An extension of the gauge group $SU(2)_L\otimes U(1)_Y$ of the standard model to the symmetry group $SU(4)_L\otimes U(1)_X$ (3-4-1 for short) is presented. The model does not contain exotic electric charges and anomaly cancellation is achieved with a family of quarks transforming differently from the other two, thus leading to FCNC. By introducing a discrete $Z_2$ symmetry we obtain a consistent fermion mass spectrum, and avoid unitarity violation of the CKM mixing matrix arising from the mixing of ordinary and exotic quarks. The neutral currents coupled to all neutral vector bosons are studied, and by using CERN LEP and SLAC Linear Collider data at Z-pole and atomic parity violation data, we bound parameters of the model related to tree-level $Z-Z^\prime$ mixing. These parameters are further constrained by using experimental input from neutral meson mixing in the analysis of sources of FCNC present in the model. Constraints coming from the contribution of exotic particles to the one-loop oblique electroweak parameters $S$, $T$ and $U$ are also briefly discussed. Finally, a comparison is done of the predictions of different classes of 3-4-1 models without exotic electric charges.
Based on previous studies deriving the chiral Lagrangian for pseudo scalar mesons from the first principle of QCD in the path integral formalism, we derive the electroweak chiral Lagrangian and dynamically compute all its coefficients from the one family technicolor model. The numerical results of the $p^4$ order coefficients obtained in this paper are proportional to the technicolor number $N_{\rm TC}$ and the technifermion number $N_{\rm TF}$, which agrees with the arguments in previous works, and which confirms the reliability of this dynamical computation.
In models of dynamical electroweak symmetry breaking due to strongly coupled fourth-family quarks and leptons, their low-energy effective descriptions may involve multiple composite Higgs fields, leading to a possibility that the electroweak phase transition at finite temperature is first order due to the Coleman-Weinberg mechanism. We examine the behavior of the electroweak phase transition based on the effective renormalizable Yukawa theory which consists of the fourth-family quarks and two SU(2)-doublet Higgs fields corresponding to the bilinear operators of the fourth-family quarks with/wi…
We propose a dynamical model with a (2 + 1)-structure of composite Higgs doublets: two nearly degenerate composites of the fourth family quarks t' and b', $Φ_{t^{\prime}} \sim \bar{t^{\prime}}_{R}(t^{\prime},b^{\prime})_L$ and $Φ_{b^{\prime}} \sim \bar{b^{\prime}}_{R}(t^{\prime},b^{\prime})_L$, and a heavier top-Higgs resonance $Φ_t \sim \bar{t}_{R}(t,b)_L$. This model naturally describes both the top quark mass and the electroweak symmetry breaking. Also, a dynamical mechanism providing the quark mass hierarchy can be reflected in the model. The properties of these composites are analyzed in …
While it is known that third family hypercharge models can explain the neutral current $B-$anomalies, it was hitherto unclear whether the $Z-Z^\prime$ mixing predicted by such models could simultaneously fit electroweak precision observables. Here, we perform global fits of several third family hypercharge models to a combination of electroweak data and those data pertinent to the neutral current $B-$anomalies. While the Standard Model is in tension with this combined data set with a $p-$value of $.00068$, simple versions of the models (fitting two additional parameters each) provide much impr…
We construct a one-family technicolor model which is consistent with the precision experiments on the electroweak interaction. The Majorana mass of the right-handed techni-neutrino is introduced and the techni-$U(1)_{B-L}$ symmetry is gauged to obtain the correct breaking of the electroweak symmetry. The tree-level kinetic mixing between the techni-$U(1)_{B-L}$ and $U(1)_Y$ gauge bosons plays an important role for having the consistent value of the $S$ parameter.
