Brando Bellazzini, Alberto Mariotti, Diego Redigolo, Filippo Sala, Javi Serra
备注：
7 pages, 2 figures. v2: typos fixed, appendix added. v3: R-axion as motivation for ALP phenomenological studies made explicit, minor clarifications. Accepted for publication on PRL
We study the effective theory of a generic class of hidden sectors where supersymmetry is broken together with an approximate R-symmetry at low energy. The light spectrum contains the gravitino and the pseudo-Nambu-Goldstone boson of the R-symmetry, the R-axion. We derive new model-independent constraints on the R-axion decay constant for R-axion masses ranging from GeV to TeV, which are of relevance for hadron colliders, lepton colliders and B-factories. The current bounds allow for the exciting possibility that the first sign of SUSY will be the R-axion. We point out its most distinctive signals, providing a new experimental handle on the properties of the hidden sector and a solid motivation for searches of axion-like particles.
Inspired by the possibility of high-scale supersymmetry breaking in the string landscape where the cosmological constant problem and the gauge hierarchy problem can be solved while the strong CP problem is still a challenge for naturalness, we propose a supersymmetric KSVZ axion model with an approximate universal intermediate-scale ($\sim 10^{11}$ GeV) supersymmetry breaking. To protect the global Peccei--Quinn (PQ) symmetry against quantum gravitational violation, we consider the gauged discrete $Z_N$ PQ symmetry. In our model the axion can be a cold dark matter candidate, and the intermedia…
Various authors have noted that in particular models, the upper bound on the axion decay constant may not hold. We point out that within supersymmetry, this is a generic issue. For large decay constants, the cosmological problems associated with the axion's scalar partner are far more severe than those of the axion. We survey a variety of models, both for the axion multiplet and for cosmology, and find that in many cases where the cosmological problems of the saxion are solved, the usual upper bound on the axion is significantly relaxed. We discuss, more generally, the cosmological issues rais…
In rigid supersymmetry, generic models of dynamical supersymmetry breaking contain a light Goldstone boson, called the R axion. We show that supergravity effects explicitly break the R symmetry and give mass to the R axion. For visible and renormalizable hidden sector models, the massive R axion is free from astrophysical and cosmological problems. For nonrenormalizable hidden sector models, the R axion suffers from cosmological difficulties similar to those of the moduli fields in string theory.
Various theoretical and experimental considerations motivate models with high scale supersymmetry breaking. While such models may be difficult to test in colliders, we propose looking for signatures at much lower energies. We show that a keV line in the X-ray spectrum of galaxy clusters (such as the recently disputed 3.5 keV observation) can have its origin in a universal string axion coupled to a hidden supersymmetry breaking sector. A linear combination of the string axion and an additional axion in the hidden sector remains light, obtaining a mass of order 10 keV through supersymmetry break…
Similarities between the gauge meditation of supersymmetry breaking and the QCD axion model suggest that they originate from the same dynamics. We present a class of models where supersymmetry and the Peccei-Quinn symmetry are simultaneously broken. The messengers that mediate the effects of these symmetry breakings to the Standard Model are identical. Since the axion resides in the supersymmetry breaking sector, the saxion and the axino are heavy. We show constraints on the axion decay constant and the gravitino mass.
String theoretic axion is a prime candidate for the QCD axion solving the strong CP problem. For a successful realization of the QCD axion in string theory, one needs to stabilize moduli including the scalar partner (saxion) of the QCD axion, while keeping the QCD axion unfixed until the low energy QCD instanton effects are turned on. We note that a simple generalization of KKLT moduli stabilization provides such set-up realizing the axion solution to the strong CP problem. Although some details of moduli stabilization are different from the original KKLT scenario, this set-up leads to the mir…
We present a model where the QCD axion is at the TeV scale and visible at a collider via its decays. Conformal dynamics and strong CP considerations account for the axion coupling strongly enough to the standard model to be produced as well as the coincidence between the weak scale and the axion mass. The model predicts additional pseudoscalar color octets whose properties are completely determined by the axion properties rendering the theory testable.
The recently proposed model of using the dynamical phase of the gluino to solve the strong CP problem is shown to admit a specific realization in terms of fundamental singlet superfields, such that the breaking of supersymmetry occurs only at the TeV scale, despite the large axion scale of 10^{9} to 10^{12} GeV. Phenomenological implications are discussed.
