O bóson de Higgs no modelo padrão das interações eletrofracas: aspectos fenomenológicos do setor escalar e resultados experimentais

✳

▲❯❈■❆◆❖ ❏❊❋❋❊❘❨

❖ ❜ós♦♥ ❞❡ ❍✐❣❣s ♥♦ ▼♦❞❡❧♦ P❛❞rã♦ ❞❛s ✐♥t❡r❛çõ❡s ❡❧❡tr♦❢r❛❝❛s✿

❆s♣❡❝t♦s ❢❡♥♦♠❡♥♦❧ó❣✐❝♦s ❞♦ s❡t♦r ❡s❝❛❧❛r ❡ r❡s✉❧t❛❞♦s

❡①♣❡r✐♠❡♥t❛✐s

✳

▲❯❈■❆◆❖ ❏❊❋❋❊❘❨

❖ ❜ós♦♥ ❞❡ ❍✐❣❣s ♥♦ ▼♦❞❡❧♦ P❛❞rã♦ ❞❛s ✐♥t❡r❛çõ❡s ❡❧❡tr♦❢r❛❝❛s✿ ❆s♣❡❝t♦s

❢❡♥♦♠❡♥♦❧ó❣✐❝♦s ❞♦ s❡t♦r ❡s❝❛❧❛r ❡ r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s

❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ à ❋❛❝✉❧❞❛❞❡ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞♦ ❈❛♠♣✉s ❞❡ ●✉❛r❛t✐♥❣✉❡tá✱ ❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ P❛✉❧✐s✲ t❛✱ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ♠❡str❡ ❡♠ ❋ís✐❝❛✳

✳

❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❋❡r♥❛♥❞♦ ▲✉✐s ❞❡ ❈❛♠♣♦s ❝❛r✈❛❧❤♦

❉❆❉❖❙ ❈❯❘❘■❈❯▲❆❘❊❙

▲❯❈■❆◆❖ ❏❊❋❋❊❘❨

◆❆❙❈■▼❊◆❚❖ ✸✵✳✵✽✳✶✾✼✽ ✴ P■❘❆❏❯✲❙P

❋■▲■❆➬➹❖ ❏♦sé ❆♣❛r❡❝✐❞♦ ❏❡✛❡r②

❇❡♥❡❞✐t❛ ❙❛❧✈✐❛♥❛ ❞♦s ❙❛♥t♦s ❏❡✛❡r②

✷✵✵✷ ✴ ✷✵✵✻ ❈✉rs♦ ❞❡ ●r❛❞✉❛çã♦ ❡♠ ▲✐❝❡♥❝✐❛t✉r❛ ❡♠ ▼❛t❡♠át✐❝❛ ♥❛ ❋❛❝✉❧❞❛❞❡ ❞❡ ❋✐❧♦s♦✜❛✱ ❈✐ê♥❝✐❛ ❡ ▲❡tr❛s ❞❡ ❏❛❝❛r❡③✐♥❤♦ ❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ ❞❡ ▲♦♥❞r✐♥❛ ✲ ❯❊▲✱ ❏❛❝❛r❡③✐♥❤♦✲P❘

✷✵✵✽ ✴ ✲ ❈✉rs♦ ●r❛❞✉❛çã♦ ❡♠ ❇❛❝❤❛r❡❧❛❞♦ ❡♥ ❋ís✐❝❛ ❡♠ ❛♥❞❛♠❡♥t♦ ♥❛ ❋❛❝✉❧❞❛❞❡ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞♦ ❈❛♠♣✉s ❞❡ ●✉❛r❛t✐♥❣✉❡tá

❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ P❛✉❧✐st❛ ✲ ❯◆❊❙P✱ ●✉❛r❛t✐♥❣✉❡tá✲❙P

❆●❘❆❉❊❈■▼❊◆❚❖❙

❆❣r❛❞❡ç♦ ✐♥✐❝✐❛❧♠❡♥t❡ ❛ ❉❡✉s✳ ❖❢❡r❡ç♦ ❛ ♠✐♥❤❛ ♠❛✐s ♣r♦❢✉♥❞❛ ❣r❛t✐❞ã♦ àq✉❡❧❡s q✉❡ ♠❡ ❛♣♦✐❛r❛♠ ❡ ✐♥❝❡♥t✐✈❛r❛♠ ♥❡st❛ ❞✐ss❡rt❛çã♦✱ ❡♠ ❡s♣❡❝✐❛❧✿

• ➚ ♠✐♥❤❛ ❢❛♠í❧✐❛✿ ❡s♣❡❝✐❛❧♠❡♥t❡ ❛♦s ♠❡✉s ♣❛✐s ❏♦sé ❡ ❇❡♥❡❞✐t❛✳

• ❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✿ ❋❡r♥❛♥❞♦ ▲✳ ❞❡ ❈✳ ❈❛r✈❛❤♦✱ q✉❡♠ r❡✢❡t✐♥❞♦ ❛ s✉❛ ❛❧t❛ ❢♦r♠❛çã♦ ❛❝❛❞ê♠✐❝❛✱ ♠❡ ❞á ❛s ♣❛✉t❛s ♣❛r❛ ❛ ♠✐♥❤❛✳

• Pr♦❢✳ ❘♦❜❡rt♦ ❨s✉♠✐ ❍♦♥❞❛ ♣❡❧♦ ✐♥❝❡♥t✐✈♦ ❡♠ ♠✐♥❤❛ ❢♦r♠❛çã♦ ❛❝❛❞ê♠✐❝❛ ❡ ♣❡❧❛ ❛♠✐③❛❞❡ q✉❡ ♠❡ ❛❧✐♠❡♥t❛ ❝♦♠ ❝❡rt❡③❛s ❡ ❢♦rç❛✳

• Pr♦❢✳ ❈❛r❧♦s ❆♠♦r✐♥ ❈❛❧❞❡✐r❛ ♣❡❧❛ ❛♠✐③❛❞❡ ❡ ✐♥❝❡♥t✐✈♦ í♠♣❛r ❡♠ ♠✐♥❤❛ ❢♦r♠❛çã♦ ❛❝❛❞ê♠✐❝❛✳

❖s ✜❧ós♦❢♦s s❡ ❧✐♠✐t❛r❛♠ ❛ ✐♥t❡r♣r❡t❛r ♦ ♠✉♥❞♦ ❞❡ ❞✐✈❡rs❛s ♠❛♥❡✐r❛s❀ ♦ q✉❡

❏❊❋❋❊❘❨✱ ▲✳ ❖ ❜ós♦♥ ❞❡ ❍✐❣❣s ♥♦ ♠♦❞❡❧♦ ♣❛❞rã♦ ❞❛s ✐♥t❡r❛çõ❡s ❡❧❡tr♦❢r❛❝❛s✿ ❆s♣❡❝t♦s ❢❡♥♦♠❡♥♦❧ó❣✐❝♦s ❞♦ s❡t♦r ❡s❝❛❧❛r ❡ r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s✳ ✷✵✶✺✳ ✶✶✷ ❢✳ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ✲ ❋❛❝✉❧❞❛❞❡ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞♦ ❈❛♠♣✉s ❞❡ ●✉❛r❛t✐♥❣✉❡tá✱ ❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ P❛✉❧✐st❛✱ ●✉❛r❛t✐♥❣✉❡tá✱ ✷✵✶✺✳

❘❡s✉♠♦

❖ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ é ❡st✉❞❛r ♦s ❛s♣❡❝t♦s ❣❡r❛✐s ❞♦ s❡t♦r ❡s❝❛❧❛r ❞♦ ▼♦❞❡❧♦ P❛✲ ❞rã♦✱ ❛ ♣❛rt✐r ♣r✐♥❝í♣✐♦ ❞❡ ❣❛✉❣❡✱ q✉❡ ❞á ❝♦♥s✐stê♥❝✐❛ t❡ór✐❝❛ à ❢♦r♠✉❧❛çã♦ ❞♦ ▼♦❞❡❧♦ ❊❧❡tr♦❢r❛❝♦✱ ❛ss✐♠ ❝♦♠♦ ❛ q✉❡❜r❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐♠❡tr✐❛ ❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❍✐❣❣s q✉❡ sã♦ ❢✉♥❞❛♠❡♥t❛✐s ♥♦ ❝♦♥t❡①t♦ ❞♦ ♠♦❞❡❧♦ ♣❛r❛ ❛ ❣❡r❛çã♦ ❞❡ ♠❛ss❛ ❞❛s ♣❛rtí❝✉❧❛s ❡❧❡♠❡♥t❛r❡s ❡✱ t❡♠ ❝♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛ ♦ s✉r❣✐♠❡♥t♦ ❞❡ ✉♠❛ ♥♦✈❛ ♣❛rtí❝✉❧❛ ❡s❝❛❧❛r ♠❛ss✐✈❛✱ ♦ ❜ós♦♥ ❞❡ ❍✐❣❣s ❞♦ ▼♦❞❡❧♦ P❛❞rã♦✱ ❝✉❥❛ ♠❛ss❛ ♥ã♦ ❡stá ❞❡✜♥✐❞❛ ♥♦ ♠♦❞❡❧♦✳ ❆♣r❡s❡♥t❛♠♦s ✉♠ ❡st✉❞♦ ❞♦s ♣r✐♥❝✐♣❛✐s ♠♦❞♦s ❞❡ ♣r♦❞✉çã♦ ❡ ❞❡❝❛✐♠❡♥t♦ ❞♦ ❜ós♦♥ ❞❡ ❍✐❣❣s ❜❡♠ ❝♦♠♦ ❛ s✉❛ ❜✉s❝❛ ❡♠ ❛❝❡❧❡r❛❞♦r❡s✳ ❆♣r❡s❡♥t❛♠♦s ✉♠ ❝♦♥❥✉♥t♦ ❞❡ r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s q✉❡ ❢♦r❛♠ ♣✉❜❧✐❝❛❞♦s ❛♦ ❧♦♥❣♦ ❞♦s ❛♥♦s ♥❛s ♣r✐♥❝✐♣❛✐s ❝♦❧❛❜♦r❛çõ❡s ❝♦♠♦ ▲❊P✱ ❚❡✈❛tr♦♥ ❡ ▲❍❈✱ q✉❡ ❝♦♥tr✐❜✉✐r❛♠ ♥❛ ❧♦♥❣❛ tr❛❥❡tór✐❛ ❞❛ ❜✉s❝❛✱ ❛té s✉❛ ✐❞❡♥t✐✜❝❛çã♦ ❡♠ ✷✵✶✷✳

❏❊❋❋❊❘❨✱ ▲✳ ❊❧❡❝tr♦✇❡❛❦ ❙t❛♥❞❛r❞ ▼♦❞❡❧ ❍✐❣❣s ❜♦s♦♥✿ ♣❤❡♥♦♠❡♥♦❧♦❣✐❝❛❧ ❛♥❞ ❡①♣❡r✐♠❡♥t❛❧ r❡s✉❧ts✳ ✷✵✶✺✳ ✶✶✷ ❢✳ ▼❛st❡r ✭P❤②s✐❝s✮ ✲ ❋❛❝✉❧❞❛❞❡ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞♦ ❈❛♠♣✉s ❞❡ ●✉❛r❛t✐♥❣✉❡tá✱ ❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ P❛✉❧✐st❛✱ ●✉❛r❛t✐♥❣✉❡tá✱ ✷✵✶✺✳

❆❜str❛❝t

❚❤❡ ♦❜❥❡❝t✐✈❡ ♦❢ t❤✐s ✇♦r❦ ✐s t♦ st✉❞② t❤❡ ❣❡♥❡r❛❧ ❛s♣❡❝ts ♦❢ t❤❡ s❝❛❧❡ s❡❝t♦r ♦❢ t❤❡ ❙t❛♥✲ ❞❛r❞ ▼♦❞❡❧ t❤❡ ♣r✐♥❝✐♣❧❡ ♦❢ ❣❛✉❣❡✱ ✇❤✐❝❤ ❣✐✈❡s t❤❡♦r❡t✐❝❛❧ ❝♦♥s✐st❡♥❝② t♦ t❤❡ ❡❧❡❝tr♦✇❡❛❦ ♠♦❞❡❧ ❢♦r♠✉❧❛t✐♦♥✱ ❛s ✇❡❧❧ ❛s s♣♦♥t❛♥❡♦✉s s②♠♠❡tr② ❜r❡❛❦✐♥❣ ❛♥❞ t❤❡ ❍✐❣❣s ♠❡❝❤❛♥✐s♠✱ t❤❛t ❛r❡ ❢✉♥❞❛♠❡♥t❛❧ ❢♦r t❤❡ ♠❛ss ❣❡♥❡r❛t✐♦♥ ♦❢ t❤❡ ❡❧❡♠❡♥t❛r② ♣❛rt✐❝❧❡s✱ ❛♥❞ ❣✐✈❡s r✐s❡ t♦ ❛ ♥❡✇ ♠❛ss✐✈❡ ♣❛rt✐❝❧❡ s❝❛❧❡✱ t❤❡ ❍✐❣❣s ❜♦s♦♥ ♦❢ ✇❤♦s❡ ✈❛❧✉❡ ✐s ♥♦t ❞❡✜♥❡❞ ✐♥ t❤❡ ♠♦❞❡❧✳ ❲❡ ♣r❡s❡♥t ❛ st✉❞② ♦❢ t❤❡ ♠❛❥♦r ♠♦❞❡s ♦❢ ♣r♦❞✉❝t✐♦♥ ❛♥❞ ❞❡❝❛② ♦❢ ❍✐❣❣s ❜♦s♦♥ ❛s ✇❡❧❧ ❛s s❡❛r❝❤ ♦❢ s✉❝❤ ♣❛rt✐❝❧❡ ✐♥ ❛❝❝❡❧❡r❛t♦rs✳ ❲❡ ♣r❡s❡♥t ❛ s❡t ♦❢ ❡①♣❡r✐♠❡♥t❛❧ r❡s✉❧ts t❤❛t ❤❛✈❡ ❜❡❡♥ ♣✉❜❧✐s❤❡❞ ♦✈❡r t❤❡ ②❡❛rs ✐♥ t❤❡ ♠❛❥♦r ❝♦❧❧❛❜♦r❛t✐♦♥s ❛s ▲❊P✱ ❚❡✈❛tr♦♥ ❛♥❞ ▲❍❈✱ ✇❤✐❝❤ ❝♦♥tr✐❜✉t❡❞ ✐♥ t❤❡ ❧♦♥❣ ❤✐st♦r② ♦❢ t❤❡ ❍✐❣❣s ❜♦s♦♥ s❡❛r❝❤✱ ✉♥t✐❧ ✐ts ✐❞❡♥t✐✜❝❛t✐♦♥ ✐♥ ✷✵✶✷✳

