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We respond to the criticism raised in the paper arXiv:1704.07831.
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The clockwork mechanism has recently been proposed as a natural way to generate hierarchies among parameters in quantum field theories. The mechanism is characterized by a very specific pattern of spontaneous and explicit symmetry breaking, and the presence of new light states referred to as `gears. In this paper we begin by investigating the self-interactions of these gears in a scalar clockwork model and find a parity-like selection rule at all orders in the fields. We then proceed to investigate how the clockwork mechanism can be realized in 5D linear dilaton models from the spontaneous symmetry breaking of a complex bulk scalar field. We also discuss how the clockwork mechanism is manifest in the scalar components of 5D gauge theories in the linear dilaton model, and build their 4D deconstructed analogue. Finally we discuss attempts at building both 4D and 5D realizations of a non-abelian scalar clockwork mechanism, where in the latter we consider scenarios in which the Goldstone bosons arise from 5D scalar and 5D gauge fields.
Inspired by our recent paper reshuffled SIMP dark matter, we notice that the reaction rate of the two-loop induced $2 to 2$ process may dominate over or be comparable with that of the $3 to 2$ process at the chemical freezeout of Co-SIMP dark matter [Phys. Rev. Lett. 125, 131301 (2020)], especially when the Co-SIMP mass is close to the standard model particle mass (called the edge case). To check our point, we then derive the Boltzmann equation with all relevant annihilation cross sections in an electrophilic model and numerically solve it to obtain the cosmological evolution of Co-SIMP dark matter. Our result shows that the two-loop induced $2 to 2$ process does modify the parameter space of the coupling for the edge case in the Co-SIMP mechanism and has to be taken into account in UV completion models.
We comment on the paper Feynman Effective Classical Potential in the Schrodinger Formulation[Phys. Rev. Lett. 81, 3303 (1998)]. We show that the results in this paper about the time evolution of a wave packet in a double well potential can be properly explained by resorting to a variational principle for the effective action. A way to improve on these results is also discussed.
We introduce a set of clockwork models of flavor that can naturally explain the large hierarchies of the Standard Model quark masses and mixing angles. Since the clockwork only contains chains of new vector-like fermions without any other dynamical fields, the flavor constraints allow for relatively light new physics scale. For two benchmarks with gear masses just above 1 TeV, allowed by flavor constraints, we discuss the collider searches and the possible ways of reconstructing gear spectra at the LHC. We also examine the similarities and differences with the other common solutions to the SM flavor puzzle, i.e., with the Froggatt-Nielsen models, where we identify a new {it clockworked } version, and with the Randall-Sundrum models.
We present a pedagogical overview of the nonperturbative mechanism that endows gluons with a dynamical mass. This analysis is performed based on pure Yang-Mills theories in the Landau gauge, within the theoretical framework that emerges from the combination of the pinch technique with the background field method. In particular, we concentrate on the Schwinger-Dyson equation satisfied by the gluon propagator and examine the necessary conditions for obtaining finite solutions within the infrared region. The role of seagull diagrams receives particular attention, as do the identities that enforce the cancellation of all potential quadratic divergences. We stress the necessity of introducing nonperturbative massless poles in the fully dressed vertices of the theory in order to trigger the Schwinger mechanism, and explain in detail the instrumental role of these poles in maintaining the Becchi-Rouet-Stora-Tyutin symmetry at every step of the mass-generating procedure. The dynamical equation governing the evolution of the gluon mass is derived, and its solutions are determined numerically following implementation of a set of simplifying assumptions. The obtained mass function is positive definite, and exhibits a power law running that is consistent with general arguments based on the operator product expansion in the ultraviolet region. A possible connection between confinement and the presence of an inflection point in the gluon propagator is briefly discussed.
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