Light hidden U(1)s in LARGE volume string compactifications

Transcription

1 Light hidden U(1)s in LARGE volume string compactifications Andreas Ringwald DESY Dark Forces Workshop Searches for New Forces at the GeV-Scale, Sept , 2009, SLAC, CA, USA

2 Light hidden U(1)s... 1 Mainly based on: S. A. Abel, J. Jaeckel, V. V. Khoze, AR, Illuminating the hidden sector of string theory by shining light through a magnetic field, Phys. Lett. B 666 (2008) 66 [arxiv:hep-ph/ ] S. A. Abel, M. D. Goodsell, J. Jaeckel, V. V. Khoze, AR, Kinetic Mixing of the Photon with Hidden U(1)s in String Phenomenology, JHEP 0807 (2008) 124 [arxiv: [hep-ph]] M. Goodsell, J. Jaeckel, J. Redondo, AR, Naturally Light Hidden Photons in LARGE Volume String Compactifications, arxiv: [hep-ph]

3 Light hidden U(1)s... 2 Table of Content: 1. Introduction 2. Hidden U(1)s in LARGE volume string compactifications 3. Kinetic mixing between visible U(1) and hidden U(1) 4. Mass of hidden U(1)s 5. Discussion and outlook

4 Light hidden U(1)s Introduction Non-abelian hidden sector gauge factors often exploited in extensions of Standard Model (cf. SUSY by gaugino condensation) Hidden sector may contain also Abelian, i.e. U(1), gauge factors Generically mix with visible U(1), i.e. low energy effective Lagrangian: [Okun 82; Holdom 85] L 1 4ga 2 F µν (a) F µν (a) 1 4gb 2 F µν (b) F µν (b) + χ ab F µν (a) F (b)µν + m2 aba (a) µ A (b)µ 2g a g b g a g b Kinetic and mass mixing terms, χ ab and m 2 ab, provide a unique window to hidden sectors

5 Light hidden U(1)s... 4 Phenomenology (very strong limits on photon mass) requires structure: χ = ( 0 χ χ 0 ) ; m 2 ( m 2 γ ) Massless photon and massive U(1) (hidden photon), with mass squared m 2 γ / 1 χ 2

6 Light hidden U(1)s... 5 Rich phenomenology of hidden photons: Limits: [Okun 82;Bartlett,.. 88;Kumar,.. 06;Coriano,... 07;Ahlers,.. 07;Jaeckel,.. 07;Redondo,.. 08;...;Bjorken,.. 09;...] Promising islands: 09; Arkani-Hamed et al. 08;...] [Jaeckel,Redondo,AR 08; Pospelov,Ritz,Voloshin 07; Redondo,Postma 08; Ibarra,AR,Weniger

7 Light hidden U(1)s... 6 Light Shining through a Wall (LSW): γ γ γ γ ALPS (DESY), GammeV (Fermilab), LIPSS (JLab), OSQAR (CERN)

8 Light hidden U(1)s... 7 Rich phenomenology of hidden photons: Limits: [Okun 82;Bartlett,.. 88;Kumar,.. 06;Coriano,... 07;Ahlers,.. 07;Jaeckel,.. 07;Redondo,.. 08;...;Bjorken,.. 09;...] Promising islands: 09; Arkani-Hamed et al. 08;...] [Jaeckel,Redondo,AR 08; Pospelov,Ritz,Voloshin 07; Redondo,Postma 08; Ibarra,AR,Weniger

9 Light hidden U(1)s... 8 Embeddings of the standard model in string compactifications often contain even several hidden sector U(1) gauge factors (cf. consistency conditions, e.g. tadpole/anomaly cancellation), e.g. in orbifold compactifications of heterotic string theory: e.g. E 8 E 8 G SM U(1) 4 [SU(4) SU(2) U(1) 4] or E 8 E 8 G SM U(1) 4 [SO(8) SU(2) U(1) 3]

