Abstract The interference between amplitudes corresponding to different intermediate resonances plays an important role in generating large CP asymmetries in phase space in multi-body decays of bottom and charmed mesons. In this paper, we study the CP violation in the decay channel ${\overline{B}}^{0}\rightarrow K^{-}\pi^{+}\pi^{0}$ in phase space region where the intermediate resonances $\overline{K}^{*}(892)^{0}$ and ${\overline{K}^{*}_{0}(700)}$ dominate. The Forward-Backward Asymmetry (FBA) and the CP asymmetry induced by FBA (FB-CPA), which are closely related to the interference effects between the two aforementioned resonances, are especially investigated. The non-trivial correlation between FBA and FB-CPA is analyzed. The analysis indicates that the FB-CPAs around the resonance $\overline{K}^{*}(892)^{0}$ can be as large as about 35\%, which can be potentially accessible by Belle and Belle-II collaborations in the near future. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

A bstract The LHCb collaboration has recently measured the CP asymmetry in B + → J/ψπ + decay, while the Belle II collaboration has recently measured the CP asymmetries in B 0 → J/ψπ 0 decay. Within the Standard Model, and using flavor-SU(3) relations including first-order breaking corrections, these measurements lead to new predictions with regard to CP violation in B + → J/ψK + and $${B}_{s}\to J/\psi {\overline{K} }^{0}$$ decays, the difference between $${S}_{\psi {K}_{S}}$$ and sin 2 β , and the rate and CP asymmetries in B s → J/ψπ 0 decay.

The unification of gravity, electromagnetism, the weak nuclear force, and the strong nuclear force has been a central goal of theoretical physics. This paper presents a comprehensive framework based on Dynamic Vacuum Field Theory (DVFT), where all four forces emerge from variations in a single complex scalar vacuum field \phi\left(x\right)=\rho\left(x\right)e^{i\theta\left(x\right)}, with \rho\left(x\right) representing vacuum amplitude and \theta\left(x\right) the vacuum phase. Gravity arises from gradients in amplitude \nabla\rho, electromagnetism from organized phase gradients \nabla\theta, the weak force from higher-order phase excitations leading to CP violation and neutrino masses, and the strong force from topological phase constraints enforcing confinement and the mass gap. Detailed derivations are provided to demonstrate causality, locality, and consistency with observations. DVFT resolves longstanding issues like the strong CP problem, neutrino masses, and baryonic asymmetry, offering a pathway to a Grand Unified Theory without singularities or infinities.

A bstract The precise measurement of the top-Higgs coupling is crucial in particle physics, offering insights into potential new physics Beyond the Standard Model (BSM) carrying $$ \mathcal{CP} $$ CP Violation (CPV) effects. In this paper, we explore the $$ \mathcal{CP} $$ CP properties of a Higgs boson coupling with a top quark pair, focusing on events where the Higgs state decays into a pair of b -quarks and the top-antitop system decays leptonically. The novelty of our analysis resides in the exploitation of two conditional Deep Learning (DL) networks: a Multi-Layer Perceptron (MLP) and a Graph Convolution Network (GCN). These models are trained for selected CPV phase values and then used to interpolate all possible values ranging from 0 to π /2. This enables a comprehensive assessment of sensitivity across all $$ \mathcal{CP} $$ CP phase values, thereby streamlining the process as the models are trained only once. Notably, the conditional GCN exhibits superior performance over the conditional MLP, owing to the nature of graph-based Neural Network (NN) structures. Specifically, for Higgs top coupling modifier set to 1, with $$ \sqrt{s} $$ s = 13.6 TeV and integrated luminosity of 3 ab −1 GCN excludes the $$ \mathcal{CP} $$ CP phase larger than 5 ° at 95 . 4% Confidence Level (C.L). Our Machine Learning (ML) informed findings indicate that assessment of the $$ \mathcal{CP} $$ CP properties of the Higgs coupling to the $$ t\overline{t} $$ t t ¯ pair can be within reach of the High Luminosity Large Hadron Collider (HL-LHC), quantitatively surpassing the sensitivity of more traditional approaches.

