We study a class of gauge groups that can automatically yield a perturbatively exact Peccei-Quinn symmetry, and we outline a model in which the axion quality problem is solved at all operator dimensions. Gauge groups belonging to this class can also enforce and protect accidental symmetries of the clockwork type, and we present a toy model where an `invisible' axion arises from a single breaking of the gauge and global symmetries.
We present several models where the QCD axion arises accidentally. Confining gauge theories can generate axion candidates whose properties are uniquely determined by the quantum numbers of the new fermions under the Standard Model. The Peccei-Quinn symmetry can emerge accidentally if the gauge theory is chiral. We generalise previous constructions in a unified framework. In some cases these models can be understood as the deconstruction of 5-dimensional gauge theories where the Peccei-Quinn symmetry is protected by locality but more general constructions are possible.
An accidental U(1) Peccei-Quinn (PQ) symmetry automatically arises in a class of SO(10) unified theories upon gauging the SU(3)$_{f}$ flavour group. The PQ symmetry is protected by the $\mathbb{Z}_4 \times \mathbb{Z}_3$ center of $\text{SO(10)} \times \text{SU(3)}_f$ up to effective operators of canonical dimension six. However, high-scale contributions to the axion potential posing a PQ quality problem arise only at $d=9$. In the pre-inflationary PQ breaking scenario the axion mass window is predicted to be $m_a \in [7 \times 10^{-8}, 10^{-3}]$ eV, where the lower end is bounded by the seesaw…
We discuss the problem of constructing models containing an axion and axion-like particles, motivated by astrophysical observations, with decay constants at the intermediate scale ranging from $10^9$GeV to $10^{13}$GeV. We present examples in which the axion and axion-like particles arise accidentally as pseudo Nambu-Goldstone bosons of automatic global chiral symmetries, in models having exact discrete symmetries.
We introduce a class of composite axion models that provide a natural solution to the strong CP problem, and possibly account for the observed dark matter abundance. The QCD axion arises as a composite Nambu-Goldstone boson (NGB) from the dynamics of a chiral gauge theory with a strongly-interacting and confining SU(N) factor and a weakly-interacting U(1), with no fundamental scalar fields. The Peccei-Quinn (PQ) symmetry is accidental and all the mass scales are generated dynamically. We analyze specific models where the PQ symmetry is broken only by operators of dimension 12 or higher. We als…
In this note, we study a large class of four-dimensional R-symmetric theories, and we describe a new quantity, τ_U, which is well-defined in these theories. Furthermore, we conjecture that this quantity is larger in the ultraviolet (UV) than in the infrared (IR), i.e. that τ_U^{UV}>τ_U^{IR}. While we do not prove this inequality in full generality, it is straightforward to show that our conjecture holds in the subset of theories that do not have accidental symmetries. In addition, we subject our inequality to an array of non-trivial tests in theories with accidental symmetries and dramatically…
We show how an accidental $U(1)$ Peccei-Quinn (PQ) symmetry can arise from a discrete $A_4$ family symmetry combined with a discrete flavour symmetry $ \mathbb{Z}_3 \times \mathbb{Z}_5^2 $, in a realistic Pati-Salam unified theory of flavour. Imposing only these discrete flavour symmetries, the axion solution to the strong $ CP $ problem is protected from PQ-breaking operators to the required degree. A QCD axion arises from a linear combination of $ A_4 $ triplet flavons, which are also responsible for fermion flavour structures due to their vacuum alignments. We find that the requirement of a…
We argue that accidental approximate scaling symmetries are robust predictions of weakly coupled string vacua, and show that their interplay with supersymmetry and other (generalised) internal symmetries underlies the ubiquitous appearance of no-scale supergravities in low-energy 4D EFTs. We identify 4 nested types of no-scale supergravities, and show how leading quantum corrections can break scale invariance while preserving some no-scale properties (including non-supersymmetric flat directions). We use these ideas to classify corrections to the low-energy 4D supergravity action in perturbati…
