Mixing CP Research Articles

Fast Inclusive Flavour Tagging at LHCb

The task of identifying B meson flavor at the primary interaction point in the LHCb detector is crucial for measurements of mixing and timedependent CP violation. Flavor tagging is usually done with a small number of expert systems that find important tracks to infer the B meson flavor from. Recent advances show that replacing all of those expert systems with one ML algorithm that considers all tracks in an event yields an increase in tagging power. However, training the current classifier takes a long time and it is not suitable for use in real time triggers. In this work we present a new classifier, based on the DeepSet architecture. With the right inductive bias of permutation invariance, we achieve great speedups in training (multiple hours vs 10 minutes), a factor of 4-5 speed-up in inference for use in real time environments like the trigger and less tagging asymmetry. For the first time we investigate and compare performances of these “Inclusive Flavor Taggers” on simulation of the upgraded LHCb detector for the third run of the LHC.

The minimal flavor structure of quarks and leptons

A flavor structure with minimal parameters is proposed to address the fermion mass hierarchy and flavor mixing for quarks and leptons. Yukawa interaction is reconstructed in a new basis to show a common flat structure for up-type quarks, down-type quarks, charged leptons, and Dirac neutrinos. A flavor symmetry is found from the hierarchy masses of quarks and leptons, which dominated Cabibbo–Kobayashi–Maskawa (CKM) mixing for quarks and Pontecorvo–Maki–Nakagawa–Sakata mixing for leptons. It results that the minimal flavor structure successfully addresses flavor mixings of quarks and leptons even in the mass hierarchy limit, which means that mass hierarchy and flavor mixing are two independent questions. As a prediction, a sum rule on the mixing angles and CP violation phase (CPV) is suggested, which explains the smallness of s 13 as a natural result of the mass hierarchy. Generalizing the flat structure to quarks and leptons, a unified Yukawa interaction is also achieved for all fermions with only a single coupling.

A4 modular flavour model of quark mass hierarchies close to the fixed point τ = i∞

We study the possibility to generate the quark mass hierarchies as well as the CKM quark mixing and CP violation without fine-tuning in a quark flavour model with modular A4 symmetry. The quark mass hierarchies are considered in the vicinity of the fixed point τ = i∞, τ being the vacuum expectation value of the modulus. We consider first a model in which the up-type and down-type quark mass matrices Mu and Md involve modular forms of level 3 and weights 6, 4 and 2 and each depends on four constant parameters. Two ratios of these parameters, gu and gd, can be sources of the CP violation. If Mu and Md depend on the same τ, it is possible to reproduce the up-type and down-type quark mass hierarchies in the considered model for |gu| ~ mathcal{O} (10) with all other constants being in magnitude of the same order. However, reproducing the CP violation in the quark sector is problematic. A correct description of the quark mass hierarchies, the quark mixing and CP violation is possible close to τ = i∞ with all constant being in magnitude of the same order and complex gu and gd, if there are two different moduli τu and τd in the up-type and down-type quark sectors. We also consider the case of Mu and Md depending on the same τ and involving modular forms of weights 8, 4, 2 and 6, 4, 2, respectively, with Mu receiving a tiny SUSY breaking or higher dimensional operator contribution. Both the mass hierarchies of up-type and down-type quarks as well and the CKM mixing angles and CP violating phase are reproduced successfully with one complex parameter and all parameters being in magnitude of the same order. The relatively large value of Im τ, needed for describing the down-type quark mass hierarchies, is crucial for obtaining the correct up-type quark mass hierarchies.

Measurement of the CP -even fraction of D0→π+π−π+π−

A measurement of the CP-even fraction of the decay D0→π+π−π+π− is performed with a quantum-correlated ψ(3770)→DD¯ data sample collected by the BESIII experiment, corresponding to an integrated luminosity of 2.93 fb−1. Using a combination of CP eigenstates, D→π+π−π0 and D→KS,L0π+π− as tagging modes, the CP-even fraction is measured to be F+4π=0.735±0.015±0.005, where the first uncertainty is statistical and the second is systematic. This is the most precise determination of this quantity to date. It provides valuable model-independent input for the measurement of the angle γ of the Cabibbo-Kobayashi-Maskawa matrix with B±→DK± decays, and for time-dependent studies of CP violation and mixing in the D0−D¯0 system.Received 22 August 2022Accepted 21 October 2022DOI:https://doi.org/10.1103/PhysRevD.106.092004Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasParticle mixing & oscillationsPropertiesCP violationParticles & Fields

