Families Of Leptons Research Articles

An Explanation for the Violation of Lepton Universality in Beauty-Quark Decays: The Binary Isotope Mixture of Beauty-Quarks

This paper purposes an explanation for the recent evidence for the violation of lepton universality in beauty-quark decays at CERN’s Large Hadron Collider. A beauty meson (B+) transforms into a strange meson (K+) with the emission of either electron-positron (e+e-) or muon-antimuon (μ+μ-). The ratio (RK) of branching fractions for B+ → K+μ+μ- and B+→ K+e+e- decays is measured to be RK = 0.846 instead of 1 in the violation of lepton universality in the Standard Model. This paper proposes that the violation is derived from the binary isotope mixture of two beauty-quarks, b7 (4979 MeV mass) and b8 (143,258 MeV mass) whose masses are calculated from the periodic table of elementary particles. b7 is the observable B, while b8 is the hidden B to preserve the generation number symmetry between the three lepton family generations and the three quark family generations in the Standard Model. The preservation of the generation number symmetry forbids b8 to decay into K+μ+μ-. In the transition state involving the virtual particles (γ, W± and Z°) before the decay, b7 and b8 emerge to form the binary isotope mixture from B. The rates of emergence as the rates of diffuse in Graham’s law of diffusion are proportional to inverse square root of mass. The rate ratio between b8/b7 is (4979/143,258)1/2 = 0.1864. Since b7 decays into K+, e+e-, and μ+μ-, while b8 decays into K+, e+e-, and forbidden μ+μ-, the calculated ratio (RK) of branching fractions for B+→ K+μ+μ- and B+→ K+e+e- is 0.5/(0.1864 × 0.5+ 0.5) = 0.843 in excellent agreement with the observed 0.846. The agreement between the calculated RK and the observed RK confirms the validity of the periodic table of elementary particles which provides the answers for the dominance of matter over antimatter, dark-matter, and the mass hierarchy of elementary particles.

U(1)_{B_3-L_2} explanation of the neutral current B-anomalies

We investigate a speculative short-distance force, proposed to explain discrepancies observed between measurements of certain neutral current decays of B hadrons and their Standard Model predictions. The force derives from a spontaneously broken, gauged U(1)_{B_3-L_2} extension to the Standard Model, where the extra quantum numbers of Standard Model fields are given by third family baryon number minus second family lepton number. The only fields beyond those of the Standard Model are three right-handed neutrinos, a gauge field associated with U(1)_{B_3-L_2} and a Standard Model singlet complex scalar which breaks U(1)_{B_3-L_2}, a ‘flavon’. This simple model, via interactions involving a TeV scale force-carrying Z^prime vector boson, can successfully explain the neutral current B-anomalies whilst accommodating other empirical constraints. In an ansatz for fermion mixing, a combination of up-to-date B-anomaly fits, LHC direct Z^prime search limits and other bounds rule out the domain 0.15 hbox {TeV}< M_{Z^prime }< 1.9 TeV at the 95% confidence level. For more massive Z^prime s, the model possesses a flavonstrahlung signal, where pp collisions produce a Z^prime and a flavon, which subsequently decays into two Higgs bosons.

Split left-right symmetry and scotogenic quark and lepton masses

A model of split left-right symmetry is proposed, where the first family of quarks and leptons transforms under SU(2)R but the heavier two families do not. The Higgs scalar sector consists only of an SU(2)L doublet and an SU(2)R doublet. The u,d quarks and the electron, as well as the neutrinos, are massless at tree level, but become massive radiatively through their interactions with a simple dark sector. Verifiable consequences include Z′ and Higgs properties, neutrino mixing and rare decays, etc.

