A new approach to ttbar @ NNLO e Ren Angeles-Mart nez Sebastian - PowerPoint PPT Presentation

A new approach to ttbar @ NNLO e ´ Ren´ Angeles-Mart´ ınez Sebastian Sapeta Michał Czakon IFJ PAN, Krak´ ow Matter to the deepest Rene Angeles-Martinez (IFJ PAN, Krak´ ow ) A new approach to ttbar @ NNLO September 2017 1 / 31

t ¯ t production at the LHC L [ fb − 1 ] LHC σ ( tt ) [ pb ] N event 8 , 6 × 10 5 7 TeV 172.676 5 4 , 8 × 10 6 8 TeV 246.652 19.7 1 , 8 × 10 6 13 TeV 807.296 2.3 Top Pair Decay Channels Top Pair Branching Fractions "alljets" 46% cs electron+jets muon+jets tau+jets all-hadronic τ +jets 15% ud τ – tau+jets e τ µτ s ττ τ + τ 1% n o µ – t τ + µ 2% muon+jets e µ p µµ µτ e τ + e 2% l i d e – electron+jets µ + µ 1% ee e µ e τ µ +jets 15% µ + e 2% e + e 1% W decay e + µ + τ + ud cs e +jets 15% "dileptons" " l e p t o n + j e t s " This give us a strong motivation to test, develop and improve pQCD for this process. Rene Angeles-Martinez (IFJ PAN, Krak´ ow ) A new approach to ttbar @ NNLO September 2017 2 / 31

Status of pQCD for t ¯ t production Only one complete NNLO calculation of inclusive and differential cross section, improved by NNLL resummation, Czakon, Heymes, Mitov (2015) Czakon, Heymes, Mitov (2015) Czakon, Heymes, Mitov (2015) Czakon, Heymes, Mitov (2015) 1.25 1.25 1.25 1.25 NNLO cross section [pb] ≤ -1 Tevatron combined 1.96 TeV (L 8.8 fb ) NLO ATLAS+CMS Preliminary May 2017 -1 CMS dilepton,l+jets* 5.02 TeV (L = 27.4 pb ) LO µ -1 ATLAS e 7 TeV (L = 4.6 fb ) LHC LHC top top WG WG 1 1 1 1 µ -1 CMS e 7 TeV (L = 5 fb ) µ -1 3 ATLAS e 8 TeV (L = 20.2 fb ) - [pb/GeV] - [pb/GeV] - [pb/GeV] - [pb/GeV] 10 µ -1 CMS e 8 TeV (L = 19.7 fb ) µ -1 LHC combined e 8 TeV (L = 5.3-20.3 fb ) 0.75 0.75 0.75 0.75 µ -1 ATLAS e 13 TeV (L = 3.2 fb ) µ CMS e 13 TeV (L = 2.2 fb -1 ) µ µ -1 ATLAS ee/ * 13 TeV (L = 85 pb ) d σ /dm tt d σ /dm tt d σ /dm tt d σ /dm tt -1 -+X (8 TeV) -+X (8 TeV) -+X (8 TeV) -+X (8 TeV) ATLAS l+jets* 13 TeV (L = 85 pb ) PP PP PP PP → tt → tt → tt → tt -1 0.5 0.5 0.5 0.5 CMS l+jets 13 TeV (L = 2.3 fb ) m t =173.3 GeV m t =173.3 GeV m t =173.3 GeV m t =173.3 GeV -1 CMS all-jets* 13 TeV (L = 2.53 fb ) 900 t MSTW2008 MSTW2008 MSTW2008 MSTW2008 Inclusive t * Preliminary µ F,R /m t ∈ {0.5,1,2} µ F,R /m t ∈ {0.5,1,2} µ F,R /m t ∈ {0.5,1,2} µ F,R /m t ∈ {0.5,1,2} 2 10 0.25 0.25 0.25 0.25 800 0 0 0 0 700 400 400 400 400 500 500 500 500 600 600 600 600 700 700 700 700 800 800 800 800 900 900 900 900 1000 1000 1000 1000 NNLO/NLO 1.2 NNLO+NNLL (pp) 1.1 NNLO+NNLL (p p ) 13 1 [TeV] s Czakon, Fiedler, Mitov, PRL 110 (2013) 252004 10 0.9 α ± NNPDF3.0, m = 172.5 GeV, (M ) = 0.118 0.001 top s Z 400 500 600 700 800 900 1000 1.6 2 4 6 8 10 12 14 NLO/LO 1.4 1.2 [TeV] 1 s 0.8 400 500 600 700 800 900 1000 m tt - [GeV] Overall good agreement. Scale uncertainty varies with kinematics: within 5 % for regions of interest for run I and II, JHEP 04 (17) 071. Other theoretical uncertainties for the total cross-section are: PDF ∼ 2 − 3 % , α s ∼ 1 , 5 % , m ∼ 3 % for the total XS. Rene Angeles-Martinez (IFJ PAN, Krak´ ow ) A new approach to ttbar @ NNLO September 2017 3 / 31

