We construct a complete basis of dimension-8 operators in the Low-Energy Effective Field Theory below the Electroweak Scale (LEFT). We find there are 35058 dimension-8 operators in the LEFT for two generations of up-type quarks and three generations of down-type quarks, charged leptons, and left-handed neutrinos. The existence of this operator basis is a necessary prerequisite for matching to the Standard Model Effective Field Theory at the dimension-8 level.
I describe a new way for baryogenesis to proceed, which evades many of the problems of GUT and electroweak scenarios. If the reheat temperature after inflation is below the electroweak scale, neither GUT baryon production nor traditional electroweak baryogenesis can occur. However, non-thermal production of sphaleron configurations via preheating could generate the observed baryon asymmetry of the universe. Such low scale baryon production is particularly attractive since it evades a number of strong constraints on reheating from gravitino and moduli production.
We consider a minimal extension of the Standard Model which advocates a dark neutrino sector charged under a hidden $U(1)^\prime$. We show that neutrino masses can arise radiatively in this model. The observed values are compatible with a light dark sector below the electroweak scale and would imply new heavy fermions which may be testable in the next generation of beam dump searches at DUNE, NA62 and SHIP.
If the neutrino is Majorana type and the electroweak phase transition is second or weak first order, neutrino-induced interactions together with sphaleron transitions have the potential to erase a previously generated baryon asymmetry of the universe. Taking correctly into account the evolution of the vacuum expectation of the Higgs field the effective light neutrino masses are constrained to be lighter than order 10 MeV, while the effective heavy masses are constrained to be heavier than order 10^7 GeV.
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…
We estimate the thermal masses and damping rates of active (m < eV) and sterile (M ~ GeV) neutrinos with thermal momenta k ~ 3T at temperatures below the electroweak crossover (5 GeV < T < 160 GeV). These quantities fix the equilibration or "washout" rates of Standard Model lepton number densities. Sterile neutrinos interact via direct scatterings mediated by Yukawa couplings, and via their overlap with active neutrinos. Including all leading-order reactions we find that the washout rate generally exceeds the Hubble rate for 5 GeV < T < 30 GeV. Therefore it is challenging to generate a large l…
The low-energy effective field theory is constructed by integrating out Standard Model states with masses proximate to the electroweak scale. We report the equations of motion for this theory, including corrections due to higher dimensional operators up to mass dimension six. We construct the corresponding symmetry currents, and discuss how the $\rm SU(2)_L \times U(1)_{\mathsf{y}}$ symmetry, and global symmetries, are manifested when Standard Model states are integrated out. Including contributions from higher dimensional operators to the equations of motion modifies the interpretation of con…
We derive bounds on nine dimension-six operators involving electroweak gauge bosons and the Higgs boson from precision electroweak data. Four of these operators contribute at tree level, and five contribute only at one loop. Using the full power of effective field theory, we show that the bounds on the five loop-level operators are much weaker than previously claimed, and thus much weaker than bounds from tree-level processes at high-energy colliders.
We introduce in an arbitrary supersymmetric version of the standard model without elementary scalars a logarithmic operator which is irrelevant in the limit in which all symmetries are respected. However through a dynamical mechanism of the Nambu Jona Lasinio type this operator may produce two fermion vacuum condensates that may account for electroweak and contribute to supersymmetry breaking. Some of the phenomenological consequences of this set-up are discussed.
General analyses of $B$-physics processes beyond the Standard Model require accounting for operator mixing in the renormalization-group evolution from the matching scale down to the typical scale of $B$ physics. For this purpose the anomalous dimensions of the full set of local dimension-six operators beyond the Standard Model are needed. We present here for the first time a complete and non-redundant set of dimension-six operators relevant for $B$-meson mixing and decay, together with the complete one-loop anomalous dimensions in QCD and QED. These results are an important step towards the au…
The possibility of a strongly first-order electroweak phase transition by means of a dimension-six Higgs operator in the Higgs potential of the standard model is studied at finite temperature at the one-loop level. Exact calculation of the one-loop effective Higgs potential at finite temperature suggests that for the Higgs boson with its mass between 115 and 132 GeV the strongly first-order electroweak phase transition is possible if a dimension-six operator is present.
