Trong mô hình chuẩn các neutrino đều cơ khối lượng bằng không và không có sự chuyển hóa lẫn nhau giữa các thế hệ lepton. Thực nghiệm: neutrino có khối lượng khác không dù rất nhỏ và có sự chuyển hóa lẫn nhau giữa các neutrino khác thế hệ. Giải pháp: Bổ sung các neutrino phải; Bổ sung các trường mới...Nghiên cứu mô hình Zê Babu với việc bổ sung các trường vô hướng và kết hợp sử dụng phương pháp lấy đạo hàm theo các toán tử trường.
❇❐ ●■⑩❖ ❉Ư❈ ❱⑨ ✣⑨❖ ❚❸❖ ❚❘×❮◆● ✣❸■ ❍➴❈ ❙× P❍❸▼ ❍⑨ ◆❐■ ✷ ❑❍❖❆ ❱❾❚ ▲Þ P❍❸▼ ❚❍➚ ❚❍Õ❨ ❈⑩❈ ◗❯⑩ ❚❘➐◆❍ ❘❶ ❱■ P❍❸▼ ❙➮ ▲❊P❚❖◆ ❚❍➌ ❍➏ ei → ej ek e¯l ❚❘❖◆● ▼➷ ❍➐◆❍ ❩❊❊ ✲ số t ỵ ỵ tt t ỵ t ữớ ữợ P●❙✳❚❙✳ ❍⑨ ❚❍❆◆❍ ❍Ị◆● ❍⑨ ◆❐■✱ ✷✵✶✽ ✶ ▲í✐ ❝↔♠ ì♥ ✣➛✉ t✐➯♥ ❡♠ ①✐♥ ✤÷đ❝ ❜➔② tä ❧á♥❣ ❜✐➳t ì♥ s➙✉ s➢❝ tỵ✐ P●❙✳❚❙✳ ❍⑨ ❚❍❆◆❍ ❍Ị◆● ✤➣ trü❝ t ữợ tr sốt q tr ự ✈➔ ❤♦➔♥ t❤➔♥❤ ❧✉➟♥ ✈➠♥ ♥➔②✳ ❊♠ ①✐♥ ❝❤➙♥ t❤➔♥❤ ❝↔♠ ì♥ ❚❙✳ ▲➊ ❚❍➴ ❍❯➏ ❝ỉ♥❣ t→❝ t↕✐ ❱✐➺♥ t ỵ ổ t ũ t ổ tr t ỵ ❚r÷í♥❣ ✣↕✐ ❤å❝ ❙÷ ♣❤↕♠ ❍➔ ◆ë✐ ✷ ✤➣ t➟♥ t➻♥❤ ❝❤➾ ❞↕② ❝❤♦ ❡♠ tr♦♥❣ q✉→ tr➻♥❤ ❤å❝ t➟♣ ự tr trồ ỡ qỵ t ổ tr ỗ ữỡ ỗ t õ ỵ ✤➸ ❧✉➟♥ ✈➠♥ ❝õ❛ ❡♠ ✤÷đ❝ ❤♦➔♥ t❤✐➺♥ ❤ì♥✳ ❊♠ ỷ ỡ tợ trữớ ✣↕✐ ❤å❝ ❙÷ ♣❤↕♠ ❍➔ ◆ë✐ ✷ ✤➣ t↕♦ ✤✐➲✉ ❦✐➺♥ t❤✉➟♥ ❧đ✐ ✤➸ ❡♠ ✤÷đ❝ ❤å❝ t➟♣✱ ♥❣❤✐➯♥ ❝ù✉ t↕✐ tr÷í♥❣✳ ❳✐♥ ❝❤➙♥ t❤➔♥❤ ❝↔♠ ì♥ ❝→❝ ❜↕♥ ❤å❝ ợ t ỵ ỵ tt t ỵ t ú ù tổ tr q tr ❤å❝ t➟♣ ✈➔ ♥❣❤✐➯♥ ❝ù✉✳ ❈✉è✐ ❝ò♥❣✱ tỉ✐ ①✐♥ ❣û✐ ỡ tợ ỗ ❝ơ♥❣ ♥❤÷ ❜❛♥ ❧➣♥❤ ✤↕♦ tr÷í♥❣ ❚❍P❚ ❈❤✉②➯♥ ◆❣✉②➵♥ ❚r➣✐ ✲ ❍↔✐ ❉÷ì♥❣ ✤➣ t↕♦ ✤✐➲✉ ❦✐➺♥ ✈➔ ❧✉ỉ♥ ❦❤➼❝❤ ❧➺ ✤ë♥❣ ✈✐➯♥ tæ✐ tr♦♥❣ s✉èt q✉→ tr➻♥❤ ❤å❝ t➟♣ ✈➔ ♥❣❤✐➯♥ ❝ù✉✳ ❍➔ ◆ë✐✱ ♥❣➔② ✸✵ t❤→♥❣ ✵✹ ♥➠♠ ✷✵✶✽ ❍å❝ ✈✐➯♥ P❤↕♠ ❚❤à ❚❤õ② ✷ ▲í✐ ❝❛♠ ✤♦❛♥ ❚æ✐ ①✐♥ ❝❛♠ ✤♦❛♥ r➡♥❣ ♥❤ú♥❣ sè ❧✐➺✉ ✈➔ ❦➳t q✉↔ ♥❣❤✐➯♥ ❝ù✉ t❤✉ ✤÷đ❝ tr♦♥❣ ❧✉➟♥ ✈➠♥ ♥➔② ❧➔ tr✉♥❣ t❤ü❝ ✈➔ ❦❤ỉ♥❣ trò♥❣ ❧➦♣ ✈ỵ✐ ❝→❝ ✤➲ t➔✐ ❦❤→❝✳ ❚ỉ✐ ❝ơ♥❣ ①✐♥ ❝❛♠ ✤♦❛♥ r➡♥❣ ♠å✐ sü ❣✐ó♣ ✤ï ❝❤♦ ✈✐➺❝ t❤ü❝ ❤✐➺♥ ❧✉➟♥ ✈➠♥ ♥➔② ✤➣ ✤÷đ❝ ❝↔♠ ì♥ ✈➔ ❝→❝ t❤ỉ♥❣ t✐♥ tr➼❝❤ ❞➝♥ tr♦♥❣ ❧✉➟♥ ữủ ró ỗ ố ✸✵ t❤→♥❣ ✵✹ ♥➠♠ ✷✵✶✽ ❍å❝ ✈✐➯♥ P❤↕♠ ❚❤à ❚❤õ② ✸ ▼ư❝ ❧ư❝ ▲í✐ ❝↔♠ ì♥ ✶ ▲í✐ ❝❛♠ ✤♦❛♥ ✷ ❉❛♥❤ s→❝❤ t❤✉➟t ♥❣ú ✈✐➳t t➢t ✺ ❉❛♥❤ s→❝❤ ❤➻♥❤ ✈➩ ✻ ❉❛♥❤ s→❝❤ ❜↔♥❣ ✾ ▼ð ✤➛✉ ✶✶ ✶ ●✐ỵ✐ t❤✐➺✉ ♠ỉ ❤➻♥❤ ❩❡❡ ✲ ❇❛❜✉ ✶✻ ✶✳✶ ❚ê♥❣ q✉❛♥ ✈➲ ♠æ ❤➻♥❤ ❝❤✉➞♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✳✷ ❙➢♣ ①➳♣ ❤↕t tr♦♥❣ ♠æ ❤➻♥❤ ❩❡❡ ✲ ố ữủ tr t t ỵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷ ❑➯♥❤ r➣ ✈✐ ♣❤↕♠ sè ❧❡♣t♦♥ t❤➳ ❤➺ ei → ej ek el ✷✳✶ ✷✸ ❈→❝ ✤➾♥❤ t÷ì♥❣ t→❝ ❝õ❛ q✉→ tr➻♥❤ r➣ ✈✐ ♣❤↕♠ sè ❧❡♣t♦♥ t❤➳ ❤➺ ✷✳✷ ✶✻ ei → ej ek el ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỗ r➣ ✈➔ t➾ ❧➺ r➣ ♥❤→♥❤ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸ ❑❤↔♦ s→t sè ✹✻ ✸✳✶ ❚❤✐➳t ❧➟♣ ❣✐ỵ✐ ❤↕♥ t❤❛♠ sè ❝❤♦ ♠ỉ ❤➻♥❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✸✳✷ ❑❤↔♦ s→t sè ✈➔ s♦ s→♥❤ ✈ỵ✐ t❤ü❝ ♥❣❤✐➺♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹ ❑➳t ❧✉➟♥ ✺✹ P❤ö ❧ö❝ ✺✺ ❆ ◗✉→ tr➻♥❤ r➣ τ − → e−νeντ ✺✻ ❚➔✐ ❧✐➺✉ t❤❛♠ ❦❤↔♦ ✻✸ ✺ ❉❛♥❤ s→❝❤ t❤✉➟t ♥❣ú ✈✐➳t t➢t ❱✐➳t t➢t ❱✐➳t ✤➛② ✤õ ●❤✐ ❝❤ó ▲❍❈ ▲❛r❣❡ ❍❛❞r♦♥ ❈♦❧❧✐❞❡r ▼→② ❣✐❛ tè❝ ❧ỵ♥ ❍❛❞r♦♥ ▲❋❱ ▲❡♣t♦♥ ❢❧❛✈♦r ✈✐♦❧❛t✐♥❣ ❱✐ ♣❤↕♠ sè ❧❡♣t♦♥ t❤➳ ❤➺ ❙▼ ❙t❛♥❞❛r❞ ♠♦❞❡❧ ▼æ ❤➻♥❤ ❝❤✉➞♥ ●▼❙ ●❧❛s❤♦✇✲❲❡✐❜❡r❣✲❙❛❧❛♠ ❚➯♥ ❜❛ ♥❤➔ ❦❤♦❛ ❤å❝ ✻ ❉❛♥❤ s→❝❤ s ỗ ❋❡②♥♠❛♥ ❝❤♦ q✉→ tr➻♥❤ r➣ ♥❤→♥❤ τ − → e− e e+ ỗ q tr r e e e+ ỗ ❋❡②♥♠❛♥ ❝❤♦ q✉→ tr➻♥❤ r➣ ♥❤→♥❤ τ − → e− e+ ỗ q tr r➣ ♥❤→♥❤ τ − → µ− µ− e+ ✸✵ ✷✳✺ ỗ q tr r e e à+ ỗ q✉→ tr➻♥❤ r➣ ♥❤→♥❤ τ − → e− µ− µ+ ỗ q tr r à à+ ỗ ❋❡②♥♠❛♥ ❝❤♦ q✉→ tr➻♥❤ r➣ ✈✐ ♣❤↕♠ sè ❧❡♣t♦♥ t❤➳ ❤➺ ✸✳✶ ✸✳✻ → e− e− e+ ) t❤❡♦ ❤❛✐ t❤❛♠ sè gee − → e− µ− e+ ) t❤❡♦ ❤❛✐ t❤❛♠ sè geµ geτ − → µ− µ− e+ ) t❤❡♦ ❤❛✐ t❤❛♠ sè gµτ → e− µ− µ+ ) t❤❡♦ ❤❛✐ t❤❛♠ sè ✹✽ ✹✾ gµµ → e− e− µ+ ) t❤❡♦ ❤❛✐ t❤❛♠ sè gee − ✹✼ ✈➔ ✺✵ ✈➔ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❚➾ sè r➣ ♥❤→♥❤ ❇r(τ ✸✷ ✈➔ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ − ✷✽ ✈➔ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❚➾ sè r➣ ♥❤→♥❤ ❇r(τ ✈➔ gee ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❚➾ sè r➣ ♥❤→♥❤ ❇r(τ gµτ t❤❡♦ ❤❛✐ t❤❛♠ sè ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❚➾ sè r➣ ♥❤→♥❤ ❇r(τ ✈➔ ✸✳✺ → e− e− e+ ) − geτ ✸✳✹ − ❚➾ sè r➣ ♥❤→♥❤ ❇r(µ geµ ✸✳✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❚➾ sè r➣ ♥❤→♥❤ ❇r(τ geτ ✸✳✷ − − + e− i → ej ek el ✳ ✺✶ geµ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✽ ✸✳✼ ❚➾ sè r➣ ♥❤→♥❤ ❇r(τ ✈➔ ❆✳✶ gµτ − → µ− µ− µ+ ) t❤❡♦ ❤❛✐ t❤❛♠ sè gµµ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỗ q tr r → e− νe ντ ✳ ✳ ✳ ✳ ✳ ✺✸ ✺✻ ✾ ❉❛♥❤ s→❝❤ ❜↔♥❣ ✺✵ ❚➾ ❧➺ r➣ ♥❤→♥❤ ❇r(τ − → µ− µ− e+ ) ❝❤♦ tr➯♥ ❤➻♥❤ ✸✳✹✳ Br(τ- →μ- μ- e + )×10`8 14 g'eτ [GeV-1 ] 12 10 1.7 0.1 2 g'μμ 10 [GeV-1 ] ❍➻♥❤ ✸✳✹✿ ❚➾ sè r➣ ♥❤→♥❤ ❇r(τ − → µ−µ−e+) t❤❡♦ ❤❛✐ t số gàà ge ợ tỹ ♥❣❤✐➺♠ ❝õ❛ Br(τ − → µ− µ− e+ < 1.7 ì 108 ) õ tứ ỗ t ❝❤ó♥❣ t❛ ❝â ❝→❝ ♥❤➟♥ ①➨t s❛✉✿ • ❱ò♥❣ ❦❤ỉ♥❣ tr ữớ 1.7 ì 108 ổ r tữủ t ỵ ũ ổ tr ữợ ữớ 1.7 ì 108 Br( à e+ ) = Br(τ − → µ− µ− e+ ) = ❧➔ ✈ò♥❣ ổ t ỵ số tữỡ t à e+ ) = 10−7 geτ ❣✐↔♠ ❝❤➟♠ t❤❡♦ gµµ ✳ ❈❤➥♥❣ ❤↕♥✱ ❦❤✐ Br(τ − → t❤➻ ❝→❝ ❝➦♣ ❣✐→ tr tữỡ ự gàà = 4GeV t ge = 4, 5GeV −1 ❀ gµµ = 6GeV −1 t❤➻ geτ = 3GeV −1 gµµ = 8GeV −1 t❤➻ geτ = 2, 25GeV −1 ✳ ✈➔ ✺✶ ❚➾ ❧➺ r➣ ♥❤→♥❤ ❇r(τ − → e− e− µ+ ) ❝❤♦ tr➯♥ ❤➻♥❤ ✸✳✺✳ Br(τ- →e - e - μ+ )×10`8 12 g'μτ [GeV-1 ] 10 1.5 0.1 2 g'ee 10 12 [GeV-1 ] ❍➻♥❤ ✸✳✺✿ ❚➾ sè r➣ ♥❤→♥❤ ❇r(τ − → e−e−µ+) t t số gee gà ợ ❤↕♥ t❤ü❝ ♥❣❤✐➺♠ ❝õ❛ Br(τ − → e− e− µ+ < 1.5 ì 108 ) õ tứ ỗ t ✭❤➻♥❤ ✸✳✺✮ ❝❤ó♥❣ t❛ ❝â ❝→❝ ♥❤➟♥ ①➨t s❛✉✿ • ❱ò♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ♠➔✉ ①❛♥❤ ♥➡♠ ♣❤➼❛ tr➯♥ ✤÷í♥❣ 1.5 ì 108 ổ r tữủ t ỵ ũ ổ tr ữợ ữớ 1.5 ì 108 Br( e e à+ ) = Br(τ − → e− e− µ+ ) = ũ ổ t ỵ số tữỡ t e− e− µ+ ) = 10−7 gµτ ❣✐↔♠ ❝❤➟♠ t❤❡♦ gee ✳ ❈❤➥♥❣ ❤↕♥✱ ❦❤✐ Br(τ − → t❤➻ ❝→❝ ❝➦♣ ❣✐→ trà t÷ì♥❣ ù♥❣ ❧➔✿ gee = 4GeV −1 t❤➻ gµτ = 4, 5GeV −1 ❀ gee = 6GeV −1 t❤➻ gµτ = 3GeV −1 gee = 8GeV −1 t❤➻ gµτ = 2, 25GeV −1 ✳ ✈➔ ✺✷ ❚➾ ❧➺ r➣ ♥❤→♥❤ ❇r(τ − → e− µ− µ+ ) ❝❤♦ tr➯♥ ❤➻♥❤ ✸✳✻✳ Br(τ- →e - μ- μ+ )×10`8 12 g'μτ [GeV-1 ] 10 2.7 0.1 2 g'eμ 10 12 [GeV-1 ] ❍➻♥❤ ✸✳✻✿ ❚➾ sè r➣ ♥❤→♥❤ ❇r(τ − → e−µ−µ+) t❤❡♦ ❤❛✐ t❤❛♠ sè geµ ✈➔ gµτ ❚❤❡♦ ❬✾❪✱ ợ tỹ Br( e à+ < 2.7 ì 108 ) õ tứ ỗ t❤à ✭❤➻♥❤ ✸✳✻✮ ❝❤ó♥❣ t❛ ❝â ❝→❝ ♥❤➟♥ ①➨t s❛✉✿ • ❱ò♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ♠➔✉ ①❛♥❤ ♥➡♠ ♣❤➼❛ tr➯♥ ✤÷í♥❣ 2.7 ì 108 ổ r tữủ t ỵ ũ ổ tr ữợ ữớ 2.7 ì 108 Br( e µ+ ) = Br(τ − → e− µ− µ+ ) = ũ ổ t ỵ số tữỡ t→❝ e− µ− µ+ ) = 10−7 gµτ ❣✐↔♠ ❝❤➟♠ t❤❡♦ geµ ✳ ❈❤➥♥❣ ❤↕♥✱ ❦❤✐ Br(τ − → t❤➻ tr tữỡ ự geà = 4GeV −1 t❤➻ gµτ = 3, 2GeV −1 ❀ geµ = 6GeV −1 t❤➻ gµτ = 2, 25GeV −1 geµ = 8GeV −1 t❤➻ gµτ = 1, 16GeV −1 ✳ ✈➔ ✺✸ ❚➾ ❧➺ r➣ ♥❤→♥❤ ❇r(τ − → µ− µ− µ+ ) ❝❤♦ tr➯♥ ❤➻♥❤ ✸✳✼✳ Br(τ- →μ- μ- μ+ )×10`8 12 10 g'μτ [GeV-1 ] 2.1 0.1 2 g'μμ 10 12 [GeV-1 ] ❍➻♥❤ ✸✳✼✿ ❚➾ sè r➣ ♥❤→♥❤ ❇r(τ − → µ−µ−µ+) t❤❡♦ ❤❛✐ t❤❛♠ sè gµµ ✈➔ gµτ ❚❤❡♦ ợ tỹ Br( 3à < 2.1 ì 108 ) õ tứ ỗ t ✸✳✼✮ ❝❤ó♥❣ t❛ ❝â ❝→❝ ♥❤➟♥ ①➨t s❛✉✿ • ❱ò♥❣ ổ tr ữớ 2.1 ì 108 ổ r tữủ t ỵ ũ ổ tr ữợ ữớ 2.1 ì 108 Br( 3à) = ũ ổ t ỵ số tữỡ t 3à) = 107 Br(τ → 3µ) = gµτ ❣✐↔♠ ❝❤➟♠ t❤❡♦ gµµ ✳ ❈❤➥♥❣ ❤↕♥✱ ❦❤✐ Br(τ → t❤➻ ❝→❝ ❝➦♣ ❣✐→ trà tữỡ ự gàà = 4GeV t gà = 4, 5GeV −1 ❀ gµµ = 6GeV −1 t❤➻ gµτ = 3GeV −1 gµµ = 8GeV −1 t❤➻ gµτ = 2, 25GeV −1 ✳ ✈➔ ✺✹ ❑➳t ❧✉➟♥ ❚r♦♥❣ q✉→ tr➻♥❤ ♥❣❤✐➯♥ ❝ù✉ ✤➸ ♠ð rë♥❣ ♠ỉ ❤➻♥❤ ❝❤✉➞♥✱ ❝❤ó♥❣ tæ✐ t➟♣ tr✉♥❣ ✈➔♦ ♥❣❤✐➯♥ ❝ù✉ ✈➲ ❝→❝ q✉→ tr➻♥❤ ✈✐ ♣❤↕♠ sè ❧❡♣t♦♥ tr♦♥❣ ♠æ ❤➻♥❤ ❩❡❡ ✲ ❇❛❜✉✱ ❝ö t❤➸ ❧➔ q✉→ tr➻♥❤ r➣ τ − → e− e− e+ ✈➔ τ − → e− µ− e+ ✱ ✤➣ t❤✉ ✤÷đ❝ ♠ët sè ❦➳t q✉↔ s❛✉ ✤➙②✿ ✲ ợ t sỡ ữủ t r ❙▼ tr♦♥❣ ✤â♥❣ ❣â♣ ✈➔♦ ♠æ ❤➻♥❤ ❩❡❡ ✲ ❇❛❜✉✳ ✲ ❚r➻♥❤ ❜➔② ♥❤ú♥❣ ♥ë✐ ❞✉♥❣ ❝❤➼♥❤ ❝õ❛ ♠æ ❤➻♥❤ ❩❡❡ ✲ ❇❛❜✉✿ ❣✐ỵ✐ t❤✐➺✉ ♠ỉ ❤➻♥❤ ✈➔ ❝→❝❤ s➢♣ ①➳♣ ❝→❝ ❤↕t✱ ①→❝ ✤à♥❤ ❦❤è✐ ❧÷đ♥❣ ✈➔ tr↕♥❣ t❤→✐ t ỵ t tr ổ ❦❤✐ ♥❣❤✐➯♥ ❝ù✉ ✈➔ t➼♥❤ t♦→♥ ❜➡♥❣ ♣❤÷ì♥❣ ♣❤→♣ ✤↕♦ ❤➔♠ ❝→❝ t♦→♥ tû tr÷í♥❣ tr♦♥❣ ▲❛❣r❛♥❣✐❛♥ t÷ì♥❣ t→❝ (2.7) ❝❤ó♥❣ tỉ✐ t❤➜② ❝â ①✉➜t ❤✐➺♥ ❤➺ sè ✷ tr♦♥❣ ❤➺ sè ✤➾♥❤ t÷ì♥❣ t→❝ ❝õ❛ ❝→❝ q✉→ tr➻♥❤ r➣ − + ei → e− j ek el ❝â ❤❛✐ ❤↕t ❣✐è♥❣ ♥❤❛✉ ð tr↕♥❣ t❤→✐ ❝✉è✐ ❬✻❪✳ ✲ ❳→❝ ữủ ỗ tự t ✤ë r➣ ♥❤→♥❤✱ ❜➲ rë♥❣ r➣ ✈➔ t➾ ❧➺ r➣ ♥❤→♥❤ ❝õ❛ q✉→ tr➻♥❤ r➣ τ − → e− e− e+ ❀ τ − → e− µ− e+ ✳ ❚ø ✤â ✤÷❛ r❛ ❜✐➸✉ t❤ù❝ tê♥❣ q✉→t t➼♥❤ ❜➲ rë♥❣ r➣ ♥❤→♥❤ ✈➔ t➾ ❧➺ r➣ ♥❤→♥❤ ❝õ❛ ❝→❝ q✉→ tr➻♥❤ r➣ ✈✐ ♣❤↕♠ sè ❧❡♣t♦♥ t❤➳ ❤➺ − + ei → e− j ek el ✳ ❈→❝ ❦➳t q✉↔ t➼♥❤ ❣✐↔✐ t➼❝❤ tr♦♥❣ ♠ỉ ❤➻♥❤ ❩❡❡ ✲ ❇❛❜✉ ✈ỵ✐ ❤❛✐ ✤ì♥ t✉②➳♥ ✭♠ët t➼❝❤ ✤✐➺♥ ✤ì♥ h+ ✈➔ ♠ët t➼❝❤ ✤✐➺♥ ✤æ✐ k ++ ✮ ❜ê s✉♥❣ ✈➔♦ ❙▼ t q ợ ữ ữủ ự tr ổ tr ữủ ổ ố trữợ õ số ỗ t tở t ❧➺ r➣ ♥❤→♥❤ ✈➔♦ ❝→❝ t❤❛♠ sè gjk = gli g∗jk , gli = mk++ mk++ tr♦♥❣ ♠æ ❤➻♥❤ ❩❡❡ ✲ ❇❛❜✉✳ ✲ ✣→♥❤ ❣✐→ ✈➔ t❤↔♦ ❧✉➟♥ ❦➳t q✉↔ t số ợ ỗ t tở t r➣ ♥❤→♥❤ ❝õ❛ ❝→❝ q✉→ tr➻♥❤ tr♦♥❣ ♠æ ❤➻♥❤ ❩❡❡ ✲ ❇❛❜✉ t❤❡♦ ❜ë t❤❛♠ sè ♣❤ò ❤đ♣✳ ✲ ●✐↔✐ t❤➼❝❤ ✈➔ s♦ s→♥❤ ❦➳t q✉↔ ♥❣❤✐➯♥ ❝ù✉ ❝õ❛ ❧✉➟♥ ✈➠♥ s♦ ✈ỵ✐ t❤ü❝ ♥❣❤✐➺♠ ♠➔ ❝→❝ ♥❤➔ ❦❤♦❛ ❤å❝ ự trữợ õ ữợ t tr t➔✐✿ ⑩♣ ❞ư♥❣ ❝→❝ ♣❤÷ì♥❣ ♣❤→♣ t➼♥❤ tr♦♥❣ ♠ỉ ❤➻♥❤ ự ổ ợ ữủ ❞ü♥❣ tr♦♥❣ t❤í✐ ❣✐❛♥ ❣➛♥ ✤➙② ❞ü❛ tr➯♥ ❝ì ❝❤➳ ❩❡❡✲❇❛❜✉ s✐♥❤ ❦❤è✐ ❧÷đ♥❣ ♥❡✉tr✐♥♦✳ ✺✻ P❤ư ❧ư❝ ❆ ◗✉→ tr➻♥❤ r➣ τ − → e−νeντ ❚ø ❬✶✶✱ ♠ö❝ ✽✳✹❪✱ ú t õ t ữủ ỗ e e P3 P2 P1 k ỗ q tr➻♥❤ r➣ τ − → e−νeντ ✺✼ ❍↕t ✈➔ ♣❤↔♥ ❤↕t ❳✉♥❣ ❧÷đ♥❣ ❙♣✐♥ ❙♣✐♥♦r τ− p1 s1 u1 (p1 , s1 ) e− p2 s2 u2 (p2 , s2 ) νe p3 s3 v3 (p3 , s3 ) ντ p4 s4 u4 (p4 , s4 ) ứ ỗ ✭❍➻♥❤ ❆✳✶✮✱ t❛ ❝â✿ ❇✐➯♥ ✤ë t→♥ ①↕✿ √ Mf i = −i2 2GF [u4 (p4 , s4 ) γ ρ PL u1 (p1 , s1 )] [u2 (p2 , s2 ) γρ PL v3 (p3 , s3 )] ✭❆✳✶✮ √ Mf∗i = i2 2GF [u1 (p1 , s1 ) PR γ σ u4 (p4 , s4 )] [v3 (p3 , s3 ) PR γσ u2 (p2 , s2 )] ✭❆✳✷✮ ✈ỵ✐ GF ❣å✐ ❧➔ ❤➡♥❣ sè ❋❡r♠✐ ✭❝â t❤➸ ✤÷đ❝ ①→❝ ✤à♥❤ tø q✉→ tr➻♥❤ r➣ ❝→❝ ❧❡♣t♦♥ ❜➟❝ số 2 ởt q ữợ ❝â tr♦♥❣ ❧à❝❤ sû ♥❣❤✐➯♥ ❝ù✉✳ ❚r♦♥❣ ✭❆✳✶✮✱ ✭❆✳✷✮ ❝â sû ❞ö♥❣✿ ePR γ ρ νe = eγ ρ PL νe = eγ ρ (1 − γ5) νe ✭❆✳✸✮ ❑❤✐ ✤â✿ |Mf i |2 = Mf∗i Mf i = 8G2F [u4 (p4 , s4 ) γ ρ PL u1 (p1 , s1 )] [u2 (p2 , s2 ) γρ PL v3 (p3 , s3 )] × [u1 (p1 , s1 ) PR γ σ u4 (p4 , s4 )] [v3 (p3 , s3 ) PR γσ u2 (p2 , s2 )] ✭❆✳✹✮ ❝❤ó♥❣ t❛ ❝â t❤➸ ❜ä q✉❛ ❦❤è✐ ❧÷đ♥❣ ❝õ❛ ❝→❝ ❤↕t ð tr↕♥❣ t❤→✐ ❝✉è✐ ❦❤✐ ✺✽ me /mτ 0.005✳ ⑩♣ ❞ö♥❣✿ u1 (p1 , s1 ) u1 (p1 , s1 ) = s1 ( p1 + mτ ) u2 (p2 , s2 ) u2 (p2 , s2 ) = ( p2 + me− ) = p2 s2 v3 (p3 , s3 ) v3 (p3 , s3 ) = ( p3 − mνe ) = p3 s3 u4 (p4 , s4 ) u4 (p4 , s4 ) = ( p4 + mνe ) = p4 s4 ❉♦ ♠é✐ t❤ø❛ sè tr♦♥❣ ♥❣♦➦❝ ✈✉æ♥❣ ❝õ❛ ✭❆✳✹✮ ❧➔ ♠ët sè ♥➯♥ t❛ ❝â t❤➸ t❤❛② ❜➡♥❣ ✈➳t ✤➸ t❤ü❝ ❤✐➺♥ ❝→❝ ♣❤➨♣ ❤♦→♥ ✈à ♠❛ tr➟♥ ♠➔ ❦➳t q✉↔ t➼♥❤ ❦❤ỉ♥❣ t❤❛② ✤ê✐✳ ❈ư t❤➸ ❧➔✿ |Mf i |2 = 8G2F T r [u4 (p4 , s4 ) γ ρ PL u1 (p1 , s1 )] T r [u2 (p2 , s2 ) γρ PL v3 (p3 , s3 )] × T r [u1 (p1 , s1 ) PR γ σ u4 (p4 , s4 )] T r [v3 (p3 , s3 ) PR γσ u2 (p2 , s2 )] = 8G2F T r [u4 (p4 , s4 ) γ ρ PL u1 (p1 , s1 )] T r [u1 (p1 , s1 ) PR γ σ u4 (p4 , s4 )] × T r [u2 (p2 , s2 ) γρ PL v3 (p3 , s3 )] T r [v3 (p3 , s3 ) PR γσ u2 (p2 , s2 )] = 8G2F T r [u4 (p4 , s4 ) γ ρ PL ( p1 + mτ ) PR γ σ u4 (p4 , s4 )] × T r [u2 (p2 , s2 ) γρ PL ( p3 − mνe ) PR γσ u2 (p2 , s2 )] = 8G2F T r [u4 (p4 , s4 ) u4 (p4 , s4 ) γ ρ PL p1 PR γ σ ] × T r [u2 (p2 , s2 ) u2 (p2 , s2 ) γρ PL p3 PR γσ ] |Mf i |2 = 8G2F T r [ p4 γ ρ PL p1 PR γ σ ] T r [ p2 γρ PL p3 PR γσ ] = 8G2F T r [γ ρ p1 PR γ σ p4 ] T r [γρ p3 PR γσ p2 ] ✺✾ ❈❤ó♥❣ t❛ ①➨t✿ T r [γ ρ p1 PR γ σ p4 ] T r [γρ p3 PR γσ p2 ] = {p1α p4β T r γ ρ γ α γ σ γ β + T r γ ρ p1 γ σ p4 γ } × {p3α p2β T r [γρ γα γσ γβ ] + T r γρ p3 γσ p2 γ } = {p1α p4β × g ρα g σβ − g ρσ g αβ + g ρβ g ασ + p1α p4β × 4i ρασβ } × {pα3 pβ2 × [gρα gσβ − gρσ gα β + gρβ gα σ ] + pα3 pβ2 × 4i ρα σβ } = 4{p1 ρpσ4 − (p1 p4 ) g ρσ + pσ1 pρ4 + ip1α p4β ρασβ × {p3ρ p2σ − (p3 p2 ) gρσ + p3σ p2ρ + ipα3 pβ2 ρα σβ } } = 4{2 (p1 p3 ) (p3 p4 ) + (p1 p2 ) (p1 p4 ) − p1α p4β pα3 pβ2 −2δαα δββ + 2δβα δαβ } = 16 (p1 p3 ) (p2 p4 ) ❚r♦♥❣ ✤â ❝❤ó♥❣ tỉ✐ ❝â sû ❞ư♥❣ ♠ët sè ❤➺ t❤ù❝ ❬✶❪✿ T r [γ ρ p1 γ σ p4 ] = p1α p4β T r γ ρ γ α γ σ γ β T r γ ρ γ α γ σ γ β = g ρα g σβ − g ρσ g αβ + g ρβ g ασ T r γ ρ γ α γ σ γ β γ = 4ip1α p4β ρασβ g ρσ gσρ = 4; gσρ pσ1 pρ4 = (p1 p4 ) ; g ρσ p3σ p2ρ = (p2 p3 ) ρασβ ρα σβ = −2δαα δββ + 2δβα δαβ ❑❤✐ ✤â✿ |Mf i |2 = 128G2F (p1 p3 )(p2 p4 ) ✭❆✳✺✮ ▲➜② tr✉♥❣ ❜➻♥❤ s♣✐♥ ❝õ❛ tr↕♥❣ t❤→✐ ✤➛✉ ❧➔ ❤↕t t❛✉ t❛ t❤✉ ✤÷đ❝ ❜➻♥❤ ♣❤÷ì♥❣ ❜✐➯♥ ✤ë r➣ tr✉♥❣ ❜➻♥❤✿ |Mf