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 KHOA VẬT LÝ LUẬN ÁN TIẾN SĨ THẾ HIGGS TRONG MƠ HÌNH 3-3-1 VỚI CƠ CHẾ CKS VÀ PHÂN LOẠI CÁC MƠ HÌNH 3-3-1 DỰA TRÊN DỮ LIỆU TÍCH YẾU Chuyên ngành: Vật lý lý thuyết Vật lý toán Mã số: 44 01 03 Nghiên cứu sinh: Nguyễn Văn Hợp Hướng dẫn khoa học: GS.TS HoàngNgọc Long TS Nguyễn Huy Thảo -2020- ▲❯❾◆ ⑩◆ ❚■➌◆ ❙➒ ❚❍➌ ❍■●●❙ ❚❘❖◆● ▼➷ ❍➐◆❍ ✸✲✸✲✶ ❱❰■ ❈❒ ❈❍➌ ❈❑❙ ❱⑨ P❍❹◆ ▲❖❸■ ❈⑩❈ ▼➷ ❍➐◆❍ ✸✲✸✲✶ ❉Ü❆ ❚❘➊◆ ❉Ú ▲■➏❯ ❚➑❈❍ ❨➌❯ ◆❣✉②➵♥ ❱➠♥ ❍ñ♣ ◆❣➔② ✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✷✵ ▲í✐ ❝↔♠ ì♥ ❚ỉ✐ ✈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✐ tỉ✐ t➼♥❤ ❝❤♦ ✤➳♥ ❧ó❝ ♥➔②✳ ❍➔♥❤ tr➻♥❤ trð t❤➔♥❤ ❚✐➳♥ s➽ tü❛ ữ ởt r ợ ũ õ sỹ ❝❤✉➞♥ ❜à ❝❤✉ ✤→♦ ✤➳♥ ✤➙✉✱ ✈➔ ❦➸ ❝↔ ❦❤✐ ✤➣ ❞ü ❧✐➺✉ ♠ët ✤➼❝❤ ✤➳♥ tèt ✤➭♣✱ t❤➻ ❝↔♠ ❣✐→❝ ❧♦ ❧➢♥❣ ✈➔ ✤ỉ✐ ❧ó❝ ♥❛♦ ♥ó♥❣ ❧➔ ❦❤ỉ♥❣ t❤➸ tr→♥❤ ❦❤ä✐✳ ▼❛② ♠➢♥ ❧➔ tỉ✐ ✤÷đ❝ ✤✐ ❝ị♥❣ ♠ët t❤õ② t❤õ ✤♦➔♥ ❝â ❤♦❛ t✐➯✉ ❞↕♥ ❞➔②✱ ❝â t ổ t õ ỗ st ❝ị♥❣ ♥❤ú♥❣ ✈➻ s❛♦ ❞➝♥ ✤÷í♥❣ ❧ó❝ ✤➯♠ tè✐✱ ✤➸ ❝✉è✐ ❝ị♥❣✱ ❣✐í ✤➙② tỉ✐ ✤➣ ✤➦t ♠ët ❝❤➙♥ ð rữợ t tổ t ỡ ❚❤➛② tỉ✐✱ ●❙✳❚❙✳ ❍♦➔♥❣ ◆❣å❝ ▲♦♥❣✱ ♥❣÷í✐ ✤➣ ♥❤➟♥ tỉ✐ õ ự ữợ ự t ♣❤↕♠ ❦ÿ ♥➠♥❣ ✈➔ tr✉②➲♥ t❤ư ❦✐➳♥ t❤ù❝ ❝❤✉②➯♥ ♠ỉ♥ tổ tứ s trữợ ✤➳♥ ❜➟❝ ❚✐➳♥ s➽ ❧➛♥ ♥➔②✳ ❚ỉ✐ ❦❤ỉ♥❣ ❜❛♦ ❣✐í q✉➯♥ ì♥ ❚❤➛② tỉ✐✱ ❝ị♥❣ t➜t ❝↔ ❚❤➛② ❈ỉ ❝ơ trữợ tổ ỳ t ❤å❝ t❤✉➟t ✈➔ ❦❤❛✐ s→♥❣ ❝❤♦ tæ✐ ♥❤ú♥❣ ❜➔✐ ❤å❝ ❝✉ë❝ sè♥❣ ✤➸ tỉ✐ ✤÷đ❝ ♥❤÷ ♥❣➔② ❤ỉ♠ ♥❛②✳ ❚ỉ✐ rt t ỡ ữợ ♥❣÷í✐ ✤➣ ❧✉ỉ♥ s♦♥❣ ❤➔♥❤ ❝ị♥❣ tỉ✐ tr♦♥❣ ❝❤✉②➯♥ ♠ỉ♥✱ s ỗ ộ trủ tổ tè✐ ✤❛ tr♦♥❣ ✈✐➺❝ ❧➟♣ ❦➳ ❤♦↕❝❤ ❤å❝ t➟♣ ❝ô♥❣ ♥❤÷ ❤♦➔♥ t➜t ♠å✐ t❤õ tư❝ ❧✐➯♥ q✉❛♥ ✤➳♥ q✉→ tr➻♥❤ ✤➔♦ t↕♦ t✐➳♥ s➽✳ ❚æ✐ ①✐♥ ❝â ✤æ✐ ❞á♥❣ ❝↔♠ ì♥ ❚❙✳ ▲➯ ❚❤å ❍✉➺✱ ♠ët ♥❣÷í✐ ❛♥❤ ❡♠ ❦➲ ✈❛✐ s→t ❝→♥❤ ❝ị♥❣ tỉ✐✱ ❝❤➥♥❣ ♥❤ú♥❣ ❤é trđ tỉ✐ ♥❤ú♥❣ ❦❤â ❦❤➠♥ tr♦♥❣ s✐♥❤ ❤♦↕t ❧ó❝ ✤✐ ❤å❝ ♠➔ ❝á♥ ❝❤♦ tæ✐ ♥❤ú♥❣ ❝❤➾ ❞➝♥ ❝❤✉②➯♥ ♠æ♥ tø ❆ ✤➳♥ ❩ ♥❤ú♥❣ ❦❤✐ tæ✐ ❦❤æ♥❣ ✶ ❝â ❚❤➛② ❜➯♥ ❝↕♥❤✳ ❈↔♠ ì♥ P●❙✳❚❙ ❍➔ ❚❤❛♥❤ ❍ị♥❣✱ ♥❣÷í✐ ❜↕♥ s s s ỗ tæ✐ tr♦♥❣ ♥❤ú♥❣ t❤→♥❣ ♥❣➔② tæ✐ sè♥❣ ✈➔ ❧➔♠ ✈✐➺❝ ỡ qỵ ổ q ỵ t trữớ ữ P t qỵ ổ t ỵ t t ủ ữợ tt tổ t ✈➔ ♥❤✐➺t t➻♥❤ ❤é trđ ❝❤♦ tỉ✐ tr♦♥❣ ♠å✐ t❤õ tử t ỡ ỗ tỉ✐ t↕✐ ❚r÷í♥❣ ✣↕✐ ❍å❝ ❈➛♥ ❚❤ì✱ ✤➦❝ ❜✐➺t ❧➔ ỗ ✈→❝ ❜ỵt ❝ỉ♥❣ ✈✐➺❝ ❤ë tỉ✐ tr♦♥❣ ♠å✐ ❧ó❝✳ ❳✐♥ ❝↔♠ ì♥ ❚❤➛② ❤✐➺✉ tr÷ð♥❣ ✲ P●❙✳❚❙ ❍➔ ❚❤❛♥❤ ❚♦➔♥✱ ❝ỉ ❚r÷ð♥❣ ❑❤♦❛ ❑❍❚◆ ✲ P●❙✳❚❙ ❇ị✐ ❚❤à ❇û✉ ❍✉➯✱ ♥❤ú♥❣ ♥❣÷í✐ ✤➣ tr✉②➲♥ ❝↔♠ ❤ù♥❣ ❝❤♦ tỉ✐✳ ❙❛✉ ❝ị♥❣✱ tæ✐ ①✐♥ ❞➔♥❤ ✈✐♥❤ ❞ü ✈➔ t❤➔♥❤ q✉↔ ♥➔② ❝❤♦ ❈❤❛✱ ▼➭✱ ❆♥❤ ❈❤à ❊♠✱ ❱ñ ✈➔ ❝→❝ ❝♦♥ ❝õ❛ tỉ✐✱ ♥❤ú♥❣ ♥❣÷í✐ ✤➣ ❧✉ỉ♥ ②➯✉ t❤÷ì♥❣✱ ❝❤✐❛ s➩✱ ❤② s ó t ữợ tổ ✤➦❝ ❜✐➺t ❝↔♠ ì♥ ❝♦♥ ❣→✐ ❜↔② t✉ê✐ ◆❣✉②➵♥ ❚❤ị② ❉÷ì♥❣ ❝õ❛ tỉ✐✱ t✉② ❜➨ ♥❤÷♥❣ ❧✉ỉ♥ ❧➔ ✤ë♥❣ ❧ü❝✱ ♥✐➲♠ ❛♥ õ✐ ✈➔ ❧➔ ❝❤é ❞ü❛ t✐♥❤ t❤➛♥ ✈ú♥❣ ❝❤➢❝ ❝õ❛ tæ✐✳ ▲✉➟♥ →♥ ♥➔② ❧➔ t❤➔♥❤ q✉↔ ❝õ❛ ❤♦↕t ✤ë♥❣ ♥❣❤✐➯♥ ❝ù✉ tr♦♥❣ ❦❤♦↔♥❣ ✸ ♥➠♠ tỉ✐ ✤÷đ❝ ❧➔♠ ✈✐➺❝ tr♦♥❣ ♥❤â♠ ♥❣❤✐➯♥ ❝ù✉ ❞♦ ●❙✳ ❍♦➔♥❣ ◆❣å❝ ▲♦♥❣ ❝❤õ tr➻✳ ▼ët ❧➛♥ ♥ú❛✱ tỉ✐ ①✐♥ ❣ð✐ ❧í✐ ❝↔♠ ì♥ ●❙✳ ❍♦➔♥❣ ◆❣å❝ ▲♦♥❣✱ ❚❙✳ ◆❣✉②➵♥ ❍✉② ❚❤↔♦ ✈➔ ❚❙✳ ▲➯ ❚❤å ❍✉➺ ✤➣ ❝❤♦ tæ✐ ♥❤ú♥❣ ✤à♥❤ ữợ ổ ỳ ộ trủ t t❤➛♥✱ ✈➟t ❝❤➜t tr♦♥❣ t❤í✐ ❣✐❛♥ ✈ø❛ q✉❛✳ ❳✐♥ ❝❤➙♥ t❤➔♥❤ ❝↔♠ ì♥✳ ◆❣✉②➵♥ ❱➠♥ ❍đ♣ ✷ ▲í✐ ❝❛♠ ✤♦❛♥ ❚æ✐ ①✐♥ ❝❛♠ ✤♦❛♥ ❝→❝ ❦➳t q✉↔ ❦❤♦❛ ❤å❝ ❝❤➼♥❤ ✤÷đ❝ tr➻♥❤ ❜➔② tr♦♥❣ ❧✉➟♥ →♥ ♥➔② ❧➔ s↔♥ ♣❤➞♠ ❦❤♦❛ ❤å❝ ❝â ✤÷đ❝ ❞♦ ❜↔♥ t❤➙♥ tỉ✐ ✤â♥❣ ❣â♣ ✈➔♦ ❤♦↕t ✤ë♥❣ ♥❣❤✐➯♥ ❝ù✉ tr♦♥❣ t❤í✐ ❣✐❛♥ ✸ ♥➠♠ tỉ✐ ❧➔♠ ♥❣❤✐➯♥ ❝ù✉ s✐♥❤ t↕✐ ❚r÷í♥❣ ✳✳✳ ❚r♦♥❣ ❧✉➟♥ ữỡ ợ t ố ❝↔♥❤ ✈➔ ❝→❝ t❤➔♥❤ tü✉ ❦❤♦❛ ❤å❝ ♠➔ ❞ü❛ tr➯♥ ✤â ❝→❝ ❝æ♥❣ tr➻♥❤ ❦❤♦❛ ❤å❝ ❝â tæ✐ t❤❛♠ ❣✐❛ ✈➔ ❧✉➟♥ →♥ ❝õ❛ tỉ✐ ✤÷đ❝ ①➙② ❞ü♥❣✱ ♣❤➛♥ ❝á♥ ❧↕✐ ❝õ❛ ❝❤÷ì♥❣ ♥➔② ❧➔ ✤â♥❣ ❣â♣ ❦❤♦❛ ❤å❝ ❝õ❛ ♥❤â♠ ❝❤ó♥❣ tỉ✐✳ ❈❤÷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✐ ❝ị♥❣✱ tỉ✐ ①✐♥ ❝❛♠ ❦➳t ❝→❝ ❦➳t q✉↔ ❝❤➼♥❤ tr♦♥❣ ❧✉➟♥ →♥ ✧❚❤➳ ❍✐❣❣s tr♦♥❣ ♠æ ❤➻♥❤ ✸✲✸✲✶ ✈ỵ✐ ❝ì ❝❤➳ ❈❑❙ ✈➔ ♣❤➙♥ ❧♦↕✐ ❝→❝ ♠ỉ ❤➻♥❤ ✸✲✸✲✶ ❞ü❛ tr➯♥ ❞ú ❧✐➺✉ t➼❝❤ ②➳✉✧ ❧➔ t❤➔♥❤ q✉↔ ❦❤♦❛ ❤å❝ ❝õ❛ tæ✐ ✈➔ ♥❤â♠ ♥❣❤✐➯♥ ❝ù✉ ♠➔ tỉ✐ t❤❛♠ ❣✐❛✱ ❦❤ỉ♥❣ trị♥❣ ❧➦♣ ✈ỵ✐ ❦➳t q✉↔ tr♦♥❣ ❧✉➟♥ →♥ ❦❤→❝ ❤❛② ❝æ♥❣ tr➻♥❤ ❦❤♦❛ ❤å❝ ❦❤→❝ ✤➣ õ t ử ỵ ❤✐➺✉ ✈➔ ❝❤ú ✈✐➳t t➢t ❉❛♥❤ ♠ö❝ ❝→❝ ❜↔♥❣ ❉❛♥❤ ♠ư❝ ❝→❝ ❤➻♥❤ ✈➩ P❤➛♥ ♠ð ✤➛✉ ❈❤÷ì♥❣ ✶✳ ▼ỉ ❤➻♥❤ ✸✲✸✲✶ ✈ỵ✐ ❝ì ❝❤➳ ❈❑❙ ✻ ✼ ✶✵ ✶✶ ✶✾ ✶✳✶ ❙ì ❧÷đ❝ ✈➲ ❝→❝ ♠ỉ ❤➻♥❤ ✸✲✸✲✶ ✈➔ ❜♦s♦♥ ❝❤✉➞♥ tr✉♥❣ ❤á❛ ♠ỵ✐ ✳ ✳ ✳ ✶✾ ✶✳✷ ▼ỉ ❤➻♥❤ ✸✲✸✲✶ ✈ỵ✐ ❝ì ❝❤➳ ❈❑❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✶✳✷✳✶ P❤➛♥ ❢❡r♠✐♦♥ ❝õ❛ ▼ỉ ❤➻♥❤ ✸✲✸✲✶ ✈ỵ✐ ❝ì ❝❤➳ ❈❑❙ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✶✳✷✳✷ ❇♦s♦♥ ❝❤✉➞♥✱ ❣â❝ trë♥ ✈➔ ❦❤è✐ ❧÷đ♥❣ ❝õ❛ ❝❤ó♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✶✳✷✳✸ ❳→❝ ✤à♥❤ ❣✐ỵ✐ ❤↕♥ t❤❛♠ số ổ ợ ố ữủ ❜♦s♦♥ ❝❤✉➞♥ ❞ü❛ ✈➔♦ t❤❛♠ sè ρ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✶✳✷✳✹ ❚✐➳t ❞✐➺♥ t→♥ ①↕ t♦➔♥ ♣❤➛♥ ❝❤♦ q✉→ tr➻♥❤ s✐♥❤ ❜♦s♦♥ ❝❤✉➞♥ ♥➦♥❣ ❩✷ ð ▲❍❈ t❤❡♦ ❝ì ❝❤➳ ❉r❡❧❧✲❨❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ❈❤÷ì♥❣ ✷✳ ❚❤➳ ❍✐❣❣s ✈➔ ♠ët sè ✈➜♥ ✤➲ ❤✐➺♥ t÷đ♥❣ ❧✉➟♥ ❝â ❧✐➯♥ q✉❛♥ ✤➳♥ ❍✐❣❣s tr♦♥❣ ▼ỉ ❤➻♥❤ ✸✲✸✲✶ ✈ỵ✐ ❝ì ❝❤➳ ❈❑❙ ✸✷ ✷✳✶ ❚❤➳ ❍✐❣❣s t♦➔♥ ♣❤➛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✷ ❚❤➳ ❍✐❣❣s ❜↔♦ t♦➔♥ sè ❧❡♣t♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✸ ❈→❝ tr÷í♥❣ ❤đ♣ ❣✐↔♥ ❧÷đ❝ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✷✳✸✳✶ P❤➛♥ ❍✐❣❣s ❈P✲❧➫ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✷✳✸✳✷ P❤➛♥ ❍✐❣❣s ❈P✲❝❤➤♥ ✈➔ ❍✐❣❣s ♥❤÷ ♠ỉ ❤➻♥❤ ❝❤✉➞♥ ✳ ✳ ✳ ✳ ✳ ✹✷ ✷✳✸✳✸ P❤➛♥ ❍✐❣❣s ♠❛♥❣ ✤✐➺♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✷✳✹ ❚❤➳ ❍✐❣❣s ✈✐ ♣❤↕♠ sè ❧❡♣t♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹ ✷✳✺ ▼ët sè ❤✐➺♥ t÷đ♥❣ ❧✉➟♥ ❧✐➯♥ q✉❛♥ ✤➳♥ ♥ë✐ ❞✉♥❣ ❍✐❣❣s tr♦♥❣ ▼æ ❤➻♥❤ ✸✲✸✲✶ ✈ỵ✐ ❝ì ❝❤➳ ❈❑❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✺✳✶ ✣â♥❣ ❣â♣ ổ ữợ t số ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✺✳✷ ❍✐➺♥ t÷đ♥❣ ❧✉➟♥ ✈➲ ❜♦s♦♥ ❍✐❣❣s ♥➦♥❣ ❍✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✺✳✸ ▼➟t ✤ë t➔♥ ❞÷ ❝õ❛ ✈➟t ❝❤➜t tè✐ ✭❉❛r❦ ♠❛tt❡r r❡❧✐❝ ❞❡♥s✐t②✮ ✹✻ ✹✻ ✺✵ ✺✸ ❈❤÷ì♥❣ ✸✳ ❇✐➺♥ ❧✉➟♥ ❝→❝ ✤➦❝ t➼♥❤ ❝õ❛ ❝→❝ ♠æ ❤➻♥❤ ✸✲✸✲✶ ❞ü❛ ✈➔♦ ❞ú ❧✐➺✉ t➼❝❤ ②➳✉ ❝õ❛ ✶✸✸ ❈s ✈➔ ❝õ❛ ♣r♦t♦♥ ✺✼ ✸✳✶ ●✐→ trà t❤ü❝ ♥❣❤✐➺♠ ❝õ❛ t➼❝❤ ②➳✉ ❝õ❛ ✶✸✸❈s✱ ♣r♦t♦♥ ✈➔ ❝æ♥❣ t❤ù❝ t➼❝❤ ②➳✉ tr♦♥❣ ❝→❝ ♠æ ❤➻♥❤ ♠ð rë♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✳✷ ❍✐➺♥ t÷đ♥❣ ❆P❱ tr♦♥❣ ▼ỉ ❤➻♥❤ ✸✲✸✲✶ ✈ỵ✐ ❝ì ❝❤➳ ❈❑❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✳✷✳✶ ❚÷ì♥❣ t→❝ ❞á♥❣ tr✉♥❣ ❤á❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✳✷✳✷ ❇✐➸✉ t❤ù❝ ❜ê ✤➼♥❤ t➼❝❤ ②➳✉ tr♦♥❣ ▼æ ❤➻♥❤ ✸✲✸✲✶ ❈❑❙ ✳ ✳ ✳ ✸✳✸ ❍✐➺♥ t÷đ♥❣ ❆P❱ tr♦♥❣ ❝→❝ ♠æ ❤➻♥❤ ✸✲✸✲✶ β ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ √ ✸✳✸✳✶ ❆P❱ tr♦♥❣ ♠ỉ ❤➻♥❤ ✸✲✸✲✶ ✈ỵ✐ β = ± ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✳✸✳✷ ❆P❱ tr♦♥❣ ♠ỉ ❤➻♥❤ ✸✲✸✲✶ ✈ỵ✐ β = ± √13 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✳✸✳✸ ❆P❱ tr♦♥❣ ♠æ ❤➻♥❤ ✸✲✸✲✶ ✈ỵ✐ β = ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ P❤➛♥ ❦➳t ❧✉➟♥ ✺✼ ✻✷ ✻✷ ✻✸ ✻✺ ✻✽ ✼✷ ✼✸ ✼✽ P❤ö ❧ö❝ ❆✿ ✣â♥❣ ❣â♣ ❝õ❛ t➼❝❤ ②➳✉ ❤↕t ♥❤➙♥ ✈➔♦ ❆P❱ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ P❤ư ❧ư❝ ❇✿ ❚❤✐➳t ❧➟♣ ❝ỉ♥❣ t❤ù❝ t➼❝❤ ②➳✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ữ ỵ ỵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ❇✳✷ ❚➼❝❤ ②➳✉ ◗❙▼ ❲ tr♦♥❣ ▼æ ❤➻♥❤ ❝❤✉➞♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ tr♦♥❣ ❝→❝ ♠æ ❤➻♥❤ ♠ð rë♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷ ❇✳✸ ❚➼❝❤ ②➳✉ ◗❇❙▼ ❲ ❝õ❛ ♠æ ❤➻♥❤ ♠ð rë♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹ ❇✳✹ ❇ê ✤➼♥❤ t➼❝❤ ②➳✉ ∆◗❇❙▼ ❲ ❇✳✺ ❙ü ✤ë❝ ❧➟♣ ♣❤❛ ❝õ❛ ❝æ♥❣ t❤ù❝ t➼❝❤ ②➳✉ tr♦♥❣ ♠æ ❤➻♥❤ ✸✲✸✲✶✲β ✶✶✼ ✺ ỵ ỳ t tt P ❱✐ ♣❤↕♠ t➼♥❤ ❝❤➤♥ ❧➫ tr♦♥❣ ♥❣✉②➯♥ tû ✭❆t♦♠ P❛r✐t② ❱✐♦❧❛t✐♦♥✮ ❇✳P✳❑✳▲ ❇➻♥❤ ♣❤÷ì♥❣ ❦❤è✐ ❧÷đ♥❣ ❇❙▼ ▼ỉ ❤➻♥❤ ♠ð rë♥❣ tø ▼æ ❤➻♥❤ ❝❤✉➞♥ ✭❇❡②♦♥❞ ❙t❛♥❞❛r❞ ▼♦❞❡❧✮ ❈❑❙ ❚ø ✈✐➳t t➢t ❝õ❛ t➯♥ ❝→❝ t→❝ ❣✐↔✿ ❈→r❝❛♠♦✱ ❑♦✈❛❧❡♥❦♦ ✈➔ ❙❝❤♠✐❞t ❉▼ ❱➟t ❝❤➜t tè✐ ▲❍❈ ▼→② ❣✐❛ tè❝ ❤❛❞r♦♥ ❧ỵ♥ ✭▲❛r❣❡ ❍❛❞r♦♥ ❈♦❧❧✐❞❡r✮ ▲◆❈ ❇↔♦ t♦➔♥ sè ❧❡♣t♦♥ ✭▲❡♣t♦♥ ♥✉♠❜❡r ❝♦♥s❡r✈❛t✐♦♥✮ ▲◆❱ ❱✐ ♣❤↕♠ sè ❧❡♣t♦♥ ✭▲❡♣t♦♥ ♥✉♠❜❡r ✈✐♦❧❛t✐♦♥✮ ▼æ ❤➻♥❤ ▼✸✸✶ ▼æ ❤➻♥❤ ✸✲✸✲✶ tè✐ t❤✐➸✉ ✭▼✐♥✐♠❛❧ ✸✲✸✲✶ ♠♦❞❡❧✮ ▼ỉ ❤➻♥❤ ✸✲✸✲✶✲β ▼ỉ ❤➻♥❤ ✸✲✸✲✶ ✈ỵ✐ t❤❛♠ sè β tr♦♥❣ ❜✐➸✉ t❤ù❝ t♦→♥ tû ✤✐➺♥ t➼❝❤ ❝õ❛ ♠æ ❤➻♥❤ P❱ ❱✐ ♣❤↕♠ t➼♥❤ ❝❤➤♥ ❧➫ ✭P❛r✐t② ❱✐♦❧❛t✐♦♥✮ P❱❊❙ ❚→♥ ①↕ ❡❧❡❝tr♦♥ ✈✐ ♣❤↕♠ t➼♥❤ ❝❤➤♥ ❧➫ ✭P❛r✐t② ❱✐♦❧❛t✐♦♥ ❊❧❡❝tr♦♥ ❙❝❛tt❡r✐♥❣✮ ❙▼ ▼æ ❤➻♥❤ ❝❤✉➞♥ ✭❙t❛♥❞❛r❞ ▼♦❞❡❧✮ ❲■▼P ❍↕t ♥➦♥❣ t÷ì♥❣ t→❝ ②➳✉ ✭❲❡❛❦❧② ✐♥t❡r❛❝t✐♥❣ ♠❛ss✐✈❡ ♣❛rt✐❝❧❡✮ ✻ ❉❛♥❤ ♠ư❝ ❝→❝ ❜↔♥❣ ✶ ✷ ✸ ✹ ❙è ❧÷đ♥❣ tû trữớ ổ ữợ s ố ợ õ Z4 ×Z2 ✷✸ ❈→❝ tr÷í♥❣ ❝â sè ❧❡♣t♦♥ L ❦❤→❝ ❦❤ỉ♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ❇➻♥❤ ♣❤÷ì♥❣ ❦❤è✐ ữủ trữớ s P ữợ ✈➔ vχ ≫vη ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ❇➻♥❤ ♣❤÷ì♥❣ ❦❤è✐ ❧÷đ♥❣ ❝õ❛ ❝→❝ tr÷í♥❣ ❍✐❣❣s ❈P✲❝❤➤♥ ữợ v v ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✺ ❈→❝ ❤➡♥❣ sè t÷ì♥❣ t→❝ ✈❡❝t♦r ✈➔ ✈❡❝t♦r✲trư❝ ❞ị♥❣ ❝❤♦ ❝→❝ t➼♥❤ t♦→♥ ❆P❱ tr♦♥❣ ♥❣✉②➯♥ tû ❝❡s✐✉♠ ❞ü❛ t❤❡♦ ▼æ ❤➻♥❤ ❝❤✉➞♥ ✈➔ ❞ü❛ t❤❡♦ ▼æ ❤➻♥❤ ✸✲✸✲✶ ❈❑❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✻ ❈→❝ ❤➡♥❣ sè t÷ì♥❣ t→❝ ✈❡❝t♦r ✈➔ ✈❡❝t♦r✲trư❝ ❝➛♥ ✤➸ t➼♥❤ ❆P❱ tr♦♥❣ ▼æ ❤➻♥❤ ✸✲✸✲✶β ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ữợ MZ2 tr tr÷í♥❣ ❤đ♣ β = ± ✤÷đ❝ rót r❛ ❞ü❛ ✈➔♦ ❞ú ❧✐➺✉ ❆P❱ ❝õ❛ ❝❡s✐✉♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✽ ❈→❝ ❤➡♥❣ sè t÷ì♥❣ t→❝ ✈❡❝t♦r ✈➔ ✈❡❝t♦r✲trư❝ ❝➛♥ ✤➸ t➼♥❤ ❆P❱ tr♦♥❣ ❝→❝ ▼ỉ ❤➻♥❤ ✸✲✸✲✶ tè✐ t❤✐➸✉✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✾ ▼✐➲♥ ❣✐→ trà ❝õ❛ MZ2 ✤÷đ❝ t✐➯♥ ✤♦→♥ ❜ð✐ ▼ỉ ❤➻♥❤ ✸✲✸✲✶ tè✐ t❤✐➸✉✳ ✶✵ ▼✐➲♥ ❣✐→ trà ❝õ❛ MZ2 ✭❚❡❱✮ tr♦♥❣ tr÷í♥❣ ❤đ♣ β = ± √13 ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✶✶ ✶✷ ✼✷ ▼✐➲♥ ❣✐→ trà ✤÷đ❝ t✐➯♥ ✤♦→♥ ❝õ❛ MZ2 tr♦♥❣ tr÷í♥❣ ❤đ♣ β = ✳ ✳ ✳ ✼✺ ▲✐➯♥ ❤➺ ❣✐ú❛ ❝→❝ ❤➡♥❣ sè t÷ì♥❣ t→❝ ❝õ❛ ❞á♥❣ ✈❡❝t♦r✲trö❝ ✈➔ ❝õ❛ ❞á♥❣ ✈❡❝t♦r ✤â♥❣ ❣â♣ ✈➔♦ ❆P❱ tr♦♥❣ ♥❣✉②➯♥ tû ❝❡s✐✉♠ ①➨t tr♦♥❣ ▼æ ❤➻♥❤ ❝❤✉➞♥ ✈➔ tr♦♥❣ ▼æ ❤➻♥❤ ✸✲✸✲✶ ❈❑❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷ ✼ ❉❛♥❤ ♠ư❝ ❝→❝ ❤➻♥❤ ✈➩ ✶ ❍➻♥❤ tr→✐ ♠ỉ t↔ t❤❛♠ sè ρ ❧➔ ❤➔♠ ❝õ❛ vχ✱ ❝→❝ ✤÷í♥❣ t❤➥♥❣ tr ữợ ỹ t ✭✶✳✸✺✮✳ ❍➻♥❤ ♣❤↔✐ t❤➸ ❤✐➺♥ ♠è✐ ❧✐➯♥ ❤➺ ❣✐ú❛ vχ ✈➔ MZ2 ✱ ❝→❝ ✤÷í♥❣ t❤➥♥❣ ♥❣❛♥❣ ❧➔ ❝➟♥ tr➯♥ ữợ v ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ❍➻♥❤ tr→✐ ♠æ t↔ t✐➳t ❞✐➺♥ t→♥ ①↕ t♦➔♥ ♣❤➛♥ s✐♥❤ Z2 t❤❡♦ ❝ì ❝❤➳ √ ❉r❡❧❧✲❨❛♥ ð ▲❍❈ ✈ỵ✐ S = 13 ❚❡❱ ❧➔ ❤➔♠ t❤❡♦ ❦❤è✐ ❧÷đ♥❣ Z2 ❍➻♥❤ ♣❤↔✐ t❤➸ ❤✐➺♥ t✐➳t ❞✐➺♥ t→♥ ①↕ t♦➔♥ ♣❤➛♥ s✐♥❤ Z2 t❤❡♦ ❝ì ❝❤➳ ❉r❡❧❧✲❨❛♥ ð ♠ù❝ ♥➠♥❣ ❧÷đ♥❣ ❞ü ❦✐➳♥ ✤÷đ❝ ♥➙♥❣ ❝➜♣ t↕✐ ▲❍❈ √ S = 28 ❚❡❱ ❧➔ ❤➔♠ t❤❡♦ ❦❤è✐ ❧÷đ♥❣ Z2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỗ t ổ t↔ t❤❛♠ sè ρ ✭❝→❝ ✤÷í♥❣ ❝❤➜♠ ❞ùt ♥➨t✮ ✈➔ ❝õ❛ MZ ✭❝→❝ ✤÷í♥❣ ❧✐➲♥ ♠➔✉ ✤❡♥✮ ❧➔ ❤➔♠ ❝õ❛ vχ ✈➔ mH ❈→❝ ♠✐➲♥ ♠➔✉ ①❛♥❤ ❧➔ ✈ò♥❣ ❦❤æ♥❣ ❣✐❛♥ t❤❛♠ sè ❜à ❧♦↕✐ trø ❞ü❛ ✈➔♦ ❞ú ❧✐➺✉ t❤ü❝ ♥❣❤✐➺♠ ♠ỵ✐ ✤➙② ❝õ❛ t❤❛♠ sè ρ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ❚✐➳t ❞✐➺♥ t→♥ ①↕ t♦➔♥ ♣❤➛♥ s✐♥❤ H4 t❤❡♦ ❝ì ❝❤➳ tr✉②➲♥ ❣❧✉♦♥ ð √ ▲❍❈ tr♦♥❣ tr÷í♥❣ ❤đ♣ S = 13 ❚❡❱ ❧➔ ❤➔♠ t❤❡♦ vχ ①➨t tr♦♥❣ ✤✐➲✉ ❦✐➺♥ ✭✷✳✺✼✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ❚✐➳t ❞✐➺♥ t→♥ ①↕ t♦➔♥ ♣❤➛♥ s✐♥❤ H4 t❤❡♦ ❝ì ❝❤➳ tr✉②➲♥ ❣❧✉♦♥ ð √ ▲❍❈ tr♦♥❣ tr÷í♥❣ ❤ñ♣ S = 28 ❚❡❱ ❧➔ ❤➔♠ t❤❡♦ vχ ①➨t tr♦♥❣ ✤✐➲✉ ❦✐➺♥ ✭✷✳✺✼✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ′ + ✹ ✺ ✽ ❬✷✶✼❪ ❚✳ ❍♦❜❜s ❛♥❞ ❏✳ ▲✳ ❘♦s♥❡r✱ ✏❊❧❡❝tr♦✇❡❛❦ ❈♦♥str❛✐♥ts ❢r♦♠ ❆t♦♠✐❝ P❛r✐t② ❱✐♦❧❛t✐♦♥ ❛♥❞ ◆❡✉tr✐♥♦ ❙❝❛tt❡r✐♥❣✱✧ P❤②s✳ ❘❡✈✳ ❉ ✽✷✱ ✵✶✸✵✵✶ ✭✷✵✶✵✮ ❬❤❡♣✲ ♣❤✴✶✵✵✺✳✵✼✾✼❪ ❬✷✶✽❪ ❙✳ ●✳ P♦rs❡✈✱ ❑✳ ❇❡❧♦② ❛♥❞ ❆✳ ❉❡r❡✈✐❛♥❦♦✱ ✏Pr❡❝✐s✐♦♥ ❞❡t❡r♠✐♥❛t✐♦♥ ♦❢ ✇❡❛❦ ❝❤❛r❣❡ ♦❢ 133 ❈s ❢r♦♠ ❛t♦♠✐❝ ♣❛r✐t② ✈✐♦❧❛t✐♦♥✱✧ P❤②s✳ ❘❡✈✳ ❉ ✽✷✱ ✵✸✻✵✵✽ ✭✷✵✶✵✮ ❬❤❡♣✲♣❤✴✶✵✵✻✳✹✶✾✸❪ ❬✷✶✾❪ ▼✳✲❆✳ ❇♦✉❝❤✐❛t✱ ✏❆t♦♠✐❝ P❛r✐t② ❱✐♦❧❛t✐♦♥✳ ❊❛r❧② ❞❛②s✱ ♣r❡s❡♥t r❡s✉❧ts✱ ♣r♦s♣❡❝ts✱✧ ✭✷✵✶✶✮ ❬♣❤②s✐❝s✳❛t♦♠✲♣❤✴✶✶✶✶✳✷✶✼✷❪ ❬✷✷✵❪ ●✳ ❆❧t❛r❡❧❧✐✱ ❘✳ ❈❛s❛❧❜✉♦♥✐✱ ❙✳ ❉❡ ❈✉rt✐s✱ ◆✳ ❉✐ ❇❛rt♦❧♦♠❡♦✱ ❋✳ ❋❡r✉❣❧✐♦ ❛♥❞ ❘✳ ●❛tt♦✱ P❤②s✳ ▲❡tt✳ ❇ ✷✻✶ ✭✶✾✾✶✮ ✶✹✻✳ ❬✷✷✶❪ ❘✳ ❉✐❡♥❡r✱ ❙✳ ●♦❞❢r❡② ❛♥❞ ■✳ ❚✉r❛♥✱ P❤②s✳ ❘❡✈✳ ❉ ✽✻ ✭✷✵✶✷✮ ❬❤❡♣✲ ♣❤✴✶✶✶✶✳✹✺✻✻❪✳ ❬✷✷✷❪ ●✳ ❆❧t❛r❡❧❧✐✱ ❘✳ ❈❛s❛❧❜✉♦♥✐✱ ❉✳ ❉♦♠✐♥✐❝✐✱ ❋✳ ❋❡r✉❣❧✐♦ ❛♥❞ ❘✳ ●❛tt♦✱ ◆✉❝❧✳ P❤②s✳ ❇ ✸✹✷ ✭✶✾✾✵✮ ✶✺✳ ❬✷✷✸❪ ●✳ ❆❧t❛r❡❧❧✐✱ ◆✳ ❉✐ ❇❛rt♦❧♦♠❡♦✱ ❋✳ ❋❡r✉❣❧✐♦✱ ❘✳ ●❛tt♦ ❛♥❞ ▼✳ ▲✳ ▼❛♥❣❛♥♦✱ P❤②s✳ ▲❡tt✳ ❇ ✸✼✺ ✭✶✾✾✻✮ ✷✾✷ ❞♦✐✿✶✵✳✶✵✶✻✴✵✸✼✵✲✷✻✾✸✭✾✻✮✵✵✷✸✼✲✼ ❬❤❡♣✲ ♣❤✴✾✻✵✶✸✷✹❪✳ ❬✷✷✹❪ ❋✳ P✐s❛♥♦ ❛♥❞ ❱✳ P❧❡✐t❡③✱ P❤②s✳ ❘❡✈✳ ❉ ✺✶✱ ✸✽✻✺ ✭✶✾✾✺✮ ❞♦✐✿✶✵✳✶✶✵✸✴P❤②s❘❡✈❉✳✺✶✳✸✽✻✺ ❬❤❡♣✲♣❤✴✾✹✵✶✷✼✷❪✳ ❬✷✷✺❪ ❏✳ ▲✳ ◆✐s♣❡r✉③❛ ❛♥❞ ▲✳ ❆✳ ❙❛♥❝❤❡③✱ P❤②s✳ ❘❡✈✳ ❉ ✽✵✱ ✵✸✺✵✵✸ ✭✷✵✵✾✮ ❞♦✐✿✶✵✳✶✶✵✸✴P❤②s❘❡✈❉✳✽✵✳✵✸✺✵✵✸ ❬❛r❳✐✈✿✵✾✵✼✳✷✼✺✹ ❬❤❡♣✲♣❤❪❪✳ ❬✷✷✻❪ ❋✳ ❋✳ ❋r❡✐t❛s✱ ❈✳ ❆✳ ❞❡ ❙✳ P✐r❡s ❛♥❞ P✳ ❱❛s❝♦♥❝❡❧♦s✱ P❤②s✳ ❘❡✈✳ ❉ ✾✽ ✭✷✵✶✽✮ ♥♦✳✸✱ ✵✸✺✵✵✺ ❬❛r❳✐✈✿✶✽✵✺✳✵✾✵✽✷ ❬❤❡♣✲♣❤❪❪✳ ❬✷✷✼❪ ▼✳ ❆❛❜♦✉❞ ❡t ❛❧✳ ❬❆❚▲❆❙ ❈♦❧❧❛❜♦r❛t✐♦♥❪✱ ❬❛r❳✐✈✿✶✼✵✼✳✵✷✹✷✹ ❬❤❡♣✲❡①❪❪✳ ✶✵✺ ❏❍❊P ✶✼✶✵ ✭✷✵✶✼✮ ✶✽✷ ❬✷✷✽❪ ❆✳ ▼✳ ❙✐r✉♥②❛♥ ❡t ❛❧✳ ❬❈▼❙ ❈♦❧❧❛❜♦r❛t✐♦♥❪✱ ❏❍❊P ✶✽✵✻ ✭✷✵✶✽✮ ✶✷✵ ❬❛r❳✐✈✿✶✽✵✸✳✵✻✷✾✷ ❬❤❡♣✲❡①❪❪✳ ❬✷✷✾❪ ●✳ ❆❛❞ ❡t ❛❧✳ ❬❆❚▲❆❙ ❈♦❧❧❛❜♦r❛t✐♦♥❪✱ ✏❙❡❛r❝❤ ❢♦r ❤✐❣❤✲♠❛ss ❞✐❧❡♣t♦♥ r❡s♦✲ −1 ♦❢ ♥❛♥❝❡s ✉s✐♥❣ ✶✸✾ ❢❜ pp ❝♦❧❧✐s✐♦♥ ❞❛t❛ ❝♦❧❧❡❝t❡❞ ❛t √ s =✶✸ ❚❡❱ ✇✐t❤ t❤❡ ❆❚▲❆❙ ❞❡t❡❝t♦r✱✑ ❛r❳✐✈✿✶✾✵✸✳✵✻✷✹✽ ❬❤❡♣✲❡①❪✳ ❬✷✸✵❪ ●✳ ❈♦r❝❡❧❧❛✱ ❈✳ ❈♦r✐❛♥á✱ ❆✳ ❈♦st❛♥t✐♥✐ ❛♥❞ P✳ ❍✳ ❋r❛♠♣t♦♥✱ P❤②s✳ ▲❡tt✳ ❇ ✼✽✺ ✭✷✵✶✽✮ ✼✸ ❬❛r❳✐✈✿✶✽✵✻✳✵✹✺✸✻ ❬❤❡♣✲♣❤❪❪✳ ❬✷✸✶❪ ❙✳ ❈✳ ❇❡♥♥❡tt ❛♥❞ ❈✳ ❊✳ ❲✐❡♠❛♥✱ P❤②s✳ ❘❡✈✳ ▲❡tt✳ ❬P❤②s✳ ❘❡✈✳ ▲❡tt✳ ✽✷ ✭✶✾✾✾✮ ✷✹✽✹ ❊rr❛t✉♠✿ ✽✷ ✭✶✾✾✾✮ ✹✶✺✸❪ ❊rr❛t✉♠✿ ❬P❤②s✳ ❘❡✈✳ ▲❡tt✳ ✽✸ ✭✶✾✾✾✮ ✽✽✾❪ ❬❤❡♣✲❡①✴✾✾✵✸✵✷✷❪✳ ❬✷✸✷❪ ❈✳ ❇♦✉❝❤✐❛t ❛♥❞ P✳ ❋❛②❡t✱ P❤②s✳ ▲❡tt✳ ❇ ✻✵✽ ✭✷✵✵✺✮ ✽✼ ❬❤❡♣✲♣❤✴✵✹✶✵✷✻✵❪✳ ❬✷✸✸❪ ❍✳ ❉❛✈♦✉❞✐❛s❧✱ ❍✳ ❙✳ ▲❡❡ ❛♥❞ ❲✳ ❏✳ ▼❛r❝✐❛♥♦✱ P❤②s✳ ❘❡✈✳ ▲❡tt✳ ✶✵✾ ✭✷✵✶✷✮ ✵✸✶✽✵✷ ❬❛r❳✐✈✿✶✷✵✺✳✷✼✵✾ ❬❤❡♣✲♣❤❪❪✳ ❬✷✸✹❪ ❏✳ ▲✳ ❘♦s♥❡r✱ P❤②s✳ ❘❡✈✳ ❉ ✻✺ ✭✷✵✵✷✮ ✵✼✸✵✷✻ ❬❤❡♣✲♣❤✴✵✶✵✾✷✸✾❪✳ ❬✷✸✺❪ ❏✳ ❙✳ ▼✳ ●✐♥❣❡s ❛♥❞ ❱✳ ❱✳ ❋❧❛♠❜❛✉♠✱ P❤②s✳ ❘❡♣t✳ ✸✾✼ ✭✷✵✵✹✮ ✻✸ ❬♣❤②s✐❝s✴✵✸✵✾✵✺✹❪✳ ❬✷✸✻❪ ❏✳ ●✉❡♥❛✱ ▼✳ ▲✐♥t③ ❛♥❞ ▼✳ ❆✳ ❇♦✉❝❤✐❛t✱ ▼♦❞✳ P❤②s✳ ▲❡tt✳ ❆ ✷✵ ✭✷✵✵✺✮ ✸✼✺ ❬♣❤②s✐❝s✴✵✺✵✸✶✹✸❪✳ ❬✷✸✼❪ ❏✳ ❊r❧❡r✱ ❈✳ ❏✳ ❍♦r♦✇✐t③✱ ❙✳ ▼❛♥tr② ❛♥❞ P✳ ❆✳ ❙♦✉❞❡r✱ ❆♥♥✳ ❘❡✈✳ ◆✉❝❧✳ P❛rt✳ ❙❝✐✳ ✻✹ ✭✷✵✶✹✮ ✷✻✾ ❬❛r❳✐✈✿✶✹✵✶✳✻✶✾✾ ❬❤❡♣✲♣❤❪❪✳ ❬✷✸✽❪ ❱✳ ❆✳ ❉③✉❜❛✱ ❏✳ ❈✳ ❇❡r❡♥❣✉t✱ ❱✳ ❱✳ ❋❧❛♠❜❛✉♠ ❛♥❞ ❇✳ ❘♦❜❡rts✱ P❤②s✳ ❘❡✈✳ ▲❡tt✳ ✶✵✾ ✭✷✵✶✷✮ ✷✵✸✵✵✸ ❬❛r❳✐✈✿✶✷✵✼✳✺✽✻✹ ❬❤❡♣✲♣❤❪❪✳ ❬✷✸✾❪ ❏✳ ❊r❧❡r ❛♥❞ ❙✳ ❙✉✱ Pr♦❣✳ P❛rt✳ ◆✉❝❧✳ P❤②s✳ ❬❤❡♣✲♣❤❪❪✳ ✶✵✻ ✼✶ ✭✷✵✶✸✮ ✶✶✾ ❬❛r❳✐✈✿✶✸✵✸✳✺✺✷✷ ❬✷✹✵❪ P✳ ❙♦✉❞❡r ❛♥❞ ❑✳ ❉✳ P❛s❝❤❦❡✱ ❋r♦♥t✳ P❤②s✳ ✭❇❡✐❥✐♥❣✮ ✶✶ ✭✷✵✶✻✮ ♥♦✳✶✱ ✶✶✶✸✵✶✳ ❞♦✐✿✶✵✳✶✵✵✼✴s✶✶✹✻✼✲✵✶✺✲✵✹✽✷✲✵ ❬✷✹✶❪ ❉✳ ❆♥❞r♦➼❝ ❡t ❛❧✳ ❬◗✇❡❛❦ ❈♦❧❧❛❜♦r❛t✐♦♥❪✱ ◆❛t✉r❡ ❬✷✹✷❪ ❍✳ ◆✳ ▲♦♥❣ ❛♥❞ ▲✳ P✳ ❚r✉♥❣✱ P❤②s✳ ▲❡tt✳ ❇ ✺✺✼ ✭✷✵✶✽✮ ♥♦✳✼✼✵✹✱ ✷✵✼✳ ✺✵✷ ✭✷✵✵✶✮ ✻✸ ❬❤❡♣✲♣❤✴✵✵✶✵✷✵✹❪✳ ❬✷✹✸❪ ❉✳ ❆✳ ●✉t✐❡rr❡③✱ ❲✳ ❆✳ P♦♥❝❡ ❛♥❞ ▲✳ ❆✳ ❙❛♥❝❤❡③✱ ■♥t✳ ❏✳ ▼♦❞✳ P❤②s✳ ❆ ✷✶ ✭✷✵✵✻✮ ✷✷✶✼ ❬❤❡♣✲♣❤✴✵✺✶✶✵✺✼❪✳ ❬✷✹✹❪ P✳ ❱✳ ❉♦♥❣✱ ❍✳ ◆✳ ▲♦♥❣ ❛♥❞ ❉✳ ❚✳ ◆❤✉♥❣✱ P❤②s✳ ▲❡tt✳ ❇ ✻✸✾ ✭✷✵✵✻✮ ✺✷✼ ❬❤❡♣✲♣❤✴✵✻✵✹✶✾✾❪✳ ❬✷✹✺❪ ❏✳ ❈✳ ❙❛❧❛③❛r✱ ❲✳ ❆✳ P♦♥❝❡ ❛♥❞ ❉✳ ❆✳ ●✉t✐❡rr❡③✱ P❤②s✳ ❘❡✈✳ ❉ ✼✺ ✭✷✵✵✼✮ ✵✼✺✵✶✻ ❬❤❡♣✲♣❤✴✵✼✵✸✸✵✵ ❬❍❊P✲P❍❪❪✳ ❬✷✹✻❪ ❘✳ ●❛✉❧❞✱ ❋✳ ●♦❡rt③ ❛♥❞ ❯✳ ❍❛✐s❝❤✱ ✶✹✵✶ ❏❍❊P ✭✷✵✶✹✮ ✵✻✾ ❬❛r❳✐✈✿✶✸✶✵✳✶✵✽✷ ❬❤❡♣✲♣❤❪❪✳ ❬✷✹✼❪ ❘✳ ▼❛rt✐♥❡③ ❛♥❞ ❋✳ ❖❝❤♦❛✱ P❤②s✳ ❘❡✈✳ ✾✵ ❉ ✭✷✵✶✹✮ ♥♦✳✶✱ ✵✶✺✵✷✽ ❬❛r❳✐✈✿✶✹✵✺✳✹✺✻✻ ❬❤❡♣✲♣❤❪❪✳ ❬✷✹✽❪ ❏✳ ❇❡r✐♥❣❡r ❡t ❛❧✳ ❬P❛rt✐❝❧❡ ❉❛t❛ ●r♦✉♣❪✱ P❤②s✳ ❘❡✈✳ ❉ ❬✷✹✾❪ ❘✳ ▼❛rt✐♥❡③ ❛♥❞ ❋✳ ❖❝❤♦❛✱ ❊✉r✳ P❤②s✳ ❏✳ ❈ ✽✻ ✭✷✵✶✷✮ ✵✶✵✵✵✶✳ ✺✶✱ ✼✵✶ ✭✷✵✵✼✮ ❬❤❡♣✲ ♣❤✴✵✻✵✻✶✼✸❪✳ ❬✷✺✵❪ ❋✳ ❖❝❤♦❛ ❛♥❞ ❘✳ ▼❛rt✐♥❡③✱ ✏❩✲❩✬ ♠✐①✐♥❣ ✐♥ ❙❯✭✸✮✭❝✮ ① ❙❯✭✸✮✭▲✮ ① ❯✭✶✮✭❳✮ ♠♦❞❡❧s ✇✐t❤ ❜❡t❛ ❛r❜✐tr❛r②✑✱ ❤❡♣✲♣❤✴✵✺✵✽✵✽✷✳ ❬✷✺✶❪ ▼✳ ❊✳ P❡s❦✐♥ ❛♥❞ ❚✳ ❚❛❦❡✉❝❤✐✱ P❤②s✳ ❘❡✈✳ ▲❡tt✳ ✻✺ ✭✶✾✾✵✮ ✾✻✹✳ ❬✷✺✷❪ ▲✳ ❚✳ ❍✉❡ ❛♥❞ ▲✳ ❉✳ ◆✐♥❤✱ ❊✉r✳ P❤②s✳ ❏✳ ❈ ✼✾ ❬❛r❳✐✈✿✶✽✶✷✳✵✼✷✷✺ ❬❤❡♣✲♣❤❪❪✳ ❬✷✺✸❪ ❉✳ ◆❣✱ P❤②s✳ ❘❡✈✳ ❉ ✹✾ ✭✶✾✾✹✮ ✹✽✵✺ ❬❤❡♣✲♣❤✴✾✷✶✷✷✽✹❪✳ ✶✵✼ ✭✷✵✶✾✮ ♥♦✳✸✱ ✷✷✶ ❬✷✺✹❪ ❆✳ ●✳ ❉✐❛s✱ ❘✳ ▼❛rt✐♥❡③ ❛♥❞ ❱✳ P❧❡✐t❡③✱ ❊✉r✳ P❤②s✳ ❏✳ ❈ ✸✾ ✭✷✵✵✺✮ ✶✵✶ ❬❤❡♣✲♣❤✴✵✹✵✼✶✹✶❪✳ ❬✷✺✺❪ P✳ ❍✳ ❋r❛♠♣t♦♥✱ ▼♦❞✳ P❤②s✳ ▲❡tt✳ ❆ ❬✷✺✻❪ ❆✳ ❏✳ ❇✉r❛s ❛♥❞ ❋✳ ❉❡ ❋❛③✐♦✱ ❏❍❊P ✶✽ ✭✷✵✵✸✮ ✶✸✼✼ ❬❤❡♣✲♣❤✴✵✷✵✽✵✹✹❪✳ ✶✻✵✽ ✭✷✵✶✻✮ ✶✶✺ ❬❛r❳✐✈✿✶✻✵✹✳✵✷✸✹✹ ❬❤❡♣✲♣❤❪❪✳ ❬✷✺✼❪ ❨✳ ❨✳ ❑♦♠❛❝❤❡♥❦♦ ❛♥❞ ▼✳ ❨✳ ❑❤❧♦♣♦✈✱ ❙♦✈✳ ❏✳ ◆✉❝❧✳ P❤②s✳ ❬❨❛❞✳ ❋✐③✳ ✺✶ ✭✶✾✾✵✮ ✻✾✷ ✺✶ ✭✶✾✾✵✮ ✶✵✽✶❪✳ ❬✷✺✽❪ ❙✳ ▼✳ ❇♦✉❝❡♥♥❛✱ ❆✳ ❈❡❧✐s✱ ❏✳ ❋✉❡♥t❡s✲▼❛rt✐♥✱ ❆✳ ❱✐❝❡♥t❡ ❛♥❞ ❏✳ ❱✐rt♦✱ ❏❍❊P ✶✻✶✷ ✭✷✵✶✻✮ ✵✺✾ ❬✷✺✾❪ ❳✳ ●✳ ❍❡ ❛♥❞ ●✳ ❱❛❧❡♥❝✐❛✱ P❤②s✳ ▲❡tt✳ ❇ ✼✼✾ ✭✷✵✶✽✮ ✺✷ ❬❛r❳✐✈✿✶✼✶✶✳✵✾✺✷✺ ❬❤❡♣✲♣❤❪❪✳ ❬✷✻✵❪ ❋✳ ❘✐❝❤❛r❞✱ ✏❆ ❩✲♣r✐♠❡ ✐♥t❡r♣r❡t❛t✐♦♥ ♦❢ ❇❞→❑✯♠✉✰♠✉✲ ❞❛t❛ ❛♥❞ ❝♦♥s❡✲ q✉❡♥❝❡s ❢♦r ❤✐❣❤ ❡♥❡r❣② ❝♦❧❧✐❞❡rs✱✑ ❛r❳✐✈✿✶✸✶✷✳✷✹✻✼ ❬❤❡♣✲♣❤❪✳ ❬✷✻✶❪ ❨✳ ❆✳ ❈♦✉t✐♥❤♦✱ ❱✳ ❙❛❧✉st✐♥♦ ●✉✐♠❛r➣❡s ❛♥❞ ❆✳ ❆✳ ◆❡♣♦♠✉❝❡♥♦✱ P❤②s✳ ❘❡✈✳ ❉ ✽✼ ✭✷✵✶✸✮ ♥♦✳✶✶✱ ✶✶✺✵✶✹ ❬❛r❳✐✈✿✶✸✵✹✳✼✾✵✼ ❬❤❡♣✲♣❤❪❪✳ ❬✷✻✷❪ ❍✳ ◆✳ ▲♦♥❣ ❛♥❞ ❱✳ ❚✳ ❱❛♥✱ ❏✳ P❤②s✳ ● ✷✺✱ ✷✸✶✾ ✭✶✾✾✾✮ ❬❤❡♣✲♣❤✴✾✾✵✾✸✵✷❪✳ ❬✷✻✸❪ ▼✳ ❉✳ ❈❛♠♣♦s✱ ❉✳ ❈♦❣♦❧❧♦✱ ▼✳ ▲✐♥❞♥❡r✱ ❚✳ ▼❡❧♦✱ ❋✳ ❙✳ ◗✉❡✐r♦③ ❛♥❞ ❲✳ ❘♦❞❡❥♦❤❛♥♥✱ ❏❍❊P ✶✼✵✽ ✭✷✵✶✼✮ ✵✾✷ ❬❛r❳✐✈✿✶✼✵✺✳✵✺✸✽✽ ❬❤❡♣✲♣❤❪❪✳ ✶✵✽ P❤ö ❧ö❝ ❆✿ ✣â♥❣ ❣â♣ ❝õ❛ t➼❝❤ ②➳✉ ❤↕t ♥❤➙♥ ✈➔♦ ❆P❱ ❚r♦♥❣ ✈➟t ỵ tỷ tữỡ t tr tổ q t Z ✤â♥❣ ❣â♣ t❤➯♠ ✈➔♦ ❍❛♠✐❧t♦♥✐❛♥ ❝õ❛ ♥❣✉②➯♥ tû ♠ët số tr ợ tữỡ ố t ữ s❛✉ ❬✷✶✾❪✿ Vpv = σ e pe Q W GF √ δ (re ) + H.c me c ✭✷✽✮ ❚r♦♥❣ ❜✐➸✉ t❤ù❝ tr➯♥ ❤➺ sè ð ❝✉è✐ ❧➔ t➼❝❤ ✈❡❝t♦r✲trö❝ ❝õ❛ ❡❧❡❝tr♦♥❀ ❤➔♠ ❞❡❧t❛ ❝â ♥❣✉②➯♥ ♥❤➙♥ tø ❦❤è✐ ❧÷đ♥❣ ♥➦♥❣ ❝õ❛ Z ♥➯♥ ♣❤↔✐ ❝â ♥â ✤➸ ✤↔♠ ❜↔♦ t➛♠ ♥❣➢♥ ❝õ❛ t÷ì♥❣ t→❝ ♥➔②✱ ❣➙② ❤✐➺✉ ù♥❣ r➜t ♥❤ä tr♦♥❣ ♥❣✉②➯♥ tû❀ GF ❧➔ ❤➡♥❣ sè ❋❡r♠✐ ✈➔ QW ✤â♥❣ ✈❛✐ trá t÷ì♥❣ tü ♥❤÷ ✤✐➺♥ t➼❝❤ ❤↕t ♥❤➙♥ tr♦♥❣ t÷ì♥❣ t→❝ ❈♦✉❧♦♠❜ ❣✐ú❛ ❡❧❡❝tr♦♥✲❤↕t ♥❤➙♥✱ ♥❤÷♥❣ ð ✤➙② ❧➔ tr♦♥❣ t÷ì♥❣ t→❝ ②➳✉ ✭t❤æ♥❣ q✉❛ Z ✮ ❣✐ú❛ ❡❧❡❝tr♦♥✲♥✉❝❧❡♦♥✱ ✈➻ t❤➳ ♥â ✤÷đ❝ ❣å✐ ❧➔ t➼❝❤ ②➳✉ ❝õ❛ ❤↕t ♥❤➙♥✳ ❚➼❝❤ ②➳✉ QW ❝õ❛ ❤↕t ♥❤➙♥ ❧➔ tê♥❣ t➼❝❤ ②➳✉ ❝õ❛ t➜t ❝↔ ❝→❝ ❤↕t ❝➜✉ t❤➔♥❤ ❤↕t ♥❤➙♥ ✤â✳ ❈➛♥ ♥❤➜♥ ♠↕♥❤ r➡♥❣ t➼❝❤ ②➳✉ ❤↕t ♥❤➙♥ ❧➔ ♠ët t❤❛♠ sè ✤✐➺♥ ②➳✉ ❝➛♥ ♣❤↔✐ ①→❝ ✤à♥❤ tr♦♥❣ t➜t ❝↔ ❝→❝ t❤ü❝ ♥❣❤✐➺♠ ✈➲ ❆P❱✳ ◆❣➔② ♥❛②✱ tr♦♥❣ ♥ë✐ ❞✉♥❣ ❤↕t ❝õ❛ ♥❤✐➲✉ ♠æ ❤➻♥❤ ♠ð rë♥❣ ❝õ❛ ▼æ ❤➻♥❤ ❝❤✉➞♥ ❝â t❤➯♠ ❝→❝ ❜♦s♦♥ ❝❤✉➞♥ tr✉♥❣ ❤á❛ ✤➳♥ tø ❝→❝ tỷ ợ ữ T8 , T15 tø ❝→❝ ✈✐ tû ❝õ❛ ❝→❝ ♥❤â♠ U (1)N t❤➯♠✳ ❇♦s♦♥ ❝❤✉➞♥ tr✉♥❣ ❤á❛ tr♦♥❣ ❝→❝ ♠æ ❤➻♥❤ ♥➔② ❝❤♦ õ õ P ữợ ú tổ s➩ ♣❤➙♥ t➼❝❤ ❝❤✐ t✐➳t ✈➲ ❆P❱ ❞ü❛ tr➯♥ ❝→❝ ❜♦s♦♥ ❝❤✉➞♥ ♠ỵ✐✳ ✶✵✾ P❤ư ❧ư❝ ❇✿ ❚❤✐➳t ❧➟♣ ❝ỉ♥❣ tự t ữ ỵ ỵ ❝❤➢❝ ❝❤➢♥ ❦❤✐ →♣ ❞ư♥❣ ❝ỉ♥❣ t❤ù❝ t➼❝❤ ②➳✉ ❤↕t ♥❤➙♥ ∆QW (AZX) ✈➔♦ ❝→❝ t➼♥❤ t♦→♥✴❜✐➺♥ ❧✉➟♥ ✈➲ s❛✉✱ ✤➛✉ t✐➯♥ ❝❤ó♥❣ t❛ ❝➛♥ ①❡♠ ❧↕✐ ❝❤✐ t✐➳t ❝→❝ ữợ q tr rút r ổ tự t ❝õ❛ ✤↕✐ ❧÷đ♥❣ ♥➔②✳ ❚✉② ♥❤✐➯♥✱ ❦❤✐ ✤➲ ❝➟♣ ❝ị♥❣ ✈➜♥ ✤➲✱ ❝ị♥❣ ✤↕✐ ❧÷đ♥❣ ❝â t❤➸ ❝→❝ t→❝ ❣✐↔ tr ổ tr ũ ỳ ỵ ❝ì sð ❦❤ỉ♥❣ t❤è♥❣ ♥❤➜t✱ ❝❤➥♥❣ ❤↕♥ ♥❤÷ ✈✐➺❝ ❣→♥ ỵ t ổ tố t ❝→❝ ❤➺ sè ❣➢♥ ✈ỵ✐ ♣❤➛♥ trư❝ ✭γ 5✮✱✳✳✳ ♥➯♥ trữợ t ú t r ố ỳ ỳ ỵ ✈✐➺❝ ❝➛♥ t❤✐➳t ✤➛✉ t✐➯♥ ✤➸ ✤↔♠ ❜↔♦ sü ✤è✐ ❝❤✐➳✉✱ s♦ s→♥❤ ❝❤➼♥❤ ①→❝ ❝→❝ ❦➳t q✉↔ ❝õ❛ ❝→❝ ♥❤â♠ t→❝ ❣✐↔ ❦❤→❝ ♥❤❛✉✳ Ð ✤➙② ❝❤ó♥❣ tỉ✐ s➩ t➼♥❤ t♦→♥ ❧↕✐ ❝æ♥❣ t❤ù❝ t➼❝❤ ②➳✉ ∆QW s❛✉ ✤â s s ố t q t ữủ ợ ❝→❝ ❦➳t q✉↔ t÷ì♥❣ ù♥❣ ❝õ❛ ♥❤â♠ ●✳ ❆❧t❛r❡❧❧✐ tr♦♥❣ t ữ ỵ r sỹ tữỡ ự ỳ ỵ ú t ợ ỵ tr♦♥❣ t➔✐ ❧✐➺✉ ❬✷✷✵❪ ♥❤÷ s❛✉✿ (Z, Z ′ ) ≡ (Z0 , Z0′ ), (Z1 , Z2 ) ≡ (Z, Z ′ ), ξ ≡ φ, g˜ = g ′ = gtW , ✭✷✾✮ ð ✤➙② ξ ❧➔ t❤❛♠ sè trë♥ Z − Z ′ ▼❛ tr➟♥ trë♥ O ❧✐➯♥ ❤➺ ❤❛✐ ❝ì sð ❜♦s♦♥ ❝❤✉➞♥ tr✉♥❣ ❤á❛ ❧➔     ′ ′ f,Z f,Z gVf,Z = 2vf , gA = −2af , gVf,Z = 2vf′ , gA = −2a′f c −sφ cξ −sξ , ≡ φ O= sφ c φ sξ c ξ ✭✸✵✮ ✤↔♠ ❜↔♦ (Z1, Z2)T = O(Z, Z )T ữ ỵ r ỵ ỗ t ợ ỵ tr t ❬✷✷✵❪✳ ❇✳✷ ❙▼ ❲ tr♦♥❣ ▼æ ❤➻♥❤ ❝❤✉➞♥ ❚➼❝❤ ②➳✉ ◗ ❚r♦♥❣ ❝→❝ ♠æ ❤➻♥❤ ♠ð rë♥❣ ✤❛♥❣ ①➨t✱ ❦❤✐ ỹ s tr ỏ s ữợ ❝❤➨♦ ❤â❛ t❤ù ♥❤➜t✱ t❛ t❤✉ ✤÷đ❝ ❤❛✐ tr↕♥❣ t❤→✐ Z ✈➔ Z ′✱ ❧➔ ❝→❝ ✶✶✵ tr↕♥❣ t❤→✐ trë♥ s r tr t t ỵ ữợ ❝❤➨♦ ❤â❛ ❝✉è✐ ❝ị♥❣✳ ❚r♦♥❣ ♥❣✉②➯♥ tû✱ t÷ì♥❣ t→❝ ②➳✉ ❣✐ú❛ ❡❧❡❝tr♦♥ ✈➔ ❤↕t ♥❤➙♥ ✭tù❝ ❧➔ t÷ì♥❣ t→❝ ❡❧❡❝tr♦♥✲♥✉❝❧❡♦♥✱ ❝ơ♥❣ ❧➔ t÷ì♥❣ t→❝ ❡❧❡❝tr♦♥✲q✉❛r❦✮ t❤ỉ♥❣ q✉❛ ❝→❝ ❜♦s♦♥ ❝❤✉➞♥ tr✉♥❣ ❤á❛ Z ✱ Z ′ t❤➸ ❤✐➺♥ ❜ð✐ sè ❤↕♥❣ ❞á♥❣ ✭sè ❤↕♥❣ t❤ù ❤❛✐✮ ❝õ❛ ▲❛❣r❛♥❣✐❛♥ ✭✷✳✸✮ tr♦♥❣ t➔✐ ❧✐➺✉ ❬✷✷✵❪✳ ❚r♦♥❣ t➔✐ ❧✐➺✉ ❬✷✷✵❪✿ ❞ò♥❣ ✭✷✳✹✮ ✈➔ ✭✷✳✺✮ ✤➸ ❦❤❛✐ tr✐➸♥ sè ❤↕♥❣ t❤ù ❤❛✐ tr♦♥❣ ✭✷✳✸✮✱ s õ sỷ ỵ tữỡ ữỡ t ữủ LV f f = Jà Z + Jµ′ Zµ′ ≡ g 2cW f f,Z f γ µ (gVf,Z − γ gA )f Zµ + g 2cW ′ f ′ f,Z )f Zµ′ ✭✸✶✮ f γ µ (gVf,Z − γ gA ✈ỵ✐ g = esW ✈➔ tê♥❣ ❧➜② t❤❡♦ ❝→❝ tr↕♥❣ t❤→✐ ❢❡r♠✐♦♥ f ❧➔ ❝→❝ q✉❛r❦ u, d ✈➔ ❡❧❡❝tr♦♥ e ❉♦ ❝→❝ t❤➔♥❤ ♣❤➛♥ ❝õ❛ ❤↕t ♥❤➙♥ ❧➔ ♣r♦t♦♥ ✈➔ ♥ì✲tr♦♥ ❝❤➾ ❝❤ù❛ ❝→❝ q✉❛r❦ ♥❤➭ u ✈➔ d ♥➯♥ ▲❛❣r❛♥❣✐❛♥ ✭✸✶✮ ❝❤ù❛ số ữợ õ õ sè ❤↕♥❣ ✈✐ ♣❤↕♠ t➼♥❤ ❝❤➤♥ ❧➫ ✭P❱ t❡r♠s✮ ❬✷✷✶❪✿ LfP V g2 eγ µ γ e =+ 4cW MZ2 d q=u g m2 = 2W eγ µ γ e 4cW mW MZ 2ρGF eγ µ γ e = √ ð ✤➙② t❛ ✤➣ ❞ò♥❣ MZ2 MZ2 ′ ′ (e) gV′ (q) (qγ µ q) gA (e) gV (q) + gA d ′ (e) gV′ (q) (qγ µ q) gA (e) gV (q) + gA q=u d ′ (e) gV′ (q) (qγ µ q) gA (e) gV (q) + gA q=u MZ2 MZ2 ′ MZ2 MZ2 ′ , ✭✸✷✮ m2W GF g2 √ = , ρ ≡ 8m2W c2W MZ2 ◆❣÷í✐ t❛ ✤à♥❤ ♥❣❤➽❛ t➼❝❤ ②➳✉ ❝õ❛ ❝→❝ q✉❛r❦ ♥❤÷ s❛✉ ′ C1 (q) ≡ −4 ρ gA (e) gV (q) + gA (e) gV′ (q) MZ2 MZ2 ′ , q = u, d ✭✸✸✮ ❑❤✐ ✤â ♣❤÷ì♥❣ tr➻♥❤ ✭✸✷✮ ✤÷đ❝ ✈✐➳t ❧↕✐ t❤➔♥❤ GF LfP V = − √ eγ µ γ e 2 C1 (u) (uγ µ u) + C1 (d) dγ µ d ✶✶✶ é t ũ ỵ số tữỡ tỹ ữ ỵ tr♦♥❣ ❬✷✷✵❪✳ ◆❤➢❝ ❧↕✐ r➡♥❣ tr♦♥❣ ▼æ ❤➻♥❤ ❝❤✉➞♥ ❝❤➾ ❝â ❞✉② ♥❤➜t ❜♦s♦♥ tr✉♥❣ ❤á❛ Z ❝â ❦❤è✐ ❧÷đ♥❣ MZ t tỷ AZ X ỗ Z ♣r♦t♦♥s ✈➔ N = A − Z ♥ì✲tr♦♥ tù❝ ❧➔ ♥â ❝❤ù❛ (2Z + N ) q✉❛r❦ u ✈➔ Z + 2N q✉❛r❦ d✱ ♥➯♥ ❤↕t ♥❤➙♥ ❝â t➼❝❤ ②➳✉ ❧➔ A SM SM QSM W (Z X) = (2Z + N )C1 (u) + (Z + 2N )C1 (d) , ✭✸✺✮ tr♦♥❣ ✤â C1SM (q) ≡ −4 gA (e)gV (q), q = u, d ✭✸✻✮ ❚r♦♥❣ ❝æ♥❣ t❤ù❝ ✭✸✻✮ t❛ ✤➣ ❞ò♥❣ ❣✐→ trà ρ = tr♦♥❣ ▼ỉ ❤➻♥❤ ❝❤✉➞♥✳ ❚❤❛② ✭✸✻✮ ✈➔♦ ✭✸✺✮ ✈➔ ❞ị♥❣ t❤➯♠ ❝→❝ ❤➡♥❣ sè t÷ì♥❣ t→❝ tr♦♥❣ ❜↔♥❣ ✶✷ t❛ t❤✉ ✤÷đ❝ ✭✸✼✮ 133 QSM W (55 Cs) = −73.8684 ❇↔♥❣ ✶✷✿ ▲✐➯♥ ❤➺ ❣✐ú❛ ❝→❝ ❤➡♥❣ sè t÷ì♥❣ t→❝ ❝õ❛ ❞á♥❣ ✈❡❝t♦r✲trö❝ ✈➔ ❝õ❛ ❞á♥❣ ✈❡❝t♦r ✤â♥❣ ❣â♣ ✈➔♦ ❆P❱ tr♦♥❣ ♥❣✉②➯♥ tû ❝❡s✐✉♠ ①➨t tr♦♥❣ ▼æ ❤➻♥❤ ❝❤✉➞♥ ✈➔ tr♦♥❣ ▼æ ❤➻♥❤ ✸✲✸✲✶ ❈❑❙✳ ▼æ ❤➻♥❤ ❝❤✉➞♥ gA (e) = − 21 gV (u) = − ❇✳✸ ❇❙▼ ❲ ❚➼❝❤ ②➳✉ ◗ ′ (e) = + √ gA 4s2W gV (d) = − 21 + ▼æ ❤➻♥❤ ✸✲✸✲✶ ❈❑❙ 2s2W 3−4s2W √ W2 gV′ (u) = −3+8s 3−4sW √ W2 gV′ (d) = −3+2s 3−4sW tr♦♥❣ ❝→❝ ♠æ ❤➻♥❤ ♠ð rë♥❣ ❇➙② ❣✐í t❛ ❤➣② ♠ð rë♥❣ ❝ỉ♥❣ t❤ù❝ tr➯♥ ❝❤♦ ❝→❝ ♠æ ❤➻♥❤ ♠ð rë♥❣ tø ▼æ ❤➻♥❤ ❝❤✉➞♥✱ tr♦♥❣ ❝→❝ ♠æ ❤➻♥❤ ♥➔② ♥❣♦➔✐ Z ❜♦s♦♥ ❝á♥ ❝â t❤➯♠ ❜♦s♦♥ tr✉♥❣ ❤á❛ ♥➦♥❣ Z ′ ❱➻ Z ✈➔ Z ′ trë♥ ♥❤❛✉ ❣â❝ φ ♥➯♥ t r s t ỵ Z1 Z2 ▲❛❣r❛♥❣✐❛♥ ❤✐➺✉ ❞ư♥❣ ✭✷✳✶✮ ❝õ❛ t➔✐ ❧✐➺✉ ❬✷✷✵❪ ✤÷đ❝ ✈✐➳t t❤❡♦ ❝→❝ ❤↕t tr✉②➲♥ t÷ì♥❣ t→❝ ❧➔ ❝→❝ ❜♦s♦♥ ❝❤✉➞♥ tr ỏ t ỵ Z1 Z2 ợ ố ữủ MZ1,2 ❧➔ ✶✶✷ ✤÷đ❝ rót r❛ tø ▲❛❣r❛♥❣✐❛♥ ❝â ❞↕♥❣ t÷ì♥❣ tü ♥❤÷ ✭✸✶✮✱ ♥❤÷ s❛✉ ✤➙② LBSM V ff = g 2cW (1) (1) f f γ µ [gV (f ) − γ gA (f )]f Z1µ + g 2cW (2) (2) f f γ µ [gV (f ) − γ gA (f )]f Z2µ , ✭✸✽✮ tr♦♥❣ ✤â ❝→❝ ❤➡♥❣ sè t÷ì♥❣ t→❝ gV(1) (f )✱ gV(2) (f )✱ gA(1) (f ) ❛♥❞ gA(2) (f ) s➩ ✤÷đ❝ ①→❝ ✤à♥❤ s❛✉✳ P❤÷ì♥❣ tr➻♥❤ ✭✸✽✮ ❝❤♦ t❛ ▲❛❣r❛♥❣✐❛♥ ❤✐➺✉ ❞ư♥❣ s❛✉ ✤➙② ✤è✐ ✈ỵ✐ ❝→❝ q✉❛r❦ u✱ d✿ Lueff = + Ldeff MZ2 g2 (2) (2) (1) (1) µ (u) (e)g (u) + g (e)g (¯ e γ γ e) (¯ u γ u) g µ V A V A 4c2W MZ2 MZ2 g2 ¯ µd (¯ eγ µ γ e) dγ =+ 4cW MZ2 ✭✸✾✮ MZ2 (2) (2) (1) (1) gA (e)gV (d) + gA (e)gV (d) M Z2 ✭✹✵✮ ◆❤ỵ r➡♥❣✱ tr♦♥❣ ❦❤✉ỉ♥ ❦❤ê ❝→❝ ♠æ ❤➻♥❤ ♠ð rë♥❣ ✤❛♥❣ ①➨t✱ t❤❛♠ sè ρ ✈➔ t➼❝❤ ②➳✉ C1BSM (u, d) ❝õ❛ ❝→❝ q✉❛r❦ ✤÷đ❝ ✤à♥❤ ♥❣❤➽❛ ❧➔ m2W ρ ≡ , cW MZ2 C1BSM (u, d) ≡ −4ρ ❙û ❞ö♥❣ ✭✹✶✮✱ ✭✹✷✮ ✈➔ G √F = ✭✹✶✮ MZ2 (2) (2) (1) (1) gA (e)gV (u, d) + gA (e)gV (u, d) M Z2 g2 8m2W , ✭✹✷✮ t❛ ✈✐➳t ❧↕✐ ữ s GF e e) ( u u) ì C1BSM (u) , Lueff = ( 2 GF d ì C BSM (d) , Ldeff = − √ (¯ eγ µ γ e) dγ 2 ✭✹✸✮ ✭✹✹✮ ❉ü❛ ✈➔♦ ♠❛ tr➟♥ trë♥ O ð ✭✸✵✮ t❛ ❝â t❤➸ ❞✐➵♥ t↔ ❝→❝ tr↕♥❣ t❤→✐ Z ✈➔ Z ′ t❤❡♦ Z1,2 ✱ s❛✉ ✤â t❤❛② ❝→❝ ❜✐➸✉ t❤ù❝ ♥➔② rỗ ỗ t r t❛ t❤✉ ✤÷đ❝ (1) (1) gV (f ) = cφ gV (f ) − sφ gV′ (f ), (2) gV (f ) = sφ gV (f ) + cφ gV′ (f ) ′ (f ), gA (f ) = cφ gA (f ) − sφ gA ′ (f ), gA (f ) = sφ gA (f ) + cφ gA (2) ỗ tớ t ữ s C1BSM (u, d) = −4ρ − c2φ + s2φ MZ2 