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Gravitons and Dark Matter in Universal Extra Dimensions
Nausheen R. ShahCarlos E. M. WagnerPRD 74:104008, 2006 [arXiv: hep-ph/0608140]
Enrico Fermi Institute and Kavli Institute for Cosmological Physics, University of Chicago.
HEP Division, Argonne National Labs.
Universal Extra Dimensions
Models beyond Standard Model (SM) frequently y ( ) q yimply existence of extra dimensions (ED).
Simplest incorporation of ED: Universal Extra Simplest incorporation of ED: Universal Extra Dimensions.
All fi ld t i EDAll fields propagate in ED.
Only one free parameter: mKK~1/R. Only one free parameter: mKK 1/R.
Nausheen R. Shah Fermilab May 2007
Universal Extra Dimensions
D = 5:D 5:S1/Z2 (-1)KK KK Parity
LKP Stable
LKP DM Candidate w/ mKK ~ O(1) TeVKK ( )
Nausheen R. Shah Fermilab May 2007
Gravitons?
G1 as the LKP very tightly constrained by G as the LKP very tightly constrained by Big Bang Nucleosynthesis (BBN) and diffuse gamma spectrum. diffuse gamma spectrum. Usually effect of the G1 when it is not the LKP considered not important, since all LKP considered not important, since all interactions are Planck suppressed. We will show that in fact the gravitons We will show that in fact the gravitons can have significant effects on the DM density.
Nausheen R. Shah Fermilab May 2007
y
Reheating Temperature
LKP Freeze OutNonthermal
Graviton Production
Thermal Productionof LKP
BBN
LKP Freeze Out Graviton ProductionVia collisions
BBN and Diffuse Gamma
Gravitons decay to the LKP
BBN and Diffuse GammaRay Constraints on
Graviton Decay. ΩGn ~ C [TR / mKK]7/2
Present Day ΩDM = ΩLKP + ΩG
Gn [ R KK]
Nausheen R. Shah Fermilab May 2007
Present Day ΩDM ΩLKP + ΩGn
Reheating Temperature
Demanding that ΩDM = ΩLKP + ΩGn be Demanding that ΩDM ΩLKP + ΩGn be consistent with observation, shows us that we can lower the LKP mass as much as we wish as long as the reheating temperature behaves accordingly:
Nausheen R. Shah Fermilab May 2007
Values of the reheating temperature obtained by demanding a proper DM density, for different values of the graviton production
t C f D 5 Al h li f t t ti f th parameter C for D=5. Also shown are lines of constant ratios of the reheating temperature to the lightest KK mass.
210210210
)
210
)
210
)
210 C = 0.01
C = 0.1
KK = 100mRT
KK = 70mRT
(TeV
)RT (T
eV)
RT (T
eV)
RT
C = 1
C = 0.1
KK = 40m
RT
T
10
T
10
T
10
(TeV)m0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
(TeV)m0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
(TeV)m0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Nausheen R. Shah Fermilab May 2007
(TeV)KKm (TeV)KKm (TeV)KKm
Additional Contributions to the Annihilation Cross-Section
A precise calculation for LKP density must include co-p yannihilation and second KK resonances effects. This changes the numerical results obtained, but the qualitative picture presented remains unchanged. These corrections can be quantified by noting that due to the weak logarithmic dependence of xF, we can approximately parameterize Y as being proportional to mKK:pp y p g p p KK
The change in mWG necessary to reproduce the correct DM density for a given T is given by:density for a given TR is given by:
Nausheen R. Shah Fermilab May 2007
Values of the ratio of the LKP mass consistent with DM density to the one obtained in the absence of gravitons, mWG, for TR = 20 mKK and D 5D=5
111C = 0.1
C = 0.01
W
G 0.9
0.95
W
G 0.9
0.95
W
G 0.9
0.95
C = 0.1
C = 1
WG
/mK
Km
0.85
0.9WG
/mK
Km
0.85
0.9WG
/mK
Km
0.85
0.9
0.75
0.8
0.75
0.8
0.75
0.8 KK = 20mRT
(TeV)WGm0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
0.7
0.75
(TeV)WGm0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
0.7
0.75
(TeV)WGm0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
0.7
0.75
Nausheen R. Shah Fermilab May 2007
(TeV)WGm (TeV)WGm (TeV)WGm
TR = 40 mKK, D = 5.
1
1.1
1
1.1
1
1.1
C = 0.01
W
G
0.7
0.8
0.9
W
G
0.7
0.8
0.9
W
G
0.7
0.8
0.9
C = 1
C = 0.1
W/m
KK
m
0.5
0.6
0.7W/m
KK
m
0.5
0.6
0.7W/m
KK
m
0.5
0.6
0.7
0.3
0.4
0.5
0.3
0.4
0.5
0.3
0.4
0.5
KK = 40mRT
(TeV)WGm0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
0.2
0.3
(TeV)WGm0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
0.2
0.3
(TeV)WGm0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
0.2
0.3
Nausheen R. Shah Fermilab May 2007
(TeV)WGm (TeV)WGm (TeV)WGm
TR = 100 mKK, D=5.
