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arXiv:hep-ph/0410178v1 12 Oct 2004

SuperWIMP Cosmology and Collider Physicsa

JONATHAN L. FENG∗, ARVIND RAJARAMAN∗, BRYAN T. SMITH∗,

SHUFANG SU†, FUMIHIRO TAKAYAMA∗

∗Department of Physics and Astronomy, University of California

Irvine, CA 92697, USA

†Department of Physics, University of Arizona

Tucson, AZ 85721, USA

ABSTRACT

Dark matter may be composed of superWIMPs, superweakly-interacting mas-

sive particles produced in the late decays of other particles. We focus here on

the well-motivated supersymmetric example of gravitino LSPs. Gravitino su-

perWIMPs share several virtues with the well-known case of neutralino dark

matter: they are present in the same supersymmetric frameworks (supergravity

with R-parity conservation) and naturally have the desired relic density. In con-

trast to neutralinos, however, gravitino superWIMPs are impossible to detect by

conventional dark matter searches, may explain an existing discrepancy in Big

Bang nucleosynthesis, predict observable distortions in the cosmic microwave

background, and imply spectacular signals at future particle colliders.

1. Introduction

In recent years, there has been tremendous progress in understanding the universe on

the largest scales. In particular, the energy density in non-baryonic dark matter is known

to be [1]

ΩDM= 0.23 ± 0.04

in units of the critical density. At the same time, we have no idea what the microscopic

identity of non-baryonic dark matter is. The dark matter problem therefore provides

precise, unambiguous evidence for new physics and has motivated new particles such

as axions [2,3,4], neutralinos [5,6], Q balls [7], wimpzillas [8], axinos [9], self-interacting

dark matter [10], annihilating dark matter [11], Kaluza-Klein dark matter [12,13], bra-

nons [14,15], and many others.

Here we review a new class of dark matter candidates: superWIMPs, superweakly-

interacting massive particles produced in the late decays of other particles [16,17,18].

SuperWIMPs have several strong motivations:

(1)

• They are present in well-motivated frameworks for new physics, including models

with supersymmetry (supergravity with R-parity conservation) and extra dimen-

sions (universal extra dimensions with KK-parity conservation).

• Their relic density is naturally in the right range to be dark matter without the

need to introduce and fine-tune new energy scales.

aPlenary talk given by JLF at SUSY2004, the 12th International Conference on Supersymmetry and

Unification of Fundamental Interactions, Tsukuba, Japan, 17-23 June 2004.

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• They can explain an existing anomaly, namely the observed underabundance of7Li

relative to the prediction of standard Big Bang nucleosynthesis.

• They have rich implications for early universe cosmology and imply spectacular

signals at the Large Hadron Collider (LHC) and the International Linear Collider

(ILC).

2. The Basic Idea

As noted above, superWIMPs exist in theories with supersymmetry and in models

with extra dimensions. We concentrate on the supersymmetric scenarios here. Details of

the extra dimensional realizations may be found in Refs. [16,17,18].

In the simplest supersymmetric models, supersymmetry is transmitted to standard

model superpartners through gravitational interactions, and supersymmetry is broken at

a high scale. The mass of the gravitino˜G is

m˜G=

F

√3M∗

, (2)

and the masses of standard model superpartners are

˜ m ∼

F

M∗

,(3)

where M∗ = (8πGN)−1/2≃ 2.4 × 1018GeV is the reduced Planck scale and F ∼

(1011GeV)2is the supersymmetry breaking scale squared. The precise ordering of masses

depends on unknown, presumably O(1), constants in Eq. (3). Most supergravity studies

assume that the lightest supersymmetric particle (LSP) is a standard model superpartner,

such as the neutralino. In this case, it is well-known that the neutralino naturally freezes

out with a relic density that is in the right range to account for dark matter [19].

