SLIDE 1
Phenomenology of top-quark pair production at the LHC: studies with DiffTop
Marco Guzzi in collaboration with Katerina Lipka and Sven-Olaf Moch “High Energy Theory Divisional Seminars”, Liverpool, March 2015
SLIDE 2 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¯
t),
- 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¯ t pair production ( √ S = 7 and 8 TeV) as a function of different
- bservables of interest with unprecedented accuracy:
SLIDE 3
Physics Beyond the SM: is there any? from F. Maltoni and R. Frederix, JHEP 0901 (2009) 047
SLIDE 4 GeV
t T
p
50 100 150 200 250 300 350 400
GeV
t T
dp σ d σ 1
1 2 3 4 5 6 7 8 9 10
10 × Data MadGraph MC@NLO POWHEG
= 7 TeV s at
CMS, 5.0 fb + Jets Combined µ e/
(arXiv:1009.4935)
t
y
0.5 1 1.5 2 2.5 t
dy σ d σ 1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 Data MadGraph MC@NLO POWHEG
= 7 TeV s at
CMS, 5.0 fb + Jets Combined µ e/
(arXiv:1105.5167)
GeV
t t
m
400 600 800 1000 1200 1400 1600
GeV
t t
dm σ d σ 1
10
10
10
10
10 Data MadGraph MC@NLO POWHEG = 7 TeV s at
CMS, 5.0 fb + Jets Combined µ e/
GeV
t t T
p
50 100 150 200 250 300
GeV
t t T
dp σ d σ 1
5 10 15 20 25
10 × Data MadGraph MC@NLO POWHEG = 7 TeV s at
CMS, 5.0 fb + Jets Combined µ e/
The CMS Collaboration EPJC 2013,
√ S = 7 TeV, TOP-12-028 →
√ S = 8 TeV
SLIDE 5 100 200 300 400 500 600 700 800
GeV
t T
dp σ d σ 1
10
10
Data ALPGEN+HERWIG MC@NLO+HERWIG POWHEG+HERWIG ATLAS Preliminary
L dt = 4.6 fb
∫
= 7 TeV s [GeV]
T t
p 100 200 300 400 500 600 700 800 Data MC 0.5 1 1.5 500 1000 1500 2000 2500
GeV
t t
dm σ d σ 1
10
10
10
Data ALPGEN+HERWIG MC@NLO+HERWIG POWHEG+HERWIG ATLAS Preliminary
L dt = 4.6 fb
∫
= 7 TeV s [GeV]
t t
m 500 1000 1500 2000 2500 Data MC 0.5 1 1.5 100 200 300 400 500 600 700 800 900 1000
GeV
T t t
dp σ d σ 1
10
10
10
10
Data ALPGEN+HERWIG MC@NLO+HERWIG POWHEG+HERWIG ATLAS Preliminary
L dt = 4.6 fb
∫
= 7 TeV s [GeV]
T t t
p 100 200 300 400 500 600 700 800 900 1000 Data MC 0.5 1 1.5
0.5 1 1.5 2 2.5
t t
dy σ d σ 1
10 1
Data ALPGEN+HERWIG MC@NLO+HERWIG POWHEG+HERWIG ATLAS Preliminary
L dt = 4.6 fb
∫
= 7 TeV s
t t
y
0.5 1 1.5 2 2.5 Data MC 0.8 1 1.2
The ATLAS Collaboration ATLAS-CONF-2013-099, lepton+jets,
√ S = 7 TeV
SLIDE 6
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¯ t production cross sections by using approximate calculations.
◮ DiffTop calculates t¯
t differential cross sections in 1PI kinematics at approximate NLO (O(α3
s)), and NNLO O(α4 s). ◮ Exploratory work for future PDF fits using the exact NNLO
theory when available and usable.
SLIDE 7
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(α4
s) full QCD calculation for the t¯
t 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.
