We discuss the Higgs mass and cosmological constant in the context of an emergent Standard Model, where the gauge symmetries "dissolve" in the extreme ultraviolet. In this scenario the cosmological constant scale is suppressed by power of the large scale of emergence and expected to be of similar size to neutrino masses. Cosmology constraints then give an anthropic upper bound on the Higgs mass.
Hadron properties and interactions are emergent from QCD. Atomic and condensed matter physics are emergent from QED. Could the local gauge symmetries of particle physics also be emergent? We give an introduction to this question and recent ideas connecting it to the (meta)stability of the Standard Model Higgs vacuum. With an emergent Standard Model the gauge symmetries would "dissolve" in the ultraviolet. This scenario differs from unification models which exhibit maximum symmetry in the extreme ultraviolet. With emergence, new global symmetry violations would appear in higher dimensional oper…
Gauge symmetries play an essential role in determining the interactions of particle physics. Where do they come from? Might the gauge symmetries of the Standard Model unify in the ultraviolet or might they be emergent in the infrared, below some large scale close to the Planck scale? Emergent gauge symmetries are important in quantum many-body systems in quantum phases associated with long range entanglement and topological order, e.g., they arise in high temperature superconductors, with string-net condensation and in the A-phase of superfluid He-3. String-nets and superfluid He-3 exhibit eme…
We investigate origin of three features that are often assumed in analysis of two-Higgs doublet models: (i) softly broken Z2 symmetry, (ii) CP invariant Higgs potential, and (iii) degenerated mass spectra. We extend electroweak gauge symmetry, introducing extra gauge symmetry and extra scalars, and we show that our models effectively derive two-Higgs dou- blet models at low energy which naturally hold the three features. We also find that the models can solve the strong CP problem.
Quintessential inflation provides a unified description of inflation and dark energy in terms of a single scalar degree of freedom, the cosmon. We present here a comprehensive overview of this appealing paradigm, highlighting its key ingredients and keeping a reasonable and homogeneous level of details. After summarizing the cosmological evolution in a simple canonical case, we discuss how quintessential inflation can be embedded in a more general scalar-tensor formulation and its relation to variable gravity scenarios. Particular emphasis is placed on the role played by symmetries. In particu…
We address emergent higher-form symmetry in Higgs phases with superfluidity. The emergent symmetry appears if a matter field is invariant under a transformation of a common subgroup of gauge and global $\mathrm{U}(1)$ symmetries. We explicitly construct the symmetry generator that is topological and gauge invariant in a low-energy effective theory. Such emergent symmetry is helpful to distinguish the Higgs and other phases with superfluidity, such as phases of QCD at finite density. We also discuss the possibility of phase transition between these phases.
We show how, using multipartite entanglement, the symmetries among bosons and fermions of the Standard Model of particle physics emerge. Fermions belong to tripartite maximally entangled classes starting with basic chiral right and left states. Quarks and leptons belong to different classes, with only leptons appearing as asymptotic states in three space dimensions. The Higgs boson is the scalar mode with a nonvanishing vacuum expectation value, other bosons are as usual linked to symmetry generators.
We explain how an $SU(2)_R$ R-symmetry allows alignment of the vacuum expectation value and the mass eigenstates in the Higgs bosons squared-mass matrix. More important, we discuss how our parametrization of the breaking of this global symmetry allows to quantitatively apprehend the diverse sources of misalignment, which are kept, by supersymmetry, small.
The Higgs mechanism well describes the electroweak symmetry breaking in nature. We consider a possibility that the microscopic origin of the Higgs field is UV physics of QCD. We construct a UV complete model of a higher dimensional Yang-Mills theory as a deformation of a deconstructed (2,0) theory in six dimensions, and couple the top and bottom (s)quarks to it. We see that the Higgs fields appear as magnetic degrees of freedom. The model can naturally explain the masses of the Higgs boson and the top quark. The rho meson-like resonances with masses such as 1 TeV are predicted.
