Status of predictions for the total t ¯ t cross section and measurement of the pole mass Christian Schwinn — Univ. Freiburg — 11.08.2014 (See also “High precision fundamental constants at the TeV scale”, arXiv:1405.4781 [hep-ph] ) C. Schwinn Theory status of t ¯ t cross section and pole mass. MIAPP ”Top quark physics day”
Introduction 1 Total t ¯ t cross section measurements (in pb) σ Tevatron = 7 . 60 +0 . 41 − 0 . 41 (D0+CDF) t ¯ t 162 +7 (CMS) σ LHC @7 TeV − 7 = t ¯ t 177 +11 (ATLAS) − 10 237 +13 (CMS) σ LHC @8 TeV − 13 = t ¯ t 242 +10 (ATLAS) − 10 Top mass from kinematic measurements 173 . 20 ± 0 . 87GeV (Tevatron comb. 8 . 7 fb − 1 ) m t = 173 . 29 ± 0 . 95GeV (LHC comb. 4 . 9 fb − 1 ) Relation to theoretical mass definition? Difference ∼ 1GeV to well-defined mass definition expected C. Schwinn Theory status of t ¯ t cross section and pole mass. MIAPP ”Top quark physics day”
Mass measurement from cross section 2 Theory prediction for σ t ¯ t in QCD : function of α s , m t , PDFs Proposal: determine m t in well-defined scheme (pole, MS,...) from σ t ¯ t measurement (Langenfeld/Moch/Uwer 09) Experimental measurement depends on m MC t Latest experimental results: • CMS: m pole = 176 . 7 +3 . 8 − 3 . 4 GeV t (using NNPDF2.3) • ATLAS: m pole = 172 . 9 +2 . 5 − 2 . 6 GeV t (using PDF4LHC) C. Schwinn Theory status of t ¯ t cross section and pole mass. MIAPP ”Top quark physics day”
Total top-pair production cross-section 3 Full NNLO calculation (B¨ arnreuther/Czakon/Fiedler/Mitov 12–13) NNLL resummation Soft threshold logarithms α s log β (Czakon/Mitov/Sterman 09) Threshold logs and Coulomb corrections α s /β (Beneke/Falgari/CS 09) Resummation for distributions (Kidonakis, Ahrens et al. ⇒ Adrian’s talk) Programs including exact NNLO result • top++ v2.0 : NNLO+NNLL (soft) (Czakon/Mitov) • HATHOR v1.5 : NNLO (Aliev et al.) • Topixs v2.0 NNLO+NNLL (soft+Coulomb) (Beneke et al.) EW corrections ∼ 2% (Bernreuther/F¨ ucker/Si; K¨ uhn/Scharf/Uwer, 05/06) QED (e.g. qγ induced) ∼ 1% (Hollik/Kollar 07) C. Schwinn Theory status of t ¯ t cross section and pole mass. MIAPP ”Top quark physics day”
Total top-pair production cross-section 4 Comparison of different approximations (excluding PDF + α s uncertainties) • ± 5% scale uncertainty at NNLO; ± 3 – 4% at NNLL Σ tt � pb � Topixs � Beneke et al. � SCET 1PI � PIM � Ahrens et al. � 280 mt � 173.3, MSTW2008 1PI � Kidonakis � HATHOR 1.3 � Aliev et al. � top �� � Czakon � Mitov � 260 240 220 200 NNLL NNLL NNLO app N3LO app ATLAS � NLO NNLO 180 � NNLO app � NNLO CMS C. Schwinn Theory status of t ¯ t cross section and pole mass. MIAPP ”Top quark physics day”