The gravitino may be the LSP, however [16,17,18,20,21,22,23,24,25,26,27,28]. In su-

pergravity, the gravitino has weak scale mass Mweak∼ 100 GeV and couplings suppressed

by M∗. The gravitino’s extremely weak interactions imply that it is irrelevant during ther-

mal freeze out. The next-to-lightest supersymmetric particle (NLSP) therefore freezes out

as usual, and if the NLSP is a slepton, sneutrino, or neutralino, its thermal relic density is

again ΩNLSP∼ 0.1. However, eventually the NLSP decays to its standard model partner

and the gravitino. The resulting gravitino relic density is

Ω˜G=

m˜G

mNLSPΩNLSP. (4)

In supergravity, where m˜G∼ mNLSP, the gravitino therefore inherits a relic density of the

right order to be much or all of non-baryonic dark matter. The superWIMP gravitino

scenario preserves the prime virtue of WIMPs, namely that they give the desired amount

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of dark matter without relying on the introduction of new, fine-tuned energy scales.b

Because superWIMP gravitinos interact only gravitationally, with couplings suppressed

by M∗, they are impossible to detect in conventional direct and indirect dark matter search

experiments. At the same time, the extraordinarily weak couplings of superWIMPs imply

other testable signals. The NLSP is a weak-scale particle decaying gravitationally and so

has a natural lifetime of

M2

∗

M3

weak

This decay time, outlandishly long by particle physics standards, implies testable cosmo-

logical signals, as well as novel signatures at colliders.

∼ 104− 108s . (5)

3. Cosmology

The most sensitive probes of late decays with lifetimes in the range given in Eq. (5)

are from Big Bang nucleosynthesis (BBN) and the Planckian spectrum of the cosmic

microwave background (CMB). The impact of late decays to gravitinos on BBN and

the CMB are determined by only two parameters: the lifetime of NLSP decays and

the energy released in these decays. The energy released is quickly thermalized, and so

the cosmological signals are insensitive to the details of the energy spectrum and are

determined essentially only by the total energy released.

The width for the decay of a slepton to a gravitino is

Γ(˜l → l˜G) =

1

48πM2

∗

m5

m2

˜l

˜G

?

1 −m2

˜ G

m2

˜l

?4

, (6)

assuming the lepton mass is negligible. (Similar expressions hold for the decays of a

neutralino NLSP.) This decay width depends on only the slepton mass, the gravitino mass,

and the Planck mass. In many supersymmetric decays, dynamics brings a dependence on

many supersymmetry parameters. In contrast, as decays to the gravitino are gravitational,

dynamics is determined by masses, and so no additional parameters enter. In particular,

there is no dependence on left-right mixing or flavor mixing in the slepton sector. For

m˜G/m˜l≈ 1, the slepton decay lifetime is

?100 GeV

τ(˜l → l˜G) ≃ 3.6 × 108s

m˜l− m˜G

?4 ?m˜G

TeV

?

. (7)

This expression is valid only when the gravitino and slepton are nearly degenerate, but it

is a useful guide and verifies the rough estimate of Eq. (5).

The energy release is conveniently expressed in terms of

ξEM≡ ǫEMBEMYNLSP

superWIMPscenario

Gravitinos are

(8)

bIn this aspect,

scenarios.

thediffers

original

markedly

supersymmetric

from previous

dark

gravitino

candi- dark

dates [29,30,31,32,33,34,35,36,37,38,39,40].

produced either thermally, with Ω˜ G∼ 0.1 obtained by requiring m˜ G∼ keV, or through reheating, with

Ω˜ G∼ 0.1 obtained by tuning the reheat temperature to TRH∼ 1010GeV.

matterthe matter

Previously, however, gravitinos were expected to be

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for electromagnetic energy, with a similar expression for hadronic energy. Here ǫEMis the

initial EM energy released in NLSP decay, and BEMis the branching fraction of NLSP

decay into EM components. YNLSP≡ nNLSP/nγis the NLSP number density just before

NLSP decay, normalized to the background photon number density nγ= 2ζ(3)T3/π2. It

can be expressed in terms of the superWIMP abundance:

YNLSP≃ 3.0 × 10−12

?TeV

m˜G

??Ω˜G

0.23

?

. (9)

Once an NLSP candidate is specified, and assuming superWIMPs make up all of the

dark matter, with Ω˜G= ΩDM= 0.23, the early universe signals are completely determined

by only two parameters: m˜Gand mNLSP.

