Families Of Quarks Research Articles

Third family quark–lepton unification at the TeV scale

We construct a model of quark–lepton unification at the TeV scale based on an SU(4) gauge symmetry, while still having acceptable neutrino masses and enough suppression in flavor changing neutral currents. An approximate U(2) flavor symmetry is an artifact of family-dependent gauge charges leading to a natural realization of the CKM mixing matrix. The model predicts sizeable violation of PMNS unitarity as well as a gauge vector leptoquark U1μ=(3,1,2/3) which can be produced at the LHC – both effects within the reach of future measurements. In addition, recently reported experimental anomalies in semi-leptonic B-meson decays, both in charged b→cτν and neutral b→sμμ currents, can be accommodated.

Hierarchical fermions and detectable Z′ from effective two-Higgs-triplet 3-3-1 model

We develop a ${\rm SU}(3)_C\otimes {\rm SU}(3)_L\otimes {\rm U}(1)_X$ model where the number of fermion generations is fixed by cancellation of gauge anomalies, being a type of 3-3-1 model with new charged leptons. Similarly to the economical 3-3-1 models, symmetry breaking is achieved effectively with two scalar triplets so that the spectrum of scalar particles at the TeV scale contains just two CP even scalars, one of which is the recently discovered Higgs boson, plus a charged scalar. Such a scalar sector is simpler than the one in the Two Higgs Doublet Model, hence more attractive for phenomenological studies, and has no FCNC mediated by scalars except for the ones induced by the mixing of SM fermions with heavy fermions. We identify a global residual symmetry of the model which guarantees mass degeneracies and some massless fermions whose masses need to be generated by the introduction of effective operators. The fermion masses so generated require less fine-tuning for most of the SM fermions and FCNC are naturally suppressed by the small mixing between the third family of quarks and the rest. The effective setting is justified by an ultraviolet completion of the model from which the effective operators emerge naturally. A detailed particle mass spectrum is presented, and an analysis of the $Z^\prime$ production at the LHC run II is performed to show that it could be easily detected by considering the invariant mass and transverse momentum distributions in the dimuon channel.

SU(5) grand unified theory, its polytopes and 5-fold symmetric aperiodic tiling

We associate the lepton–quark families with the vertices of the 4D polytopes 5-cell [Formula: see text] and the rectified 5-cell [Formula: see text] derived from the [Formula: see text] Coxeter–Dynkin diagram. The off-diagonal gauge bosons are associated with the root polytope [Formula: see text] whose facets are tetrahedra and the triangular prisms. The edge-vertex relations are interpreted as the [Formula: see text] charge conservation. The Dynkin diagram symmetry of the [Formula: see text] diagram can be interpreted as a kind of particle-antiparticle symmetry. The Voronoi cell of the root lattice consists of the union of the polytopes [Formula: see text] whose facets are 20 rhombohedra. We construct the Delone (Delaunay) cells of the root lattice as the alternating 5-cell and the rectified 5-cell, a kind of dual to the Voronoi cell. The vertices of the Delone cells closest to the origin consist of the root vectors representing the gauge bosons. The faces of the rhombohedra project onto the Coxeter plane as thick and thin rhombs leading to Penrose-like tiling of the plane which can be used for the description of the 5-fold symmetric quasicrystallography. The model can be extended to [Formula: see text] and even to [Formula: see text] by noting the Coxeter–Dynkin diagram embedding [Formula: see text]. Another embedding can be made through the relation [Formula: see text] for more popular [Formula: see text]. Appendix A includes the quaternionic representations of the Coxeter–Weyl groups [Formula: see text] which can be obtained directly from [Formula: see text] by projection. This leads to relations of the [Formula: see text] polytopes with the quasicrystallography in 4D and [Formula: see text] polytopes. Appendix B discusses the branching of the polytopes in terms of the irreducible representations of the Coxeter–Weyl group [Formula: see text].

