
The NNLO O(αs4 ) full QCD calculation for the t t̄ total cross
section has been accomplished:
◮
◮
Czakon, Fiedler, Mitov (2013); Czakon, Mitov (2012), (2013);
Baernreuther, Czakon, Mitov (2012)
Top++ Czakon, Mitov (2011); Hathor Aliev, Lacker,
Langenfeld, Moch, Uwer, Wiedermann (2011)
Exact NLO tools available
◮
MNR,HVQMNR Mangano, Nason, Ridolfi;
MCFM Campbell, Ellis, Williams; MadGraph5 Alwall, Maltoni,
et al.; MC@NLO Frixione, Stoeckli, Torrielli, Webber, White;
POWHEG Alioli, Hamilton, Nason, Oleari, Re.
Exact NLO calculations for t t¯ total and differential cross
sections have been implemented into publicly available Monte
Carlo numerical codes.
Full NNLO calculation for the t t¯ production cross section at
differential level is on the way. (See Alex Mitov’s talk)
NLO predictions are not accurate enough to describe the data:
◮
◮
perturbative corrections are large,
systematic uncertainties associated to various scales
entering the calculation are important.
In the meanwhile, one can use approximate calculations based on
threshold expansions in QCD to make esploratory studies at
phenomenological level
LHC 7 TeV, mt=173 GeV
approx. NNLO × MSTW08NNLO
MCFM × MSTW08NLO
–
dσ/dpT (pp→tt+X) (pb/GeV)
Uncertainty due to scale variation, µr=µf
1
0.5
50
100
150
200
250
300
350
400
pT(GeV)
–
1.3
–
dσ/dpT/σ (pp→tt+X) , mt=173 GeV
1.3
N. Kidonakis, Phys.Rev. D82 (2010)
1.2
theory/data, dσ/dpT/σ
theory/data, dσ/dpT/σ
N. Kidonakis, Phys.Rev. D82 (2010)
Uncertainty due to scale variation, µr=µf
approx. NNLO × MSTW08NNLO
MCFM × MSTW08NLO
1.2
dσ/dpT/σ (pp→tt+X) , mt=173 GeV
1.1
1
0.9
Uncertainty due to scale variation, µr=µf
approx. NNLO × MSTW08NNLO
MCFM × MSTW08NLO
1.1
1
0.9
data CMS, √s=7 TeV
0.8
50
100
150
200
data ATLAS, √s=7 TeV
250
300
350
t
400
p (GeV)
T
0.8
50
100
150
200
250
300
t
350
p (GeV)
T
Development of tools for phenomenology
DiffTop: Fortran based computer code for calculating differential
and total cross section for heavy-flavor production at hadron
colliders at approximate NLO and NNLO by using threshold
expansions in QCD.
Implementation based on the calculation by N.Kidonakis,
S.-O.Moch, E.Laenen, R.Vogt (2001) - (Mellin-space
resummation).
DiffTop stand alone (1PI kinematics branch) is now available at:
http://difftop.hepforge.org/
arXiv:1406.0386[hep-ph] to be published on JHEP
The FastNLO-DiffTop code to produce grids will be available
soon. (few grids are already available)
What’s in the Box ?
Single-particle inclusive (1PI) kinematics
In our calculation, heavy-quark hadroproduction near the threshold
is approximated by considering the partonic subprocesses
q(k1 ) + q̄(k2 ) → t(p1 ) + X [t̄](p2′ ) ,
g (k1 ) + g (k2 ) → t(p1 ) + X [t̄](p2′ )
p2′ = p̄2 + k,
(1)
where is k any additional radiation, and s4 = p2′ − m2 → 0
momentum at the threshold.
This kinematic is used to determine the pTt and rapidity y t
distribution of the final-state top-quark.