▲✐st❛ ❞❡ ❋✐❣✉r❛s

✶ P♦t❡♥❝✐❛❧ ❡s❝❛❧❛r✳ ❛✮ P❛r❛ µ2 _{> 0 ❤á ❛♣❡♥❛s ✉♠ ♠í♥✐♠♦ ❡♠ φ = 0✳ ❜✮}

◗✉❛♥❞♦ µ2 _{<0 ❤á ❞♦✐s ♠í♥✐♠♦sφ =±}qµ2

2λ =±v✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣ó❧♦s ♥♦ ♣❧❛♥♦ ❝♦♠♣❧❡①♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸ Pr♦❝❡ss♦ ❞❡ ❛♥✐q✉✐❧❛çã♦ ❡❧étr♦♥✲♣ós✐tr♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹ ❱ért✐❝❡ ❞❡ ✐♥t❡r❛çã♦ ♣❛r❛ ❧é♣t♦♥✲❢ót♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✺ ❱ért✐❝❡ ❞❛ ✐♥t❡r❛çã♦ ❡♥tr❡ ❢ér♠✐♦♥s ❡ ♦ ❜ós♦♥ ✈❡t♦r✐❛❧ ♥❡✉tr♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✻ ❱ért✐❝❡ ❞❛ ✐♥t❡r❛çã♦ ❡♥tr❡ ❢é♠✐♦♥s ❡ ♦s ❜ós♦♥s ❝❛rr❡❣❛❞♦s W✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶

✼ ❱ért✐❝❡ ❡♥tr❡ ❍✐❣❣s✲❢ér♠✐♦♥s ❡ ❍✐❣❣s✲❜ós♦♥s ✈❡t♦r✐❛✐s ✭Z0_{, W✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷}

✽ Pr♦♣❛❣❛❞♦r ♣❛r❛ ♦ ❢ót♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✾ Pr♦♣❛❣❛❞♦r ♣❛r❛ ♦s ❜ós♦♥s ✈❡t♦r✐❛✐s ❞❛ ❢♦rç❛ ❢r❛❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✶✵ Pr♦❝❡ss♦ ❞❡ ♣r♦❞✉çã♦ ❍✐❣❣s✲str❛❤❧✉♥❣✱ ❛ ♣❛rt✐r ❞❛ ❝♦❧✐sã♦ ❡♥tr❡ ❢ér♠✐♦♥s ✳ ✹✸ ✶✶ ❙❡çã♦ ❞❡ ❝❤♦q✉❡ ✈❡rs✉s ❛ ❡♥❡r❣✐❛ ❞♦ ❝❡♥tr♦ ❞❡ ♠❛ss❛ √s❀ s❡çã♦ ❞❡ ❝❤♦q✉❡

✈❡rs✉s ❛ ♠❛ss❛ ❞♦ ❍✐❣❣s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✶✷ Pr♦❝❡ss♦ ❞❡ ♣r♦❞✉çã♦ ❞♦ ❜ós♦♥ ❞❡ ❍✐❣❣s ✈✐❛ ❢✉sã♦ ❞❡ ❜ós♦♥ ✈❡t♦r✐❛✐s✳ ✳ ✳ ✺✶ ✶✸ Pr♦❝❡ss♦ ❞❡ ♣r♦❞✉çã♦ ❞♦ ❜ós♦♥ ❞❡ ❍✐❣❣s✱ ♣❡❧♦s ❝❛♥❛✐sννH¯ ✱e+_e−_{H ❡ ¯ttH✳}

❙❡çã♦ ❞❡ ❝❤♦q✉❡ ✈❡rs✉s ❡♥❡r❣✐❛ ❞❡ ❝❡♥tr♦ ❞❡ ♠❛ss❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✶✹ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❛ ♣r♦❞✉çã♦ ❍✐❣❣s✲str❛❤❧✉♥❣ ❡ ❢✉sã♦ ❞❡ ❜ós♦♥ ✈❡t♦r✐❛✐s✳ ✺✻ ✶✺ ❉❡❝❛✐♠❡♥t♦ ❞♦ ❍✐❣❣s ❡♠ ❢é♠✐♦♥ ❡ ❛♥t✐❢ér♠✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✶✻ ❉❡❝❛✐♠❡♥t♦ ❞♦ ❍✐❣❣s ❡♠ ❞♦✐s ❜ós♦♥s ✈❡t♦r✐❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✶✼ ❉❡❝❛✐♠❡♥t♦ ❞♦ ❜ós♦♥ ❞❡ ❍✐❣❣s ♦✛✲❙❤❡❧❧✿ ❛✮ ❡♠ ✉♠ ❜ós♦♠ ✈❡t♦r✐❛❧W ❡ ✉♠

♣❛r ❞❡ ❢ér♠✐♦♥s✱ ❜✮ ❞❡❝❛✐♠❡♥t♦ ❞♦ ❍✐❣❣s ❡♠ ✹✲❢ér♠✐♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✶✽ ❉❡❝❛✐♠❡♥t♦ ❞♦ ❜ós♦♥ ❞❡ ❍✐❣❣s✿ ❛✮ ✉♠ ❜ós♦♥ ✈❡rt♦r✐❛❧ ❡ ✉♠ ❢ót♦♥✱ ❜✮ ❡♠

❢ót♦♥ ❡ ❢ér♠✐♦♥ ❡ ❛♥t✐❢ér♠✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✶✾ ❉❡❝❛✐♠❡♥t♦ ❞♦ ❜ós♦♥ ❞❡ ❍✐❣❣s ❡♠ ❞♦✐s ❢ót♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✷✵ ▼♦❞♦s ❞❡ ❞❡❝❛✐♠❡♥t♦ ❞♦ ❜ós♦♥ ❞❡ ❍✐❣❣s ❞♦ ▼♦❞❡❧♦ P❛❞rã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✷✶ ❛✮ Pr♦❝❡ss♦ ❞❡ ♣r♦❞✉çã♦ ❞♦ ❜ós♦♥ ❞❡ ❍✐❣❣s✳ ❜✮ ❆❧❣✉♥s ❢✉♥❞♦s q✉❡ ❛♣r❡✲

s❡♥t❛♠ ♦ ♠❡s♠♦ ❡st❛❞♦ ✜♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✷✷ ▼♦♠❡♥t♦ tr❛♥s✈❡rs❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✷✸ Ps❡✉❞♦r❛♣✐❞❡③ ✈❡rs✉s â♥❣✉❧♦ θ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾

✷✹ ❘❡❝♦♥str✉çã♦ ❞♦ ❡✈❡♥t♦ H _→W W(∗)_{+ 2jatos✱ ❍✐❣❣s ♣r♦❞✉③✐❞♦ ✈✐❛qq →} Hqq✳ mjj = 1.5T eV✱ mll = 21GeV✱ mT = 95GeV✳ ◆❛ ✜❣✉r❛ ♦ ❡❧étr♦♥ ❡stá r❡♣r❡s❡♥t❛❞♦ ♣❡❧♦ tr❛ç♦ ✈❡r❞❡ ❡ ♣♦ss✉✐ pT = 51GeV✱ ♦ ♠ú♦♥ ♣❡❧♦ tr❛ç♦ ❧❛r❛♥❥❛✱ ♣♦ss✉✐ pT = 15GeV✱ ♦ ❥❛t♦ ❞❛ ❞✐r❡✐t❛ ✭❝♦♥❡ ❛③✉❧✮ ♣♦ss✉✐

pT = 68GeV✱ ♦ ❥❛t♦ ❞❛ ❡sq✉❡r❞❛ ✭❝♦♥❡ ❛③✉❧✮ t❡♠pT = 42GeV ❡ ♦ ♥❡✉tr✐♥♦ ✭❡♠ ✈❡r♠❡❧❤♦✮ E/T = 33GeV✳ ❊✈❡♥t♦ ♦❜t✐❞♦ ❡♠ ✶✼ ❞❡ ♥♦✈❡♠❜r♦ ❞❡ ✷✵✶✷✳ ✼✵

✶✷

✷✻ ❉✐str✐❜✉✐çã♦ ❞❡ ❡✈❡♥t♦s ❡♠ ❢✉♥çã♦ ❞❡ cosθmax✳ ❛✮ ❞✐str✐❜✉✐çã♦ ❞♦s ❞❛❞♦s✱

♦♥❞❡ ❢♦r❛♠ ❛♣❧✐❝❛❞♦s ♦s ❝r✐tér✐♦s ❞❡ s❡❧❡çã♦ ✭✶✮✱ ✭✷✮✱ ✭✸✮ ❡ ✭✺✮✳ ❜✮ s✐♠✉❧❛çã♦ ❞❡ ♠♦♥t❡ ❝❛r❧♦ ♣❛r❛ H0_{νν¯ ♣❛r❛ ✉♠ ♣♦ssí✈❡❧ ❍✐❣❣s ❝♦♠ ♠❛ss❛ ❞❡ ✺●❡❱✳ ✳ ✳ ✼✷}

✷✼ ◆ú♠❡r♦ ❞❡ ❊✈❡♥t♦s ❊①♣❡r❛❞♦ ❡♠ ❢✉♥çã♦ ❞❛ ♠❛ss❛ ❞♦ ❍✐❣❣s✳ ❚rês ❝❛♥❛✐s ♣❛r❛ ♠❛ss❛ ❞♦ ❍✐❣❣s ❛❝✐♠❛ ❞❡ ✷✶✷▼❡❱ ♣❛r❛ Z0 _{→ H}0_l+_l− _{♦♥❞❡ l}+_l− _→

e+_e−_{, µ}+_µ−_{, τ}+_τ−_❀Z0 _→H0_{νν¯ ❡ Z}0 _{→ H}0_{qq¯ ✳ ❚❛♠❜é♠ ❛ s♦♠❛ t♦t❛❧ ♣❛r❛}

♦s três ❝❛♥❛✐s ❡ ✉♠❛ ❜❛rr❛ ❤♦r✐③♦♥t❛❧ ❞á ♦ ❧✐♠✐t❡ ❝♦♠ ✾✺✪ ❞❡ ♥í✈❡❧ ❞❡ ❝♦♥✜❛♥ç❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✷✽ ❈♦♠❜✐♥❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❝♦♠ ✾✺✪✳ ▲✐♠✐t❡ ❊①♣❡r❛❞♦ ❡♠ ❱❡r♠❡❧❤♦❀ ❧✐✲

♠✐t❡ ❖❜s❡r✈❛❞♦ ♥❛ ❧✐♥❤❛ tr❛❝❡❥❛❞❛ ❡♠ ❛③✉❧❀ ♥❛ ❧✐♥❤❛ tr❛❝❡❥❛❞❛ ❡♠ ♣r❡t♦ t❡♠♦s ♦ ✈❛❧♦r ♣r❡✈✐st♦ ♣❡❧♦ ▼♦❞❡❧♦ P❛❞rã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✷✾ ▲✐♠✐t❡ ❊s♣❡r❛❞♦ ❡ ❖❜s❡r✈❛❞♦ ❝♦♠ ✾✺✪❈✳▲✳ ❆ ❧✐♥❤❛ ❡♠ ❛③✉❧ r❡♣r❡s❡♥t❛ ♦

▼♦❞❡❧♦ P❛❞rã♦✳ ❆ ❧✐♥❤❛ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❊①♣❡r❛❞♦ ❡ ❛ ❧✐♥❤❛ ❝♦♥t✐♥✉❛ ♦ ❧✐♠✐t❡ ❖❜s❡r✈❛❞♦✳ ❆s ❢❛✐①❛s ✈❡r❞❡ ❡ ❛♠❛r❡❧❛ sã♦ ♦s ❞❡s✈✐♦s ❞❡ ✉♠ ❡ ❞♦✐s s✐❣♠❛ ♥❛ ❢❛✐①❛ ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✸✵ ❉✐❛❣r❛♠❛ ❞♦ ♣r♦❝❡ss♦s ❞❡ ♣r♦❞✉çã♦ ❞❡ ❞✐❜ós♦♥✳ ❛✮ ♣r♦❝❡ss♦ W W✱ ❜✮

♣r♦❝❡ss♦ ❲❩✱ ❝✮ ♣r♦❞✉çã♦ ZZ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹

✸✶ ❋✉♥❞♦ ❞❛ ♣r♦❞✉çã♦ ❞❡t¯t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺

✸✷ ❉✐❛❣r❛♠❛ ♣❛r❛ ♦ ♣r♦❝❡ss♦ ❞❡ ♣r♦❞✉çã♦ ❞♦ ❍✐❣❣s ♣♦r ♠❡✐♦ ❞❛ ❢✉sã♦ ❞❡ ❣❧✉♦♥s ✭♣r♦❝❡ss♦ ❛ ✉♠ ❧♦♦♣✮ ❡ ♦ ❞❡❝❛✐♠❡♥t♦ ❞♦ ❜ós♦♥ ❞❡ ❍✐❣❣s ❡♠ ❞♦✐s ❢ót♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✸✸ ❊♥❡r❣✐❛ ❞❡♣♦s✐t❛❞❛ ✭❡♠ ❛♠❛r❡❧♦✮ ♥♦ ❝❛❧♦rí♠❡tr♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦✭✈❡r❞❡✮ ❡

