We investigate the properties of a Finite Electroweak (FEW) Theory first proposed in 1991. The theory predicts a running of the electroweak coupling constants and a suppression of tree level amplitudes, ensuring unitarity without a Higgs particle. We demonstrate this explicitly by calculating W_L^+W_L^- -> W_L^+W_L^- and e+e- -> W_L^+W_L^- in both the electroweak Standard Model and the FEW model.
We report the "state of the art" of the problem of $B+L$ violation in high-energy electroweak scatterings. Results of various analyses point toward (though do not prove rigorously yet) the "half-suppression", i.e., that the $B+L$ violating cross section remains suppressed at least by the negative exponent of the single instanton action, at all energies. Most interesting techniques developed in this field are reviewed. Particular attention is paid to unitarity constraints on the anomalous cross section, and to some conceptual problem involving the use of the optical theorem in the presence of i…
Potential implications of a new constrained instanton solution in the electroweak standard model are discussed. Notably, there may be a non-perturbative unitarity violating contribution to the total cross-section at high collision energies.
We study perturbative unitarity and electroweak oblique corrections in the electroweak symmetry breaking models including an arbitrary number of neutral Higgs bosons. Requiring the perturbative unitarity of the high energy scattering amplitudes of weak gauge bosons and the neutral Higgs bosons at tree level, we obtain a set of conditions among the Higgs coupling strengths (unitarity sum rules). It is shown that the unitarity sum rules require the tree level rho parameter to be 1 if there are only neutral Higgs bosons. Moreover, we find that the one-loop finiteness of the electroweak oblique co…
In the conventional metric formulation of gravity, the Higgs Inflation model violates unitarity in the electroweak vacuum in Higgs scattering at the energy scale $Λ\sim M_{Pl}/ξ$, where $ξ\sim 10^4$ is the non-minimal coupling of the Higgs to the Ricci scalar. In the Palatini formulation it is commonly believed that $Λ\sim M_{Pl}/\sqrtξ$, where $ξ\sim 10^{9}$. Here we reconsider unitarity violation in the electroweak vacuum in the Palatini formulation. We argue that there is no unitarity violation in Higgs scattering in the Palatini non-minimally coupled Standard Model in the electroweak vacuu…
Introducing arbitrary number of neutral Higgs bosons in the electroweak symmetry breaking sector, we derive a set of conditions among Higgs couplings which need to be satisfied to maintain the unitarity of the high energy scattering amplitudes of weak gauge bosons at the tree level (unitarity sum rules). It is shown that the unitarity sum rules require the tree level $ρ$ parameter to be 1, without explicitly invoking the custodial symmetry arguments. The one-loop finiteness of the electroweak oblique corrections is automatically guaranteed once these unitarity sum rules are imposed among Higgs…
Problems related to fermions, unitarity and chiral anomaly in high energy electroweak interactions, are investigated. Particular attention is paid to the correct functional integration over fermion fields in the background of instanton-anti\-instanton type configurations. This leads to an expansion of correlation functions in terms of a small parameter, $ρ/R$, when the instanton-antiinstanton separation ($R$) is large compared to their sizes ($ρ$). Applying such a method to widely discussed cases of fermion-number violation in the electroweak theory, we conclude that there are no theoretical b…
An electroweak (EW) model has been investigated (Moffat) in which the energy $E < μ=\sqrtλM_W$, where $λ$ is a gauge parameter and $M_W$ is the $W$ boson mass. For large enough $λ$ the scalar boson mass $μ=\sqrtλM_W$ can be heavy enough to avoid detection in LHC experiments. The theory is perturbatively renormalizable for the decoupled scalar interactions. The Born approximation tree graph unitarity can be ensured by postulating that the effective coupling constant $g_{\rm eff}(s)$ vanishes as $1/\sqrt{s}$ or faster as $s\rightarrow\infty$, predicting that the EW interactions become weaker at …
We present a broad study of collider processes that embed $2 \to 2$ scattering amplitudes involving top quarks in the Electroweak sector. We parametrise the modified interactions using the Standard Model Effective Field Theory framework and discuss how the New Physics effects lead to unitarity violating behaviour at the amplitude level. For each scattering amplitude we compute the helicity amplitudes in the high energy limit paying special attention to the effects of the higher dimensional operators. We also discuss whether and to what extent the unitarity violating effects are retained in phy…
We replace the standard model scalar doublet by a doublet of vector fields and generate masses by dynamical symmetry breaking. Oblique radiative corrections are small if the new vector bosons ($ B^+$, $ B^0 $) are heavy. In this note it is shown that the model has a low momentum scale and above $ Λ\simeq 2 $ TeV it does not respect the perturbative unitarity. From tree-graph unitarity the allowed region of $B ^+ (B^0) $ mass is estimated as $m_{B^+} \geq 369 \hbox{GeV} \quad (m_{B^0} \geq 410 $ GeV) at $Λ= 1 $ TeV.