We explore the viability of baryogenesis from light scalar decays after the electroweak phase transition. A minimal model of this kind is constructed with new CP violating interactions involving a heavy fourth family. The departure from thermal equilbrium must come from topological defects like cosmic strings, and we show that almost any mechanism for producing the cosmic strings at the electroweak scale results in a viable theory. Baryogenesis occurs in the fourth generation but the baryon number is later transported to the visible generations. This mechanism of indirect baryogenesis allows u…
We construct the most general effective Lagrangian of the matter sector of the Standard Model, including mixing and CP violating terms. The Lagrangian contains the effective operators that give the leading contribution in theories where the physics beyond the Standard Model shows at a scale $Λ>>M_{W}$. We perform the diagonalization and passage to the physical basis in full generality. We determine the contribution to the different observables and discuss the possible new sources of CP violation, the idea being to be able to gain some knowledge about new physics beyond the Standard Model from …
A solution of the standard electroweak theory with a single lepton family is constructed, consisting of a cosmic string and a fermion condensate within its core. The stability of this system to small perturbations is examined, and it is found that stability is not enhanced relative to the bare electroweak string. The presence of quark zero modes is shown to violate the existence criteria for embedded defects.
We describe how isospin splitting and techniquark-technilepton splitting in one-family technicolor models can reduce the predicted value of the electroweak radiative correction parameter S, without making a large contribution to the T parameter.
We present a top-condensation model in which the CP symmetry is spontaneously broken at the electroweak scale due to the condensation of two composite Higgs doublets. In particular the CP-violating phase of the CKM matrix is generated. A simpler model where only one quark family is included is also discussed. In this case, for a general four-fermion interaction ($G_{tb}\neq 0$), the particle spectrum is the one of the one Higgs doublet model.
In this proceeding, we highlight the computation of leading fermionic three-loop corrections to electroweak precision observables (EWPOs) accomplished recently. We summarize the numerical analysis and provide an outlook.
The top condensate see-saw mechanism of Dobrescu and Hill allows electroweak symmetry to be broken while deferring the problem of flavour to an electroweak singlet, massive sector. We provide an extended version of the singlet sector that naturally accommodates realistic masses for all the standard model fermions, which play an equal role in breaking electroweak symmetry. The models result in a relatively light composite Higgs sector with masses typically in the range of (400-700)~GeV. In more complete models the dynamics will presumably be driven by a broken gauged family or flavour symmetry …
We consider the extended electroweak gauge group SU(2)_1 \times SU(2)_2 \times U(1)_Y where the first and second families of fermions couple to SU(2)_1 while the third family couples to SU(2)_2. Bounds based an precision electroweak observables and heavy gauge boson searches are placed on the new parameters of the theory. The extra gauge bosons can be as light as about a TeV and can be discovered at future colliders such as the NLC and LHC for a wide range of the parameter space. FCNC interactions are also considered.
We consider an extended electroweak gauge group: SU(2)$_1 \times$ SU(2)$_2 \times$ U(1)$_Y$ where the first and second generation of fermions couple to SU(2)$_1$ and the third generation couples to SU(2)$_2$. Bounds based on heavy gauge boson searches and current precision electroweak measurements are placed on the masses of the new heavy gauge bosons. In particular we find that the mass of the heavy W boson can not be less than 800 GeV. For some range of the allowed parameter space, these heavy gauge bosons produce observable signals at the Tevatron and LEP-II.
We calculate next-to-leading order (NLO) QCD corrections to electroweak Higgs plus three jet production. Both vector boson fusion (VBF) and Higgs-strahlung type contributions are included along with all interferences. The calculation is implemented within the Matchbox NLO framework of the Herwig++ event generator.
We compute the contribution of three-loop mixed QCD-electroweak corrections ($α_S^2α^2$) to the $gg \to H$ scattering amplitude. We employ the method of differential equations to compute the relevant integrals and express them in terms of Goncharov polylogarithms.
The uniqueness of the hypercharge assignments in the three fermion families leptoquark-bilepton $SU(3)_C \times SU(4)_L \times U(1)_N$ model is established. Although the gauge group contains an explicit U(1) factor, freedom from triangle anomalies combined with the requirement of nonvanishing charged fermion masses uniquely fix the electric charges of all fermions independently of the neutrinos being massless or not. The electric-charge quantization, family replication, and the existence of three colors are interwoven.
