Top Yukawa Deviation in Extra Dimension ( ) ( ) ( ) - PowerPoint PPT Presentation

✝ � ✂ ☎ ✞ ✄ ✆ ✁ Top Yukawa Deviation in Extra Dimension ✟ ✠ ( ) ( ) ( ) arXiv:0904.3813 [hep-ph] Contents ✡ ☛ 1. Introduction ☞ 2. Bulk Higgs with Brane Potential 3. 4.

� � ✁ ✁ ✄ ✂ 1. Introduction ☎ Large Hadron Collider (LHC) ! ✟ ✆ ✞ ✝ ✟ ✠ ⇓ ✟ ✠ [ (SM)] [ (BSM)] [ (BSM)]

� � ✁ ✁ ✄ ✂ 1. Introduction ☎ Large Hadron Collider (LHC) ! ✟ ✆ ✞ ✝ ✟ ✠ ⇓ ✟ ✠ [ (SM)] ☛ [ (BSM)] [ (BSM)] ✂ ☛ ✆ ✞ ✁ � ✂ ✝ • • Brane localized

� � ✁ ✁ ✄ ✂ 1. Introduction ☎ Large Hadron Collider (LHC) ! ✟ ✆ ✞ ✝ ✟ ✠ ⇓ ✟ ✠ [ (SM)] ☛ [ (BSM)] [ (BSM)] ✂ ☛ ✆ ✞ ✁ � ✂ ✝ • ✁ ✆ ✞ � ✂ ✠ ☞ ☛ � ✝ • Brane localized ✆ ✁ ✁ ✂ ✂ ✝ ☎ ☛ ☎ ☞ ✠ ✄ ✄ ✞ ✟ ✝ ☛ ✠ ✠ ✞ • Brane localized • ⇒ T op Y ukawa Deviation

✆ • • LHC ✟ ✂ ✝ ✡ ✝ ✞ ✠ ☛ ✆ ☞ ✄ � ✆ ✁ ☛ ☞ ✆ ☛ ✝ ✝ ☛ ✞ ✞ ✁ ☎ ☛ ✂ ✄ ✠ ☛ ✠ ✝ ✟ ✟ ☎ ☞ ☞ ☛ ✠ � ✟ ✆ ☞ ✝ ✁ ✠ � ✞ ✆ ☛ ☛ ☎ ✠ � ✞ ✠ � ✞ ✝ ☛

T op Y ukawa Deviation ✆ • • LHC ✟ ✂ ✝ ✡ ✝ ✞ ✠ ☛ ✆ ☞ ✄ � ✆ ✁ ☛ ☞ ✆ ☛ ✝ ✝ ☛ ✞ ✞ ✁ ☎ ☛ ✂ ✄ ✠ ☛ ✠ ✝ ✟ ✟ ☎ ☞ ☞ ☛ ✠ � ✟ ✆ ☞ ✝ ✁ ✠ � ✞ ✆ ☛ ☛ ☎ ✠ � ✞ ✠ � ✞ ✝ ☛

✆ ✞ ✝ ☞ ☛ ✝ � ☛ ✆ ✞ ☎ ☛ ☛ ✝ ✁ ✂ ✄ ☎ ✁ ☎ � ✟ ✝ ✄ ✆ ☛ ☞ ✆ � ✝ ✞ ✠ ✠ ✠ ✞ ✝ ✟ ✟ ☛ ☞ � ✆ ✞ ☛ ✠ ✠ ✝ • LHC ✡ ✟ ✂ ✆ ✁ ☞ ☛ ☛ ☞ � ✠ ☛ ✠ ✞ • T op Y ukawa Deviation −L ( SM ) ⊃ m t ¯ tt + y t H ¯ tt + h.c. ✝ t ✆ ✞ ✟ ☛ ✝ ✝ ✂ � ✂ = y t v ¯ tt + y t H ¯ tt + h.c. y t = m t v = [ - ( y H ¯ tt )]

✆ ✞ ✝ ☞ ☛ ✝ � ☛ ✆ ✞ ☎ ☛ ☛ ✝ ✁ ✂ ✄ ☎ ✁ ☎ � ✟ ✝ ✄ ✆ ☛ ☞ ✆ � ✝ ✞ ✠ ✠ ✠ ✞ ✝ ✟ ✟ ☛ ☞ � ✆ ✞ ☛ ✠ ✠ ✝ • LHC ✡ ✟ ✂ ✆ ✁ ☞ ☛ ☛ ☞ � ✠ ☛ ✠ ✞ • T op Y ukawa Deviation −L ( SM ) ⊃ m t ¯ tt + y t H ¯ tt + h.c. ✝ t ✆ ✞ ✟ ☛ ✝ ✝ ✂ � ✂ = y t v ¯ tt + y t H ¯ tt + h.c. ✝ y t = m t ✆ ✞ ☎ ✝ ✄ ✂ v = [ - ( y H ¯ tt )] ✝ ✆ ✞ ✟ ☛ ✝ ✝ ✂ ✂ � [Non-standard ] y t = m t v � = [ - ( y H ¯ tt )] “ T op Y ukawa Deviation ”

