Top-Quark Pair Production Close to Threshold QCD and Electroweak - PowerPoint PPT Presentation

Top-Quark Pair Production Close to Threshold QCD and Electroweak Effects Johann H. K¨ uhn I. QCD (based on EPJ (2009); Kiyo, JK, Moch, Steinhauser, Uwer) II. Electroweak Corrections (with Scharf, Uwer)

I) QCD and Threshold Effects Remember the ILC Original idea from e + e − annihilation | Ψ n ( 0 ) | 2 πδ ( √ s − M n ) t ) ∼ ∑ σ ( e + e − → t ¯ n for narrow t ¯ t -resonances with masses M n and “stable” top quarks. Finite width: πδ ( √ s − M n ) ⇒ Im 1 M n − i Γ t −√ s Ψ n ( 0 ) Ψ ∗ r ′ = 0 , √ s + i Γ t ) n ( 0 ) ∑ M n − i Γ t −√ s = Im G ( � r = 0 ,� n numerical or perturbative analytical solution of Lippmann-Schwinger equation � � �� − ∇ 2 r ′ = 0 , E + i Γ t ) = δ ( ( E + i Γ t ) − + V ( � r ) G ( � r ,� � r ) m 2 t 2

Greens function G involves “long distances” ( � P � ∼ 20 GeV) still in perturbative region α s In addition: short distance corrections ( 1 − 16 π + ... ) 3 1.8 1.8 1.6 1.6 1.4 1.4 1.2 1.2 1.0 1.0 R R 0.8 0.8 0.6 0.6 0.4 0.4 Hoang � Teubner MYYNOS 0.2 0.2 0.0 0.0 344 345 346 347 348 349 350 351 352 344 345 346 347 348 349 350 351 352 ������ ������ q 2 � GeV � q 2 � GeV � 1.8 1.8 1.6 1.6 1.4 1.4 1.2 1.2 1.0 1.0 R R 0.8 0.8 0.6 0.6 0.4 0.4 Penin � Pivovarov Beneke � Signer � Smirnov 0.2 0.2 0.0 0.0 344 345 346 347 348 349 350 351 352 344 345 346 347 348 349 350 351 352 ������ ������ q 2 � GeV � q 2 � GeV � determination of m t with δ m t ∼ 50 MeV (Linear Collider) ⇒ important impact on stability of vacuum in the SM. 3

Hadron Colliders Tevatron, LHC: δ m t ∼ 1 GeV systematics limited: Kinematical reconstruction from decay products of top quarks (color triplet) “Monte Carlo” defintion ( ∼ close to pole mass) 4

fundamental processes: g ∗ t + ¯ → → q ¯ q t (Tevatron) տ ր color octet ( 8 s ) gg → t + ¯ t 8 ⊗ 8 = 1 s ⊕ 8 s ⊕ 8 a ⊕ 10 a ⊕ 10 a ⊕ 27 s 3 ⊗ ¯ 3 = 1 s ⊕ 8 s QCD potential � � � � − 4 πα s ( µ r ) C [ 1 , 8 ] 1 + α s ( µ r ) β 0 ln µ 2 V [ 1 , 8 ] r � ( � q ) = q 2 + a 1 + ... , 4 π C q 2 � � with C [ 1 ] = C F = 4 / 3 and C [ 8 ] = C F − C A / 2 = − 1 / 6 , and a 1 = ( 31 / 9 ) C A − ( 20 / 9 ) T F n f singlet: attractive octet: repulsive 5

t ¯ t bound states? Γ t ≈ 1 . 36 GeV; Rydberg constant ( C [ 1 ] α s ) 2 m t 4 ≈ 1 . 5 GeV singlet ⇒ enhancement around 1 S peak octet ⇒ suppression 0.05 0.04 0.03 2 Im G c / m t 0.02 0.01 0 335 340 345 350 355 360 M [ GeV ] Imaginary part of the Green’s functions for the color singlet (upper solid line) and color octet (lower solid line) cases as functions of top quark invariant mass. For comparison, also the expansions of G in fixed order up to O ( α s ) with (dashed) and without (dotted line) Γ t are plotted. The imaginary part of the NNLO Green’s function for the color-singlet case is shown as dash-dotted line. 6

