The ATIC/PAMELA Experiments and Decaying Hidden Dark Matter in Warped Compactification

1. The ATIC/PAMELA Experiments and Decaying Hidden Dark Matter in Warped Compactification Xingang Chen CTP, MIT arXiv:0902.0008

2. Overwhelming evidence of existence of dark matter

3. 85% of matter in the Universe is dark matter; but all evidence comes from its gravitational properties, its particle identities remains a mystery

4. Searching for dark matter • Accelerator: Create dark matter particles in colliders • Direct detection: Scatter dark matter by detector materials • Indirect detection: Look for dark matter annihilation or decay products

5. ATIC observed an excess of electrons/positrons at 300 – 800 GeV (Chang, et.al., 08)

6. PAMELA observed an excess of positron fraction excess, but not anti-proton from 10 GeV up to at least 100 GeV (Adriani et al, 09)

7. Explanations • Dark matter annihilation or decay? Other possibilities include • Astrophysical origin, such as nearby pulsars • Cosmic ray interactions • Cosmic strings …… See Xiao-Jun Bi’s talk for a review

8. Conventional WIMP would annihilate into both electrons/positrons and protons/anti-protons (Cirelli, Kadastik, Raidal, Strumia, 08)

9. Increasing DM energy does not help

10. Assuming only annihilate into leptons fit the data

11. Similar conclusions for decaying dark matter (Yin, Yuan, Liu, Zhang, Bi, Zhu, Zhang, 08) Decay to gauge boson pairs

12. Decay to quark pairs

13. Decay to lepton pairs

14. Long lifetime, of order Puzzles • Annihilating dark matter • No excess in anti-proton flux • Cross section needs to be boosted, of order 200 • Decaying dark matter • No excess in anti-proton flux

15. In this talk: A decaying hidden dark matter model that incorporates the following two ingredients: • Light particles decay to Standard Model (Finkbeiner, Weiner, 07) • Hidden dark matter scenario in warped compactification (X.C., Tye, 06)

16. Ingredient 1 Final decay to Standard Model is due to light particles, with mass between 1 MeV and 1.8 GeV, so it is kinetically forbidden to decay on-shell to proton/anti-proton (Finkbeiner, Weiner, 07; Cholis, Goodenough, Weiner, 08; Arkani-Hamed, Finkbeiner, Slatyer, Weiner; 08) The annihilation process or decay chain before this decay should be somewhat hidden from Standard Model

17. SM Ingredient 2 Hidden dark matter scenario in warped compactification (X.C., Tye, 06) • Fluxes generate warped spaces (throats) • in extra dimensions • Matter can be trapped in throats by • gravitational potentials of throats • During reheating, such as in brane inflation, • matter can be left in or tunnel to throats If Standard Model is located somewhere else, these matter become the hidden dark matter

18. Some philosophy • In pure bottom-up approach, one may add or forbit terms • to fit the data • Need justification for other terms from top-down Introducing a hidden sector introduces a whole package of fields and interactions. For example, would the type of fields mediating the light particle decay causes a direct decay of hidden dark matter to SM? • Construct models that have reasonable UV completion • allows explicit examinations of such issues.

19. 1. Unstable hidden dark matter decaying to light particles, lifetime of order • Hidden light particles decay on-shell to SM, • lifetime shorter than the age of universe Model building requirements: • Direct decay of hidden dark matter to SM is much • slower than the above two channels combined We aim to parametrically suppress the hadron production.

20. Radius of shrinks to zero; radius of remains finite • Wrap higher dimensional branes on radial direction and (part of) , • so that the throat and branes share an angular isometry Configuration of the hidden throat • The higher dimensional branes extend outside the throat, • and intersect with the Standard Model • Spacetime-filling D3 or anti-D3-branes at the tip of the throat, they • preserve the above isometry; open strings on (anti)-D3-branes are light • Minimum warped KK (WKK) scale: TeV (from ATIC); • Mass of light particles: 1 MeV -- 1.8 GeV (from PAMELA)

21. add brane Wrapped and warped brane: Configuration of the hidden throat (cartoon) Warped space: warped throat

22. Specific example: • Klebanov-Strassler throat: • D7-branes as higher dimensional branes Configuration of the hidden throat • l-th (l>0) WKK partial waves has non-trivial angular dependence, • so their wavefunctions vanish at the tip; • wavefunction of s-wave remains finite at the tip

23. Cutoff warp factor • Massless Abelian gauge field consider: Decompose: where is the 4d mass. Gauge fields on warped branes • Warped space

24. for for c.f. Gravity WKK s-wave: Gauge field spectrum • Zero mode: mass = 0; constant wavefunction on D7 • A tower of warped KK (WKK) particles: • Mass quantized in unit of • Each level of WKK, different partial waves labeled by l decay faster

25. l-th WKK (DM) s-wave WKK light particles zero-mode gauge field

26. l-th WKK (DM) s-wave WKK light particles zero-mode gauge field

27. Decay of hidden dark matter within hidden throat extra branes (extra branes located at: ) • Isometry is broken, l-th wave and s-wave mix • Mixing coefficient: Isometry breaking objects are separated by potential, so mixing is suppressed by powers of warp factor.