Status of pQCD for t ¯ t production There are other results for top production at O ( α 2 s ) and beyond but they are partial or approximate: Abelof et. al. 2015. Leading N c total cross-section NNLO. Catani , et. al, 2015. Partial results for NNLO +resummation. Small- q T resummation + qT subtraction. Missing piece: soft NNLO evolution. Broggio et. al. 2014, Ahrens et.al, 2010 (SCET). Threshold resummation + RG. Kidonakis 2015. Approximate NNNLO, soft gluon corrections to single top production. See also 2012, NNLL threshold resummation. Making comparisons is highly non-trivial. In this talk: New approach to t ¯ t production @ NNLO in the small q ⊥ (= p t + p ¯ t ) ⊥ region. Our approach is numerical and highly automated (graph independent) and has the potential to be extend to other processes (e.g. gg → H @ NNNLO). Rene Angeles-Martinez (IFJ PAN, Krak´ ow ) A new approach to ttbar @ NNLO September 2017 4 / 31

Why to look at the small q T region? Top pair production with q T = 0 only occurs for Born kinematics and this implies that (Catani & Grazzini 2007, 2015) � � � � � � d σ t ¯ = d σ t ¯ t t + jet � � NNLO NLO � � q ⊥ = q 0 ⊥ > 0 q ⊥ = q 0 ⊥ Hence, cross-sections (distributions) integrated over q ⊥ can be written as � q 0 ⊥ � σ t ¯ d q ⊥ d σ t ¯ d q ⊥ d σ t ¯ t + jet t t NNLO = NNLO + NLO q 0 ⊥ The NLO results exists (e.g. Catani et. al. 2002, Czakon 2010) for tt + jet. The first part is missing and we aim for it! Rene Angeles-Martinez (IFJ PAN, Krak´ ow ) A new approach to ttbar @ NNLO September 2017 5 / 31

Soft collinear Effective Theory for t ¯ t at small q ⊥ Y } q = p t + p ¯ p t t θ ( t ¯ t at rest ) p ¯ t Λ QCD ≪ q 2 ⊥ ≪ m 2 , s = ( p 1 + p 2 ) 2 , q 2 , P 1 P 2 ( p 1 − p t ) 2 − m 2 , p 1 = ξ 1 P 1 p 2 = ξ 2 P 2 t ) 2 − m 2 ( p 1 − p ¯ X Leading radiation ( X ) factorises as ( Xing Zhu, et. al PRD 88 (13) 074004) � � � Λ 2 Λ 2 d σ QCD QCD ⊥ d θ d Y = B 1 ⊗ B 2 ⊗ H ⊗ S + O , d q 2 d q 2 q 2 q 2 ⊥ X i.e. covers wide range of differential observables. B i and H known at NNLO ( Gehrmann et. al. (‘14) and Czakon et. al. (‘13) ). We aim for S . Advatages of this approach: recycles the most and it is generable! Rene Angeles-Martinez (IFJ PAN, Krak´ ow ) A new approach to ttbar @ NNLO September 2017 6 / 31

SCET factorisation � ⊥ /q 2 are q 2 In the small q ⊥ limit, four regions are not power suppressed by λ = ( k + , k − , k ⊥ ) Hard (1 , 1 , 1) Collinear (1 , λ 2 , λ ) Anti-collinear ( λ, 1 , λ ) Soft ( λ, λ, λ 1 ⊥ ) After azimuthal averaging the cross section factorises as � � d 4 σ ⊥ d y d q 2 d cos θ ∼ d ξ 1 d ξ 2 d x ⊥ ( ... ) × d q 2 i = q , ¯ q , g � ⊥ ) · Tr � v t ) � B LT ( ξ 1 , x 2 ⊥ ) B LT ( ξ 2 , x 2 H LT i ( q 2 , m,� d Ω d − 3 + O ( α 3 v t ) x T S i ¯ i ( � x ⊥ ,� s ) i ¯ i ¯ i v t is the top momenta in the t ¯ where � t rest frame, i.e. p t = ( p 0 t ,� v t ) ¯ t X Rene Angeles-Martinez (IFJ PAN, Krak´ ow ) A new approach to ttbar @ NNLO September 2017 7 / 31