✝ ☛ ✁ ✁ ☎ � � ✆ ✟ � ✝ � ✂ ✠ ✞ Top Yukawa deviation Top Yukawa deviation MSSM multi-Higgs doublet . MSSM: H u and H d √ −L ( MSSM ) ⊃ y t H 0 u ¯ t R t L + h.c. ⇒ y t = 2 m t /v u t � H 0 h 0 G 0 1 � �� � � � � � � �� v u cos α sin α u = √ + + iR β 0 H 0 H 0 A 0 v d − sin α cos α 2 d √ ⊃ y t cos α h 0 cos α h 0 2 m t −L ( MSSM ) ¯ ¯ √ tt + h.c. = √ tt + h.c. t v u 2 2 √ ⇒ y h 0 ¯ tt = ( 2 m t /v u ) cos α � = y t

✝ ☛ ✁ ✁ ☎ � � ✆ ✟ � ✝ � ✂ ✠ ✞ Top Yukawa deviation Top Yukawa deviation MSSM multi-Higgs doublet . MSSM: H u and H d √ −L ( MSSM ) ⊃ y t H 0 u ¯ t R t L + h.c. ⇒ y t = 2 m t /v u t � H 0 h 0 G 0 1 � �� � � � � � � �� v u cos α sin α u = √ + + iR β 0 H 0 H 0 A 0 v d − sin α cos α 2 d √ ⊃ y t cos α h 0 cos α h 0 2 m t −L ( MSSM ) ¯ ¯ √ tt + h.c. = √ tt + h.c. t v u 2 2 √ ✆ ✝ ✆ ✞ ✝ ⇒ y h 0 ¯ tt = ( 2 m t /v u ) cos α � = y t ✝ � ✄ [One-Higgs-doublet ] ✆ ✞ ✁ ✝ � ✂ ✄ • SO (5) × U (1) - Hosotani and Kobayashi, PLB 674 (2009) 192 ( ) • Brane-localized Haba, Oda and RT, arXiv:0904.3813 [hep-ph] ( )

2. Bulk Higgs with Brane Potential Haba, Oda and RT, arXiv:0904.3813 [hep-ph] � L � dy [ −| ∂ M Φ | 2 − V (Φ) d 4 x S = 0 − δ ( y − L ) V L (Φ) − δ ( y ) V 0 (Φ)] L : Compactification length V 0 (Φ) V (Φ) V L (Φ) y = 0 Φ( x, y ) y = L 4D y → z ≡ y − L 2

2. Bulk Higgs with Brane Potential Haba, Oda and RT, arXiv:0904.3813 [hep-ph] � + L/ 2 � dz [ −| ∂ M Φ | 2 − V (Φ) d 4 x S = − L/ 2 − δ ( z − L/ 2) V + (Φ) − δ ( z + L/ 2) V − (Φ)] L : Compactification length V − (Φ) V (Φ) V + (Φ) z = − L z = + L Φ( x, z ) 2 2 4D y → z ≡ y − L 2

: V (Φ) = 0, Real Φ � + L/ 2 � dz [ − ( ∂ M Φ) 2 − δ ( z − L/ 2) V + (Φ) d 4 x S = − L/ 2 − δ ( z + L/ 2) V − (Φ)] V − (Φ) = V + (Φ) V − (Φ) V + (Φ) V − V + = λ = λ 4(Φ 2 − v 2 ) 2 4(Φ 2 − v 2 ) 2

: V (Φ) = 0, Real Φ � + L/ 2 � dz [ − ( ∂ M Φ) 2 − δ ( z − L/ 2) V + (Φ) d 4 x S = − L/ 2 − δ ( z + L/ 2) V − (Φ)] V − (Φ) = V + (Φ) V − (Φ) V + (Φ) V − V + = λ = λ 4(Φ 2 − v 2 ) 2 4(Φ 2 − v 2 ) 2 Φ( x, z ) = Φ c ( x, z ) + φ ( x, z ) Kaluza-Klein ∂ 2 z Φ c ( z ) = 0 ∂ 2 z f n = − k 2 � n f n , φ ( x, z ) = f n ( z ) φ n ( x ) n =0 ± ∂ z Φ c + ∂V + � � � � � ± ∂ z + ∂ 2 V + � Φ=Φ c = 0 � � � ∂ Φ � f n ( z ) = 0 � � ∂ Φ 2 � � ( ± for z = ± L/ 2) � Φ=Φ c � z = ± L/ 2

✁ ✂ ✄ ☎ ☎ � ✁ ✂ ✄ ✆ ✝ ✞ ✟ ± ∂ z Φ c + ∂V + � ∂ 2 z Φ c ( z ) = 0 � Φ=Φ c = 0 ( ± for z = ± L/ 2) � ∂ Φ ✌ � ☞ ✍ ✑ ✠ ✡ ☛ ✎ ✏ �� � � � 2 A ± BL A ± BL � ⇒ Φ c ( z ) = A + Bz − v 2 ⇒ ± B + λ = 0 2 2 ⇒ Φ c ( z ) = v :

