<p>We present a model-independent method to study the four-body decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math>, based on extracting continuous observables with a moments approach. The method allows the observables to be determined unbinned in both the dilepton and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> invariant masses on which the decay dynamics depend. This will allow the method to shed new light on how the observables depend on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave contributions to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> system. This approach contrasts with the state-of-the-art analyses, which bin in dilepton and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> mass or use a model for the dependence of the underlying decay amplitudes on these masses. The method does not require making a statistical fit and so avoids problems of biases and poor uncertainty estimation when dealing with small samples or a large number of fit parameters. We provide the Standard Model predictions for the unbinned optimized observables, derive new geometrical bounds on their values, and study the robustness of these bounds in the presence of a scalar new physics contribution. We explore the zero-crossing points of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mrow><mn>4</mn><mo>,</mo><mn>5</mn></mrow><mo>′</mo></msubsup></math> observables as a function of a new physics contribution to the dominant vector Wilson coefficient, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>C</mi></mrow><mrow><mn>9</mn></mrow><mrow><mi>NP</mi></mrow></msubsup></mrow></math>. We also discuss the conditions that can be used to test the theoretical model of the amplitudes needed for an experimental amplitude analysis. Finally, as an illustration, we show how the proposed method might be used to extract the zero-crossing points, make a comparison with the bounds and test a nontrivial relation between the observable values.</p>

Spain

Bernat Capdevila

Joaquim Matias

Martín Novoa-Brunet

United Kingdom

Mitesh Patel

Mark Smith

Model-independent unbinned analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>B</mi><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mo stretchy="false">(</mo><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math>: Zeroes, bounds, Wilson coefficients, and symmetries

We study two-site deconstructions of the SU(2) L  gauge group factor of the SM. Models based on this approach can explain the hierarchies of the quark masses and CKM mixing between third and light families if these fields are localised on different sites by the presence of hierarchical new physics scales. The model leads to an accidental global U(2) q  × U(3) u  × U(3) d  flavour symmetry which prevents dangerously large effects in flavour observables, making a TeV extension of the SM possible. Given the structure of the PMNS matrix in the neutrino sector, we explore different possibilities for the arrangement of the leptons on the two sites, and consider different models with U(2) ℓ  or U(3) ℓ  flavour symmetries. The phenomenology of the models is mostly governed by a massive vector triplet of SU(2) L . We study the interesting interplay between LHC searches and precision observables. In particular, one of the models can give a sizeable lepton flavour universal effect in the Wilson coefficient C 9 while naturally suppressing contributions to C 10, as suggested by current b → sℓ + ℓ  −  data, predicting simultaneously a mild positive shift in the W boson mass.

