Physics Letters B 746 (2015) 410–416
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Chiral power counting of one- and two-body currents in direct
detection of dark matter
Martin Hoferichter
a,b,∗
, Philipp Klos
a,b
, Achim Schwenk
a,b
a
Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany
b
ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany
a r t i c l e i n f o a b s t r a c t
Article history:
Received
19 March 2015
Received
in revised form 12 May 2015
Accepted
16 May 2015
Available
online 21 May 2015
Editor:
J.-P. Blaizot
Keywords:
Dark
matter
WIMPs
Chiral
Lagrangians
We present a common chiral power-counting scheme for vector, axial-vector, scalar, and pseudoscalar
WIMP–nucleon interactions, and derive all one- and two-body currents up to third order in the
chiral expansion. Matching our amplitudes to non-relativistic effective field theory, we find that chiral
symmetry predicts a hierarchy amongst the non-relativistic operators. Moreover, we identify interaction
channels where two-body currents that previously have not been accounted for become relevant.
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Elucidating the nature of dark matter is one of the most press-
ing
challenges in contemporary particle physics and astrophysics.
Still, one of the dominant paradigms rests on a weakly-interacting
massive particle (WIMP), such as the neutralino in supersymmetric
extensions of the standard model (SM). AWIMP can be searched
for at colliders, in annihilation signals, or in direct-detection exper-
iments,
where the recoil energy deposited when the WIMP scatters
off nuclei is measured. Recent years have witnessed an impres-
sive
increase in sensitivity, e.g., from XENON100 [1], LUX [2], and
SuperCMDS [3], which will further improve dramatically with the
advent of ton-scale detectors, XENON1T [4] and LZ [5]. In the ab-
sence
of a signal, direct-detection experiments provide more and
more stringent constraints on the parameter space of WIMP candi-
dates.
To derive these constraints and to interpret a future signal,
it is mandatory that the nucleon matrix elements and the nuclear
structure factors, which are required when transitioning from the
SM to the nucleon to the nucleus level, be calculated systemati-
cally
and incorporate what we know about QCD.
Effects
at the level of the nucleus can be described by an
effective field theory (EFT) whose degrees of freedom are non-
relativistic
(NR) nucleon and WIMP fields [6,7]. This NREFT has
been recently used in an analysis of direct-detection experi-
*
Corresponding author at: Institut für Kernphysik, Technische Universität Darm-
stadt,
64289, Darmstadt, Germany.
E-mail
address: hoferichter@theorie.ikp.physik.tu-darmstadt.de (M. Hoferichter).
ments [8]. In this approach, scales related to the spontaneous
breaking of chiral symmetry of QCD are integrated out, with the
corresponding effects subsumed into the coefficients of the EFT. In
the context of nuclear forces, such an EFT is called pionless EFT. To
derive limits on the WIMP parameter space, information from QCD
has then to be included in the analysis in a second step.
Alternatively,
one can start directly from chiral EFT (ChEFT)
to incorporate the QCD constraints from chiral symmetry [9–16],
which makes predictions for the hierarchy among one- and two-
body
currents. Based on ChEFT, scalar and axial-vector two-body
currents were recently considered in [10] and [11,12], respectively.
Moreover, lattice QCD can be used to constrain the couplings of
two-body currents [17].
The
goal of this Letter is to combine vector, axial-vector, scalar,
and pseudoscalar interactions in a common chiral power count-
ing,
collect all relevant one- and two-body matrix elements, and
match the result onto NREFT. This combines our knowledge of
QCD at low energies: the one-body matrix elements correspond to
the standard decomposition into form factors, while the two-body
scalar [9,10], vector [18–20], and axial-vector [15,21] currents have
been calculated as well, the vector current even at one-loop order.
Here, we combine these results for their application in direct de-
tection,
extending the axial-vector two-body currents to finite mo-
mentum
transfer and generalizing to the three-flavor case where
appropriate. By matching to the NREFT, we find that the chiral
symmetry of QCD predicts a hierarchy among the different oper-
ators
and that two-body currents can be as important as one-body
currents in some channels.
http://dx.doi.org/10.1016/j.physletb.2015.05.041
0370-2693/
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.