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
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:
Physics Beyond the SM: is there any? from F. Maltoni and R. Frederix, JHEP 0901 (2009) 047
-1 -1 CMS, 5.0 fb at s = 7 TeV CMS, 5.0 fb at s = 7 TeV × -3 10 10 0.7 -1 σ t dy µ µ GeV e/ + Jets Combined Data d e/ + Jets Combined Data 9 MadGraph 1 σ MadGraph 0.6 8 MC@NLO MC@NLO T σ t dp POWHEG POWHEG d 0.5 7 1 Approx. NNLO Approx. NNLO σ 6 (arXiv:1009.4935) (arXiv:1105.5167) 0.4 5 0.3 4 3 0.2 2 0.1 1 0 0 0 50 100 150 200 250 300 350 400 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 t p GeV y t T -1 -1 CMS, 5.0 fb at s = 7 TeV CMS, 5.0 fb at s = 7 TeV × -3 10 25 -1 -1 µ µ GeV e/ + Jets Combined Data GeV e/ + Jets Combined Data MadGraph MadGraph -2 10 MC@NLO 20 MC@NLO t t T σ t dm σ t POWHEG dp POWHEG d d 1 1 σ σ -3 10 15 10 -4 10 -5 10 5 -6 10 0 400 600 800 1000 1200 1400 1600 0 50 100 150 200 250 300 p t t GeV m t t GeV T √ � Ldt = 5 . 0[fb] − 1 , The CMS Collaboration EPJC 2013, S = 7 TeV, √ Ldt ≈ 12[fb] − 1 , � TOP-12-028 → S = 8 TeV
-1 -1 GeV GeV Data Data ALPGEN+HERWIG -3 ALPGEN+HERWIG T t 10 σ t dp σ dm t d d 1 MC@NLO+HERWIG MC@NLO+HERWIG σ -3 1 σ 10 POWHEG+HERWIG POWHEG+HERWIG ATLAS Preliminary ATLAS Preliminary ∫ 10 -4 ∫ -1 -1 L dt = 4.6 fb L dt = 4.6 fb 10 -4 s = 7 TeV s = 7 TeV -5 10 1.5 0 100 200 300 400 500 600 700 800 1.5 0 500 1000 1500 2000 2500 Data Data MC MC 1 1 0.5 0.5 0 100 200 300 400 500 600 700 800 0 500 1000 1500 2000 2500 p t [GeV] m [GeV] t t T t -1 σ t dy GeV d ATLAS Preliminary -2 Data Data 10 1 σ ∫ -1 L dt = 4.6 fb ALPGEN+HERWIG ALPGEN+HERWIG σ t t T dp d s = 7 TeV 1 σ MC@NLO+HERWIG 1 MC@NLO+HERWIG -3 10 POWHEG+HERWIG POWHEG+HERWIG ATLAS Preliminary ∫ -1 L dt = 4.6 fb 10 -4 s = 7 TeV -1 10 -5 10 1.5 0 100 200 300 400 500 600 700 800 900 1000 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 1.2 Data Data MC MC 1 1 0.8 0.5 0 100 200 300 400 500 600 700 800 900 1000 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 y p t t [GeV] t t T The ATLAS Collaboration ATLAS-CONF-2013-099, lepton+jets, √ 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 ¯ t production cross sections by using approximate calculations. ◮ DiffTop calculates t ¯ t differential cross sections in 1PI 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.
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 ( α 4 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.
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
LHC 7 TeV, m t =173 GeV Uncertainty due to scale variation, µ r = µ f approx. NNLO × MSTW08NNLO MCFM × MSTW08NLO – +X) (pb/GeV) 1 d σ /dp T (pp → tt 0.5 50 100 150 200 250 300 350 400 p T (GeV) – +X) , m t =173 GeV – +X) , m t =173 GeV d σ /dp T / σ (pp → tt d σ /dp T / σ (pp → tt 1.3 1.3 N. Kidonakis, Phys.Rev. D82 (2010) N. Kidonakis, Phys.Rev. D82 (2010) Uncertainty due to scale variation, µ r = µ f Uncertainty due to scale variation, µ r = µ f 1.2 approx. NNLO × MSTW08NNLO 1.2 approx. NNLO × MSTW08NNLO theory/data, d σ /dp T / σ MCFM × MSTW08NLO theory/data, d σ /dp T / σ MCFM × MSTW08NLO 1.1 1.1 1 1 0.9 0.9 data CMS, √ s=7 TeV data ATLAS, √ s=7 TeV 0.8 0.8 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 p t p t T (GeV) T (GeV)
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)
What’s in the Box ?
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 on which final state momenta are reconstructed. In threshold resummation, a kinematic choice manifests itself at next-to-leading-logarithmic level.
Single-particle inclusive (1PI) kinematics In our calculation, heavy-quark hadroproduction near the threshold is approximated by considering the partonic subprocesses q ( k 2 ) → t ( p 1 ) + X [¯ t ]( p ′ q ( k 1 ) + ¯ 2 ) , g ( k 1 ) + g ( k 2 ) → t ( p 1 ) + X [¯ t ]( p ′ p ′ 2 ) 2 = ¯ p 2 + k , (1) 2 − m 2 → 0 where is k any additional radiation, and s 4 = p ′ momentum at the threshold. This kinematic is used to determine the p t T and rapidity y t distribution of the final-state top-quark. Hard scattering functions are expanded in terms of � ∆ ln l ( s 4 / m 2 ln l ( s 4 / m 2 � � � � � t ) t ) 1 l + 1 ln l +1 = lim θ ( s 4 − ∆) + δ ( s 4 ) , m 2 s 4 s 4 ∆ → 0 t + where corrections are denoted as leading-logarithmic (LL) if l = 2 i + 1 at O ( α i +3 ) with i = 0 , 1 , . . . , as next-to-leading logarithm (NLL) if l = 2 i , s as next-to-next-to-leading logarithm (NNLL) if l = 2 i − 1, and so on.
The hard scattering expansion The factorized differential cross section is written as � 1 � 1 S 2 d 2 σ ( S , T 1 , U 1 ) dx 1 dx 2 � x 2 f i / H 1 ( x 1 , µ 2 F ) f j / H 2 ( x 2 , µ 2 = F ) dT 1 dU 1 x 1 x − x − i , j = q , ¯ q , g 1 2 × ω ij ( s , t 1 , u 1 , m 2 t , µ 2 F , α s ( µ 2 R )) + O (Λ 2 / m 2 t ) , � 2 ω (2) � α s ω ij ( s 4 , s , t 1 , u 1 ) = ω (0) π ω (1) + α s + + · · · ij ij ij π where ω (2) at parton level in 1PI kinematics is given by ij σ (2) � ˆ α 2 s ( µ 2 � ln 3 ( s 4 / m 2 � � R ) t ) � ω (2) ij D (3) = s 2 = F Born � ij ij π 2 ij du 1 dt 1 � s 4 + � 1 PI � 1 � ln 2 ( s 4 / m 2 � ln ( s 4 / m 2 t ) � t ) � � � + D (2) + D (1) + D (0) + R (2) ij δ ( s 4 ) . ij ij ij s 4 s 4 s 4 + + +
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