We compute the one-loop matching between the Standard Model Effective Field Theory and the low-energy effective field theory below the electroweak scale, where the heavy gauge bosons, the Higgs particle, and the top quark are integrated out. The complete set of matching equations is derived including effects up to dimension six in the power counting of both theories. We present the results for general flavor structures and include both the $CP$-even and $CP$-odd sectors. The matching equations express the masses, gauge couplings, as well as the coefficients of dipole, three-gluon, and four-fer…
We study the combined effects of both strong and electroweak dimension six effective operators on flavour changing top quark physics at the LHC. Analytic expressions for the cross sections and decay widths of several flavour changing processes will be presented, as well as an analysis of the feasibility of their observation at the LHC.
We discuss a preliminary study of the impact of duality violations on extractions from tau decay data of the D=6 VEVs which determine chiral limit Standard Model K-->pi pi matrix elements of the electroweak penguin operators.
In the two Higgs doublet model, perturbativity breaks down below the Planck scale: For top mass values 170-180 GeV, the Yukawa coupling reaches the pole below 1000 TeV, if the ratio of vev's v_u/v_d is below 1. We discuss top condensate scenarios for 150 GeV < m_top < 200 GeV, showing that a version with two composite Higgses is a viable option. Within electroweak gauge extensions the second Higgs does not come with additional parameters, but is dictated by the symmetry.
We give the complete $O(p^2)$ bosonization of the electroweak Penguin operators $Q_{7,8}$ and compare the result with that of the gluon Penguin operators $Q_{5,6}$. We find that, in addition to the usual (constant and current-current) parts, there are three new terms not discussed previously in the literature. Two of these are present in the factorization approximation and should be included in the standard definition of the $B_{7,8}$-factors. The impact of these corrections on the direct $CP$-violating parameter $\varepsilon '/\varepsilon$ is briefly discussed.
In the Standard Model Effective Field Theory (SMEFT), operators involving the top quark are generally difficult to probe, and can generate sizable loop contributions to the electroweak precision observables, measured by past and future lepton colliders. Could the high precision of the electroweak measurements compensate the loop suppression and provide competitive reaches on these operators? Would the inclusion of these contributions introduce too many additional parameters for a meaningful global electroweak analysis to be done? In this paper, we perform a detailed phenomenological study to a…
We propose a new alternative for baryogenesis which resolves a number of the problems associated with GUT and electroweak scenarios, and which may allow baryogenesis even in modest extensions of the standard model. If the universe never reheats above the electroweak scale following inflation, GUT baryon production does not occur and at the same time thermal sphalerons, gravitinos and monopoles are not produced in abundance. Nevertheless, non-thermal production of sphaleron configurations via preheating could generate the observed baryon asymmetry of the universe.
Constraining four-heavy-quark operators with top-quark, Higgs, and electroweak precision data
Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院）；University of Manchester（曼彻斯特大学）；Università di Padova（帕多瓦大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
We consider hadronic top quark pair production and pair production in association with a photon or a $Z$ boson to probe electroweak dipole couplings in $t\bar{b}W$, $t\bar{t}γ$ and $t\bar{t}Z$ interactions. We demonstrate how measurements of these processes at the 13 TeV LHC can be combined to disentangle and constrain anomalous dipole operators. The construction of cross section ratios allows us to significantly reduce various uncertainties and exploit orthogonal sensitivity between the $t\bar{t}γ$ and $t\bar{t}Z$ couplings. In addition, we show that angular correlations in $t\bar{t}$ product…
The Standard Model extended with right-handed neutrinos whose masses are below the electroweak scale provides a simultaneous solution for the origin of neutrino masses and of the baryon asymmetry of the Universe, that can be tested in current experiments. If three right-handed neutrinos participate to the processes, their parameter space of solutions extends to very large mixing angles, saturating the current experimental constraints. Solutions with right-handed neutrino masses at the GeV scale can be probed in the decay of $B$ mesons at the LHC. For this channel the collision of isotopes of i…
We compute bounds on coefficients of effective operators in the Standard Model that can be inferred from observations of neutrino scattering by the COHERENT experiment. While many operators are bound extremely well by past experiments the full future data set from COHERENT will provide modest improvements for some operators.
