Joseph Tooby-Smith's research while affiliated with Cornell University and other places
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Publications (31)
We introduce HepLean, an open-source project to digitalise definitions, theorems, proofs, and calculations in high energy physics using the interactive theorem prover Lean 4. HepLean has the potential to benefit the high energy physics community in four ways: making it easier to find existing results, allowing the creation of new results using arti...
We present a Mathematica package that takes any reductive gauge algebra and fully-reducible fermion representation, and outputs all semisimple gauge extensions under the condition that they have no additional fermions, and are free of local anomalies. These include all simple completions, also known as grand unified theories. We additionally provid...
We present a Mathematica package that takes any reductive gauge algebra and fully-reducible fermion representation, and outputs all semisimple gauge extensions under the condition that they have no additional fermions, and are free of local anomalies. These include all simple completions, also known as grand unified theories (GUT). We additionally...
A bstract
We present a novel construction for a Higgs-VEV sensitive (HVS) operator, which can be used as a trigger operator in cosmic selection models for the electroweak hierarchy problem. Our operator does not contain any degrees of freedom charged under the SM gauge symmetries, leading to reduced tuning in the resulting models. Our construction...
A bstract
We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed is forgotten. Doing so allows many questions of physical interest to be answered using the tools of h...
We present a novel construction for a Higgs-VEV sensitive operator, which can be used as a trigger operator in cosmic selection models for the electroweak hierarchy problem. Our operator does not contain any degrees of freedom charged under the SM gauge symmetries, leading to reduced tuning in the resulting models. Our construction is based on the...
We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed is forgotten. Doing so allows many questions of physical interest to be answered using the tools of homotopy th...
A bstract
We propose that the electroweak and flavour quantum numbers of the Standard Model (SM) could be unified at high energies in an SU(4) × Sp(6) L × Sp(6) R anomaly-free gauge model. All the SM fermions are packaged into two fundamental fields, Ψ L ∼ ( 4 , 6 , 1 ) and Ψ R ∼ ( 4 , 1 , 6 ), thereby explaining the origin of three families of fer...
A bstract
We parametrise the space of all possible flavour non-universal $$ \mathfrak{u} $$ u (1) X extensions of the Standard Model that embed inside anomaly-free semi-simple gauge theories, including up to three right-handed neutrinos. More generally, we parametrise all abelian extensions (i.e. by any number of $$ \mathfrak{u} $$ u (1)’s) of the...
DOI:https://doi.org/10.1103/PhysRevD.106.019901
We parametrise the space of all possible flavour non-universal $\mathfrak{u}(1)_X$ extensions of the Standard Model that embed inside anomaly-free semi-simple gauge theories, including up to three right-handed neutrinos. More generally, we parametrise all abelian extensions (i.e. by any number of $\mathfrak{u}(1)$'s) of the SM with such semi-simple...
The inverse Higgs phenomenon, which plays an important r\^ole in physical systems with Goldstone bosons (such as the phonons in a crystal) involves nonholonomic mechanical constraints. By formulating field theories with symmetries and constraints in a general way using the language of differential geometry, we show that many examples of constraints...
A bstract
Extensions of the minimal supersymmetric standard model (MSSM) gauge group abound in the literature. Several of these include an additional U(1) X gauge group. Chiral fermions’ charge assignments under U(1) X are constrained to cancel local anomalies in the extension and they determine the structure and phenomenology of it. We provide all...
We propose that the electroweak and flavour quantum numbers of the Standard Model (SM) could be unified at high energies in an $SU(4)\times Sp(6)_L \times Sp(6)_R$ anomaly-free gauge model. All the SM fermions are packaged into two fundamental fields, $\Psi_L \sim (\mathbf{4}, \mathbf{6}, \mathbf{1})$ and $\Psi_R\sim (\mathbf{4}, \mathbf{1},\mathbf...
We show how one may classify all semisimple algebras containing the su(3)⊕su(2)⊕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 cataloged. With just a single generation of Standard Model fermions plus a s...
