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◆❡✇ Pr♦❞✉❝t✐♦♥ ▼❡❝❤❛♥✐s♠ ❢♦r ❈♦♠♣♦s✐t❡ ❍✐❣❣s ❛t t❤❡ ▲❍❈

❆❞r✐á♥ ❈❛r♠♦♥❛ ❇❡r♠ú❞❡③

■♥st✐t✉t❡ ❢♦r ❚❤❡♦r❡t✐❝❛❧ P❤②s✐❝s

❖✉t❧✐♥❡

❍✐❣❣s ❛s ❛ ♣s❡✉❞♦✲●♦❧❞st♦♥❡ ❜♦s♦♥ ▲✐❣❤t ❝✉st♦❞✐❛♥s ❚✇♦✲s✐t❡ ♠♦❞❡❧ ◆❡✇ ❝♦♠♣♦s✐t❡ ❍✐❣❣s ♣r♦❞✉❝t✐♦♥ ♠❡❝❤❛♥✐s♠ ❈♦♥❝❧✉s✐♦♥s

❍✐❣❣s ❞✐s❝♦✈❡r②

❈▼❙ ❛♥❞ ❆❚▲❆❙ ❤❛✈❡ ♦❜s❡r✈❡❞ ❛ ✶✷✻ ●❡❱ ❜♦s♦♥ ■s ✐t t❤❡ ❍✐❣❣s ❜♦s♦♥❄ ■s ✐t ❛ ❢✉♥❞❛♠❡♥t❛❧ s❝❛❧❛r ❧✐❦❡ ✐♥ t❤❡ ❙▼❄ ■♥ t❤❛t ❝❛s❡ t❤❡r❡ ✐s ❛ ❤✐❡r❛r❝❤② ♣r♦❜❧❡♠

✁

❤ =

✁

t t ❤ +

✁

❤ ❤ ❤ +

✁

❤ ❤ ❲ /❩ + . . . δ♠✷

❍ =

• ✷▼✷

❲ + ▼✷ ❩ + ♠✷ ❍ − ✹♠✷ t

✸●❋Λ✷ ✶✻ √ ✷π✷ ❖♥❡ ✐♥t❡r❡st✐♥❣ ♣♦ss✐❜✐❧✐t② ✐s t❤❛t t❤❡ ❍✐❣❣s ✐s ❝♦♠♣♦s✐t❡✱ t❤❡ r❡♠♥❛♥t ♦❢ s♦♠❡ ♥❡✇ str♦♥❣ ❞②♥❛♠✐❝s

❬❑❛♣❧❛♥✱ ●❡♦r❣✐ ✬✽✺❪

❈♦♠♣♦s✐t❡ ♣s❡✉❞♦✲●♦❧❞st♦♥❡ ❜♦s♦♥s

■t ✐s ♣❛rt✐❝✉❧❛r❧② ❝♦♠♣❡❧❧✐♥❣ ✇❤❡♥ t❤❡ ❍✐❣❣s ✐s t❤❡ P●❇ ♦❢ s♦♠❡ ♥❡✇ str♦♥❣ ✐♥t❡r❛❝t✐♦♥✳ ❙♦♠❡t❤✐♥❣ ❧✐❦❡ ♣✐♦♥s ✐♥ ◗❈❉✳

CFT

L = L❈❋❚ − ✶ ✹❋ α

µν❋ µνα + ❆α µ❏µα + ϕ · Oϕ,

α = ❛, ¯ ❛,

✁

πˆ

❛

πˆ

❛

ϕ +

✁

πˆ

❛

πˆ

❛

❆❛

µ, ❆¯ ❛ µ

♠✷

π = ♠✷ ❍ ∼

❣ ✷

❡❧

✶✻π✷ Λ✷

❆❞❙✴❈❋❚ ❝♦rr❡s♣♦♥❞❛♥❝❡

▼♦❞❡❧s ✇✐t❤ ✇❛r♣❡❞ ❡①tr❛ ❞✐♠❡♥s✐♦♥s ❛r❡ ✇❡❛❦❧② ❝♦✉♣❧❡❞ ❞✉❛❧s t♦ str♦♥❣❧② ❝♦✉♣❧❡❞ ✹❉ ❝♦♥❢♦r♠❛❧ t❤❡♦r✐❡s

❬▼❛❧❞❛❝❡♥❛ ✬✾✽❪

❆ˆ

❛ µ(−, −)

❚ ˆ

❛ ∈ ❆❧❣{●/(❍✵ ∪ ❍✶)}

▼♦❞❡❧ ♦❢ ❣❛✉❣❡✲❍✐❣❣s ✉♥✐✜❝❛t✐♦♥ ❆(✵)ˆ

❛ ✺

∼ ❍ˆ

❛

❚❤❡ ❍✐❣❣s ✐s ♠❛ss❧❡ss ❛t tr❡❡✲❧❡✈❡❧ ❞✉❡ t♦ t❤❡ ✺❉ ❣❛✉❣❡ s②♠♠❡tr②✱ ✐ts ♠❛ss ❛r✐s❡s r❛❞✐❛t✐✈❡❧② ❛t ♦♥❡✲❧♦♦♣✳ ❚❤❡s❡ ❝♦rr❡❝t✐♦♥s ❛r❡ ✜♥✐t❡ ❛♥❞ ❯❱ ✐♥s❡♥s✐t✐✈❡✳

▼✐♥✐♠❛❧ ❈♦♠♣♦s✐t❡ ❍✐❣❣s ▼♦❞❡❧

❲❡ ❝❤♦♦s❡ ● = ❙❖(✺) ⊗ ❯(✶)❳ ❚❤❡ ♠✐♥✐♠❛❧ ❣r♦✉♣ t❤❛t ❝♦♥t❛✐♥s t❤❡ ❊❲ ❣r♦✉♣ : ❙❯(✷)▲ × ❯(✶)❨ ⊂ ● ❝♦♥t❛✐♥s t❤❡ ❝✉st♦❞✐❛❧ ❣r♦✉♣ : ❙❯(✷)▲ × ❙❯(✷)❘ ∼ ❙❖(✹) ⊂ ● ❋❡r♠✐♦♥s ❝❛♥ tr❛♥s❢♦r♠ ✐♥ t❤❡ ❢✉♥❞❛♠❡♥t❛❧ ✭▼❈❍▼✺✮ ♦r ✐♥ t❤❡ ❛❞❥♦✐♥t r❡♣r❡s❡♥t❛t✐♦♥ ✭▼❈❍▼✶✵✮

❬❆❣❛s❤❡✱❈♦♥t✐♥♦✱P♦♠❛r♦❧✱ ✬✵✹❪

P❛rt✐❛❧ ❝♦♠♣♦s✐t❡♥❡ss

❋❡r♠✐♦♥ ♠❛ss❡s ❛r❡ ❣✐✈❡♥ ❜② t❤❡ ♦✈❡r❧❛♣s ✇✐t❤ t❤❡ ❍✐❣❣s ❜♦s♦♥✱ ✇❤✐❝❤ ✐s ♣❡❛❦❡❞ t♦✇❛r❞s t❤❡ ■❘ ❜r❛♥❡✳ ❑❑ ❡①❝✐t❛t✐♦♥s ❛r❡ ■❘ ❧♦❝❛❧✐③❡❞ t♦♦