Heavy charged scalars from coverline{s} fusion: a generic search strategy applied to a 3HDM with U(1) \xd7 U(1) family symmetry

We describe a class of three Higgs doublet models (3HDMs) with a softly broken U(1) × U(1) family symmetry that enforces a Cabibbo-like quark mixing while forbidding tree-level flavour changing neutral currents. The hierarchy in the observed quark masses is partly explained by a softer hierarchy in the vacuum expectation values of the three Higgs doublets. As a consequence, the physical scalar spectrum contains a Standard Model (SM) like Higgs boson h125 while exotic scalars couple the strongest to the second quark family, leading to rather unconventional discovery channels that could be probed at the Large Hadron Collider. In particular, we describe a search strategy for the lightest charged Higgs boson H±, through the process coverline{s}to {H}^{+}to {W}^{+}{h}_{125} , using a multivariate analysis that leads to an excellent discriminatory power against the SM background. Although the analysis is applied to the proposed class of 3HDMs, we employ a model-independent formulation such that it can be applied to any other model with the same discovery channel.

Heavy Higgs searches: flavour matters

We point out that the stringent lower bounds on the masses of additional electrically neutral and charged Higgs bosons crucially depend on the flavour structure of their Yukawa interactions. We show that these bounds can easily be evaded by the introduction of flavour-changing neutral currents in the Higgs sector. As an illustration, we study the phenomenology of a two Higgs doublet model with a Yukawa texture singling out the third family of quarks and leptons. We combine constraints from low-energy flavour physics measurements, LHC measurements of the 125 GeV Higgs boson rates, and LHC searches for new heavy Higgs bosons. We propose novel LHC searches that could be performed in the coming years to unravel the existence of these new Higgs bosons.

Discrete symmetries with neutral mesons

Symmetries, and Symmetry Breakings, in the Laws of Physics play a crucial role in Fundamental Science. Parity and Charge Conjugation Violations prompted the consideration of Chiral Fields in the construction of the Standard Model, whereas CP-Violation needed at least three families of Quarks leading to Flavour Physics. In this Lecture I discuss the Conceptual Basis and the present experimental results for a Direct Evidence of Separate Reversal-in-Time T, CP and CPT Genuine Asymmetries in Decaying Particles like Neutral Meson Transitions, using Quantum Entanglement and the Decay as a Filtering Measurement. The eight transitions associated to the Flavour-CP eigenstate decay products of entangled neutral mesons have demonstrated with impressive significance a separate evidence of TRV and CPV in Bd-physics, whereas a CPTV asymmetry shows a 2σ effect interpreted as an upper limit. Novel CPTV observables are discussed for K physics at KLOE-2, including the difference between the semileptonic asymmetries from KL and KS, the ratios of double decay rate Intensities to Flavour-CP eigenstate decay products and the ω-effect. Their observation would lead to a change of paradigm beyond Quantum Field Theory, however there is nothing in Quantum Mechanics forbidding CPTV.

Martin L. Perl (1927–2014): A Biographical Memoir

Particle physicist Martin Lewis Perl was recognized worldwide for his discovery of the τ (tau) lepton. For that achievement he received the 1982 Wolf Prize and shared the 1995 Nobel Prize in Physics. He was also a Fellow of the American Physical Society and a member of the National Academy of Sciences (elected 1981). Martin's distinctive approach to scientific investigation had its origins in his upbringing and in the influence of I. I. Rabi, his graduate advisor at Columbia University. After coming to Stanford University in 1963, Martin sought to understand why there should be two and only two families of leptons: the electron and its associated neutrino; and the muon and the muon neutrino. His discovery of the τ provided evidence for a third family of fundamental leptons. The bottom quark was discovered shortly afterward at the Fermi National Accelerator Laboratory, providing evidence for a third family of quarks. Direct evidence for the τ neutrino came later, thereby completing the third lepton generation, while the discovery of the top quark in 1995 completed the third generation of quarks. These achievements established leptons and quarks as fundamental constituents of matter and, along with the fundamental forces, provided the experimental basis of the “Standard Model,” our picture of how all matter is made up and how its components interact. Why there are three and only three families of leptons and quarks remains an unsolved mystery to this day.