In the axionic solution of the strong CP problem, fermions which transform under quantum chromodynamics (QCD) are required. In supersymmetry, by equating U(1)_{PQ} with U(1)_R, the natural candidates are the gluinos, as pointed out some years ago. A new specific implementation of this idea is proposed, linking the gluino axion scale to that of the canonical seesaw mechanism for neutrinos. Gaugino masses are generated dynamically and the A term is predicted to be very small.
A simple hadronic axion model is proposed in the framework of gauge-mediated supersymmetry breaking. Dynamics of Peccei-Quinn symmetry breaking is governed by supersymmetry breaking effects and the Peccei-Quinn breaking scale $f_{PQ}$ is inversely proportional to the gravitino mass. The gravitino mass range which corresponds to the axion window $f_{PQ} \simeq 10^{9}$ GeV -- $10^{13}$ GeV lies in the region predicted by gauge-mediated supersymmetry breaking models. The model is also shown to be cosmologically viable.
By eschewing finetuning from the electroweak and QCD sectors of supersymmetry (natural supersymmetry or SUSY), and by invoking the Kim-Nilles solution to the SUSY mu problem, one is lead to models wherein the dark matter is comprised of a mixture of axions and higgsino-like WIMPs. Over a large range of Peccei-Quinn breaking scale f_a~ 10^9-10^{12} GeV, one then expects about 90-95% axion dark matter. In such a scenario, both axion and WIMP direct detection may be expected.
We illustrate the structure and the main phenomenological features of a supersymmetric model (the USSM-A) built following a bottom-up approach and containing an anomalous abelian gauge symmetry. This model supports a gauged axion in its spectrum and provides a generalization of the global (supersymmetric) Peccei-Quinn construction. Complete simulations of the neutralino relic density are performed. Bounds from CAST and WMAP, combined with dark matter simulations, provide significant constraints on the scale of the interactions between the axion and the gauge fields.
We study properties of moduli stabilization in the four dimensional N = 1 supergravity theory with heavy moduli and would-be saxion-axion multiplets including light string-theoretic axions. We give general formulation for the scenario that heavy moduli and saxions are stabilized while axions remain light, assuming that moduli are stabilized near the supersymmetric solution. One can find stable vacuum, i.e. non-tachyonic saxions, in the non-supersymmetric Minkowski vacua. We also discuss the cases, where the moduli are coupled to the supersymmetry breaking sector and/or moduli have contribution…
If in addition to the standard model fields, a new pseudoscalar field that couples to hypercharge topological number density, the hypercharge axion, exists, it can be produced in colliders in association with photons or Z bosons, and detected by looking for its decay into photons or Z's. For a range of masses below a TeV and coupling above a fraction of 1/TeV, existing data from LEP II and the Tevatron can already put interesting constraints, and in future colliders accessible detection range is increased significantly. The hypercharge axion can help in explaining the matter-antimatter asymmet…
All generic, calculable models of dynamical supersymmetry breaking have a spontaneously broken $R$ symmetry and therefore contain an $R$ axion. We show that the axion is massive in any model in which the cosmological constant is fine-tuned to zero through an explicit $R$-symmetry-breaking constant. In visible-sector models, the axion mass is in the 100 MeV range and thus evades astrophysical bounds. In nonrenormalizable hidden-sector models, the mass is of order of the weak scale and can have dangerous cosmological consequences similar to those already present from other fields. In renormaliza…
While axions seem ubiquitous in critical string theories, whether they might survive in any string theoretic description of nature is a difficult question. With some mild assumptions, one can frame the issues in the case that there is an approximate supersymmetry below the underlying string scale. The problem of axions is then closely tied to the question of how moduli are fixed. We consider, from this viewpoint, the possibility that supersymmetry is broken at an intermediate scale, as in "gravity mediation," at a low scale, as in gauge mediation, and at a very high scale, to model the possibi…
The minimal supersymmetric standard model (MSSM) of particle interactions is extended to include three singlet (right-handed) neutrino superfields together with three other singlet superfields. The resulting theory is assumed to be invariant under an anomalous global U(1) (Peccei-Quinn) symmetry with one fundamental mass $m_2$. The soft breaking of supersymmetry at the TeV scale is shown to generate an axion scale $f_a$ of order $m_2$. Neutrino masses are generated by $f_a$ according to the usual seesaw mechanism.
