Phenomenology of top-quark pair production at the LHC: studies with DiffTop

Transcription

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 205

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 M t t), -extent of QCD factorization, -PDFs determination in global QCD analyses: Clean constraints on the gluon at large x, Correlation between α s, top-quark mass m t, 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 observables of interest with unprecedented accuracy:

3 Physics Beyond the SM: is there any? from F. Maltoni and R. Frederix, JHEP 090 (2009) 047

4 - GeV dσ dp tt tt T t T t σ e/µ + Jets Combined - CMS, 5.0 fb at s = 7 TeV Data MadGraph MC@NLO POWHEG Approx. NNLO (arxiv: ) dy σ dσ e/µ + Jets Combined - CMS, 5.0 fb at s = 7 TeV Data MadGraph MC@NLO POWHEG Approx. NNLO (arxiv:05.567) t p T GeV y t - GeV dσ dm σ e/µ + Jets Combined - CMS, 5.0 fb at s = 7 TeV Data MadGraph MC@NLO POWHEG - GeV dσ σ dp e/µ + Jets Combined - CMS, 5.0 fb at s = 7 TeV Data MadGraph MC@NLO POWHEG m tt GeV tt p T GeV The CMS Collaboration EPJC 203, Ldt = 5.0[fb], S = 7 TeV, TOP Ldt 2[fb], S = 8 TeV

5 - GeV t Data - GeV Data dσ σ T T dp -3 0 ALPGEN+HERWIG MC@NLO+HERWIG dσ dm tt σ -3 0 ALPGEN+HERWIG MC@NLO+HERWIG POWHEG+HERWIG POWHEG+HERWIG -4 0 ATLAS Preliminary - L dt = 4.6 fb s = 7 TeV -4 0 ATLAS Preliminary - L dt = 4.6 fb s = 7 TeV -5 0 MC Data p t [GeV] T MC Data m [GeV] tt - GeV dσ tt dp σ -2 0 Data -3 0 ALPGEN+HERWIG MC@NLO+HERWIG POWHEG+HERWIG dσ dy tt σ ATLAS Preliminary - L dt = 4.6 fb s = 7 TeV Data ALPGEN+HERWIG MC@NLO+HERWIG POWHEG+HERWIG -4 0 ATLAS Preliminary - L dt = 4.6 fb s = 7 TeV MC Data p tt [GeV] T MC Data y tt The ATLAS Collaboration ATLAS-CONF , lepton+jets, Ldt = 4.6[fb], S = 7 TeV

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 PI kinematics at approximate NLO (O(α 3 s)), and NNLO O(α 4 s). Exploratory work for future PDF fits using the exact NNLO theory when available and usable.

7 Available calculations NLO exact computations available since many years: Nason, Dawson, Ellis (988); Beenakker, Kuijif, Van Neerven, Smith (989); Meng, Schuler, Smith, Van Neerven (990); Beenakker, Van Neerven, Schuler, Smith (99); Mangano, Nason, Rodolfi (992). The NNLO O(α 4 s) full QCD calculation for the t t total cross section has been accomplished: Czakon, Fiedler, Mitov (203); Czakon, Mitov (202), (203); Baernreuther, Czakon, Mitov (202) Top++ Czakon, Mitov (20); Hathor Aliev, Lacker, Langenfeld, Moch, Uwer, Wiedermann (20) 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.

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

9 LHC 7 TeV, m t =73 GeV dσ/dp T (pp tt +X) (pb/gev) 0.5 Uncertainty due to scale variation, µ r =µ f approx. NNLO MSTW08NNLO MCFM MSTW08NLO p T (GeV).3 dσ/dp T /σ (pp tt +X), m t =73 GeV N. Kidonakis, Phys.Rev. D82 (200).3 dσ/dp T /σ (pp tt +X), m t =73 GeV N. Kidonakis, Phys.Rev. D82 (200) theory/data, dσ/dp T /σ.2. Uncertainty due to scale variation, µ r =µ f approx. NNLO MSTW08NNLO MCFM MSTW08NLO theory/data, dσ/dp T /σ.2. Uncertainty due to scale variation, µ r =µ f approx. NNLO MSTW08NNLO MCFM MSTW08NLO data CMS, s=7 TeV data ATLAS, s=7 TeV p t (GeV) T p t (GeV) T

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 (200) - (Mellin-space resummation). DiffTop stand alone (PI kinematics branch) is now available at: arxiv: [hep-ph] published on JHEP (204) The FastNLO-DiffTop code to produce grids will be available soon. (few grids are already available)

11 What s in the Box?

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 (987); S. Catani and L. Trentadue (989); H. Contopanagos, E. Laenen, and G. Sterman (997) The kinematics of inclusive heavy quark hadroproduction depend on which final state momenta are reconstructed. In threshold resummation, a kinematic choice manifests itself at next-to-leading-logarithmic level.

