Planck Scale Research Articles

Vacuum stability in the Standard Model with vectorlike fermions

The discovery of Standard-Model like Higgs at 125 GeV may raise more questions than the answers it provides. In particular, the hierarchy problem remains unsolved, and the Standard Model Higgs quartic self-coupling becomes negative below the Planck scale, necessitating new physics beyond the Standard Model. In this work we investigate a popular scenario, extensions of the Standard Model with vector-like fermion fields, such as the ones present in models with extra dimensions or in Higgs composite models, using a model independent approach. Since fermions decrease the Higgs quartic coupling at high energies, only exacerbating the self-coupling problem, we introduce first an additional scalar, which by itself is enough to overcome the vacuum stability limit, and then explore the effects of vector-like fermions in singlet, doublet and triplet representations. For each model, we identify the allowed fermion masses and mixing angles with the third family fermions required to satisfy the vacuum stability condition, and compare different representations. Allowed fermion masses emerge at around 1 TeV, raising hope that these will be found at the LHC. We also examine corrections to oblique parameters S and T from additional scalar and vector-like quarks which also impose constraints on mixing and mass splitting of both sectors., but these restrictions are relatively weak compared to the vacuum stability.

T Violation in Four Flavour Neutrino Oscillation in Planck Scale

The Planck scale effects have been studied in the four flavour, we discussthe Planck scale effects in the four flavour neutrino sector on the asymmetrybetween T-conjugate oscillation probabilities. ∆PT = P (να → νβ ) −P (νβ → να), for four flavor framework. In this paper, we also discusssome aspect of T violation effects in four flavor neutrino oscillation abovethe GUT scale.

Dimension-five baryon-number violation in low-scale Pati-Salam models

The gauge bosons of Pati-Salam do not mediate proton decay at the renormalisable level, and for this reason it is possible to construct scenarios in which $SU(4) \otimes SU(2)_{R}$ is broken at relatively low scales. In this Letter we show that such low-scale models generate dimension-5 operators that can give rise to nucleon decays at unacceptably large rates, even if the operators are suppressed by the Planck scale. We find an interesting complementarity between the nucleon-decay limits and the usual meson-decay constraints. Furthermore, we argue that these operators are generically present when the model is embedded into $SO(10)$, lowering the suppression scale. Under reasonable assumptions, the lower limit on the breaking scale can be constrained to be as high as $\mathcal{O}(10^{8})$ GeV.

Modified hybrid inflation, reheating, and stabilization of the electroweak vacuum

We propose a modification to the standard hybrid inflation model \cite{Linde:1993cn}, that connects a successful hybrid inflation scenario to the standard model Higgs sector, via the electroweak vacuum stability. The proposed model results in an effective inflation potential of a hilltop-type, with both the trans-Planckian and sub-Planckian inflation regimes consistent with the recent Planck/BICEP combined results. Reheating via the inflation sector decays to right-handed neutrinos is considered. An upper bound on the reheating temperature $T_{\rm R} \lsim 2\times 10^{11}~(1\times 10^{13})$ GeV, for large~(small) field inflation, will suppress contributions from one-loop quantum corrections to the inflation potential. This may push the neutrino Yukawa couplings to be ${\cal O}(1)$ and affect the vacuum stability. We show that the couplings of the SM Higgs to the inflation sector can guarantee the electroweak vacuum stability up to the Planck scale. The so-called hybrid Higgs-inflaton model leads to a positive correction for the Higgs quartic coupling at a threshold scale, which is shown to have a very significant effect in stabilizing the electroweak vacuum. We find that even with ${\cal O}(1)$ neutrino Yukawa couplings, threshold corrections leave the SM vacuum stability intact.

