Luận án Tiến sĩ Thế higgs trong mô hình 331 với cơ chế KCS và phân loại các mô hình 331 dựa trên những dữ liệu

BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC SƯ PHẠM HÀ NỘI 2 KHOA VẬT LÝ LUẬN ÁN TIẾN SĨ THẾ HIGGS TRONG MÔ HÌNH 3-3-1 VỚI CƠ CHẾ CKS VÀ PHÂN LOẠI CÁC MÔ HÌNH 3-3-1 DỰA TRÊN DỮ LIỆU TÍCH Y

BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC SƯ PHẠM HÀ NỘI 2

KHOA VẬT LÝ

LUẬN ÁN TIẾN SĨ

THẾ HIGGS TRONG MÔ HÌNH 3-3-1 VỚI

CƠ CHẾ CKS VÀ PHÂN LOẠI CÁC MÔ

HÌNH 3-3-1 DỰA TRÊN DỮ LIỆU TÍCH YẾU

Chuyên ngành: Vật lý lý thuyết và Vật lý toán

▲í✐ ❝↔♠ ì♥

❚æ✐ ✈è♥ ❧➔ ♠ët ❤å❝ trá t✐♥❤ t➜♥ ✈➔ ❝ô♥❣ ❧➔ ♠ët ♥❣÷í✐ t❤➛② ❝❤➠♠ ❝❤➾✱ ♥❤÷♥❣

♣❤↔✐ t❤ó t❤➟t r➡♥❣ q✉➣♥❣ t❤í✐ ❣✐❛♥ ❧➔♠ ♥❣❤✐➯♥ ❝ù✉ s✐♥❤ ❚✐➳♥ s➽ ❧➔ ❣✐❛✐ ✤♦↕♥t❤→❝❤ t❤ù❝ ♥❤➜t tr♦♥❣ ✤í✐ tæ✐ t➼♥❤ ❝❤♦ ✤➳♥ ❧ó❝ ♥➔②✳ ❍➔♥❤ tr➻♥❤ trð t❤➔♥❤ ❚✐➳♥s➽ tü❛ ♥❤÷ ♠ët ❝❤✉②➳♥ ✤✐ r❛ ❜✐➸♥ ❧î♥✳ ❉ò ❝â sü ❝❤✉➞♥ ❜à ❝❤✉ ✤→♦ ✤➳♥ ✤➙✉✱ ✈➔

❚æ✐ r➜t ❜✐➳t ì♥ ❚❤➛② ❤÷î♥❣ ❞➝♥✱ ❚❙✳ ◆❣✉②➵♥ ❍✉② ❚❤↔♦✱ ♥❣÷í✐ ✤➣ ❧✉æ♥s♦♥❣ ❤➔♥❤ ❝ò♥❣ tæ✐ tr♦♥❣ ❝❤✉②➯♥ ♠æ♥✱ ❝❤✐❛ s➫ ❦❤✐ ✈✉✐ ❜✉ç♥ ✈➔ ✤➣ ❤é trñ tæ✐ tè✐

✤❛ tr♦♥❣ ✈✐➺❝ ❧➟♣ ❦➳ ❤♦↕❝❤ ❤å❝ t➟♣ ❝ô♥❣ ♥❤÷ ❤♦➔♥ t➜t ♠å✐ t❤õ tö❝ ❧✐➯♥ q✉❛♥ ✤➳♥q✉→ tr➻♥❤ ✤➔♦ t↕♦ t✐➳♥ s➽✳

❚æ✐ ①✐♥ ❝â ✤æ✐ ❞á♥❣ ❝↔♠ ì♥ ❚❙✳ ▲➯ ❚❤å ❍✉➺✱ ♠ët ♥❣÷í✐ ❛♥❤ ❡♠ ❦➲ ✈❛✐ s→t

❝→♥❤ ❝ò♥❣ tæ✐✱ ❝❤➥♥❣ ♥❤ú♥❣ ❤é trñ tæ✐ ♥❤ú♥❣ ❦❤â ❦❤➠♥ tr♦♥❣ s✐♥❤ ❤♦↕t ❧ó❝ ✤✐

❤å❝ ♠➔ ❝á♥ ❝❤♦ tæ✐ ♥❤ú♥❣ ❝❤➾ ❞➝♥ ❝❤✉②➯♥ ♠æ♥ tø ❆ ✤➳♥ ❩ ♥❤ú♥❣ ❦❤✐ tæ✐ ❦❤æ♥❣

✶

❝â ❚❤➛② ❜➯♥ ❝↕♥❤✳ ❈↔♠ ì♥ P●❙✳❚❙ ❍➔ ❚❤❛♥❤ ❍ò♥❣✱ ♥❣÷í✐ ❜↕♥ s➤♥ s➔♥❣ ❝❤✐❛s➩ ✈✉✐ ❜✉ç♥✱ ✤ë♥❣ ✈✐➯♥ ❦❤➼❝❤ ❧➺ tæ✐ tr♦♥❣ ♥❤ú♥❣ t❤→♥❣ ♥❣➔② tæ✐ sè♥❣ ✈➔ ❧➔♠ ✈✐➺❝

❙❛✉ ❝ò♥❣✱ tæ✐ ①✐♥ ❞➔♥❤ ✈✐♥❤ ❞ü ✈➔ t❤➔♥❤ q✉↔ ♥➔② ❝❤♦ ❈❤❛✱ ▼➭✱ ❆♥❤ ❈❤à

❊♠✱ ❱ñ ✈➔ ❝→❝ ❝♦♥ ❝õ❛ tæ✐✱ ♥❤ú♥❣ ♥❣÷í✐ ✤➣ ❧✉æ♥ ②➯✉ t❤÷ì♥❣✱ ❝❤✐❛ s➩✱ ❤② s✐♥❤

✈➔ ❞ã✐ t❤❡♦ ♠å✐ ❜÷î❝ ✤✐ ❝õ❛ tæ✐✳ ❳✐♥ ✤➦❝ ❜✐➺t ❝↔♠ ì♥ ❝♦♥ ❣→✐ ❜↔② t✉ê✐ ◆❣✉②➵♥

❚❤ò② ❉÷ì♥❣ ❝õ❛ tæ✐✱ t✉② ❜➨ ♥❤÷♥❣ ❧✉æ♥ ❧➔ ✤ë♥❣ ❧ü❝✱ ♥✐➲♠ ❛♥ õ✐ ✈➔ ❧➔ ❝❤é ❞ü❛t✐♥❤ t❤➛♥ ✈ú♥❣ ❝❤➢❝ ❝õ❛ tæ✐✳

▲✉➟♥ →♥ ♥➔② ❧➔ t❤➔♥❤ q✉↔ ❝õ❛ ❤♦↕t ✤ë♥❣ ♥❣❤✐➯♥ ❝ù✉ tr♦♥❣ ❦❤♦↔♥❣ ✸ ♥➠♠tæ✐ ✤÷ñ❝ ❧➔♠ ✈✐➺❝ tr♦♥❣ ♥❤â♠ ♥❣❤✐➯♥ ❝ù✉ ❞♦ ●❙✳ ❍♦➔♥❣ ◆❣å❝ ▲♦♥❣ ❝❤õ tr➻✳ ▼ët

