A closed clockwork theory: $\mathbb{Z}_2$ parity and more

arXiv (Cornell University), 2016

To be compatible with general relativity, every fundamental theory should be invariant under general coordinate transformations including spatial reflection. This paper describes an extension of the standard model in which the action is invariant under spatial reflection, and the vacuum spontaneously breaks parity by giving a mean value to a pseudoscalar field. This field and the scalar Higgs field make the gauge bosons, the known fermions, and a set of mirror fermions suitably massive while avoiding flavor-changing neutral currents. In the model, there is no strong-CP problem, there are no anomalies, fermion number (quark-plus-lepton number) is conserved, and heavy mirror fermions form heavy neutral mirror atoms which are dark-matter candidates. In models with extended gauge groups, nucleons slowly decay into pions, leptons, and neutrinos.

Physical Review D, 2014

In this work we discuss a new SU (3) C ⊗ SU (3) L ⊗ U (1) X ⊗ U (1) N (3-3-1-1) gauge model that overhauls the theoretical and phenomenological aspects of the known 3-3-1 models. Additionally, we sift the outcome of the 3-3-1-1 model from precise electroweak bounds to dark matter observables. We firstly advocate that if the B − L number is conserved as the electric charge, the extension of the standard model gauge symmetry to the 3-3-1-1 one provides a minimal, self-contained framework that unifies all the weak, electromagnetic and B − L interactions, apart from the strong interaction. The W-parity (similar to the R-parity) arises as a remnant subgroup of the broken 3-3-1-1 symmetry. The mass spectra of the scalar and gauge sectors are diagonalized when the scale of the 3-3-1-1 breaking is compatible to that of the ordinary 3-3-1 breaking. All the interactions of the gauge bosons with the fermions and scalars are obtained. The standard model Higgs (H) and gauge (Z) bosons are realized at the weak scales with consistent masses despite of their mixings with the heavier particles, respectively. The 3-3-1-1 model provides two dark matters which are stabilized by the W-parity conservation: one fermion which may be either a Majorana or Dirac fermion and one complex scalar. We conclude that in the fermion dark matter setup the Z 2 gauge boson resonance sets the dark matter observables, whereas in the scalar one the Higgs portal dictates them. The standard model GIM mechanism works in the model because of the W-parity conservation. Hence, the dangerous flavor changing neutral currents due to the ordinary and exotic quark mixing are suppressed, while those coming from the nonuniversal couplings of the Z 2 and Z N gauge bosons are easily evaded. Indeed, the K 0 −K 0 and B 0 s −B 0 s mixings limit m Z 2,N > 2.037 TeV and m Z 2,N > 2.291 TeV, respectively, while the LEPII searches provide a quite close bound m Z 2,N > 2.737 TeV. The violation of the CKM unitarity due to the loop effects of the Z 2 and Z N gauge bosons is negligible.

Physics Letters B, 2017

We discuss a non-supersymmetric scenario which addresses the origin of the matter-parity symmetry, P M = (−1) 3(B−L)+2s , leading to a viable Dirac fermion dark matter candidate. Implications to electroweak precision, muon anomalous magnetic moment, flavor changing interactions, lepton flavor violation, dark matter and collider physics are discussed in detail. We show that this non-supersymmetric model is capable of generating the matter-parity symmetry in agreement with existing data with gripping implications to particle physics and cosmology.

We provide the first details on the unexpected theoretical discovery of a spin-one-half matter field with mass dimension one. It is based upon a complete set of dual-helicity eigenspinors of the charge conjugation operator. Due to its unusual properties with respect to charge conjugation and parity, it belongs to a non-standard Wigner class. Consequently, the theory exhibits non- locality with (CP T )2^2 = − 1. We briefly discuss its relevance to the cosmological ‘horizon problem’. Because the introduced fermionic field is endowed with mass dimension one, it can carry a quartic self-interaction. Its dominant interaction with known forms of matter is via Higgs, and with gravity. This aspect leads us to contemplate the new fermion as a prime dark matter candidate. Taking this suggestion seriously we study a supernova-like explosion of a galactic-mass dark matter cloud to set limits on the mass of the new particle and present a calculation on relic abundance to constrain the relevant cross-section. The analysis favours light mass (roughly 20 MeV) and relevant cross-section of about 2 pb. Similarities and differences with the WIMP and mirror matter proposals for dark matter are enumerated. In a critique of the theory we reveal a hint on non-commutative aspects of spacetime, and energy–momentum space.