Italy

Switzerland

Andreas Crivellin

Javier Lizana

Poland

Stefan Pokorski

SU(2) L  deconstruction and flavour (non)-universality

We discuss the impact of the recent LHCb update on the two lepton-flavour universality ratios  $$R_K$$  <math> <msub> <mi>R</mi> <mi>K</mi> </msub> </math>   and  $$R_{K^*}$$  <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mo>∗</mo> </msup> </msub> </math>  , and the CMS update of  $$B({B_s \rightarrow \mu ^+\mu ^-})$$  <math> <mrow> <mi>B</mi> <mo>(</mo> <mrow> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>→</mo> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> </mrow> <mo>)</mo> </mrow> </math>   regarding the possibility of New Physics in  $$b\rightarrow s\ell ^+\ell ^-$$  <math> <mrow> <mi>b</mi> <mo>→</mo> <mi>s</mi> <msup> <mi>ℓ</mi> <mo>+</mo> </msup> <msup> <mi>ℓ</mi> <mo>-</mo> </msup> </mrow> </math>   decays. We perform global fits of the New Physics Wilson coefficients defined in the model-independent approach of the Weak Effective Theory at the b-quark mass. We discuss three different frameworks for this analysis: (i) an update limited to the experimental data but using the same theoretical framework as in earlier works, (ii) a full update concerning both the experimental inputs and the theoretical framework, (iii) an analysis without the LHCb results on electron modes. The comparison between these various sets of results allows us to identify the differences stemming from the various components of the analysis: new experimental results, new inputs for the hadronic form factors, the role played by LHCb data on electron modes. As expected, the significance of all New Physics hypotheses gets reduced after the LHCb announcements on  $$R_{K^{(*)}}$$  <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msup> </msub> </math>   while the hypothesis of a lepton-flavour-universal contribution to the Wilson coefficient of the semileptonic  $$O_{9\ell }$$  <math> <msub> <mi>O</mi> <mrow> <mn>9</mn> <mi>ℓ</mi> </mrow> </msub> </math>   operators (possibly with a very small lepton-flavour-universality violating component) is clearly reinforced. We also discuss the possibility of a long-distance charm-loop contribution through a mode-by-mode analysis and we find that the preferred values for the  $${\mathcal C}_{9\mu }$$  <math> <msub> <mi>C</mi> <mrow> <mn>9</mn> <mi>μ</mi> </mrow> </msub> </math>   Wilson coefficient are consistent throughout the different  $$b\rightarrow s\mu ^+\mu ^-$$  <math> <mrow> <mi>b</mi> <mo>→</mo> <mi>s</mi> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> </mrow> </math>   modes and that there is no significant evidence of non-constant  $$q^2$$  <math> <msup> <mi>q</mi> <mn>2</mn> </msup> </math>   dependencies, which would indicate the presence of a long-distance charm-loop contribution beyond those already included.

Marcel Algueró

Aritra Biswas

France

Sébastien Descotes-Genon

Martin Novoa-Brunet

To (b)e or not to (b)e: no electrons at LHCb

The field of particle physics is at the crossroads. The discovery of a Higgs-like boson completed the Standard Model (SM), but the lacking observation of convincing resonances Beyond the SM (BSM) offers no guidance for the future of particle physics. On the other hand, the motivation for New Physics has not diminished and is, in fact, reinforced by several striking anomalous results in many experiments. Here we summarise the status of the most significant anomalies, including the most recent results for the flavour anomalies, the multi-lepton anomalies at the LHC, the Higgs-like excess at around 96 GeV, and anomalies in neutrino physics, astrophysics, cosmology, and cosmic rays. While the LHC promises up to 4  $$\hbox {ab}^{-1}$$  <math> <msup> <mtext>ab</mtext> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </math>   of integrated luminosity and far-reaching physics programmes to unveil BSM physics, we consider the possibility that the latter could be tested with present data, but that systemic shortcomings of the experiments and their search strategies may preclude their discovery for several reasons, including: final states consisting in soft particles only, associated production processes, QCD-like final states, close-by SM resonances, and SUSY scenarios where no missing energy is produced. New search strategies could help to unveil the hidden BSM signatures, devised by making use of the CERN open data as a new testing ground. We discuss the CERN open data with its policies, challenges, and potential usefulness for the community. We showcase the example of the CMS collaboration, which is the only collaboration regularly releasing some of its data. We find it important to stress that individuals using public data for their own research does not imply competition with experimental efforts, but rather provides unique opportunities to give guidance for further BSM searches by the collaborations. Wide access to open data is paramount to fully exploit the LHCs potential.

