Diphotons, New Vacuum Angles, and Strong CP

The Standard Model contains a well-understood, natural, spin-0 diphoton resonance: the $\pi^0$. Numerous studies have pointed out that the hint of a new diphoton resonance at 750 GeV could be a pion analog, identified with the pseudo-Nambu-Goldstone boson of a chiral symmetry spontaneously broken by new strong dynamics at the TeV scale. These "hypercolor" models are generically expected to violate parity through a topological angle $\tilde\theta$. We discuss the physics of $\tilde\theta$ and its impact on the phenomenology of the new sector. We also describe some of the theoretical implications of a nonzero $\tilde\theta$. In particular, $\tilde\theta$ can generate an ${\cal O}(1)$ threshold correction to the QCD vacuum angle $\theta$ near the TeV scale, sharply constraining ultraviolet solutions to the strong CP problem. Alternatively, finding that $\tilde\theta$ is small may be interpreted as evidence in favor of UV solutions to strong CP, particularly those based on spontaneously broken P or CP symmetries.Comment: 23 pages, 6 figures. v2: references added, fig 1 update

A Noninformative Prior on a Space of Distribution Functions

In a given problem, the Bayesian statistical paradigm requires the specification of a prior distribution that quantifies relevant information about the unknowns of main interest external to the data. In cases where little such information is available, the problem under study may possess an invariance under a transformation group that encodes a lack of information, leading to a unique prior---this idea was explored at length by E.T. Jaynes. Previous successful examples have included location-scale invariance under linear transformation, multiplicative invariance of the rate at which events in a counting process are observed, and the derivation of the Haldane prior for a Bernoulli success probability. In this paper we show that this method can be extended, by generalizing Jaynes, in two ways: (1) to yield families of approximately invariant priors, and (2) to the infinite-dimensional setting, yielding families of priors on spaces of distribution functions. Our results can be used to describe conditions under which a particular Dirichlet Process posterior arises from an optimal Bayesian analysis, in the sense that invariances in the prior and likelihood lead to one and only one posterior distribution

Diphotons from Tetraphotons in the Decay of a 125 GeV Higgs at the LHC

Recently the ATLAS and CMS experiments have presented data hinting at the presence of a Higgs boson at $m_h\simeq125$ GeV. The best-fit $h\rightarrow\gamma\gamma$ rate averaged over the two experiments is approximately $2.1\pm0.5$ times the Standard Model prediction. We study the possibility that the excess relative to the Standard Model is due to $h\rightarrow aa$ decays, where $a$ is a light pseudoscalar that decays predominantly into $\gamma\gamma$. Although this process yields $4\gamma$ final states, if the pseudoscalar has a mass of the order tens of MeV, the two photons from each $a$ decay can be so highly collimated that they may be identified as a single photon. Some fraction of the events then contribute to an effective $h\rightarrow\gamma\gamma$ signal. We study the constraints on the parameter space where the net $h\rightarrow\gamma\gamma$ rate is enhanced over the Standard Model by this mechanism and describe some simple models that give rise to the pseudoscalar-photon interaction. Further tests and prospects for searches in the near future are discussed.Comment: 14 pages, 7 figures, revtex4-1; v2: references added and rearranged, g-2 limit improved, published version; v3: typos correcte

A Tale of Two Populations: The Contribution of Merger and Secular Processes to the Evolution of Active Galactic Nuclei

Due to the co-evolution of supermassive black holes and their host galaxies, understanding the mechanisms that trigger active galactic nuclei (AGN) are imperative to understanding galaxy evolution and the formation of massive galaxies. It is observationally difficult to determine the trigger of a given AGN due to the difference between the AGN lifetime and triggering timescales. Here, we utilize AGN population synthesis modeling to determine the importance of different AGN triggering mechanisms. An AGN population model is computed by combining an observationally motivated AGN triggering rate and a theoretical AGN light curve. The free parameters of the AGN light curve are constrained by minimizing a \chi squared test with respect to the observed AGN hard X-ray luminosity function. The observed black hole space density, AGN number counts, and X-ray background spectrum are also considered as observational constraints. It is found that major mergers are not able to account for the entire AGN population. Therefore, non-merger processes, such as secular mechanisms, must also trigger AGN. Indeed, non-merger processes are the dominant AGN triggering mechanism at z \lesssim 1--1.5. Furthermore, the shape and evolution of the black hole mass function of AGN triggered by major mergers is intrinsically different from the shape and evolution of the black hole mass function of AGN triggered by secular processes.Comment: Accepted Ap

Power-Expected-Posterior Priors for Variable Selection in Gaussian Linear Models

In the context of the expected-posterior prior (EPP) approach to Bayesian variable selection in linear models, we combine ideas from power-prior and unit-information-prior methodologies to simultaneously produce a minimally-informative prior and diminish the effect of training samples. The result is that in practice our power-expected-posterior (PEP) methodology is sufficiently insensitive to the size n* of the training sample, due to PEP's unit-information construction, that one may take n* equal to the full-data sample size n and dispense with training samples altogether. In this paper we focus on Gaussian linear models and develop our method under two different baseline prior choices: the independence Jeffreys (or reference) prior, yielding the J-PEP posterior, and the Zellner g-prior, leading to Z-PEP. We find that, under the reference baseline prior, the asymptotics of PEP Bayes factors are equivalent to those of Schwartz's BIC criterion, ensuring consistency of the PEP approach to model selection. We compare the performance of our method, in simulation studies and a real example involving prediction of air-pollutant concentrations from meteorological covariates, with that of a variety of previously-defined variants on Bayes factors for objective variable selection. Our prior, due to its unit-information structure, leads to a variable-selection procedure that (1) is systematically more parsimonious than the basic EPP with minimal training sample, while sacrificing no desirable performance characteristics to achieve this parsimony; (2) is robust to the size of the training sample, thus enjoying the advantages described above arising from the avoidance of training samples altogether; and (3) identifies maximum-a-posteriori models that achieve good out-of-sample predictive performance