→♥ ❝õ❛ tæ✐ ✤÷ñ❝ ①➙② ❞ü♥❣✱ ♣❤➛♥ ❝á♥ ❧↕✐ ❝õ❛ ❝❤÷ì♥❣ ♥➔② ❧➔ ✤â♥❣ ❣â♣ ❦❤♦❛ ❤å❝

❝õ❛ ♥❤â♠ ❝❤ó♥❣ tæ✐✳ ❈❤÷ì♥❣ ✷ ✈➔ ❝❤÷ì♥❣ ✸ tr➻♥❤ ❜➔② ❝❤õ ②➳✉ ❞ü❛ tr➯♥ ❝→❝ ❝æ♥❣tr➻♥❤ ❦❤♦❛ ❤å❝ ❝õ❛ ♥❤â♠ ♥❣❤✐➯♥ ❝ù✉ ❝â tæ✐ t❤❛♠ ❣✐❛✳ P❤➛♥ ❦➳t ❧✉➟♥ tâ♠ t➢t ❧↕✐

❝→❝ ❦➳t q✉↔ ❦❤♦❛ ❤å❝ ❝❤➼♥❤ ❝õ❛ ❧✉➟♥ →♥✳

❈✉è✐ ❝ò♥❣✱ tæ✐ ①✐♥ ❝❛♠ ❦➳t ❝→❝ ❦➳t q✉↔ ❝❤➼♥❤ tr♦♥❣ ❧✉➟♥ →♥ ✧❚❤➳ ❍✐❣❣str♦♥❣ ♠æ ❤➻♥❤ ✸✲✸✲✶ ✈î✐ ❝ì ❝❤➳ ❈❑❙ ✈➔ ♣❤➙♥ ❧♦↕✐ ❝→❝ ♠æ ❤➻♥❤ ✸✲✸✲✶

❝ù✉ ♠➔ tæ✐ t❤❛♠ ❣✐❛✱ ❦❤æ♥❣ trò♥❣ ❧➦♣ ✈î✐ ❦➳t q✉↔ tr♦♥❣ ❧✉➟♥ →♥ ❦❤→❝ ❤❛② ❝æ♥❣tr➻♥❤ ❦❤♦❛ ❤å❝ ❦❤→❝ ✤➣ ❝â✳

✭t→❝ ❣✐↔✮

✸

✻ ▼➟t ✤ë t➔♥ ❞÷ Ωh2 ❧➔ ❤➔♠ t❤❡♦ ❦❤è✐ ❧÷ñ♥❣ m ϕ ❝õ❛ ù♥❣ ✈✐➯♥ ✈➟t

❝❤➜t tè✐ ✈æ ❤÷î♥❣ ϕ✱ ❦❤✐ ①➨t ✈î✐ ♠ët sè ❣✐→ trà ❝õ❛ ❤➺ sè ✈æ ❤÷î♥❣

❜➟❝ ❤❛✐ λh2 ϕ 2 = 0.5, 0.7, 0.8, 0.9, 1✱ t÷ì♥❣ ù♥❣ ✈î✐ ❝→❝ ✤÷í♥❣ ❝♦♥❣ tøtr➯♥ ①✉è♥❣ ❞÷î✐✳ ✣÷í♥❣ t❤➥♥❣ ♥➡♠ ♥❣❛♥❣ t❤➸ ❤✐➺♥ ❣✐→ trà q✉❛♥s→t ✤÷ñ❝ Ωh2 = 0.1198 ❬✷✵✼❪ ❝õ❛ ♠➟t ✤ë t➔♥ ❞÷✳ ❈→❝ ✤÷í♥❣ t❤➥♥❣

✤ù♥❣ t÷ì♥❣ ù♥❣ ✈î✐ ❝→❝ ❣✐→ trà ❜✐➯♥ ❞÷î✐ 300 ●❡❱ ✈➔ ❜✐➯♥ tr➯♥570

●❡❱ ❝õ❛ ❦❤è✐ ❧÷ñ♥❣ m ϕ ❞ü❛ t❤❡♦ ♣❤➨♣ ✤♦ t❤ü❝ ♥❣❤✐➺♠ ✤è✐ ✈î✐

♠➟t ✤ë t➔♥ ❞÷ ✈➟t ❝❤➜t tè✐✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹

✼ ❚÷ì♥❣ q✉❛♥ ❣✐ú❛ ❤➡♥❣ sè ✈æ ❤÷î♥❣ ❜➟❝ ❤❛✐ ✈➔ ❦❤è✐ ❧÷ñ♥❣ m ϕ ❝õ❛ù♥❣ ✈✐➯♥ ✈➟t ❝❤➜t tè✐ ✈æ ❤÷î♥❣ϕ✱ ♣❤ò ❤ñ♣ ✈î✐ ❣✐→ trà t❤ü❝ ♥❣❤✐➺♠

✶✶ ∆QM331W (Cs) ❧➔ ❤➔♠ t❤❡♦ M Z 2 ✤è✐ ✈î✐ ♠æ ❤➻♥❤ ✸✲✸✲✶ ❧♦↕✐ ❆ ✭❤➻♥❤

❜➯♥ tr→✐✮ ✈➔ ❧♦↕✐ ❈ ✭❤➻♥❤ ❜➯♥ ♣❤↔✐✮✳ ❚➼♥❤ t♦→♥ ✈î✐s2W(M Z 2 ) = 0.246

✈➔ g = 0.636 ❬✶✽✵❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷

✾

❝ë♥❣ ♥❣❤➺ ❦❤→❝✳ ❱➼ ❞ö ♥❤÷ ❦❤→♠ ♣❤→ r❛ ♣❤➙♥ tû✱ ♥❣✉②➯♥ tû ❧➔ t✐➲♥ ✤➲ ❝❤♦ sü

♣❤→t tr✐➸♥ ♥❤↔② ✈åt ❝õ❛ ❤â❛ ❤å❝✱ s✐♥❤ ❤å❝ ✈➔ ❝→❝ ♥❣➔♥❤ ❝æ♥❣ ♥❣❤➺❀ ❦❤→♠ ♣❤→r❛ ❡❧❡❝tr♦♥ ❧➔ ❝ó ❤➼❝❤ ❝❤♦ sü ♣❤→t tr✐➸♥ ❝õ❛ ✤✐➺♥ ❤å❝✱ ❦❤♦❛ ❤å❝ ✈➟t ❧✐➺✉ ✈➔ ❦❤♦❛

❤å❝ ♠→② t➼♥❤❀ t➻♠ r❛ t÷ì♥❣ t→❝ ✤✐➺♥ tø ✈➔ ❤↕t ♣❤♦t♦♥ ❧➔ ❝❤➻❛ ❦❤â❛ ❝❤♦ sü ♣❤→ttr✐➸♥ ♥❣➔♥❤ ✤✐➺♥ tû✲✈✐➵♥ t❤æ♥❣❀ sü ❤✐➸✉ ✈➲ t÷ì♥❣ t→❝ ♠↕♥❤ ✈➔ ❝→❝ ❤↕t q✉❛r❦ ❧➔

❝ì sð ♣❤→t tr✐➸♥ ❝æ♥❣ ♥❣❤➺ ❤↕t ♥❤➙♥ ✈➔ t↕♦ r❛ ❝→❝ ù♥❣ ❞ö♥❣ ✤ët ♣❤→ tr♦♥❣ ②

❤å❝✱ s✐♥❤ ❤å❝ ✈➔ ♥æ♥❣ ♥❣❤✐➺♣✱✈✳✈✳✳✳

❈ô♥❣ ♥❤÷ ♥❤✐➲✉ ♥❣➔♥❤ ❦❤♦❛ ❤å❝ ❦❤→❝✱ ♥❤ú♥❣ t❤➔♥❤ tü✉ ♠➔ ♥❣➔♥❤ ✈➟t ❧þ ❤↕t

❝ì ❜↔♥ ✤↕t ✤÷ñ❝ ♥❤÷ ♥❣➔② ♥❛② ❧➔ ❞ü❛ ✈➔♦ ♥❣❤✐➯♥ ❝ù✉ ❧þ t❤✉②➳t ✈➔ ♥❣❤✐➯♥ ❝ù✉t❤ü❝ ♥❣❤✐➺♠✱ ❝❤ó♥❣ ❜ê s✉♥❣ ❝❤♦ ♥❤❛✉✱ ❞ü❛ ✈➔♦ ♥❤❛✉ ✈➔ t❤ó❝ ✤➞② ♥❤❛✉ ❝ò♥❣