i |2 ≡ ❳➨t ❤➺ q✉✐ ❝❤✐➳✉ ❤↕t trö❝ ③✿ τ |Mf i |2 = 64G2F (p1 p3 )(p2 p4 ) ✤ù♥❣ ②➯♥✱ ❤➺ tå❛ ✤ë ❝â p1 = (mτ , 0, 0, 0)✱ p3 = (Eνe , 0, 0, Eνe )✱ p3 ✭❆✳✻✮ ❝❤✉②➸♥ ✤ë♥❣ ❞å❝ t❤❡♦ ✻✵ ❑❤✐ ✤â✿ p1 p3 = mτ Eνe ❱➻ ✈➟②✿ p2 p4 = = 21 (p2 + p4 )2 − p22 − p24 = p21 + p23 − 2.p1 p3 = 2 (p1 − p3 )2 − − m2τ − 2.mτ Eνe tr♦♥❣ ✤â t❛ ✤➣ ❜ä q✉❛ ❦❤è✐ ❧÷đ♥❣ ❝→❝ ❤↕t ♥❤➭ ð tr↕♥❣ t❤→✐ ❝✉è✐✳ ❑❤✐ ✤â✱ tø ✭❆✳✻✮ t❛ ❝â ✿ |Mf i |2 ≡ |Mf i |2 = 32G2F m3τ Eνe − 2.mτ Eν2e ✭❆✳✼✮ ❚ø ❬✶✶✱ ✹✳✺❪✱ ❝❤ó♥❣ t❛ ①→❝ ✤à♥❤ ✤÷đ❝ ❜➲ rë♥❣ r➣ ❝õ❛ q✉→ tr➻♥❤ r➣ ❜❛ ❤↕t ✈ỵ✐ ❤➺ q✉② ❝❤✐➳✉ pτ = (M, 0, 0, 0) dΓ = ❧➔✿ |M|2 dφ3 2M ✭❆✳✽✮ ❚r♦♥❣ ✤â✿ ▼ ✲ ❦❤è✐ ❧÷đ♥❣ ❝õ❛ ❤↕t ð tr↕♥❣ t❤→✐ ✤➛✉✳ |M|2 ✲ ❜➻♥❤ ♣❤÷ì♥❣ ❜✐➯♥ ✤ë r➣ tr✉♥❣ ❜➻♥❤✳ d3 p3 d3 p4 d3 p2 dφ3 = (2π) (p1 − p2 − p3 − p4 ) (2π)3 2E2 (2π)3 2E3 (2π)3 2E4 = dE2 dE3 dφ1 d (cos θ1 ) dα2 256π E2 , E3 ✲ ◆➠♥❣ ❧÷đ♥❣ ❝õ❛ ❤❛✐ ❤↕t ð tr↕♥❣ t❤→✐ ❝✉è✐✳ ✣➸ ❜↔♦ t♦➔♥ ♥➠♥❣ ❧÷đ♥❣✱ ❤↕t t❤ù ❜❛ ð tr↕♥❣ t❤→✐ ❝✉è✐ ✤÷đ❝ ①→❝ ✤à♥❤✿ ❇❛ ❣â❝ ❊✉❧❡r φ1 , θ1 ❧➔ ❣â❝ q✉❛② ❝õ❛ ❤↕t ✶✱ α2 E4 = M − E2 − E3 ❧➔ ❣â❝ q✉❛② ❝õ❛ ❤↕t ✷ tr♦♥❣ tr↕♥❣ t❤→✐ ❝✉è✐✳ ◆➳✉ s♣✐♥ ❤↕t tr↕♥❣ t❤→✐ ❜❛♥ ✤➛✉ ✤÷đ❝ t➼♥❤ tr✉♥❣ ❜➻♥❤✱ t ổ õ ữợ t ữợ ❝õ❛ ♠➦t ♣❤➥♥❣ ♣❤➙♥ r➣ ❝õ❛ tr↕♥❣ t❤→✐ ❝✉è✐✳ ❚r♦♥❣ trữớ ủ õ ố ợ E2 tỷ tr ✤➣ ❣✐↔♠ ❦❤ỉ♥❣ t❤➸ ♣❤ư t❤✉ë❝ ✈➔♦ ❝→❝ ❣â❝ E3 ❝ö t❤➸✱ ♣❤➛♥ φ1 , θ1 ❤♦➦❝ t❤➳ t❛ ❝â t❤➸ t❤ü❝ ❤✐➺♥ t➼❝❤ ♣❤➙♥✿ 2π dφ1 2π d (cos θ1 ) −1 dα2 = (2π) (2) (2π) = (8π)2 α2 ✈➻ ✻✶ ❑❤✐ ✤â✿ dφ3 = =⇒ dΓ = ❚❤❛② ✭❆✳✼✮ ✈➔♦ ✭❆✳✾✮ ✈ỵ✐ dE2 dE3 32π |M|2 dE2 dE3 64π M M = mτ ✈➔ E2 = Ee− , E3 = Eνe ✱ G2F dΓ = dEe− dEνe m2τ Eνe − 2mτ Eν2e 2π ✭❆✳✾✮ t❛ ❝â✿ ✭❆✳✶✵✮ ❚r♦♥❣ tr÷í♥❣ ❤ñ♣ ✤➦❝ ❜✐➺t✱ t➜t ❝↔ ❝→❝ ❤↕t ð tr↕♥❣ t❤→✐ ❝✉è✐ ❝ò♥❣ ❦❤ỉ♥❣ ❝â ❦❤è✐ ❧÷đ♥❣ ✭❤♦➦❝ ✤õ ♥❤ä ✤➸ ❜ä q✉❛✮ mτ − Ee− < Eνe < mτ ;0 < Ee− < me = mνe = mντ = 0✳ ❉♦ mτ ✳ ❑❤✐ ✤â ❝❤ó♥❣ t❛ ❝â✿ mτ dΓ = dE e− G2F dEνe m2τ Eνe − 2mτ Eν2e mτ 2π −Ee− G2F = dEe− π m2τ Ee2− mτ Ee3− − ❈❤ó♥❣ t❛ t❤✉ ✤÷đ❝ t➾ ❧➺ ♣❤➙♥ r➣ ✈✐ ♣❤➙♥ ❝❤♦ ♥➠♥❣ ❧÷đ♥❣ ❝õ❛ ❡❧❡❝tr♦♥ ð tr↕♥❣ t❤→✐ ❝✉è✐✿ dΓ G2F m2τ 4Ee− = E − − dEe− 4π e 3mτ ✭❆✳✶✶✮ ❚÷ì♥❣ tü✱ ❝❤ó♥❣ t❛ ❝â t❤➸ t➼♥❤ ✤÷đ❝✿ G2F m2τ dΓ = E dEντ 4π ντ 4Eντ 3mτ ✭❆✳✶✷✮ dΓ G2F m2τ 4Eνe = Eνe − dEνe 4π 3mτ ✭❆✳✶✸✮ 1− ❚ø ✭❆✳✶✶✮✱ ✭❆✳✶✷✮✱ ✭❆✳✶✸✮ ❝❤ó♥❣ t❛ t➼♥❤ ✤÷đ❝ rở r tr ỗ τ − → e− νe ντ = = = = = mτ mτ dΓ dEe− = dEe− 0 mτ dΓ dEνe dE ν e mτ G2 m2 4Ee− F τ − E − e 4π 3mτ mτ GF mτ mτ − 4π 24 48mτ GF mτ 192π dΓ dEντ dEντ dEe− ✭❆✳✶✹✮ ✻✸ ❚➔✐ ❧✐➺✉ t❤❛♠ ❦❤↔♦ ❬✶❪ ❍♦➔♥❣ ◆❣å❝ ▲♦♥❣ ✭✷✵✵✻✮✱ ỡ s t ỵ t ỡ ố ❍➔ ◆ë✐✳ ❬✷❪ ❚❤❡ ❆❚▲❆❙ ❈♦❧❧❛❜♦r❛t✐♦♥✱ P❤②s✳▲❡tt✳ ❇ ✼✶✻✱ ✶ ✭✷✵✶✷✮✳ ❬✸❪ ❚❤❡ ❈▼❙ ❈♦❧❧❛❜♦r❛t✐♦♥✱ ●✳ ❆❛❞ ❡t ❛❧✱ P❤②s✳ ▲❡tt✳ ❇ ✼✶✻✱ ✸✵ ✭✷✵✶✷✮✳ ❬✹❪ ❑✳ ❙✳ ❇❛❜✉ ❛♥❞ ❈✳ ▼❛❝❡s❛♥✉✱ ✏❚✇♦ ❧♦♦♣ ♥❡✉tr✐♥♦ ♠❛ss ❣❡♥❡r❛t✐♦♥ ❛♥❞ ✐ts ❡①♣❡r✐♠❡♥t❛❧ ❝♦♥s❡q✉❡♥❝❡s✱✑ P❤②s✳ ❘❡✈✳ ❉ ✻✼ ✭✷✵✵✸✮ ✵✼✸✵✶✵ ❬❤❡♣✲♣❤✴✵✷✶✷✵✺✽❪✳ ❬✺❪ ❩✳ ✷✽ ▼❛❦✐✱ ▼✳ ✭✶✾✻✷✮ ✽✼✵❀ ◆❛❦❛❣❛✇❛ ❇✳ ❛♥❞ ❙✳ P♦♥t❡❝♦r✈♦✱ ❙❛❦❛t❛✱ Pr♦❣✳ ❙♦✈✳P❤②s✳❏❊❚P ❚❤❡♦r✳ ✼✱ ✶✼✷ P❤②s✳ ✭✶✾✺✽✮✱ ❩❤✳❊❦s♣✳❚❡♦r✳❋✐③✳ ✸✹✱ ✷✹✼ ✭✶✾✺✼✮✳ ❬✻❪ ▼✳ ◆❡❜♦t✱ ❏✳ ❋✳ ❖❧✐✈❡r✱ ❉✳ P❛❧❛♦ ❛♥❞ ❆✳ ❙❛♥t❛♠❛r✐❛✱ ✏Pr♦s♣❡❝ts ❢♦r t❤❡ ❩❡❡✲❇❛❜✉ ▼♦❞❡❧ ❛t t❤❡ ❈❊❘◆ ▲❍❈ ❛♥❞ ❧♦✇ ❡♥❡r❣② ❡①♣❡r✐✲ ♠❡♥ts✱✑ P❤②s✳ ❘❡✈✳ ❉ ✼✼ ✭✷✵✵✽✮ ✵✾✸✵✶✸ ❬❛r❳✐✈✿✵✼✶✶✳✵✹✽✸ ❬❤❡♣✲♣❤❪❪✳ ❬✼❪ ❏✳ ❍❡rr❡r♦✲●❛r❝✐❛✱ ▼✳ ◆❡❜♦t✱ ◆✳ ❘✐✉s ❛♥❞ ❆✳ ❙❛♥t❛♠❛r✐❛✱ ✏❚❤❡ ❩❡❡✕❇❛❜✉ ♠♦❞❡❧ r❡✈✐s✐t❡❞ ✐♥ t❤❡ ❧✐❣❤t ♦❢ ♥❡✇ ❞❛t❛✱✑ ◆✉❝❧✳ P❤②s✳ ❇ ✽✽✺ ✭✷✵✶✹✮ ✺✹✷ ❬❛r❳✐✈✿✶✹✵✷✳✹✹✾✶ ❬❤❡♣✲♣❤❪❪✳ ❬✽❪ ❯✳ ❇❡❧❧❣❛r❞t ✶ ✭✶✾✽✽✮✳ ❡t ❛❧✳ ❬❙■◆❉❘❯▼ ❈♦❧❧❛❜♦r❛t✐♦♥❪✱ ◆✉❝❧✳ P❤②s✳ ❇ ✷✾✾ ✱ ✻✹ ❬✾❪ ❑✳ ❍❛②❛s❛❦❛ ❡t ❛❧✳✱ ✏❙❡❛r❝❤ ❢♦r ▲❡♣t♦♥ ❋❧❛✈♦r ❱✐♦❧❛t✐♥❣ ❚❛✉ ❉❡❝❛②s ✐♥t♦ ❚❤r❡❡ ▲❡♣t♦♥s ✇✐t❤ ✼✶✾ ▼✐❧❧✐♦♥ Pr♦❞✉❝❡❞ ❚❛✉✰❚❛✉✲ P❛✐rs✱✑ P❤②s✳ ▲❡tt✳ ❇ ✻✽✼ ✭✷✵✶✵✮ ✶✸✾ ❬❛r❳✐✈✿✶✵✵✶✳✸✷✷✶ ❬❤❡♣✲❡①❪❪✳ ❬✶✵❪ P❤❡♥♦♠❡♥♦❧♦❣② ♦❢ P❛rt✐❝❧❡ P❤②s✐❝s ✲ ◆♦rt❤❡r♥ ■❧❧✐♥♦✐s ❯♥✐✈❡r✲ s✐t② ✇✇✇✳♥✐✉✳❡❞✉✴s♣♠❛rt✐♥✴♣❤②s✻✽✻✴♣♣♣✳♣❞❢ ❤tt♣✿✴✴③✐♣♣②✳♣❤②s✐❝s✳♥✐✉✳❡❞✉✴♣♣♣✴✳ ✲ ❋♦r ❝♦rr❡❝t✐♦♥s✱ s❡❡✿ ❏❛♥✉❛r② ✳✳✳✳✳ ❙t❛♥❞❛r❞ ▼♦❞❡❧ ♦❢ ♣❛rt✐❝❧❡ ♣❤②s✐❝s ♣r❡❞✐❝ts t❤❡ ✇✐❞t❤ ♦❢ t❤❡ ❲ ❜♦s♦♥ ❢❛r ♠♦r❡ ✳✳✳ ❬✶✶❪ ▼✳ ❊✳ P❡s❦✐♥ ❛♥❞ ❉✳ ❱✳ ❙❝❤r♦❡❞❡r✱ ✏❆♥ ■♥tr♦❞✉❝t✐♦♥ t♦ q✉❛♥t✉♠ ❢✐❡❧❞ t❤❡♦r②✱✑ ✶✶✷✺ ❝✐t❛t✐♦♥s ❝♦✉♥t❡❞ ✐♥ ■◆❙P■❘❊ ❛s ♦❢ ✵✻ ❏✉♥ ✷✵✶✽✳