We have calculated spin-independent cross section of nucleon-dark matter scattering process at loop level, which is relevant to dark matter direct detection. Paying particular attention to scattering of gluon with dark matter, which contributes as leading order in the perturbation, we have systematically evaluated loop diagrams with tracking the characteristic loop momentum which dominates in the loops. Here loop diagrams whose typical loop momentum scales are the masses of quarks and other heavier particles are separately presented. Then, we have properly taken into account each contribution to give the cross section. We assume that the dark matter is pure Bino or Wino in the supersymmetric models. Junji Hisano, Koji Ishiwata, and Natsumi Nagata, arXiv: [hep- ph] p.1 COSMO/CosPA 2010 : September 27 - October 1 Natsumi Nagata Nagoya University/University of Tokyo

The effective interactions of Majorana DM with light quarks and gluon We’d like to determine the coefficients of these operators by integrating out heavy fields (except the DM field) in a theory. Twist-2 operators traceless parts of the energy- momentum tensor p.2 Light quarks Gluon

The matrix elements of the effective operators The mass fractions of light quarksThe matrix elements of twist-2 operators The second moments of PDF The matrix element of the gluon field strength M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Phys. Lett. B 78 (1978) 443. p.3 Trace anomaly of the energy-momentum tensor in QCD :

The effective coupling of DM with nucleon The effective coupling of Majorana DM with nucleon : Spin-Independent cross section of DM with target nuclei : This term gives the leading contribution to the cross section even if it is suppressed by one-loop factor. negligible ! p.4 Input parameters

‘Long-’ and ‘Short-distance’ contribution Long-distance contribution Short-distance contribution p.5 The effective interaction of DM with gluon is generated by loop diagrams. We classify these diagrams into two types : loop momentum quark mass scale loop momentumheavy particle mass scale We must not include the long-distance contribution of light quarks into the evaluation of Light quark masses are smaller than the QCD scales !

p.6 Bino-like neutralino dark matter Tree-level diagrams One-loop diagrams Short- distance Long- distance Tree- and loop-level contributions in the effective coupling, Ref. : M. Drees and M. Nojiri, Phys. Rev. D 48 (1993) The diagrams (a) and (c) vanish in our calculation. Light quark contribution must not be included. SI scattering cross section

p.7 Wino-like neutralino dark matter One-loop contribution Two-loop contribution J. Hisano, S. Matsumoto, M. Nojiri, O. Saito, Phys. Rev. D 71 (2005) M. Cirelli, N. Fornengo, A. Strumia, Nucl. Phys. B 753 (2006) 178 R. Essig, Phys. Rev. D 78 (2008) J. Hisano, K. Ishiwata, and N. Nagata, Phys. Lett. B 690 (2010) 311. These interactions are not suppressed even if Wino mass is much larger than W boson mass. Light quarks do not contribute in this diagram LEFT : scattering cross section RIGHT : Each contribution in Spin-Independent coupling,

Loop diagrams of neutralino-gluon scattering yield leading contribution to the spin-independent (SI) scattering cross section. We have separately evaluated short- and long- distance contribution in the loop diagrams The contribution of light quarks must not be included in the long-distance diagrams p.8