Download DM-nucleon scattering cross sections

Direct search of electroweak-charged
dark matter
Natsumi Nagata
Univ. of Minnesota/Kavli IPMU
High Energy Theory Lunchtime Seminar
April 23, 2015
in collaboration with J. Hisano, K. Ishiwata, S. Shirai, T. Takesako
1. Introduction
Introduction Evidence for dark matter (DM)
Galactic scale
Scale of galaxy clusters
Clowe et. al. (2006)
Begeman et. al. (1991)
Cosmological scale
90◦
18◦
2
10
1◦
Angular scale
0.2◦
0.1◦
0.07◦
6000
D [µK2]
5000
4000
3000
2000
1000
0
50
500
1000
1500
2000
2500
Multipole moment,
Planck (2013)
Planck (2013)
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.
Introduction
Electroweak-interacting dark matter
Quantum numbers of DM
Uncolored & uncharged
SU(2)L × U(1)Y charges are not determined.
(n, Y)
(1,0), (2, ± ½), (3,0), (3, ± 1), (4, ± ½) …
Such a DM candidate often appears in high-energy theories.
•
Higgsino/wino DM in SUSY models
•
A remnant Z2 symmetry in SO(10) GUTs yield this class
of DM candidates
Work in progress with Y. Mambrini, K. Olive, and J. Zheng
Introduction
Electroweak-interacting dark matter
Quantum numbers of DM
Uncolored & uncharged
SU(2)L × U(1)Y charges are not determined.
(n, Y)
(1,0), (2, ± ½), (3,0), (3, ± 1), (4, ± ½) …
Such a DM candidate often appears in high-energy theories.
•
Higgsino/wino DM in SUSY models
•
A remnant Z2 symmetry in SO(10) GUTs yield this class
of DM candidates
Work in progress with Y. Mambrini, K. Olive, and J. Zheng
Introduction Direct detection experiments
Nucleus
WIMP DM
Recoil energy
[Large Underground Xenon (LUX), arXiv: 1310.8214]
•
LUX experiment gives a stringent constraint on spinindependent WIMP-nucleon scattering cross section.
(for WIMPs of mass 33 GeV)
•
Ton-scale detectors for direct detection experiments are
expected to yield significantly improved sensitivities.
Introduction
Electroweak-interacting fermion dark matter
In what follows, we calculate the scattering cross sections of
Majorana fermion DM (Y = 0)
with a nucleon.
•
In this case, the cross sections are determined only by
the gauge interactions
•
Scalar DM suffers from model-dependence
•
I will comment on the hypercharged DM cases
(if I have enough time…)
Introduction
Electroweak-interacting fermion dark matter
In what follows, we calculate the scattering cross sections of
Majorana fermion DM (Y = 0)
with a nucleon.
Outline
1. Introduction
2. Direct detection of electroweak-interacting
fermion DM
3. Hypercharged DM
1. Conclusion and discussion
2. Direct detection of electroweakinteracting dark matter
Method of effective theories
1. By integrating out heavy particles, we obtain the effective
interactions of WIMP DM with quarks and gluons.
Operator Product Expansion (OPE)
Ci (μ)：Wilson coefficients
include short-distant effects
Oi (μ)：Effective operators
Higer-dimensional operators. Their nucleon matrix
elements contain the effects of long-distance.
μ：factorization scale
A scale at which a high-energy theory is matched with
the effective theory.
Method of effective theories
1. By integrating out heavy particles, we obtain the effective
interactions of WIMP DM with quarks and gluons.
Operator Product Expansion (OPE)
Ci (μ)：Wilson coefficients
include short-distant effects
Oi (μ)：Effective operators
Higer-dimensional operators. Their nucleon matrix
elements contain the effects of long-distance.
μ：factorization scale
A scale at which a high-energy theory is matched with
the effective theory.
Method of effective theories
1. By integrating out heavy particles, we obtain the effective
interactions of WIMP DM with quarks and gluons.
Operator Product Expansion (OPE)
Ci (μ)：Wilson coefficients
include short-distant effects
Oi (μ)：Effective operators
Higer-dimensional operators. Their nucleon matrix
elements contain the effects of long-distance.
μ：factorization scale
A scale at which a high-energy theory is matched with
the effective theory.
Method of effective theories
2. Evaluate the nucleon matrix elements of the effective
operators (at a certain scale).
When evolving the operators down to the scale, we need to match
the effective theories above/below each quark threshold.