We discuss a scheme to implement the relaxion solution to the hierarchy problem with multiple axions, and present a UV-completed model realizing the scheme. All of the $N$ axions in our model are periodic with a similar decay constant $f$ well below the Planck scale. In the limit $N\gg 1$, the relaxion $ϕ$ corresponds to an exponentially long multi-helical flat direction which is shaped by a series of mass mixing between nearby axions in the compact field space of $N$ axions. With the length of flat direction given by $Δϕ=2πf_{\rm eff} \sim e^{ξN} f$ for $ξ={\cal O}(1)$, both the scalar potent…
Recently we have proposed a simple hadronic axion model within gauge-mediated supersymmetry breaking. In this paper we discuss various cosmological consequences of the model in great detail. A particular attention is paid to a saxion, a scalar partner of an axion, which is produced as a coherent oscillation in the early universe. We show that our model is cosmologically viable, if the reheating temperature of inflation is sufficiently low. We also discuss the late decay of the saxion which gives a preferable power spectrum of the density fluctuation in the standard cold dark matter model when …
The axion solution to the strong CP problem makes use of a global Peccei-Quinn (PQ) U(1) symmetry which is susceptible to violations from quantum gravitational effects. We show explicitly how discrete gauge symmetries can protect the axion from such violations. PQ symmetry emerges as an accidental global symmetry from discrete gauge symmetries which are subgroups of the anomalous U(1) of string origin. We also show how the Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) axion model provides a natural solution to mu problem of supersymmetry as mu ~ M_{SUSY} ~ M^2_{PQ}/M_{Pl}.
We construct hadronic axion models in the framework of the anomaly-mediated supersymmetry breaking scenario. If the Peccei-Quinn symmetry breaking is related to the supersymmetry breaking, mass spectrum of the minimal anomaly-mediated scenario is modified, which may solve the negative slepton mass problem in the minimal anomaly-mediated model. We find several classes of phenomenologically viable models of axion within the framework of the anomaly mediation and, in particular, we point out a new mechanism of stabilizing the axion potential. In this class of models, the Peccei-Quinn scale is rel…
We show that the hierarchically small mu term in supersymmetric theories is a consequence of two identical pairs of Higgs doublets taking a democratic form for their mass matrix. We briefly discuss the discrete symmetry S2xS2 toward the democratic mass matrix. Then, we show that there results an approximate Peccei-Quinn symmetry and hence the value mu is related to the axion decay constant.
We propose a three-beam stimulated resonant photon collider with focused laser fields in order to directly produce an axion-like particle (ALP) with the two beams and to stimulate its decay by the remaining one. The expected sensitivity around the eV mass range has been evaluated. The result shows that the sensitivity can reach the ALP-photon coupling down to $\mathcal{O}(10^{-14})$ GeV${}^{-1}$ with 1 J class short-pulsed lasers.
The effects of possible explicit violation of the Peccei-Quinn symmetry responsible for the solution of the strong CP problem are studied in supersymmetric models. It is shown that automatic models with an abelian $U(1)$ gauge symmetry are easy to construct both in the context of fundamental and composite models of axions. It is argued that it is preferable to use abelian rather than nonabelian gauge groups in order to obtains automatic symmetries. A composite model with no exact $R$ symmetry is studied and it is found that, unlike common belief, supersymmetry is broken.
We investigate the possible detection of the Hypercharge Axion (HCA) in colliders. The HCA is a hypothetical pseudoscalar that couples to weak hypercharge topological density and could potentially explain the dominance of matter over antimatter in the observable universe. If the HCA exists, it can be produced in colliders via vector boson fusion or in association with a photon or with a Z boson, and detected by looking for its decay into photons or Z bosons. We find that for certain values of the HCA mass and coupling scales, both of the order of a TeV, existing data from the Large Hadron Coll…
The spontaneous breakdown of the scale, the chiral and the superconformal symmetries for a hidden $SU(N)$ gauge group is studied in an effective lagrangean approach. The relevant low-energy degrees of freedom are taken to be the composite Goldstone particles associated with these three broken symmetries. Supersymmetry is spontaneously broken in the large $N$ limit and soft breaking terms in the observable sector are generated, together with nonrenormalisable Nambu-Jona-Lasinio type interactions.
