We derive a saturation theorem for general Effective Field Theories (EFTs) constructed using spurion analysis. Let $\textit{S}$ be a set of spurion fields introduced to organize the breaking of a global symmetry $\textit{G}$ , and $\textit{H}$ be the subgroup of $\textit{G}$ that remains unbroken under a generic vacuum expectation value ⟨$\textit{S}$⟩; we show that the EFT Lagrangian constructed from the spurion analysis $\textit{saturates}$ the EFT Lagrangian without the spurions but restricted to $\textit{H}$ invariance, provided that arbitrary powers of the spurion fields are allowed. As examples, we study several implementations of the Minimal Lepton Flavor Violation (MLFV) principle, corresponding to various origins of the neutrino masses. In each scenario, we compute the Hilbert series to obtain the numbers of independent lepton flavor covariants that appear in the corresponding EFT at mass dimension 6. These numbers agree with the number of $\textit{H}$ invariants in the EFT without the spurions, demonstrating the saturation theorem. Motivated by phenomenological connections, we provide linearly independent spurion polynomials for selected lepton flavor covariants. A supplementary material file supplies , a Mathematica notebook that provides functions for computing general Hilbert series of invariants and covariants of compact classical groups. It presents examples demonstrating the use of the code, including the Hilbert series for our MLFV scenarios.

United States

Benjamín Grinstein

Xiaochuan Lu

Spain

Carlos Miró

Pablo Quílez

Most general EFTs from spurion analysis Hilbert series and minimal lepton flavor violation

Accidental symmetries in effective field theories can be established by computing and comparing Hilbert series. This invites us to study them with the tools of invariant theory. Applying this technology, we spotlight three classes of accidental symmetries that hold to all orders for non-derivative interactions. They are broken by derivative interactions and become ordinary finite-order accidental symmetries. To systematically understand the origin and the patterns of accidental symmetries, we introduce a novel mathematical construct — a (non-transitive) binary relation between subgroups that we call . Equipped with this, we derive new criteria for all-order accidental symmetries in terms of , and criteria for finite-order accidental symmetries in terms of . They allow us to verify and identify accidental symmetries more efficiently without computing the Hilbert series. We demonstrate the success of our new criteria by applying them to a variety of sample accidental symmetries, including the custodial symmetry in the Higgs sector of the Standard Model effective field theory.

Accidental symmetries, Hilbert series, and

A correction to this paper has been published: https://doi.org/10.1007/JHEP06(2024)154

Luca Merlo

Erratum to: Hilbert series for covariants and their applications to minimal flavor violation

To reduce the current theory uncertainties a novel way to determine the <math altimg='si1.svg'><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></math> lifetime, <math altimg='si2.svg'><msub><mrow><mi>&#964;</mi></mrow><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></msub></math>, is proposed. Taking the difference of the <math altimg='si1.svg'><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></math>, and <italic>B</italic> and <italic>D</italic> meson decay rates eliminates the leading contributions from the calculation, which exhibit large scale and scheme dependence. The uncertainties in the proposed determination of <math altimg='si2.svg'><msub><mrow><mi>&#964;</mi></mrow><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></msub></math> are analyzed and improvements are proposed. The method predicts a value of <math altimg='si2.svg'><msub><mrow><mi>&#964;</mi></mrow><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></msub></math> in tension with the experimental determination. Several explanations are considered, including underestimation of uncertainties, duality violation and new physics. We discuss quantitative evidence that our method is vitiated by duality violation in the large mass OPE used to calculate nonleptonic decay rates of <italic>B</italic> and <italic>D</italic> mesons.

Jason Aebischer

A novel determination of the <italic>B</italic> <inf><italic>c</italic></inf> lifetime

We elaborate how to apply the Hilbert series method to enumerating group covariants, which transform under any given representation, including but going beyond group invariants. Mathematically, group covariants form a module over the ring of the invariants. The number of independent covariants is given by the rank of the module, which can be computed by taking a ratio of two Hilbert series. In many cases, the rank equals the dimension of the group covariant representation. When this happens, we say that there is a . We apply this technology to revisit the hypothesis of Minimal Flavor Violation in constructing Effective Field Theories beyond the Standard Model. We find that rank saturation is guaranteed in this case, leading to the important consequence that the MFV symmetry principle does not impose any restriction on the EFT, i.e. MFV SMEFT = SMEFT, in the absence of additional assumptions.

Hilbert series for covariants and their applications to minimal flavor violation

Dark sector particles at the GeV scale carrying baryon number provide an attractive framework for understanding the origin of dark matter and the matter-antimatter asymmetry of the universe. We demonstrate that dark decays of hadronic states containing strange quarks—hyperons—offer excellent prospects for discovering such dark baryons. Building up on novel calculations of the matrix elements relevant for hyperon dark decays, and in view of various collider, flavor, and astrophysical constraints, we determine the expected rates at hyperon factories like BESIII and LHCb. We also highlight the interesting theoretical connections of hyperon dark decays to the neutron lifetime anomaly and mesogenesis.