Separate T, CP, CPT Asymmetries in Neutral Meson Transitions

Symmetries, and Symmetry Breakings, in the Laws of Physics play a crucial role in Fundamental Science. Parity and Charge Conjugation Violations prompted the consideration of Chiral Fields in the construction of the Standard Model, whereas CP-Violation needed at least three families of Quarks leading to Flavour Physics. In this Lecture I will discuss the Conceptual Basis and the present experimental results for a Direct Evidence of Separate Reversal-in-Time T, CP and CPT Genuine Asymmetries in Decaying Particles like Neutral Meson Transitions, using Quantum Entanglement and the Decay as a Filtering Measurement. The eight transitions associated to the Flavour-CP eigenstate decay products of entangled neutral mesons have demonstrated with impressive significance a separate evidence of TRV and CPV in Bd-physics, whereas a CPTV asymmetry shows a 2-σ effect interpreted as an upper limit. Novel CPTV observables are discussed for K and Bd transitions. Their observation would lead to a change of paradigm beyond Quantum Field Theory, however there is nothing in Quantum Mechanics forbidding CPTV. A clean methodology to disentangle CPTV effects in the Hamiltonian dynamics and the ω-effect weakening Entanglement in a given experiment is discussed.

An Energy Based Analysis of the Quark/Hadron Impact on Cosmic Decoupling

The initial state of the cosmos is analytically modeled as a radiation filled spherical cavity that expands from a singularity to later act as a clock and energy source in support of a 3-stage, radiation to a quark-hadron based, decoupling process. The model thereby avoids a need for Inflation and the presence of matter at start-up and during the radiation dominated phase, but nevertheless remains strongly consistent with attributes of the Guth Inflationary model. At decoupling, only quark family #1 with up-down attributes has adequate energy to successfully complete decoupling. Earlier in a 3-stage process, attempts at hadronization by quark families #2 and #3 fail due to large quark size and binding energy requirements that exceed the available radiation energy supply. These attempts decay rapidly to take a quark family #1 form. Decoupling is further modeled as half-spin based radiation resonance forms that are linked, via particle time dilation, to matter based micro-black-holes.

What if the masses of the first two quark families are not generated by the standard model Higgs boson?

We point out that, in the context of the SM, $|V^2_{13}| + | V^2_{23}|$ is expected to be large, of order one. The fact that $|V^2_{13}| + |V^2_{23}| \approx 1.6 \times 10^{-3}$ motivates the introduction of a symmetry S which leads to $V_{CKM} ={1\>\!\!\!\mathrm{I}} $, with only the third generation of quarks acquiring mass. We consider two scenarios for generating the mass of the first two quark generations and full quark mixing. One consists of the introduction of a second Higgs doublet which is neutral under S. The second scenario consists of assuming New Physics at a high energy scale , contributing to the masses of light quark generations, in an effective field theory approach. This last scenario leads to couplings of the Higgs particle to $s\overline s$ and $c \overline c$ which are significantly enhanced with respect to those of the SM. In both schemes, one has scalar-mediated flavour- changing neutral currents which are naturally suppressed. Flavour violating top decays are predicted in the second scenario at the level $ \mbox{Br} (t \rightarrow h c ) \geq 5\times 10^{-5}$.

Generalized gauge U(1) family symmetry for quarks and leptons

If the standard model of quarks and leptons is extended to include three singlet right-handed neutrinos, then the resulting fermion structure admits an infinite number of anomaly-free solutions with just one simple constraint. Well-known examples satisfying this constraint are $B-L$, $L_{\mu}-L_{\tau}$ , $B-3L_{\tau}$ , etc. We derive this simple constraint, and discuss two new examples which offer some insights to the structure of mixing among quark and lepton families, together with their possible verification at the Large Hadron Collider.

