The QCD Axion from Aligned Axions and Diphoton Excess

We argue that the QCD axion can arise from many aligned axions with decay constants much smaller than the conventional axion window. If the typical decay constant is of {\cal O}{(100)} GeV to 1 TeV, one or more of the axions or saxions may account for the recently found diphoton excess at \sim 750 GeV. Our scenario predicts many axions and saxions coupled to gluons with decay constants of order the weak scale, and therefore many collider signatures by heavy axions and saxions will show up at different energy scales. In particular, if the inferred broad decay width is due to multiple axions or saxions, a non-trivial peak structure may become evident when more data is collected. We also discuss cosmological implications of the aligned QCD axion scenario. In the Appendix we give a possible UV completion and argue that the high quality of the Peccei-Quinn symmetry is naturally explained in our scenario.

The ATLAS and CMS experiments at the Large Hadron Collider recently announced that they observed an excess in the diphoton resonance search at ∼ 750 GeV with 2 − 3σ level [1].
The excess may be interpreted as a new particle decaying into two photons. Among various theoretical possibilities, a heavy axion field is an interesting and promising candidate [2][3][4][5][6][7][8][9][10][11]. 1 Then, the question is why such heavy axion exists in nature. The purpose of this letter is to point out that many axions with the decay constant at the weak scale may conspire together to form the QCD axion with an axion decay constant f QCD 10 9 GeV by the alignment mechanism [13]. Such multiple axions have been studied in the so-called axiverse scenario [14,15] and the alignment mechanism [16,17]. In particular, multiple axions naturally form axion landscape [17,18] if the number of shift symmetry breaking terms is greater than the number of axions. 2 The Peccei-Quinn (PQ) mechanism solves the strong CP problem by promoting the strong CP phase θ to a dynamical variable, the axion a QCD [21,22] (see Refs. [23][24][25][26] for recent reviews). The conventional axion window for the axion decay constant f QCD is given In this letter we point out a possibility that the QCD axion arises from a combination of many axions with decay constants much smaller than the conventional axion window, based on the so-called alignment mechanism [13]. As was noticed in Ref. [16], implemented by many axions, the alignment mechanism can exponentially enhance the effective axion decay constant without introducing extremely large charges. The alignment with many axions was discussed further in Refs. [17][18][19][27][28][29], and the application of the alignment mechanism to the QCD axion was also considered in Ref. [30]. If this is the case, there are many axions and saxions in the low energy, some of which may be within the reach of collider experiments such as LHC. Interestingly, the ATLAS and CMS experiments have found an excess in the 1 Cosmological and collider experimental signatures of such heavy axions were studied in Ref. [12]. 2 See also Refs. [19,20] for recent studies on the vacuum selection and stability in the axion landscape.
diphoton resonance search at about 750 GeV. The excess may be due to the decay of one or more of heavy axions needed to form the QCD axion by the alignment mechanism. Our scenario predicts that many other excesses in the diphoton resonance search will show up at different energy scales because there must be at least of order 10 such heavy axions.
Alternatively, it is similarly possible that the observed diphoton excess is due to one of the saxions, and in this case, the axions can be lighter and searched for by different techniques.
To implement the axion alignment mechanism, we consider a hidden sector with multiple periodic axions, where i = 1, 2, .., N, and the axions are assumed to have a similar decay constant Then the alignment mechanism can make one of the axions have an exponentially enhanced effective decay constant [16,27,28]: where ξ = O(1). We will identify this axion with the QCD axion, a QCD , that solves the strong CP problem. An enhanced effective decay constant can be achieved, for instance, in the simple model with the interactions [16,27] for Λ i ≫ Λ QCD , with n i , k s and k being integers which parameterize the discrete degrees of freedom in the underlying nonperturbative dynamics responsible for the axion potential.
We give one possible UV completion in the Appendix. Here B µν and G µν are the U(1) Y and SU(3) c field strength, respectively, and the tilded ones are their dual tensor. In the model we have assumed that φ N does not couple to the SU(2) L gauge bosons, which would be the case when the PQ quarks are singlet under SU(2) L . As noticed in Refs. [16,27], the model has a flat direction composed as which obtains a mass from the QCD instanton effects. The effective action for a QCD reads in the canonical basis, where the effective axion constant is given by with ξ = O(1). In order to enhance the effective decay constant by a factor of 10 6 , we need N ≃ 10 or more axions.
In the scenario under consideration, there are N − 1 axions much heavier than the QCD axion, and their decay constants are of the order f . Let us consider the case where one of them, a hid , has mass m hid = 750 GeV and decay constant f hid ∼ f . The effective couplings of a hid can be easily read off from the action (4): where we have omitted a mixing parameter which is considered to be of order unity. The axion a hid is produced via gluon fusion process, and decays into SM gauge bosons through the above interactions. Note that the decay rates are given Γ a hid →γγ : Γ a hid →Zγ : Γ a hid →ZZ ≃ 1 : 2 tan 2 θ W : tan 4 θ W = 1 : 0.6 : 0.08, with So there is a mild tension with the constraint on the Zγ channel at the 8 TeV LHC run [31] if the excess is due to the axion a hid . The production cross section for a hid is estimated to for the 8 and 13 TeV measurements at the LHC, respectively. Because the branching ratio into diphoton is given by one can find Hence the hidden axion can account for the observed diphoton excess at 750 GeV. For instance, we may take f hid ∼ 1 TeV with k = 10. It is also worth noting that the production cross section times branching ratio for the process pp → a hid → γγ is approximately independent of k s because in our scenario the axion is produced by gluon fusion and dominantly decays into gluons. To explain the diphoton excess, we need f hid around k × 100 GeV, which can be above TeV for large k. Such large k may give information on the PQ sector as k s corresponds to the number of PQ quark pairs and k is roughly 3 times larger than k s for PQ quarks carrying an electric charge of order unity. A large k may indicate that there are also PQ leptons having masses around f hid .
Note that our aligned QCD axion scenario requires many axions, some of which may have masses close to each other. This raises a possibility that multiple axions or saxions contribute to the diphoton excess, in which case the inferred broad width may be due to multiple peaks. If this is the case, a non-trivial peak structure may show up when more data is collected in the rest of LHC Run-2. Another interesting feature is that there can be dark radiation from the hidden sector. The potential (4) for multiple axions can be generated by hidden strong interactions. In such scenario a plausible possibility is that the hidden sector also possesses unbroken Abelian or weakly coupled non-Abelian gauge groups, and then the hidden sector can give a sizable contribution to (self-interacting) dark radiation [32].
So far we have focused on the mixings between axions and implications for the diphoton excess. In the UV completion, there also exists a saxion s i for each axion φ i , and the saxions are generically coupled to both gluons and axions with decay constants f i . In particular, there is no special reason to expect the alignment to occur for the saxion mixings. If one of the saxions, s hid , has a coupling like We also note that, in our model of the QCD axion from the aligned axions, the alignment does not necessarily take place for the saxions. Therefore, the saxions generically have unsuppressed couplings around 1/f to other particles including axions, and thus they are short-lived in contrast to the conventional scenario where the saxion is long-lived and tends to dominate the energy density of the Universe.
There are several cosmological and astrophysical constraints on the axions. One of the most stringent bounds comes from the supernovae (SN1987A). Axions can be efficiently produced in the core of the supernovae having the extremely high temperature T ∼ 30 MeV and high density (ρ ∼ 3 × 10 14 g cm −3 ) environment. The most efficient process for axion production is the nucleon-nucleon bremsstrahlung, N + N → N + N + (axion). In order to be consistent with the energy-loss rate in the supernovae, axion must be weakly coupled with the nucleon, which is roughly f 10 9 GeV, or the axion mass must be much larger than the supernovae core temperature. For the decay constant of order the weak scale, the axion mass should be heavier than about 1 GeV [36].
In this letter, we have pointed out a possibility that the QCD axion with a decay constant Appendix A: Aligned QCD axion

