<p>Through a holographic model of QCD, we present a phenomenological approach to study the running of the strong coupling constant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> in both nonperturbative and perturbative regimes. The renormalization of the metric tensor, driven by the Ricci Flow, and the breaking of conformal and chiral symmetries—thanks to introducing a double dilaton model and large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> corrections—allows us to relate the existence of an infrared fixed point in the coupling constant with a smooth matching to perturbative QCD well above 2 GeV. This is done through a model with two fit parameters and one matching point. The proposed dilaton model yields linear Regge trajectories and decay constants for scalar, vector, and tensor meson families similar to their experimental counterparts.</p>

Spain

Héctor Cancio

Pere Masjuan

Holographic QCD running coupling constant from the Ricci flow

The MUonE experiment is designed to extract the hadronic contribution to the electromagnetic coupling in the spacelike region <math><mi>Δ</mi><msub><mi>α</mi><mrow><mi>had</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math> from elastic <math><mi>e</mi><mi>μ</mi></math> scattering. The leading-order hadronic vacuum polarization contribution to the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math>, <math><msubsup><mi>a</mi><mi>μ</mi><mrow><mi>HVP</mi><mo>,</mo><mi>LO</mi></mrow></msubsup></math>, can then be obtained from a weighted integral over <math><mi>Δ</mi><msub><mi>α</mi><mrow><mi>had</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math>. This, however, requires knowledge of <math><mi>Δ</mi><msub><mi>α</mi><mrow><mi>had</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math> in the whole domain of integration, which cannot be achieved by experiment. In this work, we propose to use Padé and D-Log Padé approximants as a systematic and model-independent method to fit and reliably extrapolate the future MUonE experimental data, extracting <math><msubsup><mi>a</mi><mi>μ</mi><mrow><mi>HVP</mi><mo>,</mo><mi>LO</mi></mrow></msubsup></math> with a conservative but competitive uncertainty, using no or very limited external information. The method relies on fundamental analytic properties of the two-point correlator underlying <math><msubsup><mi>a</mi><mi>μ</mi><mrow><mi>HVP</mi><mo>,</mo><mi>LO</mi></mrow></msubsup></math> and provides lower and upper bounds for the result for <math><msubsup><mi>a</mi><mi>μ</mi><mrow><mi>HVP</mi><mo>,</mo><mi>LO</mi></mrow></msubsup></math>. We demonstrate the reliability of the method using toy datasets generated from a model for <math><mi>Δ</mi><msub><mi>α</mi><mrow><mi>had</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math> reflecting the expected statistics of the MUonE experiment.

Brazil

Diogo Boito

Cristiane Y. London

Camilo Rojas

Model-independent extrapolation of MUonE data with Padé and D-Log approximants

We compute for the first time the τ data-driven Euclidean windows for the hadronic vacuum polarization contribution to the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math>. We show that τ-based results agree with the available lattice window evaluations and with the full result. On the intermediate window, where all lattice evaluations are rather precise and agree, τ-based results are compatible with them. This is particularly interesting, given that the disagreement of the <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> data-driven result with the lattice values in this window is the main cause for their discrepancy, affecting the interpretation of the <math><msub><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow></msub></math> measurement in terms of possible new physics.