Oliver Fischer

South Africa

Bruce Mellado

Stefan Antusch

Emanuele Bagnaschi

CERN

Shankha Banerjee

Geoff Beck

Benedetta Belfatto

United States

Matthew Bellis

Zurab Berezhiani

Germany

Monika Blanke

Taiwan

Kingman Cheung

India

Nishita Desai

Bhupal Dev

Rohini Godbole

Tao Han

Philip Harris

Martin Hoferichter

Matthew Kirk

Austria

Suchita Kulkarni

Clemens Lange

Finland

Kati Lassila-Perini

Zhen Liu

Farvah Mahmoudi

Claudio Manzari

David Marzocca

Biswarup Mukhopadhyaya

Antonio Pich

Xifeng Ruan

Luc Schnell

Jesse Thaler

Susanne Westhoff

Unveiling hidden physics at the LHC

We present an up-to-date complete model-independent global fit to  $$b\rightarrow s\ell \ell $$  <math> <mrow> <mi>b</mi> <mo>→</mo> <mi>s</mi> <mi>ℓ</mi> <mi>ℓ</mi> </mrow> </math>   observables that confirms patterns of New Physics able to explain the data. We include the recent LHCb measurements of  $$R_K$$  <math> <msub> <mi>R</mi> <mi>K</mi> </msub> </math>  ,  $$R_{K_S}$$  <math> <msub> <mi>R</mi> <msub> <mi>K</mi> <mi>S</mi> </msub> </msub> </math>  ,  $$R_{K^{*+}}$$  <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mrow> <mrow></mrow> <mo>∗</mo> <mo>+</mo> </mrow> </msup> </msub> </math>  ,  $$B_s \rightarrow \phi \mu ^+\mu ^-$$  <math> <mrow> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>→</mo> <mi>ϕ</mi> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> </mrow> </math>   and  $$B_s\rightarrow \mu ^+\mu ^-$$  <math> <mrow> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>→</mo> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> </mrow> </math>   in our analysis, which now includes 254 observables. This updates our previous analyses and strengthens their two main outcomes. First, the presence of right-handed couplings encoded in the Wilson coefficients  $${{\mathcal {C}}}_{9'\mu }$$  <math> <msub> <mi>C</mi> <mrow> <msup> <mn>9</mn> <mo>′</mo> </msup> <mi>μ</mi> </mrow> </msub> </math>   and  $${{\mathcal {C}}}_{10'\mu }$$  <math> <msub> <mi>C</mi> <mrow> <msup> <mn>10</mn> <mo>′</mo> </msup> <mi>μ</mi> </mrow> </msub> </math>   remains a viable possibility. Second, a lepton flavour universality violating (LFUV) left-handed lepton coupling ( $${{\mathcal {C}}}_{9\mu }^{\mathrm{V}}=-{{\mathcal {C}}}_{10\mu }^{\mathrm{V}}$$  <math> <mrow> <msubsup> <mi>C</mi> <mrow> <mn>9</mn> <mi>μ</mi> </mrow> <mi>V</mi> </msubsup> <mo>=</mo> <mo>-</mo> <msubsup> <mi>C</mi> <mrow> <mn>10</mn> <mi>μ</mi> </mrow> <mi>V</mi> </msubsup> </mrow> </math>  ), often preferred from the model building point of view, accommodates the data better if lepton-flavour universal New Physics is allowed, in particular in  $${{\mathcal {C}}}_{9}^{\mathrm{U}}$$  <math> <msubsup> <mi>C</mi> <mrow> <mn>9</mn> </mrow> <mi>U</mi> </msubsup> </math>  . We observe that the LFUV observable  $$Q_5$$  <math> <msub> <mi>Q</mi> <mn>5</mn> </msub> </math>   offers a very interesting possibility to separate both types of scenarios.

$$b\rightarrow s\ell ^+\ell ^-$$  <math> <mrow> <mi>b</mi> <mo>→</mo> <mi>s</mi> <msup> <mi>ℓ</mi> <mo>+</mo> </msup> <msup> <mi>ℓ</mi> <mo>-</mo> </msup> </mrow> </math>   global fits after  $$R_{K_S}$$  <math> <msub> <mi>R</mi> <msub> <mi>K</mi> <mi>S</mi> </msub> </msub> </math>   and  $$R_{K^{*+}}$$  <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mrow> <mrow></mrow> <mo>∗</mo> <mo>+</mo> </mrow> </msup> </msub> </math>

We discuss the impact of the recent <math><mi>O</mi><mo>(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mo>)</mo></math> calculations of the semileptonic width of the b quark and of the relation between pole and kinetic heavy quark masses by Fael et al. on the inclusive determination of <math><mo>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo>|</mo></math>. The most notable effect is a reduction of the uncertainty. Our final result is <math><mo>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo>|</mo><mo>=</mo><mn>42.16</mn><mo>(</mo><mn>51</mn><mo>)</mo><mspace width="0.2em"></mspace><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>.