Extensions of the minimal supersymmetric standard model (MSSM) gauge group abound in the literature. Several of these include an additional $U(1)_X$ gauge group. Chiral fermions' charge assignments under $U(1)_X$ are constrained to cancel local anomalies in the extension and they determine the structure and phenomenology of it. We provide all anoma...
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 (gauged or global) to be catalogued. With just a sin...
The inverse Higgs phenomenon, which plays an important r\^ole in physical systems with Goldstone bosons (such as the phonons in a crystal) involves nonholonomic mechanical constraints. By formulating field theories with symmetries and constraints in a general way using the language of differential geometry, we show that many examples of constraints...
A bstract
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 fi...
Many extensions of the standard model include an extra gauge boson, whose couplings to fermions are constrained by the requirement that anomalies cancel. We find a general solution to the resulting diophantine equations in the plausible case where the chiral fermion content is that of the standard model plus three right-handed neutrinos.
In a supersymmetric theory, the IR contributions to the Higgs mass are calculable below the mediation scale ΛUV in terms of the IR field content and parameters. However, logarithmic sensitivity to physics at ΛUV remains. In this Letter, we present a first example of a framework, dictated by symmetries, to supersoften these logarithms from the matte...
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, resul...
Many extensions of the Standard Model include an extra gauge boson, whose couplings to fermions are constrained by the requirement that anomalies cancel. We find a general solution to the resulting diophantine equations in the plausible case where the chiral fermion content is that of the Standard Model plus 3 right-handed neutrinos.
Costa et al. [Phys. Rev. Lett.123 (2019) 151601] recently gave a general solution to the anomaly equations for n charges in a U(1) gauge theory. ‘Primitive’ solutions of chiral fermion charges were parameterised and it was shown how operations performed upon them (concatenation with other primitive solutions and with vector-like solutions) yield th...
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 c...
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...
In a supersymmetric (SUSY) theory, the IR-contributions to the Higgs mass are calculable below the mediation scale $\Lambda_{\text{UV}}$ in terms of the IR field content and parameters. However, logarithmic sensitivity to physics at $\Lambda_{\text{UV}}$ remains. In this work we present a first example of a framework, dictated by symmetries, to sup...
We consider local (or perturbative) gauge anomalies in models featuring an extra $Z^\prime$ boson compared to the Standard Model (SM), along with $n$ SM-singlet fermions. Assuming that the gauge group is compact, we give a general solution to the anomaly cancellation conditions (ACCs) for the ACCs that involve only SM fermions and we examine whethe...
Costa et al. [Phys. Rev. Lett. 123, 151601 (2019)] recently gave a solution to the anomaly equations for $n$ charges in a $U(1)$ gauge theory, which is general except that it omits solutions which do not correspond to chiral representations of $U(1)$, or which are obtainable by permuting charges, or concatenating solutions of lower $n$, or by addin...
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...
Citations
... The most down-to-earth example of this symmetry structure, which in general is described using higher category theory (see e.g. [37]), is the notion of a 2-group symmetry whereby a 1-form symmetry H [1] and a 0-form symmetry G [0] combine non-trivially. This occurs, for example [38,39], when a bunch of Wilson lines (which are charged under a discrete 1-form centre symmetry) can be screened by a dynamical fermion (which is charged under a 0-form flavour symmetry). ...
Reference: Toric 2-group anomalies via cobordism
... More generally, the SU(5) 3 framework proposed here may embed a broader class of gauge non-universal models, reconciling the ideas of gauge non-universality with gauge coupling unification at the GUT scale. In particular, SU(5) 3 may embed theories based on the family decomposition of the SM group, such as the SU(2) 3 L model [10][11][12][13][14][15], the SU(3) 3 c model [16] or the aforementioned tri-hypercharge model, as an alternative to the existing ultraviolet (UV) completions which are all based on (variations of) the Pati-Salam (PS) group [17][18][19][20][21][22][23][24]. We note however that while most of the previous papers explain the origin of the flavour structure of the SM, none of them provides a gauge unified framework. ...
