◆❡✇ 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 � ✸ ● ❋ Λ ✷ � δ ♠ ✷ ✷ ▼ ✷ ❲ + ▼ ✷ ❩ + ♠ ✷ ❍ − ✹ ♠ ✷ ❍ = √ t ✷ 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 ❈❋❚ − ✶ µν ❋ µνα + ❆ α µ ❏ µα + ϕ · O ϕ , ✹ ❋ α α = ❛ , ¯ ❛ , ❆ ❛ ❛ µ , ❆ ¯ ϕ µ ✁ ✁ ❣ ✷ ♠ ✷ π = ♠ ✷ ✶✻ π ✷ Λ ✷ ❡❧ ❍ ∼ + π ˆ ❛ π ˆ ❛ π ˆ ❛ π ˆ ❛
❆❞❙✴❈❋❚ ❝♦rr❡s♣♦♥❞❛♥❝❡ ▼♦❞❡❧s ✇✐t❤ ✇❛r♣❡❞ ❡①tr❛ ❞✐♠❡♥s✐♦♥s ❛r❡ ✇❡❛❦❧② ❝♦✉♣❧❡❞ ❞✉❛❧s t♦ str♦♥❣❧② ❝♦✉♣❧❡❞ ✹❉ ❝♦♥❢♦r♠❛❧ t❤❡♦r✐❡s ❬▼❛❧❞❛❝❡♥❛ ✬✾✽❪ ❛ ∈ ❆❧❣ { ● / ( ❍ ✵ ∪ ❍ ✶ ) } ❛ ❆ ˆ ❚ ˆ µ ( − , − ) ▼♦❞❡❧ ♦❢ ❣❛✉❣❡✲❍✐❣❣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❤❡✱❈♦♥t✐♥♦✱P♦♠❛r♦❧✱ ✬✵✹❪ ❲❡ ❝❤♦♦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✐♦♥ ✭ ▼❈❍▼ ✶✵ ✮
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 ❬❈♦♥t✐♥♦✱❞❛ ❘♦❧❞✱P♦♠❛r♦❧✱ ✬✵✻❪ ❚♦♣ q✉❛r❦ ❛❧s♦ r❡s♣♦♥s✐❜❧❡ ❢♦r tr✐❣❣❡r✐♥❣ t❤❡ ❊❲❙❇ � � ❞ ✹ ♣ ❞ ✹ ♣ � � = ✾ ❱ ( ❤ ) ∼ ♣ ✷ Π t ▲ Π t ❘ − Π ✷ ( ✷ π ) ✹ ❧♦❣ Π ❲ − ✷ ◆ ❝ ( ✷ π ) ✹ ❧♦❣ t ▲ t ❘ ✷ � ♠ ∗ ◆ ❝ ② t q ♠ ❤ ≈ ✈ ✷ π ❢ π
❚♦♣ ❈✉st♦❞✐❛♥s ❬❈♦♥t✐♥♦✱❞❛ ❘♦❧❞✱P♦♠❛r♦❧✱ ✬✵✻❪ ❚♦♣ q✉❛r❦ ❛❧s♦ r❡s♣♦♥s✐❜❧❡ ❢♦r tr✐❣❣❡r✐♥❣ t❤❡ ❊❲❙❇ � � ❞ ✹ ♣ ❞ ✹ ♣ � � = ✾ ❱ ( ❤ ) ∼ ♣ ✷ Π t ▲ Π t ❘ − Π ✷ ( ✷ π ) ✹ ❧♦❣ Π ❲ − ✷ ◆ ❝ ( ✷ π ) ✹ ❧♦❣ t ▲ t ❘ ✷ � ♠ ∗ ◆ ❝ ② t q ♠ ❤ ≈ ✈ ✷ π ❢ π ▲✐❣❤t r❡s♦♥❛♥❝❡s ❛t t❤❡ r❡❛❝❤ ♦❢ t❤❡ ▲❍❈✦
❚❛✉ ❈✉st♦❞✐❛♥s ❬❞❡❧ ➪❣✉✐❧❛✱❈❛r♠♦♥❛✱❙❛♥t✐❛❣♦✱ ❛r❳✐✈✿✶✵✵✶✳✺✶✺✶ ❪ ❲❤❛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