28. At the hidden (anti)-D3-branes, 8d gauge field induces • the 4d hidden gauge fields, • The hidden 4d gauge fields couples to, for example, hidden • fermions, Fermions can quickly cascade to lighter particles, such as a stable neutral boson Neither depends on the warp factor • So the decay of the s-wave Decay rate:

29. For example, To have the lifetime , we need Numerical example The mass of WKK is TeV • In warped compactification, the minumum warp factor • is given by flux numbers (K and M) expoentially (Gidding, Kachru, Polchinski, 01) • Lifetime of WKK naturally is very long cosmologically; • however the precise decay rate or energy are not specific predictions • It is natural in this scenario to have multiple peaks • with different energies and lifetimes

30. l-th WKK (DM) s-wave WKK light particles zero-mode gauge field

31. + e y zero-mode c or s-wave _ y e • 1st vertex, Yukawa coupling • 2nd and 3rd vertices, similar to but suppressed by the D7-brane volume Decay of hidden light particles • Compare to s-wave: no warp factor • Compare to graviton zero-mode (effectively ): 1) Smaller size: ; 2) fewer dimensions to integrate over; 3) coupling is dimensionless so not affected by warping. Zero-mode gauge field is an efficient mediator

32. + e y zero-mode c or s-wave _ y e Decay rate of hidden light particle is momentum cutoff in loop; ; • Same numerical example: take for example: Decay rate ranges from to , for from GeV to MeV

33. + e y zero-mode c or s-wave _ y e s-wave as mediator • 3rd vertex has a suppression factor • Decay rate In the same numerical example: Much slower than the zero-mode mediation; but still cosmologically short

34. + e y zero-mode c or s-wave _ y e If use graviton KK mode as mediator, another factor of , lifetime easily exceeds the age of the universe. s-wave as mediator • 3rd vertex has a suppression factor • Decay rate In the same numerical example:

35. l-th WKK (DM) s-wave WKK light particles zero-mode gauge field

36. A suppression factor to the decay rate. • Decay rate: Decrease drastically as l increases, because larger angular momentum introduces higher effective potential Direct decay of dark matter to SM Direct decay produce both leptons and hadrons, would generically contradict with the PAMELA results. 1) WKK dark matter itself has damping tail outside hidden throat: ; Intersect with SM branes at a distance D;

37. Suppress , relative to • For , suppressed by powers of warp factor • For , need • Increase D to move away SM branes • Decrease to increase isometry breaking effect, besides SM branes Does not affect c decay with zero-mode as mediator, but WKK. For the most difficult case , is enough. Numerical example

38. l-th WKK (DM) s-wave WKK light particles zero-mode gauge field

39. Decay rate: for In order to suppress this, need to use the D7-brane volume suppression. can be as small as , enough for all . Direct decay of dark matter to SM (continue) 2) Through mixing with virtual particles • WKK  (virtual s-wave)  leptons and hadrons suppressed by both small mixing and tunneling • WKK  (virtual zero-mode)  leptons and hadrons Zero-mode has constant wavefunction, so integration for mixing is less peaked at tip

40. For example, a discrete symmetry on the azimuthal angle Alternative treatment on low-l modes • Absence of the first few low-l (l > 0) partial waves can be • achieved by some discrete symmetries in angular directions Partial waves start from l = 4

41. Summary • An angular isometry shared by hidden throat and • wrapped higher dimensional branes • Isometry is not broken by (anti-)D3-branes • Mass hierarchy b.t. WKK modes and light fields on D3-branes: • Hidden dark matter and hidden light particles • Communication b.t. hidden throat and SM: • Zero-mode (or s-wave WKK) gauge fields on higher dim branes

42. Summary l-th WKK (DM) s-wave WKK light particles zero-mode gauge field • Isometry breaking objects are separated by potential from • warp geometry, so lifetime of hidden dark matter (either gauge • field or gravity WKK) is very long

43. Summary l-th WKK (DM) s-wave WKK light particles zero-mode gauge field • Zero-mode gauge field is an efficient mediator: • wavefunction does not damp as WKK; • volume suppression is much weaker than gravity zero-mode; • coupling can be dimensionless

44. Summary l-th WKK (DM) s-wave WKK light particles zero-mode gauge field • s-wave mediation is also sufficient, but much weaker; • can be important if zero-mode gets lifted

45. Summary l-th WKK (DM) s-wave WKK light particles zero-mode gauge field • Direct tunneling is suppressed by potential of the warped space, • and, in addition, effective potential from angular momentum

46. Summary l-th WKK (DM) s-wave WKK light particles zero-mode gauge field • Channel through virtual zero-mode (or s-wave) is suppressed • by both the small mixing and the volume of higher dim branes • (or the tunneling)

47. Summary l-th WKK (DM) s-wave WKK light particles zero-mode gauge field • Finally, since the mediator here conserves the SM lepton and hadron • number, the stable SM particles do not decay to hidden sector

48. Future aspects • Lighter particles, such as neutrino and photon, are kinematically • allowed, but can have different branching ratios • Hidden D3-branes can also naturally have hidden massless particles • Observational effects such as high energy gamma ray and neutrinos • In warped compactification, there are other components and fields • --- explore their roles • Possible collider physics signals