IFIC

1. IFIC

2. Outline

3. I. Top-pair production near threshold Future linear colliders (ILC/CLIC) with will produce lots of pairs, allowing for a threshold scan of the top cross section Precise determination of the top mass , thewidth and the Yukawa coupling Seidel, Simon, Tesar (2012) is a crucial input for electroweak precision observables! Requires also precise theoretical prediction QCD corrections are known (almost) up to NNLL/NNNLO, but electroweak (NLO) contributions due to top decaymissinguntilrecently! Note!once EW effects are turned on, the physical final state is

4. STATUS OF QCD CORRECTIONS Top quarks move slowly near threshold: sum from“Coulomb gluons” to all orders→ NRQCD → vNRQCD pNRQCD Further RG improvement by summing also : LL, NLL, ... • NNLO QCD corrections • NNLL • NNNLO (fullanalysissoon...) Hoang, Teubner'98-99; Melnikov, Yelkhovsky'98; Yakovlev ´98; Beneke, Signer, Smirnov'99; Nagano, Ota, Sumino'99; Penin, Pivovarov'98-99 Hoang, Manohar, Stewart, Teubner '00-01; Hoang ´03; Pineda, Signer '06; Hoang, Stahlhofen'06-11 see Y. Kiyo's talk Beneke, Kiyo, Schuller '05-08

5. STATUS OF QCD CORRECTIONS (cont.) Hoang, Stahlhofen (2013) “threshold masses” ● missing QCD soft NNLL contributionssmall ● EW effectsbeyond LO and specially non-resonanteffectsgive contributions at thelevel of the QCD uncertainty

6. EFFECTS FROM TOP QUARK INSTABILITY BEYOND LO ● Resonantcontributionsto top and antitopclosetothemass-shell ● Non-resonant (hard) corrections:accountfor the productionof the pairs byhighly virtual tops ordiagramswithonly one or no top Effective field theory (EFT) for pair production of unstable particles near threshold, based on separation of resonant and nonresonant fluctuations ● power counting for finite width effects: Extractcross section for from appropriate cuts of the forward-scatteringamplitude resonant contributions non-resonantcontributions

7. ELECTROWEAK EFFECTS Electroweakeffects at LO Fadin, Khoze (1987) ● Replacement rule: • unstable top propagator Electroweak effects at NLO ● Exchange of “Coulomb photon”: trivially extension of QCD corrections ● Gluon exchange involving the bottom quarks in the final state these contributions vanish at NLO for the total cross section, also negligible if loose top invariant-mass cuts are applied; remains true at NNLO Fadin, Khoze, Martin; Melnikov, Yakovlev (1994) ● Non-resonant (hard) corrections to which account for the production of the pairs by highly virtual tops or with only one or no top Hoang, Reisser (2005); Beneke, Jantzen, RF (2010) Beneke, Jantzen, RF (2010)

8. ELECTROWEAK EFFECTS (cont.) Electroweak (non-trivial) effects at NNLO ● absorptivepartsin the 1-loop matchingcoeffs. of the productionoperators (arisingfromcuts) Hoang, Reisser(2006) reproduce interferences between double and single resonant amplitudes Complex matching conditions ● real part of hard one-loop EW corrections Kuhn, Guth(1992); Hoang, Reisser(2006) ● NNLO non-resonantcontributions (gluoncorrectionsto NLO ones) Exact computationis hard, but can compute dominant terms for moderate invariant masscuts this talk

9. II. Non-resonant (electroweak) NLO contributions

10. II. Non-resonant NLO contributions Beneke, Jantzen , RF (2010) cutsthrough (seediagrams) and (notshown) in the 2-loop forward scatteringamplitude ● treat loop-momenta as hard: ● suppressed w.r.t. LO by

11. FORM OF NON-RESONANT CONTRIBUTIONS Applyingtop invariant-mass cuts

12. SIZE OF EW NLO CORRECTIONS Relative sizes of EW NLO correctionswithrespect LO LO includesresummation of Coulomb gluons QED resonant correction (“Coulomb photons”) Combined EW NLO corrections ~ -30 fb (-3% above and up to -20% below threshold) Non-resonant NLO correction Beneke, Jantzen , RF (2010)

13. Phase space matching Alternative approach to compute non-resonant contributions Hoang, Reisser, PRF (2010)

14. III. Non-resonant NNLO contributions

15. Finite-widthdivergences in theresonantcontributions Resonantcontributionsobtainedbyassumingthe top quarks are nearlyon-shell (potential), butintegratedoverallmomenta uncancelledUV-singularityfromhardmomenta: NNLO Relatedtofinite top widthin EFT cutpropagator Thesedivergencesmustcancel withnon-resonant (hard) NNLO terms, whicharisefromgluoncorrectionsto NLO non-resonantdiagrams h1-h10

16. Endpointdivergences in the non-resonantcontributions

17. ENDPOINT-DIVERGENT NON-RESONANT NNLO DIAGRAMS

18. Endpoint-divergent non-resonant NNLO contribution Jantzen, PRF (2013)

19. Non-resonant NNLO contributionfor total crosssection Alternativeframework computes non-resonantcontributionstothe total crosssectionbyexpanding in [Penin, Piclum, 2012]

20. IV. Results & comparisons

21. Resultsforthenon-resonant NNLO contributions

22. Inclusive top-pairproductioncrosssection Hoang, Reisser, RF (2010)

23. Inclusive top-pairproductioncrosssection Hoang, Stahlhofen (2013)

24. IV. Summary Resonantcorrections(top and antitopclosetomassshell) ● QCD contributions: • fixed-orderapproach:allN3LOpiecesknown (compilation of allcontributions • shallappearsoon...) • RG improvedcalculation: NNLL almost complete (remainingpiecesmall) ● ElectroweakcontributionsknowntoNNLL accuracy Theoreticaluncertainties ~ 5% at NNLL, at N3LO ? ... 3% theoreticaluncertaintyonthe total crosssectionhereseemsrealistic... Non-resonantcorrections(bWpairsfrom virtual tops orwithonlyoneor no top) ✔ computed at NLOforthe total crosssection and withtop invariant-mass cuts ✔ Beyond: NNLO and NNNLO termsknownonlywith top invariantmasscuts In progress: NNLO correctionsto total crosssection, expectedto be small (fewpercent at most), butcan becomeveryimportantbelowthepeakregion include non-resonantcorrections in future ILC top-quark mass measurementstudy

25. Backup slides

26. COMPARISON TO MADGRAPH/MADEVENT

27. COMPARISON TO MADGRAPH/MADEVENT

28. Non-QCD correctionsbeyond NNLO Hoang, Reisser, RF (2010) Sizes of NNLL EW and non-resonant corrections