Total top-pair production cross-section 4 Comparison of different approximations (excluding PDF + α s uncertainties) • ± 5% scale uncertainty at NNLO; ± 3 – 4% at NNLL PDF+ α s uncertainties now comparable to scale uncertainty Σ NNLO � pb � LHC � 8 TeV � MSTW08 CT10 NNPDF2.3 ABM12 ATLAS � CMS C. Schwinn Theory status of t ¯ t cross section and pole mass. MIAPP ”Top quark physics day”
NNLL vs NNLO 5 Reduction of scale uncertainty from threshold resummation 245 . 89 +6 . 24(2 . 5%) NNLL(top + +) : − 8 . 41(3 . 4%) pb 239 . 18 + 9 . 29(3 . 9%) NNLO : − 14 . 85(6 . 2%) pb ⇒ 241 . 04 + 8 . 65(3 . 6%) NNLL(topixs) : − 11 . 09(4 . 3%) pb top++ : Mellin space resummation (Sterman 87; Catani/Trentadue 89) • Includes 2-loop constant term H 2 in threshold expansion | H 2 =0 = 242 . 74 pb σ NLLL t ¯ t C. Schwinn Theory status of t ¯ t cross section and pole mass. MIAPP ”Top quark physics day”
NNLL vs NNLO 5 Reduction of scale uncertainty from threshold resummation 245 . 89 +6 . 24(2 . 5%) NNLL(top + +) : − 8 . 41(3 . 4%) pb 239 . 18 + 9 . 29(3 . 9%) NNLO : − 14 . 85(6 . 2%) pb ⇒ 241 . 04 + 8 . 65(3 . 6%) NNLL(topixs) : − 11 . 09(4 . 3%) pb top++ : Mellin space resummation (Sterman 87; Catani/Trentadue 89) • Includes 2-loop constant term H 2 in threshold expansion | H 2 =0 = 242 . 74 pb σ NLLL t ¯ t topixs: combined soft/Coulomb resummation • RGE for momentum-space resummation (Becher/Neubert 06) • dependence on scales µ f , µ h ∼ 2 M : ∆ scale σ NNLL = +5 . 64 − 6 . 56 pb t ¯ t • resummation uncertainty: choice of µ s ∼ Mβ 2 , kinematic ambiguities, higher-order terms: ∆ res σ NNLL = +6 . 56 − 4 . 01 pb t ¯ t C. Schwinn Theory status of t ¯ t cross section and pole mass. MIAPP ”Top quark physics day”
NNLL vs NNLO 6 Heavy Quarks as test case for resummation methods K NNLL 1.30 NNLL � Topixs � NNLL fix � Topixs � 1.25 NNLL � top �� � 1.20 NNLL H2 � 0 � top �� � ( K NNLL = σ NNLL /σ NLO , 1.15 LHC √ s = 8 TeV) 1.10 1.05 m Q � GeV � 1.00 500 1000 1500 2000 NNLL: momentum-space, running µ s = 2 m Q β 2 ( Topixs default) NNLL fix : momentum-space, fixed µ s ( Topixs ) NNLL (top++): Mellin-space (Cacciari et al. 11; Czakon/Mitov 11-13) NNLL H 2=0 (top++): Mellin-space, two-loop constant term set to zero C. Schwinn Theory status of t ¯ t cross section and pole mass. MIAPP ”Top quark physics day”
NNLL vs NNLO 6 Heavy Quarks as test case for resummation methods K NNLL 1.30 NNLL � Topixs � NNLL fix � Topixs � 1.25 NNLL � top �� � 1.20 NNLL H2 � 0 � top �� � ( K NNLL = σ NNLL /σ NLO , 1.15 LHC √ s = 8 TeV) 1.10 1.05 m Q � GeV � 1.00 500 1000 1500 2000 ⇒ resummation methods agree well for larger masses • differences at m t : estimate of resummation ambiguities and higher-order effects s log β 2 terms (NNLL’) • main difference: treatment of H 2 ⇒ α 3 C. Schwinn Theory status of t ¯ t cross section and pole mass. MIAPP ”Top quark physics day”
