Narrow Results

This paper reviews and updates the Standard Model prediction of the τ lepton g-2. Updated QED and electroweak contributions are presented, together with new values of the leading-order hadronic term, based on the recent low energy e⁺ e^- data from BaBar, CMD-2, KLOE and SND, and hadronic light-by-light contribution. The total prediction is confronted to the available experimental bounds on the τ lepton anomaly, and prospects for its future measurements are briefly discussed.

When performing a full calculation within the standard model (SM) or its extensions, it is crucial that one utilizes a consistent set of signs for the gauge couplings and gauge fields. Unfortunately, the literature is plagued with differing signs and notations. We present all SM Feynman rules, including ghosts, in a convention-independent notation, and we table the conventions in close to 40 books and reviews.

We continue the study undertaken in Ref. 16 of the exceptional Jordan algebra $J=J_3^8$ as (part of) the finite-dimensional quantum algebra in an almost classical space–time approach to particle physics. Along with reviewing known properties of $J$ and of the associated exceptional Lie groups we argue that the symmetry of the model can be deduced from the Borel–de Siebenthal theory of maximal connected subgroups of simple compact Lie groups.

The Composition Algebra-based Methodology (CAM) [B. Wolk, Pap. Phys.9, 090002 (2017); Phys. Scr.94, 025301 (2019); Adv. Appl. Clifford Algebras27, 3225 (2017); J. Appl. Math. Phys.6, 1537 (2018); Phys. Scr.94, 105301 (2019), Adv. Appl. Clifford Algebras30, 4 (2020)], which provides a new model for generating the interactions of the Standard Model, is geometrically modeled for the electromagnetic and weak interactions on the parallelizable sphere operator fiber bundle$B_n=(T𝕄,S^n\to {\mathcal{𝒮}}^n,SO(n+1),\pi )$ consisting of base space, the tangent bundle $T𝕄$ of space–time $𝕄$, projection operator $\pi$, the parallelizable spheres $S^n=\{S^1,S^3\}$ conceived as operator fibers $S^n\to {\mathcal{𝒮}}^n$ attaching to and operating on $T_p𝕄$$\forall p\in 𝕄$ as $p$ varies over $𝕄$, and as structure group, the norm-preserving symmetry group $SO(n+1)$ for each of the division algebras which is simultaneously the isometry group of the associated unit sphere. The massless electroweak $SU{(2)}_L\otimes U{(1)}_Y$ Lagrangian is shown to arise from $B_{3\otimes 1}$’s generation of a local coupling operation on sections of Dirac spinor and Clifford algebra bundles over $𝕄$. Importantly, CAM is shown to be a new genre of gauge theory which subsumes Yang–Mills Standard Model gauge theory. Local gauge symmetry is shown to be at its core a geometric phenomenon inherent to CAM gauge theory. Lastly, the higher-dimensional, topological architecture which generates CAM from within a unified eleven $(1,10)$-dimensional geometro-topological structure is introduced.

General Relativity (GR) and the Standard Model (SM) of particle physics are two enormously successful frameworks for our understanding the fundamental laws of nature. However, these theoretical schemes are widely disconnected, logically independent and unrelated in scope. Yet, GR and SM at some point must intersect, producing claims about phenomena that should be reconciled. Be it as it may, both schemes share a common basic ground: symmetry under local Lorentz transformations. Here, we will focus on the consequences of assuming this feature from the beginning to combine geometry, matter fields and gauge interactions. We give a rough description of how this could be instrumental for the construction of a unified scheme of gravitation and particle physics.

There must exist a reformulation of quantum field theory which does not refer to classical time. We propose a pre-quantum, pre-spacetime theory, which is a matrix-valued Lagrangian dynamics for gravity, Yang–Mills fields, and fermions. The definition of spin in this theory leads us to an eight-dimensional octonionic spacetime. The algebra of the octonions reveals the standard model; model parameters are determined by roots of the cubic characteristic equation of the exceptional Jordan algebra. We derive the asymptotic low-energy value 1/137 of the fine structure constant, and predict the existence of universally interacting spin one Lorentz bosons, which replace the hypothesised graviton. Gravity is not to be quantized, but is an emergent four-dimensional classical phenomenon, precipitated by the spontaneous localisation of highly entangled fermions.