On the discrete version of the Kerr–Newman solution

This paper continues our work on black holes in the framework of the Regge calculus, where the discrete version (with a certain edge length scale [Formula: see text] proportional to the Planck scale) of the classical solution emerges as an optimal starting point for the perturbative expansion after functional integration over the connection, with the singularity resolved. An interest in the present discrete Kerr–Newman-type solution (with the parameter [Formula: see text]) may be to check the classical prediction that the electromagnetic contribution to the metric and curvature on the singularity ring is (infinitely) greater than the contribution of the [Formula: see text]-function-like mass distribution, no matter how small the electric charge is. Here, we encounter a kind of a discrete diagram technique, but with three-dimensional (static) diagrams and with only a few diagrams, although with modified (extended to complex coordinates) propagators. The metric (curvature) in the vicinity of the former singularity ring is considered. The electromagnetic contribution does indeed have a relative factor that is infinite at [Formula: see text], but, taking into account some existing estimates of the upper bound on the electric charge of known substances, it is not so large for habitual bodies and can only be significant for practically nonrotating black holes.

Are nonsingular black holes with super-Planckian hair ruled out by S2 star data?

We investigate a nonsingular black hole spacetime representing a strong deformation of the Schwarzschild solution with mass $M$ by an additional hair $\ensuremath{\ell}$, which may be hierarchically larger than the Planck scale. The spacetime is an exact solution of Einstein's equations sourced by an anisotropic fluid. The model presents a de Sitter core and $\mathcal{O}({\ensuremath{\ell}}^{2}/{r}^{2})$ slow-decaying corrections to the Schwarzschild solution. These solutions are thermodynamically preferred when $0.2\ensuremath{\lesssim}\ensuremath{\ell}/GM\ensuremath{\lesssim}0.3$ and are characterized by strong deviations in the orbits of test particles from the Schwarzschild case. In particular, we find corrections to the perihelion precession angle scaling linearly with $\ensuremath{\ell}$. We test our model using the available data for the orbits of the S2 star around ${\text{SgrA}}^{*}$. These data strongly constrain the value of the hair $\ensuremath{\ell}$, casting an upper bound on it of $\ensuremath{\sim}0.47GM$ but do not rule out the possible existence of regular black holes with super-Planckian hair.

Spin-2 Kaluza-Klein scattering in a stabilized warped background

Scattering amplitudes involving massive spin-2 particles typically grow rapidly with energy. In this paper we demonstrate that the anomalous high-energy growth of the scattering amplitudes cancel for the massive spin-2 Kaluza-Klein modes arising from compactified five-dimensional gravity in a stabilized warped geometry. Generalizing previous work, we show that the two sum rules which enforce the cancellations between the contributions to the scattering amplitudes coming from the exchange of the (massive) radion and those from the exchange of the tower of Goldberger-Wise scalar states (admixtures of the original gravitational and scalar fields of the theory) still persist in the case of the warping which would be required to produce the hierarchy between the weak and Planck scales in a Randall-Sundrum model. We provide an analytic proof of one combination of these generalized scalar sum rules and show how the sum rule depends on the Einstein equations determining the background geometry and the mode-equations and normalization of the tower of physical scalar states. Finally, we provide a consistent and self-contained derivation of the equations governing the physical scalar modes, and we list, in appendixes, the full set of sum rules ensuring proper high-energy growth of all $2\ensuremath{\rightarrow}2$ massive spin-2 scattering amplitudes.