Marzia Bordone

Paolo Gambino

Three loop calculations and inclusive

We compute the O(α  s ) corrections to the Wilson coefficients of the dimension five operators in inclusive semileptonic B decays in the limit of a massless final quark. Our calculation agrees with reparametrization invariance and with previous results for the total width and improves the constraints on the shape functions that enter those decays.

Soumitra Nandi

Perturbative corrections to power suppressed effects in   <math> <mover> <mi>B</mi> <mo>¯</mo> </mover> </math>  $$ \overline{B} $$  → X  u  ℓν

The most statistically significant hints for new physics in the flavor sector are discrepancies between theory and experiment in <math><mi>B</mi></math> decays to lepton pairs (<math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math>) and a deficit in the unitarity constraints to the 1st row of the Cabibbo-Kobayashi-Maskawa matrix (the Cabibbo angle anomaly). We propose that these anomalies can be reconciled by a simplified model with massive gauge bosons transforming in the adjoint representation of <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>L</mi></msub></math>. After calculating the impact of this model on <math><mi>B</mi></math> decays, observables testing charged current lepton flavor universality (LFU), electro-weak precision observables and LHC searches we perform a global fit to all available data. We find that our model can provide a consistent common explanation of both anomalies and that the fit to the data is more than <math><mn>7</mn><mi>σ</mi></math> better than the fit of the Standard Model. The model also predicts interesting correlations between LFU violation in the charged current and <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> data which can be tested experimentally in the near future.

Claudio Andrea Manzari

Marc Montull

Explaining <math><mrow><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> and the Cabibbo angle anomaly with a vector triplet

This paper is an addendum to Ref. Eur. Phys. J. C79 (2019) no. 8, 714 that supersedes all results (Tables and Figures) in that paper after including the new data on the $$B\rightarrow K^*\mu \mu $$ <math><mrow><mi>B</mi><mo>→</mo><msup><mi>K</mi><mo>∗</mo></msup><mi>μ</mi><mi>μ</mi></mrow></math>  angular distribution released in 2020 by the LHCb collaboration. The new results confirm all the conclusions in Eur. Phys. J. C79 (2019) no. 8, 714, exhibiting an increase in the coherence and significance of the hypotheses and confirming the existence of a puzzle.

Pere Masjuan

Javier Virto

Addendum to: Emerging patterns of New Physics with and without Lepton Flavour Universal contributions

The deviations with respect to the Standard Model that are currently observed in b → sℓℓ transitions, or B anomalies, can be interpreted in terms of different New Physics (NP) scenarios within a model-independent effective approach. We identify a set of internal tensions of the fit that require further attention and whose theoretical or experimental nature could be determined with more data. In this landscape of NP, we discuss possible ways to discriminate among favoured NP hypotheses in the short term thanks to current and forthcoming observables. While an update of R  K  should help to disentangle the type of NP we may be observing (Lepton-Flavour Universality Violating and/or Lepton Flavour Universal), additional observables, in particular Q 5, turn out to be central to determine which NP hypothesis should be preferred. We also analyse the preferences shown by the current global fit concerning various NP hypotheses, using two different tools: the behaviour of the pulls of individual observables under NP scenarios and the directions favoured by approximate quadratic parametrisations of the observables in terms of Wilson coefficients.

What R  K  and Q 5 can tell us about New Physics in b→sℓℓ transitions?