The potential of $n$-Higgs Doublet Models ($n$HDMs) contains a large number of SU(2)$_L$-preserving accidental symmetries as subgroups of the symplectic group Sp(2$n)$. To classify these, we introduce prime invariants and irreducible representations in bilinear field space that enable us to explicitly construct accidentally symmetric $n$HDM potentials. We showcase the classifications of symmetries and present the relationship among the theoretical parameters of the scalar potential for; (i) the Two Higgs Doublet Model (2HDM) and (ii) the Three Higgs Doublet Model (3HDM). We recover the maximum…
The recent detection of the cosmic microwave background polarimeter experiment BICEP2 of tensor fluctuations in the B-mode power spectrum basically excludes all plausible axion models where its decay constant is above $10^{13}$ GeV. Moreover, there are strong theoretical, astrophysical, and cosmological motivations for models involving, in addition to the axion, also axion-like particles (ALPs), with decay constants in the intermediate scale range, between $10^9$ GeV and $10^{13}$ GeV. Here, we present a general analysis of models with an axion and further ALPs and derive bounds on the relativ…
We study QCD axion or cosmological axion-like particles (ALPs) in a model inspired by the recent interest in 4-dimensional clockwork models, with the global symmetry being accidentally enforced by a gauge abelian quiver with scalar bifundamental fields. For the QCD axion, we analyze the connection between the degree of protection of the axion mass against gravitational corrections, the explanation of the hierarchy $f_a \ll M_P$ and the number of colored fermions needed to generate anomalous couplings to gluons, all linked together by the underlying gauge symmetries. Based on that model and on …
We consider a new approach to fermion masses and mixings in which no special "horizontal" dynamics is invoked to account for the hierarchical pattern of charged fermion masses and for the peculiar features of neutrino masses. The hierarchy follows from the vertical, family-independent structure of the model, in particular from the breaking pattern of the Pati-Salam group. The lightness of the first two fermion families can be related to two family symmetries emerging in this context as accidental symmetries.
We construct accidentally symmetric potentials in the framework of Two Higgs Model Effective Field Theory (2HDMEFT) including higher-order operators of dimension 6 and dimension 8. Our construction is facilitated by an earlier developed technique based on prime invariants. In addition, we employ an alternative method that utilises the generators of each symmetry in the bi-adjoint representation and show how this method can be used to identify operators of any higher dimension. The accidentally symmetric 2HDMEFT potentials exhibit two classes of symmetries: (i) continuous symmetries and (ii) di…
The extension of the Standard Model (SM) with two Higgs triplets offers an appealing way to account for both tiny Majorana neutrino masses via the type-II seesaw mechanism and the cosmological matter-antimatter asymmetry via the triplet leptogenesis. In this paper, we classify all possible accidental symmetries in the scalar potential of the two-Higgs-triplet model (2HTM). Based on the bilinear-field formalism, we show that the maximal symmetry group of the 2HTM potential is ${\rm SO(4)}$ and eight types of accidental symmetries in total can be identified. Furthermore, we examine the impact of…
The two-Higgs-triplet model (2HTM) provides us with an attractive way to simultaneously account for tiny neutrino masses and the observed matter-antimatter asymmetry in our Universe. In this talk, we study the accidental symmetries of the scalar potential in the 2HTM using the bilinear-field formalism. Based on the group-theoretical arguments, we prove that the maximal symmetry group is ${\rm SO(4)}$. We carefully analyze all the subgroups of ${\rm SO(4)}$, and find that there are eight distinct kinds of accidental symmetries in the scalar potential of the 2HTM.
Recently, it has been shown [arXiv:1106.3482] that the two-Higgs-doublet-model potential may exhibit a maximum of 13 distinct accidental symmetries. Such a classification is based on a six-dimensional bilinear scalar field formalism realizing the SO(1,5) symmetry group. This note presents the transformation relations for each of the 13 symmetries in the original scalar field space and their one-to-one correspondence to the space of scalar bilinears, thereby providing firm support for the completeness of the classification.