DM
DM
DM
DM
Q
Q
Q
g
g
3. By using the nucleon matrix elements, we evaluate
the scattering cross section of DM with a nucleon
Effective Lagrangian for Majorana DM
Spin-independent
Scalar-type
Twist-2 type
Twist-2 operator
Effective Lagrangian for Majorana DM
Spin-independent
Scalar-type
Induces coupling of DM with
“mass of nucleon”
Twist-2 type
Twist-2 operator
Effective Lagrangian for Majorana DM
Spin-independent
Scalar-type
Induces coupling of DM with
“quark and gluon momenta”
Twist-2 type
Twist-2 operator
Nucleon matrix elements Quark (scalar-type)
Nucleon matrix elements of scalar-type quark operators are
evaluated by using the QCD lattice simulations.
mass fractions
(mN：Nucleon mass)
Gluon contribution
Mass fractions for proton
H. Ohki et al. (2008)
Remarks.
Strange quark content is much smaller than those
evaluated with the chiral perturbation theory.
Nucleon matrix elements Gluon (scalar-type)
Nucleon matrix element of scalar-type gluon operator is evaluated
by using the trace anomaly of the energy-momentum tensor.
 Trace anomaly of the energy-momentum tensor in QCD（Nf = 3）
L.O. in αs
M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Phys. Lett. B 78 (1978) 443.
Nucleon matrix elements Twist-2 operators
Nucleon matrix elements of twist-2 operators are evaluated
by using the parton distribution functions (PDFs).
Here, q(2) and G(2) are called the second moments of PDFs,
which are defined by
J. Pumplin et al., JHEP 0207:012
Effective coupling of Majorana DM with nucleon
The SI coupling of Majorana DM with nucleon is given as
The gluon contribution turns out to be comparable to
the quark contributions even if it is induced by higher
loop diagrams.
Effective coupling of Majorana DM with nucleon
The SI coupling of Majorana DM with nucleon is given as
The gluon contribution turns out to be comparable to
the quark contributions even if it is induced by higher
loop diagrams.
Effective coupling of Majorana DM with nucleon
The SI coupling of Majorana DM with nucleon is given as
suppressed by αs
The gluon contribution turns out to be comparable to
the quark contributions even if it is induced by higher
loop diagrams.
Electroweak-interacting DM
(n, 0)
Interactions
Mass difference
Mass difference between the neutral and charged components is
induced at loop level after the electroweak symmetry breaking.
(Negligible in the following calculation)
DM-nucleon scattering cross sections
•
Not induced at tree-level (loop-induced)
•
Determined as a function of DM mass
Diagrams 1-loop
``Scalar”
``twist-2”
These interactions are not suppressed even if the
DM mass is much larger than the W boson mass.
Non-decoupling effects
J. Hisano, S. Matsumoto, M. Nojiri, O. Saito, Phys. Rev. D 71 (2005) 015007.
Diagrams 2-loop
Gluon contribution
 Neglected in previous calculations
 2-loop gluon contribution can be comparable to
1-loop quark contribution
 non-decoupling
J. Hisano, K. Ishiwata, and NN, Phys. Lett. B 690 (2010) 311.
Fock-Schwinger gauge
Fock-Schwinger gauge
10
-45
10
-46
10
-47
10
-48
Matrix element
Higgs mass
2
SI cross section (cm )
Results Triplet case (3,0)
1000
2000
3000
DM Mass (GeV)
•
Cancellations among the contributions
•
Resultant SI cross sections are suppressed
J. Hisano, K. Ishiwata, and NN, Phys. Lett. B 690 (2010) 311.
Uncertainty
Cancellation results in large uncertainties
QCD higher order
Nucleon matrix
R. J. Hill, M. P Solon (2011)
•
Uncertainty mainly comes from the perturbative QCD.
•
Need for higher order calculation.
NLO calculation !
NLO result
〜 2.3 × 10-47 cm2
DM mass [GeV]
•
Perturbative QCD uncertainty is now smaller than the
hadron matrix error
•
Resultant scattering cross sections are above neutrino BG
J. Hisano, K. Ishiwata, and NN, [arXiv:1504.00915].
Wino-like DM Tree-level
χ̃ 0
χ̃ 0
h
χ̃ 0
χ̃ 0
h0
0
Q
q
q
g
g
Effective coupling
(Zij: Neutralino mixing matrix)
Wino-like DM Scattering cross sections with a proton
•
Cancellations between tree- and loop-level
contributions occur at a certain value of μ
•
Loop contribution is dominant in a wide range of
parameter region
J. Hisano, K. Ishiwata, N. Nagata, Phys. Rev. D87, 035020 (2013) .
Wino-like DM Scattering cross sections with a proton
Tree-level contribution interferes constructively to
the loop contribution in the case of low tanβ
The cross sections are within a reach of future experiments
in a wide range of parameter regions
J. Hisano, K. Ishiwata, N. Nagata, Phys. Rev. D87, 035020 (2013) .
3. Hypercharged DM
Hypercharged DM
Hypercharged DM is excluded by direct detection experiments
χ0
χ0
Dirac fermion
Z0
q
q
DM-nucleon scattering cross section is too large.