Heavy Fermions Light Fermions

✲ ❚❤❡ t♦♣ q✉❛r❦ ✐s✱ ❞✉❡ t♦ ✐ts ❧❛r❣❡ ♠❛ss✱ t❤❡ ♠♦r❡ ❝♦♠♣♦s✐t❡ ❢❡r♠✐♦♥ ✲ ▲❛r❣❡r r❡♣r❡s❡♥t❛t✐♦♥s r❡q✉✐r❡❞ ❜② ●❍❯ ♠♦❞❡❧s ❝❛♥ ❧❡❛❞ t♦ ♥❡✇ ❧✐❣❤t

r❡s♦♥❛♥❝❡s✱ t❤❡ ❝✉st♦❞✐❛❧ ♣❛rt♥❡rs ♦❢ t❤❡ t♦♣ q✉❛r❦

❚♦♣ ❈✉st♦❞✐❛♥s

❚♦♣ q✉❛r❦ ❛❧s♦ r❡s♣♦♥s✐❜❧❡ ❢♦r tr✐❣❣❡r✐♥❣ t❤❡ ❊❲❙❇ ❱ (❤) ∼ = ✾ ✷

• ❞✹♣

(✷π)✹ ❧♦❣ Π❲ − ✷◆❝

• ❞✹♣

(✷π)✹ ❧♦❣

• ♣✷Πt▲Πt❘ − Π✷

t▲t❘

• ♠❤ ≈
• ◆❝

✷ ②t π ♠∗

q

❢π ✈

❬❈♦♥t✐♥♦✱❞❛ ❘♦❧❞✱P♦♠❛r♦❧✱ ✬✵✻❪

❚♦♣ ❈✉st♦❞✐❛♥s

❚♦♣ q✉❛r❦ ❛❧s♦ r❡s♣♦♥s✐❜❧❡ ❢♦r tr✐❣❣❡r✐♥❣ t❤❡ ❊❲❙❇ ❱ (❤) ∼ = ✾ ✷

• ❞✹♣

(✷π)✹ ❧♦❣ Π❲ − ✷◆❝

• ❞✹♣

(✷π)✹ ❧♦❣

• ♣✷Πt▲Πt❘ − Π✷

t▲t❘

• ♠❤ ≈
• ◆❝

✷ ②t π ♠∗

q

❢π ✈ ▲✐❣❤t r❡s♦♥❛♥❝❡s ❛t t❤❡ r❡❛❝❤ ♦❢ t❤❡ ▲❍❈✦

❬❈♦♥t✐♥♦✱❞❛ ❘♦❧❞✱P♦♠❛r♦❧✱ ✬✵✻❪

❚❛✉ ❈✉st♦❞✐❛♥s

❲❤❛t ❛❜♦✉t ❧❡♣t♦♥s❄

✲ ▲♦♦❦✐♥❣ ❛t t❤❡ ❧❡♣t♦♥ ♠❛ss❡s ✇❡ ✇♦✉❧❞ s❛② t❤❛t ❧❡♣t♦♥s ❛r❡ ♠♦st❧②

❡❧❡♠❡♥t❛r②

✲ ❍♦✇❡✈❡r✱ ✐t ✇❛s s❤♦✇♥ t❤❛t ✐t ✐s ♥♦ ♥❡❝❡ss❛r② t❤❡ ❝❛s❡ ✇❤❡♥ ✇❡ tr② t♦

❡①♣❧❛✐♥ t❤❡ ♥♦♥✲❤✐❡r❛r❝❤✐❝❛❧ ♠✐①✐♥❣ ❛♥❣❧❡s ✐♥ ❆✹ ♠♦❞❡❧s

It has to be A4 symmetric

■♥ ❆✹ ♠♦❞❡❧s t❛✉ ❝❛♥ ❜❡ ♠♦r❡ ❝♦♠♣♦s✐t❡ t❤❛♥ ❡①♣❡❝t❡❞ ⇒ τ✲❝✉st♦❞✐❛♥s

❬❞❡❧ ➪❣✉✐❧❛✱❈❛r♠♦♥❛✱❙❛♥t✐❛❣♦✱ ❛r❳✐✈✿✶✵✵✶✳✺✶✺✶❪

❚❛✉ ❈✉st♦❞✐❛♥s

ζτ = ντ[+−] ˜ ❡τ[+−] ❡τ[+−]

• ❨τ[+−]
• ⊕ ❡′

τ[−−],

❝τ ∼ ✵.✺ ❚❤❡ ❜✐❞♦✉❜❧❡t ❤❛s✱ ❢♦r ❝τ ∼ ✵.✺✱ ❛♥ ✉❧tr❛✲❧✐❣❤t ❑❑ ♠♦❞❡ ✇✐t❤ ❛❧♠♦st ❞❡❣❡♥❡r❛t❡ ❧❡♣t♦♥s ❊✶, ❊✷, ❨ ❛♥❞ ◆✱ ✇✐t❤ ♠❛ss❡s ∼ ✵.✺ ❚❡❱ ❛♥❞ ❧❛r❣❡ ❝♦✉♣❧✐♥❣s t♦ τ

❬❞❡❧ ➪❣✉✐❧❛✱ ❙❛♥t✐❛❣♦✱ ✬✵✷❪ ❬❆tr❡✱ ❈❛r❡♥❛✱ ❍❛♥✱ ❙❛♥t✐❛❣♦✱ ✬✵✽❪

❲❡ st✉❞✐❡❞ ♣❛✐r ♣r♦❞✉❝t✐♦♥ ♦❢ τ ❝✉st♦❞✐❛♥s ❛t t❤❡ ▲❍❈ ✇✐t❤

✲ ❛❧❧ ❧❡♣t♦♥✐❝ τ✬s ✭❢✉❧❧②

❝♦❧❧✐♠❛t❡❞✮

✲ ♦♥❡ ❧❡♣t♦♥✐❝ ❩

♣♣ → ¯ ττ❩❩/❲ /❍ → ❧+❧−❧′+❧′′−❥❥ ❊ ❚

10 100 1000 10000 200 300 400 500 600 700 800 L (fb-1) M (GeV)

❬❞❡❧ ➪❣✉✐❧❛✱❈❛r♠♦♥❛✱❙❛♥t✐❛❣♦✱ ❛r❳✐✈✿✶✵✵✼✳✹✷✵✻ ❪

❚❛✉ ❈✉st♦❞✐❛♥s

❖r✐❣✐♥❛❧❧② ❝♦♥s✐❞❡r❡❞ ✐♥ ▼❈❍▼✺ ❬❞❡❧ ➪❣✉✐❧❛✱❆❈✱❙❛♥t✐❛❣♦✱ ❛r❳✐✈✿✶✵✵✼✳✹✷✵✻❪ ▲(✵)

✶▲,❘ =

• ◆(✵)

▲,❘

❊ (✵)

✶▲,❘

• ∼ (✷)− ✶

✷

▲(✵)

