Within $$Z^\prime $$ models, neutral meson mixing severely constrains beyond the Standard Model (SM) effects in flavour changing neutral current (FCNC) processes. However, in certain regions of the $$Z^\prime $$ parameter space, the contributions to meson mixing observables become negligibly small even for large $$Z^\prime $$ couplings. While this a priori allows for significant new physics (NP) effects in FCNC decays, we discuss how large $$Z^\prime $$ couplings in one neutral meson sector can generate effects in meson mixing observables of other neutral mesons, through correlations stemming from $${\text {SU}(2)}_L$$ gauge invariance and through Renormalization Group (RG) effects in the SM Effective Field Theory (SMEFT). This is illustrated with the example of $$B_s^0-{\bar{B}}_s^0$$ mixing, which in the presence of both left- and right-handed $$Z^\prime bs$$ couplings $$\Delta _L^{bs}$$ and $$\Delta _R^{bs}$$ remains SM-like for $$\Delta _R^{bs}\approx 0.1\,\Delta _L^{bs}.$$ We show that in this case, large $$Z^\prime bs$$ couplings generate effects in $\textit{D}$ and $\textit{K}$ meson mixing observables, but that the $\textit{D}$ and $\textit{K}$ mixing constraints and the relation between $$\Delta _R^{bs}$$ and $$\Delta _L^{bs}$$ are fully compatible with a lepton flavour universality (LFU) conserving explanation of the most recent $$b\rightarrow s\ell ^+\ell ^-$$ experimental data without violating other constraints like $$e^+ e^-\rightarrow \ell ^+\ell ^-$$ scattering. Assuming LFU, invariance under the $${\text {SU}(2)}_L$$ gauge symmetry leads then to correlated effects in $$b\rightarrow s\nu {\bar{\nu }}$$ observables presently studied intensively by the Belle II experiment, which allow to probe the $$Z^\prime $$ parameter space that is opened up by the vanishing NP contributions to $$B_s^0-{\bar{B}}_s^0$$ mixing. In this scenario the suppression of $$B\rightarrow K(K^*)\mu ^+\mu ^-$$ branching ratios implies $\textit{uniquely}$ enhancements of $$B\rightarrow K(K^*)\nu {\bar{\nu }}$$ branching ratios up to $$20\%.$$

Germany

Andrzej Buras

Switzerland

Peter Stangl

On the interplay of constraints from $$B_{s},$$ $\textit{D}$, and $\textit{K}$ meson mixing in $$Z^\prime $$ models with implications for $$b\!\rightarrow \! s \nu {\bar{\nu }}$$ transitions

In recent years, theoretical and phenomenological studies with effective field theories have become a trending and prolific line of research in the field of high-energy physics. In order to discuss present and future prospects concerning automated tools in this field, the SMEFT-Tools 2022 workshop was held at the University of Zurich from 14th–16th September 2022. The current document collects and summarizes the content of this workshop.

