ELECTROWEAK CORRECTIONS TO GAUGE BOSON AND TOP QUARK PRODUCTION AT HADRON COLLIDERS

Transcription

1 ELECTROWEAK CORRECTIONS TO GAUGE BOSON AND TOP QUARK PRODUCTION AT HADRON COLLIDERS J.H. Kühn, Karlsruhe I. Introduction II. Z- and Photon Production Phys. Lett. B609( Nucl. Phys. B727( JHEP 0603:059,2006 III. Top Production Eur. Phys. J., C45, ( J.H.K., A.Kulesza, S.Pozzorini, M.Schulze J.H.K., A.Scharf, P.Uwer IV. Conclusions J.H. Kühn/ LL 06/ Eisenach 1

2 I. Introduction α weak π 10 2 expectation for typical size of electroweak corrections for hadronic processes building blocks: q Z q t Z,W Z,W g +... qg qz q q t t J.H. Kühn/ LL 06/ Eisenach 2

3 new aspects at LHC: ŝ 1-2TeV s ŝ M 2 W,Z strong enhancement of negative corrections one-loop example: massive U(1 M Born [ 1 + α 4π ( ln 2 s M 2 + 3ln s M π2 3 ] s M 2 ( 1000 ln 2 s M 2 +3ln s M π2 3 Σ 4 α w 4π 80 ( % % (four-fermion cross section factor 4 J.H. Kühn/ LL 06/ Eisenach 3

4 leading log 2 multiplied by (charge 2 = I(I + 1 = { 3/4 I = 1/2 2 I = 1 important subleading logarithms (NLL+... ( Penin: f f f f two-loop terms may be relevant interplay between electroweak and QCD corrections important differences between fermions and electroweak gauge bosons J.H. Kühn/ LL 06/ Eisenach 4

5 II. Z and Photon Production J.H.K., Kulesza, Pozzorini, Schulze Large rate for Z-boson and photon production at LHC at large p T (1-2 TeV Large electroweak corrections (ŝ M 2 W,Z q Z q Z + g g J.H. Kühn/ LL 06/ Eisenach 5

6 one-loop corrections W,Z W,Z W,Z W,Z W,Z W,Z W ± W W W ± W ± W,Z W,Z W plus counter terms J.H. Kühn/ LL 06/ Eisenach 6

7 Result decomposed into abelian (A and non-abelian (N parts M1 2 = 8π 2 αα s (N 2 c 1 λ=r,l [ + c w s w T 3 q λ I Z q λ ( I Z qλ 2 [H 0 ( 1 + 2δC A qλ + α 2π ] 2H 0 δcq N λ + α 1 2πs 2 1 wh N (M2 W V =Z,W ± ( I V I V qλ H A 1 (M2 V ] with H 0 = ˆt 2 +û 2 +2ŝM 2 Z ˆtû ; I V, T 3 couplings H A,N 1, δc A,N given in closed analytical form consisting of kinematical functions (ŝ,ˆt, û and 14 combinations of 1 A 0, 5 B 0, 5 C 0, 3 D 0 J.H. Kühn/ LL 06/ Eisenach 7

8 High energy limit consider q q Zg NLL ˆ= double + single logarithmic terms [ ( H1 A (M2 V NLL = log 2 ŝ MW 2 [ ( H1 N (M2 W NLL = log 2 ˆt MW 2 3log ( ŝ ] MW 2 + log 2 ( û M 2 W H 0, ( ] log 2 ŝ MW 2 H 0 δc A q λ NLL = δc N q λ NLL = 0 (remaining subleading terms 2.5% J.H. Kühn/ LL 06/ Eisenach 8

9 NNLL: includes non-enhanced terms (angular dependent H A/N 1 (M 2 V NNLL = Re [ g A/N 0 (M 2 V ˆt 2 + û 2 ˆtû ( g0 N (M2 W = 2 UV + log 2 ŝ [ M 2 W log 2 ( 3 (û (ˆt log 2 + log 2 2 ŝ ŝ [ g1 N (M2 W = 1 (û (ˆt log 2 log 2 2 ŝ ŝ [ (û (ˆt g2 N (M2 W = 2 log 2 + log 2 ŝ ŝ ( g0 A (M2 V = ŝ log2 M 2 V + 3log (û (ˆt + log + log ŝ ŝ [ g1 A (M2 V = gn 1 (M2 W + 3 (û log 2 ŝ g A 2 (M2 V = gn 2 (M2 W ], ( + g A/N 1 (M 2 V ˆt 2 û 2 ˆtû ˆt M 2 W log 2 ( ] 20π2 9 2π 3 + 4, (ˆt + log ŝ ŝ M 2 V ] + 7π [ 3 5 2, (ˆt log ŝ (û + log ŝ log 2 (ˆt ŝ + g A/N 2 (M 2 V ] û M 2 W ] 4π 2 + log 2 (û + simple approximations for finite parts of counter terms ], (ˆt + log 2 û ŝ J.H. Kühn/ LL 06/ Eisenach 9

10 size of the correction: ŝ δσ = 200 GeV : σ 0.3% ŝ = 4000GeV : δσ σ 20 30% quality of the approximation: R ( NLL / NLO 2.5% R ( NNLL / NLO 1% J.H. Kühn/ LL 06/ Eisenach 10