In a gauge theory with SU(5) broken to SU(2)$\times$U(1), the Higgs mass squared receives only logarithmic divergence from all scalar-gauge interactions at one loop. The same pattern of gauge symmetry breaking can be achieved without any scalar fields in a five-dimensional model.
We present a semiclassical study of the suppression of topology changing, baryon number violating transitions induced by particle collisions in the electroweak theory. We find that below the sphaleron energy the suppression exponent is remarkably close to the analytic estimates based on a low energy expansion about the instanton. Above the sphaleron energy, the relevant semiclassical solutions have qualitatively different properties from those below the sphaleron: they correspond to jumps on top of the barrier. Yet these processes remain exponentially suppressed, and, furthermore, the tunnelin…
A revised and complete list of the electroweak chiral lagrangian operators up to dimension-four is provided. The connection of these operators to the $S$, $T$ and $U$ parameters and the parameters describing the triple gauge boson vertices $WWγ$ and $WWZ$ is made, and the size of these parameters from new heavy physics is estimated using a one flavor-doublet model of heavy fermions. The coefficients of the chiral lagrangian operators are also computed in this model.
We study Radiative Electroweak Symmetry Breaking in the Minimal Supersymmetric Standard Model (MSSM). We employ the 2-loop Renormalization Group equations for running masses and couplings taking into account sparticle threshold effects. The decoupling of each particle below its threshold is realized by a step function in all one-loop Renormalization Group equations (RGE). This program requires the calculation of all wavefunction, vertex and mass renormalizations for all particles involved. Adapting our numerical routines to take care of the succesive decoupling of each particle below its thres…
We obtain the bounds on arbitrary linear combinations of operators of dimension 6 in the Standard Model. We consider a set of 21 flavor and CP conserving operators. Each of our 21 operators is tightly constrained by the standard set of electroweak measurements. We perform a fit to all relevant precision electroweak data and include neutrino scattering experiments, atomic parity violation, W mass, LEP1, SLD, and LEP2 data. Our results provide an efficient way of obtaining bounds on weakly coupled extensions of the Standard Model.
We reconsider the prospects for observing a dimension-6, CP-violating operator involving $W^+W^-Z$ at the LHC. Firstly, we correct a number of earlier calculations of the loop contribution to the neutron electric dipole moment of a companion operator, involving $W^+W^-γ$, showing that measurements imply a very strong bound on the companion operator. Secondly, we quantify the link between the two operators, showing that strongly-coupled new physics could only be observable in proposed searches if it appeared at a scale below $\sim 170$ GeV. This is most unlikely, given the null results of other…
We study the collider phenomenology of the electroweak phase transition and electroweak baryogenesis in the framework of the effective field theory. Our study shows that the effective theory using the dimension-6 operators can enforce strong first order phase transition and provide sizable CP violation to realize a successful electroweak baryogenesis. Such dimension-6 operators can induce interesting Higgs phenomenology that can be verified at colliders such as the LHC and the planning CEPC. We then demonstrate that this effective theory can originate from vector-like quarks and the triplet Hi…
Extensions of the Standard Model which involve a new scale, $Λ$, may, for energies sufficiently small compared to this new scale, be expressed in terms of operators with energy dimension greater than four. The coefficients of just four SU(2)$\times$U(1)-gauge-invariant energy-dimension-six operators are sufficient to parameterize the contributions of new physics in the electroweak bosonic sector to electroweak precision measurements. In this letter we update constraints on the coefficients of these four operators due to recent precision measurements of electroweak observables. We further demon…
This is a pedagogical and self-contained review on obtaining electroweak precision constraints on TeV scale new physics using the effective theory method. We identify a set of relevant effective operators in the standard model and calculate from them corrections to all major electroweak precision observables. The corrections are compared with data to put constraints on the effective operators. Various approaches and applications in the literature are reviewed.