SLIDE 8
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. 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
SLIDE 9 LHC 7 TeV, mt=173 GeV Uncertainty due to scale variation, µr=µf
- approx. NNLO × MSTW08NNLO
MCFM × MSTW08NLO
pT(GeV) dσ/dpT (pp→tt
–+X) (pb/GeV)
0.5 1 50 100 150 200 250 300 350 400 dσ/dpT/σ (pp→tt
–+X) , mt=173 GeV
data CMS, √s=7 TeV
- N. Kidonakis, Phys.Rev. D82 (2010)
Uncertainty due to scale variation, µr=µf
- approx. NNLO × MSTW08NNLO
MCFM × MSTW08NLO
pt
T (GeV)
theory/data, dσ/dpT/σ
0.8 0.9 1 1.1 1.2 1.3 50 100 150 200 250 300 350 400 dσ/dpT/σ (pp→tt
–+X) , mt=173 GeV
data ATLAS, √s=7 TeV
- N. Kidonakis, Phys.Rev. D82 (2010)
Uncertainty due to scale variation, µr=µf
- approx. NNLO × MSTW08NNLO
MCFM × MSTW08NLO
pt
T (GeV)
theory/data, dσ/dpT/σ
0.8 0.9 1 1.1 1.2 1.3 50 100 150 200 250 300 350
SLIDE 10 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] published on JHEP (2014) The FastNLO-DiffTop code to produce grids will be available
- soon. (few grids are already available)
SLIDE 11
What’s in the Box ?
SLIDE 12 Remnants of long-distance dynamics in a hard scattering function can be large in regions of phase space near partonic threshold and dominate higher order corrections: → logarithmic corrections Threshold resummation organizes double-logarithmic corrections to all orders, thereby extending the predictive power of QCD to these phase space regions. G. Sterman (1987); S. Catani and L. Trentadue (1989); H. Contopanagos, E. Laenen, and G. Sterman (1997) The kinematics of inclusive heavy quark hadroproduction depend
- n which final state momenta are reconstructed.
In threshold resummation, a kinematic choice manifests itself at next-to-leading-logarithmic level.
SLIDE 13 Single-particle inclusive (1PI) kinematics
In our calculation, heavy-quark hadroproduction near the threshold is approximated by considering the partonic subprocesses q(k1) + ¯ q(k2) → t(p1) + X[¯ t](p′
2) ,
g(k1) + g(k2) → t(p1) + X[¯ t](p′
2)
p′
2 = ¯
p2 + k, (1) where is k any additional radiation, and s4 = p′
2 − m2 → 0
momentum at the threshold. This kinematic is used to determine the pt
T and rapidity yt
distribution of the final-state top-quark. Hard scattering functions are expanded in terms of
t )
s4
= lim
∆→0
t )
s4 θ(s4 − ∆) + 1 l + 1 lnl+1 ∆ m2
t
where corrections are denoted as leading-logarithmic (LL) if l = 2i + 1 at O(αi+3
s
) 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.
SLIDE 14 The hard scattering expansion
The factorized differential cross section is written as
S2 d2σ(S, T1, U1) dT1 dU1 =
q,g
1
x−
1
dx1 x1 1
x−
2
dx2 x2 fi/H1(x1, µ2
F)fj/H2(x2, µ2 F)
×ωij(s, t1, u1, m2
t , µ2 F, αs(µ2 R)) + O(Λ2/m2 t ) ,
ωij(s4, s, t1, u1) = ω(0)
ij
+ αs
π ω(1) ij
+ αs
π
2 ω(2)
ij
+ · · · where ω(2)
ij
at parton level in 1PI kinematics is given by
ω(2)
ij
= s2 ˆ σ(2)
ij
du1dt1
= F Born
ij
α2
s(µ2 R)
π2
ij
ln3(s4/m2
t )
s4
+D(2)
ij
ln2(s4/m2
t )
s4
+ D(1)
ij
ln(s4/m2
t )
s4
+ D(0)
ij
1 s4
+ R(2)
ij δ(s4)
SLIDE 15 Few more details...
◮ Hard and soft functions: Hij = H(0) ij
+ (αs/π)H(1)
ij
+ · · · and Sij = S(0)
ij
+ (αs/π)S(1)
ij
+ · · · , H(2)
ij
and S(2)
ij
are set to zero.
