Top pair production near threshold at LHC (NLO/NLL analysis in NRQCD)

Transcription

1 LHC TTbar-Threshold Green Functions Top pair production near threshold at LHC (NLO/NLL analysis in NRQCD) Yuichiro Kiyo TTP, Universität Karlsruhe Collaboration with: J. H. Kühn(KA), S. Moch(Zeuthen), M. Steinhauser(KA), P. Uwer(Berlin) arxiv: [hep-ph]

2 LHC TTbar-Threshold Green Functions Millions of LHC will produce 8 million t t pairs/year studies of top quark properties: δm exp t 1GeV, δ s t s t exp 10%, tw b-coupling, a possibility to be standard candle current theory status; δσ NNLO 8% NLO Nason-Dawson-Ellis 88, Mangano-Nason-Ridolfi (HVQMNR) 92 NLL Laenen-Smith-vanNeeerven 94, Berger-Contopanagos 95, Catani-Mangano-Nason-Trentadue 96 NNLL Bonciani-Catani-Mangano-Nason 98 NNLO Moch-Uwer 08, Kidonakis-Vogt 08, Cacciari-Frixione-Mangano-Nason-Ridolfi 08 (Fig. from Moch-Uwer 08)

3 LHC TTbar-Threshold Green Functions LHC t t near threshold Our work was stimulated by Hagiwara-Sumino-Yokoya (08): Bound-state effects on top quark production@lhc We try to add some on top of HSY08 study, assembling existing knowledge@nlo/nll: Accumulation of knowledge Color-singlet result before dawn of NRQCD: Kühn-Mirkes 93 Advent of NRQCD factorization: Bodwin-Braaten-Lepage 95 Complete NLO NRQCD result sitting since 1997: Petrelli-Cacciari-Greco-Maltoni-Mangano 97 Threshold-logs Kodaira-Trentadue 82, Catani-d Emilio-Trentadue 88

4 LHC TTbar-Threshold Green Functions vs LHC fixed s: threshold scan QCD vacuum t t( 3 S [1] 1 ) No-ISR/soft-FSR ŝ integrated out:[ dl dτ ](τ) color combination t t( 2s+1 S [1,8] J ) ISR/FSR soft-collinear dynamics NRQCD Factorization Threshold: s 2m t σ ILC (s) = C 2 (s) G( s)

5 LHC TTbar-Threshold Green Functions vs LHC fixed s: threshold scan QCD vacuum t t( 3 S [1] 1 ) No-ISR/soft-FSR ŝ integrated out:[ dl dτ ](τ) color combination t t( 2s+1 S [1,8] J ) ISR/FSR soft-collinear dynamics NRQCD Factorization Threshold: M 2m t (M 2 = (p t + p t) 2 ) σ LHC (S) = dl ij dτ ( ) ŝ F ij T (ŝ, M) G(M) S

6 LHC TTbar-Threshold Green Functions vs LHC fixed s: threshold scan QCD vacuum t t( 3 S [1] 1 ) No-ISR/soft-FSR ŝ integrated out:[ dl dτ ](τ) color combination t t( 2s+1 S [1,8] J ) ISR/FSR soft-collinear dynamics NRQCD Factorization Threshold: M 2m t (M 2 (p t + p t) 2 ) dσ LHC dm = dl ij dτ ( ) ŝ F ij T (ŝ, M) G(M) S

7 LHC TTbar-Threshold Green Functions Green Functions: Coulomb resummation { [2mt 2 m t + V [1,8] V [8] C = α s (µ) 4πC[1,8] q 2 (i + α sc [1,8] G = v 4π C (r) ] } (M + iγ t ) v ( 1 + δ NLO + [iπ 2 G [1,8] ( r; M + iγ t ) = δ (3) ( r) ) (C [8] < 0) ) ln v] + O(αs) 2 v:relative velocity solid: C-Resum with Γ t red-dash: 1-loop (stable top) fixed order perturbation blue-dash: 1-loop with Γ t

8 LHC TTbar-Threshold Green Functions Green Functions: Coulomb resummation { [2mt 2 m t + V [1,8] V [8] C = α s (µ) 4πC[1,8] q 2 (i + α sc [1,8] G = v 4π C (r) ] } (M + iγ t ) v ( 1 + δ NLO + [iπ 2 G [1,8] ( r; M + iγ t ) = δ (3) ( r) ) (C [8] < 0) ) ln v] + O(αs) 2 v:relative velocity solid: C-Resum with Γ t red-dash: 1-loop (stable top) fixed order perturbation blue-dash: 1-loop with Γ t G [1] NNLO (for error estimate)

9 Partonic cross in NRQCD Numerics 1 Part I Free top pair production in NRQCD

10 Partonic cross in NRQCD Numerics 1 Partonic cross section Kühn-Mirkes 93,Petrelli-Cacciari-Greco-Maltoni-Mangano 97 M dσ ij T dm (ŝ, M, µ f ) = F ij T (z) 1 m 2 ImG [1,8] (M + iγ t ) t Free t t production rate: F ij T = σ V R(z) Virtual Corr: σ V = N ij T π 2 α s(µ) 3ŝ ( α s(µ) 1 + π C ) h Real emission: R(z) = δ ij T δ(1 z) + α s π ( Ac (z) + A nc (z) ) δ ij T = 1 for gg 1 S [1,8] 0, q q 3 S [8] 1 otherwise zero z = M 2 /ŝ: momentum fraction of a parton F, G are separately C h : non-decoupling top loop included (Hagiwara-Sumino-Yokoya 08)

