1. Gluon Contribution to Dark Matter Direct Detection
Natsumi Nagata
Nagoya University / University of Tokyo
18 December, Nagoya University (GCOE Workshop 2011)
Based on [J. Hisano, K. Ishiwata, N. N., , and ]
[J. Hisano, K. Ishiwata, N. N., M. Yamanaka, ]
and [J. Hisano, K. Ishiwata, N. N., T. Takesako, ]

2. Outline Introduction The method of Effective theory Some results
Summary
Wino DM in the MSSM (Split SUSY scenario)
EWIMP DM
KK photon DM in the MUED model
Degenerate scenario

3. 1. Introduction

4. Introduction Observational evidence for dark matter (DM)
Galactic scale
Scale of galaxy clusters
Begeman et. al. (1991).
Clowe et. al. (2006).
Cosmological scale
About 80% of the matter in the Universe is nonbaryonic dark matter.
Komatsu et. al. (2010).

5. Weakly Interacting Massive Particles
Introduction
Weakly Interacting Massive Particles (WIMPs)
One of the most promising candidates for dark matter is
Weakly Interacting Massive Particles
(WIMPs)
have masses roughly between 10 GeV ~ a few TeV.
interact only through weak and gravitational interactions.
Their thermal relic abundance is naturally consistent with the cosmological observations [thermal relic scenario].
appear in models beyond the Standard Model.

6. Introduction
Direct Detection Experiments
[XENON100 collaboration, arXiv: ]
Xenon100 collaboration gives a stringent constraint on spin-independent elastic WIMP-nucleon scattering cross section.
Ton-scale detectors for direct detection experiments are expected to yield significantly improved sensitivities.
(for WIMPs of mass 50 GeV)

7. the WIMP-nucleon elastic scattering cross section
Motivation
To study the nature of dark matter based on direct detection experiments,
the precise calculation of
the WIMP-nucleon elastic scattering cross section
is required.
■ Previous works
For Majorana DM
For vector DM
e.g.) M. Drees and M. Nojiri, Phys. Rev. D 48 (1993) 3483.
H. C. P. Cheng, J. L. Feng and K. T. Matchev, Phys. Rev. Lett. 89, (2002).
G. Servant and T. M. P. Tait, New J. Phys. 4, 99 (2002).
In these works, some of the leading contributions (especially those of gluon) to the scattering cross sections are not properly taken into accounted.
We study the way of evaluating the cross section systematically by using the method of effective field theory

8. 2. The method of effective theory

9. Effective Theory
Formulate the effective Lagrangian of the WIMP DM with light quarks (u, d, s) and gluon by integrating out the rest of heavy particles in the high energy theory.
Evaluate the WIMP-nucleon elastic scattering cross section using the effective Lagrangian.
We need to evaluate the nucleon matrix element of quark/gluon operators in the effective Lagrangian.

10. Effective Lagrangian for Majorana Dark Matter
Spin-dependent interaction
Spin-independent interaction
Twist-2 operator
Scalar-type interaction
Couplings of DM with “nucleon mass”
Nucleon matrix element is evaluated with lattice simulations
Couplings of DM with “quark momentum”
Parton Distribution Functions (PDF)
Twist-2-type interaction

11. Gluon contribution
Scalar-type interactions, , induce
The couplings of DM with “nucleon mass”
Nucleon matrix elements:
By using the trace anomaly of the energy momentum tensor in QCD,
This enhancement originates from the large gluon contribution to the nucleon mass.
Mass fractions for proton
The gluon contribution turns out to be comparable to the quark contribution even if the DM-gluon interaction is induced by higher loop diagrams.

12. 3. Some results

13. We found O(10)% alteration in the SI cross section.
Majorana DM
Pure Bino DM (MSSM)
The tree-level diagram:
Each contribution to the effective coupling f_p
1-loop diagrams:
ref. ) M. Drees and M. Nojiri, Phys. Rev. D 48 (1993) 3483.
We found O(10)% alteration
in the SI cross section.
Due to a failure of matching…
J. Hisano, K. Ishiwata, and N. Nagata, Phys. Rev. D 82 (2010)

14. Majorana DM Pure wino DM (with heavy squarks)
If squarks are quite heavy (>> 1 TeV),
Pure wino DM scatters off a nucleon through W boson loop diagrams.
The interaction Lagrangian:
Anomaly mediation with generic Kahler potential
1-loop diagrams:
2-loop diagrams:

15. There is a cancellation among these contributions.
Majorana DM
Pure wino DM (with heavy squarks)
Higgs mass
130 GeV
115 GeV
Each contribution in the effective coupling
The SI cross section of Wino DM with a proton
There is a cancellation among these contributions.
The SI cross section turns out to be smaller than those in the previous works by more than an order of magnitude.
J. Hisano, K. Ishiwata, and N. Nagata, Phys. Lett. B 690 (2010) 311.

