arXiv subjects

Joe Davighi

Publications and source records attributed to Joe Davighi.

48 records · Page 3Linked to original sources

arXiv2021

The algebra of anomaly interplay

We give a general description of the interplay that can occur between local and global anomalies, in terms of (co)bordism. Mathematically, such an interplay is encoded in the non-canonical splitting of short exact sequences known to classify invertible field theories. We study various examples of the phenomenon in 2, 4, and 6 dimensions. We also describe how this understanding of anomaly interplay provides a rigorous bordism-based version of an old method for calculating global anomalies (starting from local anomalies in a related theory) due to Elitzur and Nair.

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arXiv2021

Anomalies and accidental symmetries: charging the scalar leptoquark under $L_μ$-$L_τ$

While the $S_3$ scalar leptoquark presents a possible tree-level explanation of the $b \to s \ell \ell$ flavour anomalies, it suffers from two conceptual problems which are often disregarded by model-builders. Firstly, the quantum numbers of the $S_3$ allow for a renormalisable diquark operator that would trigger rapid proton decay unless its coupling were tuned away. Secondly, one expects the leptoquark to have generic couplings to leptons, which require tuning to avoid stringent experimental bounds on lepton flavour violation. By gauging a $U(1)$ current that acts as $L_μ- L_τ$ on the Standard Model (SM) fermions, and under which the leptoquark has charge $-1$, one can remedy both these problems. The additional $U(1)$, which is spontaneously broken at some high scale, is associated with a massive $Z^\prime$ gauge boson and a scalar SM singlet $Φ$, which play no direct role in mediating the anomalous $B$ meson decays. By computing one- and two-loop mass corrections, we show that this pair of particles can be hidden away at much higher mass scales without destabilising either the Higgs or the leptoquark masses. The only low-energy relic of gauging $L_μ- L_τ$ is thus the accidental global symmetry structure of the lagrangian. On the other hand, we find quite generally that an $S_3$ leptoquark that mediates the $b \to s \ell \ell$ anomalies cannot be much heavier than a few TeV without itself inducing large Higgs mass corrections.

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arXiv2020

Naturalising the Third Family Hypercharge Model for Neutral Current $B-$Anomalies

We consider a deformation of the Third Family Hypercharge Model, which arguably makes the model more natural. Additional non-zero charges of the spontaneously broken, family-dependent $U(1)_F$ gauge symmetry are assigned to the second family leptons, and the third family leptons' charges are deformed away from their hypercharges in such a way that the $U(1)_F$ gauge symmetry remains anomaly-free. Second family $U(1)_F$ lepton charges allow a $Z^\prime$ coupling to muons without having to assume large charged lepton mixing, which risks violating tight lepton flavour violation bounds. In this deformed version, only the bottom and top Yukawa couplings are generated at the renormalisable level, whereas the tauon Yukawa coupling is absent. The $Z^\prime$ mediates a beyond the Standard Model contribution to an effective $(\bar b s) (\bar μμ)$ vertex in the combination $C_9=-9C_{10}$ and is able to fit the apparent discrepancy between Standard Model predictions in flavour changing neutral-current $B-$meson decays and their measurements, whilst simultaneously avoiding current constraints from direct $Z^\prime$ searches and other measurements, when $1.2\ \text{TeV} < M_{Z^\prime} < 12.5\ \text{TeV}$.

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arXiv2020

Undulating Dark Matter

We suggest that an interplay between microscopic and macroscopic physics can give rise to dark matter (DM) whose interactions with the visible sector fundamentally undulate in time, independent of celestial dynamics. A concrete example is provided by fermionic DM with an electric dipole moment (EDM) sourced by an oscillating axion-like field, resulting in undulations in the scattering rate. The discovery potential of light DM searches can be enhanced by additionally searching for undulating scattering rates, especially in detection regions where background rates are large and difficult to estimate, such as for DM masses in the vicinity of 1 MeV where DM-electron scattering dominantly populates the single electron bin. An undulating signal could also reveal precious dark sector information after discovery. In this regard we emphasise that, if the recent XENON1T excess of events is due to light DM scattering exothermically off electrons, future analyses of the time-dependence of events could offer clues as to the microscopic origins of the putative signal.