Cosmological colliders can preserve information from interactions at very high energy scale, and imprint them on cosmological observables. Taking the squeezed limit of cosmological perturbation bispectrum, information of the intermediate particle can be directly extracted from observations such as cosmological microwave background (CMB). Thus cosmological colliders can be powerful and promising tools to test theoretical models. In this paper, we study extremely light axions (including QCD axions and axion-like-particles), and consider them constituting cold dark matter (CDM) at late times. We …
We explore the possibility that supersymmetry breaking is mediated to the Standard Model sector through the interactions of a generalized axion multiplet that gains a F-term expectation value. Using an effective field theory framework we enumerate the most general possible set of axion couplings and compute the Standard Model sector soft-supersymmetry-breaking terms. Unusual, non-minimal spectra, such as those of both natural and split supersymmetry are easily implemented. We discuss example models and low-energy spectra, as well as implications of the particularly minimal case of mediation vi…
We present a simple supersymmetric axion model that can naturally explain the origin of the Higgs mu and Bmu terms in gauge mediation while solving the strong CP problem. To stabilize the Peccei-Quinn scale, we consider mixing between the messenger fields that communicate the supersymmetry and Peccei-Quinn symmetry breaking to the visible sector. Such mixing leads to the radiative stabilization of the Peccei-Quinn scale. In the model, a Higgs coupling to the axion superfield generates the B parameter at the soft mass scale while a small mu term is induced after the Peccei-Quinn symmetry breaki…
This Resource Book reviews the physics opportunities of a next-generation e+e- linear collider and discusses options for the experimental program. Part 2 reviews the possible experiments on Higgs bosons and supersymmetric particles that can be done at a linear collider.
We extend the work of Carone, Chaurasia and Vasquez on non-supersymmetric models of flavor based on the double tetrahedral group. Three issues are addressed: (1) the sector of flavor-symmetry-breaking fields is simplified and their potential studied explicitly, (2) a flavorful axion is introduced to solve the strong CP problem and (3) the model is extended to include the neutrino sector. We show how the model can accommodate the strong hierarchies manifest in the charged fermion Yukawa matrices, while predicting a qualitatively different form for the light neutrino mass matrix that is consiste…
We present a supersymmetric version of a two-field relaxion model that naturalizes tuned versions of supersymmetry. This arises from a relaxion mechanism that does not depend on QCD dynamics and where the relaxion potential barrier height is controlled by a second axion-like field. During the cosmological evolution, the relaxion rolls with a nonzero value that breaks supersymmetry and scans the soft supersymmetric mass terms. Electroweak symmetry is broken after the soft masses become of order the supersymmetric Higgs mass term and causes the relaxion to stop rolling for superpartner masses up…
We review the status of searches for Supersymmetry at the Tevatron Collider. After discussing the theoretical aspects relevant to the production and decay of supersymmetric particles at the Tevatron, we present the current results for Runs Ia and Ib as of the summer of 1997. To appear in the book "Perspectives in Supersymmetry", edited by G.L. Kane, World Scientific.
We investigate the prospects for discovering axion-like particles (ALPs) via a light-by-light (LBL) scattering at two colliders, the future circular collider (FCC-ee) and circular electron-positron collider (CEPC). The promising sensitivities to the effective ALP-photon coupling $g_{aγγ}$ are obtained. Our numerical results show that the FCC-ee and CEPC might be more sensitive to the ALPs with mass 2 GeV $\sim$ 10 GeV than the LHC and CLIC.
We have examined the sensitivity to the axion-like particle (ALP) couplings to electroweak gauge bosons in the diphoton production at a future muon collider. The collisions at the $μ^+ μ^-$ energies of 3 TeV, 14 TeV, and 100 TeV are addressed. The differential cross sections versus the invariant mass of the final photons and total cross section versus minimal diphoton invariant mass are presented. We have derived the exclusion regions for the ALP-gauge boson coupling. The obtained bounds are much stronger than the current experimental bounds in the ALP mass region 10 GeV -- 10 TeV. The partial…
We consider the class of effective supergravity theories from the weakly coupled heterotic string in which local supersymmetry is broken by gaugino condensation in a hidden sector, with dilaton stabilization achieved through corrections to the classical dilaton Kähler potential. If there is a single hidden condensing (simple) gauge group, the axion is massless (up to contributions from higher dimension operators) above the QCD condensation scale. We show how the standard relation between the axion mass and its Planck scale coupling constant is modified in this class of models due to a contribu…
Axion-like particles are an important part of the spectrum of anomalous gauge theories involving modified mechanisms of cancellation of the gauge anomalies. Among these are intersecting brane models, which are characterized by the presence of one physical axion. We overview a recent study of their supersymmetric construction and some LHC studies of the productions rates for a gauged axion.