11 (a uu (b dd (c gu ˆR ij ˆR ij NLO/LO ˆR ij NLL/NLO NNLL/NLO (d gd ŝ [GeV] ŝ [GeV] 4000 Relative one-loop corrections to the partonic differential cross sections dˆσ ij /dcosθ at cos θ = 0 for (a ūu channel, (b dd channel, (c gu channel, (d gd channel. The solid, dashed and dashed-dotted lines denote the modulus of the ˆR ratios for the full NLO cross section, the NLL approximation and the NNLL approximation of the one-loop cross section, respectively. J.H. Kühn/ LL 06/ Eisenach 11

12 one-loop: A (1 = Result consistent with general considerations (Phys. Lett. B609( [ Iq Z λ λ=l,r I Z q λ C ew q λ ( L 2ŝ 3Lŝ c w + Tq 3 ( λ L 2ˆt + L2 û L2 ŝ two-loop (NLL, based on Denner, Melles, Pozzorini: A (2 = ( with L ṋ r = ˆr logn MW 2 λ=l,r 1 2 ( Iq Z λ Cq ew λ + c w s 3 w s 3 w + c w s 3 T 3 ( q λ L 4ˆt + L4 û L4 ŝ T3 q λ Y qλ w 8s 4 w ( Yqλ 2 + b IZ q λ I Z q λ ( b1 c 2 w 2 Tq 3 λ I q Z λ Cq ew ( λ L 4ŝ 6L 3 ŝ s 2 C qλ w ] ( L 4ˆt + L4 û L4 ŝ + c w s 3 w, b 1 = 41/(6c 2 w and b 2 = 19/(6s 2 w T 3 q λ b 2 L 3 ŝ J.H. Kühn/ LL 06/ Eisenach 12

13 Complete one loop calculation NLL approximation at two loops (= NNLO NLO/LO-1 NNLO/LO-1 statistical error T [GeV] p cut one-loop effects are large ( 30% at p T 1Tev two-loop effects (based on Denner, Melles, Pozzorini; Melles become relevant above 1 TeV important angular-dependent logarithmic terms experiment will explore p T up to 2 TeV Relative NLO and NNLO corrections w.r.t. the LO and statistical error for the unpolarized integrated cross section for pp Zj at s = 14 TeV. J.H. Kühn/ LL 06/ Eisenach 13

14 Compact analytical formulae for one-loop results in NNLL approximation (ln 2 +ln+const. provide an excellent description (better than of complete result R had NLO/LO R had R had NLL/LO NNLL/LO p T distribution for pp Zj at s = 14 TeV: (b (c p T [GeV] R had R had NLL/NLO NNLL/NLO (b Relative NLO, NLL and NNLL weak correction w.r.t. the LO distribution. (c NLL and NNLL approximations compared to the full NLO result J.H. Kühn/ LL 06/ Eisenach 14

15 Corrections at the Tevatron ( s=2 TeV amount up to 5% NLO/LO-1 NNLO/LO-1 statistical error Relative NLO and NNLO corrections w.r.t. the LO and statistical error (shaded area for the unpolarized integrated cross section for p p Zj at s=2 TeV as a function of p cut T p cut T [GeV] J.H. Kühn/ LL 06/ Eisenach 15

16 Photon production also large corrections NLO and approximations ( NLL, NNLL dominant two-loop terms available ( NNLO NLO/LO-1 NNLO/LO-1 statistical error T [GeV] p cut J.H. Kühn/ LL 06/ Eisenach 16

17 Photons vs. Z at large p T 1.30 dσ Z dp T dσ γ dp T / LO NLO NNLO p T [GeV] numerical results in qualitative agreement with Maina, Moretti, Ross J.H. Kühn/ LL 06/ Eisenach 17

18 III. Top Production (q q t t J.H.K., Scharf, Uwer work on gg t t in progress q t g O(α s no interference with q t Z O(α weak J.H. Kühn/ LL 06/ Eisenach 18

19 O(α 2 sα weak weak corrections from Z,W + Z,W,H,φ,χ also Beenakker et. al q q q q t + t cuts of second group individually IR-divergent J.H. Kühn/ LL 06/ Eisenach 19

20 analytical & numerical results available: q q t t (independent evaluation of Bernreuther & Fücker, many independent checks gg t t in progress (box contribution up quark = (box contribution down quark suppression box contribution moderately ŝ-dependent strong increase with ŝ sizable M h -dependence, large effect close to threshold J.H. Kühn/ LL 06/ Eisenach 20

21 large corrections for large ŝ partonic contributions relative weak corrections: qq tt [%] vertices boxes sum s [GeV] J.H. Kühn/ LL 06/ Eisenach 21

22 sizable M h -dependence relative weak corrections: qq tt [%] partonic contributions M h = 120 GeV M h = 240 GeV M h = 1000 GeV s [GeV] J.H. Kühn/ LL 06/ Eisenach 22

23 effect on the total cross section at LHC (σ tot =833pb weak corrections [pb] M h = 120 GeV M h = 200 GeV M h = 1000 GeV m t [GeV] J.H. Kühn/ LL 06/ Eisenach 23

24 effect on the total cross section at Tevatron (σ tot =5.75pb weak corrections [pb] M h = 120 GeV M h = 200 GeV M h = 1000 GeV m t [GeV] J.H. Kühn/ LL 06/ Eisenach 24

25 IV. Conclusions LHC will explore the TeV-region: ŝ / M 2 W 1 electroweak corrections amount to O(10% 20% in the interesting kinematic region p T -distributions of Z, γ and their ratio will be strongly affected higher orders might become relevant top-quark distributions at large ŝ are strongly modified sizable m H -dependence interplay between electroweak and QCD effects J.H. Kühn/ LL 06/ Eisenach 25