Theoretical uncertainties in predictions for direct detection experiments Felix Kahlhoefer Dark Matter @ LHC 27 September 2014 Oxford Rudolf Peierls Centre for Theoretical Physics © Banksy

Introduction We have discussed the uncertainties of LHC searches for DM: PDF uncertainties QCD corrections & scale ambiguities Systematics in background estimates Let us assume that all of these are under control and we can really constrain the fundamental interactions of dark matter with quarks. How do we compare these results with dark matter direct detection? Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

Outlook How reliable is this procedure? Identify relevant operators in the non-relativistic limit Calculate nuclear matrix elements Include nuclear form factors Calculate recoil spectra Predict experimental event rates Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

From the LHC to the non-relativistic limit Step 1: We need to work out which effective operators give the dominant contribution in the non-relativistic limit. March-Russell et al. (2012) Vector operator (e.g. Z’ exchange) Axialvector operator (Majorana DM) Careful: These operators induce spin-independent interactions at the 1-loop level. Haisch & FK, arXiv:1302.4454 Scalar operator (Higgs) Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

From quarks to nucleons Step 2: We need to work out the effective couplings of dark matter to protons and neutrons (fp, fn or ap, an). Easy for vector current: fp = 2 gu + gd, fn = 2 gd + gu Slightly more complicated for the axial current: Typically gu = -gd = -gs  ap = (1.36 ± 0.05) gu Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

From quarks to nucleons Difficult for the scalar current: Young, 1301.1765 Large uncertainties in the strange contents of the nucleus: fTs = σs / mN could be anywhere between zero and 0.15. The resulting fp then varies between 0.27 and 0.38. Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

From nucleons to nuclei Step 3: We need to include the loss of coherence for finite momentum transfer Spin dependent form factor XENON100 Collaboration, 1301.6620 Neutron (10-30%) The necessary form factors depend on the nuclear shell models. Proton (200-300%) Spin-independent form factor Typical momentum transfer in direct detection experiments Zheng et al. 1403.5134 Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

From nucleons to nuclei Even for spin-independent interactions, there are small differences between the distribution of protons and neutrons (neutron skin thickness), leading to different form factors for the two contributions. Zheng et al. 1403.5134 Zheng et al. 1403.5134 Only really matters for models with destructive interference. Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

From matrix elements to recoil spectra Step 4: Calculate differential event rates with The local DM density can be measured in essentially two different ways: Locally from the vertical motion of stars Globally from the rotation curve of the Milky Way Since dσ/dER ~ 1/v2, direct detection experiments probe the velocity integral Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

Local dark matter density Global measurements need to assume certain properties of the DM halo, such as a certain density profile or spherical symmetry. For sufficiently strong assumptions, the (averaged) local DM density can be determined with very high precision: Catena & Ullio, 0907.0018: 0.385 ± 0.027 GeV / cm3 McMillan, 1102.4340: 0.4 ± 0.04 GeV / cm3 Relaxing these assumptions, however, a much wider range becomes allowed: Iocco et al. 1107.5810: 0.2 – 0.56 GeV / cm3 Weber & de Boer, 1011.6323: 0.2 – 0.4 GeV / cm3 Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

Local dark matter density What if the halo is not spherical? What if there are additional structures (e.g. a dark disk)? Read, 1404.1938 Typical results: 0.35 ± 0.15 GeV / cm3 Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

The Standard Halo Model v0: Velocity dispersion (= circular velocity) vesc: Escape velocity Frandsen et al. 1111.0292 McCabe, 1005.0579 Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

The dark matter velocity distribution Moreover, the dark matter velocity distribution may deviate significantly from the simple Maxwell-Boltzmann form: Anisotropic halos Debris flows A dark disk contribution Vogelsberger et al. 0812.0362 Frandsen et al. 1111.0292 Fairbairn et al. 1206.2693 Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

Extracting particle physics Given all these astrophysical uncertainties, can we hope to extract particle physics properties from direct detection experiments? No, if we only have data from a single experiment. Yes, if we combine the data from several different targets. Basic idea: Map differential event rates into vmin-space in order to compare them independently of astrophysical uncertainties. Fox et al. 1011.1915 Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

Dark Matter @ LHC 2014, Oxford A few simple steps Introducing the rescaled velocity integral We can write and solve for g(vmin): Feldstein & FK, 1403.4606 Repeating this procedure for different values of mDM, we can find the one(s) that give the best fit to the data (lowest χ2). Best-fit velocity integral Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

Integrating the velocity integral If we ‘know’ g(vmin) and mχ, we can reconstruct ρ σp. Only problem: Low-energy threshold of direct detection. ? We can never probe the lowest velocity dark matter particles. Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

A lower bound on the cross section But: Since the velocity integral g(vmin) must be monotonically decreasing, we can always construct a lower bound. Conservative lower bound Feldstein & FK, 1409.5446 If we have an upper bound on ρ, we obtain a lower bound on σ! Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

More uncertainties beyond this talk! Frandsen et al. 1304.6066 Collar, 1302.0796 Sorensen, 1007.3549 Experimental uncertainties: Quenching factors detector resolution Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford

Dark Matter @ LHC 2014, Oxford Conclusions Various uncertainties have to be taken into account when comparing LHC searches to direct detection experiments: Contributions from loop-induced spin-independent interactions. Nuclear matrix elements (in particular for scalar mediators) Form factors (in particular for spin-dependent interactions and isospin- dependent scattering) Local dark matter density (uncertainties are large if we relax our assumptions on the global structure of the halo) Velocity distribution (it is not enough to just vary the parameters of the Standard Halo Model) Experimental uncertainties (quenching factors, detector resolution) New tools are in development to deal with astrophysical uncertainties by combining data from several direct detection experiments. Felix Kahlhoefer Dark Matter @ LHC 2014, Oxford