Alejandro Miranda

Mexico

Pablo Roig

data-driven evaluation of Euclidean windows for the hadronic vacuum polarization

We determine the bottom quark mass  $${\hat{m}}_b$$  <math> <msub> <mover> <mi>m</mi> <mo>^</mo> </mover> <mi>b</mi> </msub> </math>   from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD to  $${{\mathcal {O}}} ({\hat{\alpha }}_s^3)$$  <math> <mrow> <mi>O</mi> <mo>(</mo> <msubsup> <mover> <mi>α</mi> <mo>^</mo> </mover> <mi>s</mi> <mn>3</mn> </msubsup> <mo>)</mo> </mrow> </math>  . Our approach is based on the mutual consistency across a set of moments where experimental data are required for the resonance contributions only. Additional experimental information from the continuum region can then be used for stability tests and to assess the theoretical uncertainty. We find  $${\hat{m}}_b({\hat{m}}_b) = (4180.2 \pm 7.9)$$  <math> <mrow> <msub> <mover> <mi>m</mi> <mo>^</mo> </mover> <mi>b</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>m</mi> <mo>^</mo> </mover> <mi>b</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>4180.2</mn> <mo>±</mo> <mn>7.9</mn> <mo>)</mo> </mrow> </mrow> </math>   MeV for  $${\hat{\alpha }}_s(M_Z) = 0.1182$$  <math> <mrow> <msub> <mover> <mi>α</mi> <mo>^</mo> </mover> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>M</mi> <mi>Z</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.1182</mn> </mrow> </math>  .

Germany

Jens Erler

Hubert Spiesberger

Bottom quark mass with calibrated uncertainty

We use rational approximants to study missing higher orders in the massless scalar-current quark correlator. We predict the yet unknown six-loop coefficient of its imaginary part, related to Γ(H → b   <math> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ \overline{b} $$ ), to be c 5 = −6900 ± 1400. With this result, the perturbative series becomes almost insensitive to renormalization scale variations and the intrinsic QCD truncation uncertainty is tiny. This confirms the expectation that higher-order loop computations for this quantity will not be required in the foreseeable future, as the uncertainty in Γ(H → b   <math> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ \overline{b} $$ ) will remain largely dominated by the Standard Model parameters.

Austria

Cristiane London

Higher-order QCD corrections to H → b   <math> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ \overline{b} $$  from rational approximants

In light of the first observation of the semileptonic decay <math><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><mo>→</mo><msup><mi>K</mi><mo>−</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub></math> by the LHCb Collaboration, we revisit the determination of the Cabibbo-Kobayashi-Maskawa parameter <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo>|</mo></math> from exclusive semileptonic <math><mi>B</mi></math>-meson decays. A controlled theoretical input on the Standard Model <math><mi>B</mi><mo>→</mo><mi>π</mi></math> and <math><msub><mi>B</mi><mi>s</mi></msub><mo>→</mo><mi>K</mi></math> vector and scalar form factors from Lattice QCD in the large <math><msup><mi>q</mi><mn>2</mn></msup></math> region, in combination with experimental measurements of the differential <math><mi>B</mi><mo>→</mo><mi>π</mi><mo>ℓ</mo><msub><mi>ν</mi><mo>ℓ</mo></msub></math> and <math><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><mo>→</mo><msup><mi>K</mi><mo>−</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub></math> branching ratio distributions, has allowed us determine <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo>|</mo><mo>=</mo><mn>3.86</mn><mo>(</mo><mn>11</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> and <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo>|</mo><mo>=</mo><mn>3.58</mn><mo>(</mo><mn>9</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> from the analyses of the individual decay channels, respectively, and <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo>|</mo><mo>=</mo><mn>3.68</mn><mo>(</mo><mn>5</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> from a simultaneous analysis of both decays, which is only a 1.4% error and differs by <math><mn>1.8</mn><mi>σ</mi></math> with respect to the value from inclusive determinations <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo>|</mo><mo>=</mo><mn>4.25</mn><mo>(</mo><mn>12</mn><msubsup><mo>)</mo><mrow><mo>−</mo><mn>14</mn></mrow><mrow><mo>+</mo><mn>15</mn></mrow></msubsup><mo>(</mo><mn>23</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>. Our results are based on the use of Padé approximants to the participating form factors, highlighting the importance of the decay <math><msub><mi>B</mi><mi>s</mi></msub><mo>→</mo><mi>K</mi><mi>μ</mi><msub><mi>ν</mi><mi>μ</mi></msub></math> in complementing the traditional <math><mi>B</mi><mo>→</mo><mi>π</mi><mo>ℓ</mo><msub><mi>ν</mi><mo>ℓ</mo></msub></math> one in the exclusive determination of <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo>|</mo></math> and allowing us to obtain, to the best of our knowledge, the first correlated results for the <math><mi>B</mi><mo>→</mo><mi>π</mi></math> and <math><msub><mi>B</mi><mi>s</mi></msub><mo>→</mo><mi>K</mi></math> vector and scalar form factors. We hope that our study strengthens the case for precise measurements of the differential <math><msub><mi>B</mi><mi>s</mi></msub><mo>→</mo><mi>K</mi><mo>ℓ</mo><msub><mi>ν</mi><mo>ℓ</mo></msub></math> decay rate with a finer resolution of the <math><msup><mi>q</mi><mn>2</mn></msup></math> bins, as it would definitely allow achieving more conclusive results for <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo>|</mo></math>.