❤❛❞rô♥✐❝♦✭✈❡r♠❡❧❤♦✮✳ P♦❞❡♠♦s ♦❜s❡r✈❛ ♦ r❛str♦ ❞❡✐①❛❞♦ ♣❡❧♦s ❞♦✐s ❝❛♥❞✐✲ ❞❛t♦s ❛ ❢ót♦♥s ♥♦ ❝❛❧♦r✐♠❡tr♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦✳ ❘❡❝♦♥str✉çã♦ ❛ ♣❛rt✐r ❞❡ ❞❛❞♦s ♦❜t✐❞♦s ❡♠ ❡♥❡r❣✐❛ ✽❚❡❱ ♥♦ ❆t❧❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ✸✹ ❉✐str✐❜✉✐çã♦ ♣♦♥❞❡r❛❞❛ ❞♦s ❡✈❡♥t♦s ❡♠ ❢✉♥çã♦ ❞❛ ♠❛ss❛ ❞♦ ♣❛r ❞❡ ❢ót♦♥s✳

◆❡❧❛ ♣♦❞❡♠♦s ♦❜s❡r✈❛r ♦ ♣✐❝♦ ♥❛ r❡❣✐ã♦ ♣❡rt♦ ❞❡ ✶✷✺●❡❱✳ ❊♥❡r❣✐❛ ❞❡ ❝❡♥tr♦ ❞❡ ♠❛ss❛√s ❡ ❧✉♠✐♥♦s✐❞❛❞❡ ✐♥t❡❣r❛❞❛ ❞❡ ✼✭✽✮❚❡❱ ❡ ✹✳✽✭✺✳✾✮f b−1_{✳ ✳ ✳ ✳ ✳ ✳ ✾✹}

✸✺ ❉✐str✐❜✉✐çã♦ ❞❡ ❡✈❡♥t♦s ❞❡ ✹ ❧é♣t♦♥s ❞♦ ❞❡❝❛✐♠❡♥t♦ H _→ ZZ ❡♠ ❢✉♥çã♦

❞❛ ♠❛ss❛ mllll✱ ♣❛r❛ ♦ ❆❚▲❆❙ ❡♠ ✭❛✮ ❡ ❈▼❙ ❡♠ ✭❜✮✳ ◆❛ r❡❣✐ã♦ ♣❡rt♦ ❞❡

✾✶●❡❱ t❡♠♦s ♦ ♣✐❝♦ r❡❧❛t✐✈♦ ❛♦ ❜ós♦♥ ❩ ❡ ♣❡rt♦ ❞❛ ♠❛ss❛ ❞❡ ✶✷✺●❡❱✱ ♦ s✐♥❛❧ ❞♦ ❍✐❣❣s✱ ❡♠ ❛③✉❧ ❡♠ ✭❛✮❆❚▲❆❙ ❡ ✈❡r♠❡❧❤♦ ❡♠ ✭❜✮❈▼❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✸✻ ●rá✜❝♦s ❝♦♠ ♦s ✺ ❝❛♥❛✐s ❞❡ ❞❡❝❛✐♠❡♥t♦ ❞♦ ❍✐❣❣s ❡♠ r❡❧❛çã♦ σ/σSM✱ q✉❡

r❡♣r❡s❡♥t❛ ❛ r❛③ã♦ ❡♥tr❡ ❛ s❡çã♦ ❞❡ ❝❤♦q✉❡ ✈❡rs✉s ♦ ❜r❛♥❝❤✐♥❣ ♦❜s❡✈❛❞♦ σ

♣❡❧♦ ▼♦❞❡❧♦ P❛❞rã♦ σSM ♣❛r❛ ❞❛❞♦s ♦❜t✐❞♦s ❡♠ ✷✵✶✷ ❡ ✷✵✶✹✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✸✼ ❱❛❧♦r σ/σSM ❡♠ r❡❧❛çã♦ ❛ ♠❛ss❛ ❞♦ ❍✐❣❣s ❡♥❝♦tr❛❞♦ ♥♦s ❝❛♥❛✐s H → γγ

❡ H _→ ZZ✳ ❖s ❝♦♥t♦r♥♦s ❝♦rr❡s♣♦♥❞❡♠ ❛ ✻✽✪ ♥í✈❡❧ ❞❡ ❝♦♥✜❛♥ç❛ ♣❛r❛ ♦

✶✸

✸✽ ❊①❡♠♣❧♦ ❞❡ ❛❝❡❧❡r❛❞♦r ❧✐♥❡❛r✿ ♦ ❙▲❆❈ ◆❛t✐♦♥❛❧ ❆❝❝❡❧❡r❛t♦r ▲❛❜♦r❛t♦r② ✉♠ ❝♦❧✐s♦r ❞❡ e−_e+_{✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾}

✸✾ ❉✐❛❣r❛♠❛ ❡sq✉❡♠át✐❝♦ ❞♦ ▲❊P✱ ❝♦♠ ♦s s❡✉ ❞❡t❡❝t♦r❡s✿ ❆▲❊P❍✱ ❉❊▲P❍✱ ❖P❆▲ ❡ ▲✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵ ✹✵ ❉❡s❡♥❤♦ ❡sq✉❡♠át✐❝♦ ❞♦s ✐♥❥❡t♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ✹✶ ❉❡t❡t♦r ▲✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸ ✹✷ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ❉❡t❡t♦r ❖P❆▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✹✸ ❈♦♠♣❧❡①♦ ❞❡ ❛❝❡❧❡r❛❞♦r❡s ❋❡r♠✐❧❛❜ ✭❚❡✈❛tr♦♥✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺

✹✹ ❉❡t❡t♦r ❈❉❋✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻

✹✺ ❉✐❛❣r❛♠❛ ❝♦♠ ❛s ♣r✐♥❝✐♣❛✐s ❝♦♠♣♦♥❡♥t❡s ❞♦ ❉✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✹✻ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ❝♦♠♣❧❡①♦ ❞❡ ❛❝❡❧❡r❛❞♦r❡s ❞♦ ▲❍❈✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾

✹✼ ❉❡t❡❝t♦r ❆❚▲❆❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵

▲✐st❛ ❞❡ ❚❛❜❡❧❛s

✶ ◆❛ t❛❜❡❧❛ ❛❜❛✐①♦ t❡♠♦s ❛s três ❢❛♠í❧✐❛s ❞❡ ❧é♣t♦♥s✱ ❝♦♠ s✉❛s ❝♦♠♣♦♥❡♥t❡s r✐❣❤t ❡ ❧❡❢t❀ t❛♠❜é♠ ❛s três ❢❛♠í❧✐❛s ❞❡ q✉❛r❦s✱ ❝♦♠ s✉❛s ❝♦♠♣♦♥❡♥t❡s r✐❣❤t ❡ ❧❡❢t✳ ❆ss✐♠ ❝♦♠♦ ♦ ✈❛❧♦r ❞♦ s❡✉ ✐s♦s♣✐♥✱ ❞❡ s✉❛ ❤✐♣❡r❝❛r❣❛ ❡ ❞❛ ❝❛r❣❛ ❡❧étr✐❝❛ ◗ ❞❡ ❝❛❞❛ ❢ér♠✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷ ▲✐♠✐t❡ ❊s♣❡r❛❞♦ ❡ ❖❜s❡r✈❛❞♦ ♣❛r❛ ♦ ❜ós♦♥ ❞❡ ❍✐❣❣s✱ ♦❜t✐❞♦ ❝♦♠ ❉✵✲

❚❡✈❛tr♦♥ ✷✵✵✽✱ ♣❛r❛ ♦ ♣r♦❝❡ss♦ σ(¯pp _→ Z/W H) ❡ ❝♦♠❜✐♥❛çã♦✱ ♦♥❞❡ ♦ (H _→¯bb)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷

✸ ▲✐♠✐t❡ ❊s♣❡r❛❞♦ ❡ ❖❜s❡✈❛❞♦ ❡♠ r❡❧❛çã♦ ❛♦ ▼♦❞❡❧♦ P❛❞rã♦ ❝♦♠ ✾✺✪ ❞❡ ♥í✈❡❧ ❞❡ ❝♦♥✜❛♥ç❛ ♦❜t✐❞♦ ♣❡❧♦ ❈❉❋✲❚❡✈❛tr♦♥ ❡♠ ✷✵✶✵ ♣❛r❛ ♠❛ss❛ ❞♦ ❜ós♦♥ ❞❡ ❍✐❣❣s ❡♥tr❡ ✶✶✵ ❡ ✷✵✵●❡❱✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✹ ◆❛ t❛❜❡❧❛ ❛❝✐♠❛ t❡♠♦s ❝❛❞❛ ❡stá❣✐♦ ❡ ❡♥❡r❣✐❛ ❛❞q✉✐r✐❞❛ ❡♠ ❝❛❞❛ ❛❝❡❧❡r❛❞♦r

▲■❙❚❆ ❉❊ ◗❯❆❉❘❖❙

▲■❙❚❆ ❉❊ ❆❇❘❊❱■❆❚❯❘❆❙ ❊ ❙■●▲❆❙ ❆▲❊P❍ ❆♣♣❛r❛t✉s ❢♦r ▲❊P P❍②s✐❝s ❛t ❈❊❘◆

❆❚▲❆❙ ❆r❣♦♥♥❡ ❚❛♥❞❡♠ ▲✐♥❡❛r ❆❝❝❡❧❡r❛t♦r ❙②st❡♠ ❈❉❋ ❈♦❧❧✐❞❡r ❉❡t❡❝t♦r ❛t ❋❡r♠✐❧❛❜

❈▼❙ ❈♦♠♣❛❝t ▼✉♦♥ ❙♦❧❡♥♦✐❞

❉❊▲P❍■ ❉❊t❡❝t♦r ✇✐t❤ ▲❡♣t♦♥✱ P❤♦t♦♥ ❛♥❞ ❍❛❞r♦♥ ■❞❡♥t✐✜❝❛t✐♦♥ ❋❊❘▼■▲❆❇ ❋❡r♠✐ ◆❛t✐♦♥❛❧ ❆❝❝❡❧❡r❛t♦r ▲❛❜♦r❛t♦r②

▲❊P ▲❛r❣❡ ❊❧❡❝tr♦♥✕P♦s✐tr♦♥ ❈♦❧❧✐❞❡r ▲❍❈ ●r❛♥❞❡ ❈♦❧✐s♦r ❞❡ ❍á❞r♦♥s

❙✉♠ár✐♦

✶ ■◆❚❘❖❉❯➬➹❖ ✶✾

✷ ❈❖◆❙■❉❊❘❆➬Õ❊❙ ❚❊Ó❘■❈❆❙ ✷✶

✷✳✶ ❙■▼❊❚❘■❆ ❉❊ ●❆❯●❊ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✷ ▼❖❉❊▲❖ ❉❊ ❲❊■◆❇❊❘●✲❙❆▲❆▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✷✳✶ ◗✉❡❜r❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐♠❡tr✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✷✳✷ ▼❡❝❛♥✐s♠♦ ❞❡ ❍✐❣❣s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✸ ❆ ❉❊◆❙■❉❆❉❊ ▲❆●❘❆◆●■❆◆❆ ❉❖ ▼❖❉❊▲❖ P❆❉❘➹❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✹ ▼❆❚❘■❩ ❊❙P❆▲❍❆▼❊◆❚❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

✸ P❘❖❉❯➬➹❖ ❊ ❉❊❈❆■▼❊◆❚❖ ❉❖ ❇Ó❙❖◆ ❉❊ ❍■●●❙ ✹✸

✸✳✶ P❘❖❉❯➬➹❖ ❉❖ ❇Ó❙❖◆ ❉❊ ❍■●●❙ e−_e+_→HZ0 _{✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸}

✸✳✷ P❘❖❉❯➬➹❖ ❉❖ ❇Ó❙❖◆ ❉❊ ❍■●●❙ P❊▲❆ ❋❯❙➹❖ ❉❊ ❇Ó❙❖◆❙ ❱❊✲ ❚❖❘■❆■❙ e−_e+_{= ¯ννH ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶}

✸✳✸ ❉❊❈❆■▼❊◆❚❖ ❉❖ ❇Ó❙❖◆ ❉❊ ❍■●●❙ ❊▼ ❋➱❘▼■❖◆ ❊ ❆◆❚■❋➱❘✲ ▼■❖◆ ff¯ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✸✳✹ ❉❊❈❆■▼❊◆❚❖ ❉❖ ❇Ó❙❖◆ ❉❊ ❍■●●❙ ❊▼ ❉❖■❙ ❇Ó❙❖◆ ❱❊❚❖❘■❆■❙ ✺✾ ✸✳✺ ❉❊❈❆■▼❊◆❚❖ ❉❖ ❇Ó❙❖◆ ❉❊ ❍■●●❙ ❊▼ ❋Ó❚❖◆ ❊ ❇Ó❙❖◆ ❱❊❚❖✲

❘■❆▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✸✳✻ ❉❊❈❆■▼❊◆❚❖ ❉❖ ❇Ó❙❖◆ ❉❊ ❍■●●❙ ❊▼ ❉❖■❙ ❋Ó❚❖◆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸

✹ ❇Ó❙❖◆ ❉❊ ❍■●●❙ ✻✻

✹✳✶ ❇Ó❙❖◆ ❉❊ ❍■●●❙ ◆❖ ▲❊P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✶✳✶ ❆▲❊P❍ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✶✳✷ ❉❊▲P❍■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✹✳✶✳✸ ▲✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✹✳✶✳✹ ❖P❆▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✹✳✷ ❇Ó❙❖◆ ❉❊ ❍■●●❙ ◆❖ ❚❊❱❆❚❘❖◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✹✳✷✳✶ ❈❉❋ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✹✳✷✳✷ ❉✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✹✳✸ ❇Ó❙❖◆ ❉❊ ❍■●●❙ ◆❖ ▲❍❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✹✳✸✳✶ ❆❚▲❆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✹✳✸✳✷ ❈▼❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵

✺ ❉❊❙❈❖❇❊❘❚❆ ❉❖ ❇Ó❙❖◆ ❉❊ ❍■●●❙ ✾✷

✶✽

❆ ❆❈❊▲❊❘❆❉❖❘❊❙ ❉❊ P❆❘❚❮❈❯▲❆❙ ✾✾

✶✾

✶ ■◆❚❘❖❉❯➬➹❖

◆❡st❛ ❞✐ss❡rt❛çã♦✱ ❛♣r❡s❡♥t❛r❡♠♦s ✉♠ ❡st✉❞♦ ❞❛ ❜✉s❝❛ ❞♦ ❜ós♦♥ ❞❡ ❍✐❣❣s ❞♦ ▼♦✲ ❞❡❧♦ P❛❞rã♦ ✭❙▼✮ q✉❡ ❛❜r❛♥❣❡ s✉❛ ❢♦r♠✉❧❛çã♦ t❡ór✐❝❛ ❡ ✉♠ ❧❡✈❛♥t❛♠❡♥t♦ ❞♦s ♣r✐♥❝✐♣❛✐s r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ♣✉❜❧✐❝❛❞♦s ♣❡❧❛s ❝♦❧❛❜♦r❛çõ❡s q✉❡ ❝♦♥tr✐❜✉ír❛♠ ♥❛ s✉❛ ❜✉s❝❛ ❡ ❞❡t❡❝çã♦✳ ❉✐✈✐❞✐♠♦s ❛ ❛♣r❡s❡♥t❛çã♦ ❞♦ tr❛❜❛❧❤♦ ❡♠ ❝✐♥❝♦ s❡çõ❡s✿ ♥❛ ♣r✐♠❡✐r❛ s❡çã♦ ❛♣r❡s❡♥t❛♠♦s ✉♠❛ ❜r❡✈❡ ❛❜♦r❞❛❣❡♠ t❡ór✐❝❛ ❞♦ ♠♦❞❡❧♦ ❞❡ ❲❡✐♥❜❡r❣✲❙❛❧❛♠ q✉❡ ❡stá ❢✉♥✲ ❞❛♠❡♥t❛❞♦ ♥♦ ♣r✐♥❝í♣✐♦ ❞❡ ❣❛✉❣❡✳ ❆♣r❡s❡♥t❛♠♦s ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ❞♦ ▼♦❞❡❧♦ P❛trã♦ ❊❧❡tr♦❢r❛❝♦✱ ❛ q✉❡❜r❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐♠❡tr✐❛ ❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❍✐❣❣s✱ q✉❡ ❧❡✈❛ ❛♦ ❛♣❛r❡❝✐♠❡♥t♦ ❞❡ ✉♠❛ ♣❛rtí❝✉❧❛ ❡s❝❛❧❛r ✭♦ ❜ós♦♥ ❞❡ ❍✐❣❣s✮ ❡ ♣❡r♠✐t❡ ❣❡r❛r ❛ ♠❛ss❛ ❛♦s ❜ós♦♥s ✐♥t❡r♠❡❞✐❛❞♦r❡s ❞❛ ❢♦rç❛ ❢r❛❝❛ ❡ ❛s ♦✉tr❛s ♣❛rtí❝✉❧❛s ❞♦ ▼♦❞❡❧♦ P❛❞rã♦✳ ❆ s❡❣✉♥❞❛ s❡çã♦ tr❛t❛ ❞♦s ♣r✐♥❝✐♣❛✐s ♣r♦❝❡ss♦s ❞❡ ♣r♦❞✉çã♦ ❡ ❞❡❝❛✐♠❡♥t♦ ❞♦ ❜ós♦♥ ❞❡ ❍✐❣❣s✱ q✉❡ ❢♦r❛♠ r❡❧❡✈❛♥t❡s ❞✉r❛♥t❡ ❛ ♣❡sq✉✐s❛ ♥❛ t❡♥t❛t✐✈❛ ❞❡ ❡♥❝♦♥trá✲❧♦✳ ◆❛ t❡r❝❡✐r❛ s❡çã♦ ❛♣r❡s❡♥t❛♠♦s ❛❧❣✉♥s r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❞❛ ❜✉s❝❛ ❞♦ ❜ós♦♥ ❞❡ ❍✐❣❣s ❛♥t❡s ❞❡ s✉❛ ❞❡s❝♦❜❡rt❛✳ ❊st❡s r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s✱ ❢♦r❛♠ ♦❜t✐❞♦s ❛♦ ❧♦♥❣♦ ❞♦s ❛♥♦s ❡ ❞❡s❝r❡✲ ✈❡♠ ❛ ❡✈♦❧✉çã♦ ❤✐stór✐❝❛ q✉❡ ❝♦♠❡ç♦✉ ♣♦r ✈♦❧t❛ ❞❡ ✶✾✾✵ ♥♦ ▲❊P ❛té ❛s ♣✉❜❧✐❝❛çõ❡s q✉❡ ❛♥t❡❝❡❞❡ s✉❛ ❞❡t❡❝çã♦ ❡♠ ❛❣♦st♦ ❞❡ ✷✵✶✷ ♥♦ ▲❍❈✳ ◆♦ ú❧t✐♠♦ ❝❛♣ít✉❧♦✱ ❛♣r❡s❡♥t❛♠♦s ❛ ❞❡s❝♦❜❡rt❛ ❞♦ ❇ós♦♥ ❞❡ ❍✐❣❣s✱ ❡✈❡♥t♦ ✐♠♣♦rt❛♥t❡ t❛♥t♦ ♥❛ ❢ís✐❝❛ t❡ór✐❝❛ ❝♦♠♦ ♥❛ ❢ís✐❝❛ ❡①♣❡r✐♠❡♥t❛❧✳ ❯♠ ❡sq✉❡♠❛ s♦❜r❡ ♦s ♣r✐♥❝✐♣❛✐s ❛❝❡❧❡r❛❞♦r❡s ❞❡ ♣❛rtí❝✉❧❛s ❡ ❞❡t❡❝t♦r❡s q✉❡ ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ♥❛ ♣❡sq✉✐s❛ ❞❡ss❛ ♣❛rtí❝✉❧❛ ❡stã♦ ♥♦ ❛♣ê♥❞✐❝❡ ❆✳

❖ ▼♦❞❡❧♦ P❛❞rã♦ ❞❡ ❋ís✐❝❛ ❞❡ P❛rtí❝✉❧❛s✱ ❥á ❢♦✐ s✉❜♠❡t✐❞♦ ❛ ✈ár✐♦s t❡st❡s ❡①♣❡r✐♠❡♥✲ t❛✐s ❛♦ ❧♦♥❣♦ ❞♦s ✺✵ ❛♥♦s ❞❡st❡ s✉❛ ♣r♦♣♦st❛✱ ♠♦str❛♥❞♦✲s❡ ❜❡♠ s✉❝❡❞✐❞♦ ❛♦ ❞❡s❝r❡✈❡r ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❡ ♣r❡✈❡r ♥♦✈♦s r❡s✉❧t❛❞♦s✳ ❊❧❡ ❞❡s❝r❡✈❡ ❞❡ ❢♦r♠❛ ✉♥✐✜❝❛❞❛✱ três ❞❛s q✉❛tr♦s ❢♦rç❛s ❢✉♥❞❛♠❡♥t❛✐s ❞❛ ♥❛t✉r❡③❛✿ ❛ ❢♦rç❛ ❡❧❡tr♦♠❛❣♥ét✐❝❛✱ ❛ ❢♦rç❛ ❢r❛❝❛ ❡ ❛ ❢♦rç❛ ❢♦rt❡✱ ✜❝❛♥❞♦ ❞❡ ❢♦r❛ ❛ ❢♦rç❛ ❣r❛✈✐t❛❝✐♦♥❛❧✳ ❆ ❢♦rç❛ ❡❧❡tr♦♠❛❣♥ét✐❝❛ s❡ ♠❛♥✐❢❡st❛ ❡♥tr❡ ❝❛r❣❛s ❡❧étr✐❝❛s✱ ❝✉❥❛ ♣❛rtí❝✉❧❛ ✐♥t❡r♠❡❞✐❛❞♦r❛ é ♦ ❢ót♦♥ ❡ ♣♦❞❡ s❡r t❛♥t♦ ❛tr❛t✐✈❛ ❝♦♠♦ r❡♣✉❧s✐✈❛✳ ❆ ❢♦rç❛ ❢r❛❝❛✱ q✉❡ ❛t✉❛ t❛♥t♦ ❡♥tr❡ ♦s ❧é♣t♦♥s ❝♦♠♦ ❡♥tr❡ q✉❛r❦s✱ ♣❡r♠✐t❡ q✉❡ ❡ss❛s ♣❛rtí❝✉❧❛s ♠✉❞❡♠ ❞❡ s❛❜♦r✳ ❙✉❛s ♣❛rtí❝✉❧❛s ✐♥t❡r♠❡❞✐❛❞♦r❛s sã♦ ♦s ❜ós♦♥s ✈❡t♦r✐❛✐s ♠❛ss✐✈♦s✱ q✉❡ ❢♦r❛♠ ❝♦♥✜r♠❛❞♦s ❡♠ ❡①♣❡r✐ê♥❝✐❛ ♥♦ ❈❊❘◆ ❡♠ ✶✾✽✸✱ ❡♠ ❝♦❧✐sã♦ ❡♥tr❡ ♣rót♦♥ ❡ ❛♥t✐♣rót♦♥✳ ❆ ❢♦rç❛ ❢r❛❝❛ é r❡s♣♦♥sá✈❡❧ ♣♦r ❢❡♥ô♠❡♥♦s ❝♦♠♦ ♦ ❞❡❝❛✐♠❡♥t♦ ❜❡t❛✳ ❆ ❢♦rç❛ ❢♦rt❡✱ ❡♠❜♦r❛ s❡❥❛ ❛ ♠❛✐s ❢♦rt❡ ❞❛s q✉❛tr♦s ✐♥t❡r❛çõ❡s✱ t❡♠ ✉♠ ❛❧❝❛♥❝❡ ❝✉rt♦ ❡✱ é r❡s♣♦♥sá✈❡❧ ♣♦r ♠❛♥t❡r ♦s ♥ú❝❧❡♦♥s ✭♣rót♦♥s ❡ ♥❡✉tr♦♥s✮ ❝♦❡s♦s✳ ❙✉❛s ♣❛rtí❝✉❧❛s ✐♥✲ t❡r♠❡❞✐❛❞♦r❛s sã♦ ♦s ❣❧ú♦♥s✳ ❈♦♥s✐❞❡r❛♥❞♦ ❛ ✐♥t❡♥s✐❞❛❞❡ ❞❛ ❢♦rç❛ ❢♦rt❡ ❝♦♠♦ ✶✱ ❛ ❢♦rç❛ ❡❧❡tr♦♠❛❣♥ét✐❝❛ s❡rá ✶✴✶✸✼✱ ❛ ❢♦rç❛ ❢r❛❝❛10−6 _{❡ ❛ ❢♦rç❛ ❣r❛✈✐t❛❝✐♦♥❛❧10}−39_{✱ ♥❡st❛ ❡s❝❛❧❛✳}

✷✵

❛ ❢♦rç❛ ❡❧❡tr♦♠❛❣♥ét✐❝❛✳ ❊♠ ❛♥❛❧♦❣✐❛ ❝♦♠ ♦ ❢ót♦♥✱ ❡❧❡ ♣r♦♣ôs ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ❜ós♦♥ ✈❡t♦r✐❛❧✱ ♥♦ ❝❛s♦ ♠❛ss✐✈♦✱ ❥á q✉❡ ❛ ❢♦rç❛ ❢r❛❝❛ t❡r✐❛ q✉❡ s❡r ❞❡ ❝✉rt♦ ❛❧❝❛♥❝❡✳ ❈♦♠ ❡ss❛ t❡♦r✐❛ s❡r✐❛ ♣♦ssí✈❡❧ ❡①♣❧✐❝❛r ♦ ❞❡❝❛✐♠❡♥t♦ ❜❡t❛✳ ▼❛s ❛ ❢♦rç❛ ❡❧❡tr♦♠❛❣♥ét✐❝❛ ❡ ❛ ❢♦rç❛ ❢r❛❝❛ ❡r❛♠ ✈✐st❛s ❝♦♠♦ t❡♦r✐❛s s❡♣❛r❛❞❛s✳ ❈♦♠ ❛ ✉♥✐✜❝❛çã♦ ❞❡ ❲❡✐♥❜❡r❣ ❡ ❙❛❧❛♠✱ ♦ ❡❧❡tr♦♠❛❣♥❡t✐s♠♦ ❡ ❛ ❢♦rç❛ ❢r❛❝❛ ♣❛ss❛r❛♠ ❛ ❢❛③❡r ♣❛rt❡ ❞❡ ✉♠❛ ú♥✐❝❛ t❡♦r✐❛✱ ❛ t❡♦r✐❛ ❡❧❡tr♦❢r❛❝❛✳ ❈♦♠ ♦ s✉❝❡ss♦ ❞♦ ▼♦❞❡❧♦ ❊❧❡tr♦❢r❛❝♦✱ ❛ ✉♥✐✜❝❛çã♦ ❢♦✐ ❡st❡♥❞✐❞❛✱ ✐♥❝❧✉✐♥❞♦ t❛♠❜é♠ ❛ ❢♦rç❛ ❢♦rt❡ ✭q✉❛r❦s ❡ ❣❧✉♦♥s✮ ❞❛♥❞♦ ♦r✐❣❡♠ ❛♦ q✉❡ ❝❤❛♠❛♠♦s ❞❡ ▼♦❞❡❧♦ P❛❞rã♦ ❞❛s ■♥t❡r❛çõ❡s ❋✉♥❞❛♠❡♥t❛✐s✳ ❆ ♣❛rtí❝✉❧❛ q✉❡ ❢❛❧t❛✈❛ s❡r ❞❡t❡❝t❛❞❛ ❡ q✉❡ ❞❡✜♥✐t✐✈❛♠❡♥t❡ ♠♦str❛r✐❛ q✉❡ ♦ ▼♦❞❡❧♦ P❛❞rã♦ é ✉♠ ♠♦❞❡❧♦ r❡❛❧♠❡♥t❡ ❝♦♥s✐st❡♥t❡ ❝♦♠ s✉❛s ♣r❡✈✐sõ❡s ❡ ❝♦♥✜r♠❛çõ❡s ❡r❛ ♦ ❜ós♦♥ ❞❡ ❍✐❣❣s✳ P❛rtí❝✉❧❛ q✉❡ ♠✉✐t♦s ✈❡③❡s ❡r❛ ✈✐st❛ ❝♦♠♦ ✐♠♣♦ssí✈❡❧ ❞❡ s❡r ❞❡t❡❝t❛❞❛✱ ❝♦♠♦ ❡①♣♦st♦ ♣♦r ❏♦❤♥ ❊▲▲■❙ ❡ ▼❛r② ❑✳ ●❆■▲▲❆❘❉ ❞❡ ✶✾✼✻✱ ♦♥❞❡ ❛♣ós ✉♠ ❧♦♥❣♦ tr❛❜❛❧❤♦ ❢❡♥♦♠❡♥♦❧ó❣✐❝♦ s♦❜r❡ ♦ ❜ós♦♥ ❞❡ ❍✐❣❣s ❡❧❡ ❞✐③✿