We study the neutrino mass generation in the $SU(4)_L \otimes U(1)_X$ electroweak extension of the standard model by considering non-renormalizable dimension five effective operators. It is shown that there exist two topologies for the realizations of such an operator at the tree-level and for one of the three-family models is explore the neutrino phenomenology after extending its particle content with an $SU(4)_L$ fermion singlet and a scalar decuplet. Constraints in the available parameters space of the model are partially discussed.
A review of the calculation of the leading three-loop electroweak corrections to the rho-parameter, sin^2 theta_eff and the W-boson mass is presented. The heavy Higgs mass expansion and the renormalization are discussed.
In this talk we discuss the implementation of the full next-to-leading order QCD corrections to electroweak Higgs boson plus three jet production at the LHC within the Matchbox framework of the Herwig++ event generator. We also present numerical results for integrated cross sections and kinematic distributions.
We compute the electroweak ${\cal O}(α^3α_s)$ corrections to three-jet production and related event-shape observables at electron-positron colliders. We properly account for the experimental photon isolation criteria and for the corrections to the total hadronic cross section. Corrections to the three-jet rate and to normalised event-shape distributions turn out to be at the few-per-cent level.
The implementation of the full next-to-leading order (NLO) QCD corrections to electroweak Higgs boson plus three jet production at hadron colliders such as the LHC within the Matchbox NLO framework of the Herwig++ event generator is discussed. We present numerical results for integrated cross sections and kinematic distributions.
We discuss a theory of flavour in which Higgs Yukawa couplings are related to those of the new scalar triplet leptoquark and/or $Z'$ responsible for $R_{K^{(*)}}$, with all couplings arising effectively from mixing with a vector-like fourth family, whose mass may be anywhere from the Planck scale to the electroweak scale for the leptoquarks explanation, but is pinned down to the TeV scale if the $Z'$ exchange plays a role. However, in this particular model, only leptoquark exchange can contribute significantly to $R_{K^{(*)}}$, since $Z'$ exchange is too constrained from $B_s$ mixing and $τ\ri…
Gauged flavor symmetries at low energies have been proposed in models of dynamical electroweak symmetry breaking and fermion mass generation. The massive flavor gauge bosons give rise to corrections to precisely measured electroweak quantities. We perform a fit to collider electroweak data and place indirect limits on such new physics. In particular we study several models from the literature: universal coloron; chiral top color; chiral, quark family symmetry; SU(9) and SU(12) chiral, flavor symmetry. The 95% exclusion limits on the mass of the heavy gauge bosons for these models, at their cri…
The pattern of quark and lepton mass matrices is unexplained in the standard model of particle interactions. I propose the novel idea of a progressive gauge U(1) symmetry where it is a reflection of the regressive electroweak symmetry breaking pattern, caused by an extended Higgs scalar sector. Phenomenological implications of this new hypothesis are discussed.
We make non perturbative estimates of the electroweak radiative correction parameter $S$ in dynamical symmetry breaking models with Majorana neutrino masses. The Majorana masses are treated as perturbations to a Non Local Chiral Model of the strong interactions. We argue that parameter ranges exist that would allow realistic values of $S$ and $T$ in one family Technicolour models.
The standard model of leptons is extended to accommodate a discrete Z_3 X Z_2 family symmetry. After rotating the charged-lepton mass matrix to its diagonal form, the neutrino mass matrix reveals itself as very suitable for explaining atmospheric and solar neutrino oscillation data. A generic requirement of this approach is the appearance of three Higgs doublets at the electroweak scale, with observable flavor violating decays.
Condensates of colored fermions driving electroweak symmetry breaking could give rise to a light pseudoscalar that would show up in the Higgs search at the LHC. The branching ratios of its decay will distinguish it from the Higgs and illuminate its origin. In particular the colored fermions may be the techniquarks of a one family technicolor theory or the quarks of a strongly interacting fourth family. The former has more difficulties in this context.
CKM mixing between third family quarks and a possible fourth family is constrained by global fits to the precision electroweak data. The dominant constraint is from nondecoupling oblique corrections rather than the Zbb vertex correction used in previous analyses. The possibility of large mixing suggested by some recent analyses of FCNC processes is excluded, but 3-4 mixing of the same order as the Cabbibo mixing of the first two families is allowed.