✷▲,❘ =

• ❊ (✵)

✷▲,❘

❨ (✵)

▲,❘

• ∼ (✷)− ✸

✷

✈❨ (−✶) =   ❝✷

❘♠τ

✵ s❘❝❘♠τ ✵ ✵ ✵ s❘❝❘♠❊✷ ✵ s✷

❘♠❊✷

  ❚❤❡② ❧❡❛❞ t♦

✲ ❙✉♣♣r❡ss✐♦♥ ♦❢ ❍ → τ ¯

τ

✲ ❙✉♣♣r❡ss✐♦♥ ♦❢ ❍ → γγ

❝✷

❘❆✶/✷(ττ) + s✷ ❘❆✶/✷(τ❊✷) ≈ ❝✷ ❘❆✶/✷(ττ) + s✷ ❘

❚❤❡② ❛r❡ ❛❧s♦ ♣r❡s❡♥t ✐♥ ▼❈❍▼✶✵ ❬❆❈✱ ●♦❡rt③✱ ■♥ ♣r❡♣❛r❛t✐♦♥❪ ✇✐t❤ ❛ q✉✐t❡ ❞✐✛❡r❡♥t ♣❤❡♥♦♠❡♥♦❧♦❣② ❙t❛② t✉♥❡❞✦

❚✇♦✲s✐t❡ ♠♦❞❡❧

❙✐♠♣❧✐❢❡❞ ♠♦❞❡❧ ✉s❡❢✉❧ ❢♦r ❝♦❧❧✐❞❡r ♣❤❡♥♦♠❡♥♦❧♦❣②

Elementary Sector Composite Sector

SM fermions + Gauge fields Bound states + Higgs

Linear Couplings

✲ ❋✉❧❧② ❝♦♠♣♦s✐t❡ ❍✐❣❣s ✲ ▲✐♥❡❛r ❝♦✉♣❧✐♥❣s ♦❢ t❤❡ ❡❧❡♠❡♥t❛r② s❡❝t♦r t♦ ❝♦♠♣♦s✐t❡ ♦♣❡r❛t♦rs

¯ q▲✐ ❉q▲ + ¯ t❘✐ ❉t❘ + ❚r{ ¯ Q

• ✐

❉∗ − ¯ ♠◗

• Q} + ¯

˜ ❚

• ✐

❉∗ − ¯ ♠❚ ˜ ❚ −λ▲¯ q▲◗❘ − λ❘ ¯ ˜ ❚▲t❘ − ❨∗❯❚r{ ¯ QH} ˜ ❚

❬❈♦♥t✐♥♦✱❑r❛♠❡✱❙♦♥✱❙✉♥❞r✉♠✱ ✵✻❪

❚✇♦✲s✐t❡ ▼❈❍▼✺

❲❡ ❝♦♥s✐❞❡r ♦♥❡ ✺ = (✷, ✷) ⊕ ✶ ♣❡r ❢❛♠✐❧② Q(✐) = (✸, ✷, ✷)✷/✸ =

• ❚ (✐)

❚ (✐)

✺/✸

❇(✐) ❚ (✐)

✷/✸

• ˜

❚ (✐) = (✸, ✶, ✶)✷/✸ ❚❤❡ ♠❛ss❡s ♦❢ t❤❡ ❧✐❣❤t q✉❛r❦s ❛r❡ ❣✐✈❡♥ ❜② t❤❡ ♠✐①✐♥❣ ✇✐t❤ t❤❡ str♦♥❣ s❡❝t♦r ♠✉(✐) ≈ ✈ √ ✷ ❨∗❯ s✐♥ φ(✐)

q s✐♥ φ(✐) ✉

♠❞(✐) ≈ ✈ √ ✷ ❨∗❉ s✐♥ φ(✐)

✷ s✐♥ φ(✐) ❞

❚❤❡r❡ ❛r❡ ♠❛ss✐✈❡ ❡①❝✐t❛t✐♦♥s ♦❢ t❤❡ ❙▼ ❣❛✉❣❡ ❜♦s♦♥s✱ ✐♥ ♣❛rt✐❝✉❧❛r ❛ ❝♦❧♦r ♦❝t❡t r❡s♦♥❛♥❝❡ − ✶ ✹❣ ✷

❡❧

❣µν❣ µν − ✶ ✹❣ ✷

∗

• µν● µν + ✶

✷ ¯ ♠✷

• ❣ ✷

∗

(❣µ − ●µ)✷ ✇✐t❤ t❤❡ ❙▼ ◗❈❉ ❝♦✉♣❧✐♥❣ ❣✸ = ❣∗ s✐♥ θ✸

❚✇♦✲s✐t❡ ▼❈❍▼✺

✁

ψ ¯ ψ

• ❣✸
• s✷

φψ ❝♦t θ✸ − ❝✷ φψ t❛♥ θ✸

• ✁

ψ ¯ Ψ

• ❣✸

sφψ❝φψ s✐♥ θ✸ ❝♦s θ✸

✁

Ψ ¯ Ψ

• ❣✸
• ❝✷

φψ ❝♦t θ✸ − s✷ φψ t❛♥ θ✸

• 10

100 1000 10000 500 1000 1500 2000 2500 3000 ΓG [GeV] MG [GeV] Anarchy MFV 0.001 0.01 0.1 1 500 1000 1500 2000 2500 3000 BR MG [GeV] BR(G → qq) BR(G → Qq) BR(G → QQ)

Too large width!!

MQ=MG/2

◆❡✇ ❈♦♠♣♦s✐t❡ ❍✐❣❣s ♣r♦❞✉❝t✐♦♥ ♠❡❝❤❛♥✐s♠

❚❤❡ ❈♦♠♣♦s✐t❡ ❍✐❣❣s ❝❛♥ ❜❡ ♣r♦❞✉❝❡❞ t❤r♦✉❣❤ ❛ ❝♦❧♦r ♦❝t❡t r❡s♦♥❛♥❝❡ ❧❡❛❞✐♥❣ t♦ s✐♥❣❧❡ ♣r♦❞✉❝t✐♦♥ ♦❢ t❤❡ ♥❡✇ q✉❛r❦ r❡s♦♥❛♥❝❡s

MFV

❚❤❡ ✜♥❛❧ st❛t❡ ✐s ❍¯ tt ♦r ❍❥❥ ✭❥✉st ✐♥ ▼❋❱✮ ▼◗ = ▼●/✷, s✉ = ✵.✻, ❣∗ ✸ = ❨∗ = ✸, s✷ = ✵.✶ ❆♥❛r❝❤② s(✶)

✉

≪ s(✷)

✉

≪ s(✸)

✉

≈ ✶ ▼❋❱ s(✶)

✉

= s(✷)

✉

= s(✸)

✉

≈ ✶ ❯s❡ ▼❛❞●r❛♣❤ ✭s✐❣♥❛❧✮✱ ❆❧♣❣❡♥ ✭t¯ t, t¯ t❜¯ ❜, ❲ , ❩, ❲❲ , . . . , + ❥❡ts✮✱ P②t❤✐❛ ❛♥❞ ❉❡❧♣❤❡s