13 Single-particle inclusive (PI) kinematics In our calculation, heavy-quark hadroproduction near the threshold is approximated by considering the partonic subprocesses q(k )+ q(k 2 ) t(p )+X[ t](p 2), g(k )+g(k 2 ) t(p )+X[ t](p 2) p 2 = p 2 +k, () where is k any additional radiation, and s 4 = 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 [ ] { ln l (s 4 /mt) 2 ln l (s 4 /m = lim t) 2 θ(s 4 )+ ( ) } s 4 0 s 4 l + lnl+ δ(s 4 ), + where corrections are denoted as leading-logarithmic (LL) if l = 2i + at O(αs i+3 ) with i = 0,,..., as next-to-leading logarithm (NLL) if l = 2i, as next-to-next-to-leading logarithm (NNLL) if l = 2i, and so on. m 2 t

14 The hard scattering expansion The factorized differential cross section is written as S 2 d 2 σ(s,t,u ) dt du = i,j=q, q,g x dx x x 2 dx 2 x 2 f i/h (x,µ 2 F)f j/h2 (x 2,µ 2 F) ω ij (s,t,u,m 2 t,µ 2 F,α s(µ 2 R))+O(Λ 2 /m 2 t), ω ij (s 4,s,t,u ) = ω (0) ij + αs π ω() ij + ( ) α s 2ω (2) π ij + where ω (2) ij at parton level in PI kinematics is given by ij = s 2 ˆσ (2) { [ ] ij = F Born αs(µ 2 2 R) ij D (3) ln 3 (s 4/mt) 2 du dt π 2 ij s 4 PI [ ] [ ] [ ] ln 2 (s 4/mt) 2 +D () ln(s4/mt) 2 ij +D (0) ij s 4 s 4 s 4 ω (2) +D (2) ij } +R (2) ij δ(s 4).

15 Few more details... Hard and soft functions: H ij = H (0) ij +(α s /π)h () ij + and S ij = S (0) ij +(α s /π)s () ij +, H (2) ij and S (2) ij are set to zero. Soft anomalous dimension matrices: Γ S = (α s /π)γ () S +(α s/π) 2 Γ (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: γ i = (α s /π)γ () i +(α s /π) 2 γ (2) i + The Coulomb interactions, due to gluon exchange between the final-state heavy quarks, are included at -loop level. we work with the pole mass definition of the heavy quark.

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 () S (0) +H (0) S () } (2) are included. Beenakker, Kuijf, Van Neerven, Smith (989), Beenakker, Van Neerven, Meng, Schuler, Smith (99), Mangano, Nason, Ridolfi (992). Matching terms at NNLO are set to zero. Tr{H () S () },Tr{H (0) S (2) },Tr{H (2) S (0) } (3)

17 Systematic uncertainties due to missing terms The uncertainties due to missing contributions in D (0) ij and R 2 are part of the systematic uncertainty associated to approximate calculations of this kind which are based on threshold expansions. LHC 7 TeV, m t = 73 GeV, MSTW08 PDFs LHC 7 TeV, m t = 73 GeV, MSTW08 PDFs.4.2 C 0 (2) ± 5%.4.2 R 2 ± 2 R 2 R 2 ± R 2 dσ/dp T [pb/gev] dσ/dp T [pb/gev] t p T [GeV] t p T [GeV] Left: The coefficient C (2) 0 (scale ind. contribution in D (0) ij ) is varied within its 5% while R 2 is kept fixed. Right: here the coefficient R 2 is varied by adding and subtracting 2R 2 while C (2) 0 is kept fixed.

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 p T 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 (α s, m t, gluon ); easy to implement different heavy-quark mass definitions. Dowling, Moch (204) Very sensitive to the missing contribution in D (0) and R 2. 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.

19 Phenomenology: Exploratory studies at the LHC 7 TeV

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.: TeV LHC parton kinematics WJS200 x,2 = (M/7 TeV) exp(±y) Q = M M = 7 TeV 0 7 Q 2 (GeV 2 ) M = 0 GeV M = TeV M = 00 GeV y = HERA fixed target 6 Figure by J. Stirling x

21 approx. NNLO CT0NNLO, m t =73 GeV approx. NNLO MST08NNLO, m t =73 GeV LHC 7 TeV GeV < p t < 00 GeV T LHC 7 TeV GeV < p t < 00 GeV T 00 GeV < p t < 200 GeV T 00 GeV < p t < 200 GeV T GeV < p t < 300 GeV T GeV < p t < 300 GeV T cos(φ) GeV < p t < 400 GeV T cos(φ) GeV < p t < 400 GeV T x gluon x gluon Here we choose MSTW08 and CT0 as representative. ABM, HERA.5 and NNPDF2.3 show a similar behavior.