10 Light hidden U(1)s... 9 Embeddings of the standard model in string compactifications often contain even several hidden sector U(1) gauge factors (cf. consistency conditions, e.g. tadpole/anomaly cancellation), e.g. in type II string theory with branes:

11 Light hidden U(1)s Hidden U(1)s in LARGE volume string compactifications Compactification of string theory with D3 and D7 branes Visible sector on stack of space-time filling D-branes wrapping collapsed cycles Gravity propagates in bulk of volume V/l 6 s V MP 2 = 4π gs 2 VMs 2 M s = GeV, for V 100 M s = GeV, for V M s = 10 3 GeV, for V 10 28

12 Light hidden U(1)s Hidden U(1)s in LARGE volume string compactifications Compactification of string theory with D3 and D7 branes Visible sector on stack of space-time filling D-branes wrapping small cycles Gravity propagates in bulk of volume V/l 6 s V MP 2 = 4π gs 2 VMs 2 Hidden Sectors CY 3 M 4 U(2) Q L e L M s = GeV, for V 100 M s = GeV, for V M s = 10 3 GeV, for V U(3) Q R U(1) e R U(1) Visible Sector (SM)

13 Light hidden U(1)s Hidden U(1)s in LARGE volume string compactifications Visible sector on stack of spacetime filling D-branes wrapping collapsed cycles Hidden U(1)s: located on space-time filling D-branes not intersecting with visible branes 1. D7 wraps LARGE cycle 2. D7 wraps collapsed cycle 3. anti D3 D(3 + q)-brane: g 2 (q) = 2πg s Z 2πg s V q [...;Conlon,Maharana,Quevedo 08;...]

14 Light hidden U(1)s Hidden U(1)s in LARGE volume string compactifications Visible sector on stack of spacetime filling D-branes wrapping collapsed cycles Hidden U(1)s: located on space-time filling D-branes not intersecting with visible branes 1. D7 wraps LARGE cycle 2. D7 wraps collapsed cycle 3. anti D3 D(3 + q)-brane: g 2 (q) = 2πg s Z 2πg s V q [...;Conlon,Maharana,Quevedo 08;...]

15 Light hidden U(1)s Hidden U(1)s in LARGE volume string compactifications Visible sector on stack of spacetime filling D-branes wrapping collapsed cycles Hidden U(1)s: located on space-time filling D-branes not intersecting with visible branes 1. D7 wraps LARGE cycle 2. D7 wraps collapsed cycle 3. anti D3 D(3 + q)-brane: g 2 (q) = 2πg s Z 2πg s V q [...;Conlon,Maharana,Quevedo 08;...]

16 Light hidden U(1)s Hidden U(1)s in LARGE volume string compactifications Visible sector on stack of spacetime filling D-branes wrapping collapsed cycles Hidden U(1)s: located on space-time filling D-branes not intersecting with visible branes 1. D7 wraps LARGE cycle 2. D7 wraps collapsed cycle 3. anti D3 D(3 + q)-brane: g 2 (q) = 2πg s Z 2πg s V q

17 Light hidden U(1)s Hidden U(1)s in LARGE volume string compactifications Visible sector on stack of spacetime filling D-branes wrapping collapsed cycles Hidden U(1)s: located on space-time filling D-branes not intersecting with visible branes 1. D7 wraps LARGE cycle 2. D7 wraps collapsed cycle 3. anti D3 1. hyperweak interactions [Burgess,Conlon,Hung,Kom,Maharana,Quevedo 08] gh 2 2πg ( s 4π (V) = 2πg 2/3 s g 2 s Ms 2 ) 2/3 MP 2

