Particle Physics

Recently, an intriguing connection between the exceptional Jordan algebra h_3(O) and the standard model of particle physics was noticed by Dubois-Violette and Todorov (with further interpretation by Baez). How do the standard model fermions fit into this story? I will explain how they may be neatly incorporated by complexifying h_3(O) or, relatedly, by passing from RxO to CxO in the so-called "magic square" of normed division algebras. This, in turn, suggests that the standard model, with gauge group SU(3)xSU(2)xU(1), is embedded in a left/right-symmetric theory, with gauge group SU(3)xSU(2)xSU(2)xU(1). This theory is not only experimentally viable, but offers some explanatory advantages over the standard model (including an elegant solution to the standard model's "strong CP problem"). Ramond's formulation of the magic square, based on triality, provides further insights, and possible hints about where to go next.

The Muon g-2 experiment at Fermilab has recently confirmed Brookhaven's earlier measurement of the muon anomalous magnetic moment aμ. This new result increases the discrepancy Δaμ with the Standard Model (SM) prediction and strengthens its "new physics" interpretation as well as the quest for its underlying origin. In this talk I will review the SM prediction of the muon g-2, focusing on some of the latest developments, and discuss the connection of the discrepancy Δaμ to precision electroweak predictions via their common dependence on hadronic vacuum polarization effects.

This talk will be about two applications of Jordan algebras. The first, to quantum mechanics, follows on from the talk of John Baez. I will explain how time dependence makes use of the associator, and how this is related to the commutator in the standard density matrix formulation. The associator of a Jordan algebra also determines the curvature of a Riemannian metric on its positive cone, invariant under the symmetry group of the norm (mentioned in the talk of John Baez); the cone is foliated by hypersurfaces of constant norm. This geometry is relevant to a class of N=2 5D supergravity theories (from the early 1980s) which arise (in some cases, at least) from Calabi-Yau compactification of 11D supergravity. The 5D interactions are determined by the structure constants of a euclidean Jordan algebra with cubic norm. The exceptional JA of 3x3 octonionic matrices yields an ``exceptional’’ 5D supergravity which yields, on reduction to 4D, an ``exceptional’’ N=2 supergravity with many similarities to N=8 supergravity, such as a non-compact global E7 symmetry. However, it has a compact `composite’ E6 gauge invariance (in contrast to the SU(8) of N=8 supergravity). An old speculation is that non-perturbative effects break the N=2 supersymmetry and cause the E6 gauge potentials to become the dynamical fields of an E6 GUT. Potentially (albeit improbably) this provides a connection between M-theory, the exceptional Jordan algebra, and the Standard Model.

I will take a look at the SO(10) grand unified theories from the perspective of the typical phenomenology constraints imposed on their structure. The current status of the minimal potentially realistic models will be briefly commented upon.

It is known that constraints imposed by causality and unitarity of four-particle scattering amplitudes lead to non-trivial requirements on the low energy effective field theory coefficients. We introduce families of linear and nonlinear inequalities resulting from a systematic study of positive geometry structure hidden in those constraints.

 

 

The fermionic fields of one generation of the Standard Model, including the Lorentz spinor degrees of freedom, can be identified with components of a single real 64-dimensional semi-spinor representation S of the group Spin(11,3). I will describe an octonionic model for Spin(11,3) in which the semi-spinor representation gets identified with S=OxO', where O,O' are the usual and split octonions respectively. It is then well-known that choosing a unit imaginary octonion u in Im(O) equips O with a complex structure J. Similarly, choosing a unit imaginary split octonion u' in Im(O') equips O' with a complex structure J', except that there are now two inequivalent complex structures, one parametrised by a choice of a timelike and the other of a spacelike unit u'. In either case, the identification S=OxO' implies that there are two natural commuting complex structures J, J' on S. Our main new observation is that there is a choice of J,J' so that the subgroup of Spin(11,3) that commutes with both is the direct product SU(3)xU(1)xSU(2)_LxSU(2)_R x Spin(1,3) of the group of the left/right symmetric extension of the SM and Lorentz group. The splitting of S into eigenspaces of J corresponds to splitting into particles and anti-particles. The splitting of S into eigenspaces of J' corresponds to splitting of Lorentz Dirac spinors into two different chiralities.

The dark photon is a well-motivated extension of the Standard Model which can mix with the regular photon. This mixing is enhanced whenever the dark photon mass matches the primordial plasma frequency, leading to resonant conversions between photons and dark photons. These conversions can produce observable cosmological signatures, including distortions to the cosmic radiation background. In this talk, I will discuss a new analytic formalism for these conversions that can account for the inhomogeneous distribution of matter in our universe, leading to new and revised limits on the mixing parameter of light dark photons derived from the COBE/FIRAS measurement of the cosmic microwave background spectrum. I will then describe some ongoing work on a dark sector model that can explain the longstanding ARCADE radio background excess through resonant conversions of dark photons.

Dubois-Violette and Todorov have shown that the Standard Model gauge group can be constructed using the exceptional Jordan algebra, consisting of 3×3 self-adjoint matrices of octonions. After an introduction to the physics of Jordan algebras, we ponder the meaning of their construction. For example, it implies that the Standard Model gauge group consists of the symmetries of an octonionic qutrit that restrict to symmetries of an octonionic qubit and preserve all the structure arising from a choice of unit imaginary octonion. It also sheds light on why the Standard Model gauge group acts on 10d Euclidean space, or Minkowski spacetime, while preserving a 4+6 splitting.

Far-infrared spectroscopy can reveal secrets of galaxy evolution and heavy-element enrichment throughout cosmic time, and astronomers worldwide are designing cryogenic space telescopes for far-IR spectroscopy. The most challenging aspect is a far-IR detector which is both exquisitely sensitive (limited by the zodiacal-light noise in a narrow band (lambda/delta lambda ~1000)) and array able to tens of thousands of pixels. The quantum capacitance detector (QCD) being developed at MDL, is a 50mK device adapted from quantum computing applications in which photon-produced free electrons in a superconductor tunnel into a small capacitive island embedded in a resonant circuit. The QCD has optically-measured noise equivalent power (NEP) of 2x10-20 W Hz-1/2 at 1.5THz under 10-19W of optical loading, making it the most sensitive far-IR detector ever demonstrated. The QCD has further demonstrated individual far-IR photon counting, confirming the exquisite sensitivity and suitability for cryogenic space astrophysics. In this lecture, the development of the Quantum Capacitance detector will be highlighted, from inception through proof of concept devices, culminating with the demonstration of single photon detection. Current development efforts will be discussed.

 

40 years trying to go beyond the Standard Model hasn't yet led to any clear success. As an alternative, we could try to understand why the Standard Model is the way it is. In this talk we review some lessons from grand unified theories and also from recent work using the octonions. The gauge group of the Standard Model and its representation on one generation of fermions arises naturally from a process that involves splitting 10d Euclidean space into 4+6 dimensions, but also from a process that involves splitting 10d Minkowski spacetime into 4d Minkowski space and 6 spacelike dimensions. We explain both these approaches, and how to reconcile them.

In this talk I will discuss the application of the so-called “consistency relations” for large scale structures to the study of primordial non-Gaussianities of the local f_NL type. I will first introduce the consistency relations themselves, commenting on some important aspects and underlying assumptions. I will then verify them (and their violation) using N-body simulations for the matter density in the Universe. This proves consistency relations to be a promising tool to apply in the forthcoming large scale structures surveys. I will conclude describing some work in progress aimed at finding a practical recipe to constrain f_NL from these relations.