Hard scattering functions are expanded in terms of
"
lnl (s4 /mt2 )
s4
#
= lim
+
∆→0
(
lnl (s4 /mt2 )
1
θ(s4 − ∆) +
lnl+1
s4
l +1
)
∆
δ(s4 ) ,
mt2
where corrections are denoted as leading-logarithmic (LL) if l = 2i + 1 at
O(αsi+3 ) with i = 0, 1, . . . , as next-to-leading logarithm (NLL) if l = 2i,
as next-to-next-to-leading logarithm (NNLL) if l = 2i − 1, and so on.
The hard scattering expansion
The factorized differential cross section is written as
S2
d 2 σ(S, T1 , U1 )
dT1 dU1
=
X Z
i,j=q,q̄,g
1
x1−
dx1
x1
Z
1
x2−
dx2
fi/H1 (x1 , µ2F )fj/H2 (x2 , µ2F )
x2
×ωij (s, t1 , u1 , mt2 , µ2F , αs (µ2R )) + O(Λ2 /mt2 ) ,
(0)
ωij (s4 , s, t1 , u1 ) = ωij +
(2)
αs (1)
π ωij
+
αs 2
π
(2)
ωij + · · ·
where ωij at parton level in 1PI kinematics is given by
3
(2)
2
2
2
σ̂ij (3) ln (s4 /mt )
Born αs (µR )
D
= s
= Fij
ij
du1 dt1 π2
s4
+
1PI
2
2
2
1
(2) ln (s4 /mt )
(1) ln(s4 /mt )
(0)
(2)
+Dij
+ Dij
+ Dij
+ Rij δ(s4 ) .
s4
s4
s4 +
+
+
(2)
ωij
2
Few more details...
◮
(0)
(1)
Hard and soft functions: Hij = Hij + (αs /π)Hij + · · · and
(0)
(1)
Sij = Sij + (αs /π)Sij + · · · ,
(2)
Hij
(2)
and Sij
are set to zero.
◮
Soft anomalous dimension matrices:
(1)
(2)
ΓS = (αs /π)ΓS + (αs /π)2 ΓS + · · ·
(2)
In our calculation, ΓS at two-loop for the massive case is
included. Becher (2009), Kidonakis (2009).
◮
Anomalous dimensions of the quantum fields i = q, g :
(1)
(2)
γi = (αs /π)γi + (αs /π)2 γi + · · ·
◮
The Coulomb interactions, due to gluon exchange between
the final-state heavy quarks, are included at 1-loop level.
◮
we work with the pole mass definition of the heavy quark.
Matching
The matching conditions are determined by comparing the
expansion in the Mellin moment space to the exact results for the
partonic cross section.
Matching terms at NLO
Tr {H (1) S (0) + H (0) S (1) }
(2)
are included. Beenakker, Kuijf, Van Neerven, Smith (1989),
Beenakker, Van Neerven, Meng, Schuler, Smith (1991), Mangano,
Nason, Ridolfi (1992).
Matching terms at NNLO
Tr {H (1) S (1) }, Tr {H (0) S (2) }, Tr {H (2) S (0) }
are set to zero.
(3)
Systematic uncertainties due to missing terms
(0)
The uncertainties due to missing contributions in Dij and R2 are
part of the systematic uncertainty associated to approximate
calculations of this kind which are based on threshold expansions.
LHC 7 TeV, mt = 173 GeV, MSTW08 PDFs
1.4
LHC 7 TeV, mt = 173 GeV, MSTW08 PDFs
1.4
(2)
C0 ± 5%
R2 ± 2 R2
R2 ± R2
1.2
1
dσ/dpT[pb/GeV]
dσ/dpT[pb/GeV]
1.2
0.8
0.6
0.4
1
0.8
0.6
0.4
0.2
0.2
0
0
0
50
100
150
200
t
pT [GeV]
250
300
(2)
350
400
0
50
100
150
200
t
pT [GeV]
250
300
(0)
350
400
Left: The coefficient C0 (scale ind. contribution in Dij ) is varied
within its 5% while R2 is kept fixed. Right: here the coefficient R2
(2)
is varied by adding and subtracting 2R2 while C0 is kept fixed.