Exceptional unification of families and forces

This work considers the remarkable suggestion that the three families of quarks and leptons may be unified, together with the Higgs and gauge fields of the Standard Model (SM), into a single “particle”, namely the 248 vector superfield of a ten-dimensional E8 super Yang Mills (SYM) theory. Towards a realistic model along these lines, a class of orbifoldings based on T6/(ZN×ZM) are proposed and explored, that can in principle break E8 SYM down to the minimal supersymmetric standard model (MSSM), embedded in a larger group such as E6, SO(10) or SU(5), together with other gauge group factors which can be broken by Wilson lines. A realistic model based on T6/(Z6×Z2) is presented. The orbifold breaks E8 SYM down to a Pati-Salam gauge group in 4d, together with other gauge groups, which are subsequently broken to the SM gauge group with proto-realistic fermion mass matrices, and experimental signals associated with a low Pati-Salam scale.

RETRACTED: Lepton number violation in a unified framework

Abstract We study the time evolution of lepton family number for a neutrino that forms an SU(2) doublet with a charged lepton. The lepton family number is defined through a weak basis of the SU(2) doublet in which the charged lepton mass matrix is a real and diagonal one. The lepton family number carried by the neutrino is defined with a left-handed current of the neutrino family. We study the time evolution of the lepton family number operator for the Majorana neutrino. To be definite, we introduce the mass term at $t=0$ and study the time evolution of the lepton family number for the later time. Since the operator in the flavor eigenstate is continuously connected to that of the mass eigenstate, the creation and annihilation operators for the flavor eigenstates are related to those of the mass eigenstates. The total lepton number of the Majorana neutrino is conserved. By choosing a specific flavor eigenstate of the neutrino as an initial state, we compute the time evolution of all lepton family numbers. They are sensitive to Majorana and Dirac phases and are also sensitive to the absolute mass and mass hierarchy of neutrinos.

A twist on broken U(3) $$\times $$ U(3) supersymmetry

What symmetry breaking would be required for gauginos from a supersymmetric theory to behave like left-handed quarks of the Standard Model? Starting with a supersymmetric SU(3) $$\times $$ SU(3) $$\times $$ U(1) $$\times $$ U(1) gauge theory, the 18 adjoint-representation gauginos are replaced with 2 families of 9 gauginos in the (3,3*) representation of the group. After this explicit breaking of supersymmetry, two-loop quadratic divergences still cancel at a unification scale. Coupling constant unification is supported by deriving the theory from an SU(3) $$\times $$ SU(3) $$\times $$ SU(3) $$\times $$ SU(3) Grand Unified Theory (GUT). $${\hbox {Sin}}^2$$ of the Weinberg angle for the GUT is 1/4 rather than 3/8, leading to a lower unification scale than usually contemplated, $$\sim 10^9 \, \hbox {GeV}$$ . After spontaneous gauge symmetry breaking to SU(3) $$\times $$ SU(2) $$\times $$ U(1), the theory reproduces the main features of the Standard Model for two families of quarks and leptons, with gauginos playing the role of left-handed quarks and sleptons playing the role of the Higgs boson. An extension to the theory is sketched that incorporates the third family of quarks and leptons.

Is it possible to explain the muon and electron g−2 in a Z′ model?

In order to address this question, we consider a simple renormalisable and gauge invariant model in which the $Z'$ only has couplings to the electron and muon and their associated neutrinos, arising from mixing with a heavy vector-like fourth family of leptons. Within this model we discuss the contributions to the electron and muon anomalous magnetic moments from $Z'$ exchange, subject to the constraints from $\mu \rightarrow e \gamma$ and neutrino trident production. Using analytic and numerical arguments, we find that such a $Z'$ model can account for either the electron or the muon $g-2$ anomalies, but not both, while remaining consistent with the experimental constraints from $\mu \rightarrow e \gamma$ and neutrino trident production.

Neutrino mass and dark matter from an approximate B \u2212 L symmetry

We argue that neutrino mass and dark matter can arise from an approximate B − L symmetry. This idea can be realized in a minimal setup of the flipped 3-3-1 model, which discriminates lepton families while keeping universal quark families and uses only two scalar triplets in order for symmetry breaking and mass generation. This proposal contains naturally an approximate non-Abelian B − L symmetry which consequently leads to an approximate matter parity. The approximate symmetries produce small neutrino masses in terms of type II and III seesaws and may make dark matter long lived. Additionally, dark matter candidate is either unified with the Higgs doublet by gauge symmetry or acted as an inert multiplet. The Peccei-Quinn symmetry is discussed. The gauge and scalar sectors are exactly diagonalized. The signals of the new physics at colliders are examined.