16. Vector DM Vector DM KK photon DM (MUED)
Minimal Universal Extra Dimension (MUED) model
The first KK photon becomes the lightest Kaluza-Klein particle (LKP).
The tree-level diagrams:
Vector DM
1-loop diagrams:
chiral fermion

17. All of the contributions have the same sign (additive).
Vector DM
KK photon DM (MUED)
All of the contributions have the same sign (additive).
Each contribution in the effective coupling
Larger than those in the previous works by about an order of magnitude.
The SI scattering cross sections
J. Hisano, K. Ishiwata, N. Nagata, and M. Yamanaka, Prog. Theor. Phys. Vol. 126, No. 3 (2011) 435.
M. Kakizaki, S. Matsumoto and M. Senami, Phys. Rev. D 74, (2006).

18. Degenerate scenario
DM LHC
Hard Jets + Large Missing Transverse Energy
In the case where the mass difference between DM and colored particles is about 100 GeV
Jets are too soft to be triggered and the missing energy signature would not be observed at the LHC.
On the other hand, DM-nucleon scattering cross sections are generally enhanced in the degenerate scenario.

19. Degenerate scenario Cross sections are considerably enhanced when
Pure wino DM (MSSM)
In the following discussion, we consider a simple case
DM is pure wino
The first generation squarks are degenerate with wino DM in mass
The other squarks are heavy enough to evade current bound
Gluino is either degenerate with wino in mass or much heavier than the present limit
Cross sections are considerably enhanced when
SI scattering cross section
J. Hisano, K. Ishiwata, and N. Nagata, Phys. Lett. B 706, 208 (2011).

20. 4. Summary

21. Summary
We evaluate the elastic scattering cross sections of WIMP DM with nucleon based on the method of effective theory.
The interaction of DM with gluon as well as quarks yields sizable contribution to the cross section, though the gluon contribution is induced at loop level.
In the wino dark matter scenario we find the cross section is smaller than the previous results by more than an order of magnitude
The cross section of the first Kaluza-Klein photon dark matter turns out to be larger by up to a factor of ten.

22. Backup

23. Nucleon matrix elements
The mass fractions ( for the scalar-type quark operators)
For the twist-2 operators
The second moments of the parton distribution functions (PDFs)

24. Trace anomaly of energy-momentum tensor in QCD
The matrix element of gluon field strength tensor can be evaluated by using the trace anomaly of the energy-momentum tensor in QCD
The trace anomaly of the energy-momentum tensor in QCD
M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Phys. Lett. B 78 (1978) 443.

25. SI coupling of Majorana DM with nucleon
The effective coupling of DM with nucleon is given as follows:
Suppressed by
The gluon contribution can be comparable to the quark contribution even if the DM-gluon interaction is induced by higher loop diagrams.

26. Long-distance contribution vs. Short-distance contribution
We classify these contributions into two types:
Long-distance contribution
Diagrams in which loop momentum around the quark mass scale dominates the loop integration yield long-distance contribution.
One should not include the long-distance contribution of light quarks.
The corresponding effect is included in the mass fraction
Short-distance contribution
Diagrams where the typical loop momentum is around the scale of heavy particles (DM, squark, …) yield short-distance contribution.
All quarks contribute to the short-distance contribution.
J. Hisano, K. Ishiwata, N. Nagata, Phys. Rev. D 82, (2010).

27. Pure Bino DM
Gluon contribution | 1-loop
Short-distance
Vanish !
Long-distance
For light quarks, we have to include only the contribution of diagram (b) into calculation.

28. Spin-Independent scattering cross section (EWIMP DM)
Electroweak interacting massive particles (EWIMPs)
The neutral component of SU(2)_L n-tuplet with the hypercharge Y
We again find the SI cross sections are significantly suppressed.
J. Hisano, K. Ishiwata, N. Nagata, and T. Takesako, JHEP 1107 (2011) 005.