❲❡ s❤♦✉❧❞ ♣❡r❤❛♣s ✜♥✐s❤ ✇✐t❤ ❛♥ ❛♣♦❧♦❣② ❛♥❞ ❛ ❝❛✉t✐♦♥✳ ❲❡ ❛♣♦❧♦❣✐③❡ t♦ ❡①♣❡r✐♠❡♥t❛❧✐sts ❢♦r ❤❛✈✐♥❣ ♥♦ ✐❞❡❛ ✇❤❛t ✐s t❤❡ ♠❛ss ♦❢ t❤❡ ❍✐❣❣s ❜♦s♦♥✱ ✉♥❧✐❦❡ t❤❡ ❝❛s❡ ✇✐t❤ ❝❤❛r♠ ❛♥❞ ❢♦r ♥♦t ❜❡✐♥❣ s✉r❡ ♦❢ ✐ts ❝♦✉♣❧✐♥❣s t♦ ♦t❤❡r ♣❛rt✐❝❧❡s✱ ❡①❝❡♣t t❤❛t t❤❡② ❛r❡ ♣r♦❜❛❜❧② ❛❧❧ ✈❡r② s♠❛❧❧✳ ❋♦r t❤❡s❡ r❡❛s♦♥s ✇❡ ❞♦ ♥♦t ✇❛♥t t♦ ❡♥❝♦✉r❛❣❡ ❜✐❣ ❡①♣❡r✐♠❡♥t❛❧ s❡❛r❝❤❡s ❢♦r t❤❡ ❍✐❣❣s ❜♦s♦♥✱ ❜✉t ✇❡ ❞♦ ❢❡❡❧ t❤❛t ♣❡♦♣❧❡ ♣❡r❢♦r♠✐♥❣ ❡①♣❡r✐♠❡♥ts ✈✉❧♥❡r❛❜❧❡ t♦ t❤❡ ❍✐❣❣s ❜♦s♦♥ s❤♦✉❧❞ ❦♥♦✇ ❤♦✇ ✐t ♠❛② t✉r♥ ✉♣✳ ✭❊▲▲■❙❀ ●❆■▲▲❆❘❉❀ ◆❆◆❖P❖❯▲❖❙✱ ✶✾✼✻✱ ♣✳ ✸✸✹✮✳

✷✶

✷ ❈❖◆❙■❉❊❘❆➬Õ❊❙ ❚❊Ó❘■❈❆❙

◆❡st❡ ❝❛♣ít✉❧♦ s❡rã♦ ❡st✉❞❛❞♦s ❛❧❣✉♥s ❛s♣❡❝t♦s ❞♦ ▼♦❞❡❧♦ P❛❞rã♦ ❞❛s ✐♥t❡r❛çõ❡s ❡❧❡tr♦❢r❛❝❛s✱ ❡♠ ❡s♣❡❝✐❛❧ ❛ ❝♦♥str✉çã♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✐♥✈❛r✐❛♥t❡ s♦❜ ❛ ❛çã♦ ❞♦ ❣r✉♣♦ ❞❡ s✐♠❡tr✐❛ ❛ss♦❝✐❛❞♦ à ✐♥t❡r❛çã♦ ❡❧❡tr♦❢r❛❝❛✳ ❙❡rá ❡st✉❞❛❞❛ ❛ q✉❡❜r❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐♠❡tr✐❛ ❞❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ❞♦ ❝❛♠♣♦ ❡s❝❛❧❛r✱ ❛ss✐♠ ❝♦♠♦ ♦ ▼❡❝❛♥✐s♠♦ ❞❡ ❍✐❣❣s✱ q✉❡ ♣r♦♣♦r❝✐♦♥❛✱ ♣❡❧♦ ♣r♦❝❡ss♦ ❞❡ q✉❡❜r❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐♠❡tr✐❛✱ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ❝❛♠♣♦s ✈❡t♦r✐❛✐s ❡ ❡s❝❛❧❛r✶_{✱ ❛ ❣❡r❛çã♦ ❞❡ ♠❛ss❛ ❛♦s ❜ós♦♥ ✈❡t♦r✐❛✐s ✭❜ós♦♥ ❞❡ ❣❛✉❣❡✮ ❡ ♦} s✉r❣✐♠❡♥t♦ ❞❡ ✉♠❛ ♥♦✈❛ ♣❛rtí❝✉❧❛ ❡s❝❛❧❛r✱ ♦ ❜ós♦♥ ❞❡ ❍✐❣❣s ❞♦ ▼♦❞❡❧♦ P❛❞rã♦✱ q✉❡ s❡rá ♦ ♦❜❥❡t♦ ❞❡ ❡st✉❞♦ ❞♦s ❝❛♣ít✉❧♦s s❡❣✉✐♥t❡s✳

✷✳✶ ❙■▼❊❚❘■❆ ❉❊ ●❆❯●❊

P❛r❛ ❝♦♥str✉✐r ✉♠❛ t❡♦r✐❛ q✉❡ ✉♥✐✜q✉❡ ♦ ❡❧❡tr♦♠❛❣♥❡t✐s♠♦ ❡ ❢♦rç❛ ❢r❛❝❛ é ♥❡❝❡ssár✐♦ q✉❡ ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ t❡♥❤❛ ❝❛♠♣♦s ✈❡t♦r✐❛✐s q✉❡ s❡rã♦ ❛ss♦❝✐❛❞♦s ❛ ❝❛❞❛ ❜ós♦♥ ✈❡t♦r✐❛❧ ❞❛ ❢♦rç❛ ❢r❛❝❛ ❡ ❛♦ ❢ót♦♥✳ ❱❛♠♦s ♠♦str❛r ❝♦♠♦ ❝♦♥str✉✐r ✉♠❛ t❡♦r✐❛ q✉❡ s❡❥❛ ✐♥✈❛r✐❛♥t❡ s♦❜ ❛ ❛çã♦ ❞❡ ❣r✉♣♦ ❞❡ s✐♠❡tr✐❛U(1) ❣❧♦❜❛❧✱ ❡♠ s❡❣✉✐❞❛ ❧♦❝❛❧ ❡✱ ♦❜s❡r✈❛r ❝♦♠♦

♦ ❝❛♠♣♦ ✈❡t♦r✐❛❧ ✭❝❛♠♣♦ ❞❡ ❣❛✉❣❡✮ é ✐♥tr♦❞✉③✐❞♦ ♥❛ t❡♦r✐❛✳ ❈♦♠♦ ❡①❡♠♣❧♦✱ ❝♦♥s✐❞❡r❡♠♦s ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ❛❜❛✐①♦✿

L = ¯Ψ(x)(iγµ∂µ−m)Ψ(x). ✭✶✮ q✉❡ ♣♦ss✉✐ ❝♦♠♦ ❡q✉❛çã♦ ❞❡ ♠♦✈✐♠❡♥t♦ ❛ ❡q✉❛çã♦ ❞❡ ❉✐r❛❝✱ ❡ ❞❡s❝r❡✈❡ ❢ér♠✐♦♥s ❞❡ s♣✐♥

1/2 ❡ ❝❛r❣❛ q✿

(iγµ∂µ−m)Ψ(x) = 0, ✭✷✮

❆ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✭✶✮ é ✐♥✈❛r✐❛♥t❡ ♣♦r ✉♠❛ tr❛♥s❢♦r♠çã♦ ❣❧♦❜❛❧ ❞♦ ❣r✉♣♦ U(1)✳

P❛r❛ ♣r♦✈❛r ❡ss❛ ✐♥✈❛r✐â♥❝✐❛✱ ❜❛st❛ ✉s❛r ✉♠❛ tr❛♥s❢♦r♠❛çã♦ ❣❧♦❜❛❧ ✉♥✐tár✐❛ ❞♦ ❣r✉♣♦

U(1)✱ ❞♦ t✐♣♦✿

Ψ′(x)_→e−iqαΨ(x). ✭✸✮

s❡♠ ❞❡♣❡♥❞ê♥❝✐❛ ❡s♣❛ç♦✲t❡♠♣♦r❛❧✱ ✐st♦ é✱ t❡♠ ♦ ♠❡s♠♦ ✈❛❧♦r ❡♠ q✉❛❧q✉❡r ♣♦♥t♦ ❞♦ ❡s♣❛ç♦✲ t❡♠♣♦ ❡ q é ❛ ❝❛r❣❛ ❛ss♦❝✐❛❞❛ à ♣❛rtí❝✉❧❛✳ ❉❡r✐✈❛♥❞♦ ❡♠ r❡❧❛çã♦ ❛ ❝♦♦r❞❡♥❛❞❛x✱ t❡♠♦s✿

∂µΨ(x)→e−iqα∂µΨ(x). ✭✹✮

❈♦♥s✐❞❡r❛♥❞♦ _Ψ(¯ _x)→e+iqα_{Ψ(¯ x) ❡ s✉❜st✐t✉✐♥❞♦ ♥❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✭✶✮ t❡♠♦s✿}

L =ie+iqα_{Ψ(¯ x)γ}µ_∂

µe−iqαΨ(x)−me+iqαΨ(¯ x)e−iqαΨ(x), ✭✺✮

✷✷

L=iΨ(¯ x)γµ∂µΨ(x)−mΨ(¯ x)Ψ(x). ✭✻✮ P♦rt❛♥t♦✱ ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ❛❝✐♠❛ é ✐♥✈❛r✐❛♥t❡ ♣♦r ✉♠❛ tr❛♥s❢♦r♠❛çã♦ ❣❧♦❜❛❧ ❞♦ ❣r✉♣♦ U(1)✳ ❆ ♠❡s♠❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ♥ã♦ é ✐♥✈❛r✐❛♥t❡ s♦❜ ✉♠❛ tr❛♥s❢♦r♠❛çã♦

❧♦❝❛❧✳ ❊♠ ✉♠❛ tr❛♥s❢♦r♠❛çã♦ ❧♦❝❛❧ ♦ ♣❛râ♠❡♥tr♦ α ♥ã♦ é ♠❛✐s ❝♦♥st❛♥t❡ ❡ ♣❛ss❛ ❛

❞❡♣❡♥❞❡r ❞❛s ❝♦♦r❞❡♥❛❞❛s ❡s♣❛ç♦✲t❡♠♣♦r❛✐s✿

Ψ′(x)_→e−iqα(x)Ψ(x). ✭✼✮

❉❡r✐✈❛♥❞♦ ❡♠ r❡❧❛çã♦ ❛ ❝♦♦r❞❡♥❛❞❛x✱ ♦❜t❡♠♦s ♦ r❡s✉❧t❛❞♦✿

∂µΨ(x)→e−iqα(x)∂µΨ(x)−iq∂µα(x)e−iqα(x)Ψ(x). ✭✽✮ ❙✉❜st✐t✉✐♥❞♦ ❡♠ ✭✻✮ ♦❜té♠✲s❡ ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ♦r✐❣✐♥❛❧ L ♠❛✐s ✉♠ t❡r♠♦ ❡①tr❛✱ q✉❡ q✉❡❜r❛ ❛ ✐♥✈❛r✐â♥❝✐❛ ❞❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛✿

˜

L=ieiqα(x)Ψ(¯ x)γµe−iqα(x)γµ∂µΨ(x)

+ q∂µα(x)eiqα(x)Ψ(¯ x)e−iqα(x)γµΨ(x)−mΨ(¯ x)Ψ(x), ✭✾✮

˜

L =iΨ(¯ x)γµ∂µΨ(x) +q∂µα(x) ¯Ψ(x)Ψ(x)−mΨ(¯ x)γµΨ(x), ✭✶✵✮

˜

L=_L+ ∂µα(x) ¯Ψ(x)γµΨ(x). ✭✶✶✮ ❱❛♠♦s r❡❡s❝r❡✈❡r ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✭✾✮ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿

˜

L=iΨ(¯ x)γµ[∂µ−i∂µα(x)]Ψ(x)−mΨ(¯ x)Ψ(x). ✭✶✷✮ P❛r❛ ♠❛♥t❡r ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✐♥✈❛r✐❛♥t❡ s♦❜ ✉♠❛ tr❛♥s❢♦r♠❛çã♦ ❧♦❝❛❧ ❞♦ U(1)

é ♣r❡❝✐s♦ ✐♥s❡r✐r ✉♠ ❝❛♠♣♦ ✈❡t♦r✐❛❧ Bµ(x)✱ q✉❡ é ♦ ❝❛♠♣♦ ❞❡ ❣❛✉❣❡✱ q✉❡ s❡ tr❛♥s❢♦r♠❛ ❝♦♠♦✿

˜

Bµ→Bµ+

i

e∂µα. ✭✶✸✮

❉❡✜♥✐♥❞♦ ❛ ❞❡r✐✈❛❞❛ ❝♦✈❛r✐❛♥t❡ ❝♦♠♦

Dµ=∂µ−iBµ(x), ✭✶✹✮

❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✭✶✷✮ ✜❝❛

˜

L =iΨ(¯ x)γµDµΨ(x)−mΨ(¯ x)Ψ(x). ✭✶✺✮ ➱ ♥❡❝❡ssár✐♦ ❡s❝r❡✈❡r ✉♠ t❡r♠♦ ❝✐♥ét✐❝♦ ♣❛r❛ ♦ ❝❛♠♣♦ Bµ✱ q✉❡ ♣♦❞❡ s❡r ❡①♣r❡ss♦ ❡♠

✷✸

tr❛♥s❢♦r♠❛çã♦ ❞❡ ❣❛✉❣❡✳

Fµν =∂µBν −∂νBµ. ✭✶✻✮

❉❡r✐✈❛♥❞♦ ✭✶✸✮ ❡ s✉❜st✐t✉✐♥❞♦ ♥♦ t❡♥s♦r ❞❡ ❝❛♠♣♦ ✭✶✻✮✱ t❡♠♦s✿

˜

Fµν =∂µB˜ν −∂νB˜µ →∂µBν +

i

e∂µ∂να−∂νBµ− i

e∂ν∂µα=Fµν, ✭✶✼✮

❯♠ t❡r♠♦ ❝✐♥ét✐❝♦ ♣❛r❛ ♦ ❝❛♠♣♦Bµ t❡♠ ❛ ❢♦r♠❛ 1₄FµνFνµ✱ ♣♦rt❛♥t♦ ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥✲ ❣✐❛♥❛ ❝♦♠♣❧❡t❛ ✭✶✺✮ ✜❝❛✿

˜

L =iΨ(¯ x)γµDµΨ(x)−mΨ(¯ x)Ψ(x)−

1 4FµνF

νµ_{. ✭✶✽✮}

P♦❞❡rí❛♠♦s ✐♥s❡r✐r ✉♠❛ t❡r♠♦ ❞❡ ♠❛ss❛ ❞♦ t✐♣♦ 1 2B

µ_B

µ ♣❛r❛ ♦ ❝❛♠♣♦ Bµ✱ ♥♦ ❝❛s♦ ❞❡ ❝♦♥s✐❞❡r❛r♠♦s ❛ ♣❛rtí❝✉❧❛ ❛ss♦❝✐❛❞❛ ❛ ❡ss❡ ❝❛♠♣♦ ♠❛ss✐✈❛✳ ▼❛s ❝♦♠♦ ♣♦❞❡♠♦s ♦❜s❡r✈❛r✱ ❡ss❡ t❡r♠♦ ✈❛✐ q✉❡❜r❛r ❛ ✐♥✈❛r✐â♥❝✐❛ ❞❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛✳ P❛r❛ ♠❛♥t❡r ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✭✶✽✮ ✐♥✈❛r✐❛♥t❡✱ ♣♦rt❛♥t♦✱ é ♣r❡❝✐s♦ q✉❡ ♦ ❝❛♠♣♦ Bµ ♥ã♦ t❡♥❤❛ t❡r♠♦ ❞❡ ♠❛ss❛✳ ❈♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛ ❞❛ ❡①✐❣ê♥❝✐❛ ❞❡ q✉❡ ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ♣❛r❛ ♣❛rtí❝✉❧❛ ❧✐✈r❡ ✭✶✮ s❡❥❛ ✐♥✈❛r✐❛♥t❡ ♣♦r ✉♠❛ tr❛♥s❢♦r♠❛çã♦ ❧♦❝❛❧ ❞♦ ❣r✉♣♦U(1)✱ ❢♦✐ ♥❡❝❡ssár✐♦ ✐♥s❡r✐r

♦ ❝❛♠♣♦ ❣❛✉❣❡Bµ✱ ❧❡✈❛♥❞♦ ❛

˜

L=iΨ(¯ x)γµ∂µΨ(x) +qΨ(¯ x)γµΨ(x)Bµ

| {z }−

mΨ(¯ x)Ψ(x)₋ 1 4FµνF

νµ_{, ✭✶✾✮}

❡ ✉♠ t❡r♠♦ ❞❡ ✐♥t❡r❛çã♦ ❡♥tr❡ ♦ ❝❛♠♣♦ ❣❛✉❣❡ Bµ ❡ ♦ ❝❛♠♣♦ ❢❡r♠✐ô♥✐❝♦ ❛♣❛r❡❝❡✉ ♥❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✭✶✾✮✳ ❖ t❡r♠♦ ❞❡ ✐♥t❡r❛çã♦ ♣♦❞❡ s❡r r❡❡s❝r✐t♦ ❝♦♠♦

Lint =−eQfΨ(¯ x)γµΨ(x)Bµ. ✭✷✵✮ ❉❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ❝♦♥str✉í♠♦s ✉♠❛ t❡♦r✐❛ ✐♥✈❛r✐❛♥t❡ s♦❜ ❛ ❛çã♦ ❞♦ ❣r✉♣♦U(1)✱ ♣♦❞❡✲

♠♦s t❛♠❜é♠ ❝♦♥str✉✐r ✉♠❛ t❡♦r✐❛ q✉❡ s❡❥❛ ✐♥✈❛r✐❛♥t❡ s♦❜ ❛ ❛çã♦ ❞♦ ❣r✉♣♦SU(2)_×U(1)✳

❯♠❛ tr❛♥s❢♦r♠❛çã♦ ✉♥✐tár✐❛ ❛❞❡q✉❛❞❛ ♣❛r❛ ❡ss❡ ❣r✉♣♦ é ❛ s❡❣✉✐♥t❡

U(x)_⇒eig′α(x)+igΩ(x)aTa/2_. ✭✷✶✮

❆ ♣r✐♠❡✐r❛ ♣❛rt❡ é ❛ tr❛♥s❢♦r♠❛çã♦ ❧♦❝❛❧ ❛ss♦❝✐❛❞❛ ❛♦ ❣r✉♣♦ U(1)✳ ❖ s❡❣✉♥❞♦ t❡r♠♦ é ❛

tr❛♥s❢♦r♠❛çã♦ ♣❛r❛ ♦ ❣r✉♣♦SU(2)✱ ♦♥❞❡ Ta _{sã♦ ♦ ❣❡r❛❞♦r❡s ❞♦ ❣r✉♣♦SU(2) ❡ r❡s♣❡✐t❛♠} ❛ r❡❣r❛ ❞❡ ❝♦♠✉t❛çã♦

✷✹

♦♥❞❡fc

ab é ❛ ❝♦♥st❛♥t❡ ❞❡ ❡str✉t✉r❛ ❞♦ ❣r✉♣♦✳ ❉❡✜♥❡✲s❡ ❛ tr❛♥s❢♦r♠❛çã♦ ♣❛r❛Ψ(x)❝♦♠♦✿

Ψ(x)_→Ψ(x) =e−igΩ(x)aTa/2_Ψ(x). ✭✷✷✮

♦♥❞❡a =✶✱ ✷ ❡ ✸✳ ❆ ❞❡r✐✈❛❞❛ ❞❡ Ψ(x) ✜❝❛✿

∂µΨ(x)⇒∂µΨ =−ig∂µΩ(x)a

Ta

2 e

−igΩ(x)aTa/2_{Ψ(x) +e}−igΩ(x)aTa/2_∂

µΨ(x), ✭✷✸✮

∂µΨ = [∂µ−ig∂µΩ(x)a

Ta

2 ]e

−igΩ(x)a.Ta/2_Ψ(x). ✭✷✹✮

❖ ❝❛♠♣♦ ❞❡ ❣❛✉❣❡Aa

µ é ❞❡✜♥✐❞♦ ♣♦r ∂µΩ(x)a✳ ▲❡♠❜r❛♥❞♦ q✉❡Ψ(¯ x) =eigΩ(x)a.T

a_/2

Ψ(x)❡

s✉❜st✐t✉✐♥❞♦_Ψ(¯ _{x)❡ ✭✷✹✮ ♥❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✭✶✮ t❡♠♦s✿}

L = ¯Ψ(x)γµ[∂µ−igAaµ

Ta

2 ]Ψ(x)−mΨ(¯ x)Ψ(x). ✭✷✺✮

❘❡❞❡✜♥✐♠♦s ❛ ❞❡r✐✈❛❞❛ ❝♦✈❛r✐❛♥t❡✱ ❝♦♠♦

Dµ=∂µ−igAaµ

Ta

2 .

❡ ♦s ❝❛♠♣♦s ❞❡ ❣❛✉❣❡Aα

µ s❡ tr❛♥s❢♦r♠❛♠ ❝♦♠♦✿

Aa_µTa _→UAa_µTa+∂µ

U−1.

❖✉ ❛✐♥❞❛✱ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ❡①♣❛♥sã♦ ✐♥✜♥✐t❡s✐♠❛❧ ❞❡U = 1₋igTa_Ωa_{(x)✱ t❡♠♦s ❛ tr❛♥s✲} ❢♦r♠❛çã♦ ♣❛r❛ ♦ ❝❛♠♣♦Aa_µ✿

Aa

µ →Aaµ−∂µΩa+gǫabcΩbAcµ, a, b, c= 1,2,3.

➱ ♥❡❝❡ssár✐♦ q✉❡ ♦s ♥♦✈♦s ❝❛♠♣♦s t❡♥❤❛♠ ✉♠ t❡r♠♦ ❝✐♥ét✐❝♦✳ ❖ t❡♥s♦r ❞❡ ❝❛♠♣♦ ♣♦❞❡ s❡r ❡s❝r✐t♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿

Aa_µν =∂µAaν −∂νAaµ−gǫabcAbνAcν. ✭✷✻✮ ❆ss✐♠✱ ♦ t❡r♠♦ ❝✐♥ét✐❝♦ t❡♠ ❛ ❢♦r♠❛ 1

4AaµνAaµν✳ P♦rt❛♥t♦✱ ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✜❝❛✿ L =iΨ(¯ x)γµDµΨ(x)−mΨ(¯ x)Ψ(x)−

1 4A

a

µνAaµν, ✭✷✼✮ ♦✉

L= ¯Ψ(x)[iγµDµ−m]Ψ(x)−

1 4A

a

✷✺

❉❛ ❡q✉❛çã♦ ✭✷✼✮✱ s✉❜st✐t✉✐♥❞♦ ❛ ❞❡r✐✈❛❞❛ ❝♦✈❛r✐❛♥t❡ Dµ✱ ♣♦❞❡♠♦s ❡s❝r❡✈ê✲❧❛ ❝♦♠♦✿

L = ¯Ψ(x)[iγµ∂µ−m]Ψ(x) +gΨ(¯ x)γµ

Ta

2 Ψ(x)A

α_µ

− 1₄Aa_µνAaµν. ✭✷✾✮

◗✉❡ ♣❡r♠✐t❡ ✐❞❡♥t✐✜❝❛r ♦ t❡r♠♦ ❞❡ ♠❛ss❛ ♣❛r❛ ❢é♠✐♦♥s✱ ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ❞❡ ✐♥✲ t❡r❛çã♦ Lint = gΨ(¯ x)γµ T

a

2 Ψ(x)A

α

µ ❡♥tr❡ ❢ér♠✐♦♥s ❡ ♦ ❝❛♠♣♦ Aαµ ❡✱ ♣♦r ú❧t✐♠♦ ♦ t❡r♠♦ ❝✐♥ét✐❝♦ ❞♦ ❝❛♠♣♦Aµ✳ P♦❞❡♠♦s ❛❣♦r❛ ❝♦♥str✉✐r ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✐♥✈❛r✐❛♥t❡ s♦❜ ❛

❛çã♦ ❞♦ ❣r✉♣♦SU(2)_×U(1)✉s❛♥❞♦ ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✭✶✾✮✳ ❘❡❞❡✜♥✐♥❞♦ ❛ ❞❡r✐✈❛❞❛

❝♦✈❛r✐❛♥t❡ ✱ t❡♠♦s✿

Dµ =∂µ−ig′Bµ(x)−igAaµ

Ta

2 .