✣➲ t➔✐ ❝õ❛ ❧✉➟♥ →♥ ♥➔② t❤✉ë❝ ❝❤✉②➯♥ ♥❣➔♥❤ ❱➟t ❧þ ❤↕t ❝ì ❜↔♥ ❧þ t❤✉②➳t✱ ❜→♠s→t ✈➔♦ ♣❤↕♠ ✈✐ ♥❣❤✐➯♥ ❝ù✉ ✈➔ ♠ö❝ t✐➯✉ ♥❣❤✐➯♥ ❝ù✉ ❝❤✉♥❣ ❝õ❛ ❝❤✉②➯♥ ♥❣➔♥❤✱

tø ✤â tr✐➸♥ ❦❤❛✐ t❤ü❝ ❤✐➺♥ ❝→❝ ❤♦↕t ✤ë♥❣ ♥❣❤✐➯♥ ❝ù✉ tr♦♥❣ ♣❤↕♠ ✈✐ ✈➔ ✈î✐ ♠ö❝t✐➯✉ ♥❣❤✐➯♥ ❝ù✉ ❝ö t❤➸ ❤ì♥✱ ♥❤÷ s➩ ✤÷ñ❝ tr➻♥❤ ❜➔② ð ♣❤➛♥ ❞÷î✐ ✤➙②✳

❚ê♥❣ q✉❛♥ t➻♥❤ ❤➻♥❤ ♥❣❤✐➯♥ ❝ù✉ ♥❣♦➔✐ ♥÷î❝ ✈➔ tr♦♥❣ ♥÷î❝

✲ ❚➼♥❤ t➜t ②➳✉ ♣❤↔✐ ♠ð rë♥❣ ▼æ ❤➻♥❤ ❝❤✉➞♥✿

❱➟t ❧þ ❤↕t ❝ì ❜↔♥ ❧þ t❤✉②➳t ✤➣ tr↔✐ q✉❛ ❤➔♥❤ tr➻♥❤ ❞➔✐ ✈î✐ ❝→❝ ❦❤→♠ ♣❤→ ✈➔t❤➔♥❤ tü✉ ✤÷ñ❝ t❤ü❝ ♥❣❤✐➺♠ ①→❝ ♥❤➟♥✱ ❤➔♥❤ tr➻♥❤ ✤â ❝ô♥❣ ✤ç♥❣ t❤í✐ ✤à♥❤ ❤➻♥❤

♥➔② ✤➣ ✤÷ñ❝ ✤→♥❤ ❣✐→ ✈➔ ①→❝ ♥❤➟♥ t↕✐ ❤ë✐ ♥❣❤à ❚♦❦②♦ ❘♦❝❤❡st❡r ❬✽❪✳

▼æ ❤➻♥❤ ❝❤✉➞♥ ❧➔ t✐♥❤ ❤♦❛ ❝õ❛ ❱➟t ❧þ ❤↕t ❝ì ❜↔♥✱ ♥â ✤➣ ✤÷❛ r❛ ❝→❝ ❦➳tq✉↔ ✈➔ t✐➯♥ ✤♦→♥ ♣❤ò ❤ñ♣ t✉②➺t ✈í✐ ✈î✐ ❝→❝ sè ❧✐➺✉ t❤ü❝ ♥❣❤✐➺♠✱ ✤➦❝ ❜✐➺t ❧➔ sü

❦✐➺♥ ❤↕t ❜♦s♦♥ ❍✐❣❣s ✶✷✻ ●❡❱ ♠➔ ♠æ ❤➻♥❤ ♥➔② t✐➯♥ ✤♦→♥ ✤➣ ✤÷ñ❝ ❦❤→♠ ♣❤→

ð ▲❍❈ ❬✶✼✱ ✶✽❪✳ ◆❣➔② ♥❛② ▼æ ❤➻♥❤ ❝❤✉➞♥ ✤➣ ✤÷ñ❝ ❝æ♥❣ ♥❤➟♥ rë♥❣ r➣✐ ❬✺✱ ✶✹❪ ✈➔trð t❤➔♥❤ ❦✐➳♥ t❤ù❝ ❣✐→♦ ❦❤♦❛ ✈➲ ❤↕t ❝ì ❜↔♥✳ ▼æ ❤➻♥❤ ❝❤✉➞♥ ✤➣ ❤♦➔♥ t❤➔♥❤ sù

♠↕♥❣ ❝õ❛ ♥â ①➨t ð ❦❤➼❛ ❝↕♥❤ ✤➣ ♠æ t↔ ✤÷ñ❝ ❝→❝ t÷ì♥❣ t→❝ ♠↕♥❤✱ ✤✐➺♥ tø ✈➔t÷ì♥❣ t→❝ ②➳✉❀ ♥ë✐ ❞✉♥❣ ❤↕t ❝ì ❜↔♥ ♠➔ ♥â ①➙② ❞ü♥❣ t➜t ❝↔ ✤➲✉ ✤➣ ✤÷ñ❝ t❤ü❝

✲ ❱✐➺❝ ①➙② ❞ü♥❣ ❝→❝ ♠æ ❤➻♥❤ ✸✲✸✲✶ ♥❤÷ ❧➔ ♠ët tr♦♥❣ ♥❤ú♥❣ ❝→❝❤t❤ù❝ ♠ð rë♥❣ ▼æ ❤➻♥❤ ❝❤✉➞♥✿

❚r♦♥❣ ▼æ ❤➻♥❤ ❝❤✉➞♥✱ ❝➜✉ tró❝ t❤❡♦ t❤➳ ❤➺ ❝õ❛ ❝→❝ t÷ì♥❣ t→❝ ❨✉❦❛✇❛ ❦❤æ♥❣

❜à ❤↕♥ ❝❤➳ ❜ð✐ ❜➜t ❜✐➳♥ ❝❤✉➞♥✳ ❉♦ ✤â✱ ❝→❝ ❦❤è✐ ❧÷ñ♥❣ ✈➔ ❣â❝ trë♥ ❢❡r♠✐♦♥ ❦❤æ♥❣

❝è ✤à♥❤ ✤è✐ ✈î✐ ❝→❝ tr÷í♥❣ ♣❤➙♥ ❝ü❝ tr→✐✱ ✈➔ ▼æ ❤➻♥❤ ❝❤✉➞♥ ❦❤æ♥❣ ✤÷❛ r❛ sü ❣✐↔✐t❤➼❝❤ ❝❤♦ sü ♣❤➙♥ ❜➟❝ rë♥❣ ❝õ❛ ❝→❝ ✤↕✐ ❧÷ñ♥❣ ♥➔②✱ sü ♣❤➙♥ ❜➟❝ ✈è♥ tr↔✐ rë♥❣tr♦♥❣ ❦❤♦↔♥❣ ♥➠♠ ❜➟❝ ✤ë ❧î♥ ♥➳✉ ❝❤➾ ①➨t r✐➯♥❣ ♣❤➛♥ q✉❛r❦ ✈➔ t➠♥❣ ❧➯♥ ✤ët ❜✐➳♥

✤➳♥ ❦❤♦↔♥❣ ✶✶ ❜➟❝ ✤ë ❧î♥ ♥➳✉ ❝❤ó♥❣ t❛ ①➨t ❣ë♣ ❝↔ ✈➔♦ ❝→❝ ♥❡✉tr✐♥♦✳ ❚❤➟♠ ❝❤➼tr♦♥❣ ▼æ ❤➻♥❤ ❝❤✉➞♥ ❝→❝ t❤❛♠ sè ♥➔② ❝❤➾ ❝â ♠➦t tr♦♥❣ ❝→❝ sè ❤↕♥❣ t÷ì♥❣ t→❝

