Symmergent Gravity, Seesawic New Physics, and their Experimental Signatures

The standard model of elementary particles (SM) suffers from various problems, such as power-law ultraviolet (UV) sensitivity, exclusion of general relativity (GR), and absence of a dark matter candidate. The LHC experiments, according to which the TeV domain appears to be empty of new particles, started sidelining TeV-scale SUSY and other known cures of the UV sensitivity. In search for a remedy, in this work, it is revealed that affine curvature can emerge in a way restoring gauge symmetries explicitly broken by the UV cutoff. This emergent curvature cures the UV sensitivity and incorporates GR as symmetry-restoring emergent gravity ({\it symmergent gravity}, in brief) if a new physics sector (NP) exists to generate the Planck scale and if SM+NP is fermi-bose balanced. This setup, carrying fingerprints of trans-Planckian SUSY, predicts that gravity is Einstein (no higher-curvature terms), cosmic/gamma rays can originate from heavy NP scalars, and the UV cutoff might take right value to suppress the cosmological constant (alleviating fine-tuning with SUSY). The NP does not have to couple to the SM. In fact, NP-SM coupling can take any value from zero to $\Lambda^2_{SM}/\Lambda^2_{NP}$ if the SM is not to jump from $\Lambda_{SM}\approx 500\, {\rm GeV}$ to the NP scale $\Lambda_{NP}$. The zero coupling, certifying an undetectable NP, agrees with all the collider and dark matter bounds at present. The {\it seesawic} bound $\Lambda^2_{SM}/\Lambda^2_{NP}$, directly verifiable at colliders, implies that: {\it (i)} dark matter must have a mass $\lesssim \Lambda_{SM}$, {\it (ii)} Higgs-curvature coupling must be $\approx 1.3\%$, {\it (iii)} the SM RGEs must remain nearly as in the SM, and {\it (iv)} right-handed neutrinos must have a mass $\lesssim 1000\, {\rm TeV}$. These signatures serve as a concise testbed for symmergence.Comment: 32 pages, 6 figures, 1 table. v3: Added a new section, new references and a figure; Reorganized sections; Journal versio

Effects of Curvature-Higgs Coupling on Electroweak Fine-Tuning

It is shown that, nonminimal coupling between the Standard Model (SM) Higgs field and spacetime curvature, present already at the renormalizable level, can be fine-tuned to stabilize the electroweak scale against power-law ultraviolet divergences. The nonminimal coupling acts as an extrinsic stabilizer with no effect on the loop structure of the SM, if gravity is classical. This novel fine-tuning scheme, which could also be interpreted within Sakharov's induced gravity approach, works neatly in extensions of the SM involving additional Higgs fields or singlet scalars.Comment: 11 pp. Added reference

Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm

In this paper, we study a method to sample from a target distribution $\pi$ over $\mathbb{R}^d$ having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler discretization of the overdamped Langevin stochastic differential equation associated with $\pi$. For both constant and decreasing step sizes in the Euler discretization, we obtain non-asymptotic bounds for the convergence to the target distribution $\pi$ in total variation distance. A particular attention is paid to the dependency on the dimension $d$, to demonstrate the applicability of this method in the high dimensional setting. These bounds improve and extend the results of (Dalalyan 2014)

High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm

We consider in this paper the problem of sampling a high-dimensional probability distribution $\pi$ having a density with respect to the Lebesgue measure on $\mathbb{R}^d$, known up to a normalization constant $x \mapsto \pi(x)= \mathrm{e}^{-U(x)}/\int_{\mathbb{R}^d} \mathrm{e}^{-U(y)} \mathrm{d} y$. Such problem naturally occurs for example in Bayesian inference and machine learning. Under the assumption that $U$ is continuously differentiable, $\nabla U$ is globally Lipschitz and $U$ is strongly convex, we obtain non-asymptotic bounds for the convergence to stationarity in Wasserstein distance of order $2$ and total variation distance of the sampling method based on the Euler discretization of the Langevin stochastic differential equation, for both constant and decreasing step sizes. The dependence on the dimension of the state space of these bounds is explicit. The convergence of an appropriately weighted empirical measure is also investigated and bounds for the mean square error and exponential deviation inequality are reported for functions which are measurable and bounded. An illustration to Bayesian inference for binary regression is presented to support our claims.Comment: Supplementary material available at https://hal.inria.fr/hal-01176084/. arXiv admin note: substantial text overlap with arXiv:1507.0502