Gauging the accidental symmetries of the standard model, and implications for the flavor anomalies

We explore the possibility that lepton family numbers and baryon number are such good symmetries of Nature because they are the global remnant of a spontaneously broken gauge symmetry. An almost arbitrary linear combination of these symmetries (together with a component of global hypercharge) can be consistently gauged, if the Standard Model (SM) fermion content is augmented by three chiral SM singlet states. Within this framework of $U(1)$ extensions of the SM one generically expects flavour non-universality to emerge in the charged leptons, in such a way that naturally prevents lepton flavour violation, by aligning the mass and weak eigenbases. For quarks, all the SM Yukawa couplings responsible for their observed masses and mixings arise at the renormalisable level. We perform fits to show that models in this class can explain $R_{K^{(\ast)}}$ and the other neutral current $B$ anomaly data if we introduce a heavy vector-like quark to mediate the required quark flavour violation, while simultaneously satisfying other constraints from direct $Z^\prime$ searches at the LHC, $B_s$ meson mixing, a number of electroweak precision observables, and neutrino trident production. Within this symmetry-motivated framework of models, we find interesting implications for the flavour anomalies; notably, any axial couplings of the $Z^\prime$ to electrons and muons must be flavour universal, with the flavour universality violation arising solely from the vector-like couplings. We also comment on the generation of neutrino masses in these models.

Naturalising the third family hypercharge model for neutral current B{-}hbox {anomalies}

We consider a deformation of the Third Family Hypercharge Model, which arguably makes the model more natural. Additional non-zero charges of the spontaneously broken, family-dependent U(1)_F gauge symmetry are assigned to the second family leptons, and the third family leptons’ charges are deformed away from their hypercharges in such a way that the U(1)_F gauge symmetry remains anomaly-free. Second family U(1)_F lepton charges allow a Z^prime coupling to muons without having to assume large charged lepton mixing, which risks violating tight lepton flavour violation bounds. In this deformed version, only the bottom and top Yukawa couplings are generated at the renormalisable level, whereas the tauon Yukawa coupling is absent. The Z^prime mediates a beyond the Standard Model contribution to an effective ({bar{b}} s) (bar{mu }mu ) vertex in the combination C_9=-9C_{10} and is able to fit the apparent discrepancy between Standard Model predictions in flavour changing neutral-current B-meson decays and their measurements, whilst simultaneously avoiding current constraints from direct Z^prime searches and other measurements, when 0.8~text {TeV}< M_{Z^prime } < 12.5 ~text {TeV}.

Scotogenic cobimaximal Dirac neutrino mixing from Delta (27) and U(1)_chi

In the context of SU(3)_C times SU(2)_L times U(1)_Y times U(1)_chi , where U(1)_chi comes from SO(10) rightarrow SU(5) times U(1)_chi , supplemented by the non-Abelian discrete Delta (27) symmetry for three lepton families, Dirac neutrino masses and their mixing are radiatively generated through dark matter. The gauge U(1)_chi symmetry is broken spontaneously. The discrete Delta (27) symmetry is broken softly and spontaneously. Together, they result in two residual symmetries, a global U(1)_L lepton number and a dark symmetry, which may be Z_2, Z_3, or U(1)_D depending on what scalar breaks U(1)_chi . Cobimaximal neutrino mixing, i.e. theta _{13} ne 0, theta _{23} = pi /4, and delta _{CP} = pm pi /2, may also be obtained.