We consider electroweak symmetry breaking by a certain class of non-local Higgs sectors. Extending previous studies employing the Mandelstam condition, a straight Wilson line is used to make the Higgs action gauge invariant. We show the unitarization of vector-boson scattering for a wide class of non-local actions, but find that the Wilson-line model leads to tree-level corrections to electroweak precision observables, which restrict the parameter space of the model. We also find that Unhiggs models cannot address the hierarchy problem, once the parameters are expressed in terms of low-energy …
Electroweak corrections to longitudinal gauge and Higgs boson scattering amplitudes are calculated. Due to Sudakov double logarithms, the effect is a suppression of amplitude that grows rapidly with increasing center of mass energy leading to significant reduction of cross sections compared to tree level results. For example, the suppression factor for the cross section of $W^+_{\text{L}}W^-_{\text{L}}$ scattering due to these corrections varies from 0.3 at the center of mass energy of $100\text{TeV}$ to a factor of $10^{-12}$ at the center of mass energy of $10^{13}\text{TeV}$. The modificati…
We calculate the form of the corrections to the electroweak interactions in the class of Higgsless models which can be "deconstructed'' to a chain of SU(2) gauge groups adjacent to a chain of U(1) gauge groups, and with the fermions coupled to any single SU(2) group and to any single U(1) group along the chain. The primary advantage of our technique is that the size of corrections to electroweak processes can be directly related to the spectrum of vector bosons ("KK modes"). In Higgsless models, this spectrum is constrained by unitarity. Our methods also allow for arbitrary background 5-D geom…
We use conditions for unitarity cancellations to constrain the couplings of the top and bottom quarks to Kaluza-Klein modes in Higgsless models of electroweak symmetry breaking. An example for the mass spectrum of quark resonances in a theory space model is given and the implications for the collider phenomenology in the top sector are discussed, comparing to signatures of Little Higgs and strong electroweak symmetry breaking models.
There are six leptonic unitarity triangles (LUTs) defined by six orthogonality conditions of the three-family lepton flavor mixing matrix in the complex plane. In the framework of the standard model or the minimal supersymmetric standard model, the evolutions of sides and inner angles of the six LUTs from a superhigh energy scale $Λ_{\rm H}^{}$ to the electroweak scale $Λ_{\rm EW}^{}$ due to the renormalization-group equation (RGE) running are derived in the integral form for both Dirac and Majorana neutrinos. Furthermore, the LUTs as an intuitively geometrical language are applied to the desc…
The scattering of longitudinally polarized W bosons in extensions of the Standard Model with anomalous Higgs couplings to the gauge sector and higher order $O(p^4)$ operators is considered. The modified couplings should be thought as the low energy remnants of some new dynamics involving the electroweak symmetry breaking sector. By imposing unitarity and causality constraints on $W_LW_L$ scattering amplitudes we relate the possible values of the effective couplings to the presence of new resonances above 300 GeV. We investigate the properties of these new resonances and their experimental dete…
Unitarity constraints on anomalous top-Higgs couplings are examined. We also compare the unitarity constraints with the constraints from electroweak baryogenesis and electric dipole moments derived earlier.