18 Light hidden U(1)s Kinetic mixing between visible U(1) and hidden U(1) Before SUSY, kinetic mixing appears as holomorphic quantity in SUGRA: { 1 L d 2 θ 4(ga) h 2W aw a + 1 4(gb h)2w bw b 1 } 2 χh abw a W b g h a, g h b and χh ab must run only at one loop Physical and holomorphic couplings related by generalisation of [Kaplunovsky,Louis 94,95] ga 2 = Re [(g ha) ] 2 Q 2 a(r) 8π log 2 detz(r) n r Q 2 a(r) K 16π 2 M 2 r r P χ ab = Re(χ h g a g ab) + 1 ( ) b 8π 2tr Q a Q b log Z π 2 n r Q a Q b (r) K MP 2 r

19 Light hidden U(1)s In analogy to structure of holomorphic gauge kinetic function cf. e.g. [Akerblom,Blumenhagen,Lüst,Schmidt-Sommerfeldt 07] χ h ab = χ 1 loop ab (z k, y i ) + χ non perturbative ab (z k,e T j,y i ) complex structure moduli z k, Kähler moduli T j, open string moduli y i T j have shift symmetries may only appear as exponentials T j depend on gs 1 cannot enter at 1-loop Generically, χ h ab χ 1 loop ab (z k, y i ) 1 16π 2 O(1) Therefore, χ ab g ag b 16π 2 O(1)

20 Light hidden U(1)s... 19

21 Light hidden U(1)s Mass of hidden U(1) Stückelberg masses: [Buican,Malyshev,Morrison,Verlinde,Wijnholt 06; Conlon,Maharana,Quevedo 08;...] m 2 St ab = g [ ag b 4π M2 s G cd Π cd 1 Π dd 2 r ad1 r bd2 + +G αβ Π D 1A α Π D 2B β (p ad1 A r ad1 b D1 A)(p bd2 B r bd2 b D2 B) ] O(1) factors: overlaps Π cd 1, Π D 1A α ; D7 brane charges r ad1 ; fluxes p ad1 A and b D1 A Size determined by metric G cd and G αβ on space of harmonic forms For anomalous U(1)s, dual cycles vanishing G 1 For bulk cycles, corresponding to non-anomalous U(1)s, G cd V 1/3, G αβ V 1/3

22 Light hidden U(1)s... 21

23 Light hidden U(1)s Masses from hidden Higgs mechanism: Expect generically m γ m Hh m hid soft In gauge mediation, for example, m vis soft g2 vis M 2 SUSY 16π 2 M mess If hidden sector couples directly to sequestered SUSY sector, m hid soft g2 h M 2 SUSY 16π 2 g h m vis M mess g vis soft If hidden sector couples only indirectly via kinetic mixing to it, [Dienes,Kolda,March-Russell 96;Suematsu 06;Baumgart et al. 09;Cui et al. 09;Morrissey,Poland,Zurek 09;...] (m hid soft) 2 = Q h g h χ D Y = Q h g h g Y χ 1 8 v2 cos2β ( ) m vis 2 soft

24 Light hidden U(1)s... 23

25 Light hidden U(1)s Discussion and outlook Extra U(1) gauge bosons kinetically mixing with the electromagnetic (or hypercharge) U(1) may provide us with a unique window into hidden sector physics Moreover, they could play a role in a number of observed phenomena possibly connected to dark matter LARGE volume scenarios allow for a variety of different extra, hidden U(1) gauge bosons a variety of possibilities, some of which overlapping with the phenomenologically interesting regions Near future astrophysical observations and laboratory experiments can test a variety of possible scenarios and an impressive range of string scales

26 Light hidden U(1)s Discussion and outlook

27 Light hidden U(1)s Discussion and outlook Extra U(1) gauge bosons kinetically mixing with the electromagnetic (or hypercharge) U(1) may provide us with a unique window into hidden sector physics Moreover, they could play a role in a number of observed phenomena possibly connected to dark matter LARGE volume scenarios allow for a variety of different extra, hidden U(1) gauge bosons a variety of possibilities, some of which overlapping with the phenomenologically interesting regions Near future astrophysical observations and laboratory experiments can test a variety of possible scenarios and an impressive range of string scales

28 Light hidden U(1)s Discussion and outlook