The black hole information problem and the firewall problem can be addressed by assuming an extra local symmetry: conformal invariance. It must be an exact symmetry, spontaneously broken by the vacuum, in a way similar to the Brout–Englert–Higgs (BEH) mechanism. We note how this symmetry formally removes the horizon and the singularity inside black holes. For the Standard Model this symmetry is severely restrictive, demanding all coupling constants, masses and even the cosmological constant to be computable, in principle. Finally, this symmetry suggests that the Weyl action (the square of the Weyl curvature) should be added to the Einstein–Hilbert action. The ensuing indefinite metric states are briefly studied, and we conclude with some remarks concerning the interpretation of quantum mechanics.

In the history of cosmology physical paradoxes played important role for development of contemporary world models. Within the modern standard cosmological model there are both observational and conceptual cosmological paradoxes which stimulate to search their solution. Confrontation of theoretical predictions of the standard cosmological model with the latest astrophysical observational data is considered. A review of conceptual problems of the Friedmann space expending models, which are in the bases of modern cosmological model, is discussed. The main paradoxes, which are discussed in modern literature, are the Newtonian character of the exact Friedmann equation, the violation of the energy conservation within any comoving local volume, violation of the limiting recession velocity of galaxies for the observed high redshift objects. Possible observational tests of the nature of the cosmological redshift are discussed.

This is a pedagogical and self-contained review on obtaining electroweak precision constraints on TeV scale new physics using the effective theory method. We identify a set of relevant effective operators in the Standard Model and calculate from them corrections to all major electroweak precision observables. The corrections are compared with data to put constraints on the effective operators. Various approaches and applications in the literature are reviewed.

Recently, many discrepancies between the Standard Model (SM) predictions and experimental results have been found in $b\to c{l}^{-}{\bar{v}}_l$ quark transitions. Motivated by these discrepancies, we investigated the semileptonic $B_c\to {\eta }_c{\tau }^{-}{\bar{v}}_{\tau }$ decay in $W^{\prime }$ model. In this paper, we have estimated different decay observables such as branching ratio, lepton flavor universality (LFU) ratio $R_{{\eta }_c}$ and forward–backward asymmetry in the SM as well as in the $W^{\prime }$ model. In $W^{\prime }$ model, we find significant deviations from the SM for the observables except for the forward–backward asymmetry. This deviation gives us a possible indication of new physics (NP).

We continue the study of irreducible representations of the exceptional Lie superalgebra E(3,6). This is one of the two simple infinite-dimensional Lie superalgebras of vector fields which have a Lie algebra sℓ(3) × sℓ(2) × gℓ(1) as the zero degree component of its consistent ℤ-grading. We provide the classification of the singular vectors in the degenerate Verma modules over E(3,6), completing thereby the classification and construction of all irreducible E(3,6)-modules that are L₀-locally finite.

The current status of the muon anomalous magnetic moment is discussed. The leading order hadronic contribution is reevaluated based on the new data on e⁺e^- annihilation. The experimental value is about 3.3 standard deviations higher than the Standard Model prediction.

We consider the standard model with local scale invariance. The theory shows exact scale invariance of dimensionally regulated action. We show that massless gauge fields, which may be Abelian or non-Abelian, lead to vanishing contribution to the cosmological constant in this theory. This result follows in the quantum theory, to all orders in the gauge couplings. However, we have not considered contributions higher orders in the gravitational coupling. Similarly we also find that massless fermion fields yield null contribution to the cosmological constant. The effective cosmological constant in this theory is nonzero due to the phenomenon of cosmological symmetry breaking, which also gives masses to all the massive fields, besides generating the Planck mass. We find a simple relationship between the curvature scalar and the vacuum value of the Higgs field in the limit when we ignore all other contributions to the energy density besides the vacuum energy.