22 What is it good for? Top-quark pair production at LHC probes high-x gluon (x 0.): but there is a strong correlation between g(x), α s and the top-quark mass m t 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 m t and α s (very sensitive) extraction of m t will benefit from the interplay between these two measurements. (recent CMS paper PLB (204))

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 α s (M Z ) is given by the central value as given by each PDF group ± α s (M Z ) = 0.00; Scale unc. is obtained by variations m t /2 µ R = µ F 2m t ; Uncertanty associated to the top-quark mass is estimated by using m t = 73 GeV (Pole mass) ± m t = GeV.

24 dσ/dp T /σ (pp tt +X), m t =73 GeV.2 approx. NNLO CT0, total unc. data CMS, s=7 TeV.2 dσ/dp T /σ (pp tt +X), m t =73 GeV approx. NNLO CT0, total unc. data ATLAS, s=7 TeV.2 dσ/dy/σ (pp tt +X), m t =73 GeV approx. NNLO CT0, total unc. data CMS, s=7 TeV theory/data, dσ/dp T /σ. δm t = GeV PDF 68%CL theory/data, dσ/dp T /σ. δm t = GeV PDF 68%CL theory/data, dσ/dy/σ. δm t = GeV PDF 68%CL α S α S α S p t (GeV) T p t (GeV) T y t dσ/dp T (pp tt +X) (pb/gev) approx. NNLO CT0NNLO, m t =73 GeV total uncertainty δm t = GeV further uncertainty contributions: PDF 68%CL α S dσ/dy (pp tt +X) (/GeV) approx. NNLO CT0NNLO, m t =73 GeV total uncertainty PDF 68%CL α S δm t = GeV relative error p t (GeV) T relative error y t Uncertainties for the top p t T and yt distribution obtained by using DiffTop with CT0 NNLO PDFs. PDF and α s(m Z ) errors are evaluated at the 68% CL.

25 dσ/dp T (pp tt +X) (pb/gev) σ/σ CT approx. NNLO, m t =73 ± GeV total uncertainty CT0NNLO MSTW08NNLO ABMNNLO HERAPDF.5NNLO NNPDF2.3NNLO p t (GeV) T dσ/dy (pp tt +X) (pb) σ/σ CT approx. NNLO, m t =73 ± GeV (total uncertainty) CT0NNLO MSTW08NNLO ABMNNLO HERAPDF.5NNLO NNPDF2.3NNLO y t PDF uncertainties S = 7 TeV p t T and yt distributions: comparison between all PDF sets (bands are total unc.).

26 dσ/dp T /σ (pp tt +X), m t =73± GeV theory/data, dσ/dp T /σ.3.2. approx. NNLO, total unc. CT0NNLO MSTW08NNLO ABMNNLO HERAPDF.5NNLO NNPDF2.3NNLO theory/data, dσ/dy/σ.3.2. dσ/dy/σ (pp tt +X), m t =73± GeV approx. NNLO, total unc. CT0NNLO HERAPDF.5NNLO MSTW08NNLO NNPDF2.3NNLO ABMNNLO data CMS, s=7 TeV p t T (GeV) data CMS, s=7 TeV y t theory/data, dσ/dp T /σ.3.2. dσ/dp T /σ (pp tt +X), m t =73± GeV approx. NNLO, total unc. CT0NNLO MSTW08NNLO ABMNNLO HERAPDF.5NNLO NNPDF2.3NNLO data ATLAS, s=7 TeV p t T (GeV) PDF uncertainties S = 7 TeV p t T and yt distributions: ratio to the LHC measurements (bands are total unc.).

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. c i,n (µ R,µ F ) = c 0 i,n +log(µ R )c R i,n +log(µ F )c F i,n +... beyond the NLO one has double log contributions..+log 2 (µ F )c (2,F) i,n +log 2 (µ R )c (2,R) i,n +log(µ F )log(µ R )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.

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 p t T.