MZ2 gA (e)gV (u, d) ′ gA (e)gV′ (u, d) + gA (e)gV (u, d) + s2φ + c2φ ▲➜② ❣➛♥ ✤ó♥❣ ✤➳♥ ❜➟❝ O MZ2 MZ2 MZ2 MZ2 ❝õ❛ ❜✐➸✉ t❤ù❝ ✭✹✻✮ ❞♦ sφ ∼ O ′ gA (e)gV′ (u, d) 1− MZ2 MZ2 sφ c φ ✭✹✻✮ , t❛ ❝â cφ ≃ 1, , s2φ ≃ tr♦♥❣ sè ❤↕♥❣ ✤➛✉ t✐➯♥ MZ2 MZ2 ❉♦ ✤â✱ gA (e)gV (u, d) ≃ gA (e)gV (u, d) − (1) (1) ′ (e)g (u, d)) sin ◆❣÷đ❝ ❧↕✐✱ sè ❤↕♥❣ t❤ù ❤❛✐ ❝õ❛ ✭✹✷✮ ✤ì♥ ❣✐↔♥ (gA (e)gV′ (u, d) + gA V φ ❧➔ gA(2) (e)gV(2) (u, d) ≃ gA′ (e)gV′ (u, d) ⑩♣ ❞ö♥❣ ♣❤➨♣ ❧➜② ❣➛♥ ✤ó♥❣ ♥➔②✱ t❛ ✈✐➳t t✐➳♣ ✭✹✻✮✿ C1BSM (u, d) = −4ρ + MZ2 MZ2 ′ gA (e)gV (u, d) − gA (e)gV′ (u, d) + gA (e)gV (u, d) sφ ′ gA (e)gV′ (u, d) +O MZ4 MZ4 ✭✹✼✮ ❚ø t➼❝❤ ②➳✉ C1BSM (u, d) ❝õ❛ q✉❛r❦ ❝❤ó♥❣ t❛ ❞➵ ❞➔♥❣ s✉② r❛ t➼❝❤ ②➳✉ ❤↕t ♥❤➙♥ tr♦♥❣ ❦❤✉æ♥ ❦❤ê ♠æ ❤➻♥❤ ♠ð rë♥❣✱ ❜➡♥❣ ❝æ♥❣ t❤ù❝✿ BSM QBSM (A (u) + (Z + 2N )C1BSM (d) W Z X) = (2Z + N )C1 ✭✹✽✮ ❇✳✹ ❇ê ✤➼♥❤ t➼❝❤ ②➳✉ ∆◗❇❙▼ ❲ ❝õ❛ ♠æ ❤➻♥❤ ♠ð rë♥❣ ◆➳✉ t➼❝❤ ②➳✉ ❤↕t ♥❤➙♥ tr♦♥❣ ▼æ ❤➻♥❤ ❝❤✉➞♥ ✈➔ tr♦♥❣ ♠æ ❤➻♥❤ ♠ð rë♥❣ ❧➛♥ ❧÷đt A BSM (A X) t❤➻ ♣❤➛♥ ❜ê ✤➼♥❤ t➼❝❤ ②➳✉ ❤↕t ♥❤➙♥ ❝õ❛ ♠æ ❤➻♥❤ ❧➔ QSM W (Z X) ✈➔ ∆QW Z ✶✶✹ ♠ð rë♥❣ ❧➔ BSM A A ∆QBSM (A (Z X) − QSM W Z X) = QW W (Z X) = (2Z + N )C1BSM (u) + (Z + 2N )C1BSM (d) − (2Z + N )C1SM (u) − (Z + 2N )C1SM (d) ′ = −4 (2Z + N )ρ gA (e)gV (u) − gA (e)gV′ (u) + gA (e)gV (u) sφ MZ2 + MZ2 MZ2 MZ2 + ′ gA (e)gV′ (u) ′ gA (e)gV′ (d) ′ + (Z + 2N )ρ gA (e)gV (d) − gA (e)gV′ (d) + gA (e)gV (d) sφ MZ4 − (2Z + N )gA (e)gV (u) − (Z + 2N )gA (e)gV (d) + O MZ4 = −4{(2Z + N )∆ρgA (e)gV (u) + (Z + 2N )∆ρgA (e)gV (d) ′ (e)gV (u) −ρsφ (2Z + N ) gA (e)gV′ (u) + gA ′ (e)gV (d) + (Z + 2N ) gA (e)gV′ (d) + gA MZ2 +ρ MZ2 = −4 ′ ′ [(2Z + N )gA (e)gV′ (u) + (Z + 2N )gA (e)gV′ (d)] N −Z + Zs2W ρ− +O MZ4 MZ4 N −Z + Zs2W ′ (e)gV (u) −sφ (2Z + N ) gA (e)gV′ (u) + gA ′ + (Z + 2N ) gA (e)gV′ (d) + gA (e)gV (d) + MZ2 MZ2 ′ ′ [(2Z + N )gA (e)gV′ (u) + (Z + 2N )gA (e)gV′ (d)] +O MZ4 MZ4 ✭✹✾✮ tr♦♥❣ ❜✐➸✉ t❤ù❝ tr➯♥ t❛ ✤➣ ❞ị♥❣ ❝→❝ ❤➡♥❣ sè t÷ì♥❣ t→❝ ❝õ❛ ❡❧❡❝tr♦♥✱ q✉❛r❦ u ✈➔ M ≃ d tr♦♥❣ ▼ỉ ❤➻♥❤ ❝❤✉➞♥ ✤÷đ❝ ❝❤♦ tr♦♥❣ ❜↔♥❣ ✶✷ ✈➔ ❦➳t q✉↔ ρsφ ≃ sφ , ρ M MZ2 MZ2 2 Z1 Z2 ✣➛✉ t✐➯♥✱ t❛ ❤➣② ❦✐➸♠ tr❛ ❧÷đ♥❣ δ(s2W ) ữủ ợ t tr t ỷ ❝ỉ♥❣ t❤ù❝ µ2 πα s2W c2W = , µ≡ √ , ✭✺✵✮ ρM Z 2GF ð ✤➙② µ ✈➔ MZ ✤÷đ❝ ❝è ✤à♥❤ ♥❤÷ ♥❤ú♥❣ t❤❛♠ sè t❤ü❝ ♥❣❤✐➺♠ ✤➛✉ ✈➔♦✳ ✣à♥❤ ♥❣❤➽❛ x = s2W ✭✈ỵ✐ c2W = x ữ số tr ữợ tr✉♥❣ ❣✐❛♥ s❛✉ ✤➙②✱ ✶✶✺ t❛ ❝â δ δρ [(x − x2 )ρ] = (1 − 2x)ρ + (x − x2 ) δx δx 2 s c x−x → δ(s2W ) = δ x = − δρ ≃ − W W ∆ρ (1 − 2x)ρ c2W (x − x2 )ρ = const → = ✭✺✶✮ ð ✤➙② t❛ ✤➣ ❞ị♥❣ ρ = + ∆ρ ✈ỵ✐ ∆ρ = O(ǫ2) ❑➳t q✉↔ tr♦♥❣ ❜✐➸✉ t❤ù❝ ✭✺✶✮ ❧➔ ♣❤ị ❤đ♣ ✈ỵ✐ ❜✐➸✉ t❤ù❝ ✭✷✳✶✸✮ tr♦♥❣ t➔✐ ❧✐➺✉ ❬✷✷✵❪✱ ữ ởt út s ợ tự tữỡ ự tr ổ tr s s ợ trữớ ❤đ♣ tr♦♥❣ ▼ỉ ❤➻♥❤ ❝❤✉➞♥✱ t❛ ♣❤↔✐ t➼♥❤ t♦→♥ ✤➸ rót r❛ s2W ✈➔ ρ tr♦♥❣ ❦❤✉ỉ♥ ❦❤ê ▼ỉ ❤➻♥❤ ❝❤✉➞♥✱ tù❝ ❧➔ ρ → 1+∆ρ ✈➔ s2W → s2W +(s2W ) ợ (s2W ) ữủ ❚❤❡♦ ❝→❝❤ t❤ù❝ t÷ì♥❣ tü ♣❤➛♥ ð tr➯♥ t❛ ❝â ∆QBSM (A W Z X) = (Z − N )(1 + ∆ρ) − 4Z[sW (1 + ∆ρ) − s2W c2W ∆ρ] − Z − N − 4Zs2W c2W ′ (e)gV (u) +4sφ (2Z + N ) gA (e)gV′ (u) + gA ′ (e)gV (d) + (Z + 2N ) gA (e)gV′ (d) + gA −4 MZ2 MZ2 ′ ′ (e)gV′ (d)] + O [(2Z + N )gA (e)gV′ (u) + (Z + 2N )gA = (Z − N )∆ρ − 4Z s2W − s2W c2W c2W MZ4 MZ4 ∆ρ ′ (e)gV (u) +4sφ (2Z + N ) gA (e)gV′ (u) + gA ′ + (Z + 2N ) gA (e)gV′ (d) + gA (e)gV (d) −4 MZ2 MZ2 ′ ′ [(2Z + N )gA (e)gV′ (u) + (Z + 2N )gA (e)gV′ (d)] + O = Z − N + 4Z s4W c2W MZ4 MZ4 ∆ρ ′ (e)gV (u) +4sφ (2Z + N ) gA (e)gV′ (u) + gA ′ + (Z + 2N ) gA (e)gV′ (d) + gA (e)gV (d) −4 MZ2 MZ2 [(2Z ′ + N )gA (e)gV′ (u) + (Z ′ + 2N )gA (e)gV′ (d)] + O ✶✶✻ MZ4 MZ4 ✭✺✷✮ ❚❤❛② N = A − Z ✈➔♦ ✭✺✷✮ t❛ ✤÷đ❝ ∆QBSM (A W Z X) ≃ 2Z − A + 4Z s4W c2W ∆ρ ′ (e)gV (u) + 4sφ (A + Z) gA (e)gV′ (u) + gA ✭✺✸✮ ′ + (2A − Z) gA (e)gV′ (d) + gA (e)gV (d) − MZ2 MZ2 ′ ′ [(2Z + N )gA (e)gV′ (u) + (Z + 2N )gA (e)gV′ (d)] ❇✳✺ ❙ü ✤ë❝ ❧➟♣ ♣❤❛ ❝õ❛ ❝æ♥❣ t❤ù❝ t➼❝❤ ②➳✉ tr♦♥❣ ♠ỉ ❤➻♥❤ ✸✲✸✲ ✶✲β ▼➦❝ ❞ị ❤✐➺♥ t÷đ♥❣ ❆P❱ ❝â t❤➸ ✤÷đ❝ ①➨t tr♦♥❣ tø♥❣ ♠ỉ ❤➻♥❤ t ữ tr ổ ợ ❝ì ❝❤➳ ❈❑❙✱ ♥❤÷♥❣ ❤✐➺♥ t÷đ♥❣ ♥➔② ❝ơ♥❣ ❝â t❤➸ ữủ t ởt qt ỡ tr ợ ❝→❝ ♠ỉ ❤➻♥❤ ✸✲✸✲✶ ✈ỵ✐ t❤❛♠ sè β ❜➜t ❦ý ✭β ✤÷đ❝ ✤à♥❤ ♥❣❤➽❛ tr♦♥❣ t♦→♥ tû ✤✐➺♥ t➼❝❤ ✭✶✳✶✮✮✳ Ð ✤➙② ❝❤ó♥❣ t❛ ①➨t ❧ỵ♣ ❝→❝ ♠ỉ ❤➻♥❤ ✸✲✸✲✶ tữớ ữủ ỹ ợ t t s ♠➔ t❛ ❣å✐ ❧➔ ♠æ ❤➻♥❤ ✸✲✸✲✶✲β ✱ tr♦♥❣ ✤â tố t õ t P ỗ ❣â❝ trë♥ sφ ✈➔ ❜♦s♦♥ ❝❤✉➞♥ tr✉♥❣ ❤á❛ ♥➦♥❣ ♣❤↔✐ ữủ t trữợ t ứ õ ổ tự ❆P❱ tr♦♥❣ ♥❤â♠ ♠ỉ ❤➻♥❤ ♥➔② ✤÷đ❝ t❤✐➳t ❧➟♣ ❬✶✼✽✱✷✹✼❪✱ t✉② ♥❤✐➯♥ ❝ỉ♥❣ t❤ù❝ ♥➔② ❝➛♥ ✤÷đ❝ ✤✐➲✉ ❝❤➾♥❤✱ ➼t ♥❤➜t ❧➔ ❜ð✐ ❣â❝ trë♥ ✈➔ sü ♣❤ö t❤✉ë❝ t❤❛♥❣ ♥➠♥❣ ❧÷đ♥❣ ❝õ❛ ❝→❝ ❤➡♥❣ sè t÷ì♥❣ t→❝ ❝❤✉➞♥ ♥❤÷ ✤÷đ❝ ❜➔♥ tr♦♥❣ √ t➔✐ ❧✐➺✉ ❬✶✽✶❪✳ ◆❣♦➔✐ r❛✱ ♥❤✐➲✉ ♠ỉ ❤➻♥❤ ✈ỵ✐ β = ± √13 , ± ữ = 0, 23 ữủ ợ ✤➙② ❝ơ♥❣ ♥➯♥ ✤÷đ❝ ①➨t ✤➳♥ ❬✶✻✾✱✶✼✸✱✶✽✶❪✳ ❍✐➺♥ t÷đ♥❣ ❆P❱ ❝â ❧✐➯♥ q✉❛♥ ✤➳♥ ❝→❝ ♠ỉ ❤➻♥❤ ♥➔② s➩ ✤÷đ❝ ♣❤➙♥ t➼❝❤ ♥❤÷ s❛✉ ✤➙②✳ ❇❛ t❛♠ t✉②➳♥ ❍✐❣❣s ✤÷đ❝ ✤à♥❤ ♥❣❤➽❛ ❣✐è♥❣ ♥❤÷ ✤÷đ❝ ♠ỉ t↔ tr♦♥❣ ❜↔♥❣ ✸ ❝õ❛ t➔✐ ❧✐➺✉ ❬✶✼✽❪✱ ❝❤➾ ❝â ❦❤→❝ ð ❝❤é ❧➔ tr✉♥❣ ❜➻♥❤ ❝❤➙♥ ❦❤æ♥❣ ❝õ❛ ❝→❝ t❤➔♥❤ ♣❤➛♥ tr✉♥❣ ❤á❛ ữủ ỵ t ỵ tr t tố t ợ ỵ tr t❤ù❝ tv tr♦♥❣ ❝æ♥❣ t❤ù❝ ✭✸✳✷✺✮✳ ✣à♥❤ ♥❣❤➽❛ ❝❤✉➞♥ ❝õ❛ ✤↕♦ ✶✶✼ ❤➔♠ ❤✐➺♣ ❜✐➳♥ ✤÷đ❝ ♥➯✉ tr♦♥❣ t➔✐ ❧✐➺✉ ❬✶✼✸❪ ❦❤ỵ♣ ✈ỵ✐ ❜✐➸✉ t❤ù❝ ✭✸✳✶✸✮ ✈➔ gX t≡ = g √ 6sW ✭✺✹✮ − (1 + β )s2W Zà ữ ố ữủ s ổ ữ Wà = W iW s❛✉ g (vρ2 + vη2 ) M2 , MZ2 = 2W MW = ✭✺✺✮ c µ µ W ❙❛✉ ❦❤✐ ♣❤→ ✈ï ✤è✐ ①ù♥❣ SU (3)L ⊗ U (1)X → U (1)Q✱ ♠æ ❤➻♥❤ s õ s tr ỏ ỗ t ổ ố ữủ ởt s ổ Zà s ợ Zà Aà = sW Wà3 + cW βtW Wµ8 + − β t2W Bµ , Zµ = cW Wµ3 − sW βtW Wµ8 + − β t2W Bµ , Zµ′ = − β t2W Wµ8 − β tW Bµ , tr t t ỵ Zà õ ữủ ợ tr t ợ ợ tr÷í♥❣ ❤đ♣ tr÷í♥❣ ❤đ♣ ❝ư t❤➸ ❧➔ ▼ỉ ❤➻♥❤ ✸✲✸✲✶ ợ ỡ ữủ õ tr r ợ ❤↕♥ vχ ≪ vρ, vη ✱ ❣â❝ trë♥ Z − Z ′ tr♦♥❣ ❜✐➸✉ t❤ù❝ ✭✸✳✶✹✮ ❣✐è♥❣ ♥❤÷ ð ✭✸✳✷✹✮✳ ❈➛♥ ♥❤➜♥ ♠↕♥❤ r➡♥❣ ❝ỉ♥❣ t❤ù❝ ♥➔② ✤÷đ❝ ✤➲ ①✉➜t ❧➛♥ ✤➛✉ t✐➯♥ tr♦♥❣ t➔✐ ❧✐➺✉ ❬✶✽✶❪✱ ✈è♥ ❧➔ ✤➸ ổ tự tr ỵ r ❝❤ó♥❣ t❛ ✤➣ ❝❤å♥ ❣â❝ trë♥ ♥➔②   cφ −sφ , CZZ ′ ≡  sφ c φ ✭✺✼✮ ✤➸ q✉② ✤à♥❤ ♠è✐ ❧✐➯♥ ❤➺ ❣✐ú❛ ❤❛✐ ❝ì sð ❝õ❛ ❝→❝ tr↕♥❣ t❤→✐ ❜♦s♦♥ ❝❤✉➞♥ tr✉♥❣ ❤á❛✿ (Z1, Z2)T = CZZ (Z, Z ′)T ●â❝ trë♥ φ ð ✤à♥❤ ♥❣❤➽❛ ♥➔② ❦❤→❝ ♠ët ❞➜✉ trø s♦ ✈ỵ✐ tr♦♥❣ t➔✐ ❧✐➺✉ ❬✶✼✽✱ ✶✽✶✱ ✷✹✼❪✳ ❑➳t ❤đ♣ ✈ỵ✐ tr↕♥❣ t❤→✐ Z ′ ✤÷đ❝ ✤à♥❤ ♥❣❤➽❛ tr♦♥❣ ❧✉➟♥ →♥ ♥➔②✱ ❜✐➸✉ t❤ù❝ ✭✸✳✷✹✮ ❝õ❛ φ ❧➔ ♣❤ị ❤đ♣ ✈ỵ✐ tr♦♥❣ t➔✐ ❧✐➺✉ ❬✶✽✶❪✳ ❚ø ✤â✱ t❛ t➼♥❤ ❝→❝ ❤➡♥❣ sè t÷ì♥❣ t tt ữ r ợ ỵ ợ ợ tr t ❬✶✼✽❪✳ ❉➵ t❤➜② r➡♥❣ ❣â❝ trë♥ φ ✈➔ ❝→❝ ❤➡♥❣ số tữỡ t ũ ủ ợ trữớ ủ t ❦❤✐ β = ✈➔ vρ = ❑❤✐ ✤è✐ ❝❤✐➳✉ ✈ỵ✐ ❦➳t q✉↔ tr♦♥❣ ❜↔♥❣ ✹ ❝õ❛ t➔✐ ❧✐➺✉ t t số tữỡ t ợ Z ❜à ♥❣÷đ❝ ❞➜✉✱ t➻♥❤ tr↕♥❣ ♥➔② ❝â t❤➸ ✤÷đ❝ ❧♦↕✐ ❜ä ❜➡♥❣ ❝→❝❤ ❝❤å♥ tr↕♥❣ t❤→✐ Z ′ ❝ò♥❣ ❞➜✉ ợ ữ tr ú õ ởt trø ❝ô♥❣ s➩ ①✉➜t ❤✐➺♥ tr♦♥❣ ✈➳ ♣❤↔✐ ❝õ❛ ❜✐➸✉ t❤ù❝ ✭✸✳✷✹✮✳ ❚â♠ ❧↕✐✱ ❞➜✉ ❝õ❛ ❝↔ sφ ✈➔ ❤➡♥❣ số tữỡ t tữỡ ự ợ Z s ♥➳✉ t❛ ✤ê✐ ♣❤❛ ❝õ❛ tr↕♥❣ t❤→✐ Z ′ ✱ ✤✐➲✉ ♥➔② ❞➝♥ ✤➳♥ ❦➳t q✉↔ ❧➔ ❜✐➸✉ t❤ù❝ ✭✸✳✺✮ ❧➔ ✤ë❝ ❧➟♣ ✤è✐ ✈ỵ✐ ♣❤❛ ❝õ❛ Z ′ ▼ët tr♦♥❣ ❝→❝ ♠è✐ q✉❛♥ t➙♠ ❝❤➼♥❤ ❝õ❛ ❧✉➟♥ →♥ ữủ 133 Cs 55 ợ (A 2.39782 × Z) ∆ρ ≃ 1.12∆ρ = O(10−4 ) ≪ |Q(Cs)| t ữủ tứ t q tỹ ợ ✤➙②✳ ❱➻ t❤➳✱ tr♦♥❣ ❦❤✉æ♥ ❦❤ê ♠æ ❤➻♥❤ ✸✲✸✲✶✲β ✱ tø ❜✐➸✉ t❤ù❝ ✭✸✳✽✮ ♠➔ tr♦♥❣ ✤â t❛ ❝â t❤➸ ❜ä q✉❛ sè ❤↕♥❣ ♣❤ö t❤✉ë❝ ✈➔♦ t❤❛♠ sè ρ✱ tự P ố ợ s ữủ t t ợ s số tữỡ t ự tữỡ ự ợ Z ữủ t ♥➯✉ tr♦♥❣ ❜↔♥❣ ✻✳ ✶✶✾ ... ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✶✸ √1 ∆Q331 W (Cs) ❧➔ ❤➔♠ t❤❡♦ MZ2 ✈ỵ✐ β = ± ✤è✐ ✈ỵ✐ ♠ỉ ❤➻♥❤ ❧♦↕✐ ❆ ✭❤➻♥❤ ❜➯♥ tr→✐✮ ✈➔ ❧♦↕✐ ❈ ✭❤➻♥❤ ❜➯♥ ♣❤↔✐✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✶✹ ∆Q331 W (Cs) ❧➔ ❤➔♠ t❤❡♦ MZ2... ❬✶✼✵❪ + − 0 LHiggsqcl = λ1 χρηϕ01 +λ3 η † ρφ− ξ +λ4 φ1 φ2 ϕ2 ξ +w1 ϕ2 ϕ01 +w2 χ† ρφ− +h.c ✭✷✳✺✮ ✣➸ s✐♥❤ ❦❤è✐ ❧÷đ♥❣ ♥❡✉tr✐♥♦✱ ♥❣♦➔✐ sè ❤↕♥❣ ✤➛✉ t✐➯♥ ð ✭✷✳✺✮✱ ❝á♥ ❝â ♣❤➛♥ t❤➯♠ ❧➔ ❬✶✼✵❪ + LHiggsneutrino... t➔♥ ❞÷ ✈➟t ❝❤➜t tè✐✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✼ ✳✳✳✳✳✳✳✳✳✳✳✳✳✳ ✈➔ ∆QCKS W (p) ❧➔ ❤➔♠ ❝õ❛ MZ ∆Q331 W (Cs) ❧➔ ❤➔♠ t❤❡♦ MZ ❦❤✐ ①➨t ✤è✐ ✈ỵ✐ ♠æ ❤➻♥❤ ❧♦↕✐ ❆ ✭❤➻♥❤ √ ❜➯♥ tr→✐✮ ✈➔ ❈ ✭❤➻♥❤ ❜➯♥ ♣❤↔✐✮