A bstract The origin of the baryon asymmetry of the universe remains one of the most pressing open questions in particle physics and cosmology. Electroweak baryogenesis offers an experimentally testable explanation, requiring new sources of CP violation and a strong first-order electroweak phase transition. The Two Higgs doublet model (2HDM) is the simplest scalar extension of the Standard Model that can accommodate both ingredients. We critically assess the viability of the complex 2HDM (C2HDM) (a 2HDM with a softly broken ℤ 2 symmetry and a single source of explicit CP violation in the Higgs sector) as a framework for electroweak baryogenesis, incorporating for the first time a comprehensive set of LHC Run 2 results at 13 TeV. By defining CP-violating benchmark planes tailored for a strong first-order electroweak phase transition, we identify regions of parameter space motivated by electroweak baryogenesis that will be testable at the LHC, and at future space-based gravitational wave experiments. The benchmark planes are intended to guide ongoing efforts in defining representative scenarios for the exploration of CP-violation in extended scalar sectors at the LHC Run 3 and beyond, while also assessing the emerging synergy between the LHC and future gravitational wave observatories such as LISA. We also quantify the current tension between the realisation of electroweak baryogenesis and the non-observation of the electron electric dipole moment (EDM), finding that the predicted electron EDMs typically exceed the experimental limits by at least an order of magnitude.

A bstract We present a renormalizable SO(10) grand unified theory with a minimal Yukawa sector consisting of a 126 H , a real 10 H and a real 120 H , where CP violation has a spontaneous origin. We show that the Yukawa sector in this setup, which consists of only 19 real parameters, is capable of simultaneously reproducing the observed fermion masses and mixings, including neutrino oscillations, as well as the baryon asymmetry of the Universe via thermal leptogenesis. In this framework, CP is spontaneously broken when a CP -odd Higgs field 54 H , used for GUT symmetry breaking, acquires a non-zero vacuum expectation value. The Yukawa sector of the model contains four independent phases which determine the Dirac phases δ CKM and δ PMNS , the neutrino Majorana phases, as well as those responsible for leptogenesis. We show that these four phases can arise from a single complex parameter in the Higgs potential involving the CP -odd Higgs field 54 H . The proposed minimal setup predicts a normal ordering of neutrino masses, with the atmospheric mixing angle θ 23 preferred in the first octant and the δ PMNS lying in the range (–37°, +31°). The fermion fits in our scenario further yield a strongly hierarchical mass spectrum for the three right-handed neutrinos, ( M 1 , M 2 , M 3 ) ∼ (10 5 , 10 12 , 5 · 10 14 ) GeV, which is shown to result in successful N 2 -dominated leptogenesis, consistent with current cosmological data.

A bstract Time reversal (T) symmetry violations in neutrino oscillations imply the presence of an L -odd component in the transition probability at fixed neutrino energy, with L denoting the distance between neutrino source and detector. Within the standard three-flavour framework, we show that the combination of the transition probabilities determined at the DUNE and T2HK experiments can establish the presence of an L -odd component, and therefore provide sensitivity to T violation, up to 4 σ significance. The optimal neutrino energy window is from 0.68 to 0.92 GeV, and therefore a crucial role is played by the low-energy part of the DUNE event spectrum covering the second oscillation maximum. We compare the sensitivity to T violation based on this energy range using neutrino data only with the more traditional search for charge-parity (CP) violation based on the comparison of neutrino versus anti-neutrino beam data. We show that for DUNE it is advantageous to run in neutrino mode only, i.e., searching for T violating effects, whereas T2HK is more sensitive to CP violation, comparing neutrino and anti-neutrino data. Hence, the two experiments offer complementary methods to determine the complex phase in the PMNS mixing matrix.

A bstract We show that baryogenesis can arise from the cosmological evolution of a scalar field that governs CP-violating parameters, such as the Yukawa couplings and the theta terms of the Standard Model. During the big bang, this scalar may reach a CP-violating minimum, where its mass can be comparable to the inflationary Hubble scale. Such dynamics can emerge in theories featuring either a spontaneously broken local U(1) symmetry or modular invariance. The latter arises naturally as the effective field theory capturing the geometric origin of CP violation in toroidal string compactifications. Modular baryogenesis is compatible with the modular approach to resolving the strong CP problem.

