Search

The CDF II measurement of $W$ boson mass is at significant ($6.9\,\sigma$) tension with the Standard Model, and moderate ($4.0\,\sigma$) tension with recent results from ATLAS. Any attempt to interpret this as a signature of new physics requires high-precision, robust, falsifiable predictions. The Classical Analogue to the Standard Model In pseudo-Riemannian spacetime (CASMIR) is an analogue model predicting $W$ and $Z$ boson masses of $80.3587(22)~\mathrm{GeV}/c^2$ and $91.1877(35)~\mathrm{GeV}/c^2$ respectively. During baryon collisions satisfying $\sqrt{s}< 3.09~\mathrm{TeV}$, CASMIR predicts a color-mediated enhancement of $W$ and $Z$ boson masses, becoming $80.4340(22)~\mathrm{GeV}/c^2$ and $91.1922(35)~\mathrm{GeV}/c^2$ respectively. The unenhanced masses are consistent with ATLAS data collected at $\sqrt{s}=7~\mathrm{TeV}$, and the enhanced masses are consistent with CDF II data collected at $\sqrt{s}=1.96~\mathrm{TeV}$. According to CASMIR, operation of the LHC at centre-of-mass energies small compared with $3.09~\mathrm{TeV}$ but large enough for $W$ boson formation should permit ATLAS to replicate the result from CDF II., Comment: 44 pages, 6 figures. Added discussion of effects on $W$ and $Z$ boson emission cross-sections. Updated calculated Higgs mass in Appendix A

This paper continues the study of quasiparticles on complex manifolds with anticommuting co-ordinates, and shows that on increasing the dimensionality of the complex manifold from $\mathbb{C}^{\wedge 2}$ to $\mathbb{C}^{\wedge 6}$, the dimension-$L^{-1/2}$ spinor excitations in the associated effective field theory on $\mathbb{R}^{1,3}$ acquire an $\mathrm{SU}(3)$ colour charge and assemble into composite spinors of dimension $L^{-3/2}$. This model provides a novel environment in which to study colour confinement, while also demonstrating the ability of the first member of the $\mathbb{C}^{\wedge 6\mathfrak{n}}$ series to support fermions having spin and dimensions consistent with the Standard Model., Comment: 22 pages. Updated to align with revisions to colour sector in Chapters 3-8

Quasiparticles and analog models are ubiquitous in the study of physical systems. Little has been written about quasiparticles on manifolds with anticommuting co-ordinates, yet they are capable of emulating a surprising range of physical phenomena. This paper introduces a classical model of free fields on a manifold with anticommuting co-ordinates, identifies the region of superspace which the model inhabits, and shows that the model emulates the behaviour of a five-species interacting quantum field theory on $\mathbb{R}^{1,3}$. The Lagrangian of this model arises entirely from the anticommutation property of the manifold co-ordinates. This is part one of a series, which continues in arXiv:2108.07719 and arXiv:0805.3819, and concludes in arXiv:2008.05893 with a first-principles calculation of the value of the gravitational constant in the classical analogue model., Comment: 58 pages, 1 figure. Updated Overview (including numerical results) and cross-references to align with revisions to Chapters 3-8

The $\mathbb{C}^{\wedge 18}$ analogue model contains counterparts to the particle spectrum and interactions of the Standard Model, and has only three tunable parameters. As the structure of this model is highly constrained, predictive relationships between constants may be obtained. In Chapters 4-6, the masses of the tau, the $W$ and $Z$ bosons, and a Higgs-like scalar boson are calculated as functions of $\alpha$, $m_e$, and $m_\mu$. They are shown to be $1.776867413(43)$ GeV/$c^2$, $80.3587(22)$ GeV/$c^2$, $91.1877(35)$ GeV/$c^2$, and $125.1261(48)$ GeV/$c^2$ respectively, with no free fitting parameters. All are within $0.1\,\sigma$ of the observed values of $1.77686(12)$ GeV/$c^2$, $80.360(16)$ GeV/$c^2$, $91.1876(21)$ GeV/$c^2$, and $125.11(11)$ GeV/$c^2$ respectively. In Chapter 7 the final ungauged freedom of the $\mathbb{C}^{\wedge 18}$ model is used to eliminate the right-handed weak interaction, while simultaneously introducing space-time curvature and a gravitational interaction emulating general relativity. The value of Newton's constant is then calculated from $\alpha$, $m_e$, and $m_\mu$, yielding $G_N=6.67426(230)\times 10^{-11}~\mathrm{m}^3\mathrm{kg}^{-1}\mathrm{s}^{-2}$, which is in agreement with the observed value of $G_N=6.67430(15)\times 10^{-11}~\mathrm{m}^3\mathrm{kg}^{-1}\mathrm{s}^{-2}$ with tension less than $0.1\,\sigma_\mathrm{exp}$. This persistent consistency with experiment suggests the existence of a unifying relationship between lepton generations, gravitation, and the electroweak mass scale. In the Classical Analogue to the Standard Model this unification arises from an underlying construction from coloured preons, with the low-energy residuals of the preon binding interactions corresponding to the strong nuclear force., Comment: 201 pages, 46 figures. Updated calculation of Higgs boson mass (0.1% correction; Secs. 5:3.3 & 6:4.5). Added some initial discussion of Higgs interactions in CASMIR (Ch. 11)