A flipped 331 model

Models based on the extended $SU(3)_{C}\times SU(3)_{L}\times U(1)_{X}$ (331) gauge group usually follow a common pattern: two families of left-handed quarks are placed in anti-triplet representations of the $SU(3)_{L}$ group; the remaining quark family, as well as the left-handed leptons, are assigned to triplets (or vice-versa). In this work we present a flipped 331 model where this scheme is reversed: all three quarks families are in the same representation and it is the lepton families which are discriminated by the gauge symmetry. We discuss fermion masses and mixing, as well as $Z'$ interactions, in a minimal model implementing this idea.

CP Asymmetries (& T Violation) in Known Matter – and Beyond

Finding \cp~violation (\CPV ) in 1964 produced a real revolution in the fundamental dynamics, although the community did not understand it right away. The paper by Kobayashi \& Maskawa \cite{KM} appeared in 1973 to describe \CPV~in classes of three (or more) families of quarks, non-minimal Higgs' dynamics and/or charged right-handed currents. The Standard Model is defined now with three families of quarks. It can describe the measured \cp~ \& \ot~violation in kaon and $B$ mesons at least as the leading source. None has been found in baryons, charm mesons, top quarks and EDMs -- except from `hot' news from LHCb data about {\bf T}-odd moment in $\Lambda_b^0 \to p \pi^-\pi^+\pi^-$ \cite{LHCbtalk}. We have failed the explain our matter vs. anti-matter huge asymmetry. Even when there is no obvious connections with that asymmetry, it makes sense to probe \CPV~for the signs of New Dynamics \& their features. Furthermore we have to measure regional \CPV~in many-body final states with accuracy. I discuss EDMs, axion's impact on cosmology \& its connection with Dark Matter; finally I talk about \CPV~in leptonic dynamics.

Higgs mass and unified gauge coupling in the NMSSM with vector matter

We consider the NMSSM extended to include one vector-like family of quarks and leptons. If (some of) these vector-like matter particles, as the Higgs doublets, have Yukawa couplings to the singlet S that exceed unity at about the same scale $\Lambda \lesssim 10^3$ TeV, this gives the order 40 % enhancement of the tree level Higgs boson mass required in the MSSM to reach 125 GeV. It is conceivable that the Yukawa couplings to the singlet S, although naively blowing up close to $\Lambda$, will not spoil gauge coupling unification. In such a case the unified coupling $\alpha_X$ could be interestingly led to a value not far from unity, thus providing a possible explanation for the number of generations. The characteristic signal is an enhanced resonant production of neutral spin zero particles at LHC, that could even explain the putative diphoton resonance hinted by the recent LHC data at 750 GeV.

Extension of Standard Model in multi-spinor field formalism — Visible and dark sectors

With multi-spinor fields which behave as triple-tensor products of the Dirac spinors, the Standard Model is extended so as to embrace three families of ordinary quarks and leptons in the visible sector and an additional family of exotic quarks and leptons in the dark sector of our Universe. Apart from the gauge and Higgs fields of the Standard Model symmetry G, new gauge and Higgs fields of a symmetry isomorphic to G are postulated to exist in the dark sector. It is the bi-quadratic interaction between visible and dark Higgs fields that opens a main portal to the dark sector. Breakdowns of the visible and dark electroweak symmetries result in the Higgs boson with mass 125 GeV and a new boson which can be related to the diphoton excess around 750 GeV. Subsequent to a common inflationary phase and a reheating period, the visible and dark sectors follow weakly-interacting paths of thermal histories. We propose scenarios for dark matter in which no dark nuclear reaction takes place. A candidate for the main component of the dark matter is a stable dark hadron with spin 3/2, and the upper limit of its mass is estimated to be 15.1 GeV/c2.