❛r❳✐✈✿✶✷✵✺✳✷✸✼✽

❍✐❣❣s ❝♦✉♣❧✐♥❣s ✐♥ ▼❈❍▼✺

❲❤❡♥ t❤❡ ❝♦♠♣♦s✐t❡ st❛t❡s ❛r❡ ❤❡❛✈② ❡♥♦✉❣❤

✲ t❤❡ str✉❝t✉r❡ ♦❢ t❤❡ ❝♦s❡t ❙❖(✺)/❙❖(✹)

❛♥❞

✲ t❤❡ ❢❡r♠✐♦♥ q✉❛♥t✉♠ ♥✉♠❜❡rs

✜① t❤❡ ❍✐❣❣s ❝♦✉♣❧✐♥❣s ✇✐t❤ t❤❡ ❙▼ ✐♥ t❡r♠s ♦❢ ξ = ✈ ✷ ❢ ✷

π

❘❍❱❱ ≡ ❣❍❱❱ ❣ ❙▼

❍❱❱

=

• ✶ − ξ

❘❍✛ ≡ ❣❍✛ ❣ ❙▼

❍✛

= ✶ − ✷ξ √✶ − ξ Γ(❍ → γγ) = (❘❍✛ ■γ + ❘❍❱❱ ❏γ)✷ (■γ + ❏γ)✷ Γ❙▼(❍ → γγ)

❊①♣❡r✐♠❡♥t❛❧ ❝♦♥str❛✐♥ts

✲ ❍✐❣❣s s❡❛r❝❤❡s

✵ ≤ ξ ≤ ✵.✹ ξ = ✈ ✷/❢ ✷

π

❢♦r ♠❍ = ✶✷✺ ●❡❱

✲ ❱❡❝t♦r✲❧✐❦❡ q✉❛r❦ s❡❛r❝❤❡s ✭▼❋❱✮

❣ ✷❝❲ ˜ κ✉❯ ✈ ♠❯ ❩µ¯ ✉❘γµ❯❘ + ❣ √ ✷ ˜ κ✉❉ ✈ ♠❉ ❲ +

µ ¯

✉❘γµ❉❘ + ❤.❝.,

1 2 3 4 5 6 7 0.4 0.5 0.6 0.7 0.8 0.9 ˜ κ2

uQ

sin φuR ˜ κ2

uU

˜ κ2

uD

˜ κ2

uU (95% CL)

˜ κ2

uD (95% CL)

❊①♣❡r✐♠❡♥t❛❧ ❝♦♥str❛✐♥ts

✲ ❚♦♣✲❛♥t✐t♦♣ r❡s♦♥❛♥❝❡ s❡❛r❝❤❡s✳ ❚r❛❞✐t✐♦♥❛❧❧② ❝♦♥s✐❞❡r❡❞ t❤❡ ❣♦❧❞❡♥

❝❤❛♥♥❡❧ ❢♦r ● ❜✉t ✐t ❝❛♥ ❝❤❛♥❣❡

• ✐❢ t❤❡ t♦♣ q✉❛r❦ ✐s ♥♦t ❢✉❧❧② ❝♦♠♣♦s✐t❡
• ✐❢ ♦t❤❡r q✉❛r❦s ❝❛♥ ❜❡ ❛s ❝♦♠♣♦s✐t❡ ❛s t❤❡ t♦♣
• ✐❢ ♥❡✇ ❞❡❝❛② ❝❤❛♥♥❡❧s ✐♥✈♦❧✈✐♥❣ ❢❡r♠✐♦♥ ❝♦♠♣♦s✐t❡ st❛t❡s ❛r❡ ♦♣❡♥

✲ ❉✐✲❥❡t s❡❛r❝❤❡s

• ❈♦♥t❛❝t ✐♥t❡r❛❝t✐♦♥s
• ❆

µ

• ❣q▲¯

q▲γµ❚ ❆q▲ + ❣✉❘ ¯ ✉❘γµ❚ ❆✉❘ + ❣❞❘ ¯ ❞❘γµ❚ ❆❞❘] ⇒ L = ❝(✶)

✉✉

▼✷ O(✶)

✉✉ + ❝(✶) ❞❞

▼✷ O(✶)

❞❞ + ❝(✽) ✉❞

▼✷ O(✽)

✉❞ + ❝(✽) qq

▼✷ O(✽)

qq + ❝(✽) q✉

▼✷ O(✽)

q✉ +

❝(✽)

q❞

▼✷ O(✽)

q❞

• ❉✐r❡❝t s❡❛r❝❤❡s

❍t¯ t

❙✐♥❣❧❡ ♣r♦❞✉❝t✐♦♥ ♦❢ t♦♣ ♣❛rt♥❡rs tr♦✉❣❤ s−❝❤❛♥♥❡❧ ❡①❝❤❛♥❣❡ ♦❢ ● ♣♣ → ● → ❚¯ t + ¯ ❚t → ❍t¯ t ❙tr❛t❡❣②

✲ ❯s❡ t❤❡ ❧❡❛❞✐♥❣ ❍ → ❜¯

❜ ❞❡❝❛② ❛♥❞ s❡♠✐❧❡♣t♦♥✐❝ t♦♣ ❞❡❝❛②s ❍¯ tt → ✹❜ + ✷❥ + ❧ + ❊ ❚

✲ ❯s❡ ❜✲t❛❣s ❛♥❞ ❙❚ ❛s ♠❛✐♥ ❞✐s❝r✐♠✐♥❛t✐♥❣ ✈❛r✐❛❜❧❡s

❙❚ ≡

♥❥

• ❥=✶

♣❚(❥) +

♥❧

• ❧=✶

♣❚(❧) + ❊ ❚

✲ ❯s❡ ❜♦♦st❡❞ t♦♣ ❛♥❞ ❍✐❣❣s t❡❝❤♥✐q✉❡s ❢♦r ❧❛r❣❡r ♠❛ss❡s

❍t¯ t ❝✉ts

▲♦✇ ❡♥❡r❣② ♣❤❛s❡✿

✲ ❆t ❧❡❛st ✹ ❥❡ts✱ ♦❢ ✇❤✐❝❤ ❛t ❧❡❛st ✸ ♠✉st ❜❡ t❛❣❣❡❞ ❛s ❜✲❥❡ts ✲ ❆t ❧❡❛st ✶ ✐s♦❧❛t❡❞ ❝❤❛r❣❡❞ ❧❡♣t♦♥ ✲ ❆ ❝✉t ♦♥ ❙❚ ✭✐♥ t❤✐s ❝❛s❡ ✇❡ ❤❛✈❡ ♥❥ = ✹ ❛♥❞ ♥❧ = ✶✮ t❤❛t ❞❡♣❡♥❞s ♦♥

t❤❡ t❡st ▼● ✇❡ ❛r❡ ❝♦♥s✐❞❡r✐♥❣ ❙❚ > ✵.✾, ✶.✶, ✶.✺ ❚❡❱ ❢♦r ▼● = ✶.✺, ✷, ✷.✺ ❚❡❱ ❍✐❣❤ ❡♥❡r❣② ♣❤❛s❡✿

