Cabibbo anomaly versus electroweak precision tests: An exploration of extensions of the Standard Model
Matthew Kirk
备注：
v2: Add acknowledgements, improved discussion in Sections 2.1 and 6.1, small numerical updates to Table 3 and Figures 5 and 6, conclusions unchanged. v3: results for L1 vector corrected due to bug in code, other conclusions unchanged. v4: Journal version - discussion improvements in introduction, secs. 2 and 3, improved analysis, plots, and discussion of fermion BSM models to clarify viable models
There is a newly emerging tension between determinations of $V_{us}$ from different sources (known as the Cabibbo anomaly), which is clearly demonstrated by the new $R(V_{us})$ observable. We explore this observable from the perspective of the Standard Model Effective Field Theory and show there is a discrepancy between $R(V_{us})$ and existing electroweak precision observables (EWPO) in a simple single operator dominated scenario. We explore all possible single particle extensions of the Standard Model that can generate the Cabibbo anomaly effect and show how they cannot reconcile the current data. We further examine the future of EWPO at the ILC or FCC-ee experiments and discuss the effect on the tension of a change in specific EW observables.
The aim of the paper is to make a comparison between the unitarity condition method and the standard version of the unitarity triangle approach by using as parameters four independent moduli $|U_{ij}|$. This choice is motivated by the measurability property and leads to a simple criterion for the separation of unistochastic matrices from the double stochastic ones, whose fulfillment is the key point of any global fit for the CKM entries. In our formulation both the methods are exact, do not depend on any assumption as the smallness of some parameter and both can be used to global fits in the q…
The "Cabibbo Angle Anomaly" (CAA) originates from the disagreement between the CKM elements $V_{ud}$ and $V_{us}$ extracted from superallowed beta and kaon decays, respectively, once compared via CKM unitarity. It points towards new physics with a significance of up to $4\,σ$, depending on the theoretical input used, and can be explained through modified $W$ couplings to leptons. In this context, vector-like leptons (VLLs) are prime candidates for a corresponding UV completion since they can affect $W\ellν$ couplings at tree-level, such that this modification can have the dominant phenomenolog…
The structure of the mixing matrix, in the electroweak quark sector with four generations of quarks is investigated. We conclude that the area of the unitarity quadrangle is not a good choice as a possible measure of the CP~violation. In search of new physics we analyze how the existence of the 4-th quark family may influence on the values of the Cabibbo-Kobayashi-Maskawa matrix and we show that one can test for the existence of the 4-th generation using the Jarlskog invariants of the known quarks only. The analysis based on the measured unitary triangle exhibits some tension with the assumpti…
Two different two-loop relations between the pole- and the MS-mass of the top quark have been derived in the literature which were based on different treatments of the tadpole diagrams. In addition, the limit M_W^2/m_t^2 \to 0 was employed in one of the calculations. It is shown that, after appropriate transformations, the results of the two calculations are in perfect agreement. Furthermore we demonstrate that the inclusion of the non-vanishing mass of the W-boson leads to small modifications only.
The first row of the Cabibbo-Cobayashi-Maskawa (CKM) matrix shows a discrepancy of $\sim $$3\,σ$ with unitarity, known as the "Cabibbo Angle Anomaly" (CAA). This tension can be explained via modified $W$ couplings to leptons, but in order to consistently assess the validity of this solution, a global fit including the electroweak (EW) precision constraints and the low energy tests of lepton flavour universality (LFU) is necessary. Performing such a fit for gauge-invariant dimension-6 operators, we find that even when assuming LFU, including the CKM elements $V_{us}$ and $V_{ud}$ into the elect…
We use the two loop effective potential to study the first order electroweak phase transition in the minimial supersymmetric standard model. A global search of the parameter space is made to identify parameters compatible with electroweak baryogenesis. We improve on previous such studies by fully incorporating squark and Higgs boson mixing, by using the latest experimental constraints, and by computing the latent heat and the sphaleron rate. We find the constraints tan beta > 2.1, top squark mass < 172 GeV, and Higgs mass < 107 GeV (becoming more or less restrictive if the heavy stop has mass …
In strongly magnetized backgrounds, electrically charged vector bosons can condense. When considering the rho-meson sector of QCD, this results in the existence of a superconducting state with Abrikosov vortices. As a next order effect, also the neutral mesons condense and one expects the resulting lattice to be a mix of neutral and charged condensates, opening a possibility to the existence of a superfluid property. We will show how the detailed structure of the vacuum can be calculated and which implications it has on the nature of the exotic superconducting state.