QCD Threshold expansions: “pros and cons”
Approximate calculations based on threshold expansions are not
perfect, but can be (easily) highly improved once the full NNLO
calculation will be available.
provide a local effective description of the pT and y
distributions that captures the main features of the full
calculation.
relatively easy interface to FastNLO or ApplGrid.
provide a fast tool for taking into account correlations (αs ,
mt , gluon ); easy to implement different heavy-quark mass
definitions. Dowling, Moch (2014)
Very sensitive to the missing contribution in D (0) and R2 .
Scale uncertainty is also affected (at approx NNLO is
underestimated at the moment. We’ll improve on this)
At the moment the description is valid near the threshold.
Phenomenology: Exploratory studies at the
LHC 7 TeV
What is it good for?
Top-quark pair production at LHC probes high-x gluon and the
differential cross section is strongly correlated at x ≈ 0.1:
7 TeV LHC parton kinematics
9
10
WJS2010
8
10
x1,2 = (M/7 TeV) exp(±y)
Q=M
M = 7 TeV
7
10
6
❍
5
10
4
M = 1 TeV
❍❍
❍
❥
❍
M = 100 GeV
10
Q
2
2
(GeV )
10
3
10
y= 6
2
4
0
2
4
6
2
10
M = 10 GeV
1
fixed
target
HERA
10
0
Figure by J. Stirling
10
-7
10
-6
10
-5
10
-4
-3
10
10
x
-2
10
-1
10
0
10
approx. NNLO × CT10NNLO, mt=173 GeV
approx. NNLO × MST08NNLO, mt=173 GeV
LHC 7 TeV
1
LHC 7 TeV
1
1 GeV < p < 100 GeV
t
1 GeV < p < 100 GeV
t
T
T
100 GeV < p < 200 GeV
100 GeV < p < 200 GeV
t
200 GeV < p < 300 GeV
0.5
T
t
300 GeV < p < 400 GeV
T
0
-0.5
-1 -6
10
T
t
200 GeV < p < 300 GeV
0.5
cos(φ)
cos(φ)
t
T
t
T
t
300 GeV < p < 400 GeV
T
0
-0.5
10
-5
10
-4
10
-3
10
-2
10
-1
1
xgluon
-1 -6
10
10
-5
10
-4
10
-3
10
-2
10
-1
1
xgluon
Here we choose MSTW08 and CT10 as representative. ABM11,
HERA1.5 and NNPDF2.3 show a similar behavior.
What is it good for?
Top-quark pair production at LHC probes high-x gluon (x ≈ 0.1): but
there is a strong correlation between g (x), αs and the top-quark mass mt
that we want to pin down
◮
Precise measurements of the total and differential cross section of t t̄
pair production provide us with a double handle on these quantities
◮
Precise measurements of the absolute differential cross section also
provides us with important information to constrain PDFs (gluon)
◮
The shape of the differential cross section is modified by mt and αs
(very sensitive)
◮
extraction of mt will benefit from the interplay between these two
measurements. (recent CMS paper PLB (2014))
DiffTop Results
In what follows:
◮
PDF unc. are computed by following the prescription given by
each PDF group at 68% CL ;
◮
The uncertainty associated to αs (MZ ) is given by the central
value as given by each PDF group ±∆αs (MZ ) = 0.001;
◮
◮
Scale unc. is obtained by variations mt /2 ≤ µR = µF ≤ 2mt ;
Uncertanty associated to the top-quark mass is estimated by
using mt = 173 GeV (Pole mass) ±∆mt = 1 GeV.
–
–
dσ/dpT/σ (pp→tt+X) , mt=173 GeV
theory/data, dσ/dpT/σ
theory/data, dσ/dpT/σ
δmt= 1 GeV
PDF 68%CL
µr=µf var.