Gauged U(1)Lμ−Lτ symmetry and two-zero textures of inverse neutrino mass matrix in light of muon (g − 2)

In the framework of anomaly free [Formula: see text] model, singlet scalar field with nonzero [Formula: see text] charge gives rise to massive gauge boson [Formula: see text] through spontaneous symmetry breaking. [Formula: see text] leads to one loop contribution to the muon anomalous magnetic moment. These scalar fields may, also, appear in the structure of right-handed neutrino mass matrix, thus, connecting the possible explanation of muon [Formula: see text] and low-energy neutrino phenomenology through vevs associated with the scalar fields. In this work, we consider textures of inverse neutrino mass matrix [Formula: see text] wherein any two elements of the mass matrix are zero. In this ansatz, with Dirac neutrino mass matrix diagonal, the zero(s) of right-handed Majorana neutrino mass matrix correspond to zero(s) in the low-energy effective neutrino mass matrix (within Type-I seesaw). We have realized two such textures of [Formula: see text] accommodating the muon [Formula: see text] and low-energy neutrino phenomenology. The requirement of successful explanation of muon [Formula: see text], further, constrains the allowed parameter space of the model and results in sharp correlations amongst neutrino mixing angles and CP invariants. The model explains muon [Formula: see text] for [Formula: see text] in the range (0.035–0.100 GeV) and [Formula: see text] which is found to be consistent with constraints coming from the current experiments CCFR, COHERENT, BABAR while being within sensitivities of future experiments such as NA62 and NA64.

Implications of A4 modular symmetry on neutrino mass, mixing and leptogenesis with linear seesaw

The present work is inspired by the application of A 4 modular symmetry in the linear seesaw framework, which restricts the use of multiple flavon fields. Linear seesaw is realized with six heavy S U ( 2 ) L singlet fermion superfields and a weighton in a supersymmetric framework. The non-trivial transformation of Yukawa couplings under the A 4 modular symmetry helps to explore the neutrino phenomenology with a specific flavor structure of the mass matrix. We discuss the phenomena of neutrino mixing and show that the obtained mixing angles and CP violating phase in this framework are compatible with the observed 3 σ range of the current oscillation data. In addition, we also investigate the non-zero CP asymmetry from the decay of lightest heavy fermion superfield to explain the preferred phenomena of baryogenesis through leptogenesis including flavor effects.

Mixing and CP violation in D0 → K−π+ decays

We review the experimental methods to measure mixing and time-dependent CP violation in D0 decays into two hadrons. While these phenomena are usually neglected for D0 → K−π+ decays, this approximation is not always justified. In particular, it produces a bias on the measurement of the parameter yCP, when this is performed by relying on D0 → K−π+ decays as a normalisation channel, whose size is around 40% of the precision of the current world average. Finally, we estimate the sensitivity to the weak mixing phases achievable by studying D0 → K−π+ and untagged D → K−π+ decays, where D stands for either of the D0 and overline{D} 0 mesons. Contrary to Cabibbo-suppressed D0 → h+h− decays, these decay channels allow to measure these phases without final-state dependent nuisance contributions from the decay amplitudes, but their sensitivity is lower by a factor of six.

Flavor mixing and CP violation from the interplay of an S4 modular group and a generalized CP symmetry

We have performed a systematical analysis of lepton and quark masses models based on $\Gamma_4\cong S_4$ modular symmetry with gCP symmetry. We have considered both cases that neutrinos are Majorana particles and Dirac particles. All possible nontrivial representation assignments of matter fields are considered, and the most general form of fermion mass matrices are given. The phenomenologically viable models with the lowest number of free parameters together with the results of fit are presented. We find out nine lepton models with seven real free parameters including the real and imaginary parts of modulus for Majorana neutrinos, which can accommodate the lepton masses and neutrino oscillation data. The prediction for leptogenesis is studied in an example lepton model. The observed baryon asymmetry as well as lepton masses and mixing angles can be explained. For Dirac neutrinos, four lepton models with five real free couplings are compatible with experimental data. Ten quark models containing seven couplings are found to be able to accommodate the hierarchical quark masses and mixing angles and CP violation phase. Furthermore, the $S_4$ modular symmetry can provide a unified description of lepton and quark flavor structure, and a benchmark model is presented.