❆ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✜❝❛✿

L=iΨ(¯ x)γµDµΨ(x)−mΨ(¯ x)Ψ(x)−

1 4FµνF

νµ

−1₄Aa_µνAaµν ✭✸✵✮

❆ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✭✸✵✮ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠❛ t❡♦r✐❛ ✐♥✈❛r✐❛♥t❡ s♦❜ ❛çã♦ ❞♦ ❣r✉♣♦

SU(2)_⊗U(1)✱ ♣♦r ❝♦♥str✉çã♦✱ ❡ ♥ã♦ ♣♦ss✉✐ t❡r♠♦ ❞❡ ♠❛ss❛ ♣❛r❛ ♦s ❝❛♠♣♦s ❞❡ ❣❛✉❣❡✳

❯♠❛ t❡♦r✐❛ q✉❡ ❞❡s❝r❡✈❛ ❛ ❢♦rç❛ ❢r❛❝❛✱ ♣r❡❝✐s❛ ❞❡ ❛❧❣✉♠❛ ❢♦r♠❛ ❣❡r❛r ♠❛ss❛ às s✉❛s ♣❛rtí❝✉❧❛s ✐♥t❡r♠❡❞✐❛❞♦r❛s✱ ♦s ❜ós♦♥s ✈❡t♦r✐❛✐s✳ ❆ ♠❛♥❡✐r❛ ✉t✐❧✐③❛❞❛ ♥♦ ▼♦❞❡❧♦ P❛❞rã♦ ❊❧❡tr♦❢r❛❝♦ ♣❛r❛ ❣❡r❛r ♠❛ss❛ às ♣❛rtí❝✉❧❛s ✐♥t❡r♠❡❞✐❛❞♦r❛s é ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❍✐❣❣s✱ q✉❡ é ♦ ❛ss✉♥t♦ ❞❛ s❡çã♦ ✭✷✳✷✳✶✮✳

✷✳✷ ▼❖❉❊▲❖ ❉❊ ❲❊■◆❇❊❘●✲❙❆▲❆▼

❖ ▼♦❞❡❧♦ P❛❞rã♦ ❞❛s ✐♥t❡r❛çõ❡s ❡❧❡tr♦❢r❛❝❛s✱ ❝♦♠♦ ♦ ❝♦♥❤❡❝❡♠♦s ❤♦❥❡✱ ❢♦✐ ♣r♦♣♦st♦ ❡♠ ✶✾✻✼ ♣♦r ❲❡✐♥❜❡r❣ ❡ ❙❛❧❛♠ ❝♦♠♦ ✉♠❛ t❡♥t❛t✐✈❛ ❞❡ ✉♥✐✜❝❛r ♦ ❡❧❡tr♦♠❛❣♥❡t✐s♠♦ ❡ ❛ ✐♥t❡r❛çã♦ ❢r❛❝❛✳ ❈♦♠♦ ❢♦✐ ♦❜s❡r✈❛❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ♦ ❡❧❡tr♦♠❛❣♥❡t✐s♠♦ t❡♠ ❝♦♠♦ ❜ós♦♥ ✐♥t❡r♠❡❞✐❛❞♦r ♦ ❢ót♦♥✱ q✉❡ é ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡ s♣✐♥ ✶ ❡ ♠❛ss❛ ♥✉❧❛✳ ❆ ❢♦rç❛ ❢r❛❝❛ t❡♠ ❝♦♠♦ ♣❛rtí❝✉❧❛s ✐♥t❡r♠❡❞✐❛❞♦r❛s ♦s ❜ós♦♥s ✈❡t♦r✐❛✐s ♠❛ss✐✈♦sW± _{❡ Z}0_{✱ ♦♥❞❡W}+ _{❡ W}− _{sã♦ ♦s} ❜ós♦♥s ✈❡t♦r✐❛s ❝❛rr❡❣❛❞♦s ❡ Z0 _{é ❜ós♦♥ ♥❡✉tr♦✳ ❈♦♠♦ ♦s ❜ós♦♥s ✈❡t♦r✐❛✐s sã♦ ♠❛ss✐✈♦s✱}

q✉❛♥❞♦ s❡ ❛❞✐❝✐♦♥❛ ✉♠ t❡r♠♦ ❞❡ ♠❛ss❛ ♣❛r❛ ❝❛❞❛ ❝❛♠♣♦✱ ❛ ✐♥✈❛r✐â♥❝✐❛ ❞❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ é q✉❡❜r❛❞❛ ❡①♣❧✐❝✐t❛♠❡♥t❡✳ ◆♦ ♠♦❞❡❧♦ ♣r♦♣♦st♦ ♣♦r ❲❡✐♥❜❡r❣ ❡ ❙❛❧❛♠✱ ❡ss❡ ♣r♦❜❧❡♠❛ ❢♦✐ r❡s♦❧✈✐❞♦ ❛♦ tr❛t❛r ♦s ❜ós♦♥ ✈❡t♦r✐❛✐s s❡♠ ♠❛ss❛✱ ♦✉ s❡❥❛✱ ♦♠✐t✐♥❞♦ ♦ t❡r♠♦ ❞❡ ♠❛ss❛ ♥❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ♣❛r❛ ❝❛❞❛ ❝❛♠♣♦ ❡ ✉t✐❧✐③❛♥❞♦ ♦ ♠❡❝❛♥✐s♠♦ ❍✐❣❣s ♣❛r❛ ❣❡r❛r ♠❛ss❛ q✉❛♥❞♦ ♥❡❝❡ssár✐♦✳

❖ ❣r✉♣♦ ❞❡ s✐♠❡tr✐❛ ❛ss♦❝✐❛❞♦ à ✐♥t❡r❛çã♦ ❡❧❡tr♦❢r❛❝❛ ❝♦rr❡s♣♦♥❞❡ ❛♦ ❣r✉♣♦SU(2)L⊗

U(1)Y✱ ♦♥❞❡ ♦ í♥❞✐❝❡Y ♥♦ ❣r✉♣♦U(1)Y ✐♥❞✐❝❛ ❛ ❝♦rr❡♥t❡ ❞❡ ❤✐♣❡r❝❛❣❛ ❢r❛❝❛ ❡L❛ ❝♦rr❡♥t❡ ❞❡ ✐s♦s♣✐♥ ❢r❛❝♦✱ ♥♦ ❣r✉♣♦ SU(2)L✳ ❆ ❤✐♣❡r❝❛r❣❛ ❡ ❛ t❡r❝❡✐r❛ ❝♦♠♣♦♥❡♥t❡ ❞♦ ✐s♦s♣✐♥ s❡

✷✻

♣❛rtí❝✉❧❛ ❡Y =B+S ✭B é ♦ ♥ú♠❡r♦ ❜❛r✐ô♥✐❝♦ ❡ ❙ é ♦ ♥ú♠❡r♦ q✉â♥t✐❝♦ r❡❧❛❝✐♦♥❛❞♦ ❝♦♠

❛ ❡str❛♥❤❡③❛✮✳ ◆♦ ▼♦❞❡❧♦ P❛❞rã♦ ♦s ❧é♣t♦♥s ❡ ♦s q✉❛r❦s sã♦ ❛❣r✉♣❛❞♦s ❡♠ três ❢❛♠í❧✐❛s✱ ♦♥❞❡ ❝❛❞❛ ❢❛♠í❧✐❛ é ❞✐✈✐❞✐❞❛ ❡♠ ❝♦♠♣♦♥❡t❡s ❧❡❢t (L)❡ r✐❣❤t (R)✳ ◆❛ ❢❛♠í❧✐❛ ❞❡ ❧é♣t♦♥s✱ ❛

❝♦♠♣♦♥❡t❡ ❧❡❢t (L)❛❣r✉♣❛ ♦ ❧é♣t♦♥ ❡ s❡✉ ♥❡✉tr✐♥♦✱ ❡♥q✉❛♥t♦ ❛ ❝♦♠♣♦♥❡t❡ r✐❣❤t(R)♣♦ss✉✐

s♦♠❡♥t❡ ❛ ❝♦♠♣♦♥❡♥t❡ ❛ss♦❝✐❛❞♦ ❛♦ ❧é♣t♦♥❀ ♥♦ ❝❛s♦ ❞♦s q✉❛r❦s ❝❛❞❛ ❝♦♠♣♦♥❡♥t❡ ❞❡ ❝❛❞❛ ❢❛♠í❧✐❛✱ ❧❡❢t (L)❡ r✐❣❤t (R)✱ ♣♦ss✉✐ ❝♦♥tr✐❜✉✐çõ❡s ❞♦s ❞♦✐s t✐♣♦s✱ ❝♦♠♦ ♣♦❞❡ s❡r ♦❜s❡r✈❛❞♦

♥❛ t❛❜❡❧❛ ✭✶✮✳ ❉❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ❛s ♣❛rtí❝✉❧❛s✱ t❛♠❜é♠ ❛s ❛♥t✐♣❛rtí❝✉❧❛s ♣♦❞❡♠ s❡r r❡♣r❡s❡♥t❛❞❛s ❞❡ss❛ ❢♦r♠❛✳ ◆❛ ❢♦r♠✉❧❛çã♦ ❞♦ ▼♦❞❡❧♦ P❛❞rã♦ ♦s ♥❡✉tr✐♥♦s t❡♠ ♠❛ss❛ ♥✉❧❛ ❡✱ ❛s ♣❛rtí❝✉❧❛s ✭❡❧étr♦♥✱ ♠ú♦♥✱ t❛✉ ❡ q✉❛r❦s✮ ❡ s✉❛ ❛♥t✐♣❛rtí❝✉❧❛s ♣♦ss✉❡♠ ♠❛ss❛ ❞✐❢❡r❡♥t❡ ❞❡ ③❡r♦✱ ❛❞q✉✐r✐❞❛s ♥♦ ♣r♦❝❡ss♦ ❞❡ q✉❡❜r❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐♠❡tr✐❛ ✭♥❛ ♣r❡s❡♥ç❛ ❞♦ ❝❛♠♣♦ ❞❡ ❍✐❣❣s✮✳

❚❛❜❡❧❛ ✶✿ ◆❛ t❛❜❡❧❛ ❛❜❛✐①♦ t❡♠♦s ❛s três ❢❛♠í❧✐❛s ❞❡ ❧é♣t♦♥s✱ ❝♦♠ s✉❛s ❝♦♠✲ ♣♦♥❡♥t❡s r✐❣❤t ❡ ❧❡❢t❀ t❛♠❜é♠ ❛s três ❢❛♠í❧✐❛s ❞❡ q✉❛r❦s✱ ❝♦♠ s✉❛s ❝♦♠♣♦♥❡♥t❡s r✐❣❤t ❡ ❧❡❢t✳ ❆ss✐♠ ❝♦♠♦ ♦ ✈❛❧♦r ❞♦ s❡✉ ✐s♦s♣✐♥✱ ❞❡ s✉❛ ❤✐♣❡r❝❛r❣❛ ❡ ❞❛ ❝❛r❣❛ ❡❧étr✐❝❛ ◗ ❞❡ ❝❛❞❛ ❢ér♠✐♦♥✳

❋ér♠✐♦♥s ❋❛♠í❧✐❛s I3 ❨ ◗

▲é♣t♦♥s νe e L νµ µ L ντ τ L

+1/2

−1/2 − 1

−1

0

−1

eR µR τR ✵ ✲✷ ✲✶

◗✉❛r❦s u d L c s L t b L

+1/2

−1/2

+1/3

−1/3

+2/3

−1/3

uR dR cR sR tR bR 0 0

+4/3

−2/3

+2/3

−1/3

❋♦♥t❡✿ ✭❘❖▼➹❖✱ ✷✵✵✸✮

❈❛❞❛ ❢❛♠í❧✐❛ é r❡♣r❡s❡♥t❛❞❛ ♣♦r ❝❛♠♣♦s✱ ♣♦r ❡①❡♠♣❧♦ ♣❛r❛ ♦ ❡❧étr♦♥ ❡ s❡✉ ♥❡✉tr✐♥♦

E = νe

e

!

✱ q✉❡ ♣♦❞❡♠ s❡r ❡①♣r❡ss♦s ❡♠ t❡r♠♦s ❞♦ ♣r♦❥❡t♦r ❞❡ ❤❡❧✐❝✐❞❛❞❡ ❧❡❢t ❡ r✐❣❤t✿

EL=

νeL

eL !

= 1−γ

5 2 νe e ! . ✭✸✶✮ ❡

eR=

1 +γ5

2 e. ✭✸✷✮

❆ ♠❡s♠❛ r❡♣r❡s❡♥t❛çã♦ ♣♦❞❡ s❡r r❡❛❧✐③❛❞❛ ♣❛r❛ ♦✉tr❛s ❢❛♠í❧✐❛s ❞❡ ♣❛rtí❝✉❧❛s✳

✷✳✷✳✶ ◗✉❡❜r❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐♠❡tr✐❛

✷✼

r❡❝❡♠ ♣❛rtí❝✉❧❛s ❛ss♦❝✐❛❞❛s ❛♦s ❝❛♠♣♦s ❝♦♠ ♠❛ss❛ ♥✉❧❛ ❡ ♠❛ss❛ ❞✐❢❡r❡♥t❡ ❞❡ ③❡r♦✳ P❛r❛ ✐❧✉str❛r ❛ q✉❡❜r❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐♠❡tr✐❛✱ ❝♦♥s✐❞❡r❡♠♦s ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ❝♦♥st✐✲ t✉í❞❛ s♦♠❡♥t❡ ♣♦r ❝❛♠♣♦s ❡s❝❛❧❛r❡s ❝♦♠♣❧❡①♦s✱ q✉❡ é ✐♥✈❛r✐❛♥t❡ s♦❜ ✉♠❛ tr❛♥s❢♦r♠❛çã♦ ❣❧♦❜❛❧ ❞♦ ❣r✉♣♦U(1)

L=∂µφ∗∂µφ−µ2φ∗φ−λ(φ∗φ)2, ✭✸✸✮ ❝✉❥♦ ♣♦t❡♥❝✐❛❧ é✿

V =µ2_φ∗_φ+λ(φ∗_φ)2_{. ✭✸✹✮}

P❛r❛ ❡♥❝♦♥tr❛r ♦ ❡st❛❞♦ ❞❡ ♠í♥✐♠❛ ❡♥❡r❣✐❛ ❞❛ t❡♦r✐❛✱ ❜❛st❛ ❡♥❝♦♥tr❛r ♦ ♣♦♥t♦ ❞❡ ♠í♥✐♠♦ ❞♦ ♣♦t❡♥❝✐❛❧✱ ❢❛③❡♥❞♦ dV

dφ = 0✳ ❖ ♣♦t❡♥❝✐❛❧ ❞❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✭✸✸✮ ❞❡♣❡♥❞❡ ❞♦ ✈❛❧♦r ❛r❜✐trár✐♦ ❞❡µ2_{✳ ◗✉❛♥❞♦ ♦ µ}2 _{>0✱ ♦ ♣♦t❡♥❝✐❛❧ t❡♠ ❛ ❢♦r♠❛ ❞❡ ✉♠❛ ♣❛rá❜♦❧❛ ❝♦♠}