N3LO approx ? 7 Expand NNLL to O ( α 3 s ) , e.g. (Beneke/Falgari/Klein/CS 13) qq, NNLL =12945 . 4 log 6 β − 37369 . 1 log 5 β + 27721 . 4 log 4 β + 41839 . 4 log 3 β ∆ σ (3) + 1 � − 6278 . 5 log β + 3862 . 5 log 2 β + 2804 . 7 log 3 β − 2994 . 5 log 4 β � β + 153 . 9 log 2 β + 122 . 9 log β − 145 + � log β 1 , 2 , 1 /β, C (3) � + scale dep. β 2 � �� � not known exactly N 3 LO A : keep all terms, including µ s , µ h -dependence and constants N 3 LO B : only keep terms known exactly d Σ qq d �Σ gg � pb � � pb � d Β d Β 2.5 1.5 � NNLOapp � NNLOapp N3LOA � kh � 2,ks � 1 � N3LOA � kh � 2,ks � 1 � 2.0 N3LOB N3LOB 1.0 1.5 1.0 0.5 0.5 Β 0.2 0.4 0.6 0.8 1.0 Β 0.2 0.4 0.6 0.8 1.0 � 0.5 � 0.5 C. Schwinn Theory status of t ¯ t cross section and pole mass. MIAPP ”Top quark physics day”
N3LO approx ? 7 Expand NNLL to O ( α 3 s ) , e.g. (Beneke/Falgari/Klein/CS 13) qq, NNLL =12945 . 4 log 6 β − 37369 . 1 log 5 β + 27721 . 4 log 4 β + 41839 . 4 log 3 β ∆ σ (3) + 1 � − 6278 . 5 log β + 3862 . 5 log 2 β + 2804 . 7 log 3 β − 2994 . 5 log 4 β � β + 153 . 9 log 2 β + 122 . 9 log β − 145 + � log β 1 , 2 , 1 /β, C (3) � + scale dep. β 2 � �� � not known exactly Approx. N3LO from one-particle inclusive kinematics (Kidonakis 14) 244 . 87 +3 . 5(1 . 5%) N3LO A : − 6 . 7(2 . 8%) pb 239 . 18 + 9 . 29(3 . 9%) 245 . 90 +6 . 7(2 . 7%) NNLO : − 14 . 85(6 . 2%) pb ⇒ N3LO B : − 5 . 0(2 . 0%) pb 248 +7(2 . 8%) N3LO 1PI : − 8(3 . 2%) pb But: strong dependence of incompletely known terms on soft scale: ∆ µ s σ N3LO A = +3 . 8 − 12 . 1 pb t ¯ t ⇒ need input beyond NNLL, use only for uncertainty estimate. C. Schwinn Theory status of t ¯ t cross section and pole mass. MIAPP ”Top quark physics day”
Mass measurement from cross section 8 Follow method from (ATLAS-CONF-2011-54) Fit m t -dependence of theoretical cross-section: � 172 . 5 c 0 + c 1 ( m t − 172 . 5) + c 2 ( m t − 172 . 5) 2 + c 3 ( m t − 172 . 5) 3 � pb , � 4 � σ th t ( m t ) = t ¯ m t c 0 = 166 . 5 , c 1 = − 1 . 15 , c 2 = 5 . 1 × 10 − 3 , c 3 = 8 . 5 × 10 − 5 Use fit of dependence of experimental result on m MC t maximize joint likelihood assuming m t = m MC t � f ( m t ) = f th ( σ | m t ) · f exp ( σ | m t ) dσ , with normalized Gaussians � � � t ( m t ) � 2 σ − σ th 1 t ¯ f th = exp − √ 2 π ∆ σ th 2(∆ σ th t ( m t )) 2 t ( m t ) t ¯ t ¯ Determine uncertainty from 68% area in upper/lower region; estimate uncertainty from assumption m t = m MC . t C. Schwinn Theory status of t ¯ t cross section and pole mass. MIAPP ”Top quark physics day”
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