◮ Soft anomalous dimension matrices:
ΓS = (αs/π)Γ(1)
S
+ (αs/π)2Γ(2)
S
+ · · · In our calculation, Γ(2)
S
at two-loop for the massive case is
- included. Becher (2009), Kidonakis (2009).
◮ Anomalous dimensions of the quantum fields i = q, g:
γi = (αs/π)γ(1)
i
+ (αs/π)2γ(2)
i
+ · · ·
◮ 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.
SLIDE 16
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)} (3) are set to zero.
SLIDE 17 Systematic uncertainties due to missing terms
The uncertainties due to missing contributions in D(0)
ij
and R2 are part of the systematic uncertainty associated to approximate calculations of this kind which are based on threshold expansions.
0.2 0.4 0.6 0.8 1 1.2 1.4 50 100 150 200 250 300 350 400 dσ/dpT [pb/GeV] pT
t [GeV]
LHC 7 TeV, mt = 173 GeV, MSTW08 PDFs C0
(2) ± 5%
0.2 0.4 0.6 0.8 1 1.2 1.4 50 100 150 200 250 300 350 400 dσ/dpT [pb/GeV] pT
t [GeV]
LHC 7 TeV, mt = 173 GeV, MSTW08 PDFs R2 ± 2 R2 R2 ± R2
Left: The coefficient C (2) (scale ind. contribution in D(0)
ij ) is varied
within its 5% while R2 is kept fixed. Right: here the coefficient R2 is varied by adding and subtracting 2R2 while C (2) is kept fixed.
SLIDE 18 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.
SLIDE 19
Phenomenology: Exploratory studies at the LHC 7 TeV
SLIDE 20 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: ❍❍❍❍ ❍ ❥
10
10
10
10
10
10
10
10 10 10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
fixed target HERA x1,2 = (M/7 TeV) exp(±y) Q = M 7 TeV LHC parton kinematics M = 10 GeV M = 100 GeV M = 1 TeV M = 7 TeV 6 6 y = 4 2
2 4
Q
2 (GeV 2)
x
WJS2010
Figure by J. Stirling
SLIDE 21
- approx. NNLO × CT10NNLO, mt=173 GeV
LHC 7 TeV 1 GeV < pt
T< 100 GeV
100 GeV < pt
T< 200 GeV
200 GeV < pt
T< 300 GeV
300 GeV < pt
T< 400 GeV
xgluon cos(φ)
0.5 1 10
10
10
10
10
10
1
- approx. NNLO × MST08NNLO, mt=173 GeV
LHC 7 TeV 1 GeV < pt
T< 100 GeV
100 GeV < pt
T< 200 GeV
200 GeV < pt
T< 300 GeV
300 GeV < pt
T< 400 GeV
xgluon cos(φ)
0.5 1 10
10
10
10
10
10
1
Here we choose MSTW08 and CT10 as representative. ABM11, HERA1.5 and NNPDF2.3 show a similar behavior.
SLIDE 22 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¯
t 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))
SLIDE 23
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.
SLIDE 24 dσ/dpT/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF 68%CL µr=µf var. αS
- approx. NNLO × CT10, total unc.
data CMS, √s=7 TeV
pt
T (GeV)
theory/data, dσ/dpT/σ
0.8 0.9 1 1.1 1.2 50 100 150 200 250 300 350 400 dσ/dpT/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF 68%CL µr=µf var. αS
- approx. NNLO × CT10, total unc.
data ATLAS, √s=7 TeV
pt
T (GeV)
theory/data, dσ/dpT/σ
0.8 0.9 1 1.1 1.2 50 100 150 200 250 300 350 dσ/dy/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF 68%CL µr=µf var. αS
- approx. NNLO × CT10, total unc.
data CMS, √s=7 TeV
yt theory/data, dσ/dy/σ
0.8 0.9 1 1.1 1.2
0.5 1 1.5 2 2.5 0.5 1 1.5
- approx. NNLO × CT10NNLO, mt=173 GeV
dσ/dpT (pp→tt
–+X) (pb/GeV)
total uncertainty δmt= 1 GeV further uncertainty contributions: PDF 68%CL µr=µf var. αS
pt
T (GeV)
relative error
0.9 1 1.1 50 100 150 200 250 300 350 400 20 40 60 80 100
- approx. NNLO × CT10NNLO, mt=173 GeV
dσ/dy (pp→tt
–+X) (1/GeV)
total uncertainty δmt= 1 GeV PDF 68%CL µr=µf var. αS
yt relative error
0.8 0.9 1 1.1 1.2
1 2 3
Uncertainties for the top pt
T and yt distribution obtained by using DiffTop with CT10 NNLO PDFs. PDF and
αs(MZ ) errors are evaluated at the 68% CL.