SCET factorisation � ⊥ /q 2 are q 2 In the small q ⊥ limit, four regions are not power suppressed by λ = ( k + , k − , k ⊥ ) Hard (1 , 1 , 1) Collinear (1 , λ 2 , λ ) Anti-collinear ( λ, 1 , λ ) Soft ( λ, λ, λ 1 ⊥ ) After azimuthal averaging the cross section factorises as � � d 4 σ ⊥ d y d q 2 d cos θ ∼ d ξ 1 d ξ 2 d x ⊥ ( ... ) × d q 2 i = q , ¯ q , g � ⊥ ) · Tr � v t ) � B LT ( ξ 1 , x 2 ⊥ ) B LT ( ξ 2 , x 2 H LT i ( q 2 , m,� d Ω d − 3 + O ( α 3 v t ) x T S i ¯ i ( � x ⊥ ,� s ) i ¯ i ¯ i v t is the top momenta in the t ¯ where � t rest frame, i.e. p t = ( p 0 t ,� v t ) ¯ t X Rene Angeles-Martinez (IFJ PAN, Krak´ ow ) A new approach to ttbar @ NNLO September 2017 7 / 31

Beam functions Generalisation of PDF , characteristic of measurements involving two scales µ Λ QCD ≪ µ B ≪ µ H , where µ B constrains the energy in forward direction PDF � 1 � �� � � d ξ ⊥ , x B i ( x ′ ξ I ij ( x ′ ⊥ , x, µ B ) = ξ , µ B ) f j ( ξ, µ B ) x j µ Λ µ B µ H changing x changing t JHEP 1009 (2010) 005 1 I ij accounts for nearly collinear radiation with wide-spread x ⊥ ≤ f ( q ⊥ , q ∗ ) � µ d d µ B i ( x ′ d x ′ ⊥ γ i B ( x ⊥ − x ′ ⊥ , µ ) B i ( x ′ ⊥ , x, µ ) = ⊥ , x, µ ) Rene Angeles-Martinez (IFJ PAN, Krak´ ow ) A new approach to ttbar @ NNLO September 2017 8 / 31

Hard function Roughly speaking, the hard function is the finite loop corrections to the born process M . More precisely, the matching condition is (Ahrens et. al. 1003.5827) � 12 H ( q 2 , m,� Z − 1 ( ǫ, µ ) |M ren � �M ren | Z − 1 † ( ǫ, µ ) v 3 , µ ) = 8(4 π ) 2 d R i = q, ¯ q,g where Z − 1 is an operator that removes the poles ( d = 4 − 2 ǫ ) the infrared part of on-shell scatterings. It has a perturbative expansion and for m = 0 it can be easily related to the Catani operators that factorises infrared poles Z (1) = 2 I (1) finite , Z (2) = I (2) − 2 I (1) Z (1) + finite . Rene Angeles-Martinez (IFJ PAN, Krak´ ow ) A new approach to ttbar @ NNLO September 2017 9 / 31

Soft function in momentum space Soft radiation with at fixed q T for the on-shell (crossing the red cut): S ( � q ⊥ ,� v t , µ ) =       1 , n + t, (1 , β ˆ v t )  t 1    � � �   � × × � �   δ + ( k i )   � δ d − 2 q ⊥ − � k i ⊥ ... ...   ( k + ) α   X s × × i i   { k i }     ¯ ¯ 2  n − t, (1 , − β ˆ v t ) t  2 , ¯ X s Feynman rules for the blob are exact, and this is connect to the hard subprocess in the Eikonal approximation: µ, a i p µ g s T a × × × × × i ... ... p i · q ± ( i 0 , 0) p i p i ± q Rene Angeles-Martinez (IFJ PAN, Krak´ ow ) A new approach to ttbar @ NNLO September 2017 10 / 31