The dark dimension and the Swampland

Motivated by principles from the Swampland program, which characterize requirements for a consistent UV completion of quantum gravity, combined with observational data, we are led to a unique corner of the quantum gravity landscape. In particular, using the Distance/Duality conjecture and the smallness of dark energy, we predict the existence of a light tower of states and a unique extra mesoscopic dimension of length lsim {Lambda}^{-frac{1}{4}}sim {10}^{-6}m , with extra massless fermions propagating on it. This automatically leads to a candidate for a tower of sterile neutrinos, and an associated active neutrino mass scale {m}_{nu}sim {leftlangle Hrightrangle}^2{Lambda}^{-frac{1}{12}}{M}_{textrm{pl}}^{-frac{2}{3}} . Moreover, assuming the mechanism for stabilization of this dark dimension leads to similar masses for active and sterile neutrinos we are led to the prediction of a Higgs vev leftlangle Hrightrangle sim {Lambda}^{frac{1}{6}}{M}_{textrm{pl}}^{frac{1}{3}} . Another prediction of the scenario is a species scale hat{M}sim {Lambda}^{frac{1}{12}}{M}_{textrm{pl}}^{frac{2}{3}}sim {10}^9hbox{--} {10}^{10} GeV, corresponding to the higher-dimensional Planck scale. This energy scale may be related to the resolution of the instability of the Higgs effective potential present at a scale of ~1011 GeV. We also speculate about the interplay between this energy scale and the GZK limit on ultra-high energy cosmic rays.

Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm

Horndeski gravity is a popular contender for a phenomenological model of dynamical dark energy, and as such subject to observational constraints. In this work, we ask whether Horndeski gravity can be more than a phenomenological model and instead become a fundamental theory, which extends towards high energy scales and includes quantum effects. We find that within the asymptotic-safety paradigm, an ultraviolet completion of a simple class of models of Horndeski gravity is achievable, but places strong constraints on the couplings of the theory. These constraints are not compatible with dynamical dark energy. Further, we find a similar result in an effective-field theory approach to this class of models of Horndeski gravity: under the assumption that there is no new strongly-coupled physics below the Planck scale, quantum gravity fluctuations force the Horndeski couplings to be too small to achieve an explanation of dynamical dark energy.

Majorana tower and cellular automaton interpretation of quantum mechanics down to Planck scales

A deterministic reformulation of quantum mechanics is thought to be able to bypass the usual philosophical interpretations of probability and stochasticity of the standard quantum mechanical scenarios. Recently ’t Hooft proposed a different perspective based on the ontological formulation of quantum mechanics, obtained by writing the Hamiltonian of a quantum system in a way to render it mathematically equivalent to a deterministic system. The ontological deterministic models consist of elementary cells, also called cellular automata, inside which the quantities describing the dynamics oscillate in periodic orbits, extending and replacing the quantum mechanical classical language based on harmonic oscillators. We show that the structure of the cellular automaton sets finds a clear physical interpretation with the Majorana infinite-component equation: the cellular automata are elementary building blocks generated by the Poincaré group of spacetime transformations with positive-definite energy down to the Planck scales, with a close relation to the Riemann Hypothesis.

Shaft inflation in Randall-Sundrum model

Shaft inflation is a model in which the inflaton potential approaches a plateau far from the origin, while it mimics chaotic inflation near the origin. Meanwhile, the Randall-Sundrum type II model (RSII) is an interesting extra-dimensional model to study cosmological phenomenology. In this paper, we study shaft inflation in the RSII model. We find that the predictions are in excellent agreement with observation. The fundamental five-dimensional Planck scale is found to be M 5 ≃ 1016 GeV, which is consistent with the lower bound M 5 ≳ 109 GeV obtained from experimental Newtonian gravitational bound. This is an important result that can be used to explore further the implications of extra dimension in other contexts.

Recent results from DEAP-3600

DEAP-3600 is the largest running dark matter detector filled with liquid argon, set at SNOLAB, in Sudbury, Canada, 2 km underground. The experiment holds the most stringent exclusion limit in argon for WIMPs above 20 GeV/c2. In the most recent published analysis, the background events due to α-induced scintillation in the neck of the detector limited the sensitivity. The sensitivity of the detector in the next WIMP search will be improved thanks to the decrease in backgrounds achieved by hardware upgrades and applying multivariate analyses. Moreover, the WIMP analysis has been revisited in terms of a non-relativistic effective field theory framework, and the impact of possible substructures in the galactic dark matter halo was explored. This analysis was motivated by the latest results from Gaia and the Sloan Sky Digital Survey. Here DEAP-3600 set the world’s best exclusion limit for xenon-phobic dark matter scenarios. Finally, a custom-developed analysis has recently pointed out the extraordinary sensitivity to ultra-heavy, multi-scattering dark matter candidates, resulting in world-leading exclusion limits on two composite dark matter candidates up to Planck scale masses. These proceedings, after a quick overview of the dark matter detection in DEAP-3600, outline the detector upgrades and the dark matter search results from the collaboration of the last three years.