Abstract Symmetries play an essential role in the construction and phenomenology of quantum field theories (QFTs). We discuss how to construct symmetries of QFTs by extending minimal “seed'' symmetry groups to larger groups that contain the seed(s) as subgroup(s). On the one hand, there are so-called “normal” extensions, which are given by outer automorphisms of the original symmetry group (including the trivial one) and contain the seed as a normal subgroup. On the other hand, there can be “unorthodox extensions” which do not have this property. We demonstrate our logic on the most general scalar potentials of the two- and three-Higgs-doublet models (2HDM and 3HDM). For the 2HDM, we show that all symmetry groups, including the different possible classes of CP and continuous symmetry groups, can be obtained from extensions of the smallest possible symmetry CP1 by consecutive outer automorphisms. Scanning over normal and unorthodox group extensions might be the easiest way to “machine learn” the possible symmetries of a QFT. However, many of the groups constructible in this way may not be realizable in a concrete model, in the sense that they lead to additional accidental symmetries. Hence, we also comment on a different, “top-down” way to obtain the possible realizable symmetry groups of a QFT based on the covariant transformation of couplings under the most general basis changes.

We analytically investigate the charge parity (CP) violation, neutrino masses, and leptogenesis in the Standard Model (SM) with an extension to Dirac neutrinos, building on our previous quark sector analysis. Using systematic top-down diagonalization of fermion mass matrices and experimental neutrino mass-squared differences, we predict the complete neutrino mass spectrum and assess leptogenesis viability. We find that our analysis yields specific mass predictions: mh≈5.01×10−2 eV, ml≈6.09×10−3 eV, and a bimodal middle mass (mm≈4.97×10−2 eV for inverted ordering, mm≈1.05×10−2 eV for normal ordering). Four viable scenarios emerge with parameter constraints ranging from highly restrictive (1<g<1.01512) to moderately broad (1<g<5.9). Crucially, Dirac neutrino leptogenesis is about 71 orders of magnitude weaker than baryogenesis, indicating that Standard Model leptogenesis is negligible and Beyond Standard Model physics is needed for significant leptogenesis contributions. CP violation emerges through SN symmetry breaking, with mass degeneracies controlled by model parameters. Remarkably, while mass-squared differences are small, individual neutrino masses can be significantly larger, potentially addressing dark matter mass requirements and enhancing cosmological significance. This work provides testable predictions for neutrino experiments and establishes a unified analytical approach to CP violation across fermion sectors.

Erratum to: Leveraging intermediate resonances to probe CP violation at colliders

Abstract We present our new findings on how various fundamental interactions decisively shape quantum entanglement and the Bell measure within and beyond the quantum field theory (QFT). In QFT, parity symmetry plays a key role in determining entanglement. Parity-conserving interactions produce maximally entangled bipartite systems, while maximally parity-violating interactions result in disentangled bipartite systems, placing the Bell measure on the boundary between classical and quantum theories. By examining the relation between quantum entanglement and Bell measure, we find that clean signals for interactions beyond QFT may be obtained. We propose methods to test these potential signals. Furthermore, we highlight the previously overlooked influence of magnetic fields within detectors, which radically alters predictions for quantum entanglement and Bell nonlocality. This environmental effect induces spurious P and charge-parity (CP) violations, which has to be carefully accounted for to reveal the true P, CP, and Bell nonlocality effects.

We propose a new UV-complete dark energy model which is neither a cosmological constant nor a slowly rolling scalar field. Our dark energy is the flux of a top form in a hidden sector gauge theory similar to QCD. The top form controls the vacuum energy generated by dark sector CP violation. Its flux discharges by the nucleation of membranes that source it. The tension and charge of the membranes are set by the chiral symmetry breaking scale ∼ 10-3 eV, and the dark energy is a transient. It decays on the order of the current age of the universe. The decays decrease dark energy discretely and randomly, instead of gradually like rolling scalars. Since the decay rate is close to the present Hubble scale, Γ ≳ H 0 4, in a time ∼ 𝒪(1/H 0) the cosmic acceleration may even cease altogether.