We study a two-Higgs-doublet model with four generalised CP symmetries in the scalar sector. Electroweak symmetry breaking leads automatically to spontaneous breaking of two of them. We require that these four CP symmetries can be extended from the scalar sector to the full Lagrangian and call this requirement the principle of maximal CP invariance. The Yukawa interactions of the fermions are severely restricted by this requirement. In particular, a single fermion family cannot be coupled to the Higgs fields. For two fermion families, however, this is possible. Enforcing the absence of flavour…
The latest electroweak precision data allow the existence of additional chiral generations in the standard model. We study prospects of search for the fourth standard model family fermions and quarkonia at $e^{+}e^{-}$ and $γγ$ options of CLIC. It is shown that CLIC will be powerfull machine for discovery and investigation of both fourth family leptons and quarkonia. Moreover, the formation of the fourth family quarkonia will give a new opportunity to investigate Higgs boson properties.
Measurements of electroweak precision observables at future electron-positron colliders, such as the CEPC, FCC-ee, and ILC, will be sensitive to physics at multi-TeV scales. To achieve this sensitivity, precise predictions for the Standard Model expectations of these observables are needed, including corrections at the three- and four-loop level. In this article, results are presented for the calculation of a subset of three-loop mixed electroweak-QCD corrections, stemming from diagrams with a gluon exchange and two closed fermion loops. The numerical impact of these corrections is illustrated…
We present an analytical calculation of the leading three-loop radiative correction to the rho-parameter in the Standard Model in the large Higgs mass limit. This correction, of order g^6 m_H^4/M_W^4, is opposite in sign to the leading two-loop correction of order g^4 m_H^2/M_W^2. The two corrections cancel each other for a Higgs mass of approximately 480 GeV. The result shows that it is extremely unlikely that a strongly interacting Higgs sector could fit the data of electroweak precision measurements.
The infrared behaviour of the standard model at finite temperature is determined by the confining phase of the SU(2)-Higgs model in three dimensions. Due to the Landau singularity of the three-dimensional gauge theory the perturbative treatment of the electroweak phase transition breaks down for Higgs masses above a critical mass $m_H^c$. Based on a renormalization group improved effective potential we find $m_H^c\sim$ 70 GeV. The scalar self-coupling has a Landau-type singularity also in the abelian U(1)-Higgs model, which leads to a breakdown of perturbation theory in the symmetric phase.
Limits on the Higgs boson mass restrict CKM mixing of a possible fourth family beyond the constraints previously obtained from precision electroweak data alone. Existing experimental and theoretical bounds on the Higgs mass already significantly restrict the allowed parameter space. Zero CKM mixing is excluded and mixing of order the Cabibbo angle is allowed. Upper and lower limits on 3-4 CKM mixing are exhibited as a function of the Higgs mass. We use the default inputs of the Electroweak Working Group and also explore the sensitivity of both the three and four family fits to alternative inpu…
It was shown recently that the original SU(5) theory of Georgi and Glashow, augmented with an adjoint fermionic multiplet 24_F, can be made compatible both with neutrino masses and gauge coupling unification. In particular, the model predicts that either electroweak-triplet states are light, within the reach of the Large Hadron Collider (LHC), or proton decay will become accessible at the next generation of megaton-scale facilities. In this paper, we present the computation of the correlation function between the electroweak-triplet masses and the unification scale at the next-to-next-to-leadi…
If no light Higgs boson exist, the interaction among the gauge bosons becomes strong at high energies (~1TeV). The effects of strong electroweak symmetry breaking (SEWSB) could manifest themselves as anomalous couplings before they give rise to new physical states, thus measurement of all couplings and their possible deviation from Standard Model (SM) values could give valuable information for understanding the true nature of symmetry breaking sector. Here we present a detailed study of the measurement of quartic gauge couplings in weak boson scattering processes and a possibility for same mea…
We calculate the three-loop soft function for the production of an electroweak boson (Higgs, $γ$, $W^\pm$, $Z$) with large transverse momentum at a hadron collider. It is the first time a soft function for a three-parton process is computed at next-to-next-to-next-to-leading order (N$^3$LO). As a technical novelty, we perform the calculation in terms of forward-scattering-type loop diagrams rather than evaluating phase space integrals. Our three-loop result contains color-tripole contributions and explicitly confirms predictions on the universal infrared structure of QCD scattering amplitudes …
We describe the impact of the full one-loop Electro-Weak terms of O($α_sα^3_{EM}$) entering the electron-positron into three-jet cross-section. We include both factorisable and non-factorisable virtual corrections, photon bremsstrahlung but not the real emission of $W^\pm$ and $Z$ bosons. We show preliminary results and we discuss the impact of the Electro-Weak corrections on three-jet observables.