We reconsider the massless up quark solution of the strong CP problem. We show that an anomaly free horizontal symmetry can naturally lead to a massless up quark and to a corresponding accidental anomalous symmetry. Reviewing the controversy about the phenomenological viability of $m_u=0$ we conclude that this possiblity is still open and can solve the strong CP problem. To appear in the Proceedings of The Yukawa Couplings and the Origins of Mass Workshop.
Axions were first introduced in connection with chiral symmetry but are now being looked for mainly as dark matter. In this paper we introduce a nonabelian analogue of axions which can also be potential candidates for dark matter. Their nonabelian symmetries, which are generalizations of the Peccei-Quinn symmetry, are interesting in their own right. Detailed analysis, using fermion measure and zeta function approaches shows that these symmetries are not anomalous.
We address two closely related problems associated with the singlet scalars' potential that are often present in supersymmetric U(1)' models, especially those which maintain the gauge unification of the MSSM in a simple way. The first is the possibility of an accidental global symmetry which results in a light Goldstone boson. The second is the problem of generating a vacuum expectation value for more than one field without reintroducing the $μ$ problem. We give sufficient conditions for addressing both issues and provide a concrete example to generate them.
We combine two popular extensions of beyond the Standard Model physics within the framework of intersecting D6-brane models: discrete Zn symmetries and Peccei-Quinn axions. The underlying natural connection between both extensions is formed by the presence of massive U(1) gauge symmetries in D-brane model building. Global intersecting D6-brane models on toroidal orbifolds of the type T6/Z2N and T6/Z2xZ2M with discrete torsion offer excellent playgrounds for realizing these extensions. A generation-dependent Z2 symmetry is identified in a global Pati-Salam model, while global left-right symmetr…
In this paper, we construct a supersymmetric composite axion (c-axion) model based on the gauge group $SU(N)\times SU(M)$, which is one possible physical application of the N=1 duality. The dual of SU(M) is interpreted as the color gauge group. We illustrate the existence of c-axion for the case of one dual quark in the dual gauge group $SU(\tilde M)$.
Unification of matter fields implies the existence of accidental permutation symmetries, which potentially remain immune to large quantum corrections up to the TeV scale. We investigate the case of a supersymmetric $SU(5)$ grand unified theory, where such a permutation symmetry is present in the up-type squark sector. We present a variety of tests allowing to challenge the $SU(5)$ hypothesis based on the observation of squarks at the LHC. These tests appear as relations among observables involving flavour-violating or chirality-flipping decays of squarks. Moreover, they rely on top-polarimetry…
In the framework of a 3-3-1 model with a minimal scalar sector, known as the economical 3-3-1 model, we study its capabilities of generating realistic quark masses. After a detailed study of the symmetries of the model, before and after the spontaneous symmetry breaking, we find a remaining axial symmetry that prevents some quarks to gain mass at all orders in perturbation theory. Since this accidental symmetry is anomalous, we also consider briefly the possibility to generate their masses for non-perturbative effects. However, we find that non-perturbative effects are not enough to generate t…
The clockwork mechanism is a novel method for generating a large separation between the dynamical scale and interaction scale of a theory. We demonstrate how the mechanism can arise from a sequence of strongly-coupled sectors. This framework avoids elementary scalar fields as well as ad hoc continuous global symmetries, both of which are subject to serious stability issues. The clockwork factor, $q$, is determined by the consistency of the strong dynamics. The preserved global $U(1)$ of the clockwork appears as an accidental symmetry, resulting from discrete or $U(1)$ gauge symmetries, and it …
Axions, periodic scalar fields coupled to gauge fields through the instanton density, have a rich variety of higher-form global symmetries. These include a two-form global symmetry, which measures the charge of axion strings. As we review, these symmetries typically combine into a higher-group, a kind of non-abelian structure where symmetries that act on operators of different dimensions, such as points, lines, and strings, are mixed. We use this structure to derive model independent constraints on renormalization group flows that realize theories of axions at long distances. These give univer…
