Current status and future prospects Top and QCD Current status and future prospects Y. Sumino (Tohoku Univ.)

☆Plan of Talk Introduction: Pert. QCD and Top quark 2. Status of pert. QCD (top processes) 3. Towards precision 𝑚 𝑡 determinations 4. Vision of quantum corrections at frontiers 5. Conclusions and future prospects

p (陽子) p (陽子) LHC ＬＨＣ実験における反応データ

強い力 _ u u _ u _ u u u ‥‥クォークを陽子・中性子の中に閉じ込めておく力 クォークを陽子・中性子の中から取り出すことは できない＝「クォークの閉じ込め」 _ u u 中間子 核子（陽子・中性子など） 決して単体のクォークは取り出せない。 常に 　核子（クォーク３つで出来ている） 　中間子（クォーク・反クォークの対で出来ている） の中に入っている。 _ u _ u u u 中間子 中間子

d u d u u u 陽子 陽子 （衝突エネルギー）／（陽子の質量×c2） くらいの数の 核子や中間子が生成される。

p (陽子) p (陽子) LHC ＬＨＣ実験におけるヒッグス粒子生成を 含む事象のシミュレーション 摂動ＱＣＤに基づく

What’s Pert. QCD? 3 types of so-called “Pert. QCD predictions” : Confusing (i) Predict observable in series expansion in 𝛼 𝑠 IR safe obs., intrinsic uncertainties ~ (Λ QCD / 𝐸) 𝑛 (ii) Predict observable in the framework of Wilsonian EFT OPE, uncertainties of (i) replaced by non-pert. matrix elements Most accurate, future applications (iii) Predict observable assisted by model predictions Many obs in high-energy experiments depend on hadronization models, PDF. Necessary (in MC) to compare with experimental data Systematic uncertainties difficult to control, O(5-10%) accuracy at LHC

ℒ 𝑄𝐶𝐷 ( 𝛼 𝑠 , 𝑚 𝑞 ;𝜇) Pert. QCD Theory of quarks and gluons renormalization scale ℒ 𝑄𝐶𝐷 ( 𝛼 𝑠 , 𝑚 𝑞 ;𝜇) Theory of quarks and gluons Same input parameters as full QCD. Systematic: own way to estimate errors (𝜇-dep.) Differs from a model ! Predictable observables 𝑞, 𝑔 |𝑞,𝑔 𝑞,𝑔| = ℎ𝑎𝑑𝑟. |ℎ𝑎𝑑𝑟. ℎ𝑎𝑑𝑟.| = 1 testable hypothesis (a) Inclusive observables (hadronic inclusive) ⋯ insensitive to hadronization 𝑅 𝐸 ≡ 𝜎 𝑒 + 𝑒 − →ℎ𝑎𝑑𝑟𝑜𝑛𝑠;𝐸 𝜎 𝑒 + 𝑒 − → 𝜇 + 𝜇 − ;𝐸 • Inclusive cross sections/decay widths e.g. • Distributions of non-colored particles, ℓ, 𝛾, 𝑊,𝐻,⋯ (b) Observables of heavy quarkonium states (only individual hadronic states) • spectrum, leptonic decay width, transition rates

What’s Pert. QCD? 3 types of so-called “Pert. QCD predictions” : Confusing (i) Predict observable in series expansion in 𝛼 𝑠 IR safe obs., intrinsic uncertainties ~ (Λ QCD / 𝐸) 𝑛 (ii) Predict observable in the framework of Wilsonian EFT OPE, uncertainties of (i) replaced by non-pert. matrix elements Most accurate, future applications (iii) Predict observable assisted by model predictions Many obs in high-energy experiments depend on hadronization models, PDF. Necessary (in MC) to compare with experimental data Systematic uncertainties difficult to control, O(5-10%) accuracy at LHC

Remarkable progress of computational technologies in the last 10-20 years Higher-loop corrections Numerical and analytical methods Intersection with frontiers of mathematics Factorization of scales in loop corrections Provide powerful and precise foundation for theory predictions PDFs Radiator fn Matrix element 𝜎 𝑖+𝑗→𝑓 𝑠 = 𝑎,𝑏 0 1 𝑑 𝑥 1 0 1 𝑑 𝑥 2 𝑃 𝑎/𝑖 𝑥 1 , 𝜇 𝐹 𝑃 𝑏/𝑗 𝑥 2 , 𝜇 𝐹 0 1 𝑑𝑧 𝑅 𝑎𝑏 𝑧, 𝜇 𝐹 , 𝑄 𝑀 𝑎𝑏→𝑓 𝑄 2 =𝑧 𝑥 1 𝑥 2 𝑠 2 𝑃 𝑎/𝑖 𝑃 𝑏/𝑗 𝜇 𝐹 𝑎 𝑏 𝑄 𝑖=𝑝 𝑗=𝑝 Separation of scales

Tree-level Higgs potential Role of top quark in the SM vacuum structure 1-loop corrections Tree-level Higgs potential 𝑣 𝐻 𝑚𝐻 1 4𝜋 2 3 4 𝜆 𝐻 Φ † Φ− 𝜇 𝐻 2 2 log 𝜆 𝐻 Φ † Φ− 𝜇 𝐻 2 𝜇 2 + 1 4 3 𝜆 𝐻 Φ † Φ− 𝜇 𝐻 2 2 log 3 𝜆 𝐻 Φ † Φ− 𝜇 𝐻 2 𝜇 2 𝜆 𝐻 1 4𝜋 2 3 2 𝑔 2 2 Φ † Φ 2 log 𝑔 2 2 Φ † Φ 𝜇 2 + 3 4 𝑔 2 + 𝑔 ′2 2 Φ † Φ 2 log 𝑔 2 + 𝑔 ′2 2 Φ † Φ 𝜇 2 𝑊,𝑍,𝛾 = 246 GeV 𝑉 Φ =− 𝜇 𝐻 2 Φ † Φ+ 𝜆 𝐻 2 Φ † Φ 2 𝑡 1 4𝜋 2 −3 𝑦 𝑡 2 Φ † Φ 2 log 𝑦 𝑡 2 Φ † Φ 𝜇 2 Φ= 1 2 0 𝑣 𝐻 +ℎ