We consider typical hadron collider detector signals sensitive to delayed decays of the lightest neutralino to photon plus goldstino and demonstrate the potential for substantially increasing the portion of the general parameter space of a gauge-mediated supersymmetry breaking model that can be probed at the Tevatron.
Recently N. Arkani-Hamed and S. Dimopoulos proposed a supersymmetric model \cite{Arkani-Hamed:2004fb}, dubbed "Split Supersymmetry" in Ref. \cite{Giudice:2004tc}, which can remove most of the unpleasant shortcomings of TeV Supersymmetry. In this model all scalars except one finely tuned Higgs boson are ultra heavy while the neutralino and chargino might remain light in order to achieve gauge coupling unification and accord with the dark matter density. In this paper, we investigated the impact of this new model on chargino pair production at next generation linear colliders. Our numerical resu…
A Supersymmetric Extension of Axionic Electrodynamics: From Axions and Photons to Axinos and Photinos
Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Instituto Federal do Espírito Santo（圣埃斯皮里图联邦学院）；Centro Federal de Educação Tecnológica C. S. da Fonseca（C.S.达丰塞卡联邦技术教育中心）
This paper discusses supersymmetry discovery potential of the upgraded DØexperiment at the Tevatron $p\bar{p}$ collider. Six final states with large transverse energy (momentum) leptons or photons (with or without large transverse momentum imbalances) are studied. These final states are expected to have small backgrounds and are thereby ideal for new physics searches. Implications of the analyses of these final states on Gauge Mediated Supersymmetry Breaking models are discussed for integrated luminosities of 2 and 30 1/fb. This study demonstrates that a large class of supersymmetry models can…
Bridging the divide: axion searches and axino phenomenology at colliders
University of Chicago（芝加哥大学）；Enrico Fermi Institute, University of Chicago（恩里科·费米研究所，芝加哥大学）；Kavli Institute for Cosmological Physics, University of Chicago（卡弗里宇宙物理学研究所，芝加哥大学）；Leinweber Institute for Theoretical Physics, University of Chicago（莱因韦伯理论物理研究所，芝加哥大学）；Kavli Institute for Physics and Mathematics of the Universe (WPI)（宇宙物理与数学卡弗里研究所（WPI））；The University of Tokyo Institutes for Advanced Study（东京大学高等研究院）；The University of Tokyo（东京大学）
Experiments at particle colliders have reached center of mass energies well above 100 GeV, equivalent to temperatures which existed shortly after the big bang. These experiments, testing the initial conditions of the universe have, with great precision, established the Standard Model of Particle Physics. In contrast, the existence of the Higgs boson and perhaps Supersymmetry remain speculative, as todays searches have failed to find signs of their existence. However, the next generation of high energy collider experiments and especially CERN's 14 TeV LHC, expected to start operation in the yea…
This review summarizes the state of the art in searches for supersymmetry at colliders on the eve of the LHC era. Supersymmetry is unique among extensions of the standard model in being motivated by naturalness, dark matter, and force unification, both with and without gravity. At the same time, weak-scale supersymmetry encompasses a wide range of experimental signals that are also found in many other frameworks. We recall the motivations for supersymmetry and review the various models and their distinctive features. We then comprehensively summarize searches for neutral and charged Higgs boso…
We study the discovery potential for heavy axion-like particles (ALPs) and the perspectives for determining their coupling properties at a muon collider. Focusing on their couplings to the Standard Model (SM) gauge bosons $γ, Z, W^\pm$, we show that a high-energy muon collider can substantially extend the mass coverage, essentially reaching the kinematic limit of the collider energy. The unique kinematics allow for non-ambiguous determination of the individual coupling strengths. The associated production via $μ^+μ^-$ annihilation and the VBF processes with the tagged outgoing muons can be uti…
In this review we discuss constraints on minimal supersymmetric models of particle physics implied by the recent astrophysical observations of WMAP. Although the prospects of detecting supersymmetry increase and 90 percent of the available MSSM parameter space can safely be reached by the sensitivity of future colliders, nevertheless we pay particular emphasis on discussing regions of the appropriate phase diagrams, which -if realized - would imply that detection of supersymmetry, at least in the context of minimal models, could be out of colliders reach. We also discuss the importance of a pr…