✈➔♦ sü ❦❤→❝ ❜✐➺t ❦❤è✐ ❧÷ñ♥❣ ✤♦ ✤÷ñ❝ ❝õ❛ ❝→❝ ♥❡✉tr✐♥♦✳ ✣✐➲✉ ♥➔② ❧➔ ❜➡♥❣ ❝❤ù♥❣t❤✉②➳t ♣❤ö❝ ❝❤ù♥❣ tä r➡♥❣ ❝â ➼t ♥❤➜t ❤❛✐ ♥❡✉tr✐♥♦ ❝â ❦❤è✐ ❧÷ñ♥❣ ❦❤→❝ ❦❤æ♥❣✱

♥❣❤✐➯♥ ❝ù✉

❚r♦♥❣ ♣❤➛♥ ❧î♥ ❝→❝ ♠æ ❤➻♥❤ ✸✲✸✲✶✱ ♠ët tr÷í♥❣ t❛♠ t✉②➳♥ ♥➦♥❣ ✈î✐ tr✉♥❣

✶✹

♠ët sè ♠æ ❤➻♥❤ t→✐ ❝❤✉➞♥ ❤â❛ ✤÷ñ❝ ♥❤÷♥❣ ❧↕✐ ❦❤æ♥❣ ❣✐↔✐ q✉②➳t ✤÷ñ❝ ♣❤➛♥ ❣â❝trë♥ ✈➔ ❦❤è✐ ❧÷ñ♥❣ ❝õ❛ ❝→❝ ❢❡r♠✐♦♥ ✤➣ ❜✐➳t ❞♦ sü ♣❤➙♥ ❜➟❝ ❧î♥ ❦❤æ♥❣ ❣✐↔✐ t❤➼❝❤

✤÷ñ❝ ❝õ❛ ❝→❝ t÷ì♥❣ t→❝ ❨✉❦❛✇❛ ❬✹✾✱ ✺✶✕✺✹✱ ✶✸✻✱ ✶✸✼✱ ✶✹✽❪ ✈➔ ♥❤ú♥❣ ♠æ ❤➻♥❤ ❝á♥

❧↕✐ ❝❤➾ t➟♣ tr✉♥❣ ❣✐↔✐ q✉②➳t ❤♦➦❝ ✈➜♥ ✤➲ ♣❤➙♥ ❜➟❝ ❦❤è✐ ❧÷ñ♥❣ q✉❛r❦ ❬✺✵✱✶✹✷✱✶✹✺❪

❤♦➦❝ ♣❤➛♥ ♥❡✉tr✐♥♦ ❬✶✸✹✱ ✶✸✽✕✶✹✶✱ ✶✹✸✱ ✶✹✻✱ ✶✹✼✱ ✶✹✾✱ ✶✺✵❪✱ ❤♦➦❝ ❝❤➾ ①➙② ❞ü♥❣ sü

♣❤➙♥ ❜➟❝ ❦❤è✐ ❧÷ñ♥❣ ❢❡r♠✐♦♥ ♠æ ❤➻♥❤ ❝❤✉➞♥ ♠➔ ❦❤æ♥❣ ❣✐↔✐ q✉②➳t ✈➜♥ ✤➲ ❣â❝trë♥ ❢❡r♠✐♦♥ ❬✶✹✹❪

✣➸ ①➙② ❞ü♥❣ ♠ët ❝→❝❤ ❣✐↔✐ q✉②➳t ❦❤→❝ ✤è✐ ✈î✐ ✈➜♥ ✤➲ ❣â❝ trë♥ ✈➔ ❦❤è✐ ❧÷ñ♥❣

❝õ❛ ♣❤➛♥ ❢❡r♠✐♦♥ ✤➣ ❜✐➳t✱♠➔ ✈➝♥ tr♦♥❣ ❦❤✉æ♥ ❦❤ê ❝→❝ ♠æ ❤➻♥❤ ✸✲✸✲✶✱ t❛ ❣✐↔ t❤✐➳tr➡♥❣ ❝❤ó♥❣ ❝â ♥❣✉ç♥ ❣è❝ tø ❝→❝ ✤â♥❣ ❣â♣ ❜ê ✤➼♥❤ ✈á♥❣ ❣✐↔♠ t✉➛♥ tü ✭s❡q✉❡♥t✐❛❧

❧♦♦♣ s✉♣♣r❡ss✐♦♥✮✳ ❈ö t❤➸ ❧➔✱ ❝→❝ ❦❤è✐ ❧÷ñ♥❣ ✤÷ñ❝ s✐♥❤ r❛ ♥❤÷ s❛✉✿ ❦❤è✐ ❧÷ñ♥❣ t♦♣q✉❛r❦ ♥➦♥❣ ♥❤➜t ð ❜➟❝ ❝➙②✱ ❦❤è✐ ❧÷ñ♥❣ ❝→❝ ❢❡r♠✐♦♥ ♥❤➭ ❤ì♥ ❣ç♠ q✉❛r❦ ❜♦tt♦♠✱

▼î✐ ✤➙②✱ ▼æ ❤➻♥❤ ✸✲✸✲✶ ✈î✐ ❝ì ❝❤➳ ❈❑❙ ✤➣ ✤÷ñ❝ ❝æ♥❣ ♥❤➟♥ ❬✶✼✵❪✱ ♥❣♦➔✐ ♥❤ú♥❣

✶✺

✶✼

♥❣✉②➯♥ tû ✭❆t♦♠ P❛r✐t② ❱✐♦❧❛t✐♦♥ ✲ ✈✐➳t t➢t ❧➔ ❆P❱✮ ✤è✐ ✈î✐ ❝❡s✐✉♠ ✈➔ tr♦♥❣ ❤✐➺♥t÷ñ♥❣ t→♥ ①↕ ❡❧❡❝tr♦♥ ✈✐ ♣❤↕♠ t➼♥❤ ❝❤➤♥ ❧➫ ✭P❛r✐t② ❱✐♦❧❛t✐♦♥ ❊❧❡❝tr♦♥ ❙❝❛tt❡r✐♥❣

❞÷î✐ ♠ët ❜✐➸✉ ❞✐➵♥ ❦❤→❝ ❣✐ó♣ ❣✐↔✐ t❤➼❝❤ sü ❝❤➯♥❤ ❧➺❝❤ ❧î♥ ✈➲ ❦❤è✐ ❧÷ñ♥❣ ❣✐ú❛ t❤➳

❤➺ q✉❛r❦ ♥➦♥❣ ♥❤➜t ✈î✐ ❤❛✐ t❤➳ ❤➺ ❦✐❛ ♥❤➭ ❤ì♥✱ ✭✐✐✐✮ ❝→❝ ♠æ ❤➻♥❤ ♥➔② ❝❤♦ ♣❤➨♣

❧÷ñ♥❣ tû ❤â❛ ✤✐➺♥ t➼❝❤ ❬✶✷✶✱✶✷✷❪✱ ✭✐✈✮ ❝→❝ ♠æ ❤➻♥❤ ♥➔② ❝❤ù❛ ✈➔✐ ♥❣✉ç♥ ✈✐ ♣❤↕♠

❈P ❬✶✷✸✱ ✶✷✹❪✱ ✭✈✮ ❝→❝ ♠æ ❤➻♥❤ ♥➔② ❣✐↔✐ t❤➼❝❤ ✤÷ñ❝ t↕✐ s❛♦ ❣â❝ trë♥ ❲❡✐♥❜❡r❣t❤ä❛ ♠➣♥ sin2θW < 14✱ ✭✈✐✮ ❝→❝ ♠æ ❤➻♥❤ ♥➔② ❝❤ù❛ ✤è✐ ①ù♥❣ P❡❝❝❡✐✲◗✉✐♥♥ tü