A bstract We present a comprehensive model independent analysis of all breaking patterns resulting from ∆(96) ⋊ H CP in the tri-direct CP approach of the minimal seesaw model with two right-handed neutrinos. The three generations of left-handed lepton doublets are assumed to transform as the irreducible triplet 3 0 of ∆(96), and the two right-handed neutrinos are assigned to singlets. In the case that both flavon fields ϕ atm and ϕ sol transform as triplet $$ {\overline{\textbf{3}}}_{\textbf{0}} $$ 3 ¯ 0 , only one phenomenologically viable lepton mixing pattern is obtained for normal ordering neutrino masses. The lepton mixing matrix is predicted to be the TM1 pattern, with neutrino masses, mixing angles, and CP violation phases depending on only three real input parameters. When ϕ sol is assigned to the $$ {\overline{\textbf{3}}}_{\textbf{1}} $$ 3 ¯ 1 representation, an additional real parameter x must be included. Then we find 42 (12) independent phenomenologically interesting mixing patterns for normal (inverted) ordering neutrino masses, and the corresponding predictions for lepton mixing parameters and neutrino masses are obtained. Furthermore, we perform a detailed numerical analysis for five (one) example breaking patterns with some benchmark values of x for normal (inverted) ordering. For the five normal examples, the absolute values of the first columns of the PMNS matrix are fixed to be $$ {\left(\sqrt{\frac{2}{3}},\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}}\right)}^T $$ 2 3 1 6 1 6 T , $$ \frac{1}{5}{\left(\sqrt{17},2,2\right)}^T $$ 1 5 17 2 2 T , $$ \frac{1}{\sqrt{38}}{\left(5,2,3\right)}^T $$ 1 38 5 2 3 T , $$ \frac{1}{\sqrt{57}}{\left(\sqrt{37},\sqrt{10},\sqrt{10}\right)}^T $$ 1 57 37 10 10 T and $$ \frac{1}{3}{\left(\sqrt{6},1,\sqrt{2}\right)}^T $$ 1 3 6 1 2 T , respectively. For the inverted example, the absolute value of the third column of the PMNS matrix is $$ \frac{1}{2\sqrt{11}}{\left(1,5,3\sqrt{2}\right)}^T $$ 1 2 11 1 5 3 2 T .

Symmetry studies represent one of the most promising frontiers in particle physics research. This investigation focuses on exploring P and symmetries in the charm system through the measurement of asymmetry decay parameters in the three-body decay of . By incorporating electron and positron beam polarization effects and utilizing the helicity formalism, we characterize the decay of and its secondary hyperons through asymmetry decay parameters. The complete angular distribution formula for these decays is systematically derived. Our study evaluates the sensitivity of the asymmetry parameters for the decay channel under various data sample sizes and beam polarization scenarios. The findings establish a robust theoretical framework for future experimental studies at the Super Tau-Charm Facility, providing valuable insights for symmetry investigations in the charm sector.

A bstract We consider the most general axion-like particle effective field theory, including both CP-odd and CP-even types of interactions, and evaluate the corresponding renormalization group equations, improving and extending previous results in the literature. Our calculations exploit on-shell and unitarity-based methods. The relevant phase-space cut-integrals are carried out using different integration methods, among which the double-cut integration via Stokes’ theorem proves to be technically simpler. A close comparison between the standard Feynman diagrammatic approach and the unitarity-based method enables us to explicitly verify the reduction of complexity in the latter case, along with a more direct and elegant way to establish a connection among anomalous dimensions of operators that are dual under the CP symmetry.

A bstract We study SU( N ) super Yang-Mills theory with a small gaugino mass m and vacuum angle θ on the four-torus $$ {\mathbbm{T}}^4 $$ T 4 with ’t Hooft twisted boundary conditions. Introducing a detuning parameter ∆, which measures the deviation from an exactly self-dual $$ {\mathbbm{T}}^4 $$ T 4 , and working in the limits mLN ≪ Λ LN ≪ 1 and $$ \frac{\left(N-1\right){m}^2{L}^2}{4\pi}\ll \Delta \ll 1 $$ N − 1 m 2 L 2 4 π ≪ ∆ ≪ 1 , where L is the torus size and Λ the strong-coupling scale, we compute the scalar and pseudo-scalar condensates to leading order in m 2 L 2 /∆. The twists generate fractional-charge instantons, and we show that summing over all such contributions is crucial for reproducing the correct physical observables in the decompactified strong-coupling regime. From a Hamiltonian perspective, the sum over twisted sectors, already at small torus size, projects in the m = 0 limit onto a definite superselection sector of the ℝ 4 theory. In the massless limit, we recover the exact value of the gaugino condensate |〈 λλ 〉| = 16 π 2 Λ 3 , and demonstrate how a spurious U(1) symmetry eliminates all $$ \mathcal{CP} $$ CP -violating effects. Our results are directly testable in lattice simulations, and our method extends naturally to non-supersymmetric gauge theories.