0.8
0.9
1
0.8
0.9
1
0.8
0.9
1
KK = 100mRT
W
G 0.6
0.7
0.8
W
G 0.6
0.7
0.8
W
G 0.6
0.7
0.8
C = 0.01
W/m
KK
m 0.4
0.5
0.6W/m
KK
m 0.4
0.5
0.6W/m
KK
m 0.4
0.5
0.6
C = 0.1
0.1
0.2
0.3
0.1
0.2
0.3
0.1
0.2
0.3C = 1
(TeV)WGm0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
0.1
(TeV)WGm0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
0.1
(TeV)WGm0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
0.1
Nausheen R. Shah Fermilab May 2007
(TeV)WGm (TeV)WGm (TeV)WGm
Decay LifetimesWe found that Gn , for n>1, primarily decays to a pair of gauge bosons with equal KK numbers, with lifetime given by:
Only long lived graviton is G1 with a lifetime given by:Only long lived graviton is G1, with a lifetime given by:
Nausheen R. Shah Fermilab May 2007
Constraints on the G1-B1 mass difference.
If we assume that the reheating temperature If we assume that the reheating temperature is such that Ω = 0.23, we find that to preserve BBN predicted light element abundances :
Additionally requiring that late decays don’t destroy the diffuse photon flux:
Nausheen R. Shah Fermilab May 2007
Combined constraints due to both BBN and observed diffuse flux on the mass difference.
Excluded to preserve BBN predictedlight element abundances.
V) -310V) -310V) -310
C=0.01
C=0.1
light element abundances.
(TeV
)1Δ
-310
(TeV
)1Δ
-310
(TeV
)1Δ
-310 C=0.1
C=1
Excluded to preserve observed
Diffuse Photon Flux
(TeV)KKm0.3 0.4 0.5 0.6 0.7 0.8 0.9
(TeV)KKm0.3 0.4 0.5 0.6 0.7 0.8 0.9
(TeV)KKm0.3 0.4 0.5 0.6 0.7 0.8 0.9
Diffuse Photon Flux
Nausheen R. Shah Fermilab May 2007
(TeV)KKm (TeV)KKm (TeV)KKm
One Loop Corrections to the KK Masses.
The gauge boson mass matrix due to the The gauge boson mass matrix due to the Higgs vev in the B n, W 3n basis:
Since the mixing is very small, the B1 is very well approximated by:well approximated by:
Nausheen R. Shah Fermilab May 2007
Absolute value of the one loop corrections to the B1 mass in the MUED as a function of mKK. The graviton would be the LKP below
800 G V masses ~ 800 GeV. -210-210-210
eV)
eV)
eV)
| (Te
V1-
Loop
|
-310| (Te
V1-
Loop
|
-310| (Te
V1-
Loop
|
-310
1δ|
-410
1δ|
-410
1δ|
-410
(TeV)m0.5 1 1.5 2
-410
(TeV)m0.5 1 1.5 2
-410
(TeV)m0.5 1 1.5 2
-410
Nausheen R. Shah Fermilab May 2007
(TeV)KKm (TeV)KKm (TeV)KKm
Determining the Reheating Temperature
Due to small couplings to matter, provided the p g , pG1 is not the LKP, it will not be produced in laboratory experiments.
If conclusive evidence for UED is found in collider experiments, and relevant properties of p , p pthe first and second modes were measured, then assuming that no other exotic particle exists we could estimate the contribution of the exists, we could estimate the contribution of the Gn to the relic density, and therefore be able to infer the reheating temperature.
Nausheen R. Shah Fermilab May 2007
If LKP observed at LHC, the reheating temperature required to make up the deficit DM density by KK gravitons.
30
35
30
35
30
35
C=1
eV)
25
30
eV)
25
30
eV)
25
30
(TeV
RT
15
20
(TeV
RT
15
20
(TeV
RT
15
20
10
15
10
15
=0.05ΩΔ
=0.1ΩΔ
=0.15ΩΔ
10
15
(TeV)KKm0.2 0.4 0.6 0.8 1 1.2
5
(TeV)KKm0.2 0.4 0.6 0.8 1 1.2
5=0.15ΩΔ
(TeV)KKm0.2 0.4 0.6 0.8 1 1.2
5
Nausheen R. Shah Fermilab May 2007
(TeV)KKm (TeV)KKm (TeV)KKm
Conclusion
We have studied the cosmological effects of the inclusion of the graviton tower in detail graviton tower in detail.
Conventionally, due to Planck suppression, the graviton has been ignored. We have shown that it can in fact have significant
ff teffects.
Requiring that the graviton decays don’t destroy BBN predicted light element abundances and the diffuse gamma ray flux, we g g y ,have obtained a bound on the mass difference between the G1
and the LKP, which is consistent with the one obtained from one loop corrections in the MUED for a large range of values of mKK.
If UED is observed experimentally, we show that an upper limit on the reheating temperature can be deduced.
Nausheen R. Shah Fermilab May 2007