Phenomenology of hidden photons from heterotic orbifolds Sa´ ul Ramos-S´ anchez UNAM PASCOS 2012 June 5, 2012 In collaboration with M. Goodsell & A. Ringwald: arXiv:1110.6901 and with H.P. Nilles, P. Vaudrevange, & A. Wingerter: arXiv:1110.5229 Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Some of today’s challenges � dark matter � SM hierarchy problem (even with SUSY, µ problem) � why only 3 fundamental forces ? � anomalous muon g µ − 2 � baryon asymmetry ⇒ new U(1) s Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Some of today’s challenges � dark matter � SM hierarchy problem (even with SUSY, µ problem) � why only 3 fundamental forces ? � anomalous muon g µ − 2 � baryon asymmetry ⇒ new U(1) s Appear naturally in � GUTs � Large extra dimensions � Brane-worlds string compactifications � Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Some of today’s challenges � dark matter � SM hierarchy problem (even with SUSY, µ problem) � why only 3 fundamental forces ? � anomalous muon g µ − 2 � baryon asymmetry ⇒ new U(1) s Appear naturally in � GUTs � Large extra dimensions � Brane-worlds string compactifications � Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Hidden photons 4 F µν F µν − 1 4 B µν B µν − 1 2 χF µν B µν + 1 2 m 2 γ ′ B µ B µ L ⊃ − 1 extra: suppressed couplings to SM matter Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
still “alive” 4 F µν F µν − 1 4 B µν B µν − 1 2 χF µν B µν + 1 2 m 2 γ ′ B µ B µ L ⊃ − 1 Goodsell, Jaeckel, Redondo, Ringwald (2009) Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Heterotic strings Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Heterotic strings 5 consistent superstring theories type I type IIA type IIB Heterotic E 8 × E 8 Heterotic SO(32) properties: � gauge bosons quantum gravity � � 10D N = 1 SUGRA no D-branes Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Heterotic strings 5 consistent superstring theories type I type IIA type IIB Heterotic E 8 × E 8 Heterotic SO(32) properties: � gauge bosons quantum gravity � � 10D − → compactifications N = 1 SUGRA no D-branes Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Orbifolds Dixon, Harvey, Vafa, Witten (’85-’86) Ib´ a˜ nez, Nilles, Quevedo (’87) Font, Ib´ a˜ nez, Quevedo, Sierra (1990) Katsuki, Kawamura, Kobayashi, Ohtsubo, Ono, Tanioka (’90) Kobayashi, Raby, Zhang (’04) F¨ orste, Nilles, Vaudrevange, Wingerter (’04) Buchm¨ uller, Hamaguchi, Lebedev, Ratz (’04-’06) Kobayashi, Nilles, Pl¨ oger, Raby, Ratz (’06) Faraggi, F¨ orste, Timirgaziu (’06) F¨ orste, Kobayashi, Ohki, Takahashi (’06) Kim, Kyae (’06-’07) Choi, Kim (’06-’08) ... Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Z 2 Orbifold in 5D Orbifolds 1D Z 2 Z 2 : X ≃ − X X X ≃ X + 2 πR X X X Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Z 2 orbifold in 10D Heterotic Orbifolds Z 2 6D T 6 / Z 2 : T 6 : Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Heterotic Orbifolds: strings and states Brane States Bulk States Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Heterotic Orbifolds: strings and states Brane States gauge bosons A µ Y , A µ X , ... Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
M 4 R 6 Z N Input and Output R 6 /T 6 ⋊ Z N Starting point: heterotic string T 16 × × M 4 SO(9 , 1) Lorentz × E 8 × E 8 gauge Z R Input Geometry: T 6 , Embedding: O 6 = ֒ → O 16 (subject to modular invariance (CFT) conditions) Output × O 6 × O 16 � SO(3 , 1) × × G 4 D ⊂ E 8 × E 8 gauge n i Lorentz + 4D matter (quarks, leptons, exotics) Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
M 4 R 6 Z N Input and Output R 6 /T 6 ⋊ Z N Starting point: heterotic string T 16 × × M 4 SO(9 , 1) Lorentz × E 8 × E 8 gauge Z R Input Geometry: T 6 , Embedding: O 6 = ֒ → O 16 (subject to modular invariance (CFT) conditions) Output × O 6 × O 16 � SO(3 , 1) × × G 4 D ⊂ E 8 × E 8 gauge n i Lorentz + 4D matter (quarks, leptons, exotics) Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