❈➠♥ ❝ù ✈➔♦ t❤❛♠ sè β ✤÷ñ❝ ❞ò♥❣ ✤➸ ✤à♥❤ ♥❣❤➽❛ t♦→♥ tû ✤✐➺♥ t➼❝❤ ❝→❝ ❤↕ttr♦♥❣ ❝→❝ ♠æ ❤➻♥❤ ✸✲✸✲✶ ♥❤÷ ❞÷î✐ ✤➙②

♥â✐ tr➯♥ ✤è✐ ✈î✐ ♣❤➛♥ q✉❛r❦ ❧➔ ð t➔✐ ❧✐➺✉ ❬✶✽✸❪ t❤❡♦ ❝→❝❤ t❤ù❝ ✤÷ñ❝ ❣å✐ ❧➔ ❝ì ❝❤➳

❋r♦❣❣❛tt✲◆✐❡❧s❡♥✳ ▼î✐ ✤➙②✱ ♠ët ❝→❝❤ t❤ù❝ ❦❤→❝ ✤÷ñ❝ ❣å✐ ❧➔ ❝ì ❝❤➳ →♣ ✈á♥❣ t✉➛♥

tü ✤÷ñ❝ ①❡♠ ❧➔ t❤✉②➳t ♣❤ö❝ ❤ì♥ ✈➻ ❤➺ sè →♣ ✭s✉♣♣r❡ss✐♦♥ ❢❛❝t♦r✮ ①✉➜t ♣❤→t tø

❤➺ sè ✈á♥❣ l ≈ (1/4π)2✱ ❝→❝❤ t❤ù❝ ♥➔② ✤÷ñ❝ ❣å✐ ❧➔ ❝ì ❝❤➳ ❈❑❙✱ ♥❤÷ ✤÷ñ❝ ✤➦t ❞ü❛t❤❡♦ t➯♥ ❝→❝ t→❝ ❣✐↔ ✤➲ ①✉➜t ♥â ❬✶✺✶❪✳ ❈ì ❝❤➳ ❋r♦❣❣❛tt✲◆✐❡❧s❡♥ ✤÷ñ❝ →♣ ❞ö♥❣ ❝❤♦

♥➔② ❞➝♥ ✤➳♥ ♥❤✉ ❝➛✉ t❤ü❝ ❤✐➺♥ ♥❣❤✐➯♥ ❝ù✉ s➙✉ ❤ì♥ ❝→❝ ❦❤➼❛ ❝↕♥❤ ❦❤→❝ ♥❤❛✉

✤➸ ①→❝ ✤à♥❤ ❦❤è✐ ❧÷ñ♥❣ ❝ò♥❣ ❝→❝ ✤➦❝ t➼♥❤ ❦❤→❝ ❝õ❛ ❜♦s♦♥ Z ′ ✣➸ ①→❝ ✤à♥❤ ❝→❝t❤❛♠ sè ♠æ ❤➻♥❤✱ t❛ t❤÷í♥❣ ❞ü❛ ✈➔♦ ❝→❝ ✤↕✐ ❧÷ñ♥❣ ✈➟t ❧þ ❦✐♥❤ ✤✐➸♥ ❝❤➥♥❣ ❤↕♥

♥❤÷ t❤❛♠ sè ρ✱ ❜ê ✤➼♥❤ t➼❝❤ ②➳✉ ❝õ❛ ❝→❝ ❤↕t ♥❤➙♥✱✈✳✈✳✳✳ ✣➙② ❧➔ ♠ö❝ ✤➼❝❤ ❝❤➼♥❤

❝õ❛ ❧✉➟♥ →♥ ♥➔②✳ ▼ët ❧÷✉ þ q✉❛♥ trå♥❣ ❧➔ ❝→❝ ✤↕✐ ❧÷ñ♥❣ ♥❤÷ t❤❛♠ sè ρ ❤❛② ❜ê

✤➼♥❤ t➼❝❤ ②➳✉ ✤➲✉ ❧✐➯♥ q✉❛♥ ✤➳♥ ❜♦s♦♥ ❝❤✉➞♥ tr✉♥❣ ❤á❛ ✈➔ ❞♦ ✤â ♣❤ö t❤✉ë❝ ✈➔♦

♠æ ❤➻♥❤✳ ❈❤♦ ♥➯♥ ♠é✐ ❦❤✐ tr✐➸♥ ❦❤❛✐ t➼♥❤ t♦→♥✱ ❦❤↔♦ s→t ð ♠é✐ ♠æ ❤➻♥❤✱ ❝❤ó♥❣t❛ ✤➲✉ ♣❤↔✐ ❞➔♥❤ ♠ët sü q✉❛♥ t➙♠ ♥❤➜t ✤à♥❤ ✤è✐ ✈î✐ ♣❤➛♥ ❜♦s♦♥ ❝❤✉➞♥ tr✉♥❣

❙❛✉ ❝ò♥❣ ❧➔ ❝→❝ ❤↕t ♥❤➭ ♥❤➜t ♥❤÷✿ q✉❛r❦ ✉♣✱ ❞♦✇♥✱ str❛♥❣❡ ✈➔ ❡❧❡❝tr♦♥ ❝â ❦❤è✐

❧÷ñ♥❣ ð ❜➟❝ ❤❛✐ ✈á♥❣✳ ✣➸ ❝➜♠ ❝→❝ t÷ì♥❣ t→❝ ❨✉❦❛✇❛ t❤æ♥❣ t❤÷í♥❣ ✭❝→❝ t÷ì♥❣t→❝ ❨✉❦❛✇❛ s✐♥❤ ❦❤è✐ ❧÷ñ♥❣ ❜➟❝ ❝➙② ♥❤÷ t❤æ♥❣ t❤÷í♥❣✮ t❤➻ t❛ ♣❤↔✐ ❞ò♥❣ ✤➳♥

✷✶

Q nL = (D n , −U n , J n )TL ∼ (3, 3∗, 0),

Q3L = (U 3 , D 3 , T )TL ∼

3, 3,13

, n = 1, 2,

DiR ∼

3, 1, −13

, UiR ∼

3, 1,23

, i = 1, 2, 3, ✭✶✳✸✮

J nR ∼

3, 1, −13

, T R ∼

3, 1,23

,e

T L,R ∼

3, 1,23

, B L,R ∼

η = hηi + η′ ∼

1, 3, −13

,

❝ô♥❣ ♥❤➟♥ ❣✐→ trà t➾ ❧➺ ✈î✐ v ξ ▲ó❝ ♥➔②✱ ♥❤â♠ ❜❛♥ ✤➛✉ ♣❤→ ✈ï t❤➔♥❤ ♥❤â♠ ❝õ❛

▼æ ❤➻♥❤ ❝❤✉➞♥ ✈➔ Z 4 × Z(Lg )