We consider and derive the gravitational soft theorem up to the sub-subleading power from the perspective of effective Lagrangians. The emergent soft gauge symmetries of the effective Lagrangian provide a transparent explanation of why soft graviton emission is universal to sub-subleading power, but gauge boson emission is not. They also suggest a physical interpretation of the form of the soft factors in terms of the charges related to the soft transformations and the kinematics of the multipole expansion. The derivation is done directly at Lagrangian level, resulting in an operatorial form o…
Hidden theories coupled to the SM may provide emergent (dark) vectors, that are composites/bound-states of the hidden fields. This is motivated by paradigms emerging from the AdS/CFT correspondence but it is a more general phenomenon. We explore the general setup and find that UV interactions among currents or charged fields give rise to emergent vectors in the IR. We study the general properties of such vectors and argue that they can be generically different from fundamental dark photons that have been studied so far.
Entanglement suppression in the strong interaction $S$-matrix is shown to be correlated with approximate spin-flavor symmetries that are observed in low-energy baryon interactions, the Wigner $SU(4)$ symmetry for two flavors and an $SU(16)$ symmetry for three flavors. We conjecture that dynamical entanglement suppression is a property of the strong interactions in the infrared, giving rise to these emergent symmetries and providing powerful constraints on the nature of nuclear and hypernuclear forces in dense matter.
We consider the Higgs sector of multi-Higgs-doublet models in the presence of simple symmetries relating the various fields. We construct basis invariant observables which may in principle be used to detect these symmetries for any number of doublets. A categorization of the symmetries into classes is required, which we perform in detail for the case of two and three Higgs doublets.
We derive the complete set of continuous maximal symmetries for Standard Model (SM) alignment that may occur in the tree-level scalar potential of multi-Higgs Doublet Models, with $n > 2$ Higgs doublets. Our results generalize the symmetries of SM alignment, without decoupling of large mass scales or fine-tuning, previously obtained in the context of two-Higgs Doublet Models.
We catalogue and study three-Higgs-doublet models in terms of all possible allowed symmetries (continuous and discrete, Abelian and non-Abelian), where such symmetries may be identified as flavour symmetries of quarks and leptons. We analyse the potential in each case, and derive the conditions under which the vacuum alignments (0,0,v), (0,v,v) and (v,v,v) are minima of the potential. For the alignment (0,0,v), relevant for dark matter models, we calculate the corresponding physical Higgs boson mass spectrum. Motivated by supersymmetry, we extend the analysis to the case of three up-type Higgs…
The new phenomenon of symbiotic symmetries is described in the context of the Two-Higgs-Doublet Model (THDM). The quartic potential has two or more separate sectors with unequal symmetries, but these unequal symmetries persist even though the different sectors are renormalized by one another. We discuss all such symmetries of the THDM, consistent with the SU(2) x U(1) gauge interactions, using the Pauli formalism.
The exact alignment of the Yukawa structures on multi-Higgs doublet models provides cancellation of tree-level flavour changing couplings of neutral scalar fields. We show that family symmetries can provide a suitable justification for the Yukawa alignment.
Within multi-Higgs-doublet models, one can impose symmetries on the Higgs potential, either discrete or continuous, that mix several doublets. In two-Higgs-doublet model any such symmetry can be conserved or spontaneously violated after the electroweak symmetry breaking (EWSB), depending on the coefficients of the potential. With more than two doublets, there exist symmetries which are always spontaneously violated after EWSB. We discuss the origin of this phenomenon and show its similarity to geometric frustration in condensed-matter physics.
In all scalar extensions of the standard model of particle interactions, the one Higgs boson responsible for electroweak symmetry breaking always mixes with other neutral scalars at tree level unless a symmetry prevents it. An unexplored important option is that the mixing may be radiative, and thus guaranteed to be small. Two first such examples are discussed. One is based on the soft breaking of the discrete symmetry $Z_3$. The other starts with the non-Abelian discrete symmetry $A_4$ which is then softly broken to $Z_3$, and results in the emergence of an interesting dark-matter candidate t…
We report the recent progress in understanding of symmetries which can be implemented in the scalar sector of electroweak symmetry breaking models with several Higgs doublets. In particular we present the list of finite reparametrization symmetry groups which can appear in the three-Higgs-doublet models.
