We investigate the lineshapes of the X(3872) in B^+ decays production within a framework that incorporates two underlying QCD configurations: a compact isosinglet state X_S and the neutral component of a molecular isotriplet X_T^0. The physical signal is interpreted as arising from the mixing of these states, induced by strong isospin breaking. The decay amplitude is constructed in a factorized form, separating short-distance production, non-relativistic propagation and final-state interactions. This setup allows for a unified description of both DD^* and J/ψ + pions final states. We show that the interplay between the two components and their mixing can qualitatively reproduce several nontrivial experimental features. In particular, interference effects can enhance the charged DD^* channel relative to the neutral one despite phase-space suppression, and generate distinctive structures in the J/ψπ^+π^- and J/ψπ^+π^-π^0 lineshapes, including the possibility of strong distortions near threshold.

We derive a saturation theorem for general Effective Field Theories (EFTs) constructed using spurion analysis. Let S be a set of spurion fields introduced to organize the breaking of a global symmetry Gf, and HS be the subgroup of Gf that remains unbroken under a generic vacuum expectation value ⟨S⟩; we show that the EFT Lagrangian constructed from the spurion analysis saturates the EFT Lagrangian without the spurions but restricted to HS 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 HS 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.

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 friendship. Equipped with this, we derive new criteria for all-order accidental symmetries in terms of friends, and criteria for finite-order accidental symmetries in terms of friends ma non troppo. 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.

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

Perturbative partial-wave amplitudes diverge in cases with a massless exchanged particle in the t-channel. We argue that the divergence is an artifact of perturbation theory and give a prescription for the all-orders correction factor that renders the partial waves finite. As an example, we apply this to longitudinal W^+W^- elastic scattering, for which there is a photon exchange t-channel contribution, and derive improved quasi-perturbative unitarity bounds on the mass of the Higgs. The method is also useful for t-channel exchange of very light particles.

The conventional loosely bound molecule interpretation of the X(3872) is not compatible with the recent LHCb experimental measurement of the ratio of branching fractions ℛ = Br(X → ψ′γ)/Br(X → ψγ). We systematically determine the entire tetraquark spectrum for J = 0, 1, 2 and refine the calculation of ℛ in an improved Born-Oppenheimer description of the X(3872) compact tetraquark. This refinement yields a significantly better agreement with experimental data on ℛ and on the spectroscopy of the states themselves. Extending the diquark-antidiquark paradigm to encompass tetraquarks that are linear super-positions of open charm singlets and color octets, we discover that these exotic resonances manifest as compact shallow bound states of quarks in color force potentials.

We compute the one-loop contribution to the $\bar{\theta}$-parameter of an axion-like particle (ALP) with CP-odd derivative couplings. Its contribution to the neutron electric dipole moment is shown to be orders of magnitude larger than that stemming from the one-loop ALP contributions to the up- and down-quark electric and chromoelectric dipole moments. This strongly improves existing bounds on ALP-fermion CP-odd interactions, and also sets limits on previously unconstrained couplings. The case of a general singlet scalar is analyzed as well. In addition, we explore how the bounds are modified in the presence of a Peccei-Quinn symmetry.

Radiative decays X --> psi(1S) + gamma and X --> psi(2S) + gamma might be expected to have a ratio of branching fractions following the phase space volumes ratio. However data suggest the opposite, indicating a value for R=B(X --> psi^prime + gamma) / B(X --> psi +gamma) consistently larger than one. In this paper we present a calculation of R for both a compact Born-Oppenheimer cc-bar q-qbar state and a DD^* molecule. In the former case R~1 or larger is found, a value to be confronted with forthcoming high statistics data analyses. In the molecular picture, with D and D^* mesons described by the universal wave function used by Voloshin, Braaten and Kusunoki, we find that R would be of order 10^-2. A more precise experimental measure would be extremely helpful in clarifying the true nature of the X(3872).

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 rank saturation. 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.

Rare meson decays are among the most sensitive probes of both heavy and light new physics. Among them, new physics searches using kaons benefit from their small total decay widths and the availability of very large datasets. On the other hand, useful complementary information is provided by hyperon decay measurements. We summarize the relevant phenomenological models and the status of the searches in a comprehensive list of kaon and hyperon decay channels. We identify new search strategies for under-explored signatures, and demonstrate that the improved sensitivities from current and next-generation experiments could lead to a qualitative leap in the exploration of light dark sectors.

The Standard Model decay rate of the $B_c$ meson is discussed together with a novel approach that uses experimental data in combination with an operator product expansion. In the new method differences of $B,\,D$ and $B_c$ meson decay rates are considered for which the free-quark contributions drop out, leading to a reduction of the theory prediction.

The Standard Model prediction of the $B_c$ lifetime is discussed, together with the dominant uncertainties and strategies on how to improve them. Furthermore, a new method to compute the $B_c$ lifetime based on the operator product expansion is proposed. It relies on differences of $B,\,D$ and $B_c$ meson decay rates, in which the free-quark contributions cancel out, reducing the uncertainty of the theory prediction.

To reduce the current theory uncertainties a novel way to determine the Bc lifetime, τBc, is proposed. Taking the difference of the Bc, and B and D meson decay rates eliminates the leading contributions from the calculation, which exhibit large scale and scheme dependence. The uncertainties in the proposed determination of τBc are analyzed and improvements are proposed. The method predicts a value of τBc 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 B and D mesons.

The Standard Model decay rate of the $B_c$ meson is discussed together with a novel approach based on the usage of experimental data in combination with an operator product expansion. In the new method differences of $B,\,D$ and $B_c$ meson decay rates are considered, for which the free-quark contributions drop out, leading to a reduction of the theory prediction.

The Standard Model prediction of the B_c lifetime is discussed, together with the dominant uncertainties and strategies on how to improve them. Furthermore, a new method to compute the B_c lifetime based on the operator product expansion is proposed. It relies on differences of B, D and B_c meson decay rates, in which the free-quark contributions cancel out, reducing the uncertainty of the theory prediction.

Using an operator product expansion (OPE) approach an updated StandardModel prediction of the 2 lifetime is presented. The computation in three different mass schemes for the heavy quarks leads to three different values consistent with each other and with experiment. Furthermore a novel way to compute the 2 lifetime is presented, taking differences of , and 2 meson decay rates. In this approach the leading contributions from free-quark decays cancel out, leading to a reduction of scale and scheme dependence.

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.