A possible UV completion
Here we give a possible UV completion of the aligned QCD axion based on Refs. [16,[27][28][29]. We consider N complex scalars Φ i with i = 1, 2, · · · , N with the following potential, where we assume that all the Φ i develop vacuum expectation values f i ∼ f of the similar size, and we introduce n q PQ quarks Q α and n ℓ PQ leptons L α . See the Table I for the the charge assignments of the PQ fermions. The above form of the potential is ensured by assigning U(1) PQ charges of Φ i as q i = 3 N −i . Integrating out these PQ fermions leads to the effective Lagrangian (4) with n i = 3, k s = n q and k = 3a 2 n q + b 2 n ℓ . Note that the diphoton excess can be explained by the hidden axion with f around k × 100 GeV while PQ fermions have masses around f , implying that large k is desirable. For instance, f around or above TeV requires k larger than 10, which can be obtained by PQ fermions with an appropriate PQ and hypercharge assignment. The required value of k is also realized without PQ leptons if the hypercharge of PQ quarks is sufficiently large, a 3/n q . The domain-wall number of the QCD axion is given by n q , and so one needs n q = 1 in order to avoid the domain-wall problem if the PQ symmetry breaking occurs after inflation. It is known that the quality of the PQ symmetry must be extremely high in order for the PQ mechanism to successfully solve the strong CP problem [37]. Considering that there are no exact continuous global symmetries in quatum gravity, the PQ symmetry is considered to be explicitly broken by Planck-suppressed operators, and therefore, such a high quality of the PQ symmetry is a puzzle. For instance, a dimension five Planck-suppressed operator induces an extra QCD axion mass, ∆m QCD ∼ 10 6 GeV f QCD 10 10 GeV which is about 10 23 times larger than required by the successful PQ mechanism.
In our scenario, the above puzzle can be naturally explained by the fact that all the scalars have vacuum expectation values much smaller than the conventional axion window, and any Planck-suppressed PQ-breaking operators are highly suppressed. The axion decay constant in the intermediate scale or higher is just a mirage due to the alignment mechanism. It is easy to see that dimension five Planck-suppressed operators are still harmful and spoil the PQ mechanism unless highly suppressed. To forbid them, we impose extra Z 2 parity under which Φ i goes to −Φ i . The Z 2 parity is nothing but a Z 2 subgroup of the U(1) PQ symmetry.
Then one of the most dangerous Planck-suppressed operators is where m QCD is the mass from the QCD instanton effects. Also it induces small shift of the minimum of the QCD axion potential, i.e. non-vanishing strong CP violation angle: θ ∼ 10 −10 Imκ f QCD 10 10 GeV which should be smaller than 10 −10 not to generate too large neutron electric dipole moment.
The contributions from the other dimension six operators are comparable to or smaller than those from (A3), and higher dimensional operators give negligible contributions. Thus the high quality of the PQ symmetry is naturally explained in our scenario. It is interesting to note that the aligned QCD axion leads to testable CP violation.