αS
50
100
150
200
data CMS, √s=7 TeV
250
1.1
1
δmt= 1 GeV
0.9
1.1
1
δmt= 1 GeV
PDF 68%CL
µr=µf var.
αS
0.9
PDF 68%CL
µr=µf var.
αS
300
350
400
0.8
50
100
150
200
250
300
t
0.8
-2.5
350
-2
-1.5
-1
-0.5
t
p (GeV)
T
dσ/dy (pp→tt+X) (1/GeV)
approx. NNLO × CT10NNLO, mt=173 GeV
1.5
total uncertainty
δmt= 1 GeV
1
0.5
–
–
further uncertainty
contributions:
PDF 68%CL
µr=µf var.
αS
0
0.5
1
1.5
2
2.5
y
p (GeV)
T
dσ/dpT (pp→tt+X) (pb/GeV)
approx. NNLO × CT10, total unc.
1.2
data ATLAS, √s=7 TeV
1
0.8
dσ/dy/σ (pp→tt+X) , mt=173 GeV
approx. NNLO × CT10, total unc.
data CMS, √s=7 TeV
1.1
0.9
–
dσ/dpT/σ (pp→tt+X) , mt=173 GeV
1.2
approx. NNLO × CT10, total unc.
theory/data, dσ/dy/σ
1.2
t
approx. NNLO × CT10NNLO, mt=173 GeV
100
80
total uncertainty
µr=µf var.
PDF 68%CL
αS
δmt= 1 GeV
60
40
20
relative error
relative error
1.2
1.1
1
0.9
0
50
100
150
200
250
300
350
t
400
p (GeV)
T
1.1
1
0.9
0.8
-3
-2
-1
0
1
2
3
y
t
t
Uncertainties for the top pT
and y t distribution obtained by using DiffTop with CT10 NNLO PDFs. PDF and
αs (MZ ) errors are evaluated at the 68% CL.
–
dσ/dy (pp→tt+X) (pb)
1
HERAPDF1.5NNLO
NNPDF2.3NNLO
0.5
80
1.2
0.6
NNPDF2.3NNLO
ABM11NNLO
20
1.4
0.8
HERAPDF1.5NNLO
MSTW08NNLO
40
1.2
1
CT10NNLO
60
1.4
σ/σCT10
σ/σCT10
approx. NNLO, mt=173 ±1 GeV (total uncertainty)
100
total uncertainty
CT10NNLO
MSTW08NNLO
ABM11NNLO
–
dσ/dpT (pp→tt+X) (pb/GeV)
approx. NNLO, mt=173 ±1 GeV
1.5
1
0.8
0.6
0
50
100
150
200
250
300
350
t
400
p (GeV)
T
-3
-2
-1
0
1
2
3
y
√
PDF uncertainties S = 7 TeV pTt and y t distributions: comparison
between all PDF sets (bands are total unc.).
t
–
dσ/dy/σ (pp→tt+X) , mt=173±1 GeV
1.3
approx. NNLO, total unc.
CT10NNLO
MSTW08NNLO
ABM11NNLO
HERAPDF1.5NNLO
NNPDF2.3NNLO
1.2
theory/data, dσ/dpT/σ
–
dσ/dpT/σ (pp→tt+X) , mt=173±1 GeV
approx. NNLO, total unc.
CT10NNLO
HERAPDF1.5NNLO
MSTW08NNLO
NNPDF2.3NNLO
ABM11NNLO
1.2
theory/data, dσ/dy/σ
1.3
1.1
1
0.9
1.1
1
0.9
data CMS, √s=7 TeV
0.8
50
100
150
data CMS, √s=7 TeV
200
250
300
350
400
0.8
-2.5
-2
-1.5
-1
-0.5
t
0
0.5
1
1.5
2
2.5
y
p (GeV)
T
t
–
1.3
dσ/dpT/σ (pp→tt+X) , mt=173±1 GeV
approx. NNLO, total unc.