The Fermi constant ($G_F$) is extremely well measured through the muon lifetime, defining one of the key fundamental parameters in the Standard Model (SM). Therefore, to search for physics beyond the SM (BSM) via $G_F$, the constraining power is determined by the precision of the second-best independent determination of $G_F$. The best alternative extractions of $G_F$ proceed either via the global electroweak (EW) fit or from superallowed $β$ decays in combination with the Cabibbo angle measured in kaon, $τ$, or $D$ decays. Both variants display some tension with $G_F$ from muon decay, albeit …
The main challenge faced by Higgsless models of electroweak symmetry breaking is to reconcile the experimental constraints imposed by the precision electroweak data and the top quark phenomenology with the unitarity constraints imposed by longitudinal gauge boson scattering amplitudes. In this paper we expand on previous work, giving details of how delocalized fermions can be used to adjust the $S$ parameter to zero, while keeping the $T$ and $U$ parameters naturally suppressed. We also show that it is possible to obtain the top quark mass, without affecting the delay of unitarity violation of…
Wilson is a Python library for matching and running Wilson coefficients of higher-dimensional operators beyond the Standard Model. Provided with the numerical values of the Wilson coefficients at a high new physics scale, it automatically performs the renormalization group evolution within the Standard Model effective field theory (SMEFT), matching onto the weak effective theory (WET) at the electroweak scale, and QCD/QED renormalization group evolution below the electroweak scale down to hadronic scales relevant for low-energy precision tests. The matching and running encompasses the complete…
The evidence for electroweak radiative corrections not contained in $α(m_Z)$ is examined. At low energies there is very strong evidence in the analysis of the unitarity of the CKM matrix. At LEP and collider experiments the current direct signals are not strong, but there is substantial indirect evidence, which will likely become sharper when $m_t$ is determined. The advantage of using $(Δr)_{res}$ as a measure of these effects is emphasized. In order to improve the direct evidence, more accurate measurements of $m_W$ and the on--resonance asymmetries are indicated.
An electroweak model with running coupling constants described by an energy dependent entire function is utraviolet complete and avoids unitarity violations for energies above 1 TeV. The action contains no physical scalar fields and no Higgs particle and the physical electroweak model fields are local and satisfy microcausality. The $W$ and $Z$ masses are compatible with a symmetry breaking $SU(2)_L\times U(1)_Y \rightarrow U(1)_{\rm em}$, which retains a massless photon. The vertex couplings possess an energy scale $Λ_W > 1$ TeV predicting scattering amplitudes that can be tested at the LHC.
Processes where $W$ and $Z$ bosons scatter into pairs of electroweak bosons $W$, $Z$, and Higgs, are sensitive probes of new physics in the electroweak sector. We study simplified models that describe typical scenarios of new physics and parameterize the range of possible LHC results between the Standard-Model prediction and unitarity limits. Extending the study beyond purely longitudinal scattering, we investigate the role of transversally polarized gauge bosons. Unitarity becomes an essential factor, and limits on parameters matched to the naive perturbative low-energy effective theory turn …
In this paper, we present the one-loop radiative corrections to the electroweak precision observable $Δρ$ coming from the $I_W=1$ multiplet excited leptons. We have calculated the couplings of the exotic lepton triplet to the vector bosons and ordinary leptons using effective Lagrangian approach. These couplings are then used to estimate the excited lepton triplet contribution to the $Δρ$ parameter. The mass degenerate excited lepton contribution to $Δρ$ is small and can be neglected. However, if the excited leptons are non-degenerate, their contribution can be large which can result in more s…
We investigate the longitudinal $WW$ scattering in models of dynamical electroweak symmetry breaking featuring a spin one axial and vector state and a composite Higgs. We also investigate the effects of a composite spin two state which has the same properties of a massive graviton. Any model of dynamical electroweak symmetry breaking will feature, depending on the dynamics, some or all these basic resonances as part of the low energy spectrum. We suggest how to take limits in the effective Lagrangian parameter space to reproduce the dynamics of different types of underlying gauge theories, fro…
We determine the constraints on the isospin and hypercharge of a scalar electroweak multiplet from partial-wave unitarity of tree-level scattering diagrams. The constraint from SU(2)_L interactions yields T <= 7/2 (i.e., n <= 8) for a complex scalar multiplet and T <= 4 (i.e., n <= 9) for a real scalar multiplet, where n = 2T+1 is the number of isospin states in the multiplet.
We present a new method for the determination of the Cabibbo-Kobayashi-Maskawa quark mixing matrix element $|V_{tb}|$ from electroweak loop corrections, in particular those affecting the process $Z\to b\bar{b}$. From a combined analysis of results from the LEP, SLC, Tevatron, and neutrino scattering experiments we determine $|V_{tb}| = 0.77^{+0.18}_{-0.24}$. This is the first determination of $|V_{tb}|$ which is independent of unitarity assumptions.