We show that the strong self-interaction of the scalar polarization of a massive graviton can be understood in terms of the propagation of an extra ghost-like degree of freedom, thus relating strong coupling to the sixth degree of freedom discussed by Boulware and Deser in their Hamiltonian analysis of massive gravity. This enables one to understand the Vainshtein recovery of solutions of massless gravity as being due to the effect of the exchange of this ghost which gets frozen at distances larger than the Vainshtein radius. Inside this region, we can trust the two-field Lagrangian perturbati…
A $SU(N)_L\times SU(N)_R$ gauge theory for a scalar multiplet $Y$ transforming in the bi-fundamental representation $(N,\bar N)$ preserves, for $N>4$, an accidental $U(1)$ symmetry firstly broken at operator dimension $N$. Two configurations are possible for the vacuum expectation value of $Y$, which correspond to the (maximal) little groups $\mathcal{H}_s=SU(N)_{L+R}$ and $\mathcal{H}_h=SU(N-1)_L\times SU(N-1)_R\times U(1)_{L+R}$. In the first case the accidental $U(1)$ gets also broken, yielding a pseudo Nambu-Goldstone boson with mass suppression controlled by $N$, while in the second case …
We consider a string inspired non-supersymmetric extension of the standard model with gauged anomalous U(1) flavor symmetries. Consistency requires the Green-Schwarz mechanism to cancel mixed anomalies. The additional required scalars provide Stuckelberg masses for the $Z'$ particles associated to the gauged flavor symmetry, so they decouple at low energies. Our models also include a complex scalar field $ϕ$ to generate Froggatt-Nielsen mass terms for light particles giving a partial solution to the fermion mass problem. A residual approximate (anomalous) global symmetry survives at low energi…
We study UV-complete Froggatt-Nielsen-like models for the generation of mass and mixing hierarchies, assuming that the integrated heavy fields are chiral with respect to an abelian Froggatt-Nielsen symmetry. It modifies the mixed anomalies with respect to the Standard Model gauge group, which opens up the possibility to gauge the Froggatt-Nielsen symmetry without the need to introduce additional spectator fermions, while keeping mass matrices usually associated to anomalous flavour symmetries. We give specific examples where this happens, and we study the flavourful axion which arises from an …
We study non-invertible global symmetries in $(3+1)$-dimensional axion electrodynamics with a massless axion and a massless photon. In addition to a previously known non-invertible 0-form shift symmetry of the axion, we find a non-invertible 1-form symmetry associated with the equation of motion for the photon. Correlation functions of non-invertible symmetry defects lead to invertible 1- and 2-form symmetry defects associated with Bianchi identities for the axion and photon. In terms of the correlation functions, we discuss several phenomena for extended objects, such as induced fractional el…
We study higher-form symmetries in a low-energy effective theory of a massless axion coupled with a photon in $(3+1)$ dimensions. It is shown that the higher-form symmetries of this system are accompanied by a semistrict 3-group (2-crossed module) structure, which can be found by the correlation functions of symmetry generators of the higher-form symmetries. We argue that the Witten effect and anomalous Hall effect in the axion electrodynamics can be described in terms of 3-group transformations.
Here I present the effect of gaugino condensation and discrete symmetries to the model-independent axion potential, collaborated with Georgi and Nilles [hep-ph/9805510].
The axion solution to the strong CP problem makes use of a global Peccei-Quinn U(1) symmetry which is susceptible to violations from quantum gravitational effects. We show how discrete gauge symmetries can protect the axion from such violations. PQ symmetry emerges as an approximate global symmetry from discrete gauge symmetries. Simple models based on Z_N symmetries with N =11,12, etc are presented realizing the DFSZ axion and the KSVZ axion. The discrete gauge anomalies are cancelled by a discrete version of the Green-Schwarz mechanism. In the supersymmetric extension our models provide a na…
We examine discrete gauge symmetries in axionic extensions of the SSM which provide a solution of the $μ$-problem. Automatic-PQ symmetry and proton stability are shown to be guaranteed by certain discrete symmetries. Focusing on the L-violating discrete symmetries we discuss two sources of neutrino masses and their relevance for the solar neutrino problem.