SLIDE 25 0.5 1 1.5
- approx. NNLO, mt=173 ±1 GeV
dσ/dpT (pp→tt
–+X) (pb/GeV)
total uncertainty CT10NNLO MSTW08NNLO ABM11NNLO HERAPDF1.5NNLO NNPDF2.3NNLO
pt
T (GeV)
σ/σCT10
0.6 0.8 1 1.2 1.4 50 100 150 200 250 300 350 400 20 40 60 80 100
- approx. NNLO, mt=173 ±1 GeV (total uncertainty)
dσ/dy (pp→tt
–+X) (pb)
CT10NNLO MSTW08NNLO ABM11NNLO HERAPDF1.5NNLO NNPDF2.3NNLO
yt σ/σCT10
0.6 0.8 1 1.2 1.4
1 2 3
PDF uncertainties √ S = 7 TeV pt
T and y t distributions: comparison
between all PDF sets (bands are total unc.).
SLIDE 26 dσ/dpT/σ (pp→tt
–+X) , mt=173±1 GeV
data CMS, √s=7 TeV
CT10NNLO MSTW08NNLO ABM11NNLO HERAPDF1.5NNLO NNPDF2.3NNLO
pt
T (GeV)
theory/data, dσ/dpT/σ
0.8 0.9 1 1.1 1.2 1.3 50 100 150 200 250 300 350 400 dσ/dy/σ (pp→tt
–+X) , mt=173±1 GeV
data CMS, √s=7 TeV
CT10NNLO MSTW08NNLO ABM11NNLO HERAPDF1.5NNLO NNPDF2.3NNLO
yt theory/data, dσ/dy/σ
0.8 0.9 1 1.1 1.2 1.3
0.5 1 1.5 2 2.5 dσ/dpT/σ (pp→tt
–+X) , mt=173±1 GeV
data ATLAS, √s=7 TeV
CT10NNLO MSTW08NNLO ABM11NNLO HERAPDF1.5NNLO NNPDF2.3NNLO
pt
T (GeV)
theory/data, dσ/dpT/σ
0.8 0.9 1 1.1 1.2 1.3 50 100 150 200 250 300 350
PDF uncertainties √ S = 7 TeV pt
T and yt distributions: ratio to the LHC measurements (bands are total unc.).
SLIDE 27
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. ci,n(µR, µF) = c0
i,n + log(µR)cR i,n + log(µF)cF i,n + ...
beyond the NLO one has double log contributions .. + log2(µF)c(2,F)
i,n
+ log2(µR)c(2,R)
i,n
+ log(µF) log(µR)c(2,R F)
i,n
♠DiffTop is now included into HERAFitter for PDF analyses
Work is in progress on fastNLO grids generation to make all publicly available soon.
SLIDE 28
QCD analysis using t¯ t production measurements
Impact of the current measurements on PDF determination: Inclusion of differential t¯ t 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 pt
T.
SLIDE 29 Particulars of the fit
The PDF determination follows the approach used in the QCD fits
◮ GM VFNS used is TR’ at NNLO with mc = 1.4 GeV and mb
= 4.75 GeV as input,
◮ αs(mZ) = 0.1176; the Q2 range of the HERA data restricted
to Q2 ≥ Q2
min = 3.5 GeV2.
At the scale Q2
0 = 1.9 GeV2, the parton distributions are represented by
xuv(x) = Auv xBuv (1 − x)Cuv (1 + Duvx + Euvx2), xdv(x) = Adv xBdv (1 − x)Cdv , xU(x) = AU xBU (1 − x)CU, xD(x) = AD xBD (1 − x)CD, xg(x) = Ag xBg (1 − x)Cg + A′
g xB′
g (1 − x)C ′ g .