Light mediators in anomaly free U (1)X models. Part II. Constraints on dark gauge bosons

We consider experimental constraints in the MeV region in order to determine the parameter space for the U(1)X extension of the Standard Model, presented in the first part of our work. In particular, we focus on the model UV-completed by cold WIMPs. We conclude that the electron anomalous magnetic moment and the neutrino trident production provide the most stringent bounds to {g}_X^2 ∼ 10−6 in the mass interval below the di-muon threshold. By allowing the axial-vector coupling of the dark gauge boson Z′, the interference effect with the SM gauge bosons may reduce the bounds coming from the neutrino trident production. At the same time, such coupling allows a region of the parameter space already favored both by the relic abundance and by the discrepancy between experimental result and theoretical prediction for the muon anomalous magnetic moment. We emphasize that light-Z′ interactions, non-universal for the two first lepton families, necessarily create a difference in the proton charge radius measured in the Lamb shift of the e-hydrogen and μ-hydrogen. Finally, we determine the effects of the new gauge boson on the forward-backward asymmetry in e+e−→ overline{f}f = μ, τ, and on the leptonic decays M → jνjl+l−, where M = π, K, D, Ds, B and j, l = e, μ.

Complete vectorlike fourth family and new U(1)′ for muon anomalies

We consider the Standard Model (SM) with the addition of a $\mathrm{U(1)^\prime}$ gauge symmetry and a complete fourth family of quarks and leptons which are vector-like with respect to the full $\mathrm{SU(3)_C}\times \mathrm{SU(2)_L} \times \mathrm{U(1)_Y}\times \mathrm{U(1)^\prime}$ gauge symmetry. The model provides a unified explanation of experimental anomalies in $(g - 2)_\mu$ as well as $b \rightarrow s \ell^+ \ell^-$ decays. We find good fits to the deviations from the SM, while at the same time fitting all other SM observables. The model includes a new $Z^\prime$ gauge boson, a $\mathrm{U(1)^\prime}$-breaking scalar, and vector-like leptons all with mass of order a few $100$ GeV. It is consistent with all currently released high energy experimental data, however, it appears imminently testable with well designed future searches. Also precision flavor experiments, especially more accurate direct determinations of CKM matrix elements, would allow to probe the best fit points.

Dark matter and flavor changing in the flipped 3-3-1 model

The flipped 3-3-1 model discriminates lepton families instead of the quark ones in normal sense, where the left-handed leptons are in two triplets plus one sextet while the left-handed quarks are in antitriplets, under SU(3)L. We investigate a minimal setup of this model and determine novel consequences of dark matter stability, neutrino mass generation, and lepton flavor violation. Indeed, the model conserves a noncommutative B−L symmetry, which prevents the unwanted vacua and interactions and provides the matter parity and dark matter candidates that along with normal matter form gauge multiplets. The neutrinos obtain suitable masses via a type I and II seesaw mechanism. The nonuniversal couplings of Z′ with leptons govern lepton flavor violating processes such as μ → 3e, μ → e overline{nu} μνe, μ-e conversion in nuclei, semileptonic τ → μ(e) decays, as well as the nonstandard interactions of neutrinos with matter. This Z′ may also set the dark matter observables and give rise to the LHC dilepton and dijet signals.

Quark masses, CKM angles and Lepton Flavour Universality violation

A properly defined and suitably broken U(2) flavour symmetry leads to successful quantitative relations between quark mass ratios and CKM angles. At the same time the intrinsic distinction introduced by U(2) between the third and the first two families of quarks and leptons may support anomalies in charged and neutral current semi-leptonic B-decays of the kind tentatively observed in current flavour experiments. We show how this is possible by the exchange of the (3, 1)2/3 vector leptoquark in two U(2)-models with significantly different values of Lepton Flavour Universality violation, observable in foreseen experiments.

Alternative perspective on gauged lepton number and implications for collider physics

A new anomaly-free gauged $U(1)_\ell$ lepton-number model is studied. Two standard model lepton generations acquire the same but oppositive sign $U(1)_\ell$ charges, while four exotic chiral leptons cancel the anomalies of the remaining lepton family. We discuss a simplified case which has the universal Yukawa couplings. It agrees with all the experimental constraints and predicts $m_e, m_\mu \ll m_\tau$, and the latter is of the electroweak scale. Due to the interference between the SM and $U(1)_\ell$ gauge interactions, this model robustly predicts that $e,\mu,\tau$ have distinctive forward-backward asymmetries at the $e^+e^-$ colliders. It can be searched for at the $e^+e^-$ machine with $\sim$ TeV center-of-mass energy and an integrated luminosity $\sim ab^{-1}$.