✲ ❆t ❧❡❛st ✸ ❥❡ts✱ ✇✐t❤ ❛ ♠✐♥✐♠✉♠ ♦❢ ✷ ❜ t❛❣s ✲ ❆t ❧❡❛st ✶ ✐s♦❧❛t❡❞ ❝❤❛r❣❡❞ ❧❡♣t♦♥ ✲ ❚✇♦ ❤❛r❞❡st ❥❡ts r❡q✉✐r❡❞ t♦ ❤❛✈❡ ✐♥✈❛r✐❛♥t ♠❛ss❡s ❝❧♦s❡ t♦ t❤❡ t♦♣ ❛♥❞

❍✐❣❣s ♠❛ss✱ |♠❥✶ − ♠t| ≤ ✹✵ ●❡❱ ❛♥❞ |♠❥✷ − ♠❍| ≤ ✹✵ ●❡❱

✲ ❆ ❝✉t ♦♥ ❙❚ t❤❛t ❞❡♣❡♥❞s ♦♥ t❤❡ t❡st ▼● ✇❡ ❛r❡ ❝♦♥s✐❞❡r✐♥❣

❙❚ > ✶.✷, ✶.✺, ✶.✼, ✷ ❚❡❱ ❢♦r ▼● = ✷, ✷.✺, ✸, ≥ ✸.✺ ❚❡❱

❍t¯ t r❡s✉❧ts

▼❋❱

MG [TeV] su 1.6 1.8 2 2.2 2.4 2.6 2.8 3 0.4 0.5 0.6 0.7 0.8 0.9 Dijets (contact) Single Q 1 20 20 t t Dijets (res.) 5 1 5 8 TeV Htt MFV MG [TeV] g*3 1.6 1.8 2 2.2 2.4 2.6 2.8 3 2 2.5 3 3.5 4 4.5 5 Dijets (contact) Single Q 1 1 5 tt Dijets (res.) 20 5 20 8 TeV Htt MFV

❍t¯ t r❡s✉❧ts

▼❋❱

MG [TeV] su 3 3.5 4 4.5 5 0.4 0.5 0.6 0.7 0.8 0.9 D i j e t s ( c

• n

t a c t ) 1 5 100 100 30 30 5 14 TeV Htt MFV MG [TeV] g*3 3 3.5 4 4.5 5 2 2.5 3 3.5 4 4.5 5 Dijets (contact) 1 5 5 100 30 100 30 14 TeV Htt MFV

❍t¯ t r❡s✉❧ts

❆♥❛r❝❤②

MG [TeV] su 1.6 1.8 2 2.2 2.4 2.6 2.8 3 0.4 0.5 0.6 0.7 0.8 0.9 Dijets (contact) 1 5 20 t t 20 5 1 8 TeV Htt Anarchy MG [TeV] g*3 1.6 1.8 2 2.2 2.4 2.6 2.8 3 2 2.5 3 3.5 4 4.5 5 Dijets (contact) 1 5 1 Dijets (res.) 5 20 20 8 TeV Htt Anarchy

❍t¯ t r❡s✉❧ts

❆♥❛r❝❤②

MG [TeV] su 3 3.5 4 4.5 5 0.4 0.5 0.6 0.7 0.8 0.9 30 5 5 30 100 100 14 TeV Htt Anarchy MG [TeV] g*3 3 3.5 4 4.5 5 2 2.5 3 3.5 4 4.5 5 Dijets (contact) 1 5 5 30 30 100 100 14 TeV Htt Anarchy

❍❥❥

❙✐♥❣❧❡ ♣r♦❞✉❝t✐♦♥ ♦❢ ✉♣ ♣❛rt♥❡rs tr♦✉❣❤ s ❛♥❞ t−❝❤❛♥♥❡❧ ❡①❝❤❛♥❣❡ ♦❢ ● ♣♣ → ● → ❯¯ ✉ + ¯ ❯✉ → ❍✉¯ ✉ → ✷❥ + ✷❧ + ❊ ❚

✲ ❚♦ ❛✈♦✐❞ ❜❡ s✇❛♠♣❡❞ ❜② ❜❛❝❦❣r♦✉♥❞ ✇❡ ✐♠♣♦s❡ ❍ → ❲ ∗❲ ✱ ✇✐t❤

❇❘(❍ → ❲ ∗❲ ) = ✵.✸✸ ✐♥ ♦✉r ❜❡♥❝❤♠❛r❦ ♠♦❞❡❧

✲ ❉✉❡ t♦ t❤❡ r❡❧❛t✐✈❡❧② ❧♦✇ ❝r♦ss s❡❝t✐♦♥s ❛♥❞ t❤❡ ❤✉❣❡ ❲ + ❥ ❜❛❝❦❣r♦✉♥❞

✇❡ ❧♦♦❦ ✐♥ t❤❡ ❞✐❧❡♣t♦♥ ❝❤❛♥♥❡❧

✲ ❏✉st √s = ✶✹ ❚❡❱

❍❥❥ ❝✉ts

✲ ❆t ❧❡❛st ✷ ❛♥❞ ♥♦ ♠♦r❡ t❤❛♥ ✻ ❥❡ts ✲ ❊①❛❝t❧② ✷ ❝❤❛r❣❡❞ ❧❡♣t♦♥s✱ ❜♦t❤ ✇✐t❤

♣❚(❧) ≥ ✺✵ ●❡❱ ❛♥❞ |∆φ(❧✶, ❧✷)| ≤ ✵.✺

✲ ❆ ✈❡t♦ ♦♥ ❜✲t❛❣❣❡❞ ❥❡ts ✭♥♦ ❥❡t s❤♦✉❧❞ ❜❡ t❛❣❣❡❞ ❛s ❛ ❜✲❥❡t✮✳ ✲ ❆ ❝✉t ♦♥ t❤❡ t✇♦ ❤❛r❞❡st ❥❡ts

♣❚(❥✶) > ✹✵✵ ●❡❱ ♣❚(❥✷) > ✷✵✵ ●❡❱

✲ ❆ ❝✉t ♦♥ t❤❡ ✐♥✈❛r✐❛♥t ♠❛ss ♦❢ t❤❡ t✇♦ ❝❤❛r❣❡❞ ❧❡♣t♦♥s

✶✺ ●❡❱ ≤ ♠❧❧ ≤ ✼✵ ●❡❱

✲ ❆ ❝✉t ♦♥ t❤❡ tr❛♥s✈❡rs❡ ♠❛ss ♦❢ t❤❡ ❍✐❣❣s ❞❡❝❛② ♣r♦❞✉❝ts

♠❚(❧, ❧, ❊ ❚) < ✶✷✵ ●❡❱

✲ ❆ ❝✉t ♦♥ ❙❚ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ t❡st ▼●

❙❚ > ✶.✺, ✷.✶ , ✷.✸ ❚❡❱ ❢♦r ▼● = ✷, ✷.✺, ≥ ✸ ❚❡❱

❍❥❥ r❡s✉❧ts

MG [TeV] su 1.5 2 2.5 3 3.5 0.4 0.5 0.6 0.7 0.8 0.9 Dijets (contact) tt 5 100 30 30 100 D i j e t s ( r e s . ) Single Q 14 TeV Hjj MFV MG [TeV] g*3 1.5 2 2.5 3 3.5 2 2.5 3 3.5 4 4.5 5 Dijets (contact) tt D i j e t s ( r e s . ) Single Q 5 30 100 30 100 1 5 14 TeV Hjj MFV