❝♦♥❝❛✈✐❞❛❞❡ ✈♦❧t❛❞❛ ♣❛r❛ ❝✐♠❛✱ ✈❡r ✜❣✉r❛ ✭✶❛✮ ✱ ❝♦♠ ✉♠ ♠í♥✐♠♦ ❡♠ φ = 0✳ P♦rt❛♥t♦✱

s♦❧✉çã♦ tr✐✈✐❛❧ ❡ s❡rá ❞❡s❝❛rt❛❞❛✳ ◗✉❛♥❞♦ µ2 _{<0 ♦ ♣♦t❡♥❝✐❛❧ t❡♠ ❛ ❢♦r♠❛ ❞❛ ✜❣✉r❛ ✭✶❜✮}

❝♦♠ ❞♦✐s ♠í♥✐♠♦s✱ ❡♠φ =_±

q µ2

2λ =±v✳

❋✐❣✉r❛ ✶✿ P♦t❡♥❝✐❛❧ ❡s❝❛❧❛r✳ ❛✮ P❛r❛ µ2 _{>0 ❤á ❛♣❡♥❛s ✉♠ ♠í♥✐♠♦ ❡♠ φ = 0✳}

❜✮ ◗✉❛♥❞♦ µ2 _{<0 ❤á ❞♦✐s ♠í♥✐♠♦sφ =±}qµ2

2λ =±v✳

❋♦♥t❡✿ ❆❞❛♣t❛❞♦ ♣❡❧♦ ❛✉t♦r ✭❈▼❙✱ ✷✵✶✺✮✳

❆❣♦r❛ q✉❡ ❡♥❝♦♥tr❛♠♦s ♦s ♣♦♥t♦s ❞❡ ♠í♥✐♠♦s ❞♦ ♣♦t❡♥❝✐❛❧ é ♣♦ssí✈❡❧ ❡st✉❞❛r ❛ r❡❣✐ã♦ ❡♠ t♦r♥♦ ❞♦ ♠í♥✐♠♦✱ ❢❛③❡♥❞♦ ✉♠❛ ♣❡q✉❡♥❛ ♣❡rt✉❜❛çã♦ ❞♦ t✐♣♦ φ(x) = v +χ(x)✳ P♦✲

❞❡r✐❛♠♦s s✉❜st✐t✉✐r φ(x) = v +χ(x) ❞✐r❡t❛♠❡♥t❡ ♥❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✭✸✸✮✱ ♠❛s é

❝♦♥✈❡♥✐❡♥t❡ ♣❛r❛♠❡tr✐③❛r ❞❡ ✉♠❛ ❢♦r♠❛ ❞✐❢❡r❡♥t❡✱ ✉s❛♥❞♦ ❛ ❢♦r♠❛ ❡①♣♦♥❡♥❝✐❛❧ ❞♦ ❝❛♠♣♦ ❝♦♠♣❧❡①♦✱ ❡♠ t❡r♠♦s ❞❡ ❞♦✐s ❝❛♠♣♦s ❡s❝❛❧❛r❡s r❡❛✐sζ(x) ❡ρ(x)✱ ❢❛③❡♥❞♦ ❛ s❡❣✉✐♥t❡ r❡❞❡✲

✜♥✐çã♦ ♣❛r❛φ(x)✿

φ(x) =e√₂i

vζ(x)(v+ ρ√(x)

2 ). ✭✸✺✮

❉❡r✐✈❛♥❞♦ ✭✸✺✮ ❡ s✉❜st✐t✉✐♥❞♦ ♥❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✭✸✸✮✱ ♦❜t❡♠♦s ✉♠❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ❝♦♠ ❞♦✐s ❝❛♠♣♦s ❡s❝❛❧❛r❡s✿

L= 1 2∂µζ∂

µ_ζ+1

2∂µρ∂

µ_ρ

✷✽

❆q✉✐ ❛ q✉❡❜r❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐♠❡tr✐❛ ♣r♦♣♦r❝✐♦♥♦✉ ✉♠❛ ♣❛rtí❝✉❧❛ ❛ss♦❝✐❛❞❛ ❛♦ ❝❛♠♣♦

ρ ❝♦♠ ♠❛ss❛ ✐❣✉❛❧ mρ = p

−2µ2 ❡ ♦✉tr❛ ❛ss♦❝✐❛❞♦ ❛♦ ❝❛♠♣♦ _ζ ❝♦♠ ♠❛ss❛ _m

ζ = 0✱ ❝❤❛♠❛❞♦ ❞❡ ❜ós♦♥ ❞❡ ◆❛♠❜✉✲●♦❧❞st♦♥❡✳ ❆ ✐♥t❡r♣r❡t❛çã♦ ♣❛r❛ ❡ss❡ r❡s✉❧t❛❞♦ é q✉❡ ♦ ❝❛♠♣♦ρ♦s❝✐❧❛ ♥❛ ❞✐r❡çã♦ r❛❞✐❛❧ ❡✱ ♣♦rt❛♥t♦✱ ❡①✐st❡ ✉♠❛ ✧❢♦rç❛✧❛❣✐♥❞♦ s♦❜r❡ ❡❧❡✱ ❡♥q✉❛♥t♦

♦ ❝❛♠♣♦ζ ♦s❝✐❧❛ ❞❡s❝r❡✈❡♥❞♦ ✉♠ â♥❣✉❧♦ ♥♦ ♣❧❛♥♦ ♦♥❞❡ ♦ ♣♦t❡♥❝✐❛❧ é ❝♦♥st❛♥t❡✱ ♣♦rt❛♥t♦

❛ ✧❢♦rç❛✧s❡r✐❛ ♥✉❧❛✳ P❛r❛ ❣r✉♣♦s ❞❡ s✐♠❡tr✐❛s q✉❡ ♣♦ss✉❡♠ ♠❛✐s ❣❡r❛❞♦r❡s✱ ♣♦❞❡♠♦s s❛❜❡r ♦ ♥ú♠❡r♦ ❞❡ ❜ós♦♥ ❞❡ ◆❛♠❜✉✲●♦❧❞st♦♥❡ q✉❡ ✈ã♦ ❛♣❛r❡❝❡r q✉❛♥❞♦ s❡ ❢❛③ ❛ q✉❡❜r❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐♠❡tr✐❛✱ ♣♦r ♠❡✐♦ ❞♦ t❡♦r❡♠❛ ❞❡ ●♦❧❞st♦♥❡✱ q✉❡ é ✉♠❛ ❣❡♥❡r❛❧✐③❛çã♦ ❞♦ q✉❡ ❢♦✐ ❛♣r❡s❡♥t❛❞♦ ❛❝✐♠❛ ♣❛r❛ ❣r✉♣♦s ❞❡ s✐♠❡tr✐❛s ♠❛✐♦r❡s✳ ❖ t❡♦r❡♠❛ ❞❡ ●♦❧❞st♦♥❡ ✭●❖▲❉❙❚❖◆❊✱ ✶✾✻✶✮ r❡❧❛❝✐♦♥❛ ♦ ♥ú♠❡r♦ ❞❡ ❣❡r❛❞♦r❡s ❞♦ ❣r✉♣♦ ❞❡ s✐♠❡tr✐❛ ♣❛r❛ q✉❛❧ ✉♠❛ t❡♦r✐❛ é ✐♥✈❛r✐❛♥t❡✱ ❝♦♠ ♦ ♥ú♠❡r♦ ❞❡ ❣❡r❛❞♦r❡s ❞♦ ❣r✉♣♦ ❞❡ s✐♠❡tr✐❛ ❞♦ ✈á❝✉♦✱ q✉❡ é ♦❜t✐❞♦ ❛♣ós ❛ q✉❡❜r❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐♠❡tr✐❛✳ ❙❡❣✉♥❞♦ ♦ t❡♦r❡♠❛✱ ♦ ♥ú♠❡r♦ ❞❡ ♣❛rtí❝✉❧❛s ❝♦♠ ♠❛ss❛ ♥✉❧❛ ✭❜ós♦♥s ❞❡ ◆❛♠❜✉ ●♦❧❞st♦♥❡✮ ❢♦r♠❛❞❛s ❛♣ós ❛ q✉❡❜r❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐♠❡tr✐❛ é ✐❣✉❛❧ à ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦ ♥ú♠❡r♦ ♦r✐❣✐♥❛❧ ❞❡ ❣❡r❛❞♦r❡s ❞❛ t❡♦r✐❛ ❡ ♦ ♥ú♠❡r♦ ❞❡ ❣❡r❛❞♦r❡s ❞♦ ❣r✉♣♦ s✐♠❡tr✐❛ ❞♦ ✈á❝✉♦✳ ◆♦ ❡①❡♠♣❧♦ ❛❝✐♠❛ ❛ t❡♦r✐❛ ❡r❛ ✐♥✈❛r✐â♥t❡ ♣❡❧♦ ❣r✉♣♦ ❞❡ s✐♠❡tr✐❛ U(1)✱ q✉❡ ♣♦ss✉✐ ✉♠ ❣❡r❛❞♦r✱ ♦ ✈á❝✉♦ ✜❝♦✉ s❡♠ s✐♠❡tr✐❛ ❛❧❣✉♠❛ ❡✱

♣♦rt❛♥t❡ t✐♥❤❛♠♦s q✉❡ ❡♥❝♦♥tr❛r ✉♠ ❜ós♦♥ ❞❡ ◆❛♠❜✉ ●♦❧❞st♦♥❡✳

✷✳✷✳✷ ▼❡❝❛♥✐s♠♦ ❞❡ ❍✐❣❣s

❖ ▼❡❝❛♥✐s♠♦ ❞❡ ❍✐❣❣s é ❞❡ ❢✉♥❞❛♠❡♥t❛❧ ✐♠♣♦rtâ♥❝✐❛ ♥♦ ▼♦❞❡❧♦ P❛❞rã♦ ♣❛r❛ ❛ ❣❡r❛çã♦ ❞❡ ♠❛ss❛ ❞❛s ♣❛rtí❝✉❧❛s ✐♥t❡r♠❡❞✐❛❞♦r❛s ❞❛s ✐♥t❡r❛çõ❡s ❢r❛❝❛s ✭W∓ _{❡ Z}0_{✮ ❜❡♠}

❝♦♠♦ ♣❛r❛ ♦ r❡st❛♥t❡ ❞❛s ♣❛rtí❝✉❧❛s ▼♦❞❡❧♦ P❛❞rã♦✳ ◆❡st❡ ❝❛s♦✱ ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ♣r❡❝✐s❛ t❡r ❛❧é♠ ❞❡ ❝❛♠♣♦s ✈❡t♦r✐❛✐s✱ ❝❛♠♣♦s ❡s❝❛❧❛r❡s ✭❝❛♠♣♦s ❞❡ ❍✐❣❣s✮✳ ❆❧é♠ ❞❡ ❣❡r❛r ♠❛ss❛ ❛♦s ❜ós♦♥s ❞❡ ❣❛✉❣❡✱ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❍✐❣❣s ❧❡✈❛ t❛♠❜é♠ ❛♦ s✉r❣✐♠❡♥t♦ ❞❡ ✉♠❛ ♥♦✈❛ ♣❛rtí❝✉❧❛✱ ♦ ❜ós♦♥ ❞❡ ❍✐❣❣s✳ ❆ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ✭✸✼✮ é ❛ ❢♦r♠❛ ♠❛✐s ❣❡r❛❧ ❞❡ r❡♣r❡s❡♥t❛r ♦ ▼♦❞❡❧♦ P❛❞rã♦✱ ❡ s❡rá ❡st✉❞❛❞❛ ❞❡t❛❧❤❛❞❛♠❡♥t❡ ♥❛ ♣ró①✐♠❛ s✉❜s❡çã♦ ✭✷✳✸✮✳ ◆❡❧❛ ♣♦❞❡♠♦s ✐♥❞❡♥t✐✜❝❛r ♦s s❡❣✉✐♥t❡s t❡r♠♦s✿ ♦ ♣r✐♠❡✐r♦ é ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ q✉❡ ❞❡s❝r❡✈❡ ❛ ❞✐♥â♠✐❝❛ ❞♦s ❝❛♠♣♦s ❞❡ ❣❛✉❣❡LY M❀ ♦ s❡❣✉♥❞♦ t❡r♠♦ é ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ❞❡ ❍✐❣❣sLH✱ q✉❡ ♣♦ss✉✐ ♦s ❝❛♠♣♦s ❞❡ ❍✐❣❣s❀ ♦ t❡r❝❡✐r♦ t❡r♠♦ é ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ❞❡ ❨✉❦❛✇❛ LY uk✱ q✉❡ ❞á ❛ ♠❛ss❛ ❛♦s ❢ér♠✐♦♥s ❞♦ ▼♦❞❡❧♦ P❛❞rã♦ ♣❡❧❛ ✐♥t❡r❛çã♦ ❝♦♠ ♦ ❝❛♠♣♦ ❞❡ ❍✐❣❣s ❛♣ós ❛ q✉❡❜r❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐♠❡tr✐❛ ❡ ♦ ú❧t✐♠♦ t❡r♠♦ Lf erm✱ é ❛ ❞❡♥s✐❞❛❞❡ ❧❛❣r❛♥❣✐❛♥❛ ❛ss♦❝✐❛❞❛ ❛♦s ❢ér♠✐♦♥s✳