In a class of supersymmetric gauge theories with asymptotic freedom, the low energy effective theory below the confinement scale is described by the composite superfields of the fundamental representation fields. Based on the supersymmetric gauge theory with N_c=2 and N_f=3 with an additional unbroken Z_2 symmetry, we propose a new model where neutrino masses, dark matter, and baryon asymmetry of the Universe can be simultaneously explained by physics below the confinement scale. This is an example for the ultraviolet complete supersymmetric extension of so-called radiative seesaw scenarios wi…
We make a change of variable in the standard model Higgs field by a fermion operator and show that the latter is responsible for the electroweak vacuum. By computing the vacuum expectation value of this fermion operator in the path integral formalism we determine a relation among the quark vacuum condensates, the quark masses and the intrinsic scale of the theory. We show that the heavy quark vacuum condensates do not justify the hypothesis of dynamical electroweak symmetry breaking with only standard model fermions.
Precision Electroweak Physics of Neutral Currents Below the Z-pole
PRISMA + Cluster of Excellence, Institute for Nuclear Physics and Helmholtz-Institut Mainz, Johannes Gutenberg-University（PRISMA卓越集群、核物理研究所与亥姆霍兹美因茨研究所，约翰内斯·古腾堡大学）；Amherst Center for Fundamental Interactions and Physics Department, University of Massachusetts（阿默斯特基础相互作用中心与物理系，马萨诸塞大学）
In a previous analysis presented in hep-ph/0412166, electroweak constraints were given on arbitrary linear combinations of a set of dimension-6 operators. Flavor universality and thus U(3)^5 flavor symmetry were assumed for the operators. In this article, we expand the analysis to account for the flavor-dependent theories that distinguish the third generation of fermions from the light two generations. We still assume flavor universality for the light two generations to avoid large FCNCs. Consequently, the U(3)^5 flavor symmetry is relaxed to [U(2)xU(1)]^5, and therefore more operators are add…
We study the electroweak phase transition in three scalar extension models beyond the Standard Model. Assuming new scalars are decoupled at some heavy scale, we use the covariant derivative expansion method to derive all of the dimension-6 effective operators, whose coefficients are highly correlated in a specific model. We provide bounds to the complete set of dimension-6 operators by including the electroweak precision test and recent Higgs measurements. We find that the parameter space of strong first-order phase transitions (induced by the $|H|^6$ operator) can be probed extensively in $Zh…
We study Radiative Electroweak Symmetry Breaking in the Minimal Supersymmetric Standard Model (MSSM). We employ the 2-loop Renormalization Group equations for running masses and couplings taking into account sparticle threshold effects. The decoupling of each particle below its threshold is realized by a step function in all one-loop Renormalization Group equations (RGE). This program requires the calculation of all wavefunction, vertex and mass renormalizations for all particles involved. Adapting our numerical routines to take care of the succesive decoupling of each particle below its thres…
We derive present constraints on, and prospective sensitivity to, the electric dipole moment (EDM) of the top quark ($d_t$) implied by searches for the EDMs of the electron and nucleons. Above the electroweak scale $v$, the $d_t$ arises from two gauge invariant operators generated at a scale $Λ\gg v$ that also mix with the light fermion EDMs under renormalization group evolution at two-loop order. Bounds on the EDMs of first generation fermion systems thus imply bounds on $|d_t|$. Working in the leading log-squared approximation, we find that the present upper bound on $|d_t|$ is roughly $10^{…