We consider the impact of imposing generalized CP symmetries on the Higgs sector of the two-Higgs-doublet model, and identify three classes of symmetries. Two of these classes constrain the scalar potential parameters to an exceptional region of parameter space which respects either a Z_2 discrete flavor symmetry or a U(1) symmetry. We exhibit a basis-invariant quantity that distinguishes between these two possible symmetries. We also show that the consequences of imposing these two classes of CP symmetry can be achieved by combining Higgs Family symmetries, and that this is not possible for t…
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…
We discuss the Higgs mass and cosmological constant hierarchy puzzles with emphasis on the interplay of Poincare invariance, mass generation and renormalization group invariance. A plausible explanation involves an emergent Standard Model with the cosmological constant scale suppressed by power of the large scale of emergence. In this scenario the cosmological constant scale and neutrino masses should be of similar size.
After elimination of the redundant variables, gauge theories may still exhibit symmetries associated with the gauge fields. The role of these residual gauge symmetries is discussed within the Abelian Higgs model and the Georgi-Glashow model. In the different phases of these models, these symmetries are realized differently. The characteristics of emergence and disappearance of the symmetries are studied in detail and the implications for the dynamics in Coulomb, Higgs, and confining phases are discussed.
The low energy effective theory ($\sim$ TeV) of the little-Higgs model with $SU(6)/Sp(6)$, as proposed by Low, Skiba and Smith (LSS), exhibits a two-Higgs doublet model (2HDM) structure. The symmetry dictates interesting Yukawa patterns, translating to non-trivial fermion couplings with both of the Higgs doublets. The couplings of the scalars with the fermions can induce flavor changing neutral currents (FCNC), which get constraints from flavor physics observables such as BR$(B\rightarrow X_sγ)$, $B_s - \bar{B}_s$ mixing etc. The precision measurement of $Z b \bar{b}$ vertex, the top and Higgs…
We discuss the implications of global symmetries on the radiative corrections to the Higgs sector. We focus on two examples: the charged Higgs mass in the minimal supersymmetric model and the Higgs couplings to vector boson pairs. In the first case, we find that in the absence of squark mixing a global SU(2)$\times$SU(2) symmetry protects the charged Higgs mass from corrections of ${\cal O}(g^2m^4_t/m^2_W)$. In the second case, it is the {\it custodial} symmetry which plays an analogous role in constraining the fermion-mass dependence of the radiative corrections.
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…
A general method for classifying the possible quark models of a multi-Higgs-doublet model, in the presence of Abelian symmetries, is presented. All the possible sets of textures that can be present in a given sector are shown, thus turning the determination of the flavor models into a combinatorial problem. Several symmetry implementations are studied for two and three Higgs doublet models. Some models implementations are explored in great detail, with a particular emphasis on models known as Branco-Grimus-Lavoura and nearest-neighbour-nnteraction. Several considerations on the flavor changing…
We discuss the classification of symmetries and the corresponding symmetry groups in the two-Higgs-doublet model (THDM). We give an easily useable method how to determine the symmetry class and corresponding symmetry group of a given THDM Higgs potential. One of the symmetry classes corresponds to a Higgs potential with several simultaneous generalised CP symmetries. Extending the CP symmetry of this class to the Yukawa sector in a straightforward way, the so-called maximally-CP-symmetric model (MCPM) is obtained. We study the evolution of the quartic Higgs-potential parameters under a change …
We show in this Letter how a new hidden gauge symmetry responsible for neutrino mass as well as dark matter (DM) in the Universe can be discovered through scalar mediators responsible for breaking the new symmetry. The new force mediator ($Z'$) may be lighter than the Standard Model (SM) gauge bosons but cannot be observed in traditional searches for new gauge bosons. We highlight a novel way of discovering such a symmetry at the Large Hadron Collider (LHC) by incorporating an existing ATLAS analysis on four lepton final states which include the Higgs resonance. In addition, we show that the h…
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.
Classifying the symmetries of the scalar sector in multi-Higgs-doublet models is the main focus of this thesis. We have found certain symmetries that are always broken in models with more than two doublets, which we name "frustrated symmetries". In the attempt towards the classification of possible symmetries in the scalar sector of the NHDM, we find that these symmetry groups are either subgroups of the maximal torus, or certain finite Abelian groups which are not subgroups of maximal tori. For the subgroups of the maximal torus, we present an algorithmic strategy that gives the full list of …
We continue our analysis of the general N-Higgs-doublet model and focus of the Higgs potential description in the space of gauge orbits. We develop a geometric technique that allows us to study the global minimum of the potential without explicitly finding its position. We discuss symmetry patterns of the NHDM potential, and illustrate the general discussion with various specific variants of the three-Higgs-doublet model.