Production cross section close to threshold partonic cross section Born: i + j → t + ¯ t QCD-corrections: i + j → t + ¯ t (+ X ) q → t + ¯ (e.g. q + ¯ t + g etc) σ i j → t ¯ M dˆ f ) 1 t Im G [ 1 , 8 ] ( M + i Γ t ) , s , M 2 , µ 2 s , M 2 , µ 2 ( ˆ f ) = t ( ˆ F i j → t ¯ m 2 d M t Perturbative NLO evaluation: � � π 2 α 2 1 + α s ( µ r ) s ( µ r ) s , M 2 , µ 2 t ( ˆ f ) = N i j → t ¯ C h F i j → t ¯ t π 3ˆ s � � �� t δ ( 1 − z )+ α s ( µ r ) δ i j → t ¯ A c ( z )+ A nc ( z ) × . π 1 S [ 1 ] 0 , 1 S [ 8 ] 0 , 3 S [ 1 ] 1 , 3 S [ 8 ] restrict to S-waves: 1 spin singlet and triplet, color singlet and octet (result for spin and color singlet: JK+Mirkes 1993) 7

• N i j : normalization • C h : hard virtual corrections • A c : collinear parton splitting (involves splitting functions) • A nc : non-collinear real emission example ( t ¯ t in spin singlet & color singlet configuration) � µ 2 � � π 2 � � � β 0 1 + π 2 C h [ gg → 1 S [ 1 ] r 0 ] = + C F 4 − 5 + C A , 2 ln M 2 12 � � �� � � � ln ( 1 − z ) � � 1 � − β 0 µ 2 M 2 A c [ gg → 1 S [ 1 , 8 ] 2 δ ( 1 − z ) ln f ] = ( 1 − z ) P gg ( z ) + , 2 ln 0 zµ 2 M 2 1 − z 1 − z + + f � � M 2 ( 1 − z ) 2 1 + C F A c [ gq → 1 S [ 1 , 8 ] ] = 2 P gq ( z ) ln 2 z , 0 zµ 2 f � − C A 12 + 11 z 2 + 24 z 3 − 21 z 4 − 24 z 5 + 9 z 6 A nc [ gg → 1 S [ 1 ] 0 ] = 6 z ( 1 − z ) 2 ( 1 + z ) 3 � � − 1 + 5 z 2 + 2 z 3 + z 4 + 3 z 6 + 2 z 7 � − 11 z 8 + 12 , ln z 32 C F q → 1 S [ 1 ] A nc [ q ¯ 0 ] = z ( 1 − z ) 3 N 2 c similarly for 1 S [ 8 ] 0 , also contributions from gq , q ¯ q 8

Results leading subprocesses: gg → 1 S [ 1 , 8 ] q → 3 S [ 8 ] and q ¯ 0 0 1.4 1.2 [ 8 ] gg → 1 S 0 d σ / dM [ pb/GeV ] 1 [ 1 ] gg → 1 S 0 0.8 0.6 – → 3 S 1 [ 8 ] 0.4 qq 0.2 LHC √  s = 14 TeV 0 335 340 345 350 355 360 365 370 375 380 M [ GeV ] suppressed (repulsive potential ⇒ Greens function) octet: enhanced (color degrees of freedom) 9

4 3.5 3.5 3 3 total 2.5 d σ / dM [ pb/GeV ] d σ / dM [ pb/GeV ] 2.5 2 2 color-octet 1.5 1.5 LHC color-singlet 1 1 √  s = 14 TeV 0.5 LHC √  s = 14 TeV 0.5 0 0 335 340 345 350 355 360 365 370 375 380 335 340 345 350 355 360 365 370 375 380 M [ GeV ] M [ GeV ] boundstate result vs NLO all production channels (continuum pQCD) 10

0.06 1.6 total 1.4 0.05 total 1.2 d σ / dM [ pb/GeV ] 0.04 d σ / dM [ pb/GeV ] 1 color-octet 0.03 0.8 color-octet 0.6 0.02 Tevatron √  s = 1.96 TeV color-singlet 0.4 0.01 LHC √  s = 10 TeV color-singlet 0.2 0 0 335 340 345 350 355 360 365 370 375 380 335 340 345 350 355 360 365 370 375 380 M [ GeV ] M [ GeV ] Tevatron (1.96 TeV) LHC (10 TeV) small gg-luminosity 12