11 Partonic cross in NRQCD Numerics 1 Numerics: Free t t production rate@nlo L F in unit of 10 6 /GeV 2 for LHC at M = 2m t L F [ij T [1] ] L F [ij T [8] ] gg 1 S gq 1 S q q 1 S gg 3 S gq 3 S q q 3 S total Dominance of leading processes: gg 1 S [1,8] 0, q q 3 S [8] 1 Collinear factorization (µ f -cancelation) gq 1 S [1,8] 0 gg 1 S [1,8] 0 ; gq 3 S [8] 1 q q 3 S [8] 1

12 Real emission End point logs Threshold resummation Numerics 2 Part II Threshold soft/collinear gluon resummation

13 Real emission End point logs Threshold resummation Numerics 2 ( Real emission: R(z) = δ ij T δ(1 z) + αs π Ac (z) + A nc (z) ) Kühn-Mirkes 93,Petrelli-Cacciari-Greco-Maltoni-Mangano 97 Collinear/Non-Coll Func A c [gg 1 S [1,8] 0 ] = (1 z)p gg (z)s + (z) β0 2 ln µ2 f M δ(1 z) 2 A nc [gg 1 S [8] 0 ] = 2C [ 1 ] A 1 z + + A nc [gg 1 S [1] 0 ] = (rational + log) func in z Altarelli-Parisi splitting Func :P gg (z) Soft Func: S + (z) = [ 2 ln(1 z) ] 1 z + + [ ] 1 1 z + ln µ2 f zm 2

14 Real emission End point logs Threshold resummation Numerics 2 End point logs@nlo Three lines for µ = µ f = (m t, 2m t, 4m t ) Three terms for LO, singular and regular terms at z=1 Hard corr C h as multiplicative common factor to all terms ( )[ L FNLO gg 1 S [1] ] 0 ( )[ L FNLO gg 1 S [8] ] 0 ( )[ L FNLO q q 3 S [8] ] 1 = = = [4.53] A+ + ( 1.68 ) A [5.66] A+ + ( 1.58 ) A [6.37] A+ + ( 1.48 ) A [16.6] A+ + ( 7.26 ) A [18.8] A+ + ( 6.52 ) A [20.0] A+ + ( 5.83 ) A [3.50] A+ + ( 2.91 ) A [3.41] A+ + ( 3.56 ) A [3.28] A+ + ( 3.97 ) A

15 Real emission End point logs Threshold resummation Numerics 2 Resummation of soft/collinear threshold logs Resummed free quark production rate (λ = α s (µ)β 0 /(4π) ln N): F ij T (N, M, µ f ) = g 0 }{{} exp { ln N g 1 ij T (λ) + g 2 ij T (λ) + } }{{} Matching term Universal exponent Factorization in N-space: M N (f) 1 0 z N 1 f(z)dz M N ((f g) [x]) = f N g N ( [ln k ] ) (1 z) M N ln k+1 N 1 z + Resummation is done invoking Factorization Theorem F ij T can be obtained by Mellin-trans back numerically

16 Real emission End point logs Threshold resummation Numerics 2 Numerics: Free t t production rate@nll NLO L F NLO ij T [1] L F NLL ij T [8] gg 1 S [1] gg 1 S [8] q q 3 S [8] few % enhancement how about scale dep? needs to combine sub-leading processes

17 Hadronic X section@lhc Fixed order vs. NRQCD Summary Part III Phenomenology

18 Hadronic X section@lhc Fixed order vs. NRQCD Summary Hadronic cross section dσ/dm

19 Hadronic X section@lhc Fixed order vs. NRQCD Summary Hadronic cross section dσ/dm

20 Hadronic X section@lhc Fixed order vs. NRQCD Summary Tevatron case

21 Hadronic X section@lhc Fixed order vs. NRQCD Summary Fixed order vs. NRQCD NLO comparison between fixed order(hvqmnr) and NLL NRQCD total cross section 840pb (10 7 t t/year) consistency check: fixed order and NRQCD matching is O.K. σ(gg t t[ 1 S [1] 0 ]) 1%, important for m t measurement (agree with HSY08)

22 Hadronic X section@lhc Fixed order vs. NRQCD Summary Fixed order vs. NRQCD NLO comparison between fixed order(hvqmnr) and NLL NRQCD m t from M-distribution can be affected by the bound-state effect. (recent study of M-distribution: Frederix-Maltoni 08)

23 Hadronic X section@lhc Fixed order vs. NRQCD Summary Summary Phenomenological NRQCD were performed for t t production near threshold at LHC : Resonance enhancement of order 1% possibility of threshold scan@lhc for m t M tt will be shifted to threshold m t fit from M tt affected Resummation of Threshold logs at most +10% shift near threshold Reduction of scale dependence Remaining Theory uncertainties Bound-state dynamics G for color singlet has largest error: 20% Scale dependence of short distance small.

24 Hadronic Cross section figs Part IV Backup

25 Hadronic Cross section figs Hadronic cross section Hadronic Cross Section (τ ŝ/s) M dσ dm (S, M) = i,j 1 0 dτ [ dlij dτ ] (τ, µ f ) M dˆσ ij T dm (ŝ, M, µ f )

26 Hadronic Cross section figs figs