❈♦♥❝❧✉s✐♦♥s

✲ ❈♦♠♣♦s✐t❡ ❍✐❣❣s ✐s ❛ ♥✐❝❡ ❡①❛♠♣❧❡ ♦❢ ❇❙▼ s♦❧✈✐♥❣ t❤❡ ❤✐❡r❛r❝❤② ♣r♦❜❧❡♠ ✲ ❚❤❡r❡ ❛r❡ ♥❡✇ ❧✐❣❤t ❡①❝✐t❛t✐♦♥s ❝♦✉♣❧✐♥❣ ♠♦st❧② t♦ t❤❡ ❘❍ t♦♣ ✲ ■t ❝❛♥ ❤❛♣♣❡♥ ❛❧s♦ ✐♥ t❤❡ ❧❡♣t♦♥ s❡❝t♦r ✭τ ❝✉st♦❞✐❛♥s✮ ✲ ❚❤❡ str♦♥❣ s❡❝t♦r ❝❛♥ ❜❡ ♣r♦❜❡❞ t❤r♦✉❣❤ ❍✐❣❣s ♣r♦❞✉❝t✐♦♥ ♠❡❞✐❛t❡❞ ❜②

❝♦❧♦r ♦❝t❡t ❛♥❞ ❢❡r♠✐♦♥ r❡s♦♥❛♥❝❡s

❇❛❝❦✉♣ ❙❧✐❞❡s

Pr♦❞✉❝t✐♦♥ ❝r♦ss s❡❝t✐♦♥s

0.0001 0.001 0.01 0.1 1 1.5 2 2.5 3 3.5 4 4.5 5 σ(pp → G → Ht¯ t) [pb] MG[TeV] 7 TeV 8 TeV 14 TeV 0.0001 0.001 0.01 0.1 1 1.5 2 2.5 3 3.5 4 4.5 5 σ(pp → G → H jj) [pb] MG[TeV] 7 TeV 8 TeV 14 TeV

❙♦♠❡ ♥✉♠❜❡rs

Pr♦❝❡ss ▲❍❈✼ ▲❍❈✽ ▲❍❈✶✹ σ ❬♣❜❪ σ ❬♣❜❪ σ ❬♣❜❪ ❍t¯ t ✭▼● = ✷ ❚❡❱✱ ▼❋❱✮ ✵✳✵✷✶✸ ✵✳✵✹✶✹ ✵✳✸✺✽ ❍t¯ t ✭▼● = ✸ ❚❡❱✱ ▼❋❱✮ ✵✳✵✵✵✹✼✽ ✵✳✵✵✶✹✷ ✵✳✵✸✸✷ ❍t¯ t ✭▼● = ✸ ❚❡❱✱ ❆♥❛r❝❤②✮ ✵✳✵✵✶✸ ✵✳✵✵✸✼ ✵✳✵✽✹ ❍❥❥ ✭▼● = ✷ ❚❡❱✱ ▼❋❱✮ ✵✳✵✹ ✵✳✵✼ ✵✳✹✹ t¯ t✰✵✲✹ ❥❡ts ✭s❡♠✐❧❡♣t♦♥✐❝✰❧❡♣t♦♥✐❝✮ ✹✼✳✾ ✼✵✳✹✼ ✷✻✽✳✺✺ t¯ t❜¯ ❜ ✵✳✵✾ ✵✳✶✺ ✵✳✽✺ ❩✰✶✲✹ ❥❡ts ✭❧❡♣t♦♥✐❝✮ ✺✸✵✳✺ ✻✹✶ ✶✹✷✸ ❲❲ ✰ ✵✲✷ ❥❡ts ✭s❡♠✐❧❡♣t♦♥✐❝✰❧❡♣t♦♥✐❝✮ ✶✺ ✷✷✳✻ ✹✾ ❲ ✰✶✲✷ ❥❡ts ✭♣❚ > ✶✺✵ ●❡❱✱ ❧❡♣t♦♥✐❝✮ − − ✽✹✳✾ ❲ ✰✶✲✹ ❥❡ts ✭❧❡♣t♦♥✐❝✮ ✺✶✸✸ ✻✹✽✾ −

❉❡t❛✐❧s ♦♥ t❤❡ ❛♥❛❧②s✐s

■♥ ♦✉r ❛♥❛❧②s❡s ✇❡ ❞❡✜♥❡

✲ ❥❡ts ✇✐t❤ ❛ ❝♦♥❡ s✐③❡ ∆❘ = ✵.✼✱ ♣❚(❥) > ✸✵ ●❡❱ ❛♥❞ |η❥| < ✺✳ ✲ ✐s♦❧❛t❡❞ ❝❤❛r❣❡❞ ❧❡♣t♦♥s ✭❡ ♦r µ✮ ✇❤❡♥ ♣❚(❧) > ✷✵ ●❡❱ ❛♥❞ |η❧| < ✷.✺

❲❡ ❤❛✈❡ ❛ss✉♠❡❞ ❛ ❜✲t❛❣❣✐♥❣ ❡✣❝✐❡♥❝② ♦❢ ✵✳✼ ✐♥ ♦✉r ❛♥❛❧②s❡s✳ ❋✐♥❛❧❧②✱ ✇❡ ✉s❡ ❛s ❞✐s❝r✐♠✐♥❛t✐♥❣ ✈❛r✐❛❜❧❡ ❙❚ ≡

♥❥

• ❥=✶

♣❚(❥) +

♥❧

• ❧=✶

♣❚(❧) + ❊ ❚ ✇❤❡r❡ ♥❥,❧ ✐s t❤❡ r❡❧❡✈❛♥t ♥✉♠❜❡r ♦❢ ❥❡ts ♦r ❧❡♣t♦♥s✳

• ✐✈❡♥ ❛ ♥✉♠❜❡r ♦❢ s✐❣♥❛❧ ✭s✮ ❛♥❞ ❜❛❝❦❣r♦✉♥❞ ✭❜✮ ❡✈❡♥ts ❛❢t❡r t❤❡

❝♦rr❡s♣♦♥❞✐♥❣ ❝✉ts✱ ✇❡ ❝♦♠♣✉t❡ t❤❡ st❛t✐st✐❝❛❧ s✐❣♥✐✜❝❛♥❝❡ ♦❢ t❤❡ s✐❣♥❛❧ ❢r♦♠ S(s, ❜) =

