We study the matching of Froggatt-Nielsen theories of flavour onto the Standard Model Effective Field Theory (SMEFT), upon integrating out a heavy Beyond-the-Standard-Model (BSM) scalar ‘flavon’ whose vacuum expectation value breaks an Abelian flavour symmetry at energies ΛFN well above the electroweak scale, ΛFN &gt; ΛSM. We include matching contributions to the infrared d SM = 6 (Warsaw basis) SMEFT sourced from ultraviolet contact terms suppressed up to order 1/   <math> <msubsup> <mi>Λ</mi> <mi>UV</mi> <mn>2</mn> </msubsup> </math>  $$ {\Lambda}_{\textrm{UV}}^2 $$  in the Froggatt-Nielsen Lagrangian, where ΛUV &gt; ΛFN is an arbitrary ultraviolet scale where further unspecified BSM particles are dynamical. This includes tree-level (one-loop) ultraviolet diagrams with d FN = 6 (5) effective vertices. We first do so with a toy model, but then generalize our findings to arbitrary Frogatt-Nielsen charges. Our results indicate a rich and non-trivial signature of Froggatt-Nielsen theories on the (otherwise) model-independent operators of the SMEFT, and we briefly speculate on extending our analysis to broader classes of BSM flavour models, e.g. non-Abelian and/or gauged theories. We thus take an important step towards determining how to use rapidly developing theoretical and experimental SMEFT technologies to gain unambiguous insight into the SM’s longstanding fermion flavour puzzle.

United Kingdom

Eetu Loisa

United States

Jim Talbert

Froggatt-Nielsen meets the SMEFT

We study the role of renormalon cancellation schemes and perturbative scale choices in extractions of the strong coupling constant <math><msub><mi>α</mi><mi>s</mi></msub><mo>(</mo><msub><mi>m</mi><mi>Z</mi></msub><mo>)</mo></math> and the leading nonperturbative shift parameter <math><msub><mi>Ω</mi><mn>1</mn></msub></math> from resummed predictions of the <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> event shape thrust. We calculate the thrust distribution to <math><mrow><mi>N</mi><mrow><mmultiscripts><mrow><mi>L</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow><msup><mrow><mi>L</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math> resummed accuracy in soft-collinear effective theory (SCET) matched to the fixed-order <math><mi>O</mi><mo>(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo>)</mo></math> prediction, and perform a new high-statistics computation of the <math><mi>O</mi><mo>(</mo><msubsup><mi>α</mi><mi>s</mi><mn>3</mn></msubsup><mo>)</mo></math> matching in EERAD3, although we do not include the latter in our final <math><msub><mi>α</mi><mi>s</mi></msub></math> fits due to some observed systematics that require further investigation. We are primarily interested in testing the phenomenological impact sourced from varying amongst three renormalon cancellation schemes and two sets of perturbative scale profile choices. We then perform a global fit to available data spanning center-of-mass energies between 35–207 GeV in each scenario. Relevant subsets of our results are consistent with prior SCET-based extractions of <math><msub><mi>α</mi><mi>s</mi></msub><mo>(</mo><msub><mi>m</mi><mi>Z</mi></msub><mo>)</mo></math>, but we are also led to a number of novel observations. Notably, we find that the combined effect of altering the renormalon cancellation scheme and profile parameters can lead to few-percent-level impacts on the extracted values in the <math><msub><mi>α</mi><mi>s</mi></msub><mo>−</mo><msub><mi>Ω</mi><mn>1</mn></msub></math> plane, indicating a potentially important systematic theory uncertainty that should be accounted for. We also observe that fits performed over windows dominated by dijet events are typically of a higher quality than those that extend into the far tails of the distributions, possibly motivating future fits focused more heavily in this region. Finally, we discuss how different estimates of the three-loop soft matching coefficient <math><msubsup><mi>c</mi><mover><mi>S</mi><mo>˜</mo></mover><mn>3</mn></msubsup></math> can also lead to measurable changes in the fitted <math><mo>{</mo><msub><mi>α</mi><mi>s</mi></msub><mo>,</mo><msub><mi>Ω</mi><mn>1</mn></msub><mo>}</mo></math> values.