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arXiv2020

Global anomalies in the Standard Model(s) and Beyond

We analyse global anomalies and related constraints in the Standard Model (SM) and various Beyond the Standard Model (BSM) theories. We begin by considering four distinct, but equally valid, versions of the SM, in which the gauge group is taken to be $G=G_{\text{SM}}/Γ_n$, with $G_{\text{SM}}=SU(3)\times SU(2) \times U(1)$ and $Γ_n$ isomorphic to $\mathbb{Z}/n$ where $n\in\left\{1,2,3,6\right\}$. In addition to deriving constraints on the hypercharges of fields transforming in arbitrary representations of the $SU(3)\times SU(2)$ factor, we study the possibility of global anomalies in theories with these gauge groups by computing the bordism groups $Ω^{\text{Spin}}_5(BG)$ using the Atiyah-Hirzebruch spectral sequence. In two cases we show that there are no global anomalies beyond the Witten anomaly, while in the other cases we show that there are no global anomalies at all, illustrating the subtle interplay between local and global anomalies. While freedom from global anomalies has been previously shown for the specific fermion content of the SM by embedding the SM in an anomaly-free $SU(5)$ GUT, our results here remain true when the SM fermion content is extended arbitrarily. Going beyond the SM gauge groups, we show that there are no new global anomalies in extensions of the (usual) SM gauge group by $U(1)^m$ for any integer $m$, which correspond to phenomenologically well-motivated BSM theories featuring multiple $Z^\prime$ bosons. Nor do we find any new global anomalies in various grand unified theories, including Pati-Salam and trinification models. We also consider global anomalies in a family of theories with gauge group $SU(N)\times Sp(M)\times U(1)$, which share the phase structure of the SM for certain $(N, M)$.

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arXiv2020

Quantum mechanics in magnetic backgrounds with manifest symmetry and locality

The usual methods for formulating and solving the quantum mechanics of a particle moving in a magnetic field respect neither locality nor any global symmetries which happen to be present. For example, Landau's solution for a particle moving in a uniform magnetic field in the plane involves choosing a gauge in which neither translation nor rotation invariance are manifest. We show that locality can be made manifest by passing to a redundant description in which the particle moves on a $U(1)$-principal bundle over the original configuration space and that symmetry can be made manifest by passing to a corresponding central extension of the original symmetry group by $U(1)$. With the symmetry manifest, one can attempt to solve the problem by using harmonic analysis and we provide a number of examples where this succeeds. One is a solution of the Landau problem in an arbitrary gauge (with either translation invariance or the full Euclidean group manifest). Another example is the motion of a fermionic rigid body, which can be formulated and solved in a manifestly local and symmetric way via a flat connection on the non-trivial $U(1)$-central extension of the configuration space $SO(3)$ given by $U(2)$.

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arXiv2020

An Anomaly-free Atlas: charting the space of flavour-dependent gauged $U(1)$ extensions of the Standard Model

Spontaneously broken, flavour-dependent, gauged $U(1)$ extensions of the Standard Model (SM) have many phenomenological uses. We chart the space of solutions to the gauge anomaly cancellation equations in such extensions, for both the SM chiral fermion content and the SM plus (up to) three right-handed neutrinos (SM$ν_R$). Methods from Diophantine analysis allow us to efficiently index the solutions arithmetically, and produce the complete solution space in particular cases. In order to solve the general case, we build a computer program which cycles through possible $U(1)$ charge assignments, providing all solutions for charges up to some pre-defined maximum absolute charge. Lists of anomaly-free $U(1)$ charge assignments result, which corroborate the results of our Diophantine analysis. We make these lists, which may be queried for further desirable properties, publicly available. This previously uncharted space of anomaly-free charge assignments has been little explored until now, paving the way for future model building and phenomenological studies.

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arXiv2019

Gauging the accidental symmetries of the Standard Model, and implications for the flavour anomalies