• ✷ ×
• (s + ❜) ❧♥
• ✶ + s

❜

• − s

▼♦❞❡❧s ✇✐t❤ ❲❛r♣❡❞ ❊①tr❛ ❉✐♠❡♥s✐♦♥s

❍✐❡r❛r❝❤② Pr♦❜❧❡♠

■♥ ❲❊❉✱ t❤❡ ❢✉♥❞❛♠❡♥t❛❧ s❝❛❧❡ ♦❢ t❤❡ t❤❡♦r② O(▼P❧) ✐s r❡❞s❤✐❢t❡❞ ❜② t❤❡ ✇❛r♣ ❢❛❝t♦r t♦ ❛ ❢❡✇ ❚❡❱ ♦♥ t❤❡ ■❘ ❜r❛♥❡✱ ✇❤❡r❡ t❤❡ ❍✐❣❣s ✐s ❧♦❝❛❧✐③❡❞

❬❘❛♥❞❛❧❧✱ ❙✉♥❞r✉♠ ✬✾✾❪

❋❡r♠✐♦♥s ❛♥❞ ❣❛✉❣❡ ❜♦s♦♥s ❝❛♥ ♣r♦♣❛❣❛t❡ ✐♥ t❤❡ ❜✉❧❦

❇✉❧❦ ❋❡r♠✐♦♥s

❚❤❡ s♠❛❧❧❡st ✐rr❡♣ ♦❢ t❤❡ ✺❉ ❈❧✐✛♦r❞ ❛❧❣❡❜r❛ {Γ▼, Γ◆} = ✷❣ ▼◆ ▼, ◆ = µ, ✺ ✐s ❢♦✉r✲❞✐♠❡♥s✐♦♥❛❧ Γ✺ = ±Γ✵Γ✶Γ✷Γ✸ ⇒ ¯ Γ ∝ ✶ ✶✳ ✺❉ ❢❡r♠✐♦♥s ψ(①, ③) ❛r❡ ✈❡❝t♦r✲❧✐❦❡ ❛♥❞ ❛ ❜✉❧❦ ♠❛ss ❝ = ▼❘ ✐s ❛❧❧♦✇❡❞ ✷✳ ❲❡ ❝❛♥ st✐❧❧ ❣❡t ❛ ✹❉ ❝❤✐r❛❧ s♣❡❝tr✉♠ ψ▲(①, −φ) = ❩ψ▲(①, φ) ❩ ✷ = ✶ ψ▲(①, ❘(′)) = ✵ ∂③ψ▲(①, ❘(′)) = ✵ ❆❢t❡r ❑❛❧✉③❛✲❑❧❡✐♥ ❞❡❝♦♠♣♦s✐t✐♦♥✱ ✇❡ ❝❛♥ ❤❛✈❡ ❛ ❝❤✐r❛❧ ♠❛ss❧❡ss st❛t❡ ψ▲(①, ③) = ❢ (✵)

▲

(③)ψ(✵)

▲ (①) + ∞

• ♥=✶

❢ (♥)

▲

(③)ψ(♥)

▲ (①)

❇✉❧❦ ❋❡r♠✐♦♥s

✲ ■t t✉r♥s ♦✉t t❤❛t ✇❡ ❝❛♥ ❡①♣❧❛✐♥ t❤❡ ❤✉❣❡ ❤✐❡r❛r❝❤② ❡①✐st✐♥❣ ❜❡t✇❡❡♥ t❤❡

❞✐✛❡r❡♥t ❢❡r♠✐♦♥ ♠❛ss❡s (♠✉,❞)✐❥ ∼ ✈ √ ✷ ❨∗❢ q

✐ ❢ ✉,❞ ❥

✲ ❲❡ ♦❜t❛✐♥ ♥❛t✉r❛❧❧② ❛❧s♦ ❛ ❤✐❡r❛r❝❤✐❝❛❧ ♠✐①✐♥❣ ✐♥ t❤❡ q✉❛r❦ s❡❝t♦r

• ❯✉,❞

▲

• ✐❥

∼ ❢ q

✐ /❢ q ❥

• ❯✉,❞

❘

• ✐❥ ∼ ❢ ✉,❞

✐

/❢ ✉,❞

❥

✐ ≤ ❥

❋❧❛✈♦r

❉✐✛❡r❡♥t ❢❡r♠✐♦♥ ❧♦❝❛❧✐③❛t✐♦♥s ❧❡❛❞ t♦ ❢❛♠✐❧② ❞❡♣❡♥❞❡♥t ❝♦✉♣❧✐♥❣s t♦ ♠❛ss✐✈❡ ❑❑ ❣❛✉❣❡ ❜♦s♦♥s✱ ✇❤✐❝❤ ❛r❡ ■❘ ❧♦❝❛❧✐③❡❞ ❣ (✶)

α

≈ ❣✺❉❘−✶/✷

• −✶

▲ + ❢ ✷

αγ(❝α)

• ▲ = ❧♦❣ ❘/❘′ ≈ ✸✺

γ(❝α) ∼ O(✶) ❲❡ ❤❛✈❡ ❋❈◆❈ ❜♦t❤ ✐♥ t❤❡ q✉❛r❦ ❛♥❞ ✐♥ t❤❡ ❧❡♣t♦♥ s❡❝t♦r ❘❙✲●■▼ ▼❡❝❤❛♥✐s♠ ❖✛✲❞✐❛❣♦♥❛❧ ❝♦✉♣❧✐♥❣s ❛r❡ s✉♣♣r❡ss❡❞ ❜② ❈❑▼ ❡♥tr✐❡s ❛♥❞ ❜② r❛t✐♦s ♦❢ ❈❑▼ ♠❛tr✐① ❡❧❡♠❡♥ts ❛♥❞ ♠❛ss❡s✳ ❙t✐❧❧✱ ∆♠❑ ❛♥❞ ǫ❑ ✐♠♣♦s❡ s♦♠❡ t✉♥♥✐♥❣✳

▲❡♣t♦♥ ▼❛ss❡s ❛♥❞ ▼✐①✐♥❣s

✲ ❋❡r♠✐♦♥ s♣❧✐tt✐♥❣ s❡❡♠s t♦ ♥❛t✉r❛❧❧② ❧❡❛❞ t♦ ❤✐❡r❛r❝❤✐❝❛❧ ♠❛ss❡s ❛♥❞ ♠✐①✐♥❣

❛♥❣❧❡s✱ ❛s t❤❡ ♦♥❡s ♦❜s❡r✈❡❞ ✐♥ t❤❡ q✉❛r❦ s❡❝t♦r

✲ ❍♦✇❡✈❡r✱ ✉♥❧✐❦❡ t❤❡ q✉❛r❦ ❝❛s❡✱ ❧❡♣t♦♥ ♠✐①✐♥❣ ❛♥❣❧❡s ❛r❡ ♥♦t ❤✐❡r❛r❝❤✐❝❛❧✳

❆ ❣♦♦❞ st❛rt✐♥❣ ♣♦✐♥t ✐s t❤❡ tr✐✲❜✐♠❛①✐♠❛❧ ♠✐①✐♥❣ |❯P▼◆❙| ∼ |❯❚❇▼| =  

• ✷/✸
• ✶/✸

✵

• ✶/✻
• ✶/✸
• ✶/✷
• ✶/✻
• ✶/✸
• ✶/✷

 