Filament structure of random waves

We investigate the small-scale equidistribution properties of random waves, u, in . Numerical evidence suggests that such objects display a fine scale filament structure. We show that the x-ray of along any line segment is uniformly equidistributed. So any limiting behaviour must be weaker than L 2 scarring. On the other hand, we show that at Planck scale in phase space there are (with high probability) logarithmic fluctuations above what would be expected given equidistribution. Taken together these results suggest that the filament structure may be a configuration space echo of the phase-space concentrations.

Probing intermediate scale Froggatt-Nielsen models at future gravitational wave observatories

The flavor symmetry-breaking scale in the Froggatt-Nielsen (FN) mechanism is very weakly constrained by present experiments, and can lie anywhere from a few TeV to the Planck scale. We construct two minimal, non-supersymmetric, ultraviolet (UV) complete models that generate the FN mechanism, with a global $U(1)_{\rm{FN}}$ flavor symmetry and a single flavon field. Using the one-loop finite temperature effective potential, we explore the possibility of a strong first order phase transition (SFOPT) induced by the flavon. We show that if the flavor symmetry-breaking occurs at intermediate scales $\sim 10^4-10^7$ GeV, then in certain regions of the parameter space, the associated stochastic gravitational wave (GW) background is strong enough to be detected by second generation GW observatories such as the Big Bang Observer (BBO), the Deci-hertz interferometer Gravitational Observatory (DECIGO), the Cosmic Explorer (CE) and the Einstein Telescope (ET). We identify viable regions of the parameter space for the best detection prospects. While both models of flavor can produce a detectable GW background, the GW signature cannot be used to discriminate between them.

Disentangling the high- and low-cutoff scales via the trilinear Higgs couplings in the type-I two-Higgs-doublet model

The type-I two-Higgs-doublet model in the inverted Higgs scenario can retain the theoretical stability all the way up to the Planck scale. The Planck-cutoff scale, $\Lambda_{\rm cut}^{\rm Planck}$, directly impacts the mass spectra such that all the extra Higgs boson masses should be light below about 160 GeV. However, the observation of the light masses of new Higgs bosons does not indicate the high cutoff scale because a low cutoff scale can also accommodate the light masses. Over the viable parameter points that satisfy the theoretical requirements and the experimental constraints, we show that the trilinear Higgs couplings for low $\Lambda_{\rm cut}$ are entirely different from those for the Planck-cutoff scale. The most sensitive coupling to the cutoff scale is from the $h$-$h$-$h$ vertex, where $h$ is the lighter CP-even Higgs boson at a mass below 125 GeV. Among the multi-Higgs productions mediated by Higgs bosons, the gluon fusion processes of $gg \to h h $ and $gg \to AA$ are insensitive to the cutoff scale, yielding a small variation of $\mathcal{O}(1)\,{\rm fb}$ according to $\Lambda_{\rm cut}$. The smoking-gun signature is from the triple Higgs production of $q\bar{q}' \to W^* \to H^\pm hh$, which solely depends on the $h$-$h$-$h$ vertex. The cross section for $\Lambda_{\rm cut}=1\,{\rm TeV}$ is about $10^3$ times larger than that for the Planck-cutoff scale. Since the decay modes of $H^\pm \to W^* h/W^* A$ and $h/A \to bb$ are dominant, the process yields the $6b+\ell\nu$ final state, which enjoys an almost background-free environment. Consequently, the precision measurement of $pp \to H^\pm hh$ can probe the cutoff scale of the model.