United States

Sergi Gonzàlez-Solís

Padé approximants to <math><mi>B</mi><mo>→</mo><mi>π</mi><mo>ℓ</mo><msub><mi>ν</mi><mo>ℓ</mo></msub></math> and <math><msub><mi>B</mi><mi>s</mi></msub><mo>→</mo><mi>K</mi><mo>ℓ</mo><msub><mi>ν</mi><mo>ℓ</mo></msub></math> and determination of <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo>|</mo></math>

In this paper we present a detailed study of the four-body decay B 0 → K + π  −  ℓ + ℓ  − , where tensions with the Standard Model predictions have been observed. Our analysis of the decay with P- and S-wave contributions to the K + π  −  system develops a complete understanding of the symmetries of the distribution, in the case of massless and massive leptons. In both cases, the symmetries determine relations between the observables in the B 0 → K + π  −  ℓ + ℓ  −  decay distribution. This enables us to define the complete set of observables accessible to experiments, including several that have not previously been identified. The new observables arise when the decay rate is written differentially with respect to   <math> <msub> <mi>m</mi> <msub> <mi>K</mi> <mi>π</mi> </msub> </msub> </math>  $$ {m}_{K_{\pi }} $$ . We demonstrate that experiments will be able to fit this full decay distribution with currently available data sets and investigate the sensitivity to new physics scenarios given the experimental precision that is expected in the future.

Marcel Algueró

United Kingdom

Paula Cartelle

Alexander Marshall

Joaquim Matias

Michael McCann

Mitesh Patel

Konstantinos Petridis

Mark Smith

A complete description of P- and S-wave contributions to the B 0 → K + π  −  ℓ + ℓ  −  decay

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.

Italy

Bernat Capdevila

Switzerland

Andreas Crivellin

France

Sébastien Descotes-Genon

Martín Novoa-Brunet

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?

We perform a model-independent global fit to $$b\rightarrow s\ell ^+\ell ^-$$ <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>  observables to confirm existing New Physics (NP) patterns (or scenarios) and to identify new ones emerging from the inclusion of the updated LHCb and Belle measurements of $$R_K$$ <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> , respectively. Our analysis, updating Refs. Capdevila et al. (J Virto JHEP 1801:093, 2018) and Algueró et al. (J Matias Phys Rev D 99(7):075017, 2019) and including these new data, suggests 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> . It also strengthens our earlier observation that 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><mspace width="0.166667em"></mspace><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 (LFU) NP 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> . Furthermore, this scenario with LFU NP provides a simple and model-independent connection to the $$b\rightarrow c\tau \nu $$ <math><mrow><mi>b</mi><mo>→</mo><mi>c</mi><mi>τ</mi><mi>ν</mi></mrow></math>  anomalies, showing a preference of $$\approx 7\,\sigma $$ <math><mrow><mo>≈</mo><mn>7</mn><mspace width="0.166667em"></mspace><mi>σ</mi></mrow></math>  with respect to the SM. It may also explain why fits to the whole set of $$b\rightarrow s\ell ^+\ell ^-$$ <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>  data or to the subset of LFUV data exhibit stronger preferences for different NP scenarios. Finally, motivated by $$Z^\prime $$ <math><msup><mi>Z</mi><mo>′</mo></msup></math>  models with vector-like quarks, we propose four new scenarios with LFU and LFUV NP contributions that give a very good fit to data.

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