Germany

Guido Bell

Christopher Lee

Italy

Yiannis Makris

China

Bin Yan

Effects of renormalon scheme and perturbative scale choices on determinations of the strong coupling from <math><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> event shapes

We revisit the phenomenological predictions of the Universal Texture Zero (UTZ) model of flavour originally presented in [1], and update them in light of both improved experimental constraints and numerical analysis techniques. In particular, we have developed an in-house Markov Chain Monte Carlo (MCMC) algorithm to exhaustively explore the UTZ’s viable parameter space, considering both leading- and next-to-leading contributions in the model’s effective operator product expansion. We also extract – for the first time – reliable UTZ predictions for the (poorly constrained) leptonic CP-violating phases, and ratio observables that characterize neutrino masses probed by (e.g.) oscillation,  $$\beta $$  <math> <mi>β</mi> </math>  -decay, and cosmological processes. We therefore dramatically improve on the proof-in-principle phenomenological analysis originally presented in [1], and ultimately show that the UTZ remains a minimal, viable, and appealing theory of flavour. Our results also further demonstrate the potential of robustly examining multi-parameter flavour models with MCMC routines.

Jordan Bernigaud

Portugal

Ivo Medeiros Varzielas

Miguel Levy

Revisiting the universal texture zero of flavour: a Markov chain Monte Carlo analysis

We write down a geometric realization of the Standard Model Effective Field Theory (SMEFT) extended by n  f  flavours of light sterile neutrinos, a so-called geoνSMEFT. As with the geoSMEFT introduced by Helset, Martin and Trott, we show that a refactorization of the νSMEFT’s operator product expansion is possible, such that two- and three-point composite operator forms are dressed with field-space connections composed of towers of Higgs dressings and symmetry generators, valid at all-orders in the   <math> <msub> <mover> <mi>v</mi> <mo>¯</mo> </mover> <mi>T</mi> </msub> <mo>/</mo> <mi>Λ</mi> </math>  $$ {\overline{v}}_T/\Lambda $$  expansion parameter of the EFT   <math> <mfenced> <mrow> <msub> <mover> <mi>v</mi> <mo>¯</mo> </mover> <mi>T</mi> </msub> <mo>≡</mo> <msqrt> <mrow> <mn>2</mn> <mfenced> <mrow> <msup> <mi>H</mi> <mo>†</mo> </msup> <mi>H</mi> </mrow> </mfenced> </mrow> </msqrt> </mrow> </mfenced> </math>  $$ \left({\overline{v}}_T\equiv \sqrt{2\left\langle {H}^{\dagger }H\right\rangle}\right) $$ . These connections are parameterized by real Higgs coordinates and contribute to the field-space geometry of the (ν)SMEFT, with structure linked to the strength of Beyond-the-(ν)Standard Model physics encoded in   <math> <msub> <mover> <mi>v</mi> <mo>¯</mo> </mover> <mi>T</mi> </msub> <mo>/</mo> <mi>Λ</mi> </math>  $$ {\overline{v}}_T/\Lambda $$ . In addition to enumerating the relevant composite operators and associated connections, we briefly outline the route to calculating all-  <math> <msub> <mover> <mi>v</mi> <mo>¯</mo> </mover> <mi>T</mi> </msub> <mo>/</mo> <mi>Λ</mi> </math>  $$ {\overline{v}}_T/\Lambda $$ -orders amplitudes, including the flavor-invariant theory required to understand the neutrino mass-eigenstate basis geometrically.

The geometric νSMEFT: operators and connections

We consider the phenomenological signatures of Simplified Models of Flavourful Leptoquarks, whose Beyond-the-Standard Model (SM) couplings to fermion generations occur via textures that are well motivated from a broad class of ultraviolet flavour models (which we briefly review). We place particular emphasis on the study of the vector leptoquark ∆ μ  with assignments (3 , 1 , 2/3) under the SM’s gauge symmetry, SU(3) C  × SU(2) L  × U(1) Y , which has the tantalising possibility of explaining both   <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </msub> </math>  $$ {\mathcal{R}}_{K^{\left(\ast \right)}} $$  and   <math> <msub> <mi>R</mi> <msup> <mi>D</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </msub> </math>  $$ {\mathcal{R}}_{D^{\left(\ast \right)}} $$  anomalies. Upon performing global likelihood scans of the leptoquark’s coupling parameter space, focusing in particular on models with tree-level couplings to a single charged lepton species, we then provide confidence intervals and benchmark points preferred by low (er)-energy flavour data. Finally, we use these constraints to further evaluate the (promising) Large Hadron Collider (LHC) detection prospects of pairs of τ-flavoured ∆ μ , through their distinct (a)symmetric decay channels. Namely, we consider direct third-generation leptoquark and jets plus missing-energy searches at the LHC, which we find to be complementary. Depending on the simplified model under consideration, the direct searches constrain the ∆ μ  mass up to 1500-1770 GeV when the branching fraction of ∆ μ  is entirely to third-generation quarks (but are significantly reduced with decreased branching ratios to the third generation), whereas the missing-energy searches constrain the mass up to 1150-1700 GeV while being largely insensitive to the third-generation branching fraction.