Jason Aebischer

CERN

Matteo Fael

Spain

Javier Fuentes-Martìn

Anders Thomsen

Javier Virto

Lukas Allwicher

Supratim Bakshi

Croatia

Hermès Bélusca-Maïto

Jorge Blas

Mikael Chala

Juan Criado

Greece

Athanasios Dedes

Renato Fonseca

United States

Angelica Goncalves

Amon Ilakovac

Matthias König

India

Sunando Patra

Paul Kühler

Marija Mador-Božinović

Poland

Mikołaj Misiak

Italy

Víctor Miralles

Ignacy Nałȩcz

United Kingdom

Méril Reboud

Laura Reina

Janusz Rosiek

Michal Ryczkowski

José Santiago

Luca Silvestrini

Dominik Stöckinger

Peter Stoffer

Avelino Vicente

Matthias Weißwange

Computing tools for effective field theories

Exclusive semileptonic b hadron decays (b → uℓν) serve as a sandbox for probing strong and electroweak interactions and for extracting the CKM element V  ub . Instead, this work investigates their underexplored potential to reveal new short-distance physics. Utilizing SMEFT as a conduit to chart territory beyond the SM, we demonstrate that substantive new physics contributions in b → uℓν are necessarily linked to correlated effects in rare neutral-current b decays, neutral B meson mixing or high-mass Drell-Yan tails. We find that measurements of the latter processes strongly restrict the allowed deviations in the former. A complete set of tree-level mediators, originating from a perturbative ultraviolet model and matching at dimension 6, is thoroughly explored to support this assertion. As a showcase application, we examine the feasibility of a new physics interpretation of the recent tension in exclusive |V  ub  | extraction from B → Vℓν where V = (ρ, ω).

Admir Greljo

Jakub Salko

Aleks Smolkovič

SMEFT restrictions on exclusive b → uℓν decays

Rare b hadron decays are considered excellent probes of new semileptonic four-fermion interactions of microscopic origin. However, the same interactions also correct the high-mass Drell-Yan tails. In this work, we revisit the first statement in the context of this complementarity and chart the space of short-distance new physics that could show up in rare b decays. We analyze the latest b → qℓ + ℓ  −  measurements, where q = d or s and ℓ = e or μ, including the most recent LHCb   <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </msub> </math>  $$ {R}_{K^{\left(\ast \right)}} $$  update, together with the latest charged and neutral current high-mass Drell-Yan data, pp → ℓν and pp → ℓ + ℓ  − . We implement a sophisticated interpretation pipeline within the flavio framework, allowing us to investigate the multidimensional SMEFT parameter space thoroughly and efficiently. To showcase the new functionalities of flavio, we construct several explicit models featuring either a Z′ or a leptoquark, which can explain the tension in b → sμ + μ  −  angular distributions and branching fractions while predicting lepton flavor universality (LFU) ratios to be SM-like,   <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </msub> <mo>≈</mo> <msubsup> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> <mi>SM</mi> </msubsup> </math>  $$ {R}_{K^{\left(\ast \right)}}\approx {R}_{K^{\left(\ast \right)}}^{\textrm{SM}} $$ , as indicated by the recent data. Those models are then confronted against the global likelihood, including the high-mass Drell-Yan, either finding tensions or compatibility.

Rare b decays meet high-mass Drell-Yan

We investigate an economical explanation for the (g − 2) μ  anomaly with a neutral vector boson from a spontaneously broken U(1) X  gauge symmetry. The Standard Model fermion content is minimally extended by 3 right-handed neutrinos. Using a battery of complementary constraints, we perform a thorough investigation of the renormalizable, quark flavor-universal, vector-like U(1) X  models, allowing for arbitrary kinetic mixing. Out of 419 models with integer charges not greater than ten, only 7 models are viable solutions, describing a narrow region in model space. These are either L  μ  − L  τ  or models with a ratio of electron to baryon number close to −2. The key complementary constraints are from the searches for nonstandard neutrino interactions. Furthermore, we comment on the severe challenges to chiral U(1) X  solutions and show the severe constraints on a particularly promising such candidate.

Jure Zupan

On (g − 2) μ  from gauged U(1) X

We develop an economical theoretical framework for combined explanations of the flavor physics anomalies involving muons: (g − 2) μ ,   <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </msub> </math>  $$ {R}_{K^{\left(\ast \right)}} $$ , and b → sμ + μ  −  angular distributions and branching ratios, that was first initiated by some of us in ref. [1]. The Standard Model (SM) is supplemented with a lepton-flavored U(1) X  gauge group. The U(1) X  gauge boson with the mass of   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (0.1) GeV resolves the (g − 2) μ  tension. A TeV-scale leptoquark, charged under the U(1) X , carries a muon number and mediates B-decays without prompting charged lepton flavor violation or inducing proton decay. We explore the theory space of the chiral, anomaly-free U(1) X  gauge extensions featuring the above scenario, and identify many suitable charge assignments for the SM+3ν  R  fermion content with the integer charges in the range   <math> <msub> <mi>X</mi> <msub> <mi>F</mi> <mi>i</mi> </msub> </msub> </math>  $$ {X}_{F_i} $$  ∈ [−10, 10]. We then carry out a comprehensive phenomenological study of the muonic force in representative benchmark models. Interestingly, we found models which can resolve the tension without conflicting the complementary constraints, and all of the viable parameter space will be tested in future muonic resonance searches. Finally, the catalog of the anomaly-free lepton-non-universal charge assignments motivated us to explore different directions in model building. We present a model in which the muon mass and the (g − 2) μ  are generated radiatively from a common short-distance dynamics after the U(1) X  breaking. We also show how to charge a vector leptoquark under U(1) μ−τ  in a complete gauge model.