The leading hadronic effects in electroweak theory derive from vacuum polarization which are non-perturbative hadronic contributions to the running of the gauge couplings, the electromagnetic alpha_{em}(s) and the SU(2)_L coupling alpha_2(s). I will report on my recent package "alphaQED", which besides the effective fine structure constant alpha_{em}(s) also allows for a fairly precise calculation of the SU(2)_L gauge coupling alpha_2(s). I will briefly review the role, future requirements and possibilities. Applied together with the "Rhad" package by Harlander and Steinhauser, the package all…
We obtain the partial-wave unitarity constraints on the lowest-dimension effective operators which generate anomalous quartic gauge couplings but leave the triple gauge couplings unaffected. We consider operator expansions with linear and nonlinear realizations of the electroweak symmetry and explore the multidimensional parameter space of the coefficients of the relevant operators: 20 dimension-eight operators in the linear expansion and 5 ${\cal O}(p^4)$ operators in the derivative expansion. We study two-to-two scattering of electroweak gauge bosons and Higgs bosons taking into account all …
We investigate the impact of extra leptons on observed tensions in the muon $g-2$ and the first-row CKM unitarity. By introducing a new SU(2)$_L$ doublet lepton and a SU(2)$_L$ triplet lepton, we find that both of the tensions can be explained simultaneously under constraints from electroweak precision observables and Higgs-boson decays. Our model could be tested by measurements of $h\toμμ$ at future collider experiments.
The energy dependency (running) of the strength of electromagnetic interactions $α$ plays an important role in precision tests of the Standard Model. The running of the former to the $Z$ pole is an input quantity for global electroweak fits, while the running of the mixing angle is susceptible to the effects of Beyond Standard Model physics, particularly at low energies. We present a computation of the hadronic vacuum polarization (HVP) contribution to the running of these electroweak couplings at the non-perturbative level in lattice QCD, in the space-like regime up to $Q^2$ momentum transfer…
The energy dependence of the electroweak gauge couplings has not been measured above the weak scale. We propose that percent-level measurements of the energy dependence of $α_{1,2}$ can be performed now at the LHC and at future higher energy hadron colliders. These measurements can be used to set limits on new particles with electroweak quantum numbers without relying on any assumptions about their decay properties. The shape of the high invariant mass spectrum of Drell-Yan, $p p \rightarrow Z^*/γ^* \rightarrow \ell^+ \ell^-$, constrains $α_{1,2}(Q)$, and the shape of the high transverse mass …
We discuss the properties of a model incorporating both a scalar electroweak Higgs doublet and an electroweak Higgs triplet. We construct the low-energy effective theory for the light Higgs-doublet in the limit of small (but nonzero) deviations in the rho parameter from one, a limit in which the triplet states become heavy. For small deviations in the rho parameter from one, perturbative unitarity of WW scattering breaks down at a scale inversely proportional to the renormalized vacuum expectation value of the triplet field (or, equivalently, inversely proportional to the square-root of the de…
We make a systematic theoretical analysis of the masses and their variation with energy by solving the renormalization group equation (RGE) in the Minimal Supersymmetric Standard Model (MSSM). The unification fermion masses of around 115 GeV at GeV scale has been derived by Deo and Maharana. Here we undertake the unfinished but the important task of calculating the masses and their running. The unification mass and group theoretic constants for the model are known. The top mass and its descent is studied very carefully. We find that the Ramond,Roberts and Ross value of the Wolfenstein paramete…
Gauge independent form factors ρ^(e; e) and \hatκ^(e; e)(q^2) for Moller scattering at s << m_W^2 are derived. It is pointed out that \hatκ^(e; e) is very different from its counterparts in other processes. The relation between the effective parameter \hatκ^(e; e)(q^2,μ) \sin^2 \hatθ_W(μ) and \sin^2 θ_eff is derived in a scale-independent manner. A gauge and process-independent running parameter \sin^2 \hatθ_W (q^2), based on the pinch-technique self-energy a_{γZ} (q^2), is discussed for all q^2 values. At q^2=0 it absorbs very accurately the Czarnecki-Marciano calculation of the Moller scatte…
As present and future experiments, on both the energy and precision frontiers, look to identify new physics beyond the Standard Model, we require more precise determinations of fundamental quantities, like the QED and electroweak couplings at various momenta. These can be obtained either entirely from experimental measurements, or from one such measurement at a particular virtuality combined with the couplings' virtuality dependence computed within the SM. Thus, a precise, entirely theoretical determination of the running couplings is highly desirable, even more since the preliminary results o…