29 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 m c =.4 GeV and m b = 4.75 GeV as input, α s (m Z ) = 0.76; the Q 2 range of the HERA data restricted to Q 2 Q 2 min = 3.5 GeV2. At the scale Q 2 0 =.9 GeV2, the parton distributions are represented by xu v (x) = A uv x Buv ( x) Cuv (+D uv x +E uv x 2 ), xd v (x) = A dv x B dv ( x) C dv, xu(x) = A U x B U ( x) C U, xd(x) = A D x B D ( x) C D, xg(x) = A g x Bg ( x) Cg +A g x B g ( x) C g. (4) where xu(x) = xū(x) and xd(x) = x d(x)+x s(x).

30 obtained by using DIS and lepton charge asymmetry, is represented by a dotted line. Results of the fit: experimental uncertainty The analysis is performed by fitting 4 free parameters. A moderate impact on the large-x gluon exp. unc. is observed. g/g ± δg exp NNLO 4 parameter fit HERA I DIS + CMS W + LHC+CDF tt - HERA I DIS + CMS W HERA I DIS g/g ± δg exp NNLO 4 parameter fit HERA I DIS + CMS W + LHC+CDF tt - HERA I DIS + CMS W HERA I DIS Q 2 =00 GeV 2 DIS + W + tt - / DIS + W x Q 2 =m 2 H DIS + W + tt - / DIS + W 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 t production measurements (dark shaded band), shown at the scales of Q 2 = 00 GeV 2 (left) and Q 2 = mh 2 (right). The ratio of g(x) obtained in the fit including t t data to that

31 Results of the fit: experimental uncertainty Data set χ 2 / dof NC cross section HERA-I H-ZEUS combined e p 09 / 45 NC cross section HERA-I H-ZEUS combined e + p 46 / 379 CC cross section HERA-I H-ZEUS combined e p 9 / 34 CC cross section HERA-I H-ZEUS combined e + p 30 / 34 CMS W charge ele Asymmetry 8. / CMS W charge muon Asymmetry 8 / CDF inclusive ttbar cross section 0.64 / CMS Norm. differential t t vs p T 7 TeV / 7 CMS total t t 8TeV m t =73.3 GeV 2.0 / CMS total t t 7TeV m t =73.3 GeV.5 / ATLAS Norm. diff. t t vs p T 7 TeV 3.6 / 6 ATLAS total t t 7TeV m t =73.3 GeV 0. / ATLAS total t t 8TeV m t =73.3 GeV / Total χ 2 / dof 664 / 68

32 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 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 only 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 m t and α s must be included in the fit.

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 m t and α s 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.

34 BACKUP

35 Behavior around the threshold By setting µ R = µ F = 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/(4mt) 2 σ ij (s,m 2 t,µ 2 ) = α2 s(µ) m 2 t k ( ) (4πα s (µ)) k f (k,l) µ ij (η)ln l 2 mt 2 k=0 l=0 η = s/(4m 2 t) distance from the threshold. Recent analysis by Moch, Vogt, and Uwer PLB (202): known threshold corrections and improved approximate NNLO results are given over the full kinematic range. (5)

36 Behavior around the threshold: NLO f qq (,0) exact f qq (,0) approx f qq (,0) thresh f gq (,0) exact f gq (,0) approx f gq (,0) thresh η η f (,0) gg exact 0.2 f (,0) gg approx 0. f (,0) gg thresh η From Moch, Vogt, Uwer PLB (202)

37 Beenakker, Kujif, Smith, Van Neerven, 989, Dawson, Ellis, Nason, Quality check: NLO Exact Calculation vs DiffTop approx NLO dσ/dp T [pb/gev] mt = 73 GeV; Q=mt; CT0 NLO MCFM NLO approx NLO, Q=m t t P T [GeV]

38 Behavior around the threshold: NNLO f (2,0) qq approx f (2,0) qq thresh A,B f (2,0) gq approx f (2,0) gq thresh η η f (2,0) gg approx A,B 0.3 f (2,0) gg thresh η A,B From Moch, Vogt, Uwer PLB (202)

39 Exact calculation for the gg channel at NNLO Approx NNLO, Leading Born Approx NNLO, Exact Born Exact NNLO Φ gg σ gg (2) LHC 8 TeV 0 m top = 73.3 GeV MSTW2008NNLO(68cl) β β = 4m 2 /s From Czakon, Fiedler, Mitov PRL (203)