We present a pedagogical introduction to supersymmetry and supersymmetric models and give an overview of the potential of the linear collider for studying them. If supersymmetry is found, its discovery will bring with it many more questions than answers. These include: -Are the newly discovered particles really superpartners? -If not all superpartners are discovered, where are the rest of them? -Do the electromagnetic, weak, and strong forces unify? -Is a supersymmetric particle the dark matter? -How are the supersymmetric flavor and CP problems solved? -What is the scale of supersymmetry brea…
Discovery of the Higgs boson and lack of discovery of superpartners in the first run at LHC are both predictions of split supersymmetry with thermal dark matter. We discuss what it would take to find gluinos at hadron supercolliders, including the LHC at 14 TeV center of mass energy, and future pp colliders at 100 TeV and 200 TeV. We generalize the discussion by re-expressing the search capacity in terms of gluino to lightest superpartner mass ratio, and apply results to other scenarios, such as gauge mediation and mirage mediation.
A class of supersymmetric grand unified theories is introduced that has a single scale below the cutoff, that of the supersymmetry breaking masses $\tilde{m}$. For a wide range of the dimensionless parameters, agreement with the observed mass of the Higgs boson determines $\tilde{m} \sim 10^9-10^{13} {\rm GeV}$, yielding Intermediate Scale Supersymmetry. We show that within this framework it is possible for seesaw neutrino masses, axions, and inflation to be described by the scale $\tilde{m}$, offering the possibility of a unified origin of disparate phenomena. Neutrino masses allowing for the…
In the post-LHC8 era, it is perceived that what is left of SUSY model parameter space is highly finetuned in the EW sector (EWFT). We discuss how conventional measures overestimate EWFT in SUSY theory. Radiatively-driven natural SUSY (RNS) models maintain the SUSY GUT paradigm with low EWFT at 10% level, but are characterized by light higgsinos ~100-300 GeV and a thermal underabundance of WIMP dark matter. Implementing the SUSY DFSZ solution to the strong CP problem explains the small μparameter but indicates dark matter should be comprised mainly of axions with a small admixture of higgsino-l…
We consider the possibility that supersymmetry is broken at a low scale, within one order of magnitude above the TeV scale. In such a case, the degrees of freedom associated with the spontaneous breaking of supersymmetry, the goldstino fermion and its scalar superpartner (the sgoldstino), can have significant interactions with the Standard Model particles and their superpartners. We discuss some characteristic processes, involving the goldstino and the sgoldstino, and the collider signatures they give rise to. These signatures involve scalar resonances in the di-photon, di-jet, di-boson and di…
Diagnostic signals of the minimal model of anomaly mediated supersymmetry breaking are discussed in the context of a $\sqrt{s}$ = 1 TeV $e^+e^-$ linear collider.
We consider a possibility to observe the axion emission from a nearby supernova (SN) in the future, which can be known in advance by the pre-SN alert system, by collider detectors like the LHC detectors (i.e., the ATLAS and the CMS) and the ILC detectors (i.e., the ILD and SiD). The axion from the SN can be converted to the photon by the strong magnetic field in the detector and the photon can be detected by electromagnetic calorimeter. We estimate the numbers of signal and background events due to a nearby SN and show that the number of signal may be sizable. The axion emission from a nearby …
One kind of particularly interesting pseudoscalar particles, called axion-like particles (ALPs), have rich physical phenomenology at high- and low-energy collider experiments. After discussing most of single production channels of ALP at electron-positron colliders, we investigate the possibility of detecting this kind of new particles through the W$^{+}$W$^{-}$ fusion process e$^{+}$e$^{-}$ $\rightarrow$ $\overlineν_{e}$$ν_{e}a$ $(\rightarrow γγ)$ at the CLIC. The 3$σ$ and 5$σ$ bounds on the ALP parameter space at the three energy stages of the CLIC are obtained. We find that the bounds given…