3.1. BBN Electromagnetic Constraints

BBN predicts primordial light element abundances in terms of one free parameter, the

baryon-to-photon ratio η ≡ nB/nγ. In the past, the fact that the observed D,4He,3He,

and7Li abundances could be accommodated by a single choice of η was a well-known

triumph of standard Big Bang cosmology.

More recently, BBN baryometry has been supplemented by CMB data, which alone

yields η10 = η/10−10= 6.1 ± 0.4 [1]. This value agrees precisely with the value of η

determined by D, considered by many to be the most reliable BBN baryometer. However,

it highlights slight inconsistencies in the BBN data. Most striking is the case of7Li. For

η10= 6.0±0.5, the value favored by the combined D and CMB observations, the standard

BBN prediction is [41]

7Li/H = 4.7+0.9

−0.8× 10−10

(10)

at 95% CL. This contrasts with observations. Three independent studies find

7Li/H = 1.5+0.9

−0.5× 10−10

−0.22× 10−10(1σ + sys) [43]

−0.32× 10−10(stat + sys, 95% CL) [44] ,

(95% CL) [42](11)

7Li/H = 1.72+0.28

7Li/H = 1.23+0.68

(12)

(13)

where depletion effects have been estimated and included in the last value. Within the

published uncertainties, the observations are consistent with each other but inconsistent

with the theoretical prediction of Eq. (10), with central values lower than predicted by a

factor of 3 to 4.

for example, by rotational mixing in stars that brings Lithium to the core where it may

be burned [45,46], but it is controversial whether this effect is large enough to reconcile

observations with the BBN prediction [44].

We now consider the effects of NLSP decays to gravitinos. For WIMP NLSPs, that

is, sleptons, sneutrinos, and neutralinos, the energy released is dominantly deposited

in electromagnetic cascades. For the decay times of Eq. (5), mesons decay before they

interact hadronically. The impact of EM energy on the light element abundances has been

7Li may be depleted from its primordial value by astrophysical effects,

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Figure 1: Predicted and excluded regions of the (τ,ζEM) plane in the superWIMP dark matter scenario,

where τ is the lifetime for˜l → l˜G, and ζEMis the normalized electromagnetic energy release. The grid gives

predicted values for m˜ G= 100 GeV−3 TeV (top to bottom) and ∆m ≡ m˜l−m˜ G= 600 GeV−100 GeV

(left to right), assuming Ω˜ G= 0.23. BBN constraints exclude the shaded regions; the circle indicates the

best fit region where7Li is reduced to observed levels without upsetting other light element abundances.

Contours of CMB µ distortions indicate the current bound (µ < 0.9 × 10−4) and the expected future

sensitivity of DIMES (µ ∼ 10−6). From Ref. [17].

studied in Refs. [47,48,49,50]. The results of Ref. [50] are given in Fig. 1. The shaded

regions are excluded because they distort the light element abundances too much. The

predictions of the superWIMP scenario for a stau NLSP with m˜Gand mNLSPvarying over

weak scale parameters are given in Fig. 1 by the grid.

We find that the BBN constraint excludes some weak scale parameters. However,

much of the weak scale parameter space remains viable. Note also that, given the7Li

discrepancy, the best fit is not achieved at ξEM= 0, but rather for τ ∼ 3 × 106s and

ξEM∼ 10−9GeV, where7Li is destroyed by late decays without changing the other relic

abundances. This point is marked by the circle in Fig. 1. The energy release predicted

in the superWIMP scenario naturally includes this region. The7Li anomaly is naturally

resolved in the superWIMP scenario by a stau NLSP with mNLSP∼ 700 GeV and m˜G∼

500 GeV.

3.2. BBN Hadronic Constraints

Hadronic energy release is also constrained by BBN [51,52,53,54,55,56,57]. In fact,

constraints on hadronic energy release are so severe that even subdominant contributions

to hadronic energy may provide stringent constraints.

Slepton and sneutrino decays contribute to hadronic energy through the higher order