Turning up the (re)heat with gravitino dark matter

Jeriek Van den Abeele

3rd N-PACT Meeting

Oslo – August 6, 2019

based on ongoing work with J. Heisig, J. Kersten and I. Strümke

A recipe for a universe

1. Start with a hot, dense state

2. Let quantum gravity do its thing for the first \(10^{-43}\) s

3. While cooling: separate gravity, the strong and electroweak forces

4. Rapidly inflate to \(> 10^{78}\) times its volume, before \(t\sim 10^{-32}\) s

5. Reheat and fill with a quark-gluon plasma

6. Break supersymmetry and electroweak symmetry (\(t\sim 10^{-12}\) s)

7. Add (anti)hadrons in a good balance, leaving \(n^0:p^+=1:7\) after 1 s

A recipe for a universe

Image: NASA/WMAP

A recipe for a universe

8. After simmering, decouple neutrinos and annihilate most leptons

9. Cool for 100 s, then synthesise light elements for 20 mins.

10. Stir dark matter into filaments after ~ 47 000 yr, matter will follow

11. Wait 330 000 yr before creating atoms, and let photons escape

12. Set a timer for \(\sim 10^8\) yr, take a nap while gravity works its magic

13. Decorate with stars and galaxies and stuff

14. Accelerate your universe's expansion; come up with a fun finale!

How to get more stuff than anti-stuff

To succeed, Big Bang nucleosynthesis requires \(\frac{n_B-n_{\bar B}}{n_\gamma}\sim 10^{-9}\).

The Sakharov conditions for generating a baryon asymmetry dynamically:

Baryon number violation (of course)
C and CP violation (else: same rate for matter and anti-matter creation)
Departure from thermal equilibrium (else: same abundance anti-particles, given CPT)

Not satisfied in the Standard Model.

Baryogenesis via thermal leptogenesis provides a minimal realisation, only requiring heavy right-handed neutrinos \(N_i\) (\(\rightarrow m_\nu\) via see-saw mechanism):

out-of-eq. CP-violating \(N\) decays at \(T\sim m_N\) cause lepton asymmetry

baryon asymmetry

SM sphalerons

Serious SUSY shopping list

Image: Claire David (CERN)

(+ RH neutrinos)

Gravitino trouble

Given R-parity, the LSP is stable and a dark matter candidate.

In a neutralino LSP scenario with \(m_{\tilde G}\sim m_\mathsf{SUSY}\):

Thermal scattering during reheating produces gravitinos with \(\Omega^\mathsf{th}_{\tilde G} \propto T_R\)
Thermal leptogenesis needs \(T_R \gtrsim 10^9\) GeV, to match observed \(\frac{n_B}{n_\gamma}\) and \(m_\nu\)
Due to \(M_\mathsf{Pl}\)-suppressed couplings, the gravitino easily becomes long-lived: \[\tau_{\tilde G} \sim 10^7~\mathsf{s} \left(\frac{100~\mathsf{GeV}}{m_{\tilde G}} \right)^3\]
Overabundant, delayed gravitino decays disrupt BBN, excluding \(T_R \gtrsim 10^5\) GeV!

So ... why not try a gravitino LSP (with neutralino NLSP)?

Gravitino trouble

Given R-parity, the LSP is stable and a dark matter candidate.

In a gravitino LSP scenario:

Planck-suppressed widths make the NLSP long-lived and a danger to BBN
Thermal leptogenesis still needs \(T_R \gtrsim 10^9\) GeV
Now, for an MSSM NLSP, thermal freeze-out (not \(T_R\)!) determines the abundance
\(\Omega^\mathsf{th}_\mathsf{NLSP}\) is controlled by MSSM parameters; if it is low, the BBN impact is minimal!

The heavy Higgs funnel

Parameter region where the neutralino NLSP dominantly annihilates via resonant heavy Higgs bosons: \[2m_{\tilde \chi_{1}^{0}} \approx m_{H^0/A^0}\]

Requires wino-higgsino NLSP
Open window facilitating tiny NLSP freeze-out abundance
- Avoids injecting too much energy into BBN
- Minimises non-thermal gravitino abundance contribution from NLSP decays

Gravitino production

The gravitino relic density should match the observed \[\Omega_\mathsf{DM} h^2 = 0.1199\pm 0.0022\]

No thermal equilibrium for gravitinos in the early universe, due to superweak couplings (unless very light, but then no longer DM candidate due to Lyman-\(\alpha\))

So no standard mechanism to lower the gravitino abundance: instead, gradual build-up!

UV-dominated freeze-in from thermal scatterings at \(T\sim T_R\) \[\Omega_{\tilde G}^{\textsf{UV}} h^2 = \left( \frac{m_{\tilde{G}}} {100 \, \textsf{GeV}} \right)\! \left(\frac{T_{\textsf{R}}}{10^{10}\,\textsf{GeV}}\right)\! \left[\,\sum_{i=1}^{3}\omega_i g_i^2 \! \left(1+\frac{M_i^2}{3m_{\tilde{G}}^2}\right) \ln\!\left(\frac{k_i}{g_i}\right) + 0.00319\, y_t^2\!\left(1+\frac{A_t^2}{3m_{\tilde{G}}^2}\right)\right]\] (accounting for 1-loop running of \(g_i, M_i, y_t, A_t\))
IR-dominated freeze-in from decays of heaviest sparticles
SuperWIMP contribution from decays of thermal neutralino NLSP
(Direct inflaton decays to gravitinos)

from processes like \((g+g\rightarrow) g \rightarrow \tilde g + \tilde G \)

Gravitino production

The gravitino relic density should match the observed \[\Omega_\mathsf{DM} h^2 = 0.1199\pm 0.0022\]

No thermal equilibrium for gravitinos in the early universe, due to superweak couplings (unless very light, but then no longer DM candidate due to Lyman-\(\alpha\))

So no standard mechanism to lower the gravitino abundance: instead, gradual build-up!