In theories with extra dimensions the Standard Model Higgs field can be identified with the internal components of higher-dimensional gauge fields (Higgs-gauge unification). The higher-dimensional gauge symmetry prevents the Higgs mass from quadratic divergences, but at the fixed points of the orbifold this symmetry is broken and divergences can arise if U(1) subgroups are conserved. We show that another symmetry, remnant of the internal rotation group after orbifold projection, can avoid the generation of such divergences.
We analyze the compatibility between abelian symmetries acting in two different sectors of a theory using the Smith Normal Form method. We focus on N-Higgs-doublet models (NHDMs) and on the compatibility between symmetries in the Higgs potential and in the Yukawa interactions, which were separately analyzed previous works. It is shown that two equal (isomorphic) symmetry groups that act in two separate sectors are not necessarily compatible in the whole theory and an upper bound is found for the size of the group that can be implemented in the entire NHDM. We also develop useful techniques to …
We continue to explore the consequences of the recently discovered Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. Here, we focus on the vacuum properties. The search for extrema of the Higgs potential is reformulated in terms of 3-quadrics in the 3+1-dimensional Minkowski space. We prove that 2HDM cannot have more than two local minima in the orbit space and that a twice-degenerate minimum can arise only via spontaneous violation of a discrete symmetry of the Higgs potential. Investigating topology of the 3-quadrics, we give concise criteria for existence of n…
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.
A large class of two- and three-Higgs-doublet models with discrete symmetries has been employed in the literature to address various aspects of flavor physics. We analyse how the precision measurement of the Higgs to diphoton signal strength would severely constrain these scenarios due to the nondecoupling behavior of the charged scalars, to the extent that the number of additional scalar doublets can be constrained no matter how heavy the nonstandard scalars are. We demonstrate that if the scalar potential is endowed with appropriate global continuous symmetries together with soft breaking pa…
We demonstrate how residual flavour symmetries, infrared signatures of symmetry breaking in complete models of flavour, can naturally forbid (or limit in a flavour specific way) flavour-changing neutral currents (FCNC) in multi-Higgs-doublet models (MHDM) without using mass hierarchies. We first review how this model-independent mechanism can control the fermionic mixing patterns of the Standard Model, and then implement the symmetries in the Yukawa sector of MHDM, which allows us to intimately connect the predictivity of a given flavour model with its ability to sequester FCNC. Finally, after…
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 classify all possible implementations of an abelian symmetry in the two-Higgs-doublet model with fermions. We identify those symmetries which are consistent with non-vanishing quark masses and a CKM matrix which is not block-diagonal. Our analysis takes us from a plethora of possibilities down to 246 relevant cases, requiring only 34 distinct matrix forms. We show that applying Z_n with n \geq 4 to the scalar sector leads to a continuous U(1) symmetry in the whole Lagrangian. Finally, we address the possibilities of spontaneous CP violation and of natural suppression of the flavour changing…
Strangeness was discovered roughly seventy years ago, lodged in a particle now known as the kaon, $K$. Kindred to the pion, $π$; both states are massless in the absence of Higgs-boson couplings. Kaons and pions are Nature's most fundamental Nambu-Goldstone modes. Their properties are largely determined by the mechanisms responsible for emergent mass in the standard model, but modulations applied by the Higgs are crucial to Universe evolution. Despite their importance, little is known empirically about $K$ and $π$ structure. This study delivers the first parameter-free predictions for all $K$ d…
N-Higgs-doublet models (NHDM) are among the most popular examples of electroweak symmetry breaking mechanisms beyond the Standard Model. Discrete symmetries imposed on the NHDM scalar potential play a pivotal role in shaping the phenomenology of the model, and various symmetry groups have been studied so far. However, in spite of all efforts, the classification of finite Higgs-family symmetry groups realizable in NHDM for any N>2 is still missing. Here, we solve this problem for the three-Higgs-doublet model by making use of Burnside's theorem and other results from pure finite group theory wh…
Using a four fermion interaction Lagrangian, we demonstrate that the spontaneous breaking of vector symmetries requires the existence of a light (comparing with the heavy fermion mass) scalar particle and the low energy effective theory (the $σ$ model) obtained after integrating out heavy fermion degrees of freedom is asymptotically a renormalizable one. When applying the idea to the electroweak symmetry breaking sector of the standard model, the Higgs particle's mass is of the order of the electroweak scale: $185 GeV /\sqrt{N_c} < m_H < 720 GeV /\sqrt{N_c}$ where $N_c$ is the color degrees of…
Classifying symmetry groups which can be implemented in the scalar sector of a model with $N$ Higgs doublets is a difficult and an unsolved task for $N>2$. Here, we make the first step towards this goal by classifying the Abelian symmetry groups. We describe a strategy that identifies all Abelian groups which can be realized as symmetry groups of the NHDM scalar potential. We give examples of the use of this strategy in 3HDM and 4HDM and prove several statements for arbitrary $N$.
Topology effects have being extensively studied and confirmed in strongly correlated condensed matter physics. In the large color number limit of QCD, baryons can be regarded as topological objects -- skyrmions -- and the baryonic matter can be regarded as a skyrmion matter. We review in this paper the generalized effective field theory for dense compact-star matter constructed with the robust inputs obtained from the skyrmion approach to dense nuclear matter, relying to possible ``emergent" scale and local flavor symmetries at high density. All nuclear matter properties from the saturation de…
Models addressing the naturalness of a light Higgs boson typically employ symmetries, either bosonic or fermionic, to stabilize the Higgs mass. We consider a setup with the minimal amount of symmetries: four shift symmetries acting on the four components of the Higgs doublet, subject to the constraints of linearly realized SU(2)xU(1) electroweak symmetry. Up to terms that explicitly violate the shift symmetries, the effective lagrangian can be derived, irrespective of the spontaneously broken group G in the ultraviolet, and is universal in all models where the Higgs arises as a pseudo-Nambu-Go…
We perform a systematic study of generic accidental Higgs-family and CP symmetries that could occur in the two-Higgs-doublet-model potential, based on a Majorana scalar-field formalism which realizes a subgroup of GL(8,C). We derive the general conditions of convexity and stability of the scalar potential and present analytical solutions for two non-zero neutral vacuum expectation values of the Higgs doublets for a typical set of six symmetries, in terms of the gauge-invariant parameters of the theory. By means of a homotopy-group analysis, we identify the topological defects associated with t…
The existence of maximal and minimal mixing angles in the neutrino mixing matrix motivates the search for extensions to the Standard Model that may explain these angles. A previous study (C.I.Low and R.R.Volkas, Phys.Rev.D68,033007(2003)), began a systematic search to find the minimal extension to the Standard Model that explains these mixing angles. It was found that in the minimal extensions to the Standard Model which allow neutrino oscillations, discrete unbroken lepton family symmetries only generate neutrino mixing matrices that are ruled out by experiment. This paper continues the searc…
So far the null results from axion searches have enforced a huge hierarchy between the Peccei-Quinn and electroweak symmetry breaking scales. Then the inevitable Higgs portal poses a large fine tuning on the standard model Higgs scalar. Now we find if the Peccei-Quinn global symmetry has a set of residually discrete symmetries, these global and discrete symmetries can achieve a chain breaking at low scales such as the accessible TeV scale. This novel mechanism can accommodate some new phenomena including a sizable coupling of the standard model Higgs boson to the axion.
It might be expected that only global symmetries are fundamental symmetries of Nature, whereas local symmetries and associated massless gauge fields could solely emerge due to spontaneous breaking of underlying spacetime symmetries involved, such as relativistic invariance and supersymmetry. This breaking, taken in the form of the nonlinear sigma-model type pattern for vector fields or superfields, puts essential restrictions on geometrical degrees of freedom of a physical field system that makes it to adjust itself in such a way that its global internal symmetry G turns into the local symmetr…
Tree-level accidental symmetries are known to play a fundamental role in the phenomenology of the Standard Model (SM) for electroweak interactions. So far, no significant deviations from the theory have been observed in precision, flavour and collider physics. Consequently, these global symmetries are expected to remain quite efficient in any attempt beyond the SM. Yet, they do not forbid rather unorthodox phenomena within the reach of current LHC experiments. This is illustrated with a vectophobic Two-Higgs-Doublet-Model (2HDM) where effects of a light, flavour-violating and custodian (pseudo…