We analyze the impact of the recently released CDF-II measurement of $W$ mass on the SMEFT analyses of the electroweak precision data as well as Higgs and electroweak diboson productions. We work in the Hagiwara, Ishihara, Szalapski, and Zeppenfeld basis in which eight generation-independent operators enter in the electroweak precision data at tree level and, unlike in the Warsaw basis, the analysis of that set of data constrains all the eight Wilson coefficients, without the need of combination with Higgs or electroweak diboson data results. We show that in the global analysis the determinati…
Negative searches for permanent electric dipole moments (EDMs) heavily constrain models of baryogenesis utilising various higher dimensional charge and parity violating (CPV) operators. Using effective field theory, we create a model independent connection between these EDM constraints and the baryon asymmetry of the universe (BAU) produced during a strongly first order electroweak phase transition. The thermal aspects of the high scale physics driving the phase transition are paramaterised by the usual kink solution for the bubble wall profile. We find that operators involving derivatives of …
Electroweak precision observables (EWPO) measured at the W and Z poles provide stringent limits on possible beyond the Standard Model physics scenarios. In an effective field theory (EFT) framework, the next-to-leading order QCD and electroweak results for EWPO yield indirect limits on possible 4-fermion operators that do not contribute to the observables at tree level. Here we calculate the next-to-leading corrections to EWPO induced by flavor non-universal 4-fermion interactions and find that the extracted limits on EFT coefficients have a strong dependence on the flavor structure of the 4-f…
We perform a comprehensive study of the Higgs couplings, gauge-boson couplings to fermions and triple gauge boson vertices. We work in the framework of effective theories including the effects of the dimension-six operators contributing to these observables. We determine the presently allowed range for the coefficients of these operators via a 20 parameter global fit to the electroweak precision data, as well as electroweak diboson and Higgs production data from LHC Run 1 and 2. We quantify the improvement on the determination of the 20 Wilson coefficients by the inclusion of the Run 2 results…
We study the effect of operators generating dipole couplings of the light quarks to electroweak gauge bosons on several observables at LHC. We start by demonstrating that the determination of the gauge boson self-couplings from electroweak diboson production at LHC is robust under the inclusion of those quark dipole operators even when let them totally unconstrained in the analysis. Conversely, we determine the bounds that the diboson data imposes on the light-quark dipole couplings and show that they represent a significant improvement over the limits arising from Z and W electroweak precisio…
Using the next-to-leading order low energy effective Hamiltonian for $ΔB=1$ transitions, the effects of electroweak penguin operators in some two-body decay modes of $B_s^0$ meson are estimated in the Standard Model (SM). We find that in $B_s^0\toπ^+ K^-$ and $B_s^0\to K^+K^-$ decay modes, the electroweak penguin effects are small, while in $B_s^0\toπ^0\bar{K^0}$, $ϕ\bar{K^0}$, $ϕϕ$, the electroweak penguin operators enhance or reduce the pure QCD penguin and tree level contributions by $20%\sim 80%$ in decay width. We also present the results of CP asymmetries in these $B_s^0$ deacy modes.