A bstract A time-integrated angular analysis of the decay $$ {B}_s^0\to J/\psi {\overline{K}}^{\ast }{(892)}^0 $$ B s 0 → J / ψ K ¯ ∗ 892 0 , with J / ψ → μ + μ − and $$ {\overline{K}}^{\ast }{(892)}^0\to {K}^{-}{\pi}^{+} $$ K ¯ ∗ 892 0 → K − π + , is presented. The analysis employs a sample of proton-proton collision data collected by the LHCb experiment during 2015–2018 at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 6 fb − 1 . A simultaneous maximum-likelihood fit is performed to the angular distributions in bins of the K − π + mass. This fit yields measurements of the CP -averaged polarisation fractions and CP asymmetries for the P-wave component of the K − π + system. The longitudinal and parallel polarisation fractions are determined to be f 0 = 0.534 ± 0.012 ± 0.009 and f || = 0.211 ± 0.014 ± 0.005, respectively, where the first uncertainty is statistical and the second is systematic. The CP asymmetries are measured with 3–7% precision and are found to be consistent with zero. These measurements, along with an updated determination of the branching fraction relative to the B 0 → J / ψK *0 decay, are combined with previous LHCb results, providing the most precise values for these observables to date.

A bstract A study of $$ {\Lambda}_b^0 $$ Λ b 0 and $$ {\Xi}_b^0 $$ Ξ b 0 baryon decays to the final states $$ p{K}_{\textrm{S}}^0{\pi}^{-} $$ p K S 0 π − and $$ p{K}_{\textrm{S}}^0{K}^{-} $$ p K S 0 K − is performed using pp collision data collected by the LHCb experiment, corresponding to an integrated luminosity of 9 fb − 1 . The decays $$ {\Lambda}_b^0\to p{K}_{\textrm{S}}^0{K}^{-} $$ Λ b 0 → p K S 0 K − and $$ {\Xi}_b^0\to p{K}_{\textrm{S}}^0{K}^{-} $$ Ξ b 0 → p K S 0 K − are observed for the first time, with significances reaching eight standard deviations. The branching fractions and integrated CP asymmetries are measured for the $$ {\Lambda}_b^0\to p{K}_{\textrm{S}}^0{\pi}^{-} $$ Λ b 0 → p K S 0 π − , $$ {\Lambda}_b^0\to p{K}_{\textrm{S}}^0{K}^{-} $$ Λ b 0 → p K S 0 K − , and $$ {\Xi}_b^0\to p{K}_{\textrm{S}}^0{K}^{-} $$ Ξ b 0 → p K S 0 K − decays. For the decay $$ {\Lambda}_b^0\to p{K}_{\textrm{S}}^0{\pi}^{-} $$ Λ b 0 → p K S 0 π − , the CP asymmetries are measured in different regions of the Dalitz plot. No evidence of CP violation is observed.

In this paper, we investigate the CP asymmetries ACPpm and ACPmp in Bc±→B±K0+B±K¯0→B±π±e∓νe and Bc±→B±K0+B±K¯0→B±π∓e±νe decays; both of them consist of three parts: the indirect CP violations in K0−K¯0 mixing ACP,mixpm and ACP,mixmp, the direct CP violations in Bc decay ACP,dirpm and ACP,dirmp, and the new CP violation effects ACP,intpm and ACP,intmp, which originate from the interference between the amplitude of the Bc−→B−K0(K¯0)→B−π−e+νe(π+e−ν¯e) decay with the difference between the oscillating effect of K0→K¯0 and that of K¯0→K0. The strong phase differences of the direct CP asymmetries ACP,dirpm and ACP,dirmp arise from K0−K¯0 mixing parameters. ACPpm and ACPmp are of the order of O(10−4) and O(10−3), respectively. The new CP violation effect ACP,intpm plays a dominant role in ACPpm; the CP asymmetry ACPmp is dominated by the indirect CP violation ACP,mixmp, so the CP asymmetry ACPpm provides an ideal place to study the new CP violation effect. We derive another two asymmetry observables ACPpp and ACPmm, which are dominated by K0−K¯0 mixing. The observables ACPpm, ACPmp, ACPpp, and ACPmm are hopefully to be marginally observed at the LHC experiment and the HL-LHC experiment.