B-anomalies from flavorful U(1)$$'$$ extensions, safely

Abstract$$U(1)^\prime $$ U ( 1 ) ′ extensions of the standard model with generation-dependent couplings to quarks and leptons are investigated as an explanation of anomalies in rare B-decays, with an emphasis on stability and predictivity up to the Planck scale. To these ends, we introduce three generations of vector-like standard model singlet fermions, an enlarged, flavorful scalar sector, and, possibly, right-handed neutrinos, all suitably charged under the $$U(1)^\prime $$ U ( 1 ) ′ gauge interaction. We identify several gauge-anomaly free benchmarks consistent with $$B_s$$ B s -mixing constraints, with hints for electron-muon universality violation, and the global $$b \rightarrow s$$ b → s fit. We further investigate the complete two-loop running of gauge, Yukawa and quartic couplings up to the Planck scale to constrain low-energy parameters and enhance the predictive power. A characteristic of models is that the $$Z^\prime $$ Z ′ with TeV-ish mass predominantly decays to invisibles, i.e. new fermions or neutrinos. $$Z^\prime $$ Z ′ -production can be studied at a future muon collider. While benchmarks feature predominantly left-handed couplings $$C_9^{\mu }$$ C 9 μ and $$C_{10}^{\mu }$$ C 10 μ , right-handed ones can be accommodated as well.

On Gauge Invariance of the Bosonic Measure in Chiral Gauge Theories

Gauge invariance of the measure associated with the gauge field is usually taken for granted, in a general gauge theory. We furnish a proof of this invariance, within Fujikawa’s approach. To stress the importance of this fact, we briefly review gauge anomaly cancellation as a consequence of gauge invariance of the bosonic measure and compare this cancellation to usual results from algebraic renormalization, showing that there are no potential inconsistencies. Then, using a path integral argument, we show that a possible Jacobian for the gauge transformation has to be the identity operator, in the physical Hilbert space. We extend the argument to the complete Hilbert space by a direct calculation.

Ambitwistor strings in six and five dimensions

Ambitwistor strings are chiral (holomorphic) strings whose target is the space of complex null geodesics, ambitwistor space. We introduce twistor representations of ambitwistor space in 6 and 5 dimensions. In 6d the twistor representation is naturally conformally invariant. Anomaly cancellation leads to models that describe biadjoint scalar amplitudes and certain conformally invariant gauge and gravity theories, respectively of 4th and 6th order. There are three such models, reflecting triality for the conformal group SO(8) associated to these 6d models. On reduction to five dimensions, gauge anomaly cancellation requires supersymmetry and the resulting models describe maximally supersymmetric Yang-Mills and gravity. The twistor representation of these ambitwistor strings lead to formulæ for maximally supersymmetric gauge and gravity amplitudes based on the polarized scattering equations in 5d, found earlier by the first two authors.

A note on gauge anomaly cancellation in effective field theories

The conditions for the absence of gauge anomalies in effective field theories (EFT) are rivisited. General results from the cohomology of the BRST operator do not prevent potential anomalies arising from the non-renormalizable sector, when the gauge group is not semi-simple, like in the Standard Model EFT (SMEFT). By considering a simple explicit model that mimics the SMEFT properties, we compute the anomaly in the regularized theory, including a complete set of dimension six operators. We show that the dependence of the anomaly on the non-renormalizable part can be removed by adding a local counterterm to the theory. As a result the condition for gauge anomaly cancellation is completely controlled by the charge assignment of the fermion sector, as in the renormalizable theory.

Masses and electric charges: gauge anomalies and anomalous thresholds

We work out in the forward limit and up to order $$e^6$$ e 6 in perturbation theory the collinear divergences. In this kinematical regime we discover new collinear divergences that we argue can be only cancelled using quantum interference with processes contributing to the gauge anomaly. This rules out the possibility of a quantum consistent and anomaly free theory with massless charges and long range interactions. We use the anomalous threshold singularities to derive a gravitational lower bound on the mass of the lightest charged fermion.

Analysis of an SU(8) model with a spin-1 2 field directly coupled to a gauged Rarita–Schwinger spin-3 2 field

In earlier work we analyzed an abelianized model in which a gauged Rarita–Schwinger spin-[Formula: see text] field is directly coupled to a spin-[Formula: see text] field. Here, we extend this analysis to the gauged [Formula: see text] model for which the abelianized model was a simplified substitute. We calculate the gauge anomaly, show that anomaly cancellation requires adding an additional left chiral representation [Formula: see text] spin-[Formula: see text] fermion to the original fermion complement of the [Formula: see text] model, and give options for restoring boson–fermion balance. We conclude with a summary of attractive features of the reformulated [Formula: see text] model, including a possible connection to the [Formula: see text] root lattice.

Status of a minimal composite Higgs theory

We analyze three sets of gauge ensembles in our extended physics program of a particularly important BSM gauge theory with a fermion doublet in the two-index symmetric (sextet) representation of the SU(3) BSM color gauge group. Our investigations include chiral symmetry breaking [Formula: see text] in the p-regime and [Formula: see text]-regime, the mass of the composite [Formula: see text] scalar, resonance spectroscopy, new physics from gauge anomaly constraints, and the role of stable sextet BSM baryons with Electroweak interactions in dark matter searches. Important new goals include studies of the [Formula: see text] scalar entangled with Goldstone dynamics in the p-regime and the [Formula: see text]-regime, the resonance spectrum with particular attention to emerging LHC signals, like recent hints for diphoton excess at 750 GeV or diboson anomalies in the 2 TeV range. All results reported here are preliminary before journal publication including some post-conference material for the discussion.