We explore the possibility that lepton family numbers and baryon number are such good symmetries of Nature because they are the global remnant of a spontaneously broken gauge symmetry. An almost arbitrary linear combination of these symmetries (together with a component of global hypercharge) can be consistently gauged, if the Standard Model (SM) fermion content is augmented by three chiral SM singlet states. Within this framework of $U(1)$ extensions of the SM one generically expects flavour non-universality to emerge in the charged leptons, in such a way that naturally prevents lepton flavour violation, by aligning the mass and weak eigenbases. For quarks, all the SM Yukawa couplings responsible for their observed masses and mixings arise at the renormalisable level. We perform fits to show that models in this class can explain $R_{K^{(\ast)}}$ and the other neutral current $B$ anomaly data if we introduce a heavy vector-like quark to mediate the required quark flavour violation, while simultaneously satisfying other constraints from direct $Z^\prime$ searches at the LHC, $B_s$ meson mixing, a number of electroweak precision observables, and neutrino trident production. Within this symmetry-motivated framework of models, we find interesting implications for the flavour anomalies; notably, any axial couplings of the $Z^\prime$ to electrons and muons must be flavour universal, with the flavour universality violation arising solely from the vector-like couplings. We also comment on the generation of neutrino masses in these models.

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arXiv2019

Connecting neutral current $B$ anomalies with the heaviness of the third family

It is possible, and for several reasons attractive, to explain a collection of recent anomalies involving $b\rightarrow sμμ$ processes with a $Z^{\prime}$ gauge boson coupled only to the third family in the weak eigenbasis. From this premise, requiring cancellation of all gauge anomalies (including mixed and gravitational anomalies) fixes a unique charge assignment for the third family Standard Model fermions, which is simply proportional to hypercharge. After a brief discussion of some general features of anomaly cancellation in $Z^\prime$ theories, we discuss the phenomenology of such a `Third Family Hypercharge Model', which is subject to a trio of important constraints: (i) $B_s-\bar{B}_s$ mixing, (ii) lepton universality of the $Z$ boson couplings, and (iii) constraints from direct searches for the $Z^\prime$ boson at the LHC. Finally, in gauging third family hypercharge, this model forbids all Yukawa couplings (at the renormalisable level) save those of the third family, leading to a possible explanation of the heaviness of the third family.

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arXiv2018

Topological terms in Composite Higgs Models

We apply a recent classification of topological action terms to Composite Higgs models based on a variety of coset spaces $G/H$ and discuss their phenomenology. The topological terms, which can all be obtained by integrating (possibly only locally-defined) differential forms, come in one of two types, with substantially differing consequences for phenomenology. The first type of term (which appears in the minimal model based on $SO(5)/SO(4)$) is a field theory generalization of the Aharonov-Bohm phase in quantum mechanics. The phenomenological effects of such a term arise only at the non-perturbative level, and lead to $P$ and $CP$ violation in the Higgs sector. The second type of term (which appears in the model based on $SO(6)/SO(5)$) is a field theory generalization of the Dirac monopole in quantum mechanics and has physical effects even at the classical level. Perhaps most importantly, measuring the coefficient of such a term can allow one to probe the structure of the underlying microscopic theory. A particularly rich topological structure, with 6 distinct terms, is uncovered for the model based on $SO(6)/SO(4)$, containing 2 Higgs doublets and a singlet. Of the corresponding couplings, one is an integer and one is a phase.

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arXiv2018

Homological classification of topological terms in sigma models on homogeneous spaces

We classify the topological terms (in a sense to be made precise) that may appear in a non-linear sigma model based on maps from an arbitrary worldvolume manifold to a homogeneous space $G/H$ (where $G$ is an arbitrary Lie group and $H \subset G$). We derive a new condition for $G$-invariance of topological terms, which is necessary and sufficient (at least when $G$ is connected), and discuss a variety of examples in quantum mechanics and quantum field theory. In the present work we discuss only terms that may be written in terms of (possibly only locally-defined) differential forms on $G/H$, leading to an action that is manifestly local. Such terms come in one of two types, with prototypical quantum-mechanical examples given by the Aharonov-Bohm effect and the Dirac monopole. The classification is based on the observation that, for topological terms, the maps from the worldvolume to $G/H$ may be replaced by singular homology cycles on $G/H$. In a forthcoming paper we apply the results to phenomenological models in which the Higgs boson is composite.

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arXiv2018

Fractal based observables to probe jet substructure of quarks and gluons

New jet observables are defined which characterize both fractal and scale-dependent contributions to the distribution of hadrons in a jet. These infrared safe observables, named Extended Fractal Observables (EFOs), have been applied to quark-gluon discrimination to demonstrate their potential utility. The EFOs are found to be individually discriminating and only weakly correlated to variables used in existing discriminators. Consequently, their inclusion improves discriminator performance, as here demonstrated with particle level simulation from the parton shower.

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