The pure electroweak three-loop mechanism for the induced electric and chromoelectric dipole moments of quarks is studied in the Kobayashi-Maskawa model with three and four generations. In the standard three generation case, this mechanism is found to produce a negligible contribution to the electric dipole moment of neutron. In the presence of the fourth heavy generation, however, pure electroweak corrections are important and might be several times larger than the corresponding QCD contribution for the masses of heaviest quarks $\sim$ 500-600 GeV. The resulting electric dipole moment of neut…
The meson-cloud model of the nucleon consisting of a system of three valence quarks surrounded by a meson cloud is applied to study the electroweak structure of the proton and neutron. The electroweak nucleon form factors are calculated within a light-front approach, by obtaining an overall good description of the experimental data. Charge densities as a function of the transverse distance with respect to the direction of the three-momentum transfer are also discussed.
We complete the list of one loop renormalization group equations and matching conditions relevant for the computation of the electroweak precision parameters $S$ and $T$ in the three site Higgsless model. We obtain one-loop formulas for $S$ and $T$ expressed in terms of physical observables such as the KK gauge boson mass $M_{W'}$, the KK fermion mass $M$, and the KK gauge boson ($W'$) couplings with light quarks and leptons $g_{W'ff}$. It is shown that these physical observables, $M_{W'}$, $M$ and $g_{W'ff}$ are severely constrained by the electroweak precision data. Unlike the tree level ana…
The addition of an Abelian family symmetry to the Minimal Supersymmetric Standard Model reproduces the observed hierarchies of quark and lepton masses and quark mixing angles, only if it is anomalous. Green-Schwarz compensation of its anomalies requires the electroweak mixing angle to be $\sin^2θ_w=3/8$ at the string scale, without any assumed GUT structure, suggesting a superstring origin for the standard model. The analysis is extended to neutrino masses and the lepton mixing matrix.
We examine the structure of the quaternion group $Q_8$ and its possible application to the physics of flavor. We find that a $Q_8$ family symmetry is suitable to explain the difference between quark and lepton mixing patterns. Distinctive phenomenological predictions are derived for the neutrino sector and the electroweak Higgs sector. We also show how the $Q_8$ symmetry suppresses the effective operators which mediate proton decay.
If supersymmetry (SUSY) is not for stabilizing the electroweak energy scale, what is it used for in particle physics? We propose that it is for flavor problems. A cyclic family symmetry is introduced. Under the family symmetry, only the $τ$-lepton is massive due to the vacuum expectation value (VEV) of the Higgs field. This symmetry is broken by a sneutrino VEV which results in the muon mass. The comparatively large sneutrino VEV does not result in a large neutrino mass due to requiring heavy gauginos. SUSY breaks at a high scale $\sim 10^{13}$ GeV. The electroweak energy scale is unnaturally …
We list all possible dimension-six CP-conserving $SU_c(3)\times SU_L(2) \times U_Y(1)$ invariant operators involving the third-family quarks which could be generated by new physics at a higher scale. Expressions for these operators after electroweak gauge symmetry breaking and the induced effective couplings $Wt\bar b$, $Xb\bar b$ and $Xt\bar t$ $( X=Z,γ,g,H)$ are presented. Analytic expressions for the tree level contributions of all these operators to the observables $R_b$ and $A^b_{FB}$ at LEP I, $σ(e^+e^-\rightarrow b\bar b)$ and $A^b_{FB}$ at LEP II, $σ(e^+e^-\rightarrow t\bar t)$ and $A_…
These three lectures review the state of our understanding of electroweak interactions and the search for the agent of electroweak symmetry breaking. The themes of the lectures are (i) the electroweak theory and its experimental status, (ii) the standard-model Higgs boson, and (iii) aspects of electroweak theory beyond the standard SU(2)_L x U(1)_Y model.