2 ❇÷î❝ t❤ù ❤❛✐ ✤÷ñ❝ ❦➼❝❤ ❤♦↕t ❜ð✐ v η s✐♥❤ ❦❤è✐

❧÷ñ♥❣ ❝❤♦ q✉❛r❦ t♦♣ ❝ô♥❣ ♥❤÷ ❝õ❛ ❝→❝ ❜♦s♦♥ ❝❤✉➞♥ W ✈➔ Z ✈➔ ✤➸ ❧↕✐ ✤è✐ ①ù♥❣

✷✸

t÷ì♥❣ tü ♥❤÷ ❝→❝ ♠❛ tr➟♥ ●❡❧❧✲▼❛♥♥ λ a , a = 1, 2, 3, · · · , 8. ✣è✐ ❝❤✐➳✉ ❝→❝ ❤➡♥❣ sèt÷ì♥❣ t→❝ ❝❤✉➞♥ ð t❤❛♥❣ ♣❤→ ✈ï ✤î✐ ①ù♥❣ SU (3)L× U(1) X✱ t❛ rót r❛ ♠è✐ ❧✐➯♥ ❤➺s❛✉ ❬✶✶✺❪

t ≡ gX

g =

3 √

2 sin θW(MZ′ )p

p18g 2 − g X2

√ 3

3 Bµ

!,

3 Aµ8+

tW

√

3Bµ,tr➯♥ ✤➙② t❛ ✤➣ ❦þ ❤✐➺✉ sW = sin θW✱ cW = cos θW✱ tW = tan θW. ❙❛✉ ❜÷î❝ t❤ù

♥❤➜t✱ ♠❛ tr➟♥Mngauge2 trð t❤➔♥❤ ❞↕♥❣ ❦❤è✐ ❝❤➨♦ ✈î✐ ♣❤➛♥ tû tr➯♥ ❝ò♥❣ ❝õ❛ ✤÷í♥❣

❝❤➨♦ ❜➡♥❣ ❦❤æ♥❣ ✭✤↔♠ ❜↔♦ sü ❦❤æ♥❣ ❦❤è✐ ❧÷ñ♥❣ ❝õ❛ ❤↕t ♣❤♦t♦♥✮✱ tr♦♥❣ ❦❤✐ ♠❛tr➟♥ 2 × 2 ❝õ❛ (Z µ , Z ′

= m

2 W

c 2 W

4v2χ+ v

2

η (1 − 2s2W )2

c4W

.

⇒√∆ ≃ M Z2′



1 − M

2 Z

v 4 χ

4c4W

v2 η

v 2 χ

❝â ✤ë ❝❤➼♥❤ ①→❝ ❝❛♦✳ ❍➺ q✉↔ ❧➔✱ t➼♥❤ ✤ó♥❣ ✤➢♥ ❝õ❛ ♠æ ❤➻♥❤ ♠î✐ ♣❤↔✐ t❤ä❛ ✤✐➲✉

❦✐➺♥ ❧➔ ❦❤æ♥❣ ♠➙✉ t❤✉➝♥ ✈î✐ ❝→❝ ❦➳t q✉↔ t❤ü❝ ♥❣❤✐➺♠ ✤â✳ ◆➯♥ ❧÷✉ þ r➡♥❣ ♠ëttr♦♥❣ ❝→❝ ✤↕✐ ❧÷ñ♥❣ t❤ü❝ ♥❣❤✐➺♠ q✉❛♥ trå♥❣ tr♦♥❣ ▼æ ❤➻♥❤ ❝❤✉➞♥ ❧➔ t❤❛♠ sè ρ✱

✤÷ñ❝ ✤à♥❤ ♥❣❤➽❛ ♥❤÷ s❛✉

ρ = m

2 W

c 2

W M 2 Z

✣è✐ ✈î✐ ♠æ ❤➻♥❤ ✤❛♥❣ ①➨t✱ t➼♥❤ ❜ê ✤➼♥❤ ♦❜❧✐q✉❡ ❞➝♥ ✤➳♥ ❞↕♥❣ s❛✉ ✤➙② ❝õ❛t❤❛♠ sè ρ ❬✶✼✹❪

√ 2G F

16π 2



M+2 + M02+ 2M

2 + M02

M+2 − M 02

lnM

2 0

M+2



−α(mZ)4π s2W



t2W lnM

2 0

2MY2+ + m2W − 2M

465●❡❱ ≤ M Y ≤ 960●❡❱. ✭✶✳✸✽✮

Ð ✤➙② t❛ ✤➣ ❞ò♥❣ ❬✶✼✺❪

m W = 80.379●❡❱.

▲÷✉ þ r➡♥❣ ❦❤♦↔♥❣ ❣✐î✐ ❤↕♥ ð tr➯♥ ❧➔ ♥❣❤✐➯♠ ♥❣➦t ❤ì♥ ❣✐→ trà ✤÷ñ❝ rót r❛ tø q✉→tr➻♥❤ r➣ ♠✉♦♥ s❛✐ ❬✶✽✷❪

M Y ≥ 230●❡❱.

✷✾

m2 Z2 S

ln

r

m2 Z2 S

ln

r

m2 Z2 S

ln

r

m2 Z2 S

♥➙♥❣ ❝➜♣ t↕✐ ▲❍❈ √S = 28 ❚❡❱ ❧➔ ❤➔♠ t❤❡♦ ❦❤è✐ ❧÷ñ♥❣ Z 2

❍➻♥❤ ❜➯♥ tr→✐ ❝õ❛ ❤➻♥❤ ✷ ❞✐➵♥ t↔ t✐➳t ❞✐➺♥ t→♥ ①↕ t♦➔♥ ♣❤➛♥ s✐♥❤ Z 2 t❤❡♦ ❝ì

✸✵

❝❤➳ ❉r❡❧❧✲❨❛♥ ð ▲❍❈ ✈î✐ √S = 13 ❚❡❱ ✈➔ ❧➔ ❤➔♠ t❤❡♦ ❦❤è✐ ❧÷ñ♥❣ M Z 2✱ ❜✐➳♥ ✤ê✐tr♦♥❣ ❦❤♦↔♥❣ tø 4 ❚❡❱ ✤➳♥ 5 ❚❡❱. ❈❤ó♥❣ tæ✐ ①➨t ❣✐î✐ ❤↕♥ ❞÷î✐ MZ2 ❧➔ 4 ❚❡❱ ✤➸t❤ä❛ ♠➣♥ ❣✐î✐ ❤↕♥ ❞➝♥ tø ❞ú ❧✐➺✉ t❤ü❝ ♥❣❤✐➺♠ ✈➲ ❝→❝ t÷ì♥❣ t→❝ ♠❡s♦♥ K✱ D ✈➔

❣✐→ trà ❜➟❝ 10−2 ♣❜ ✤è✐ ✈î✐ ❜♦s♦♥ ❝❤✉➞♥ 4 ❚❡❱✱ t÷ì♥❣ ù♥❣ ✈î✐ ❜➟❝ ❝õ❛ ❜✐➯♥ ❞÷î✐

❝õ❛ ❣✐→ trà t❤ü❝ ♥❣❤✐➺♠ ð ▲❍❈ ❬✶✾✷❪✳

✸✶

✸✷

+ λ 3 η†ρφ−3ξ0+ λ 4 φ+1φ−2ϕ02ξ0+ λ 19 φ−3φ+4 + λ 20 φ+3φ−4

ϕ02
2

+ λ 21 ϕ01
3

ϕ0∗1+ λ 22 χ†χ + λ 23 ρ†ρ + λ 24 η†η +

)

✭✷✳✶✮P❤➛♥ t❤ù ❤❛✐ ❧➔ ♣❤➛♥ ✈✐ ♣❤↕♠ sè ❧❡♣t♦♥ ✭♥❤â♠ ❝♦♥ U (1)Lg ❜à ✈✐ ♣❤↕♠✮ ❬✶✺✷❪✿

V LN V = µ2χη χ†η + η†χ

+

λ 26 (χ†χ) + λ 27 (ρ†ρ) + λ 28 (η†η)