Hypercharged scalar DM is also excluded.
e.g.) Left-handed sneutrino DM in the MSSM
Hypercharged DM
If there exists a new physics which gives mass splitting between the
neutral components,
Dirac fermion
New physics effects
Mass splitting
Two Majorana fermions
In this case,
(Majorana condition)
Direct detection constraints can be avoided.
New physics effects
The new physics effects which induce mass splitting can be described
in terms of higher-dimensional operators that break “DM number”
4Y
4Y
ψ: (n, Y), η: (n, -Y), H: Higgs field, Λ: cut-off scale
Mass matrix
M: Dirac mass
A Dirac fermion splits into two Majorana fermions.
New physics effects
Example: Doublet (2, 1/2) DM
ψ, η
ψ, η
H
H
Singlet and/or triplet Majorana fermion with a mass of 〜 Λ
Cf.) Higgsino with (bino/wino)
Inelastic scattering
If the mass difference is too small, the hypercharged DM
inelastically scatters off a nucleon
χ 01
χ 02
Z0
q
q
If the mass difference is less than 〜 100 keV, this inelastic
scattering process again yields too large cross section.
Mass splitting
To evade the direct detection constraint
Larger hypercharge requires lower new-physics scale
for
We may probe them in future experiments.
Dim-5 operators
Generically, the following dim.-5 operators are also generated.
Elastic scattering
χ̃ 0
Electric dipole moments
χ̃ 0
h
χ̃ 0
χ̃ 0
h0
0
Q
q
q
g
g
We can give a lower-bound on Λ
Constraints & Prospects
Inelast ic
EDM
SI
(8 TeV,4, 32 )
(3 TeV,4, 32 )
(3 TeV,3,1)
(1 TeV,4, 32 )
(1 TeV,3,1)
(1 TeV,2, 12 )
(m D M , n, Y )
103
104
105
106
Λ [GeV]
107
108
109
•
Y = 3/2 DM is already being disfavored
•
Future experiments have sensitivities to Y = 1 DM
•
If Y = 1 case is excluded, remaining possibilities are Y = 0, or 1/2
NN and S. Shirai, Phys. Rev. D 91 (2015) 055035.
4. Conclusion and discussion
Summary
•
We evaluate the elastic scattering cross sections of
electroweak-interacting fermionic 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.
•
NLO calculation makes the perturvative QCD
uncertainty smaller than the error from the hadron
matrix elements
•
Hypercharged DM is severely constrained. Y > ½ cases
can be probed in future experiments
NLO result
(3,0)
(2,1/2)
(5,0)
Y = 0 cases may also be probed.
J. Hisano, K. Ishiwata, and NN, [arXiv:1504.00915].
Signature??
Signature??
Still consistent with theoretical prediction
G. Giesen, et. al. , [arXiv:1504.04276].
Signature??
2.2 TeV
3 TeV
1.7 TeV
3 TeV
M. Ibe, et. al. , [arXiv:1504.05554].
K. Hamaguchi, et. al. , [arXiv:1504.05937].
〜 3 TeV triplet DM may
explain the “excess”.
3 TeV
1.2 TeV
Summary
•
We evaluate the elastic scattering cross sections of
electroweak-interacting fermionic 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.
•
NLO calculation makes the perturvative QCD
uncertainty smaller than the error from the hadron
matrix elements
•
Hypercharged DM is severely constrained. Y > ½ cases
can be probed in future experiments
Backup
Singlet scalar DM
T. Abe, R. Kitano, and R. Sato, [arXiv:1411.1335].
If we require that the thermal relic abundance is equal to the present DM
density, then λSH is determined as a function of the DM mass.
Loop functions
• Non-relativistic scattering
• No mass difference
Classical process
Scalar
Twist-2
NLO scalar
NLO Twist-2
Scale dependence
PDF scales
PDF error
QCD higher order
J. Hisano, N. Nagai, and NN, [arXiv:1502.02244].
Electroweak-interacting DM
J. Hisano, K. Ishiwata, N. Nagata, and T. Takesako, JHEP 1107 (2011) 005.
M. Farina, D. Pappadopulo, A. Strumia, JHEP 1308 (2013) 022.
Neutrino BG
J. Billard, E. Figueroa-Feliciano, L. Strigari [arXiv: 1307.5458].
Higgs-nucleon coupling
Large mass fractions (f_Tq  large)
Higgs-nucleon couplings are enhanced
Input parameters
H. Y. Cheng (1989)
■ Lattice results (ours)
■ Chiral perturbation (traditional)
M. M. Pavan et al. (2002)
H. Ohki et al. (2008)
B. Borasoy and U. G. Meissner (1997)