CT10NNLO
MSTW08NNLO
ABM11NNLO
HERAPDF1.5NNLO
NNPDF2.3NNLO
theory/data, dσ/dpT/σ
1.2
1.1
1
0.9
data ATLAS, √s=7 TeV
0.8
50
100
150
200
250
300
350
t
p (GeV)
T
PDF uncertainties
√
t
S = 7 TeV pT
and y t distributions: ratio to the LHC measurements (bands are total unc.).
QCD analysis using t t¯ production measurements
Impact of the current measurements on PDF determination:
Inclusion of differential t t̄ production cross sections into NNLO
QCD fits of PDFs.
◮
◮
◮
we interfaced DiffTop to the HERAFitter platform,
HERAFitter uses QCDNUM for NNLO DGLAP evol.,
W asymmetry at NNLO: MCFM ApplGrid + K -factors.
Data sets included in the analysis
◮
◮
◮
◮
◮
HERA I inclusive DIS,
CMS electron √
and muon charge asymmetry in W -boson
production at S = 7 TeV,
√
ATLAS and CMS total inclusive Xsec at S =7 and 8 TeV,
CDF total inclusive Xsec, Tevatron Run-II,
ATLAS
and CMS normalized differential cross-sections at
√
S = 7 TeV as a function of pTt .
Particulars of the fit
The PDF determination follows the approach used in the QCD fits
of the HERA and CMS coll.
◮
◮
GM VFNS used is TR’ at NNLO with mc = 1.4 GeV and mb
= 4.75 GeV as input,
αs (mZ ) = 0.1176; the Q 2 range of the HERA data restricted
2
to Q 2 ≥ Qmin
= 3.5 GeV2 .
At the scale Q02 = 1.9 GeV2 , the parton distributions are represented by
xuv (x)
xdv (x)
xU(x)
=
=
=
xD(x)
=
xg (x)
=
Auv x Buv (1 − x)Cuv (1 + Duv x + Euv x 2 ),
Adv x Bdv (1 − x)Cdv ,
AU x BU (1 − x)CU ,
AD x BD (1 − x)CD ,
′
′
Ag x Bg (1 − x)Cg + A′g x Bg (1 − x)Cg .
¯ + x s̄(x).
where xU(x) = x ū(x) and xD(x) = x d(x)
(4)
Results of the fit: experimental uncertainty
The analysis is performed by fitting 14 free parameters.
NNLO 14 parameter fit
1.5
-
g/g ± δgexp.
g/g ± δgexp.
A moderate impact on the large-x gluon exp. unc. is observed.
HERA I DIS + CMS W + LHC+CDF tt
HERA I DIS + CMS W
HERA I DIS
1.25
-
HERA I DIS + CMS W + LHC+CDF tt
HERA I DIS + CMS W
HERA I DIS
1.25
1
0.75
NNLO 14 parameter fit
1.5
1
2
Q =100 GeV
0.75
2
-
2
Q =mH2
DIS + W + tt / DIS + W
0.5
0.1
0.2
0.3
0.4
0.5
-
DIS + W + tt / DIS + W
0.6
0.7
0.8
0.9
1
0.5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
x
Uncertainties of the gluon distribution as a function of x, as obtained in our NNLO fit by using: inclusive DIS
measurements only (light shaded band), DIS and W lepton charge asymmetry data (hatched band), and DIS,
lepton charge asymmetry and the t t̄ production measurements (dark shaded band), shown at the scales of
2
Q 2 = 100 GeV2 (left) and Q 2 = mH
(right). The ratio of g (x) obtained in the fit including t t̄ data to that
obtained by using DIS and lepton charge asymmetry, is represented by a dotted line.