40 dσ/dp T /σ (pp tt +X), m t =73 GeV.2 approx. NNLO MSTW08, total unc. data CMS, s=7 TeV.2 dσ/dp T /σ (pp tt +X), m t =73 GeV approx. NNLO MSTW08, total unc. data ATLAS, s=7 TeV.2 dσ/dy/σ (pp tt +X), m t =73 GeV approx. NNLO MSTW08, total unc. data CMS, s=7 TeV theory/data, dσ/dp T /σ. δm t = GeV PDF 68%CL theory/data, dσ/dp T /σ. δm t = GeV PDF 68%CL theory/data, dσ/dy/σ. δm t = GeV PDF 68%CL α S α S α S p t (GeV) T p t (GeV) T y t dσ/dp T (pp tt +X) (pb/gev) approx. NNLO MST08NNLO, m t =73 GeV total uncertainty δm t = GeV further uncertainty contributions: PDF 68%CL α S dσ/dy (pp tt +X) (/GeV) approx. NNLO MST08NNLO, m t =73 GeV total uncertainty PDF 68%CL α S δm t = GeV relative error p t (GeV) T relative error y t As in the previous slide but with MSTW08 NNLO PDFs. PDF and α s(m Z ) errors are evaluated at the 68% CL.

41 dσ/dp T /σ (pp tt +X), m t =73 GeV.2 approx. NNLO ABM, total unc. data CMS, s=7 TeV.2 dσ/dp T /σ (pp tt +X), m t =73 GeV approx. NNLO ABM, total unc. data ATLAS, s=7 TeV.2 dσ/dy/σ (pp tt +X), m t =73 GeV approx. NNLO ABM, total unc. data CMS, s=7 TeV theory/data, dσ/dp T /σ. δm t = GeV theory/data, dσ/dp T /σ. PDF α S 68%CL theory/data, dσ/dy/σ. δm t = GeV PDF α S 68%CL δm t = GeV PDF α S 68%CL p t T (GeV) p t T (GeV) y t dσ/dp T (pp tt +X) (pb/gev) approx. NNLO ABMNNLO, m t =73 GeV total uncertainty δm t = GeV further uncertainty contributions: PDF α S 68%CL dσ/dy (pp tt +X) (/GeV) approx. NNLO ABMNNLO, m t =73 GeV total uncertainty PDF α S 68%CL δm t = GeV relative error p t (GeV) T relative error y t As in the previous slide but with ABM NNLO PDFs. Here the uncertainty on α s(m Z ) is already part of the total PDF uncertainty.

42 dσ/dp T /σ (pp tt +X), m t =73 GeV.2 approx. NNLO HERAPDF.5, total unc. data CMS, s=7 TeV.2 dσ/dp T /σ (pp tt +X), m t =73 GeV approx. NNLO HERAPDF.5, total unc. data ATLAS, s=7 TeV.2 dσ/dy/σ (pp tt +X), m t =73 GeV approx. NNLO HERAPDF.5, total unc. data CMS, s=7 TeV theory/data, dσ/dp T /σ. δm t = GeV PDF 68%CL + var. theory/data, dσ/dp T /σ. δm t = GeV PDF 68%CL + var. theory/data, dσ/dy/σ. δm t = GeV PDF 68%CL + var. α S α S α S p t (GeV) T p t (GeV) T y t dσ/dp T (pp tt +X) (pb/gev) approx. NNLO HERAPDF.5NNLO, m t =73 GeV total uncertainty δm t = GeV further uncertainty contributions: PDF 68%CL + var. α S PDF 68%CL+var. 80 δm t = GeV dσ/dy (pp tt +X) (/GeV) 00 approx. NNLO HERAPDF.5NNLO, mt=73 GeV total uncertainty α S relative error p t (GeV) T relative error y t As in the previous slide but with HERA.5 NNLO PDFs.

43 dσ/dp T /σ (pp tt +X), m t =73 GeV.2 approx. NNLO NNPDF2.3, total unc. data CMS, s=7 TeV.2 dσ/dp T /σ (pp tt +X), m t =73 GeV approx. NNLO NNPDF2.3, total unc. data ATLAS, s=7 TeV.2 dσ/dy/σ (pp tt +X), m t =73 GeV approx. NNLO NNPDF2.3, total unc. data CMS, s=7 TeV theory/data, dσ/dp T /σ. δm t = GeV PDF 68%CL theory/data, dσ/dp T /σ. δm t = GeV PDF 68%CL theory/data, dσ/dy/σ. δm t = GeV PDF 68%CL α S α S α S p t (GeV) T p t (GeV) T y t dσ/dp T (pp tt +X) (pb/gev) approx. NNLO NNPDF2.3 NNLO, m t =73 GeV total uncertainty δm t = GeV further uncertainty contributions: α S PDF 68%CL 80 δm t = GeV dσ/dy (pp tt +X) (/GeV) 00 approx. NNLO NNPDF2.3 NNLO, mt=73 GeV total uncertainty α S relative error p t (GeV) T relative error y t As in the previous slide but with NNPDF2.3 NNLO PDFs.