(χ†η + η†χ) + λ 29

(χ†η)2+ (η†χ)2

+ λ 30

(η†ρ)(ρ†χ) + (χ†ρ)(ρ†η)+

+ λ 36 ϕ0∗1
2i

+ χ†η

" 4X

+ ρ†χφ+3 λ 45 ξ0+ λ 46 ξ0∗
+ λ 47 φ+1
2

φ−3φ−4 + φ+1φ−2 λ 48 ϕ01ϕ0∗2 + λ 49 ϕ0∗1 ϕ0∗2 + λ 50 ϕ02ξ0∗
+ φ+3φ−4 λ 51 ϕ01ξ0+ λ 52 ϕ01ξ0∗+ λ 53 ϕ0∗1 ξ0+ λ 54 ϕ0∗1 ξ0∗

+ ϕ02
2

λ 55 ϕ01ξ0+ λ 56 ϕ01ξ0∗+ λ 57 ϕ0∗1 ξ0+ λ 58 ϕ0∗1 ξ0∗

+ h.c.o

✭✷✳✷✮P❤➛♥ ❝✉è✐ ❝ò♥❣ ❧➔ ♣❤➛♥ ♣❤→ ✈ï ✤è✐ ①ù♥❣ ♠➲♠ Z 4 × Z 2 ♥❤÷ s❛✉ ❬✶✺✷❪

Lscalarsgsof t = µ21ϕ01ϕ02+ µ22ϕ01ϕ0∗2 + µ23 ϕ02
2

+ µ24φ+2φ−3 + µ25φ+2φ−4 + µ26φ+3φ−4 + h.c

✭✷✳✸✮

✸✸

2(A − D 1 )λ 6 + v 2

η

2(A − D 1 )λ 6 + v 2

η λ26+ v 2

χ (λ 13 − λ 14 ) 2

,

✭✷✳✷✸✮tr♦♥❣ ✤â

✸✼

2(A − D 2 )λ 6 + v 2

2 cos 2 θ a

✸✾

I ϕ2 ❝â ❜➻♥❤ ♣❤÷ì♥❣ ❦❤è✐ ❧÷ñ♥❣ ❧➔

m2I

ϕ2 = µ2ϕ

2 + 12

1 2 x

3

q

1 2

q

1 2

1 2

√ 2

3 x

q

1 2

q

1 2

❑➳t ❤ñ♣ ✈î✐ ✭✶✳✸✻✮ t❛ ✤÷ñ❝ ❬✶✺✷❪✿

1.5❚❡❱< mH4 < 2.61❚❡❱, ✭✷✳✻✸✮2.6❚❡❱< m H 5 < 4.5❚❡❱.

✹✹

✷✳✸✳✸ P❤➛♥ ❍✐❣❣s ♠❛♥❣ ✤✐➺♥

P❤➛♥ ❍✐❣❣s ♠❛♥❣ ✤✐➺♥ ❣ç♠ ❤❛✐ tr÷í♥❣ ❦❤æ♥❣ ❦❤è✐ ❧÷ñ♥❣ ❧➔ GW+ ✈➔ GY+ ❧➔

❝→❝ ●♦❧❞st♦♥❡ ❜♦s♦♥s t÷ì♥❣ ù♥❣ ✤÷ñ❝ ➠♥ ❜ð✐ ❝→❝ ❜♦s♦♥ ❝❤✉➞♥ W+ ✈➔ Y+. ❈→❝tr÷í♥❣ ❝â ❦❤è✐ ❧÷ñ♥❣ ❧➔ φ+1, φ+2 ✈➔ φ+4 ✈î✐ ❦❤è✐ ❧÷ñ♥❣ t÷ì♥❣ ù♥❣ ❧➔ ❬✶✺✷❪✿

m2φ+

1 = µ2φ+

1 +12

2 (λ18+ λρξ) ≈ µ2η ,

µ2φ+

2 χ

2 (λ

χφ

✹✺

✶✳ ❑❤è✐ ❧÷ñ♥❣ ❝→❝ tr÷í♥❣ ❍✐❣❣s ❝â t❤➯♠ ✈➔✐ sè ❤↕♥❣ ✤â♥❣ ❣â♣ ♠î✐✳

❜♦s♦♥ ❍✐❣❣s tr✉♥❣ ❤á❛ ❈P✲❝❤➤♥ ❦❤→❝✳ ❍➺ q✉↔ ❧➔✱ ✤â♥❣ ❣â♣ ❜➟❝ ♠ët ✈á♥❣ ❝õ❛

❜♦s♦♥ ❍✐❣❣s ♥❤÷ ♠æ ❤➻♥❤ ❝❤✉➞♥ ✈➔♦ t❤❛♠ sè ρ ❝ô♥❣ ❣✐è♥❣ ♥❤÷ tr♦♥❣ ▼æ ❤➻♥❤

❝❤✉➞♥✳ ◆❣♦↕✐ trø ❝→❝ t❤➔♥❤ ♣❤➛♥ ❝õ❛ t❛♠ t✉②➳♥ ✈æ ❤÷î♥❣ ρ✱ ❝→❝ ❜♦s♦♥ ❍✐❣❣str✉♥❣ ❤á❛ ❈P✲❝❤➤♥ ♥➦♥❣ ❝á♥ ❧↕✐ ❦❤æ♥❣ t÷ì♥❣ t→❝ ✈î✐ ❝→❝ ❜♦s♦♥ ❝❤✉➞♥ W ✈➔ Z

❝õ❛ ♠æ ❤➻♥❤ ❝❤✉➞♥ ✈➔ ❞♦ ✤â ❝❤ó♥❣ ❦❤æ♥❣ ❝❤♦ ✤â♥❣ ❣â♣ ✈➔♦ t❤❛♠ sè ρ. ✣â♥❣

, x 21 ≡ m

2 2

✹✼

♣❤➛♥ ❍✐❣❣s ♠❛♥❣ ✤✐➺♥ H1,2,3± t÷ì♥❣ ù♥❣ ✈î✐ ❝ì sð ✭ρ±1, ρ±3, φ±3✮ ✈➔ tø ♣❤➛♥ ❍✐❣❣str✉♥❣ ❤á❛ ❈P✲❧➫ ❧✐➯♥ q✉❛♥ tî✐ Iρ. P❤➛♥ ▲❛❣r❛♥❣✐❛♥ t÷ì♥❣ ù♥❣ ✈î✐ ✤â♥❣ ❣â♣ ♥➔②

♠❛♥❣ ✤✐➺♥ s➩ t➾ ❧➺ ✈î✐f s (m s , m s ) = 0 ù♥❣ ✈î✐s = ρ±1,3, φ±3.❍ì♥ ♥ú❛✱ ✤✐➲✉ ❦✐➺♥ ❣✐↔♥

❧÷ñ❝ ✭✷✳✹✺✮ ✈î✐ λ 1 ≪ 1 ❞➝♥ ✤➳♥ m2Iρ = m2Rρ✱ ❧➔♠ ❝❤♦ ✤â♥❣ ❣â♣ ❝õ❛ ❜♦s♦♥ ❍✐❣❣str✉♥❣ ❤á❛ ✈➔♦ ΠZZ(0) tr✐➺t t✐➯✉✿ fs(mIρ, mRρ) = 0. ❉♦ ✤â ✤â♥❣ ❣â♣ ❦❤→❝ ❦❤æ♥❣