Lepton Charges in Current Descriptions of Weak Processes

A family of leptons based on charged $${{l}_{{{\text{ch}}}}}$$ and neutral (neutrino) $${{l}_{\nu }}$$ quantum numbers is described while retaining their sum $${{L}_{{{\text{ch}}}}}$$ and total aroma $${{L}_{\nu }}.$$ Representations of a four-component neutrino theory are expanded by including a tauon family and a new (fourth) lepton family. (Non)diagonal lepton processes are studied with respect to the interaction between neutral (NC) and charged (CC) weak currents. It is shown that information on current constants can be obtained by measuring the recoil electron spectra and total cross sections of elastic $$\nu e$$ and $$\tilde {\nu }e$$ types of scattering.

B\u2013L Model with mathbf{S}_{3} symmetry

We make a scalar extension of the B–L gauge model where the mathbf{S}_{3} non-abelian discrete group drives mainly the Yukawa sector. Motived by the large and small hierarchies among the quark and active neutrino masses, respectively, the quark and lepton families are not treated on the same footing under the assignment of the discrete group. As a consequence, the nearest neighbor interaction (NNI) textures appear in the quark sector, leading to the CKM mixing matrix, whereas in the lepton sector, a soft breaking of the mu leftrightarrow tau symmetry in the effective neutrino mass, which comes from type I see-saw mechanism, provides a non-maximal atmospheric angle and a non-zero reactor angle.

The SU(8) GUT with composite quarks and leptons

We consider the L-R symmetric composite model for quarks and leptons where constituent preons possessing some local SU(N)MF metaflavor symmetry are bound by the chiral SO(n)L×SO(n)R gauge metacolor forces. The strengthening of the 't Hooft's anomaly matching condition, when the massless fermion composites are required to complete a single representation of the SU(N)MF rather than some set of its representations, allows to fix the number of basic metaflavors N. Particularly, just eight left-handed and eight right-handed preons and their composites preserving the global chiral symmetry SU(8)L×SU(8)R are turned out to underlie the physical world at small distances that uniquely identifies the local metaflavor symmetry SU(8)MF as its effective unified symmetry. We next show that the spontaneous L-R symmetry violation caused by the simultaneously emerged composite scalars reduces this initially vectorlike SU(8)MF theory down to the conventional SU(5) GUT with an extra local family symmetry SU(3)F and three standard families of quarks and leptons. Though the tiny confinement scale for universal preons composing both quarks and leptons makes it impossible to directly confirm their composite nature, simultaneous emergence of several extra SU(5)×SU(3)F multiplets of heavy composite fermions may help with a model verification. Generally, they may be located at scales from O(100) TeV up to the Planck mass scale depending on an interplay between the compositeness scale and scale of the family symmetry SU(3)F. Some of them through a natural see-saw mechanism provide the physical neutrino masses which, in contrast to conventional picture, appear to follow an inverted family hierarchy. Others mix with ordinary quark-lepton families in a way that there may arise a marked violation of unitarity in the CKM matrix for leptons.

Flavour anomalies: a review

The concept of lepton flavour universality (LFU), according to which the three lepton families are equivalent except for their masses, is a cornerstone prediction of the Standard Model (SM). LFU can be violated in models beyond the SM by new physics particles that couple preferentially to certain generations of leptons. In the last few years, hints of LFU violation have been observed in both tree-level b → cℓν and loop-level b → sℓℓ transitions. These measurements, combined with the tensions observed in angular observables and branching fractions of rare semileptonic b decays, point to a coherent pattern of anomalies that could soon turn into the first observation of physics beyond the SM. These proceedings review the anomalies seen by collider experiments, and give an outlook for the near future.