the atic/pamela experiments and decaying hidden dark matter in warped compactification
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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
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