We extend the formalism of entanglement renormalization to the study of boundary critical phenomena. The multi-scale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum critical ground states. Here we show that, by adding a boundary to the scale invariant MERA, an accurate approximation to the critical ground state of an infinite chain with a boundary is obtained, from which one can extract boundary scaling operators and their scaling dimensions. Our construction, valid for arbitrary critical systems, produces an effective chain with explicit separation of energy scales that relates to Wilson's RG formulation of the Kondo problem. We test the approach by studying the quantum critical Ising model with free and fixed boundary conditions., Comment: 8 pages, 12 figures, for a related work see arXiv:0912.2893

There exist two popular energy-momentum tensors for an electromagnetic wave in a dielectric medium. The Abraham expression is robust to experimental verification but more mathematically demanding, while the Minkowski expression is the foundation of a number of simplifications commonly found within the literature, including the relative refractive index transformation often used in modelling optical tweezers. These simplifications are based on neglecting the Minkowski tensor's material counterpart, a process known to be incompatible with conservation of angular momentum, and in conflict with experimental results, yet they are very successful in a wide range of circumstances. This paper combines existing constraints on their usage with recent theoretical analysis to obtain a list of conditions which much be satisfied to safely use the simplified Minkowski approach. Applying these conditions to an experiment proposed by Padgett et al., we find their prediction in agreement with that obtained using the total energy-momentum tensor., Comment: 8 pages, RevTeX 4. Removed an erroneous factor of mu/mu_0 from Eq.(1)

The $\mathbb{C}^{\wedge 2\mathfrak{n}}$ models are analogue models which generate Lagrangians for quasiparticles on $\mathbb{R}^{1,3}$ from antisymmetric vector products on Grassmann manifolds. This paper introduces $\mathbb{C}^{\wedge 18}$, the smallest member of this series which is capable of hosting a quasiparticle spectrum analogous to the Standard Model. Once all gaugeable degrees of freedom have been fixed, the particle spectrum of $\mathbb{C}^{\wedge 18}$ is seen to resemble the Standard Model plus two additional weakly interacting bosons and a ninth gluon., Comment: 46 pages, 6 figures. Added brief discussion of the strength of the strong interaction in Sec. 3:3.5.7

As part of a study of teacher effectiveness and job satisfaction, a research team interviewed 85 elementary and secondary classroom teachers in 5 school districts in the San Francisco (California) Bay Area to gather teachers' perspectives on administrative leadership. Teachers portrayed effective principals as creating environments around the classroom that minimize uncertainty and maintain a positive atmosphere. The principal's role thus focuses neither on inspiring effective teaching nor on proposing innovations, but on limiting the factors that impede the teacher's own abilities to teach effectively. This view of the principal's role conforms neither to the research-based vision of the principal as a somewhat powerless middle manager nor to the view in the effective schools literature of the principal as actively involved in classroom affairs. Focusing on the needs of a varied staff in a given school requires principals to provide leadership based on problem-solving rather than on conformity to research-generated prescriptions. Agreement among teachers and principals on the principal's role will enhance the potential for concerted efforts at school improvement. (PGD)

Prior research has documented the failure of both staff development and teacher evaluation practices in schools to serve as sources of accountability and improvement for teachers. Few districts coordinate these two aspects of a human resource management system. Using a concept of organizational control, this study employs a qualitative methodology involving elite interviews and document inspection to investigate the experiences of four school districts engaged in a process of evaluation reform. The function of staff development as a mechanism of input control is explored, and the impact on evaluation outcomes is examined. Each district used staff development resources to address the beliefs, attitudes, and skill levels of teachers and administrators that have impeded effective evaluation in the past. The availability of developmental resources that supported evaluative feedback so that teachers could act on the results appeared to be crucial to success. Teacher evaluation, approached in this manner, expands on traditional notions of accountability and improvement that focus on the poor or marginal teacher. Maintenance of effective classroom performance becomes a legitimate goal of evaluation. These tentative findings suggest that a single teacher evaluation system, properly conceived, may be able to simultaneously serve as a source of accountability and improvement for teachers. An appendix describes the methodology employed in the study. (Author/PN)