✁ ✂ ✄ ☎ ☎ � ✁ ✂ ✄ ✆ ✝ ✞ ✟ ± ∂ z Φ c + ∂V + � ∂ 2 z Φ c ( z ) = 0 � Φ=Φ c = 0 ( ± for z = ± L/ 2) � ∂ Φ ✌ � ☞ ✍ ✑ ✠ ✡ ☛ ✎ ✏ �� � � � 2 A ± BL A ± BL � ⇒ Φ c ( z ) = A + Bz − v 2 ⇒ ± B + λ = 0 ✁ � ✁ � ☞ ✂ ✝ ✂ � ✂ ✄ ☎ ✠ � 2 2 ⇒ Φ c ( z ) = v : • ✁ ☞ ✂ � ✂ ✠ � Φ c ( z ) = v . ✆ ✁ ✂ ✝ ✄ ☎ � ✝ ✠ • and/or V + (Φ) � = V − (Φ) ✟ ☎ ☛ ☛ ✝ ✟ ✁ ✝ ☛ � ✂ ✂ ✁ � ✂ ☛ ✝ ☞ ✁ ☛ ✄ ☎ ✠ ✠ ✄ • ( Z W ) ⇒V (Φ) ∼ 0 and V + (Φ) = V − (Φ)

✁ ✆ ✞ ✂ ✝ ☛ ✄ ☎ Kaluza-Klein ∂ 2 z f n ( z ) = − k 2 n f n ( z ) ⇒ f n ( z ) = α n cos( k n z ) + β n sin( k n z ) � � � � ± ∂ z + ∂ 2 V + � � f n ( z ) = 0 � � ∂ Φ 2 � � � Φ=Φ c � z = ± L/ 2 4 λv 2 � � k n L � : f n ( z ) = α n cos( k n z ) [KK even] k n ⇒ tan = − k n 2 4 λv 2 : f n ( z ) = β n sin( k n z ) [KK odd]

✁ ✆ ✞ ✂ ✝ ☛ ✄ ☎ Kaluza-Klein ∂ 2 z f n ( z ) = − k 2 n f n ( z ) ⇒ f n ( z ) = α n cos( k n z ) + β n sin( k n z ) � � � � ± ∂ z + ∂ 2 V + � � f n ( z ) = 0 � � ∂ Φ 2 � � � Φ=Φ c � z = ± L/ 2 4 λv 2 � � k n L � : f n ( z ) = α n cos( k n z ) [KK even] � � ✁ k n ⇒ tan = ✝ − k n ✂ � � 2 ✁ ✝ ✆ ✄ ✁ � � ✂ ✁ ☎ 4 λv 2 : f n ( z ) = β n sin( k n z ) [KK odd] ✟ ✝ ☞ � ☛ ✄ ✆ � ✄ ✠ � � ✁ KK z = ± L/ 2 V + = V − ± z accidental f n ( z ) = f n ( − z ) [even] f n ( z ) = − f n ( − z ) [odd] .

✁ ✆ ✞ ✂ ✝ ☛ ✄ ☎ � f n ( z ) = α n cos( k n z ) , β n sin( k n z ) = 4 λv 2 � � k n L k n , − k n tan 2 4 λv 2 Odd O � 5 O � 3 E 0 O � 1 E 2 E 4 Even E � 4 E � 2 Even E 0 O 1 O 3 O 5 � 3 Π � � 2 Π � 2 Π 3 Π 5 Π 3 Π 3 Π 5 Π Π Π �Π Π � 2 2 2 2 2 2 k n L � 2

✁ ✆ ✞ ✂ ✝ ☛ ✄ ☎ ✝ ✝ � � � � ✁ � � ✁ ✁ ✁ ✁ ✁ ✂ ✂ ✄ ☎ ✄ ☎ KK / KK / ( λ → 0) ( λ → ∞ ) + / n = 0 + / n = 0 � L � 2 L � 2 � L � 2 L � 2 − / n = 1 − / n = 1 ⇒ � L � 2 L � 2 � L � 2 L � 2 + / n = 2 + / n = 2 � L � 2 L � 2 � L � 2 L � 2 . . . . . .

✁ ✆ ✞ ✂ ✝ ☛ ✄ ☎ f n ( z )   � 1 0 mode    L       � 2 � nπ  � [ λ → 0] L cos L z n : even       �  2 � nπ  �  L sin L z n : odd �       � ( n +∆ n ) π �  � 2 � cos  z n : even    L � 1+ sin(( n +∆ n ) π )  L =  ( n +∆ n ) π [ λ ] � ( n +∆ n ) π � � 2  � sin z n : odd    L � 1 − sin(( n +∆ n ) π )   L    ( n +∆ n ) π     � � ( n +1) π �  2 L cos z n : even     L  [ˆ � ☛ ☛ ✁ ✟ ☛  ✠ � � ☎ ✠ λ → ∞ ]  �  � ( n +1) π � 2  L sin z n : odd    L   ∆ n k n nπ/L (0 < ∆ n < 1)