Download WIMP-Nucleus Scattering

WIMP-Nucleus Scattering
Gary Prézeau
(Caltech)
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WIMP-Nucleus Scattering
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The nature of dark matter remains a
standing problem in cosmology and
particle physics.
It’s relic abundance can be used to
determine the scale of its interactions.
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Ωχ~ 3x10-27cm3s-1/<σAv>~10-1
<σA
-26
3
-1
v>~10 cm s
About the weak scale
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Thus, a particle that interacts
weakly looks like a promising dark
matter candidate (e.g. neutralinos,
KK modes, sterile neutrinos).
There is also a chance of detecting
it directly by looking at the recoil of
a nucleus that scattered a WIMP.
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WIMP-Nucleus Scattering
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Can consider the WIMP in a
particular model, such as MSSM
In that case, you know all the
couplings and the calculation of
amplitudes (like scattering) is
straightforward
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WIMP-Nucleus Scattering
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In particular, couplings of
neutralinos to quarks and gluons
can be expressed in terms of the
MSSM parameters
From there, spin-dependent (SD)
and spin-independent (SI) WIMPparton interactions can be derived.
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At tree level, the following diagrams contribute to
the effective SI neutralino-quark coupling:
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WIMP-Nucleus Scattering
SI neutralino-quark
effective coupling
after expanding in
inverse powers of the
heavy masses:
C1qqχχ
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From M. Drees and M. Nojiri Phys. Rev. D
47, 4226–4232 (1993) the following
diagrams contribute to the SI neutralinogluon coupling:
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WIMP-Nucleus Scattering
SI neutralino-gluon effective
coupling (after expansion):
C2qqGµν,aGµνa
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• From these neutralino-parton
interactions, you must now
construct the effective neutralinohadron interactions. Typically, this
means the neutralino-nucleon
vertex:
χ
N
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χ
N
WIMP-Nucleus Scattering
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Traditionally, the NNχχ vertex is the
only one considered, but there
could be other hadrons that
contribute to the SI neutralinonucleus cross-section.
What about: ππχχ?
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You need some way to estimate the
potential size of any new
contributions relative to NNχχ
Effective Field Theory (EFT) can
help.
More general than MSSM.
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Effective Field Theory
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Use symmetry properties to relate underlying
model to low-energy Lagrangian.
L(q,χ)
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SU(2)LXSU(2)R, CP, P
L(N,π,χ)
WIMP-Nucleus Scattering
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No specific model required. Can write
most general Lagrangian.
Instead of MSSM neutralino, can use a
general WIMP candidate with arbitrary
quantum numbers.
WIMP-quark interactions are set by a
heavy scale > 100GeV
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The series of possible quark operators
is truncated at leading order (LO) in
inverse powers of the heavy scale Λ.
The series of corresponding hadron
operators is truncated at some order
in p/Λh where p~mπ and Λh~1GeV
(Chiral Perturbation Theory).
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EFT can be used on a wide range of
physical problems where the
fundamental interactions are unknown,
for example, 0νββ and WIMP-nucleus
scattering.
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WIMP-Nucleus Scattering
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For 0νββ consider (GP, P. Vogel, M. RamseyMusolf Phys.Rev.D68:034016,2003)
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Let us look at the application of EFT to WIMPnucleus scattering in more detail (GP, A.
Kurylov, M. Kamionkowski, and P. Vogel Phys.
Rev. Lett. 91:231301,2003) :
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This Lagrangian will give rise to ππχχ,
πN2χχ, N2χχ vertices that will contribute
to the scattering amplitude:
New
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The new diagrams generated by
these new interactions are:
Sub-leading
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As an explicit example, consider the ππχχ
Lagrangian to NLO (one derivative):
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Expressions for the coefficients in terms of
the parameters appearing in the quarkneutralino Lagrangian can be derived using
PCAC and CVC theorems:
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Leading to:
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To leading order in p/Λh, you can generally neglect
compared to:
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So far, we have not assumed anything about
the underlying model. In MSSM however
X
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X X
X
WIMP-Nucleus Scattering
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So far, we have not assumed anything about
the underlying model. In MSSM however
X
Suppressed by p/Λh
SI interaction
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]
SD interaction
WIMP-Nucleus Scattering
In MSSM we have
Leading to the SI operators:
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WIMP-Nucleus Scattering
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Thus, the only diagrams that contribute to
the SI amplitude to LO are:
χ
+
N
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χ
N
WIMP-Nucleus Scattering
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The relative size of these two diagrams can
be expressed as a ratio:
where
=
F(A) ~ A
and r depends on the MSSM parameters and
depends on the two-nucleon matrix
element.
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The pion exchange diagram has a non-trivial
dependence on nuclear structure. It could
change from nucleus to nucleus.
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Opposite signs between the two diagrams
could have a significant effect on detection
rates from different target nuclei because of
cancellations that would occur for one
nucleus and not another.
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Summary:
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Effective field theory is a powerful tool when
estimating the relative size of WIMP-hadron
contributions to scattering amplitudes for arbitrary
DM models.
Generally, one can obtain large contributions from
pion-exchange to SI amplitude.
Detection rates could depend non-trivially on
target nuclei.
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