Canada

Gonzalo Alonso-Álvarez

Germany

Gilly Elor

Miguel Escudero

Bartosz Fornal

Jorge Martin Camalich

Strange physics of dark baryons

Motivated by renewed evidence for new physics in <math><mi>b</mi><mo>→</mo><mi>s</mi><mo>ℓ</mo><mo>ℓ</mo></math> transitions in the form of LHCb’s new measurements of theoretically clean lepton-universality ratios and the purely leptonic <math><msub><mi>B</mi><mi>s</mi></msub><mo>→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> decay, we quantify the combined level of discrepancy with the Standard Model and fit values of short-distance Wilson coefficients. A combination of the clean observables <math><msub><mi>R</mi><mi>K</mi></msub></math>, <math><msub><mi>R</mi><msup><mi>K</mi><mo>*</mo></msup></msub></math>, and <math><msub><mi>B</mi><mi>s</mi></msub><mo>→</mo><mi>μ</mi><mi>μ</mi></math> alone results in a discrepancy with the Standard Model at <math><mn>4.0</mn><mi>σ</mi></math>, up from <math><mn>3.5</mn><mi>σ</mi></math> in 2017. One-parameter scenarios with purely left-handed or with purely axial coupling to muons fit the data well and result in a <math><mo>∼</mo><mn>5</mn><mi>σ</mi></math> pull from the Standard Model. In a two-parameter fit of new-physics contributions with both vector and axial-vector couplings to muons the allowed region is much more restricted than in 2017, principally due to the much more precise result on <math><msub><mi>B</mi><mi>s</mi></msub><mo>→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math>, which probes the axial coupling to muons. Including angular observables data restricts the allowed region further. A by-product of our analysis is an updated average of <math><mi>BR</mi><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><mo>=</mo><mo>(</mo><mn>2.8</mn><mo>±</mo><mn>0.3</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>9</mn></mrow></msup></math>.

China

Li-Sheng Geng

United Kingdom

Sebastian Jäger

Shuang-Yi Li

Rui-Xiang Shi

Implications of new evidence for lepton-universality violation in <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> decays

Applying an operator product expansion approach we update the Standard Model prediction of the B  c  lifetime from over 20 years ago. The non-perturbative velocity expansion is carried out up to third order in the relative velocity of the heavy quarks. The scheme dependence is studied using three different mass schemes for the   <math> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ \overline{b} $$  and c quarks, resulting in three different values consistent with each other and with experiment. Special focus has been laid on renormalon cancellation in the computation. Uncertainties resulting from scale dependence, neglecting the strange quark mass, non-perturbative matrix elements and parametric uncertainties are discussed in detail. The resulting uncertainties are still rather large compared to the experimental ones, and therefore do not allow for clear-cut conclusions concerning New Physics effects in the B  c  decay.

Standard Model prediction of the B  c  lifetime

We propose a new strategy to search for a particular type of dark matter via nuclear capture. If the dark matter particle carries baryon number, as motivated by a class of theoretical explanations of the matter-antimatter asymmetry of the universe, it can mix with the neutron and be captured by an atomic nucleus. The resulting state de-excites by emitting a single photon or a cascade of photons with a total energy of up to several MeV. The exact value of this energy depends on the dark matter mass. We investigate the prospects for detecting dark matter capture signals in current and future neutrino and dark matter direct detection experiments.

Yue Zhao

Dark matter capture by atomic nuclei

We revisit the status of the new-physics interpretations of the anomalies in semileptonic B decays in light of the new data reported by Belle on the lepton-universality ratios R  D(*) using the semileptonic tag and on the longitudinal polarization of the D  *  in B → D  *  τν,   <math> <msubsup> <mi>F</mi> <mi>L</mi> <mrow> <mi>D</mi> <mo>∗</mo> </mrow> </msubsup> </math>  $$ {F}_L^{D\ast } $$ . The preferred solutions involve new left-handed currents or tensor contributions. Interpretations with pure right-handed currents are disfavored by the LHC data, while pure scalar models are disfavored by the upper limits derived either from the LHC or from the B  c  lifetime. The observable   <math> <msubsup> <mi>F</mi> <mi>L</mi> <mrow> <mi>D</mi> <mo>∗</mo> </mrow> </msubsup> </math>  $$ {F}_L^{D\ast } $$  also gives an important constraint leading to the exclusion of large regions of parameter space. Finally, we investigate the sensitivity of different observables to the various scenarios and conclude that a measurement of the tau polarization in the decay mode B → Dτν would effectively discriminate among them.