(4) where xU(x) = x ¯ u(x) and xD(x) = x ¯ d(x) + x¯ s(x).
SLIDE 30 Results of the fit: experimental uncertainty
The analysis is performed by fitting 14 free parameters.
A moderate impact on the large-x gluon exp. unc. is observed.
NNLO 14 parameter fit
HERA I DIS + CMS W + LHC+CDF tt
HERA I DIS Q2=100 GeV2 DIS + W + tt
x g/g ± δgexp.
0.5 0.75 1 1.25 1.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
NNLO 14 parameter fit
HERA I DIS + CMS W + LHC+CDF tt
HERA I DIS Q2=mH2 DIS + W + tt
x g/g ± δgexp.
0.5 0.75 1 1.25 1.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
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¯ t production measurements (dark shaded band), shown at the scales of Q2 = 100 GeV2 (left) and Q2 = m2
H (right). The ratio of g(x) obtained in the fit including t¯
t data to that
- btained by using DIS and lepton charge asymmetry, is represented by a dotted line.
SLIDE 31
Results of the fit: experimental uncertainty
Data set χ2 / dof NC cross section HERA-I H1-ZEUS combined e− p 109 / 145 NC cross section HERA-I H1-ZEUS combined e+ p 461 / 379 CC cross section HERA-I H1-ZEUS combined e− p 19 / 34 CC cross section HERA-I H1-ZEUS combined e+ p 30 / 34 CMS W charge ele Asymmetry 8.1 / 11 CMS W charge muon Asymmetry 18 / 11 CDF inclusive ttbar cross section 0.64 / 1 CMS Norm. differential t¯ t vs pT 7 TeV 11 / 7 CMS total t¯ t 8TeV mt=173.3 GeV 2.0 / 1 CMS total t¯ t 7TeV mt=173.3 GeV 1.5 / 1 ATLAS Norm. diff. t¯ t vs pT 7 TeV 3.6 / 6 ATLAS total t¯ t 7TeV mt=173.3 GeV 0.11 / 1 ATLAS total t¯ t 8TeV mt=173.3 GeV 0.080 / 1 Total χ2 / dof 664 / 618
SLIDE 32 A few considerations on the results
◮ HERA + CMS W lepton charge asy. vs HERA only ⇒ impact
- n 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¯
t 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
- nly the total or only the differential t¯
t cross section measurements are included in the fit.
◮ Correlations between t¯
t measurements are not included here.
◮ Correlations with mt and αs must be included in the fit.
SLIDE 33
Conclusions
◮ We have shown phenomenological studies in which differential
t¯ t 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.
SLIDE 34
BACKUP
SLIDE 35 Behavior around the threshold
By setting µR = µF = µ one can write the inclusive total partonic cross section in terms of scaling functions f (k,l)
ij
that are dimensionless and depend only on the variable η = s/(4m2
t ) − 1
σij(s, m2
t , µ2) = α2 s(µ)
m2
t ∞
(4παs(µ))k
k
f (k,l)
ij
(η) lnl µ2 m2
t
η = s/(4m2
t ) − 1 distance from the threshold.
Recent analysis by Moch, Vogt, and Uwer PLB (2012): known threshold corrections and improved approximate NNLO results are given over the full kinematic range.
