RIKEN Accel. Prog. Rep. 48 (2015)

Ⅱ-6. Particle Physics

Effective Higgs interactions of composite dark matter†
E. T. Neil∗1,∗2 for the LSD Collaboration
The recent discovery of the Higgs boson has placed
significant and direct constraints on models which predict new physics near the electroweak scale. At thesame time, recent dark matter direct-detection experiments have greatly improved their sensitivity, pushinginto the region of parameter space where dark matterinteracts with the standard model through exchangeof a Higgs boson.
These new constraints are particularly interesting in
the context of composite dark matter models (e.g.1) ).
In such a model, the lightest stable bound state of astrongly-coupled gauge sector provides a dark mattercandidate. Although the bound state itself must be net
electroweak neutral due to direct-detection experimental constraints, its constituents may carry electroweak
charges; the resulting interactions with the standard
model in the early universe can explain the observed
dark matter abundance, while scattering from presentday direct detection experiments is through suppressedhigher-dimensional operators2).
If the dark gauge interaction spontaneously breaks
a continuous symmetry, then some of the bound states
will be massless Nambu-Goldstone bosons, which
are ruled out by experiment if they are electroweak
charged. A realistic composite dark matter model
thus requires a mechanism for mass generation of
the constituents. In most models the constituentsare fermions, and they can be given mass throughthe Higgs mechanism; depending on the assignmentof charges, “vector-like” mass terms may also be allowed3) . The Higgs couplings required for mass generation are directly constrained by direct-detection experiment, in terms of the Higgs coupling of the dark
matter bound state itself.
We consider for concreteness a model consisting ofan SU(4) dark gauge force, and a set of degeneratefermions mf carrying electric charge Q = ±1/2. The
dark matter candidate is a neutral baryon-like boundstate of four such fermions, and has total mass mB .
The coupling of the Higgs boson to this baryon-likestate is given by the formula�mB � v ∂mf (h) �� f (B)gh,B =fvmf∂h �h=v

(1)fwhere v = 246 GeV is the vacuum expectation value(B)of the Higgs field. The factor ff contains the scalarmatrix element of the fermions inside the baryon-like†∗1∗2

Condensed from the article in Phys. Rev. D89, 094508(2014)RIKEN Nishina Center
Department of Physics, University of Colorado, Boulder

0.2
0.1
Αmax

0.05

0.02
0.01

01000

2000

mB GeV

3000

4000

Fig. 1. From3) , upper bound on the effective Higgs coupling α based on three lattice simulations at variousvalues of the fermion mass (green curves) and in theheavy quark limit (red dotted curve). The filled region
on the left shows values of mB ruled out by experimental bounds on light charged particles from LEP.

state, �B|f¯f |B�. This matrix element can be extracted using the Feynman-Hellmann theorem fromthe slope of the baryon mass, ∂mB /∂mf ; this is a
non-perturbative quantity, and is calculated using lattice simulations of the SU(4) theory. We find 0.15 (B)ff  0.34 in the range of fermion masses simulated.
Finally, the term in parentheses,�v ∂mf (h) ��α=,(2)mf∂h �h=v

is entirely model-dependent, and parameterizes thefraction of the fermion mass mf which is generated dueto the Higgs mechanism; if there are no “vector-like”
mass terms, then α = 1. The current upper boundon α in this model, based on our lattice calculation of(B)ff and the latest experimental results from LUX4) ,is shown in Fig. 1. For the entire range of models
considered, this constraint is significantly less than 1,
indicating that generation of mf in this model requires
more than the Higgs mechanism alone.
References
1) G. D. Kribs, T. S. Roy, J. Terning, and K. M. Zurek,Phys. Rev. D81 (2010) 095001
2) T. Appelquist et al. (LSD Collaboration): Phys. Rev. D88(2013), 014502
3) T. Appelquist et al. (LSD Collaboration): Phys. Rev. D89(2014), 094508
4) D. S. Akerib et al. (LUX Collaboration): Phys. Rev. Lett. 112(2014) 9, 091303- 156 -完全版2014_本文.indd 156

15/10/16 17:50