Gauge U(1) dark symmetry and radiative light fermion masses

A gauge $U(1)$ family symmetry is proposed, spanning the quarks and leptons as well as particles of the dark sector. The breaking of $U(1)$ to $Z_2$ divides the two sectors and generates one-loop radiative masses for the first two families of quarks and leptons, as well as all three neutrinos. We study the phenomenological implications of this new connection between family symmetry and dark matter. In particular, a scalar or pseudoscalar particle associated with this $U(1)$ breaking may be identified with the 750 GeV diphoton resonance recently observed at the Large Hadron Collider (LHC).

Masses of third family vectorlike quarks and leptons in Yukawa-unifiedE6

In supersymmetric $E_6$ the masses of the third family quarks and charged lepton, $t-b-\tau$, as well as the masses of the vector-like quarks and leptons, $D-\bar{D}$ and $ L-\bar{L}$, may arise from the coupling $27_3$ x $27_3$ x $27_H$, where $27_3$ and $27_H$ denote the third family matter and Higgs multiplets respectively. We assume that the SO(10) singlet component in $27_H$ acquires a TeV scale VEV which spontaneously breaks U(1)$_\psi$ and provides masses to the vector-like particles in $27_3$, while the MSSM doublets in $27_H$ provide masses to $ t, b$ and $\tau$. Imposing Yukawa coupling unification $h_t=h_b=h_{\tau}=h_D=h_L$ at $M_{GUT}$ and employing the ATLAS and CMS constraints on the $Z'_\psi$ boson mass, we estimate the lower bounds on the third family vector-like particles $D-\bar{D}$ and $L-\bar{L}$ masses to be around 5.85 TeV and 2.9 TeV respectively. These bounds apply in the supersymmetric limit.

Interpreting the 750 GeV diphoton excess in minimal extensions of Two-Higgs-Doublet models

It is shown that the 750 GeV diphoton excess can be explained in extensions of Two-Higgs-Doublet Models that do not involve large multiplicities of new electromagnetically charged states. The key observation is that at moderate and large $\tan\beta$ the total decay width of the 750 GeV Higgs is strongly reduced as compared to the Standard Model. This allows for much more economical choices of new states that enhance the diphoton signal to fit the data. In particular, it is shown that one family of vector-like quarks and leptons with SM charges is enough to explain the 750 GeV diphoton excess. Moreover, such charge assignment can keep the 125 GeV Higgs signal rates exactly at the SM values. The scenario can interpret the diphoton excess provided that the total decay width of a hypothetical resonance that would be measured at the LHC turns out to not exceed few GeV.

Fitting fermion masses and mixings in F-theory GUTs

We analyse the structure of Yukawa couplings in local SU(5) F-theory models with $E_7$ enhancement. These models are the minimal setting in which the whole flavour structure for the MSSM charged fermions is encoded in a small region of the entire compactification space. In this setup the $E_7$ symmetry is broken down to SU(5) by means of a 7-brane T-brane background, and further to the MSSM gauge group by means of a hypercharge flux that also implements doublet-triplet splitting. At tree-level only one family of quarks and charged leptons is massive, while the other two obtain hierarchically smaller masses when stringy non-perturbative effects are taken into account. We find that there is a unique $E_7$ model with such hierarchical flavour structure. The relative simplicity of the model allows to perform the computation of Yukawa couplings for a region of its parameter space wider than previous attempts, obtaining realistic fermion masses and mixings for large parameter regions. Our results are also valid for local models with $E_8$ enhancement, pointing towards a universal structure to describe realistic fermion masses within this framework.

Stringy explanation of b → sℓ + ℓ − anomalies

We show that the recent anomalies in $b \to s \ell^+ \ell^-$ transitions observed by the LHCb collaboration can be accommodated within string motivated models with a low mass $Z^{\prime}$ gauge boson. Such $Z^{\prime}$ gauge boson can be obtained in compactifications with a low string scale. We consider a class of intersecting D-brane models, in which different families of quarks and leptons are simultaneously realized at different D-brane intersections. The explanation of $b \to s \ell^+ \ell^-$ anomalies via a stringy $Z^{\prime}$ sets important restrictions on these viable D-brane constructions.