If there is new physics associated with the top quark, it could show up as anomalous couplings of the top quark to weak gauge bosons, such as $Z\ttbar$ and $W\tbbar$ vector and axial-vector couplings. We use the processes $\ttbar\to Z^0Z^0$, $\ttbar\to W^+W^-$, and $\ttbar\to Z^0H$ to obtain the unitarity constraints on these anomalous couplings, and combine these constraints with those from precision electroweak data. The unitarity constraints can impose additional limits on the anomalous couplings when the scale of new physics is as low as 2 TeV. A nonzero measurement of such an anomalous co…
We discuss models where the Higgs boson of the electroweak standard model plays the role of the inflaton. We focus on the question of the violation of perturbative unitarity due to the coupling of the Higgs boson either to the Ricci scalar or to the Einstein tensor and discuss the background dependence of the unitarity bounds. Our conclusion is that the simplest model which restricts itself to the standard model Higgs boson without introducing further degrees of freedom has a serious problem. However, in the asymptotically safe gravity scenario, the Higgs boson of the standard model could be t…
The hadronic contribution to the running of the electroweak gauge couplings
GSI Helmholtz Centre for Heavy Ion Research（GSI重离子研究中心）；CERN（欧洲核子研究中心）；High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）；University of Wuppertal（伍珀塔尔大学）
The electromagnetic coupling $α$ and the electroweak mixing angle $θ_{\mathrm{W}}$ are parameters of the Standard Model (SM) that enter precision SM tests and play a fundamental rôle in beyond SM physics searches. Their values are energy dependent, and non-perturbative hadronic contributions are the main source of uncertainty to the theoretical knowledge of the running with energy. We present a lattice study of the leading hadronic contribution to the running of $α$ and $\sin^2θ_{\mathrm{W}}$. The former is related to the hadronic vacuum polarization (HVP) function of electromagnetic currents,…
We present results for the hadronic running of the electromagnetic coupling and the weak mixing angle from simulations of lattice QCD with $N_f=2+1$ flavours of $O(a)$-improved Wilson fermions. Using two different discretisations of the vector current, we compute the quark-connected and -disconnected contributions to the hadronic vacuum polarisation (HVP) functions $\barΠ^{γγ}$ and $\barΠ^{Zγ}$ for spacelike squared momenta $Q^2\leq 7$ $\mathrm{GeV}^2$. Our results are extrapolated to the physical point using ensembles at four lattice spacings, with pion masses ranging from 130 to 420 MeV. We …
To avoid possible electroweak vacuum instability in the vector-like fermion model, we introduce a new singlet scalar to the model, which couples to the vector-like fermion, and also mixes with the Higgs boson after spontaneous symmetry breaking. We investigate the vector-like fermion predominantly coupled to the third generation quarks, and its mass is generated from the vacuum expectation value of the new scalar field in the model. In this setup, as running towards high energies, the new scalar provides positive contribution to the running of the higgs quartic coupling, and the matching on th…
We discuss the process of Higgs boson production in $γγ$ collider on noncommutative spacetime and compare the results with large extra dimension in KK graviton channel. Summing all KK mode on IR brane, the affections are in the same order by comparing noncommutatve model prediction. This process is completely forbidden in standard model on unitarity condition and bosonic distribution. In noncommutative theory, the effect is induced by the coordinates noncommutable relation, $[x^μ, x^ν]$ = $iθ^{μν}$. Due to the constant background strength tensor does not contain any conserved quantum number, h…
The recent discovery of a 126 GeV boson at the LHC will be followed by a detailed examination of its couplings in order to determine whether this particle is the Higgs boson of the standard model or one of many particles of an extended scalar sector. One such extension with a rich phenomenology consists of a color octet electroweak doublet scalar. The most general renormalizable scalar potential contains twelve new parameters and it is therefore desirable to constrain them. We present theoretical constraints on these parameters obtained by requiring perturbative unitarity for two-to-two scalar…
The scale of mass generation for fermions (including neutrinos) and the scale for electroweak symmetry breaking (EWSB) can be bounded from above by the unitarity of scattering involving longitudinal weak gauge bosons or their corresponding would-be Goldstone bosons. Including the exact n-body phase space we analyze the 2 --> n ($n \geq 2$) processes for the fermion-(anti)fermion scattering into multiple gauge boson final states. Contrary to naive energy power counting, we demonstrate that as $n$ becomes large, the competition between an increasing energy factor and a phase-space suppression le…
The angle $γ$ of the standard CKM unitarity triangle can be determined from tree-level $B$-meson decays essentially without hadronic uncertainties. We calculate the second-order electroweak corrections for the $B \to D π$ modes and show that their impact on the determination of $γ$ could be enhanced by an accidental cancellation of poorly known hadronic matrix elements. However, we do not expect the resulting shift in $γ$ to exceed $\big|δγ^{Dπ} /γ\big| \lesssim {\mathcal O}\big(10^{-4}\big)$.