Berry phase in axion physics, SM global structure, and generalized symmetries
School of Physics, Peking University（北京大学物理学院）；School of Physics, Zhengzhou University（郑州大学物理学院）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Department of Physics, Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院物理系）；Key Laboratory of Beam Technology of Ministry of Education, School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院教育部光束技术重点实验室）；Institute of Radiation Technology, Beijing Academy of Science and Technology（北京市科学技术研究院辐射技术研究所）
We show that by imposing local $Z_{13}\otimes Z_3$ symmetries in an $SU(2)\otimes U(1)$ electroweak model we can implement an invisible axion in such a way that (i) the Peccei-Quinn symmetry is an automatic symmetry of the classical Lagrangian; and (ii) the axion is protected from semi classical gravitational effects. In order to be able to implement such a large discrete symmetry, and at the same time allow a general mixing in each charge sector, we introduce right-handed neutrinos and enlarge the scalar sector of the model. The domain wall problem is briefly considered.
Axion fields provide the most elegant solution to the strong CP problem. In string compactifications it is difficult to obtain an axion whose decay constant is consistent with current cosmological bounds. We examine this question in theories with accidental U(1) symmetries that appear as low energy remnants of discrete symmetries. We refer to the axion-like particles from the spontaneous breakdown of these symmetries as accions. In such systems, the accion decay constant depends on the vacuum configuration and can be lowered to fit the bounds. Furthermore, we find that such accions with consis…
In this work, we discuss how the use of the symmetries well motivated in physics beyond the Standard model (BSM) can guarantee the high quality axions. We avoid to introduce symmetries only useful for addressing the axion quality problem. Rather, we rely on symmetries well motivated by other issues in BSM: supersymmetry, $U(1)_{\rm B-L}$ and the discrete R-symmetry $Z_{NR}$. We show that the interplay among these guarantees the high quality of the axion even for the gravitino mass and axion decay constant as large as $m_{3/2}=\mathcal{O}(10){\rm TeV}$ and $F_{a}=\mathcal{O}(10^{15}){\rm GeV}$ …
The hierarchy of fermion masses in the standard model may arise via the breaking of discrete gauge symmetries. The renormalizable interactions of the flavor-symmetry-breaking potential can have accidental global symmetries that are spontaneously broken, leading to pseudo-goldstone bosons that may drive inflation. We consider two-field, axion-monodromy inflation models in which the inflaton is identified with a linear combination of pseudo-goldstone bosons of the flavor sector. We show that the resulting models are nontrivially constrained by current cosmological data as well as the requirement…
Continuous global symmetries are expected to be broken by gravity, which can lead to important phenomenological consequences. A prime example is the threat that this poses to the viability of the Peccei-Quinn solution to the strong CP problem. In this paper, we explore the impact of wormholes as a source of global symmetry breaking by gravity. We review the current status of wormholes and global symmetries and note that, surprisingly, the axion has a quality problem within non-perturbative Einstein gravity. Although these wormholes lead to a large breaking of global symmetries, we show that th…
We study higher-form global symmetries and a higher-group structure of a low-energy limit of $(3+1)$-dimensional axion electrodynamics in a gapped phase described by a topological action. We argue that the higher-form symmetries should have a semi-strict 4-group (3-crossed module) structure by consistency conditions of couplings of the topological action to background gauge fields for the higher-form symmetries. We find possible 't Hooft anomalies for the 4-group global symmetry, and discuss physical consequences.
