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IFIC

IFIC. I. Top-pair production near threshold. ● Heaviest known quark ( plays an important role in EWSB in many models ). ● Important for quantum effects affecting precision observables. ● Very unstable , decays “ before hadronization ”. Threshold scan.

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IFIC

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  1. IFIC

  2. I. Top-pair production near threshold ● Heaviestknown quark (playsanimportant role in EWSB in manymodels) ● Importantfor quantum effectsaffectingprecision observables ● Veryunstable, decays “beforehadronization” Thresholdscan Precise determination of the top mass, thewidthand the Yukawa coupling in a well-definedtheoreticalscheme Seidel, Simon, Tesar (2012)

  3. Prospectsforthe top massmeasurement at the ILC Seidel, Simon, Tesar (2012) overall normalization uncertainty in the theory cross section assumed Systematicuncertaintiesin backgroundsubtraction and knowledge of the luminosityspectrumdominate top massuncertainty

  4. TOP-PAIR PRODUCTION - Theory ● Non-resonantcorrections:accountfor the productionof the pairs byhighly virtual tops ordiagramswithonly one or no top ● Resonantcontributionsto top and antitopclosetothemass-shell ● power counting forEWeffects: Theorysignal:resonant+non-resonantcorrections Note thattheorycontributionsdo notalwaysinvolvetheproduction of a top-antitoppair. Suchcontributionsshouldnot be clasified as background (even non-resonantproduction of without tops!, starts at NNNLO) Note:once EW effects are turned on, the physical final state is

  5. STATUS OF QCD (RESONANT) CORRECTIONS Top and antitopclosetomassshell, use Non-Relat. EFT Top quarks move slowly near threshold: sum from “Coulomb gluons” to all orders • fixed-orderapproach:allN3LOpiecesknown (compilationof allcontributionstocheckconvergence of perturbative series • stillpending) Further RG improvement by summing also : LL, NLL, ... Beneke, Kiyo, Schuller '05-08 • RG improvedcalculation: NNLL almost complete (missing NNLL piecesmall) Hoang, Manohar, Stewart, Teubner '00-01; Hoang ´03; Pineda, Signer '06; Hoang, Stahlhofen'06-13

  6. STATUS OF QCD (RESONANT) 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

  7. ELECTROWEAK AND INSTABILITY 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-resonantcorrectionsto 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) fullyknown at thisorder Beneke, Jantzen, RF (2010)

  8. ELECTROWEAK AND INSTABILITY 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, butdominanttermsknownformoderate invariantmasscuts. Anapproximationforthe total crosssectionrecentlyobtained Hoang, Reisser, RF (2010); Jantzen, RF (2013) RF (2014)

  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, RF (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. ENDPOINT-DIVERGENT NON-RESONANT NNLO DIAGRAMS

  17. Endpoint-divergent non-resonant NNLO contribution Jantzen, RF (2013)

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

  19. Non-resonant NNLO contribution: rho-expansion Dominantterm in rho reevaluated : [RF 2014]

  20. IV. Results & comparisons

  21. Resultsforthenon-resonantNLO & NNLO contributions

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

  23. Inclusive top-pairproductioncrosssection

  24. IV. Summary Resonantcorrections(top and antitopclosetomassshell) ● QCD contributions: • fixed-orderapproach:most ofN3LOpiecesknown (compilation of allcontributions • shallappearsoon...) • RG improvedcalculation: NNLL almost complete ● ElectroweakcontributionsknowntoNNLL accuracy Theoreticaluncertainties ~ 5% at NNLL, at N3LO ? ... 3% theoreticaluncertaintyonthe total crosssectionheremay be possible... Non-resonantcorrections(bWpairsfrom virtual tops orwithonlyoneor no top) ✔ computed at NLOforthe total crosssection and withtop invariant-mass cuts ✔ Beyond: dominant NNLO and NNNLO termsknownwhentop invariantmass cutsare included. NNLO estimateforthe total crosssection: ~1% effect 8 In progress: full NNLO correctionsto total crosssection(fewpercent at most), butcan becomeveryimportantbelowthepeakregion include non-resonantcorrections in future ILC top-quark mass measurementstudy (analysebackgroundtoavoiddouble-counting!)

  25. Endpointdivergences in the non-resonantcontributions

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

  27. Prospectsforthe top massmeasurement at the ILC includes up to NNLO QCD corrections (no EW)

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