SUMMARY on QCD differential distribution d σ d M carries important information on t − ¯ t − dynamics threshold enhancement ∼ 10 pb [small compared to σ tot ∼ 200 pb (8 TeV) ∼ 800 pb (14 TeV)] studies of d σ d M close to threshold might exhibit structure similar to those at e + e − colliders ⇒ mass of t ¯ t bound state Impact of weak corrections? 13

II) Electroweak Corrections I. Results at Partonic Level q q t t no q → t ¯ q ¯ t : interference g Z with ∼ O ( α s ) ∼ O ( α weak ) g g t t ∼ O ( α s ) gg → t ¯ t : 14

O ( α 2 s α weak ) weak corrections ( q ¯ q → t ¯ t ) + Z, W Z, W Z, W, H, φ, χ q q q q + t t cuts of second group individually IR-divergent 15

O ( α 2 s α weak ) weak corrections ( gg → t ¯ t ) Γ Γ Γ Γ Z, χ, H t, b 16

• analytical & numerical results available (earlier partial results by Beenakker et al. , some disagreements) independent evaluation by Bernreuther & F¨ ucker • ( box contribution ) up − quark = − ( box contribution ) down − quark ⇒ suppression • box contribution moderately ˆ s -dependent • strong increase of negative corrections with ˆ s • sizable M h -dependence, large effect close to threshold 17

10 0 – → tt – qq – gg → tt 0 -5 -10 M h = 120 GeV M h = 120 GeV -10 -20 M h = 240 GeV M h = 240 GeV M h = 1000 GeV M h = 1000 GeV -15 -30 3 4 3 4 10 10 10 10 ∧ [GeV] ∧ [GeV] √ s √ s � sizable negative corrections for large E cm = M ( t ¯ t ) ⇒ Sudakov logarithms � weak charges in initial and final state ⇒ factor two enhanced corrections � significant dependence on m H close to threshold 18

II. Tevatron and LHC Small effects for total cross section √ s ∼ 360 - 380 GeV) (dominated by ˆ 1 -1 relative weak corrections [%] relative weak corrections [%] Tevatron LHC -1.5 m H = 120 GeV 0 m H = 120 GeV m H = 200 GeV -2 m H = 200 GeV -1 -2.5 m H = 1000 GeV m H = 1000 GeV -2 -3 165 170 175 180 165 170 175 180 m t [GeV] m t [GeV] 19

differential distributions composition: q ¯ q vs gg 10 1 10 1 LHC (14 TeV) gg → t ¯ gg → t ¯ LHC (14 TeV) t t 10 0 10 0 q → t ¯ q → t ¯ q ¯ q ¯ t t 10 − 1 10 − 1 sum sum 10 − 2 10 − 2 10 − 3 10 − 3 10 − 4 10 − 4 d σ LO d σ LO [ pb / GeV ] 10 − 5 [ pb / GeV ] 10 − 5 d p T , t dM t¯ t 10 − 6 10 − 6 10 − 7 10 − 7 1000 2000 3000 4000 5000 250 500 750 1000 1250 1500 1750 2000 t [ GeV ] p T , t [ GeV ] M t¯ large p t : dominated by q ¯ q annihilation 20

0 M H = 126 GeV LHC (8 TeV) M H = 126 GeV LHC (8 TeV) 0 M H = 1 TeV M H = 1 TeV − 5 − 10 − 5 d δσ NLO t / d σ LO d δσ NLO d p T , t / d σ LO t [ % ] − 15 d p T , t [ % ] d M t¯ d M t¯ − 10 − 20 500 1000 1500 2000 2500 3000 0 250 500 750 1000 1250 1500 t [ GeV ] p T , t [ GeV ] M t¯ 0 LHC (14 TeV) 0 LHC (14 TeV) M H = 126 TeV M H = 126 GeV M H = 1 TeV M H = 1 TeV − 5 − 5 − 10 − 10 d δσ NLO d p T , t / d σ LO − 15 d p T , t [ % ] d δσ NLO t / d σ LO t [ % ] d M t¯ d M t¯ − 15 − 20 1000 2000 3000 4000 5000 0 250 500 750 1000 1250 1500 1750 2000 t [ GeV ] p T , t [ GeV ] M t¯ Relative weak corrections for the invariant t ¯ t mass (left) and transverse momentum (right) distribution for LHC8 (upper) and LHC14 (lower plots) and for Higgs masses of 126 GeV and 1 TeV. 21