We explore the possibility that lepton family numbers and baryon number are such good symmetries of Nature because they are the global remnant of a spontaneously broken gauge symmetry. An almost arbitrary linear combination of these symmetries (together with a component of global hypercharge) can be consistently gauged, if the Standard Model (SM) fermion content is augmented by three chiral SM singlet states. Within this framework of $U(1)$ extensions of the SM one generically expects flavour non-universality to emerge in the charged leptons, in such a way that naturally prevents lepton flavou…
We consider extensions of the Standard Model in which a spontaneously broken global chiral Peccei-Quinn (PQ) symmetry arises as an accidental symmetry of an exact $Z_N$ symmetry. For $N = 9$ or $10$, this symmetry can protect the accion - the Nambu-Goldstone boson arising from the spontaneous breaking of the accidental PQ symmetry - against semi-classical gravity effects, thus suppressing gravitational corrections to the effective potential, while it can at the same time provide for the small explicit symmetry breaking term needed to make models with domain wall number $N_{\rm DW}>1$, such as …
We show that by introducing appropriate local $Z_N(N\geq13)$ symmetries in electroweak models it is possible to implement an automatic Peccei-Quinn symmetry keeping at the same time the axion protected against gravitational effects. Although we consider here only an extension of the standard model and a particular 3-3-1 model, the strategy can be used in any kind of electroweak model. An interesting feature of this 3-3-1 model is that if: {\it i)} we add right-handed neutrinos, {\it ii)} the conservation of the total lepton number, and {\it iii)} a $Z_2$ symmetry, the $Z_{13}$ and the chiral P…
We present a model of radiative neutrino mass that automatically contains an accidental $Z_2$ symmetry and thus provides a stable dark matter candidate. This allows a common framework for the origin of neutrino mass and dark matter without invoking any symmetries beyond those of the Standard Model. The model can be probed by direct-detection experiments and $μ\rightarrow e+γ$ searches, and predicts a charged scalar that can appear at the TeV scale, within reach of collider experiments.
We show that Peccei-Quinn and lepton number symmetries can be a natural outcome in a 3-3-1 model with right-handed neutrinos after imposing a Z_11 x Z_2 symmetry. This symmetry is suitably accommodated in this model when we augmented its spectrum by including merely one singlet scalar field. We work out the breaking of the Peccei-Quinn symmetry, yielding the axion, and study the phenomenological consequences. The main result of this work is that the solution to the strong CP problem can be implemented in a natural way, implying an invisible axion phenomenologically unconstrained, free of domai…
In this paper, axion models supplemented by leptoquarks and diquarks are systematically analyzed. Turning on some couplings to and among these latter states permits to unify the Peccei-Quinn symmetry with baryon (B) and lepton (L) numbers, such that the axion becomes associated to the spontaneous breaking of the three $U(1)$ symmetries. All possible four- and six-fermion patterns of B and L violation are discussed, including those inducing proton decay, with $ΔB = 1$ and $ΔL = \pm 1, \pm 3$, neutron-antineutron oscillations with $ΔB = 2$, and Majorana neutrino masses with $ΔL = 2$. Scenarios i…
A local flavour symmetry acting on the quarks of the Standard Model can automatically give rise to an accidental global $U(1)$ which remains preserved from sources of explicit breaking up to a large operator dimension, while it gets spontaneously broken together with the flavour symmetry. Such non-fundamental symmetries are often endowed with a mixed QCD anomaly, so that the strong CP problem is automatically solved via the axion mechanism. We illustrate the general features required to realise this scenario, and we discuss a simple construction based on the flavour group $SU(3)\times SU(2) \t…
To obtain natural inflation with large tensor-to-scalar ratio in string framework, we need a special moduli stabilization mechanism which can separate the masses of real and imaginary components of Kähler moduli at different scales, and achieve a trans-Planckian axion decay constant from sub-Planckian axion decay constants. In this work, we stabilize the matter fields by F-terms and the real components of Kähler moduli by D-terms of two anomalous $U(1)_X\times U(1)_A$ symmetries strongly at high scales, while the corresponding axions remain light due to their independence on the Fayet-Iliopoul…
