The ATIC/PAMELA Experiments and

Decaying Hidden Dark Matter in Warped Compactification

Xingang Chen

CTP, MIT

arXiv:0902.0008

Overwhelming evidence of existence of dark matter

85% of matter in the Universe is dark matter;but all evidence comes from its gravitational properties,

its particle identities remains a mystery

Searching for dark matter

Create dark matter particles in colliders

Scatter dark matter by detector materials

• Accelerator:

• Direct detection:

• Indirect detection:

Look for dark matter annihilation or decay products

ATIC observed an excess of electrons/positrons

at 300 – 800 GeV

(Chang, et.al., 08)

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)

• Dark matter annihilation or decay?

• Astrophysical origin, such as nearby pulsars

• Cosmic strings

See Xiao-Jun Bi’s talk for a review

Other possibilities include

Explanations

• Cosmic ray interactions

……

Conventional WIMP would annihilate into both electrons/positrons and protons/anti-protons

(Cirelli, Kadastik, Raidal, Strumia, 08)

Increasing DM energy does not help

Assuming only annihilate into leptons fit the data

Similar conclusions for decaying dark matter

(Yin, Yuan, Liu, Zhang, Bi, Zhu, Zhang, 08)

Decay to gauge boson pairs

Decay to quark pairs

Decay to lepton pairs

Puzzles

Annihilating dark matter

• Cross section needs to be boosted, of order 200

• No excess in anti-proton flux

Decaying dark matter

• Long lifetime, of order

• No excess in anti-proton flux

A decaying hidden dark matter model that incorporatesthe following two ingredients:

Light particles decay to Standard Model

Hidden dark matter scenario in warped compactification

(Finkbeiner, Weiner, 07)

(X.C., Tye, 06)

In this talk:

Ingredient 1

Final decay to Standard Model is due to light particles,

(Finkbeiner, Weiner, 07; Cholis, Goodenough, Weiner, 08;Arkani-Hamed, Finkbeiner, Slatyer, Weiner; 08)

with mass between 1 MeV and 1.8 GeV,

so it is kinetically forbidden to decay on-shell to proton/anti-proton

The annihilation process or decay chain before this decayshould be somewhat hidden from Standard Model

Ingredient 2

Hidden dark matter scenario in warped compactification

(X.C., Tye, 06)

• Fluxes generate warped spaces (throats) in extra dimensions

• During reheating, such as in brane inflation, matter can be left in or tunnel to throats

• Matter can be trapped in throats by gravitational potentials of throats

If Standard Model is located somewhere else,these matter become the hidden dark matter

SM

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.

Model building requirements:

1. Unstable hidden dark matter decaying to light particles, lifetime of order

2. Hidden light particles decay on-shell to SM, lifetime shorter than the age of universe

3. 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.

Configuration of the hidden throat

• 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

• 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)

Configuration of the hidden throat (cartoon)

Warped space:

warped throat

Wrapped and warpedbrane:

add brane

Configuration of the hidden throat

• Specific example:

Klebanov-Strassler throat:

D7-branes as higher dimensional branes

• 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

Gauge fields on warped branes

• Warped space

Cutoff warp factor

• Massless Abelian gauge field

Decompose: consider:

where is the 4d mass.

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

for

for

c.f. Gravity WKK s-wave: decay faster

l-th WKK (DM)

s-wave WKK

light particles

zero-mode gauge field

l-th WKK (DM)

s-wave WKK

light particles

zero-mode gauge field

Decay of hidden dark matter within hidden throat

extra branes

• 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.

(extra branes located at: )

• 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,

Neither depends on the warp factor

• So the decay of the s-wave

Decay rate:

Fermions can quickly cascade to lighter particles, such as a stable neutral boson

Numerical example

• For example,

The mass of WKK is TeV

To have the lifetime , we need

• 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

l-th WKK (DM)

s-wave WKK

light particles

zero-mode gauge field

zero-mode

or s-wave

e

e

+

_

Decay of hidden light particles

• 1st vertex, Yukawa coupling

• 2nd and 3rd vertices, similar to

but suppressed by the D7-brane volume

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

Decay rate of hidden light particle

zero-mode

or s-wave

e

e

+

_

is momentum cutoff in loop; ;

• Same numerical example:

take for example:

Decay rate ranges from to , for from GeV to MeV

s-wave as mediator

zero-mode

or s-wave

e

e

+

_

• 3rd vertex has a suppression factor

• Decay rate

In the same numerical example:

Much slower than the zero-mode mediation; but still cosmologically short

s-wave as mediator

zero-mode

or s-wave

e

e

+

_

• 3rd vertex has a suppression factor

• Decay rate

In the same numerical example:

If use graviton KK mode as mediator, another factor of ,lifetime easily exceeds the age of the universe.

l-th WKK (DM)

s-wave WKK

light particles

zero-mode gauge field

Direct decay of dark matter to SM

1) WKK dark matter itself has damping tail outside hidden throat:

A suppression factor to the decay rate.

Intersect with SM branes at a distance D;

Direct decay produce both leptons and hadrons,would generically contradict with the PAMELA results.

• Decay rate:

Decrease drastically as l increases, because larger angular momentum introduces higher effective potential

;

Numerical example

Suppress

relative to

,

• For , suppressed by powers of warp factor

For the most difficult case ,

is enough.

Increase D to move away SM branes

Decrease to increase isometry breaking effect, besides SM branes

• For , need

Does not affect decay with zero-mode as mediator, but WKK.

l-th WKK (DM)

s-wave WKK

light particles

zero-mode gauge field

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

Decay rate: for

In order to suppress this, need to use the D7-brane volume suppression.

can be as small as , enough for all .

• Absence of the first few low-l (l > 0) partial waves can be achieved by some discrete symmetries in angular directions

Alternative treatment on low-l modes

For example, a discrete symmetry on the azimuthal angle

Partial waves start from l = 4

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

l-th WKK (DM)

s-wave WKK

light particles

zero-mode gauge field

Summary

• 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

l-th WKK (DM)

s-wave WKK

light particles

zero-mode gauge field

Summary

• 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

l-th WKK (DM)

s-wave WKK

light particles

zero-mode gauge field

Summary

• s-wave mediation is also sufficient, but much weaker; can be important if zero-mode gets lifted

l-th WKK (DM)

s-wave WKK

light particles

zero-mode gauge field

Summary

• Direct tunneling is suppressed by potential of the warped space, and, in addition, effective potential from angular momentum

l-th WKK (DM)

s-wave WKK

light particles

zero-mode gauge field

Summary

• 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)

l-th WKK (DM)

s-wave WKK

light particles

zero-mode gauge field

Summary

• Finally, since the mediator here conserves the SM lepton and hadron number, the stable SM particles do not decay to hidden sector

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

• In warped compactification, there are other components and fields --- explore their roles

• Possible collider physics signals

• Observational effects such as high energy gamma ray and neutrinos