Limits on the spin-dependent scattering cross section from IceCube

1. Limits on the spin-dependent scattering cross section from IceCube • Joakim Edsjö (edsjo@physto.se) • Presented by Carlos de los Heros

2. Basic idea • For the Sun, WIMP capture occurs mainly via the spin-dependent scattering on protons. • Spin-independent scattering can also be significant, but here direct detection experiments are typically more competitive • Hence, use the IceCube limits on the neutrino-induced muon flux from the Sun as a limit on the spin-dependent scattering on protons

3. Assumptions We here assume: • a standard Maxwell-Boltzmann velocity distribution of WIMPs in the halo with a local density of 0.3 GeV/cm3 • that the spin-dependent scattering on protons (Hydrogen) is the only significant cross section for capture (to get conservative limits) • that we have equilibrium between capture and annihilations in the Sun* *) will come back to this

4. How to we go to the scattering cross section c • For a given WIMP mass, we • integrate the scattering process over the solar radius (keeping track of where the Hydrogen is) and the velocity distribution to get the total capture rate in the Sun • (As we assume the spin-dependent scattering to dominate, we don’t need to care about other elements in the Sun than Hydrogen) • We then have a one-to-one conversion factor between the scattering cross section and the capture rate

5. What happens in the Sun? • In the Sun, annihilations will start to deplete the WIMPs and we have to solve the evolution equation • It has the solution • IF we have equilibrium between capture and annihilation, we can then uniquely go between the scattering cross section and annihilation rate. Evaporation can be neglected with

6. So, what do we get? Direct limits (very approx) Thomas’ A-II Gustav’s IC-22 • The limits we get are very competitive • Much better than current direct detection limits

7. What about spin-independent scatterings? • Doing the same thing, but assuming that spin-independent scattering dominates instead (summing over all elements this time) • These limits are not as competitive as the direct detection experiments are very sensitive

8. What about the equilibrium assumption (I)? • If we have equilibrium, annihilations occurs at full strength • If we do not, we get lower annihilation rates and this means that our assumptions break down, in particular our limits will not be OK as we could have higher scattering cross sections. • However, for all MSSM-models that give high rates, we do have equilibrium.

9. What about the equilibrium assumption (II)? • For all models that are excluded, we actually do have equilibrium between capture and annihilation, so the assumption is (barely) valid. • However, this is in MSSM and we are dangerously close to violating the assumption. • A more careful analysis would be required.

10. A note about velocity distributions Capture sensitive to the low-velocity region Direct detection sensitive to higher velocities • BUT, we cannot fiddle too much with this without violating the dynamical constraints from the Milky Way • Also, the local density NOW is most likely not lower than the average by a factor of two (M. Kamionkowski and S.M. Koushiappas, arXiv: 0801.3269) Remember the different velocity dependencies!

11. Conclusions • With reasonable assumptions, the IceCube limits can be converted to limits on the spin-dependent scattering cross section on protons. • These limits are better than any current direct detection limits • However, we have to assume equilibrium between capture and annihilation, which for the MSSM is just barely true.