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Register a new userSolving local anomaly equations in gauge-rank extensions of the Standard Model
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We consider local (or perturbative) gauge anomalies in models which extend the rank of the Standard Model (SM) gauge group and the chiral fermion content only by $n$ SM singlets. We give a general solution to the anomaly cancellation conditions (ACCs) of an additional $U(1)$ subgroup for the ACCs that involve only SM fermions and we examine whether a corresponding solution exists for the remaining ACCs. We show that a solution to the remaining ACCs always exists for $n geq 5$ in the family non-universal case or $n geq 3$ in the family-universal case. In the special case where only a single family carries non-vanishing charges, we find a general solution to all ACCs, for any value of $n$.
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We show how one may classify all semisimple algebras containing the $mathfrak{su}(3)oplus mathfrak{su}(2) oplus mathfrak{u}(1)$ symmetry of the Standard Model and acting on some given matter sector, enabling theories beyond the Standard Model with unification (partial or total) of symmetries (gauge or global) to be catalogued. With just a single generation of Standard Model fermions plus a singlet neutrino, the only {gauge} symmetries correspond to the well-known algebras $mathfrak{su}(5),mathfrak{so}(10),$ and $mathfrak{su}(4)oplus mathfrak{su}(2) oplus mathfrak{su}(2)$, but with two or more generations a limited number of exotic symmetries mixing flavour, colour, and electroweak degrees of freedom become possible. We provide a complete catalogue in the case of 3 generations or fewer and outline how our method generalizes to cases with additional matter.
In any gauge extension of the standard model (SM) of quarks and leptons, there is a minimal set of fermion and scalar multiplets which encompasses all the particles and interactions of the SM. Included within this set, there may be a suitable dark-matter candidate. If not, one may still exist from the judicious addition of a simple fermion or scalar multiplet without any imposed symmetry. Some new examples of such predestined dark matter are discussed.
A recent series of works by M. Dubois-Violette, I. Todorov and S. Drenska characterised the SM gauge group GSM as the subgroup of SO(9) that, in the octonionic model of the later, preserves the split O=C+C3 of the space of octonions into a copy of the complex plane plus the rest. This description, however, proceeded via the exceptional Jordan algebras J3(O), J2(O) and and this sense remained indirect. One of the goals of this paper is to provide as explicit description as possible and also clarify the underlying geometry. The other goal is to emphasise the role played by different complex structures in the spaces O and O2. We provide a new characterisation of GSM: The group GSM is the subgroup of Spin(9) that commutes with of a certain complex structure J in the space O2 of Spin(9) spinors. The complex structure J is parametrised by a choice of a unit imaginary octonion. This characterisation of GSM is essentially octonionic in the sense that J is restrictive because octonions are non-associative. The quaternionic analog of J is the complex structure in the space H2 of Spin(5) spinors that commutes with all Spin(5) transformations.
The question of whether classically conformal modifications of the standard model are consistent with experimental obervations has recently been subject to renewed interest. The method of Gildener and Weinberg provides a natural framework for the study of the effective potential of the resulting multi-scalar standard model extensions. This approach relies on the assumption of the ordinary loop hierarchy $lambda_text{s} sim g^2_text{g}$ of scalar and gauge couplings. On the other hand, Andreassen, Frost and Schwartz recently argued that in the (single-scalar) standard model, gauge invariant results require the consistent scaling $lambda_text{s} sim g^4_text{g}$. In the present paper we contrast these two hierarchy assumptions and illustrate the differences in the phenomenological predictions of minimal conformal extensions of the standard model.
The Standard Model (SM) Higgs Lagrangian is straightforwardly rewritten into the {it scale-invariant} nonlinear sigma model $G/H=[SU(2)_L times SU(2)_R]/SU(2)_{V}simeq O(4)/O(3)$, with the (approximate) scale symmetry realized nonlinearly by the (pseudo) dilaton ($=$ SM Higgs). It is further gauge equivalent to that having the symmetry $O(4)_{rm global}times O(3)_{rm local}$, with $O(3)_{rm local}$ being the Hidden Local Symmetry (HLS). In the large $N$ limit of the scale-invariant version of the Grassmannian model $G/H=O(N)/[O(N-3)times O(3)] $ $simeq O(N)_{rm global}times [O(N-3)times O(3)]_{rm local}$, identical to the SM for $Nrightarrow 4$, we show that the kinetic term of the HLS gauge bosons (SM rho) $rho_mu$ of the $O(3)_{rm local}simeq [SU(2)_V]_{rm local}$ are dynamically generated by the nonperturbative dynamics of the SM itself. The dynamical SM rho stabilizes the skyrmion (SM skyrmion) $X_s$ as a dark matter candidate within the SM: The mass $M_{X_s} ={cal O}(10, {rm GeV})$ consistent with the direct search experiments implies the induced HLS gauge coupling $g_{_{rm HLS}}={cal O}(10^3)$, which realizes the relic abundance, $Omega_{X_s} h^2 ={cal O}(0.1)$. If instead $g_{_{rm HLS}}lesssim 3.5$ ($M_rho lesssim 1.2 $ TeV), the SM rho could be detected with narrow width $lesssim 100 ,{rm GeV}$ at LHC, having all the $a=2$ results of the generic HLS Lagrangian ${cal L}_A+ a {cal L}_V$, i.e., $rho$-universality, KSRF relations and the vector meson dominance, independently of $a$. There exists the second order phase phase transition to the unbroken phase having massless $rho_mu$ and massive $pi$ (no longer NG bosons), both becoming massless free particles just on the transition point (scale-invariant ultraviolet fixed point).The results readily apply to the 2-flavored QCD as well.
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