The history of LHCb

In this paper, we describe the history of the LHCb experiment over the last three decades, and its remarkable successes and achievements. LHCb was conceived primarily as a {b} -physics experiment, dedicated to CP violation studies and measurements of very rare {{b}} decays; however, the tremendous potential for {c} -physics was also clear. At first data taking, the versatility of the experiment as a general-purpose detector in the forward region also became evident, with measurements achievable such as electroweak physics, jets and new particle searches in open states. These were facilitated by the excellent capability of the detector to identify muons and to reconstruct decay vertices close to the primary {{p}} {{p}} interaction region. By the end of the LHC Run 2 in 2018, before the accelerator paused for its second long shut down, LHCb had measured the CKM quark mixing matrix elements and CP violation parameters to world-leading precision in the heavy-quark systems. The experiment had also measured many rare decays of {b} and {c} quark mesons and baryons to below their Standard Model expectations, some down to branching ratios of order 10^{-9}. In addition, world knowledge of {{b}} and {{c}} spectroscopy had improved significantly through discoveries of many new resonances already anticipated in the quark model, and also adding new exotic four and five quark states. The paper describes the evolution of the LHCb detector, from conception to its operation at the present time. The authors’ subjective summary of the experiment’s important contributions is then presented, demonstrating the wide domain of successful physics measurements that have been achieved over the years.

S 4 modular symmetry, seesaw mechanism and lepton masses and mixing

We report on two works which exploit the approach to charged lepton and neutrino masses, neutrino mixing and leptonic CP violation based on the modular S 4 symmetry. The light neutrino masses are assumed to be generated via the type I seesaw mechanism. Realistic models without flavons and compatible with the data are constructed and the predicted correlations between neutrino mixing observables are studied.

Neutrinoless double beta decay versus other probes of heavy sterile neutrinos

We make a comparative study of the neutrinoless double beta decay constraints on heavy sterile neutrinos versus other direct and indirect constraints from both lepton number conserving and violating processes, as a sensitive probe of the extent of lepton number violation and possible interference effects in the sterile sector. We introduce a phenomenological parametrisation of the simplified one-generation seesaw model with one active and two sterile neutrino states in terms of experimentally measurable quantities, such as active-sterile neutrino mixing angles, CP phases, masses and mass splittings. This simple parametrisation enables us to analytically derive a spectrum of possible scenarios between the canonical seesaw with purely Majorana heavy neutrinos and inverse seesaw with pseudo-Dirac ones. We then go on to constrain the simplified parameters of this model from various experiments at the energy, intensity and cosmic frontiers. We emphasise that the constraints from lepton number violating processes strongly depend on the mass splitting between the two sterile states and the relative CP phase between them. This is particularly relevant for neutrinoless double beta decay, which is weakened for small mass splitting and opposite CP parities between the sterile states. On the other hand, neutrinoless double beta decay is especially sensitive for Majorana sterile neutrinos with masses around 0.1 − 10 GeV.

SU(5) grand unified theory with A4 modular symmetry

We present the first example of a grand unified theory (GUT) with a modular symmetry interpreted as a family symmetry. The theory is based on supersymmetric $SU(5)$ in 6d, where the two extra dimensions are compactified on a $T_2/\mathbb{Z}_2$ orbifold. We have shown that, if there is a finite modular symmetry, then it can only be $A_4$ with an (infinite) discrete choice of moduli, where we focus on $\tau = \omega=e^{i2\pi/3}$, the unique solution with $|\tau|=1$. The fields on the branes respect a generalised CP and flavour symmetry $A_4\ltimes \mathbb{Z}_2$ which is isomorphic to $S_4$ which leads to an effective $\mu-\tau$ reflection symmetry at low energies, implying maximal atmospheric mixing and maximal leptonic CP violation. We construct an explicit model along these lines with two triplet flavons in the bulk, whose vacuum alignments are determined by orbifold boundary conditions, analogous to those used for $SU(5)$ breaking with doublet-triplet splitting. There are two right-handed neutrinos on the branes whose Yukawa couplings are determined by modular weights. The charged lepton and down-type quarks have diagonal and hierarchical Yukawa matrices, with quark mixing due to a hierarchical up-quark Yukawa matrix.

