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

2. ☆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

3. p (陽子)
p (陽子)
LHC
ＬＨＣ実験における反応データ

4. 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

5. 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。

6. 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

7. 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

8. 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

9. 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

10. 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 𝑑 𝑥 𝑑 𝑥 2 𝑃 𝑎/𝑖 𝑥 1 , 𝜇 𝐹 𝑃 𝑏/𝑗 𝑥 2 , 𝜇 𝐹 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

11. 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 𝜆 𝐻 Φ † Φ− 𝜇 𝐻 log 𝜆 𝐻 Φ † Φ− 𝜇 𝐻 2 𝜇 2
𝜆 𝐻 Φ † Φ− 𝜇 𝐻 log 3 𝜆 𝐻 Φ † Φ− 𝜇 𝐻 2 𝜇 2
𝜆 𝐻
1 4𝜋 𝑔 Φ † Φ 2 log 𝑔 Φ † Φ 𝜇 2
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 Φ † Φ 2 𝑡
1 4𝜋 2 −3 𝑦 𝑡 2 Φ † Φ 2 log 𝑦 𝑡 2 Φ † Φ 𝜇 2
Φ= 𝑣 𝐻 +ℎ

12. Tree-level Higgs potential
Role of top quark in the SM vacuum structure
1-loop corrections
Tree-level Higgs potential
1 4𝜋 𝜆 𝐻 Φ † Φ− 𝜇 𝐻 log 𝜆 𝐻 Φ † Φ− 𝜇 𝐻 2 𝜇 2
𝜆 𝐻 Φ † Φ− 𝜇 𝐻 log 3 𝜆 𝐻 Φ † Φ− 𝜇 𝐻 2 𝜇 2
tree
top loop
𝑊,𝑍 loop
1 4𝜋 𝑔 Φ † Φ 2 log 𝑔 Φ † Φ 𝜇 2
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 Φ † Φ 2 𝑡
1 4𝜋 2 −3 𝑦 𝑡 2 Φ † Φ 2 log 𝑦 𝑡 2 Φ † Φ 𝜇 2
Φ= 𝑣 𝐻 +ℎ

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

14. Slide from Kim’s talk

15. 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.

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

17. Slides from Kawabata’s talk
Kawabata, Shimizu, YS, Yokoya

20. Result of LO simulation analysis using 𝑙+4-jets mode
S. Kawabata, [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.

21. 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

22. Slide from Kiyo’s talk

23. 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 = +

24. A new vision of loop integral based on Baikov’s method
Baikov rep. of loop integral:
𝑑 𝐷 𝑝 1 ⋯ 𝑑 𝐷 𝑝 𝐿 𝐷 1 𝑛 1 ⋯ 𝐷 𝑁 𝑛 𝑁 = 𝐶 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.

25. 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

27. Slide from Heymes’s talk
Loops&Legs2016

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

29. Slides from Kawabata’s talk
TopWS2015