Israel

Yotam Soreq

Muonic force behind flavor anomalies

The anomalies in rare B decays endure. We present results of an updated global analysis that takes into account the latest experimental input – in particular the recent results on  $$R_K$$  <math> <msub> <mi>R</mi> <mi>K</mi> </msub> </math>   and BR $$(B_s \rightarrow \mu ^+\mu ^-)$$  <math> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>→</mo> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> <mo>)</mo> </mrow> </math>   – and that qualitatively improves the treatment of theory uncertainties. Fit results are presented for the Wilson coefficients of four-fermion contact interactions. We find that muon specific Wilson coefficients  $$C_9 \simeq -0.73$$  <math> <mrow> <msub> <mi>C</mi> <mn>9</mn> </msub> <mo>≃</mo> <mo>-</mo> <mn>0.73</mn> </mrow> </math>   or  $$C_9 = -C_{10} \simeq -0.39$$  <math> <mrow> <msub> <mi>C</mi> <mn>9</mn> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>C</mi> <mn>10</mn> </msub> <mo>≃</mo> <mo>-</mo> <mn>0.39</mn> </mrow> </math>   continue to give an excellent description of the data. If only theoretically clean observables are considered, muon specific  $$C_{10} \simeq 0.60$$  <math> <mrow> <msub> <mi>C</mi> <mn>10</mn> </msub> <mo>≃</mo> <mn>0.60</mn> </mrow> </math>   or  $$C_9=-C_{10} \simeq -0.35$$  <math> <mrow> <msub> <mi>C</mi> <mn>9</mn> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>C</mi> <mn>10</mn> </msub> <mo>≃</mo> <mo>-</mo> <mn>0.35</mn> </mrow> </math>   improve over the Standard Model by  $$\sqrt{\Delta \chi ^2} \simeq 4.7\sigma $$  <math> <mrow> <msqrt> <mrow> <mi>Δ</mi> <msup> <mi>χ</mi> <mn>2</mn> </msup> </mrow> </msqrt> <mo>≃</mo> <mn>4.7</mn> <mi>σ</mi> </mrow> </math>   and  $$\sqrt{\Delta \chi ^2} \simeq 4.6\sigma $$  <math> <mrow> <msqrt> <mrow> <mi>Δ</mi> <msup> <mi>χ</mi> <mn>2</mn> </msup> </mrow> </msqrt> <mo>≃</mo> <mn>4.6</mn> <mi>σ</mi> </mrow> </math>  , respectively. In various new physics scenarios we provide predictions for lepton flavor universality observables and CP asymmetries that can be tested with more data. We update our previous combination of ATLAS, CMS, and LHCb data on BR $$(B_s \rightarrow \mu ^+\mu ^-)$$  <math> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>→</mo> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> <mo>)</mo> </mrow> </math>   and BR $$(B^0\rightarrow \mu ^+\mu ^-)$$  <math> <mrow> <mo>(</mo> <msup> <mi>B</mi> <mn>0</mn> </msup> <mo>→</mo> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> <mo>)</mo> </mrow> </math>   taking into account the full two-dimensional non-Gaussian experimental likelihoods.