Modular A4 invariance and leptogenesis

We consider a model with three right-handed neutrinos in which Yukawa coupling constants and Majorana masses are obtained by requiring the modular A4 symmetry. It has been shown that the model can explain mass hierarchies and mixing patterns of charged leptons and neutrinos with the seesaw mechanism. In this article we investigate the leptogenesis by decays of right-handed neutrinos in this model. It is shown that masses of right-handed neutrinos are about 1013 GeV in order to account for the observed baryon asymmetry of the universe. Furthermore, the positive sign of the baryon asymmetry is obtained only for the limited ranges of mixing angles and CP violation phases of active neutrinos, which can be tested by future neutrino experiments.

Measurement of CP violation and mixing in [formula omitted] in ATLAS

An overview of a measurement of time-dependent CP asymmetry parameters in Bs0→J/ψ(μ+μ−)ϕ(K+K−) decays using 80.5 fb−1 of integrated luminosity collected with the ATLAS detector from 13 TeV pp collisions at the LHC is presented. A manifestation of the CP violation is an interference between direct and mixing-mediated Bs0 decays, producing a common final state. In the Standard Model, it is characterized by a phase shift ϕs related to the CKM matrix. In the case of Bs0→J/ψϕ, this shift is predicted to be small, ϕs=−0.0363−0.0015+0.0016 rad. New physics can enhance ϕs whilst satisfying all existing constraints. Results presented in this talk are compatible with those obtained from 19.2 fb−1 of 7 TeV and 8 TeV data as well as with the Standard Model predictions and other LHC measurements.

Littlest mu-tau seesaw

We propose a μ − τ reflection symmetric Littlest Seesaw (μτ -LSS) model. In this model the two mass parameters of the LSS model are fixed to be in a special ratio by symmetry, so that the resulting neutrino mass matrix in the flavour basis (after the seesaw mechanism has been applied) satisfies μ − τ reflection symmetry and has only one free adjustable parameter, namely an overall free mass scale. However the physical low energy predictions of the neutrino masses and lepton mixing angles and CP phases are subject to renormalisation group (RG) corrections, which introduces further parameters. Although the high energy model is rather complicated, involving (S4 × U(1))2 and supersymmetry, with many flavons and driving fields, the low energy neutrino mass matrix has ultimate simplicity.

Sign of CP violating phase in quarks and leptons

We discuss the relation between the CP violation of the quark mixing and that of the lepton mixing by investigating a CP violating observable, the Jarlskog invariant, as well as the CP violating Dirac phase. The down-type quark mass matrix with three zeros is given in terms of the minimal number of parameters, while the up-type quark mass matrix is diagonal. These quark mass matrices leading to the successful CKM mixing angles and CP violation are embedded in both the Pati-Salam and SU(5) models. The leptonic Jarlskog invariant JCPl (as well as CP violating Dirac phase) is examined for two cases: the neutrino mass matrix is diagonal or non-diagonal, where no additional CP violating phase is introduced apart from the Majorana phases. In the case of the diagonal neutrino mass matrix, the favorable sign of the leptonic CP violation is obtained, however, the magnitude of JCPl is at most mathcal{O} (10−4), which is too small compared with the expected value from the observation −0.02. In the case of the non-diagonal neutrino mass matrix where the tri-bimaximal mixing pattern is taken, we obtain the successful JCPl up to its sign.

Quark and lepton mixing patterns from a common discrete flavor symmetry with a generalized CP symmetry

We have studied two approaches to predict quark and lepton mixing patterns from the same flavor symmetry group in combination with CP symmetry. The first approach is based on the residual symmetry $Z_2$ in the charged lepton sector and $Z_2\times CP$ in the neutrino sector. All lepton mixing angles and CP violation phases depend on three real parameters $\theta_{l}$, $\delta_{l}$ and $\theta_{\nu}$. This approach is extended to the quark sector, the up and down quark mass matrices are assumed to be invariant under a $Z_2$ subgroup and $Z_2\times CP$. The necessary and sufficient conditions for the equivalence of two mixing patterns are derived. The second approach has an abelian subgroup and a single CP transformation as residual symmetries of the charged lepton and neutrino sectors respectively. The lepton mixing would be determined up to a real orthogonal matrix multiplied from the right hand side. Analogously we assume that a single CP transformation is preserved by the down (or up) quark mass matrix, and the residual symmetry of the up (or down) quark sector is be an abelian subgroup. As an example, we analyze the possible mixing patterns which can be obtained from the breaking of $\Delta(6n^2)$ and CP symmetries. We find $\Delta(294)$ combined with CP is the smallest flavor group which can give a good fit to the experimental data of quark and lepton mixing in both approaches.