SLIDE 36 Behavior around the threshold: NLO
η fqq(1,0) exact fqq(1,0) approx fqq(1,0) thresh
0.02 0.04 0.06 0.08 0.1 0.12 10
10
1 10
2
10
4
10
6
η fgq(1,0) exact fgq(1,0) approx fgq(1,0) thresh
0.005 0.01 0.015 0.02 0.025 0.03 10
10
1 10
2
10
4
10
6
η fgg(1,0) exact fgg(1,0) approx fgg(1,0) thresh
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 10
10
1 10
2
10
4
10
6
From Moch, Vogt, Uwer PLB (2012)
SLIDE 37 Quality check:
NLO Exact Calculation vs DiffTop approx NLO
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 50 100 150 200 250 dσ/dPT [pb/GeV] PT
t [GeV]
mt = 173 GeV; Q=mt; CT10 NLO MCFM NLO approx NLO, Q=mt
Beenakker, Kujif, Smith, Van Neerven, 1989, Dawson, Ellis, Nason, 1988-89
SLIDE 38 Behavior around the threshold: NNLO
η fqq(2,0) approx
A,B
fqq(2,0) thresh
0.02 0.04 0.06 0.08 0.1 10
10
1 10
2
10
4
10
6
η fgq(2,0) approx
A,B
fgq(2,0) thresh
0.02 0.04 0.06 0.08 0.1 0.12 0.14 10
10
1 10
2
10
4
10
6
η fgg(2,0) approx
A,B
fgg(2,0) thresh
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 10
10
1 10
2
10
4
10
6
From Moch, Vogt, Uwer PLB (2012)
SLIDE 39 Exact calculation for the gg channel at NNLO
10 20 30 40 50 0.2 0.4 0.6 0.8 1 Φgg σgg
(2)
β LHC 8 TeV mtop = 173.3 GeV MSTW2008NNLO(68cl) Approx NNLO, Leading Born Approx NNLO, Exact Born Exact NNLO
β =
From Czakon, Fiedler, Mitov PRL (2013)
SLIDE 40 dσ/dpT/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF 68%CL µr=µf var. αS
- approx. NNLO × MSTW08, total unc.
data CMS, √s=7 TeV
pt
T (GeV)
theory/data, dσ/dpT/σ
0.8 0.9 1 1.1 1.2 50 100 150 200 250 300 350 400 dσ/dpT/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF 68%CL µr=µf var. αS
- approx. NNLO × MSTW08, total unc.
data ATLAS, √s=7 TeV
pt
T (GeV)
theory/data, dσ/dpT/σ
0.8 0.9 1 1.1 1.2 50 100 150 200 250 300 350 dσ/dy/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF 68%CL µr=µf var. αS
- approx. NNLO × MSTW08, total unc.
data CMS, √s=7 TeV
yt theory/data, dσ/dy/σ
0.8 0.9 1 1.1 1.2
0.5 1 1.5 2 2.5 0.5 1 1.5
- approx. NNLO × MST08NNLO, mt=173 GeV
dσ/dpT (pp→tt
–+X) (pb/GeV)
total uncertainty δmt= 1 GeV further uncertainty contributions: PDF 68%CL µr=µf var. αS
pt
T (GeV)
relative error
0.9 1 1.1 50 100 150 200 250 300 350 400 20 40 60 80 100
- approx. NNLO × MST08NNLO, mt=173 GeV
dσ/dy (pp→tt
–+X) (1/GeV)
total uncertainty δmt= 1 GeV PDF 68%CL µr=µf var. αS
yt relative error
0.8 0.9 1 1.1 1.2
1 2 3
As in the previous slide but with MSTW08 NNLO PDFs. PDF and αs(MZ ) errors are evaluated at the 68% CL.
SLIDE 41 dσ/dpT/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF × αS 68%CL µr=µf var.
- approx. NNLO × ABM11, total unc.
data CMS, √s=7 TeV
pt
T (GeV)
theory/data, dσ/dpT/σ
0.8 0.9 1 1.1 1.2 50 100 150 200 250 300 350 400 dσ/dpT/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF × αS 68%CL µr=µf var.
- approx. NNLO × ABM11, total unc.
data ATLAS, √s=7 TeV
pt
T (GeV)
theory/data, dσ/dpT/σ
0.8 0.9 1 1.1 1.2 50 100 150 200 250 300 350 dσ/dy/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF × αS 68%CL µr=µf var.