The standard electroweak theory admits a string solution, the Z string, in which only the electrically neutral Higgs fields are excited. This solution is unstable at zero temperature: Z strings decay by exciting charged Higgs modes. In the early Universe, however, there was a long period during which the Higgs particles were out of equilibrium but the photon field was in thermal equilibrium. We show that in this phase Z strings are stabilized by interactions of the charged Higgs modes with the photons. In a first temperature range immediately below the electroweak symmetry breaking scale, the …
The pure annihilation type decays $B^0_d\toϕγ$ and $B_s\toργ$ receive only color suppressed penguin contributions with a very small branching ratio in the standard model. When we include the previously neglected electromagnetic dipole operator, the branching ratios can be enhanced one order magnitude larger than previous study using QCD factorization approach. That is ${\cal BR}(\bar B^0_d\toϕγ)\simeq 1 \times 10^{-11}$ and ${\cal BR}(B_s\toργ) \sim (6-16)\times 10^{-10}$. The new effect can also give a large contribution, of order $10^{-9}$, to transverse polarization of $B\toϕρ$ and $B\to ωϕ…
We consider the Standard Model as an effective theory at the weak scale $v$ of a generic new strong interaction that dynamically breaks electroweak symmetry at the energy scale $Λ\sim $ (few) TeV. Assuming only the minimal field content with the Standard Model fermions and gauge bosons, but without a light Higgs particle, we construct the complete Lagrangian through next-to-leading order, that is, including terms of order $v^2/Λ^2$. The systematics behind this expansion is clarified. Although similar to chiral perturbation theory, it is not governed by the dimension of operators alone, but dep…
We develop a precise power counting rule (a generalization of Weinberg's counting method for the nonlinear sigma model) for the electroweak theories formulated by chiral Lagrangians. Then we estimate the contributions of ``all'' next-to-leading order (NLO) bosonic operators to the amplitudes of the relevant scattering processes which can be measured at high energy colliders, such as the LHC and future Linear Colliders. Based upon these results, we globally classify the sensitivities of testing all NLO bosonic operators for probing the electroweak symmetry breaking mechanism at high energy coll…
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）
Neutrino mass generation may affect the basic structure of the electroweak symmetry breaking sector. We consider a broad class of elementary particle theories where neutrinos get mass at a low mass scale. We show how these can be made natural up to few TeV or so, in the absence of supersymmetry or other possible stabilizing mechanisms. Although the standard signatures for which LHC has been optimized are absent, others are expected. A generic one among these is the possibility of an invisibly decaying Higgs boson which is characteristic of models with spontaneous breaking of lepton number symm…
We present a renormalization-group (RG) analysis of dark matter interactions with the standard model, where dark matter is allowed to be a component of an electroweak multiplet, and has a mass at or below the electroweak scale. We consider, in addition to the gauge interactions, the complete set of effective operators for dark matter interactions with the standard model above the weak scale, up to and including mass dimension six. We calculate the RG evolution of these operators from the high scale Lambda down to the weak scale, and perform the matching to the tower of effective theories below…
The existence of certain TeV suppressed higher-dimension operators may open up new decay channels for the Higgs boson to decay into lighter right-handed neutrinos. These channels may dominate over all other channels if the Higgs boson is light. For a Higgs boson mass larger than $2 m_W$ the new decays are subdominant yet still of interest. The right-handed neutrinos have macroscopic decay lengths and decay mostly into final states containing leptons and quarks. A distinguishing collider signature of this scenario is a pair of displaced vertices violating lepton number. A general operator analy…
The one loop effects of two dimension-six operators on gauge boson self energies are computed within an effective field theory framework. These self energies are translated into effects on precision electroweak observables, and bounds are obtained on the operator coefficients. The effective field theory framework allows for the divergences that arise in the loop calculations to be properly handled, and for unambiguous bounds on the coefficients to be obtained. We find that the coefficients are only weakly bounded, in contrast to previous calculations that obtained much stronger bounds. We argu…
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.
If there are no light Higgs bosons found below $\cal O$(800 GeV) or so, the interactions among longitudinally-polarized vector bosons ($\wl$) will become strong at the TeV region, and new physics that is responsible for the electroweak symmetry breaking must emerge at this energy scale. We discuss the phenomenological prospects of the Strongly-interacting Electro-Weak Sector (SEWS) at future TeV linear colliders and hadronic supercolliders.
Soft-collinear effective theory (SCET) is applied to compute electroweak radiative corrections to Higgs production via gauge boson fusion, q q -> q q H. There are several novel features which make this process an interesting application of SCET. The amplitude is proportional to the Higgs vacuum expectation value (VEV), and so is not a gauge singlet amplitude. Standard resummation methods require a gauge singlet operator and do not apply here. The SCET analysis requires operators with both collinear and soft external fields, with the Higgs VEV being described by an external soft ϕ field. There …