✲ ❉❡s♣✐t❡ t❤❡ ❘❙✲●■▼ ♠❡❝❤❛♥✐s♠✱ ✢❛✈♦r ❝♦♥str❛✐♥ts ❛r❡ q✉✐t❡ str✐❝t

❖♥❡ ♣♦ss✐❜❧❡ s♦❧✉t✐♦♥ ✐s t♦ ❛ss✉♠❡ ❛ ❞✐s❝r❡t❡ s②♠♠❡tr② ❛❝t✐♥❣ ♦♥ t❤✐s s❡❝t♦r

❆✹ ❙②♠♠❡tr②

❆✹ ✐s t❤❡ t❤❡ ❣r♦✉♣ ♦❢ ❡✈❡♥ ♣❡r♠✉t❛t✐♦♥s ♦❢ ❢♦✉r ❡❧❡♠❡♥ts✳ ❲❡ ❝❛♥ ✉s❡ t✇♦ ❣❡♥❡r❛t♦rs✱ ❙ ❛♥❞ ❚✱ s❛t✐s❢②✐♥❣ ❙✷ = ❚ ✸ = (❙❚)✸ = ✶ ■t ❤❛s ✸ ✐♥❡q✉✐✈❛❧❡♥t ♦♥❡✲❞✐♠❡♥s✐♦♥❛❧ r❡♣r❡s❡♥t❛t✐♦♥s ✶ : ❙ = ✶, ❚ = ✶, ✶′ : ❙ = ✶, ❚ = ❡✐✷π/✸ = ω, ✶′′ : ❙ = ✶, ❚ = ❡✐✹π/✸ = ω✷, ❛♥❞ ♦♥❡ t❤r❡❡✲❞✐♠❡♥s✐♦♥❛❧ ✐rr❡❞✉❝✐❜❧❡ r❡♣r❡s❡♥t❛t✐♦♥✱ ✸ ✸ ⊗ ✸ = ✸✶ ⊕ ✸✷ ⊕ ✶ ⊕ ✶′ ⊕ ✶′′ ❚❤❡r❡ ❛r❡ t✇♦ ✐♠♣♦rt❛♥t s✉❜❣r♦✉♣s✿ ❩✷ ∼ = {✶, ❙} ⊂ ❆✹ ❩✸ ∼ =

• ✶, ❚, ❚ ✷

⊂ ❆✹

❚❛✉ ❝✉st♦❞✐❛♥ ❛♥❛❧②s✐s

❲❡ ❛r❡ ✐♥t❡r❡st❡❞ ✐♥ t❤❡ ❢♦❧❧♦✇✐♥❣ s✐❣♥❛t✉r❡ ❛t ▲❍❈ ✇✐t❤ √s = ✶✹ ❚❡❱ ♣♣ → ❧+❧−❧′+❧′′−❥❥ ❊ ❚ ✇✐t❤ ❧, ❧′, ❧′′ = ❡, µ ❚❤❡ ❜❛❝❦❣r♦✉♥❞ ✇❡ ❤❛✈❡ ❝♦♥s✐❞❡r❡❞ ❛r❡ ❩t¯ t + ♥ ❥❡ts σ = ✸✾.✻ ❢❜, ❩❜¯ ❜ + ♥ ❥❡ts σ = ✺.✽✺ ♣❜, ❩❩ + ♥ ❥❡ts σ = ✷.✸✺ ♣❜, ❩❲ + ♥ ❥❡ts σ = ✶.✼✻ ♣❜, t¯ t + ♥ ❥❡ts σ = ✺✺ ♣❜, ❩❲❲ + ♥ ❥❡ts σ = ✶.✾ ❢❜, ✇✐t❤ ♦♥❡ ❩ ❛♥❞ ❜♦t❤ t♦♣s ❞❡❝❛②✐♥❣ ❧❡♣t♦♥✐❝❛❧❧②✳

✲ ❙✐❣♥❛❧ ❣❡♥❡r❛t❡❞ ✇✐t❤ ▼❛❞●r❛♣❤✴▼❛❞❊✈❡♥t ✈✹ ❛♥❞ τ ❞❡❝❛②❡❞ ✇✐t❤ ❚❛✉♦❧❛ ✲ ❇❛❝❦❣r♦✉♥❞ ❡✈❡♥ts ❣❡♥❡r❛t❡❞ ✇✐t❤ ❆❧♣❣❡♥ ✈✷✳✶✸ ✲ ■♥ ❜♦t❤ ❝❛s❡s✱ ✇❡ ❤❛✈❡ ✉s❡❞ P②t❤✐❛ ❢♦r ❤❛❞r♦♥✐③❛t✐♦♥ ❛♥❞ s❤♦✇❡r✐♥❣ ❛♥❞

P●❙✹ ❢♦r ❞❡t❡❝t♦r s✐♠✉❧❛t✐♦♥

❚❛✉ ❝✉st♦❞✐❛♥s r❡s✉❧ts

✶✹ ❚❡❱ ▼ = ✷✵✵ ●❡❱ ▼ = ✹✵✵ ●❡❱ ❩t¯ t ❩❩ ❇❛s✐❝ ✵✳✽✺ ✵✳✶✹ ✵✳✹✾ ✵✳✹✹ ▲❡♣t♦♥s ✵✳✻✽ ✵✳✶✶ ✵✳✹✶ ✵✳✹✶ ▼❥❥ ✵✳✹✾ ✵✳✵✻✸ ✵✳✶✺ ✵✳✶✸ ❚❛✉ r❡❝✳ ✵✳✹✷ ✵✳✵✺✼ ✵✳✵✸✾ ✵✳✵✺✷ P❛✐r ♣r♦❞✳ ✵✳✸✾ ✵✳✵✹✺ ✵✳✵✶✼ ✵✳✵✸✷ ▼❛ss r❡❝✳ ✵✳✸✼ ✵✳✵✹✶ ✵✳✵✵✽

• ✵✳✵✵✶✻

✵✳✵✶✻

• ✵✳✵✵✶✽

✲ ❇❛s✐❝ ❝✉ts ♣❚(❧) ≥ ✶✵ ●❡❱, ♣❚(❥) ≥ ✷✵ ●❡❱,

✚

❊ ❚ ≥ ✷✵ ●❡❱, |η❧| ≤ ✷.✺, |η❥| ≤ ✺, ∆❘❥❥ ≥ ✵.✺ ∆❘❥❧ ≥ ✵.✺ ✲ ▲❡♣t♦♥s |▼❧+❧− − ▼❩| ≤ ✶✵ ●❡❱ ❛♥❞ ❝♦s(φ❧′+❧′′−) ≥ −✵.✾✺ ✲ ▼❥❥ ✺✵ ●❡❱ ≤ ▼❥❥ ≤ ✶✺✵ ●❡❱ ✲ ❚❛✉ r❡❝♦♥str✉❝t✐♦♥ ❲❡ ❛ss✉♠❡ ❢✉❧❧② ❝♦❧❧✐♠❛t✐♦♥ ✲ P❛✐r ♣r♦❞✉❝t✐♦♥ |▼▲✶ − ▼▲✷| ≤ ✺✵ ●❡❱ ✲ ▼❛ss r❡❝♦♥str✉❝t✐♦♥ |▼τ❧+❧− − ▼t❡st

▲

| ≤ ✺✵ ●❡❱