1
x
Results of the fit: experimental uncertainty
Data set χ2 / dof
NC cross section HERA-I H1-ZEUS combined e −
NC cross section HERA-I H1-ZEUS combined e +
CC cross section HERA-I H1-ZEUS combined e −
CC cross section HERA-I H1-ZEUS combined e +
CMS W charge ele Asymmetry
CMS W charge muon Asymmetry
CDF inclusive ttbar cross section
CMS Norm. differential t t̄ vs pT 7 TeV
CMS total t t̄ 8TeV mt =173.3 GeV
CMS total t t̄ 7TeV mt =173.3 GeV
ATLAS Norm. diff. t t̄ vs pT 7 TeV
ATLAS total t t̄ 7TeV mt =173.3 GeV
ATLAS total t t̄ 8TeV mt =173.3 GeV
Total χ2 / dof
p
p
p
p
109 / 145
461 / 379
19 / 34
30 / 34
8.1 / 11
18 / 11
0.64 / 1
11 / 7
2.0 / 1
1.5 / 1
3.6 / 6
0.11 / 1
0.080 / 1
664 / 618
A few considerations on the results
◮
◮
◮
◮
◮
◮
HERA + CMS W lepton charge asy. vs HERA only ⇒ impact
on light quarks central val. and reduction of the uncertainties
Slight reduction of the gluon unc. in HERA + CMS W lepton
asy. with respect to HERA only ⇒
ascribed to the improved constraints on the light-quark
distributions through the sum rules.
Inclusion of t t̄ measurements in the NNLO PDF fit ⇒
change in the shape of the gluon distribution (softens),
moderate improvement of its uncertainty at large x.
A similar effect is observed, although less pronounced, when
only the total or only the differential t t̄ cross section
measurements are included in the fit.
Correlations between t t̄ measurements are not included here.
Correlations with mt and αs must be included in the fit.
Conclusions
◮
◮
◮
◮
◮
◮
We have shown phenomenological studies in which differential
t t̄ measurements are used in exploratory determination of the
impact of such measurements on the PDFs of the proton.
Theoretical predictions at approximate NNLO are provided by
fastNLO-DiffTop.
given the current accuracy of the data, the improvements on
the gluon are still moderate (Correlations with mt and αs not
included).
More data is needed: absolute differential cross section data
will bring more information.
It will be interesting to see how this scenario will evolve once
the full NNLO calculation will be available.
Looking forward to see all this machinery at work in more
extensive global PDF fits.
BACKUP
Quality check:
NLO Exact Calculation vs approx NLO
mt = 173 GeV; Q=mt; CT10 NLO
1.1
MCFM NLO
approx NLO, Q=mt
1
0.9
dσ/dPT[pb/GeV]
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
50
100
150
t
PT [GeV]
Beenakker, Kujif, Smith, Van Neerven, 1989, Dawson, Ellis, Nason, 1988-89
200
250
–
–
dσ/dpT/σ (pp→tt+X) , mt=173 GeV
theory/data, dσ/dpT/σ
theory/data, dσ/dpT/σ
δmt= 1 GeV
PDF 68%CL
µr=µf var.
αS
50
100
150
200
data CMS, √s=7 TeV
250
1.1
1
δmt= 1 GeV
0.9
1.1
1
δmt= 1 GeV
PDF 68%CL
µr=µf var.
αS
0.9
PDF 68%CL
µr=µf var.
αS
300
350
400
0.8
50
100
150
200
250
300
t
0.8
-2.5
350
-2
-1.5
-1
-0.5
t
p (GeV)
p (GeV)
T
dσ/dy (pp→tt+X) (1/GeV)
approx. NNLO × MST08NNLO, mt=173 GeV
1.5
total uncertainty
δmt= 1 GeV
1
0.5
–
further uncertainty
contributions:
PDF 68%CL
µr=µf var.
αS
0
0.5
1
1.5
2
2.5
y
T
–
dσ/dpT (pp→tt+X) (pb/GeV)
approx. NNLO × MSTW08, total unc.