Tree-level Higgs potential Role of top quark in the SM vacuum structure 1-loop corrections Tree-level Higgs potential 1 4𝜋 2 3 4 𝜆 𝐻 Φ † Φ− 𝜇 𝐻 2 2 log 𝜆 𝐻 Φ † Φ− 𝜇 𝐻 2 𝜇 2 + 1 4 3 𝜆 𝐻 Φ † Φ− 𝜇 𝐻 2 2 log 3 𝜆 𝐻 Φ † Φ− 𝜇 𝐻 2 𝜇 2 tree top loop 𝑊,𝑍 loop 1 4𝜋 2 3 2 𝑔 2 2 Φ † Φ 2 log 𝑔 2 2 Φ † Φ 𝜇 2 + 3 4 𝑔 2 + 𝑔 ′2 2 Φ † Φ 2 log 𝑔 2 + 𝑔 ′2 2 Φ † Φ 𝜇 2 Higgs loop 𝑊,𝑍,𝛾 𝜙 𝑐 [GeV] 𝑉 Φ =− 𝜇 𝐻 2 Φ † Φ+ 𝜆 𝐻 2 Φ † Φ 2 𝑡 1 4𝜋 2 −3 𝑦 𝑡 2 Φ † Φ 2 log 𝑦 𝑡 2 Φ † Φ 𝜇 2 Φ= 1 2 0 𝑣 𝐻 +ℎ

𝑡 𝑡 production at LHC 𝑝 𝑝 NNLO predictions Czakon, Heymes, Mitov

Slide from Kim’s talk Top@LC2016

Anomaly in top FB asymmetry has disappeared. Czakon, Heymes, Fiedler, Mitov Soon full NNLO prod.+decay corr. will bring investigations of top quark to a new phase.

Towards precise top mass determinations 𝑡 𝛾,𝑍 e+ 𝑡 ILC LHC Weight function method 𝑡 𝑡 threshold at ILC 𝑡 𝑡 threshold at up-graded LHC and beyond

Slides from Kawabata’s talk TopWG@CERN2014,TopWS2015 Kawabata, Shimizu, YS, Yokoya

Result of LO simulation analysis using 𝑙+4-jets mode S. Kawabata, 1601.07684[hep-ph] LHC 100fb-1 Currently NLO simulation analysis is being performed. NLO production NLO decay NLO prod.+decay (dilepton) [GeV] Our current goal: ∆ 𝑚 pole <1 GeV With this method many theoretical problems should go away, except non-pert. effects of background color charge distr. on top decays.

Precision 𝑚 𝑡 measurement near 𝑡 𝑡 threshold at 𝑒 + 𝑒 − collider After many years of endeavor, computation of NNNLO corrections to 𝑒 + 𝑒 − →𝑡 𝑡 cross section near threshold has recently been completed. 𝑀 1𝑆 Beneke,Kiyo,Marquard, Penin,Piclum,Steinhauser 𝑔 𝑡 color-singlet 1S resonance Our estimate: ∆ 𝑚 𝑡 =20-30 MeV Kiyo, Mishima, YS

Slide from Kiyo’s talk Top@LC2016

LHC 3 ab-1 ∆ 𝑚 𝑡 ≈2 GeV FCC 100 TeV ∆ 𝑚 𝑡 ≈0.2 GeV @ 1 ab-1 ∆ 𝑚 𝑡 ≈0.06 GeV @ 10 ab-1 𝛾 𝑡 𝑞 𝑡 = +

A new vision of loop integral based on Baikov’s method Baikov rep. of loop integral: 𝑑 𝐷 𝑝 1 ⋯ 𝑑 𝐷 𝑝 𝐿 1 𝐷 1 𝑛 1 ⋯ 𝐷 𝑁 𝑛 𝑁 = 𝐶 1 𝑑 𝑥 1 𝑥 1 𝑛 1 ⋯ 𝐶 𝑁 𝑑 𝑥 𝑁 𝑥 𝑁 𝑛 𝑁 𝑃 𝑥 1 ,⋯, 𝑥 𝑁 (𝐷−𝐸−𝐿−1)/2 𝑥 𝑖 c.f. Mahler measure 𝐶 𝑖 As 𝐷→∞, branch points turn to saddle points and using saddle-point approx. coefficients of 1/𝐷 expansion can be computed by Gauss integrals. Most difficult computation of 5-loop QCD beta fn. relies on this technique.

Conclusions and future prospects Predictability of pert. QCD is rapidly developing and will continue further. A current task is to determine 𝛼 𝑠 ( 𝑀 𝑍 ) accurately (among others). Soon scrutiny of top quark will start at LHC, however, cannot be completely free from the unclean environment. Eventually 𝑒 + 𝑒 − machine is necessary for precision physics. Hints for deeper understanding on quantum nature of field theory from progressing theories of radiative corrections. ∆ 𝑚 𝑡 <1 GeV probably reachable

Slide from Heymes’s talk Loops&Legs2016

Slide from Mitov’s talk KEK-PH2016 Anomaly in top FB asymmetry is gone. Czakon, Heymes, Fiedler, Mitov

Slides from Kawabata’s talk TopWS2015