Experimental targets for photon couplings of the QCD axion
HJE
Experimental targets for photon couplings of the QCD axion
Prateek Agrawal 0 3 4
JiJi Fan 1 3 4
Matthew Reece 0 3 4
Lian-Tao Wang 2 3 4
Oxford Street 3 4
Cambridge 3 4
U.S.A. 3 4
0 Department of Physics, Harvard University
1 Department of Physics, Brown University
2 Department of Physics, University of Chicago
3 184 Hope Street, Providence , U.S.A
4 5720 S Ellis Ave , Chicago , U.S.A
The QCD axion's coupling to photons is often assumed to lie in a narrow band as a function of the axion mass. We demonstrate that several simple mechanisms, in addition to the photophilic clockwork axion already in the literature, can signi cantly extend the allowed range of couplings. Some mechanisms we present generalize the KNP alignment scenario, widely studied as a model of in ation, to the phenomenology of a QCD axion. In particular we present KSVZ-like realizations of two-axion KNP alignment and of the clockwork mechanism. Such a \con nement tower" realization of clockwork may prove useful in a variety of model-building contexts. We also show that kinetic mixing of the QCD axion with a lighter axion-like particle can dramatically alter the QCD axion's coupling to photons, di ering from the other models we present by allowing non-quantized couplings. The simple models that we present fully cover the range of axion-photon couplings that could be probed by experiments. They motivate growing axion detection e orts over a wide space of masses and couplings.
Beyond Standard Model; Nonperturbative E ects
1 Introduction
2 Scenario I: alignment mechanism
2.1
A UV completion based on one con ning hidden gauge group
2.2 Landau pole constraint
3 Scenario II: con nement tower
3.1
Axion quality
4 Scenario III: kinetic mixing of multiple axions
4.1
Realizing large mixing
5 Results and conclusions A Mass mixing and non-quantized couplings B Two-loop RG equations for the model in section 2 C Vector-like leptons with large PQ charge
C.1 A chain of vector-like fermions
C.2 Clockwork
1
Introduction
The QCD axion is the most appealing simple solution to the strong CP problem [1{8]
as well as a classic dark matter benchmark [9{11]. Given its very weak coupling to the
standard model, searches to discover it have proved to be challenging. Yet experimental
e orts have been growing very rapidly recently [12{18] with several of them aiming at
detecting axion-photon couplings. It is thus important to chart the motivated parameter
space for this coupling.
An axion is a periodic eld, a = a + 2 Fa. This constrains its couplings to gauge elds,
as has period 2 in a coupling 32 2 e2F
F
e , where the dual gauge eld Fe
= 12
F .
(Recall that even for a U(
1
) gauge theory, the term is physical, as manifested in the Witten
e ect [19].) Compatibility of the axion period and the
angle period requires that when
we have a coupling of an axion to gauge elds (abelian or nonabelian) of the form
k
a
charge particle, the prefactor k must be an integer.1
= e2=(
4
), and e the coupling to a
minimum
The QCD axion's mass is determined by nonperturbative dynamics resulting from its
coupling to gluons,
N
s a
where em is the electromagnetic coupling strength and fa is the e ective decay constant
introduced above. The number (
4
) indicates the NLO correction [27]. The UV contribution
to the axion-photon coupling is model-dependent. It usually takes the form
gUV = r
a
em ;
2 fa
with r =
E
N
;
where E and N are the (discrete) electromagnetic and QCD anomaly coe cients of the
PQ symmetry respectively. The IR contribution indicates the smallest size of the
axionphoton coupling, provided that there is no accidental cancelation between the UV and IR
contributions. In models where E=N = 2,2 the axion-photon coupling is reduced by a factor
of
20 [28]. More extreme tuning is possible by considering multiple representations or
through a kinetic mixing contribution. Notice that mixing of multiple axions can appear to
evade the quantization rule (1.1), because the kinetic and mass terms may not be diagonal
in a basis where the axion shift symmetries are diagonal. For clarity and pedagogical
completeness, we elaborate on the origin of the non-quantized coupling (1.4) in appendix A.
The question is then: what is the upper bound of the QCD axion-photon coupling
theoretically? Traditionally it is assumed that UV and IR contributions are of the same
order and ga
O(
1
) em=(2 fa). A variety of speci c models realizing di erent O(
1
)
coe cients have been used to de ne a standard band that is often plotted [29].
More
thorough recent analyses demonstrate that in the standard KSVZ [5, 6] and DFSZ [7, 8]
frameworks, it is true that ga
O(
1
) em=(2 fa) for most representations of heavy matter
charged under the PQ symmetry and the standard model gauge groups [30, 31]. Yet special
representations of KSVZ fermions and their combinations or multiple Higgses (9 Higgses)
1Because we normalize Standard Model charges so that the smallest is 1=3 rather t (...truncated)