Monika Blanke

Denmark

Spain

José Zurita

LHC signatures of τ-flavoured vector leptoquarks

We report a set of exact formulae for computing Dirac masses, mixings, and CP-violation parameter(s) from 3×3 Yukawa matrices Y valid when YY † → U † YY † U under global   <math> <mi>U</mi> <msub> <mfenced> <mn>3</mn> </mfenced> <msub> <mi>Q</mi> <mi>L</mi> </msub> </msub> </math>  $$ \mathrm{U}{(3)}_{Q_L} $$  flavour symmetry transformations U. The results apply to the Standard Model Effective Field Theory (SMEFT) and its ‘geometric’ realization (geoSMEFT). We thereby complete, in the Dirac flavour sector, the catalogue of geoSMEFT parameters derived at all orders in the   <math> <msqrt> <mrow> <mn>2</mn> <mfenced> <mrow> <msup> <mi>H</mi> <mo>†</mo> </msup> <mi>H</mi> </mrow> </mfenced> </mrow> </msqrt> </math>  $$ \sqrt{2\left\langle {H}^{\dagger }H\right\rangle } $$  /Λ expansion. The formalism is basis-independent, and can be applied to models with decoupled ultraviolet flavour dynamics, as well as to models whose infrared dynamics are not minimally flavour violating. We highlight these points with explicit examples and, as a further demonstration of the formalism’s utility, we derive expressions for the renormalization group flow of quark masses, mixings, and CP-violation at all mass dimension and perturbative loop orders in the (geo)SM(EFT) and beyond.

Michael Trott

Dirac masses and mixings in the (geo)SM(EFT) and beyond

We consider effective Lagrangians which, after electroweak- and family-symmetry breaking, yield fermionic mass matrices and/or other flavoured couplings exhibiting residual family symmetries (RFS). Thinking from the bottom up, these RFS intimately link ultraviolet (UV) Beyond-the-Standard Model (BSM) physics to infrared flavour phenomenology without direct reference to any (potentially unfalsifiable) UV dynamics. While this discussion is typically performed at the level of RFS group generators and the UV flavour groups they can close, we now also focus on the RFS-implied shape of the low-energy mass/coupling matrices. We then show how this information can be used to algorithmically guide the reconstruction of an effective Lagrangian, thereby forming top-down models realizing the typical bottom-up phenomenological conclusions. As a first application we take results from scans of finite groups capable of controlling (through their RFS) CKM or PMNS mixing within the SM alone. We then extend this to recently studied scenarios where RFS also control special patterns of leptoquark couplings, thus providing proof-in-principle completions for such ‘Simplified Models of Flavourful Leptoquarks.’

Reconstructing effective Lagrangians embedding residual family symmetries

We discuss the possible origin of the Majorana mass scale(s) required for the “neutrino option” where the electroweak scale is generated simultaneously with light neutrino masses in a type-I seesaw model by common dimension four interactions. We establish no-go constraints on the perturbative generation of the Majorana masses required due to global symmetries of the seesaw Lagrangian.

Ilaria Brivio

CERN

No-go limitations on UV completions of the neutrino option

We extend our algorithm for automating the calculation of two-loop dijet soft functions to observables that do not obey the non-Abelian exponentiation theorem, i.e. to those that require an independent calculation of the uncorrelated-emission contribution. As the singularity structure of uncorrelated double emissions differs substantially from the one for correlated emissions, we introduce a novel phase-space parametrisation that isolates the corresponding divergences. The resulting integrals are implemented in SoftSERVE 1.0, which we release alongside of this work, and which we supplement by a regulator that is consistent with the rapidity renormalisation group framework. Using our automated setup, we confirm existing results for various jet-veto observables and provide a novel prediction for the soft-drop jet-grooming algorithm.

Netherlands

Switzerland

Rudi Rahn

Generic dijet soft functions at two-loop order: uncorrelated emissions

We consider the higher-order resummation of Sudakov double logarithms in the presence of multiple coupled gauge in. The associated evolution equations depend on the coupled β functions of two (or more) coupling constants α  a  and α  b , as well as anomalous dimensions that have joint perturbative series in α  a  and α  b . We discuss possible strategies for solving the system of evolution equations that arises. As an example, we obtain the complete three-loop (NNLL) QCD⊗QED Sudakov evolution factor. Our results also readily apply to the joint higher-order resummation of electroweak and QCD Sudakov logarithms.