16π 2 f s (mH+

1 , m R ρ ), ✭✷✳✼✹✮tr♦♥❣ ✤â

∆m2 ≡ m2R ρ − m2H+

1 = −λ9v

2 η

2 ∼ O(v η2). ✭✷✳✼✺✮

▼✐➲♥ ✤÷ñ❝ ♣❤➨♣ ❝õ❛ ❦❤æ♥❣ ❣✐❛♥ t❤❛♠ sè ❦❤✐ ①➨t ✈î✐ ♠ët sè ❣✐→ trà ❝ö t❤➸ ❝õ❛

∆m2✤÷ñ❝ ❞✐➵♥ t↔ ð ❤➻♥❤ ✸✳ ✣ç t❤à ❝❤♦ t❤➜② ❦❤æ♥❣ ❝â ❜✐➯♥ tr➯♥✱ ❝â ♥❣❤➽❛ r➡♥❣ ❝→❝

✹✽

❦❤✐ ∆m2 ≥ (0.246 TeV)2 ❬✶✺✷❪✳

✷✳✺✳✷ ❍✐➺♥ t÷ñ♥❣ ❧✉➟♥ ✈➲ ❜♦s♦♥ ❍✐❣❣s ♥➦♥❣ ❍✹

❇➙② ❣✐í ❝❤ó♥❣ tæ✐ t✐➳♣ tö❝ t➼♥❤ t✐➳t ❞✐➺♥ t→♥ ①↕ s✐♥❤ ❝õ❛ tr÷í♥❣ ✈æ ❤÷î♥❣ ♥➦♥❣

H 4 ❚r÷î❝ ❤➳t ❝➛♥ ❧÷✉ þ r➡♥❣ ✈æ ❤÷î♥❣ H 4 ❝❤õ ②➳✉ ✤÷ñ❝ s✐♥❤ r❛ t❤❡♦ ❝ì ❝❤➳tr✉②➲♥ ❣❧✉♦♥ tr♦♥❣ ❝→❝ ❣✐↔♥ ✤ç ❜➟❝ ✶ ✈á♥❣ ❜❛ ✤✐➸♠ ❝❤ù❛ ❝→❝ q✉❛r❦ ♥❣♦↕✐ ❧❛✐

♥➦♥❣ T✱ J 1 ✈➔ J 2 ❉♦ ✤â✱ t✐➳t ❞✐➺♥ t→♥ ①↕ t♦➔♥ ♣❤➛♥ s✐♥❤ H 4 t❤❡♦ ❝ì ❝❤➳ ♥➔②tr♦♥❣ ♠→② ✈❛ ❝❤↕♠ ♣r♦t♦♥✲♣r♦t♦♥ ð ♥➠♥❣ ❧÷ñ♥❣ ❦❤è✐ t➙♠ √S ✤÷ñ❝ t➼♥❤ t❤❡♦

✺✵

❜✐➸✉ t❤ù❝ s❛✉ ❬✶✺✷❪✿

σpp→gg→H4(S) = α

2

S m2H4|(R CP even3 )22|264πv 2

χ S

I

m2

H 4

m2T

+ I

ln

r m2 H4 S

dx

Z 1−x 0

dy 1 − 4xy

❍➻♥❤ ✹✿ ❚✐➳t ❞✐➺♥ t→♥ ①↕ t♦➔♥ ♣❤➛♥ s✐♥❤ H 4 t❤❡♦ ❝ì ❝❤➳ tr✉②➲♥ ❣❧✉♦♥ ð ▲❍❈tr♦♥❣ tr÷í♥❣ ❤ñ♣ √S = 13 ❚❡❱ ❧➔ ❤➔♠ t❤❡♦ v χ ①➨t tr♦♥❣ ✤✐➲✉ ❦✐➺♥ ✭✷✳✺✼✮

✳

❚r♦♥❣ ❤➻♥❤ ✹✱ t➼♥❤ t✐➳t ❞✐➺♥ t→♥ ①↕ t♦➔♥ ♣❤➛♥ s✐♥❤ H 4 ð ▲❍❈ t❤❡♦ ❝ì ❝❤➳tr✉②➲♥ ❣❧✉♦♥ tr♦♥❣ tr÷í♥❣ ❤ñ♣ √S = 13 ❚❡❱✱ ✤÷ñ❝ ❜✐➸✉ ❞✐➵♥ t❤❡♦ ❤➔♠ ❝õ❛ v χ

♥â s➩ ❝â ❝→❝ ❝❤➳ ✤ë r➣ ❝❤✐➳♠ ÷✉ t❤➳ ❧➔ r➣ t❤➔♥❤ ❝→❝ ❝➦♣ ❜♦s♦♥ ❝❤✉➞♥ ♥➦♥❣W′W′

✈➔ Z ′ Z ′ ▼➦t ❦❤→❝✱ ✤è✐ ✈î✐ tr÷í♥❣ ✈æ ❤÷î♥❣ ♥➦♥❣ H4 ❝â ❦❤è✐ ❧÷ñ♥❣ tr♦♥❣ ❣✐î✐

❤↕♥ 4.4 ❚❡❱ MH4 8 ❚❡❱✱ ♥❤÷ ♥â✐ tr♦♥❣ t➔✐ ❧✐➺✉ ❬✷✵✶❪✱ ❝ô♥❣ ①→❝ ✤→♥❣ ✤➸ ❝❤♦r➡♥❣ ❝❤➳ ✤ë r➣ ❝❤✐➳♠ ÷✉ t❤➳ ❝õ❛ ♥â s➩ ❧➔ r➣ t❤➔♥❤ ❝➦♣ t¯ t. ❍ì♥ ♥ú❛✱ tr♦♥❣ ❣✐î✐

❤↕♥ ❦❤è✐ ❧÷ñ♥❣ ❝õ❛ H 4 ✤÷ñ❝ ①➨t ♥❤÷ t❤➳ ♥➔② t❤➻ q✉→ tr➻♥❤ r➣ ❝õ❛ H 4 t❤➔♥❤ ❝➦♣q✉❛r❦ ♥❣♦↕✐ ❧❛✐ ❧➔ ❜à ❝➜♠ ①➨t ð ❦❤➼❛ ❝↕♥❤ ✤ë♥❣ ❧ü❝ ❤å❝ ❜ð✐ ❤➡♥❣ sè t÷ì♥❣ t→❝

❨✉❦❛✇❛ ✤è✐ ✈î✐ ❝→❝ q✉❛r❦ ♥❣♦↕✐ ❧❛✐ ❝â ❜➟❝ ✤ì♥ ✈à✳

❍➻♥❤ ✺✿ ❚✐➳t ❞✐➺♥ t→♥ ①↕ t♦➔♥ ♣❤➛♥ s✐♥❤ H 4 t❤❡♦ ❝ì ❝❤➳ tr✉②➲♥ ❣❧✉♦♥ ð ▲❍❈tr♦♥❣ tr÷í♥❣ ❤ñ♣ √S = 28 ❚❡❱ ❧➔ ❤➔♠ t❤❡♦ v χ ①➨t tr♦♥❣ ✤✐➲✉ ❦✐➺♥ ✭✷✳✺✼✮✳

❧÷ñ♥❣ q✉❛r❦ t♦♣ ✤÷ñ❝ ❧➜② ❧➔ m t = 173●❡❱✳ ❈❤ó♥❣ tæ✐ t❤➜② r➡♥❣ ❜➲ rë♥❣ r➣ t♦➔♥

♣❤➛♥ ❝õ❛ sü s✐♥❤ ✈æ ❤÷î♥❣ H 4 ð ▲❍❈ ❝â ❣✐→ trà ❣➛♥ 10−4 ❢❜ t÷ì♥❣ ù♥❣ ✈î✐ ❣✐→trà ❜✐➯♥ ❞÷î✐10 ❚❡❱ ❝õ❛ v χ ✭❣✐→ trà ✤÷ñ❝ rót r❛ tø ❞ú ❧✐➺✉ t❤ü❝ ♥❣❤✐➺♠ ✈➲ t÷ì♥❣t→❝ ♠❡s♦♥ K✱ D ✈➔ B ❬✶✽✻❪✮ ✈➔ ❜➲ rë♥❣ r➣ ♥➔② ❣✐↔♠ ❦❤✐ v χ t✐➳♥ ✤➳♥ ❝→❝ ❣✐→ trà

✺✷