In the Type I see-saw model, the naturalness requirement that corrections to the electroweak $μ$ parameter not exceed 1 TeV results in a rough bound on the lightest right-handed neutrino mass, $M_{N_1}\lesssim 3\times 10^7$ GeV. In this letter we derive generic bounds applicable in any three-flavour Type I see-saw model. We find $M_{N_1}\lesssim 4\times 10^7$ GeV and $M_{N_2}\lesssim 7\times 10^7$ GeV. In the limit of one massless neutrino, there is no naturalness bound on $M_{N_3}$ in the Poincare protected decoupling limit. Our results confirm that no Type I see-saw model can explain the obs…
We derive a semiclassical transport equation for fermions propagating in the presence of a CP-violating planar bubble wall at a first order electroweak phase transition. Starting from the Kadanoff-Baym (KB) equation for the two-point (Wightman) function we perform an expansion in gradients, or equivalently in the Planck constant h-bar. We show that to first order in h-bar the KB equations have a spectral solution, which allows for an on-shell description of the plasma excitations. The CP-violating force acting on these excitations is found to be enhanced by a boost factor in comparison with th…
Future electron-position colliders, such as CEPC and FCC-ee, have the capability to dramatically improve the experimental precision for W and Z-boson masses and couplings. This would enable indirect probes of physics beyond the Standard Model at multi-TeV scales. For this purpose, one must complement the experimental measurements with equally precise calculations for the theoretical predictions of these quantities within the Standard Model, including three-loop electroweak corrections. This article reports on the calculation of a subset of these corrections, stemming from diagrams with three c…
The activities of the Electroweak Physics Working Group are summarized. Three main issues are addressed: 1) prospects for measuring the $W$ mass at the Tevatron using the inclusive electron energy spectrum, 2) constraining the strange quark distribution function in $W$ + charm production, and 3) possibilities to determine the three vector boson couplings at the Tevatron and SSC.
Full Three-Loop Electroweak Multiplet Contributions to the Electron Electric Dipole Moment
Nagoya University（名古屋大学）；Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University（名古屋大学小林-益川粒子宇宙起源研究所）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学 Kavli 宇宙粒子物质起源研究所）；Department of Physics, Graduate School of Science, Chiba University（千叶大学理学研究科物理学系）
We present the results from a calculation of the full electroweak two-loop fermionic contributions to the effective leptonic mixing angle of the $Z$ boson, $\sin^2θ_{eff}$, in the Standard Model. On-shell renormalization and analytic calculations are performed for the three-point vertex functions at zero external momenta, whereas irreducible three-point integrals for non-vanishing external momenta are evaluated semi-analytically applying two different methods. Comparisons with a previous calculation show complete agreement.
We present an analytical calculation of the leading three-loop radiative correction to the S-parameter in the Standard Model in the large Higgs mass limit. Numerically, S^(3) = 1.1105*g^4/(1024 pi^3)*m_H^4/M_W^4. When combined with the corresponding three-loop correction to the rho-parameter, this leads to shifts of Delta^(3) sin^2 theta_eff = 4.6*10^-9*m_H^4/M_W^4 in the effective weak mixing angle and Delta^(3) M_W = -6.3*10^-4*MeV*m_H^4/M_W^4 in the W boson mass. For both of these observables, the sign of the three-loop correction is equal to that of the one-loop correction.
We show that higher-order coefficients required to perform threshold resummation for electroweak annihilation processes, such as Drell-Yan or Higgs production via gluon fusion, can be computed using perturbative results derived in Deep Inelastic Scattering. As an example, we compute the three-loop coefficient D_3, generating most of the fourth tower of threshold logarithms for the Drell-Yan cross section in the MSbar scheme, using the recent three-loop results for splitting functions and for the quark form factor, as well as a class of exponentiating two-loop contributions to the Drell-Yan pro…