- approx. NNLO × ABM11, total unc.
data CMS, √s=7 TeV
yt theory/data, dσ/dy/σ
0.8 0.9 1 1.1 1.2
0.5 1 1.5 2 2.5 0.5 1 1.5
- approx. NNLO × ABM11NNLO, mt=173 GeV
dσ/dpT (pp→tt
–+X) (pb/GeV)
total uncertainty δmt= 1 GeV further uncertainty contributions: PDF × αS 68%CL µr=µf var.
pt
T (GeV)
relative error
0.9 1 1.1 50 100 150 200 250 300 350 400 20 40 60 80 100
- approx. NNLO × ABM11NNLO, mt=173 GeV
dσ/dy (pp→tt
–+X) (1/GeV)
total uncertainty δmt= 1 GeV PDF × αS 68%CL µr=µf var.
yt relative error
0.8 0.9 1 1.1 1.2
1 2 3
As in the previous slide but with ABM11 NNLO PDFs. Here the uncertainty on αs(MZ ) is already part of the total PDF uncertainty.
SLIDE 42 dσ/dpT/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF 68%CL + var. µr=µf var. αS
- approx. NNLO × HERAPDF1.5, total unc.
data CMS, √s=7 TeV
pt
T (GeV)
theory/data, dσ/dpT/σ
0.8 0.9 1 1.1 1.2 50 100 150 200 250 300 350 400 dσ/dpT/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF 68%CL + var. µr=µf var. αS
- approx. NNLO × HERAPDF1.5, total unc.
data ATLAS, √s=7 TeV
pt
T (GeV)
theory/data, dσ/dpT/σ
0.8 0.9 1 1.1 1.2 50 100 150 200 250 300 350 dσ/dy/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF 68%CL + var. µr=µf var. αS
- approx. NNLO × HERAPDF1.5, total unc.
data CMS, √s=7 TeV
yt theory/data, dσ/dy/σ
0.8 0.9 1 1.1 1.2
0.5 1 1.5 2 2.5 0.5 1 1.5
- approx. NNLO × HERAPDF1.5NNLO, mt=173 GeV
dσ/dpT (pp→tt
–+X) (pb/GeV)
total uncertainty δmt= 1 GeV further uncertainty contributions: PDF 68%CL + var. µr=µf var. αS
pt
T (GeV)
relative error
0.8 1 1.2 1.4 50 100 150 200 250 300 350 400 20 40 60 80 100
- approx. NNLO × HERAPDF1.5NNLO, mt=173 GeV
dσ/dy (pp→tt
–+X) (1/GeV)
total uncertainty δmt= 1 GeV PDF 68%CL+var. µr=µf var. αS
yt relative error
0.8 1 1.2 1.4 1.6
1 2 3
As in the previous slide but with HERA1.5 NNLO PDFs.
SLIDE 43 dσ/dpT/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF 68%CL µr=µf var. αS
- approx. NNLO × NNPDF2.3, total unc.
data CMS, √s=7 TeV
pt
T (GeV)
theory/data, dσ/dpT/σ
0.8 0.9 1 1.1 1.2 50 100 150 200 250 300 350 400 dσ/dpT/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF 68%CL µr=µf var. αS
- approx. NNLO × NNPDF2.3, total unc.
data ATLAS, √s=7 TeV
pt
T (GeV)
theory/data, dσ/dpT/σ
0.8 0.9 1 1.1 1.2 50 100 150 200 250 300 350 dσ/dy/σ (pp→tt
–+X) , mt=173 GeV
δmt= 1 GeV PDF 68%CL µr=µf var. αS
- approx. NNLO × NNPDF2.3, total unc.
data CMS, √s=7 TeV
yt theory/data, dσ/dy/σ
0.8 0.9 1 1.1 1.2
0.5 1 1.5 2 2.5 0.5 1 1.5
- approx. NNLO × NNPDF2.3 NNLO, mt=173 GeV
dσ/dpT (pp→tt
–+X) (pb/GeV)
total uncertainty δmt= 1 GeV further uncertainty contributions: µr=µf var. αS
pt
T (GeV)
relative error
0.9 1 1.1 50 100 150 200 250 300 350 400 20 40 60 80 100
- approx. NNLO × NNPDF2.3 NNLO, mt=173 GeV
dσ/dy (pp→tt
–+X) (1/GeV)
total uncertainty δmt= 1 GeV PDF 68%CL µr=µf var. αS
yt relative error
0.8 0.9 1 1.1 1.2
1 2 3
As in the previous slide but with NNPDF2.3 NNLO PDFs.