1.2
data ATLAS, √s=7 TeV
1
0.8
dσ/dy/σ (pp→tt+X) , mt=173 GeV
approx. NNLO × MSTW08, total unc.
data CMS, √s=7 TeV
1.1
0.9
–
dσ/dpT/σ (pp→tt+X) , mt=173 GeV
1.2
approx. NNLO × MSTW08, total unc.
theory/data, dσ/dy/σ
1.2
t
approx. NNLO × MST08NNLO, mt=173 GeV
100
80
total uncertainty
µr=µf var.
PDF 68%CL
αS
δmt= 1 GeV
60
40
20
relative error
relative error
1.2
1.1
1
0.9
0
50
100
150
200
250
300
350
t
400
p (GeV)
T
1.1
1
0.9
0.8
-3
-2
-1
0
1
2
3
y
t
As in the previous slide but with MSTW08 NNLO PDFs. PDF and αs (MZ ) errors are evaluated at the 68% CL.
–
–
dσ/dpT/σ (pp→tt+X) , mt=173 GeV
theory/data, dσ/dpT/σ
theory/data, dσ/dpT/σ
δmt= 1 GeV
50
1
PDF × αS 68%CL
0.9
δmt= 1 GeV
µr=µf var.
µr=µf var.
150
data CMS, √s=7 TeV
1.1
PDF × αS 68%CL
100
200
250
300
350
400
0.8
50
100
1.1
1
δmt= 1 GeV
0.9
PDF × αS 68%CL
µr=µf var.
150
200
250
300
t
0.8
-2.5
350
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
t
p (GeV)
p (GeV)
T
dσ/dy (pp→tt+X) (1/GeV)
approx. NNLO × ABM11NNLO, mt=173 GeV
1.5
total uncertainty
δmt= 1 GeV
1
–
further uncertainty
contributions:
PDF × αS 68%CL
µr=µf var.
0.5
approx. NNLO × ABM11NNLO, mt=173 GeV
100
µr=µf var.
total uncertainty
PDF × αS 68%CL
80
δmt= 1 GeV
60
40
20
relative error
relative error
1.2
1.1
1
0.9
0
50
100
150
200
250
300
350
t
400
p (GeV)
T
1.1
1
0.9
0.8
-3
-2
-1
0
1
2
3
y
t
As in the previous slide but with ABM11 NNLO PDFs. Here the uncertainty on αs (MZ ) is already part of the
total PDF uncertainty.
2.5
y
T
–
dσ/dpT (pp→tt+X) (pb/GeV)
approx. NNLO × ABM11, total unc.
1.2
data ATLAS, √s=7 TeV
1
0.8
dσ/dy/σ (pp→tt+X) , mt=173 GeV
approx. NNLO × ABM11, total unc.
data CMS, √s=7 TeV
1.1
0.9
–
dσ/dpT/σ (pp→tt+X) , mt=173 GeV
1.2
approx. NNLO × ABM11, total unc.
theory/data, dσ/dy/σ
1.2
t
–
–
dσ/dpT/σ (pp→tt+X) , mt=173 GeV
theory/data, dσ/dpT/σ
theory/data, dσ/dpT/σ
δmt= 1 GeV
PDF 68%CL + var.
µr=µf var.
αS
50
100
150
200
data CMS, √s=7 TeV
250
300
1.1
1
δmt= 1 GeV
0.9
δmt= 1 GeV
PDF 68%CL + var.
µr=µf var.
αS
αS
350
400
0.8
50
100
150
200
250
300
0.8
-2.5
350
-2
-1.5
-1
-0.5
t
T
1
–
further uncertainty
contributions:
PDF 68%CL + var.
µr=µf var.
αS
0.5
–
total uncertainty
δmt= 1 GeV
dσ/dy (pp→tt+X) (1/GeV)
approx. NNLO × HERAPDF1.5NNLO, mt=173 GeV
1.5
approx. NNLO × HERAPDF1.5NNLO, mt=173 GeV
80
total uncertainty
µr=µf var.