❚❛✉ ❈✉st♦❞✐❛♥s ❬❞❡❧ ➪❣✉✐❧❛✱❈❛r♠♦♥❛✱❙❛♥t✐❛❣♦✱ ❛r❳✐✈✿✶✵✵✼✳✹✷✵✻ ❪ � ν τ [+ − ] � ˜ ❡ τ [+ − ] ⊕ ❡ ′ ζ 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✐♦♥ ♦❢ 10000 τ ❝✉st♦❞✐❛♥s ❛t t❤❡ ▲❍❈ ✇✐t❤ ✲ ❛❧❧ ❧❡♣t♦♥✐❝ τ ✬s ✭❢✉❧❧② 1000 ❝♦❧❧✐♠❛t❡❞✮ L (fb -1 ) ✲ ♦♥❡ ❧❡♣t♦♥✐❝ ❩ 100 ♣♣ → ¯ ττ ❩❩ / ❲ / ❍ → ❧ + ❧ − ❧ ′ + ❧ ′′− ❥❥ � ❊ ❚ 10 200 300 400 500 600 700 800 M (GeV)
❚❛✉ ❈✉st♦❞✐❛♥s ❖r✐❣✐♥❛❧❧② ❝♦♥s✐❞❡r❡❞ ✐♥ ▼❈❍▼ ✺ ❬❞❡❧ ➪❣✉✐❧❛✱❆❈✱❙❛♥t✐❛❣♦✱ ❛r❳✐✈✿✶✵✵✼✳✹✷✵✻❪ � � � � ◆ ( ✵ ) ❊ ( ✵ ) ▲ ( ✵ ) ▲ ( ✵ ) ▲ , ❘ ✷ ▲ , ❘ ✶ ▲ , ❘ = ∼ ( ✷ ) − ✶ ✷ ▲ , ❘ = ∼ ( ✷ ) − ✸ ❊ ( ✵ ) ❨ ( ✵ ) ✷ ✷ ✶ ▲ , ❘ ▲ , ❘ ❝ ✷ ❘ ♠ τ ✵ s ❘ ❝ ❘ ♠ τ ✈❨ ( − ✶ ) = ✵ ✵ ✵ s ✷ s ❘ ❝ ❘ ♠ ❊ ✷ ✵ ❘ ♠ ❊ ✷ ❚❤❡② ❧❡❛❞ t♦ ✲ ❙✉♣♣r❡ss✐♦♥ ♦❢ ❍ → τ ¯ τ ✲ ❙✉♣♣r❡ss✐♦♥ ♦❢ ❍ → γγ ❝ ✷ ❘ ❆ ✶ / ✷ ( τ τ ) + s ✷ ❘ ❆ ✶ / ✷ ( τ ❊ ✷ ) ≈ ❝ ✷ ❘ ❆ ✶ / ✷ ( τ τ ) + s ✷ ❘ ❚❤❡② ❛r❡ ❛❧s♦ ♣r❡s❡♥t ✐♥ ▼❈❍▼ ✶✵ ❬❆❈✱ ●♦❡rt③✱ ■♥ ♣r❡♣❛r❛t✐♦♥❪ ✇✐t❤ ❛ q✉✐t❡ ❞✐✛❡r❡♥t ♣❤❡♥♦♠❡♥♦❧♦❣② ❙t❛② t✉♥❡❞✦
❚✇♦✲s✐t❡ ♠♦❞❡❧ ❬❈♦♥t✐♥♦✱❑r❛♠❡✱❙♦♥✱❙✉♥❞r✉♠✱ ✵✻ ❪ ❙✐♠♣❧✐❢❡❞ ♠♦❞❡❧ ✉s❡❢✉❧ ❢♦r ❝♦❧❧✐❞❡r ♣❤❡♥♦♠❡♥♦❧♦❣② Composite Elementary Linear Sector Sector Couplings SM fermions + Bound states + Gauge fields Higgs ✲ ❋✉❧❧② ❝♦♠♣♦s✐t❡ ❍✐❣❣s ✲ ▲✐♥❡❛r ❝♦✉♣❧✐♥❣s ♦❢ t❤❡ ❡❧❡♠❡♥t❛r② s❡❝t♦r t♦ ❝♦♠♣♦s✐t❡ ♦♣❡r❛t♦rs � � � � ˜ Q} + ¯ ˜ ❉t ❘ + ❚r { ¯ q ▲ ✐ � ❉q ▲ + ¯ t ❘ ✐ � ✐ � ✐ � ¯ Q ❉ ∗ − ¯ ♠ ◗ ❚ ❉ ∗ − ¯ ♠ ❚ ❚ q ▲ ◗ ❘ − λ ❘ ¯ ❚ ▲ t ❘ − ❨ ∗ ❯ ❚r { ¯ ˜ QH} ˜ − λ ▲ ¯ ❚
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