Running of the Electroweak Gauge Couplings from First Principles
Johannes Gutenberg-Universität Mainz（约翰内斯·古腾堡美因茨大学）；GSI Helmholtz Centre for Heavy Ion Research（GSI重离子研究中心）；PRISMA ++ Cluster of Excellence and Institut für Kernphysik, Johannes Gutenberg-Universität Mainz（美因茨大学核物理研究所及PRISMA++卓越集群）；Theoretical Physics Department, CERN（欧洲核子研究中心理论物理部）；Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK)（高能加速器研究机构粒子与核研究研究所）；Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn（波恩大学斯特拉斯曼与核物理亥姆霍兹研究所及贝特理论物理中心）；Department of Physics, University of Wuppertal（伍珀塔尔大学物理系）
We study the scattering of longitudinally polarized W bosons in extensions of the Standard Model where anomalous Higgs couplings to gauge sector and higher order O(p^4) operators are considered. These new couplings with respect to the Standard Model should be thought as the low energy remnants of some new dynamics involving the electroweak symmetry breaking sector. By imposing unitarity and causality constraints on the WW scattering amplitudes we find relevant restrictions on the possible values of the new couplings and the presence of new resonances above 300 GeV. We investigate the propertie…
We revisit the electroweak precision tests for Higgsless models of strong EWSB. We use the Vector Meson Dominance approach and express S and T via couplings characterizing vector and axial spin-1 resonances of the strong sector. These couplings are constrained by the elastic unitarity and by requiring a good UV behavior of various formfactors. We pay particular attention to the one-loop contribution of resonances to T (beyond the chiral log), and to how it can improve the fit. We also make contact with the recent studies of Conformal Technicolor. We explain why the second Weinberg sum rule nev…
The running of the effective electromagnetic coupling is for many electroweak observables the dominant correction. It plays an important role for deriving constraints on the Standard Model in the context of electroweak precision measurements. We compute the four-loop QED corrections to the running of the effective electromagnetic coupling and perform a numerical evaluation of the different gauge invariant subsets.
In the context of non-supersymmetric SO(10) models, we analyze the renormalization group equations for the fermions (including neutrinos) from the GUT energy scale down to the electroweak energy scale, explicitly taking into account the effects of an intermediate energy scale induced by a Pati--Salam gauge group. To determine the renormalization group running, we use a numerical minimization procedure based on a nested sampling algorithm that randomly generates the values of 19 model parameters at the GUT scale, evolves them, and finally constructs the values of the physical observables and co…
If the recently discovered Higgs boson's couplings deviate from the Standard Model expectation, we may anticipate new resonant physics in the weak boson fusion channels resulting from high scale unitarity sum rules of longitudinal gauge boson scattering. Motivated by excesses in analyses of multi-leptons+missing energy+jets final states during run 1, we perform a phenomenological investigation of these channels at the LHC bounded by current Higgs coupling constraints. Such an approach constrains the prospects to observe such new physics at the LHC as a function of very few and generic paramete…
We study a model with an exotic new sector strongly coupled to the Higgs boson, in which supersymmetry is introduced to protect the quartic coupling from a large running and avoid potential vacuum stability problem. The fermionic components present vector like mass terms, through which the Higgs diphoton decay branching ratio can be tuned. The bosonic components trigger a strongly first order electroweak phase transition. We find a large parameter region of effective Yukawa coupling $y\gtrsim2$ and mass parameters $m_f\sim m_s$ of a few hundred GeV, that can simultaneously accommodate the diph…
In extensions of the standard model (SM) with d extra dimensions at the TeV scale the virtual exchange of Kaluza-Klein (KK) excitations of the gauge bosons gives contributions that change the SM relations between electroweak observables. These corrections are finite only for d=1; for d\ge 2 the infinite tower of KK modes gives a divergent contribution that has to be regularized introducing a cutoff (the string scale). However, the ultraviolet dependence of the KK effects is completely different if the running of the couplings with the scale is taken into account. We find that for larger d the …
We compute the hadronic running of the electromagnetic and weak couplings in lattice QCD with $N_{\mathrm{f}}=2+1$ flavors of $\mathcal{O}(a)$ improved Wilson fermions. Using two different discretizations of the vector current, we compute the quark-connected and -disconnected contributions to the hadronic vacuum polarization (HVP) functions $\barΠ^{γγ}$ and $\barΠ^{γZ}$ for Euclidean squared momenta $Q^2\leq 7\,\mathrm{GeV}^2$. Gauge field ensembles at four values of the lattice spacing and several values of the pion mass, including its physical value, are used to extrapolate the results to th…