Wolfgang Altmannshofer

New physics in rare B decays after Moriond 2021

The Standard Model (SM) is augmented with a <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>B</mi><mo>−</mo><mn>3</mn><msub><mrow><mi>L</mi></mrow><mrow><mi>μ</mi></mrow></msub></mrow></msub></math> gauge symmetry spontaneously broken above the TeV scale when an SM-singlet scalar condenses. Scalar leptoquarks <math><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn><mo>(</mo><mn>3</mn><mo>)</mo></mrow></msub><mo>=</mo><mo>(</mo><mover><mrow><mn>3</mn></mrow><mo>‾</mo></mover><mo>,</mo><mspace width="0.2em"></mspace><mn>1</mn><mo>(</mo><mn>3</mn><mo>)</mo><mo>,</mo><mspace width="0.2em"></mspace><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo></math> charged under <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>B</mi><mo>−</mo><mn>3</mn><msub><mrow><mi>L</mi></mrow><mrow><mi>μ</mi></mrow></msub></mrow></msub></math> mediate the intriguing effects observed in muon <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><mo>)</mo></math>, <math><msub><mrow><mi>R</mi></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo></mrow></msup></mrow></msub></math>, and <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> angular distributions, while generically evading all other phenomenological constraints. The fermionic sector is minimally extended with three right-handed neutrinos, and a successful type-I seesaw mechanism is realized. Charged lepton flavor violation is effectively suppressed, and proton decay—a common prediction of leptoquarks—is postponed to the dimension-6 effective Lagrangian. Unavoidable radiative corrections in the Higgs mass and muon Yukawa favor leptoquark masses interesting for collider searches. The parameters of the model are radiatively stable and can be evolved by the renormalization group to the Planck scale without inconsistencies. Alternative lepton-flavored gauge extensions of the SM, under which leptoquarks become muoquarks, are proposed for comparison.

Anders Eller Thomsen

A model of muon anomalies

Models in which the Higgs boson is a composite pseudo-Nambu-Goldstone boson offer attractive solutions to the Higgs mass naturalness problem. We consider three such models based on the minimal SO(5) → SO(4) symmetry breaking pattern, and perform convergent global fits on the models under a Bayesian framework in order to find the regions of their parameter spaces that best fit a wide range of constraints, including recent Higgs measurements. We use a novel technique to analyse the fine-tuning of the models, quantifying the tuning as the Kullback-Leibler divergence from the prior to the posterior probability on the parameter space. Each model is found to be able to satisfy all constraints at the 3σ level simultaneously. As a by-product of the fits, we analyse the collider phenomenology of our models in these viable regions. In two of the three models, we find that the gg → H → γγ cross section is less than ∼90% that predicted by the SM, which is already in slight tension with experiment and could potentially be ruled out in the future high-luminosity run of the LHC. In addition, the lightest fermions F arising from the new strong dynamics in these models are seen in general to lie above ∼1.1 TeV, with the F → tW + and F →   <math> <mover> <mi>b</mi> <mo>¯</mo> </mover> <msup> <mi>W</mi> <mo>+</mo> </msup> </math>  $$ \overline{b}{W}^{+} $$  decays offering particularly promising channels for probing these models in future collider searches.

Australia

Ethan Carragher

Will Handley

Daniel Murnane

Wei Su

Martin White

Anthony Williams

Convergent Bayesian global fits of 4D composite Higgs models

We present a model of composite Dark Matter (DM), in which a new QCD-like confining “hypercolor” sector generates naturally stable hyperbaryons as DM candidates and at the same time provides mass to new weakly coupled gauge bosons H that serve as DM mediators, coupling the hyperbaryons to the Standard Model (SM) fermions. By an appropriate choice of the H gauge symmetry as a horizontal SU(2) h  SM flavor symmetry, we show how the H gauge bosons can be identified with the horizontal gauge bosons recently put forward as an explanation for discrepancies in rare B-meson decays. We find that the mass scale of the H gauge bosons suggested by the DM phenomenology intriguingly agrees with the one needed to explain the rare B-decay discrepancies.

France

Alexandre Carvunis

Diego Guadagnoli

Composite Dark Matter and a horizontal symmetry