Several particles are not observed directly, but only through their decay products. We consider the possibility that they might be fakeons, i.e. fake particles, which mediate interactions but are not asymptotic states. A crucial role to determine the true nature of a particle is played by the imaginary parts of the one-loop radiative corrections, which are affected in nontrivial ways by the presence of fakeons in the loop. The knowledge we have today is sufficient to prove that most non-directly observed particles are true physical particles. However, in the case of the Higgs boson the possibility that it might be a fakeon remains open. The issue can be resolved by means of precision measurements in existing and future accelerators.

The contribution of one $W$ loop to the decay of the Higgs particle into two gammas is recalculated. Since this matrix element is finite in the standard model, it should be calculated in a straightforward way without artifacts such as regularization or ghosts. The result of the present calculation differs from the previous one, giving a Higgs decay rate smaller by a factor of 2 in the mass range of physical interest. In view of the results from the ATLAS Collaboration and the CMS Collaboration, this leads to possible far-reaching experimental consequences.

The decay of the Higgs particle into two photons through a $W$ loop was calculated in a straightforward way four years ago on the basis of the standard model. This calculation was carried out in the unitary gauge. Nevertheless, all attempts to reproduce this correct answer using the Feynman rules in the $R_1$ gauge, or the more general $R_{\xi }$ gauge, have failed. In this paper, a detailed analysis is carried out to compare the unitary gauge with the $R_{\xi }$ gauge; through this comparison, the underlying reason is determined why the answer cannot be obtained using the Feynman rules in the $R_{\xi }$ gauge.

This is the first example where the use of the Feynman rules in the $R_{\xi }$ gauge leads to an incorrect answer, and this incorrect answer cannot be ruled out by any simple argument such as gauge invariance. It means that great care must be exercised in using Feynman rules.

We review the approach to the Standard Model of particle interactions based on spectral noncommutative geometry. The paper is (nearly) self-contained and presents both the mathematical and phenomenological aspects. In particular, the bosonic spectral action and the fermionic action are discussed in detail, and how they lead to phenomenology. We also discuss the Euclidean versus Lorentz issues and how to go beyond the Standard Model in this framework.

In this paper, we briefly overview how, historically, string theory led theoretical physics first to precise problems in algebraic and differential geometry, and thence to computational geometry in the last decade or so, and now, in the last few years, to data science. Using the Calabi–Yau landscape — accumulated by the collaboration of physicists, mathematicians and computer scientists over the last four decades — as a starting-point and concrete playground, we review some recent progress in machine-learning applied to the sifting through of possible universes from compactification, as well as wider problems in geometrical engineering of quantum field theories. In parallel, we discuss the program in machine-learning mathematical structures and address the tantalizing question of how it helps doing mathematics, ranging from mathematical physics, to geometry, to representation theory, to combinatorics and to number theory.

We propose a modification of standard QCD description of the color triplet of quarks by introducing a 12-component color generalization of Dirac spinor, with built-in $Z_3$ grading playing an important algebraic role in quark confinement. In the “color Dirac equations” the $SU(3)$ color symmetry is entangled with the $Z_3$-graded generalization of Lorentz symmetry, containing three 6-parameter sectors related by $Z_3$-graded maps. The generalized Lorentz covariance requires simultaneous presence of 12 color Dirac multiplets, which lead to the description of all internal symmetries of quarks: besides $SU(3)\times SU(2)\times U(1)$, the flavor symmetries and three quark families. We also discuss the generalized gauge fields and show how the Standard Model content appears naturally due to the overall $Z_3\times Z_2\times Z_2$ symmetry.

The anomalous chromomagnetic dipole moment, with the gluon off-shell, of the Standard Model (SM) light quarks ($u$, $d$, $s$, $c$ and $b$), at the $Z$ gauge boson mass scale, is computed by using the $\overline{\mathrm{\text{MS}}}$ scheme. The numerical results disagree with all the previous predictions reported in the literature and show a discrepancy of up to two orders of magnitude in certain situations.