Physical Review D, 2021

We build rigorously the attractive five-dimensional model where bulk fermions propagate along the S 1 =Z 2 orbifold and interact with a Higgs boson localized at a fixed point of the extra dimension. The analytical calculation of the fermion mass spectrum and effective Yukawa couplings is shown to require the introduction of either essential boundary conditions (EBC) imposed by the model definition or certain bilinear brane terms (BBT) in the action, instead of the usual brane-Higgs regularizations. The obtained fermion profiles along the extra dimension turn out to undergo some discontinuities, in particular at the Higgs brane, which can be mathematically consistent if the action is well written with improper integrals. We also show that the Z 2 parity transformations in the bulk do not affect the fermion chiralities, masses and couplings, in contrast with the EBC and the BBT, but when extended to the fixed points, they can generate the chiral nature of the theory and even select the Standard Model chirality setup while fixing as well the fermion masses and couplings. Thanks to the strict analysis developed, the duality with the interval model is scrutinized.

International Journal of Quantum Foundations (ISSN 2375-4729), 2023

A codification of the internal degrees of freedom of the elementary fermions of the Standard Model is proposed in terms of overlapped triads of semiaxes in a three-dimensional Euclidean pre-space. The common orientation of these triads and the common length of their semiaxes in turn encode the fermion position in spacetime. The connection between the pre-spatial description of the fermion and its quantum description adopted by the Standard Model is established through a one-to-one correspondence between configurations of the system of triads and positional eigenstates of the fermion. The effect of the discrete symmetries C, P , T on triadic configurations in pre-space is discussed, and it is shown that the connection between the chirality of triads and ordinary space provides an intuitive explanation of the violation of parity in the weak interactions and of its conservation in the strong interactions.

2012

We present preliminary results for simulations of SO(4)-gauge theory with two Dirac Wilson fermions transforming according to the vector representation. We map out the phase diagram including the strong coupling bulk phase transition line as well as the zero PCAC-mass line. In addition, we measure the pseudo scalar and vector meson masses, and investigate whether the theory features chiral symmetry breaking. If the theory is used for breaking the electroweak symmetry dynamically it is the orthogonal group equivalent of the Minimal Walking Technicolor model but with the following distinctive features: a] It provides a natural complex weak isotriplet of Goldstone bosons of which the neutral component can be identified with a light composite dark matter state; b] It is expected to break the global symmetry spontaneously; c] It is free from fermionic composite states made by a techniglue and a technifermion.

Journal of High Energy Physics, 2007

We show that a recently constructed five-dimensional (5D) model with gauge-Higgs unification and explicit Lorentz symmetry breaking in the bulk, provides a natural dark matter candidate. This is the lightest Kaluza-Klein particle odd under a certain discrete Z2 symmetry, which has been introduced to improve the naturalness of the model, and resembles KK-parity but is less constraining. The dark matter

Physical Review D, 2019

We generalize the clockwork theory in several directions. First, we consider beyond nearest neighbors interactions. Considering such interactions keeps a larger subgroup of the original U(1) N +1 unbroken and can allow for different symmetry breaking patterns. We recover the original clockwork scenario in the presence of these additional interactions. In such case, the masses of the massive modes change, but a single massless mode remains intact. Such interactions are naturally interpreted as higher derivative terms from the point of view of extra dimensions. Second, we generalize the clockwork shift symmetry to non-abelian global groups. Third, trivial embedding of the clockwork scenario in supergravity, yields an AdS minimum as big as the clockwork interaction. Specifically, the clockwork is connected to the cosmological constant. We analyze the different ways in which a Minkowski supersymmetric minimum can be constructed, and demonstrate simple SUSY breaking mechanisms that preserve or break the clockwork symmetry. We show that the clockwork direction is actually a special SUSY breaking direction, that does not require the inclusion of additional fields or parameters. Fourth, we review the extra-dimensional origin of the mechanism and interpretation, in the case of conformal coupling to gravity.

Physical Review Letters, 2022