Lorentz-covariant sampling theory for fields

Sampling theory is a discipline in communications engineering involved with the exact reconstruction of continuous signals from discrete sets of sample points. From a physics perspective, this is interesting in relation to the question of whether spacetime is continuous or discrete at the Planck scale, since in sampling theory we have functions which can be viewed as equivalently residing on a continuous or discrete space. Further, it is possible to formulate analogues of sampling which yield discreteness without disturbing underlying spacetime symmetries. In particular, there is a proposal for how this can be adapted for Minkowski spacetime. Here we will provide a detailed examination of the extension of sampling theory to this context. We will also discuss generally how spacetime symmetries manifest themselves in sampling theory, which at the surface seems in conflict with the fact that the discreteness of the sampling is not manifestly covariant. Specifically, we will show how the symmetry of a function space with a sampling property is equivalent to the existence of a family of possible sampling lattices related by the symmetry transformations.

Massive gravitino scattering amplitudes and the unitarity cutoff of the new Fayet-Iliopoulos terms

We compute the 2 → 2 gravitino scattering amplitudes at tree level in supergravity theories where supersymmetry is spontaneously broken. In the unitary gauge, the gravitino becomes massive (of mass m3/2) by absorbing the Goldstino, and the scattering amplitudes of its longitudinal polarisations grow with energy as {kappa}^2{E}^4/{m}_{3/2}^2 , signaling a potential breakdown of unitarity at a scale {Lambda}^2sim {m}_{3/2}/kappa sim {M}_{textrm{SUSY}}^2 . As we show explicitly in the Polonyi model, this leading term is cancelled by the contributions coming from the scalar partner of the Goldstino (sgoldstino), restoring perturbative unitarity up to the Planck scale. This is expected since supersymmetry is spontaneously broken, in analogy with the situation occuring in the Standard Model, where massive gauge bosons scattering preserves unitarity at high energy once we consider the contributions from the Higgs boson. However, when supersymmetry is broken by the new Fayet-Iliopoulos D-term, with ungauged R-symmetry, the above cancellation does not occur. In this case, the unbroken phase is singular and there is no contribution able to cancel the quartic divergences of the amplitudes, leading to a cutoff Λ ~ MSUSY where the effective theory breaks down. The same behaviour is obtained when supersymmetry is non-linearly realised.

How Quantum is Quantum Gravity?

Nature does not compartmentalize its happenings into different theories or disciplines. The theories are put forth by us to approximately understand the finer workings of nature. All theories are mere mathematical models built to understand nature. Any or all of them can be superseded by a better model or combination of models. The current paper analyses the formulation of Planck scale quantities, the workings of the temporal gauge, the concept of time other related fundamental issues. In particular, the paper points out that the force at the Planck scale is non-quantum.

Experimental test of noncommutative quantum gravity by VIP-2 Lead

Pauli exclusion principle (PEP) violations induced by space-time noncommutativity, a class of universality for several models of quantum gravity, are investigated by the VIP-2 Lead experiment at the Gran Sasso underground National Laboratory of INFN. The VIP-2 Lead experimental bound on the noncommutative space-time scale $\mathrm{\ensuremath{\Lambda}}$ excludes $\ensuremath{\theta}$-Poincar\'e far above the Planck scale for non anishing ``electriclike'' components of ${\ensuremath{\theta}}_{\ensuremath{\mu}\ensuremath{\nu}}$, and up to $6.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ Planck scales if they are null. Therefore, this new bound represents the tightest one so far provided by atomic transitions tests. This result strongly motivates high sensitivity underground x-ray measurements as critical tests of quantum gravity and of the very microscopic space-time structure.

On the Fine Structure and the Other Coupling Constants at the Planck Scale

It is shown that the fine structure constant at Planck times tends to one as well as those of the weak and strong interactions. This results by constraining them at the Planck force. That seems to provide interesting new results which confirm that at the beginning of space time (Planck scale) all fundamental forces converge to the same unit value.