UV-dominated freeze-in from thermal scatterings at \(T\sim T_R\)
IR-dominated freeze-in from decays of heaviest sparticles \[\Omega_{\tilde G}^{\textsf{IR}}h^2 \simeq 0.0035 \left(\frac{915/4}{g_*}\right)^{\!3/2} \left(\frac{100 \,\mathsf{GeV} }{ m_{\tilde G}}\right) \, \sum_i g_{\widetilde f_i} \left(\frac{m_{\widetilde f_i} }{ 10^5 \,\mathsf{GeV} } \right)^{\!3}\]
SuperWIMP contribution from decays of thermal neutralino NLSP
(Direct inflaton decays to gravitinos)

Gravitino production

The gravitino relic density should match the observed \[\Omega_\mathsf{DM} h^2 = 0.1199\pm 0.0022\]

No thermal equilibrium for gravitinos in the early universe, due to superweak couplings (unless very light, but then no longer DM candidate due to Lyman-\(\alpha\))

So no standard mechanism to lower the gravitino abundance: instead, gradual build-up!

UV-dominated freeze-in from thermal scatterings at \(T\sim T_R\)
IR-dominated freeze-in from decays of heaviest sparticles
SuperWIMP contribution from decays of thermal neutralino NLSP \[\frac{\Omega_{\tilde G}^\mathsf{SW}h^2}{m_{\tilde G}} = \frac{\Omega_{\tilde \chi}^\mathsf{th} h^2}{m_{\tilde \chi}}\]
(Direct inflaton decays to gravitinos)

BBN constraints

Lifetime/abundance limits for a generic particle decaying into \[u\bar u, b\bar b, t\bar t, gg, e^+e^-, \tau^+\tau^-, \gamma\gamma, W^+W^-\] and thus injecting energy into the primordial plasma

arXiv:1709.01211

p/n conversion

hadrodissociation

photodissociation

NLSP decays

\(\tilde{\chi}_1^0 \to \tilde{G} + \gamma \)

\(\tilde{\chi}_1^0 \to \tilde{G} + Z \)

\(\tilde{\chi}_1^0 \to \tilde{G} + \gamma^* \to \tilde{G} + f \bar{f} \qquad \mathsf{for } f = u,d,s,c,b,t, e, \mu, \tau\)

\(\tilde{\chi}_1^0 \to \tilde{G} + Z^{*} \to \tilde{G} + f \bar{f} \qquad \mathsf{for } f = u,d,s,c,b,t, e, \mu, \tau\)

\(\tilde{\chi}_1^0 \to \tilde{G} + (\gamma/Z)^{*} \to \tilde{G} + f \bar{f} \qquad \mathsf{for } f = u,d,s,c,b,t, e, \mu, \tau\)

\(\tilde{\chi}_1^0 \to \tilde{G} + h^0 \to \tilde{G} + XY \qquad \mathsf{for } XY = \mu^+\mu^-,\tau^+\tau^-, c\bar c, b \bar b, g g, \gamma \gamma, Z \gamma, ZZ, W^+ W^-\)

Relevant decay channels:

Crucially, the NLSP lifetime behaves as \(\tau_{\tilde \chi} \propto M_P^2 m_{\tilde G}^2/m_{\tilde \chi}^5 \) !

Collider constraints

Last step due to computational expense, split into 5 components:

Quick veto with lower bound on EWino masses, upper bound on lifetimes and pass some gluino/neutralino exclusion limits from ATLAS search [1712.02332]
Quick veto on chargino production cross-section from CMS disappearing-track search [1804.07321]
SmodelS determines simplified model topologies and tests them against LHC limits
CheckMATE performs event generation, detector simulation, cuts for different signal regions, and applies LHC limits from 8 and 13 TeV analyses
HiggsBounds checks Higgs sector predictions against LEP/Tevatron/LHC limits

Guided scan strategy

Construct a likelihood \(\mathcal{L}_\mathsf{scan} = \mathcal{L}_\mathsf{relic\ density} \times \mathcal{L}_\mathsf{BBN} \times \mathcal{L}_\mathsf{collider} \times \mathcal{L}^\mathsf{fake}_\mathsf{T_R}\).

Nested sampling with MultiNest to zone in on region with highest \(\mathcal{L}_\mathsf{scan}\):

Focusing on funnel region and guided towards high \(\mathsf{T_R}\)
7 parameters varied in the scan: \(T_R, m_{\tilde G}, M_1, M_2, M_3, \mu, A_0\)
Fixed \(\tan \beta = 10\) and \(m_{scalars} = 15\ \mathsf{TeV}\)
External dependencies:
- SOFTSUSY (spectrum generation)
- MicrOMEGAs (thermal NLSP abundance, chargino production cross sections)
- SmodelS, CheckMATE [ROOT, Delphes, MadGraph, Pythia, HepMC], HiggsBounds (collider checks)