Mu-tau symmetry and the Littlest Seesaw

Motivated by the latest neutrino oscillation data which is consistent with maximal atmospheric mixing and maximal leptonic CP violation, we review various results in μτ symmetry, then include several new observations and clarifications, including identifying a new general form of neutrino mass matrix with μτ symmetry. We then apply the new results to the neutrino mass matrix associated with the Littlest Seesaw model, and show that it approximately satisfies the new general form with μτ symmetry, and that this is responsible for its approximate predictions of maximal atmospheric mixing and maximal CP violation in the lepton sector.

Pseudo-Dirac neutrinos from flavour dependent CP symmetry

Discrete residual symmetries and flavour dependent CP symmetries consistent with them have been used to constrain neutrino mixing angles and CP violating phases. We discuss here role of such CP symmetries in obtaining a pseudo-Dirac neutrino which can provide a pair of neutrinos responsible for the solar splitting. It is shown that if (a) 3 × 3 Majorana neutrino matrix Mν is invariant under a discrete Z2 × Z2 symmetry generated by S1,2, (b) CP symmetry X transform Mν as XTMνX = Mν*, and (c) X and S1,2 obey consistency conditions XS1,2*X† = S2,1, then two of the neutrino masses are degenerate independent of specific forms of X, S1 and S2. Explicit examples of this result are discussed in the context of Δ(6n2) groups which can also be used to constrain neutrino mixing matrix U. Degeneracy in two of the masses does not allow complete determination of U but it can also be fixed once the perturbations are introduced. We consider explicit perturbations which break Z2 × Z2 symmetries but respect CP. These are shown to remove the degeneracy and provide a predictive description of neutrino spectrum. In particular, a correlation sin 2θ23 sin δCP = ±Im[p] is obtained between the atmospheric mixing angle θ23 and the CP violating phase δCP in terms of a group theoretically determined phase factor p. Experimentally interesting case {theta}_{23}=frac{uppi}{4},{delta}_{CP}=pm frac{uppi}{2} emerges for groups which predict purely imaginary p. We present detailed predictions of the allowed ranges of neutrino mixing angles, phases and the lightest neutrino mass for three of the lowest Δ(6n2) groups with n = 2, 4, 6.

Vh@nnlo-v2: new physics in Higgs Strahlung

Introducing version 2 of the code vh@nnlo [1], we study the effects of a number of new-physics scenarios on the Higgs-Strahlung process. In particular, the cross section is evaluated within a general 2HDM and the MSSM. While the Drell-Yan-like contributions are consistently taken into account by a simple rescaling of the SM result, the gluon-initiated contribution is supplemented by squark-loop mediated amplitudes, and by the s-channel exchange of additional scalars which may lead to conspicuous interference effects. The latter holds as well for bottom-quark initiated Higgs Strahlung, which is also included in the new version of vh@nnlo. Using an orthogonal rotation of the three Higgs CP eigenstates in the 2HDM and the MSSM, vh@nnlo incorporates a simple means of CP mixing in these models. Moreover, the effect of vector-like quarks in the SM on the gluon-initiated contribution can be studied. Beyond concrete models, vh@nnlo allows to include the effect of higher-dimensional operators on the production of CP-even Higgs bosons. Transverse momentum distributions of the final state Higgs boson and invariant mass distributions of the Vϕ final state for the gluon- and bottom-quark initiated contributions can be studied. Distributions for the Drell-Yan-like component of Higgs Strahlung can be included through a link to MCFM. vh@nnlo can also be linked to FeynHiggs and 2HDMC for the calculation of Higgs masses and mixing angles. It can also read these parameters from an SLHA-file as produced by standard spectrum generators. Throughout the manuscript, we highlight new-physics effects in various numerical examples, both at the inclusive level and for distributions.