PDF 68%CL+var.
αS
δmt= 1 GeV
60
40
20
1.6
relative error
1.4
100
1.2
1
0
50
100
150
200
250
300
350
400
t
p (GeV)
T
As in the previous slide but with HERA1.5 NNLO PDFs.
1.4
1.2
1
0.8
-3
-2
-1
0
0.5
1
1.5
2
2.5
y
p (GeV)
T
dσ/dpT (pp→tt+X) (pb/GeV)
1
µr=µf var.
t
0.8
1.1
0.9
PDF 68%CL + var.
p (GeV)
relative error
approx. NNLO × HERAPDF1.5, total unc.
1.2
data ATLAS, √s=7 TeV
1
0.8
dσ/dy/σ (pp→tt+X) , mt=173 GeV
approx. NNLO × HERAPDF1.5, total unc.
data CMS, √s=7 TeV
1.1
0.9
–
dσ/dpT/σ (pp→tt+X) , mt=173 GeV
1.2
approx. NNLO × HERAPDF1.5, total unc.
theory/data, dσ/dy/σ
1.2
0
1
2
3
y
t
t
–
–
dσ/dpT/σ (pp→tt+X) , mt=173 GeV
theory/data, dσ/dpT/σ
theory/data, dσ/dpT/σ
δmt= 1 GeV
PDF 68%CL
µr=µf var.
αS
50
100
150
200
data CMS, √s=7 TeV
250
1.1
1
δmt= 1 GeV
0.9
1.1
1
δmt= 1 GeV
PDF 68%CL
µr=µf var.
αS
0.9
PDF 68%CL
µr=µf var.
αS
300
350
400
0.8
50
100
150
200
250
300
t
0.8
-2.5
350
-2
-1.5
-1
-0.5
t
p (GeV)
T
dσ/dy (pp→tt+X) (1/GeV)
approx. NNLO × NNPDF2.3 NNLO, mt=173 GeV
1.5
total uncertainty
δmt= 1 GeV
1
–
–
further uncertainty
contributions:
µr=µf var.
αS
0.5
100
approx. NNLO × NNPDF2.3 NNLO, mt=173 GeV
80
total uncertainty
µr=µf var.
PDF 68%CL
αS
δmt= 1 GeV
60
40
20
relative error
relative error
1.2
1.1
1
0.9
0
50
100
150
200
250
300
350
400
t
p (GeV)
T
As in the previous slide but with NNPDF2.3 NNLO PDFs.
1.1
1
0.9
0.8
-3
-2
-1
0
0.5
1
1.5
2
2.5
y
p (GeV)
T
dσ/dpT (pp→tt+X) (pb/GeV)
approx. NNLO × NNPDF2.3, total unc.
1.2
data ATLAS, √s=7 TeV
1
0.8
dσ/dy/σ (pp→tt+X) , mt=173 GeV
approx. NNLO × NNPDF2.3, total unc.
data CMS, √s=7 TeV
1.1
0.9
–
dσ/dpT/σ (pp→tt+X) , mt=173 GeV
1.2
approx. NNLO × NNPDF2.3, total unc.
theory/data, dσ/dy/σ
1.2
0
1
2
3
y
t
t
Interface to fastNLO(In collaboration with D. Britzger)
DiffTop has been succesfully interfaced to fastNLO.
This is important for applications in PDF fits, because NNLO
computations are generally CPU time consuming.
0
R
F
ci,n (µR , µF ) = ci,n
+ log(µR )ci,n
+ log(µF )ci,n
+ ...
beyond the NLO one has double log contributions
(2,F )
.. + log2 (µF )ci,n
(2,R)
+ log2 (µR )ci,n
(2,R F )
+ log(µF ) log(µR )ci,n
♠DiffTop is now included into HERAFitter for PDF analyses
Work is in progress on fastNLO grids generation to make all publicly
available soon.