M 4 R 6 Z N Input and Output R 6 /T 6 ⋊ Z N Starting point: heterotic string T 16 × × M 4 SO(9 , 1) Lorentz × E 8 × E 8 gauge Z R Input Geometry: T 6 , Embedding: O 6 = ֒ → O 16 (subject to modular invariance (CFT) conditions) Output × O 6 × O 16 � SO(3 , 1) × × G 4 D ⊂ E 8 × E 8 gauge n i Lorentz + 4D matter (quarks, leptons, exotics) Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Orbifolder (arXiv:1110.5229 Nilles, SR-S, Vaudrevange, Wingerter) Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Orbifolder (arXiv:1110.5229 Nilles, SR-S, Vaudrevange, Wingerter) “Program” example: create orbifold(myZ6II) with point group(6,1) 1 cd myZ6II 2 set heterotic string type(E8xE8) 3 print available space groups 4 use space group(3) 5 set shift V = (1/3 1/2 1/2 0^5 1/3 0^7) 6 cd ~ 7 create random orbifold from(myZ6II) load when done print info if(SM) 8 use(1,1,1,1,0,0,0,1) #models(1) 9 wait(1) 10 cd Model_SM1 11 cd vev-config 12 analyze config 13 Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Z 6 –II Minilandscape ∼ 300 MSSM candidates: supergravity multiplet G 4 D = G SM × G hid 3 SM families + Higgses vectorlike exotics gauge unification heavy top TeV gravitino mass seesaw R -parity flavor symmetries Lebedev, Nilles, Raby, Ramos-Sanchez, Vaudrevange, Wingerter (2006-2008) Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Z 6 –II Minilandscape ∼ 300 MSSM candidates: supergravity multiplet G 4 D = G SM × G hid 3 SM families + Higgses vectorlike exotics demanded gauge unification heavy top TeV gravitino mass seesaw R -parity flavor symmetries Lebedev, Nilles, Raby, Ramos-Sanchez, Vaudrevange, Wingerter (2006-2008) Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Z 6 –II Minilandscape ∼ 300 MSSM candidates: supergravity multiplet G 4 D = G SM × G hid 3 SM families + Higgses vectorlike exotics demanded gauge unification heavy top TeV gravitino mass seesaw for free !! � R -parity flavor symmetries Lebedev, Nilles, Raby, Ramos-Sanchez, Vaudrevange, Wingerter (2006-2008) Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Hidden photons in heterotic orbifolds Hidden Photons in heterotic orbifolds Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Hidden photons 4 F µν b A µ L ⊃ − 1 4 F µν a F µν,a − 1 b F µν,b − 1 2 χ ab F µν a F µν,b + 1 2 m 2 b A µ,b Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
Kinetic mixing In SUSY theories � � 1 4 W a W a + 1 4 W b W b − 1 � d 2 θ L canonical ⊃ 2 χ ab W a W b with 16 π 2 log M 2 χ ab b ab S = µ 2 + ∆ ab g a g b In heterotic orbifolds, string threshold: b i ab | G i | � � � � �� � | η ( T i ) | 4 Im( T i ) | η ( U i ) | 4 Im( U i ) ∆ ab = log +log 16 π 2 | G | i ab = 1 b i − 2 tr i V, N =2 ( Q a Q b ) + tr i � � H, N =2 ( Q a Q b ) 2 Goodsell, SR-S, Ringwald (2011) Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
An explicit MSSM candidate: matter spectrum 3 (net) generations � � 3 + 1 ( 3 , 2 ; 1 ) 1 / 6 , 0 q i 1 3 , 2 ; 1 q i ¯ − 1 / 6 , 0 � � 3 + 2 3 , 1 ; 1 ¯ u i 2 ( 3 , 1 ; 1 ) 2 / 3 , 0 u i − 2 / 3 , 0 3 + 2 ( 1 , 1 ; 1 ) 1 , 0 ¯ e i 2 ( 1 , 1 ; 1 ) − 1 , 0 e i ¯ � � 3 + 7 3 , 1 ; 1 d i 7 ( 3 , 1 ; 1 ) − 1 / 3 , 0 d i 1 / 3 , 0 3 ( 1 , 2 ; 1 ) − 1 / 2 , 0 ℓ i Higgses 1 + 9 ( 1 , 2 ; 1 ) − 1 / 2 , 0 h d 1 + 9 ( 1 , 2 ; 1 ) 1 / 2 , 0 h u SM Singlets ξ ± 45 ( 1 , 1 ; 1 ) 0 , 0 n i 8 ( 1 , 1 ; 1 ) 0 , ∗ i ¯ � � 7 ( 1 , 1 ; 8 ) 0 , ∗ h i 7 1 , 1 ; 8 h i 0 , ∗ Exotics � � 8 ( 3 , 1 ; 1 ) 1 / 6 , ∗ w i 8 3 , 1 ; 1 w i ¯ − 1 / 6 , ∗ s + ± s −± 8 ( 1 , 1 ; 1 ) 1 / 2 , ± √ 8 ( 1 , 1 ; 1 ) − 1 / 2 , ± √ i i 2 / 3 2 / 3 m + m − 4 ( 1 , 2 ; 1 ) 0 , √ 4 ( 1 , 2 ; 1 ) 0 , − √ 2 / 3 i 2 / 3 i Goodsell, SR-S, Ringwald (2011) Sa´ ul Ramos-S´ anchez – UNAM Hidden photons in heterotic orbifolds
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