... For example, given N g generations one can embed SUp2q L into Spp2N g q L " Spp6q L , as used in the electroweak flavour unification model of [23]. In contrast, most horizontal G SMˆU p1q F gauge theories, even those that are anomaly-free, have no semi-simple completion [24]. ...
... HepLean has the digitalisation of the main results of a series of papers in the area of local anomaly cancellation. Firstly, HepLean contains the parameterisation of the solutions to the ACCs for a pure U (1)-gauge theory with an even (see e.g., source) and odd number of fermions (see e.g, source) [14,15], for a U (1)-extension to the Standard Model (SM) with three right handed neutrinos (see e.g., source) [16], and for a U (1)-extension to the Minimal Supersymmetric Standard Model with three right handed neutrinos (see e.g., source) [17]. Secondly, it contains the main result of [18] which will be discussed in §3.3. ...
Reference: HepLean: Digitalising high energy physics
... We remark that jet bundles have been recently used in the study of scalar field theories in Ref. [42] by Gripaios and Tooby-Smith, but in an altogether different context. There, the authors use jet manifolds to rigorously formulate so-called 'inverse Higgs constraints'. ...
Reference: Jet Bundle Geometry of Scalar Field Theories
... [20]. There are also other intrinsically flavoured options, sticking to 4d, as categorised in ref. [21], in which the generations are further 're-unified' in the UV via some 'gauge-flavour-unification' symmetry [22]. For example, given N g generations one can embed SUp2q L into Spp2N g q L " Spp6q L , as used in the electroweak flavour unification model of [23]. ...
... Alternatively, the anomaly might result from new neutrino-lepton or non-standard neutrino interactions mediated by a light scalar or a vector particle [3,13,14,45,[58][59][60][61][62]. Yet more potential explanations include exotic radioactivity affecting hydrogen decays [25], fermionic DM with an electric dipole moment (EDM) sourced by an oscillating axion-like field [63], and the resurrection of the solar ALP explanation via the postulate of a "stellar basin" of gravitationally-bound axions in the Sun [64]. Finally, tritium ( 3 H) [1,65] or argon [66] present in the detector material have also been identified as possible causes, though the latter has since been excluded by the XENON Collaboration in a revised version of their initial submission [1]. ...
... HepLean has the digitalisation of the main results of a series of papers in the area of local anomaly cancellation. Firstly, HepLean contains the parameterisation of the solutions to the ACCs for a pure U (1)-gauge theory with an even (see e.g., source) and odd number of fermions (see e.g, source) [14,15], for a U (1)-extension to the Standard Model (SM) with three right handed neutrinos (see e.g., source) [16], and for a U (1)-extension to the Minimal Supersymmetric Standard Model with three right handed neutrinos (see e.g., source) [17]. Secondly, it contains the main result of [18] which will be discussed in §3.3. ...
Reference: HepLean: Digitalising high energy physics
... The only problem of low energy SUSY is that it now has a little fine-tuning (percent level for the phenomenological MSSM and per-mille level for the CMSSM [108]) caused by sizably heavier stops than the weak scale 4 . To tackle the little fine-tuning caused by heavy stops, the idea of supersoft stops was proposed to screen the UV-sensitive logs [110]. ...
... HepLean has the digitalisation of the main results of a series of papers in the area of local anomaly cancellation. Firstly, HepLean contains the parameterisation of the solutions to the ACCs for a pure U (1)-gauge theory with an even (see e.g., source) and odd number of fermions (see e.g, source) [14,15], for a U (1)-extension to the Standard Model (SM) with three right handed neutrinos (see e.g., source) [16], and for a U (1)-extension to the Minimal Supersymmetric Standard Model with three right handed neutrinos (see e.g., source) [17]. Secondly, it contains the main result of [18] which will be discussed in §3.3. ...
Reference: HepLean: Digitalising high energy physics