In models of dynamical electroweak symmetry breaking which sensitively involve the third generation, such as top quark condensation, the effects of the new dynamics can show up experimentally in Z->b\bar{b}. We compare the sensitivity of Z->b\bar{b} and top quark production at the Tevatron to models of the new physics. Z->b\bar{b} is a relatively more sensitive probe to new strongly coupled U(1) gauge bosons, while it is generally less sensitive a probe to new physics involving color octet gauge bosons as is top quark production itself. Nonetheless, to accomodate a significant excess in Z->b\b…
A composite Higgs boson of 125 GeV mass, only mildly fine-tuned, requires top partners with a semi-perturbative coupling and a mass not greater than about a TeV. We analyze the strong constraints on such picture arising from flavour and electroweak precision tests in models of partial compositeness. We consider different representations for the composite fermions and compare the case of an anarchic flavour structure to models with a U(3)^3 and U(2)^3 flavour symmetry. Although non trivially, some models emerge that look capable of accommodating a 125 GeV Higgs boson with top partners in an int…
The scalar composite representations of the electroweak symmetry group of the Standard Model are exhibited in the case of two generations of quarks. The link between `strong' and `electroweak' eigenstates is investigated, showing that the quark content commonly attributed to pseudoscalar mesons needs to be modified. After doing so, the mechanism suppressing the decays K{+} into Pi{+} Pi{0} with respect to K{short} into Pi{+} Pi{-} is unraveled, without reference to any model of quark spectator or `factorization' hypothesis. The same mechanism is shown to suppress the decays K{long} into two pi…
We have calculated the fermion contributions to the shift of the position of the poles of the massive gauge boson propagators at two-loop order in the Standard Model. Together with the bosonic contributions calculated previously the full two-loop corrections are available. This allows us to investigate the full correction in the relationship between MS and pole masses of the vector bosons Z and W. Two-loop renormalization and the corresponding renormalization group equations are discussed. Analytical results for the master-integrals appearing in the massless fermion contributions are given. A …
The determinations of the Cabibbo angle from kaon, pion, $D$ and tau decays disagree with the one from super-allowed beta decays. The resulting $\approx 3\,σ$ deficit in first row (but also first column) CKM unitarity is known as the Cabibbo angle anomaly (CAA). Determining $V_{ud}$ from beta decays requires knowledge of the Fermi constant $G_F$, usually extracted from muon decay. However, because new physics might also affect muon decay, and thus the determination of the Fermi constant, an interesting interplay with the global electroweak fit arises where $G_F$ is a crucial input. In these pr…
A brief overview is presented of the standard model of electroweak interactions, including precision tests, the role of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in describing CP violation, windows on intermediate-scale physics, and the nature of the Higgs phenomenon.
We compare two methods of analyzing the finite-temperature electroweak phase transition in the minimal supersymmetric standard model: the traditional effective potential (EP) approach, and the more recently advocated procedure of dimensional reduction (DR). The latter tries to avoid the infrared instabilities of the former by matching the full theory to an effective theory that has been studied on the lattice. We point out a limitation of DR that caused a large apparent disagreement with the effective potential results in our previous work. We also incorporate wave function renormalization int…
In this proceedings we compare phenomenological predictions for differential distributions in top-quark pair production at the LHC. In particular we consider NNLO QCD fixed-order predictions and parton-level predictions based on NLO QCD multi-jet merging following the MEPS@NLO scheme. In both predictions NLO electroweak (EW) corrections are incorporated in different approximations. We focus on several transverse-momentum distributions and on the top-quark invariant mass distribution, both highly relevant for the ongoing physics program at the LHC. We discuss comparisons between the different c…
Recently, two measures of electroweak finetuning (EWFT) have been introduced for SUSY models: Δ_{EW} compares the Z mass to each separate weak scale contribution to m_Z while Δ_{HS} compares the Z mass to high scale input parameters and their consequent renormalizaton group evolution (1/Δis the % of fine tuning). While the paradigm mSUGRA/CMSSM model has been shown to be highly finetuned under both parameters (Δ_{EW}> 10^2 and Δ_{HS}> 10^3), the two-parameter non-universal Higgs model (NUHM2) in the context of radiatively-driven natural SUSY (RNS) enjoys Δ_{EW} as low as 10, while Δ_{HS} remai…
The standard model of electroweak interactions is reviewed, stressing the top quark's impact on precision tests and on determination of parameters of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Some opportunities for the study of CP violation in the decays of $b$-flavored mesons are mentioned, and the possibility of a new ``standard model'' sector involving neutrino masses is discussed.
We present a relativistic point-form approach for the calculation of electroweak form factors of few-body bound states that leads to results which resemble those obtained within the covariant light-front formalism of Carbonell et al. Our starting points are the physical processes in which such form factors are measured, i.e. electron scattering off the bound state, or the semileptonic weak decay of the bound state. These processes are treated by means of a coupled-channel framework for a Bakamjian-Thomas type mass operator. A current with the correct covariance properties is then derived from …
Is the weak scale natural? This ever pending question makes the search for new particle production a highly motivated primary goal of the next LHC phase. These searches may or may not be successful. While waiting for a needed higher energy collider to extend the direct exploration, the search for signs of new physics might be confined to indirect tests for quite some time. In a few fully calculable models, weakly or semi-strongly interacting, we compare the significance to measure the Higgs couplings versus the electroweak observables.
By considering its generalization to composite J=0 mesons proposed in a previous work [1], I show how and why a chiral extension of the Glashow-Salam-Weinberg standard model of electroweak interactions calls, there, for right-handed charged W_R's coupled with g_R = e/cos(theta_W), and the masses of which are related to the ones of the left-handed W_L's through the relation M_L^2 + M_R^2 = M_Z^2. The mesonic sector, having vanishing baryonic and leptonic number, is neutral with respect to the corresponding U(1) symmetries, making the natural chiral gauge group to be [SU(2)left x SU(2)right], bl…
We study lepton asymmetry evolution in plasma of the early Universe before the electroweak phase transition (EWPT) accounting for chirality flip processes via Higgs decays (inverse decays) entering equilibrium at temperatures below T_RL ~ 10 TeV, T_EW < T < T_RL. We solve appropriate kinetic equations for leptons and Higgs bosons taking into account the lepton number violation due to Abelian anomalies for right and left electrons and neutrinos in the self-consistent hypercharge field obeying Maxwell equations modified by the contribution of the Standard Model of electroweak interactions. The v…
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 …
We investigate theories in which the technifermions in higher dimensional representations of the technicolor gauge group dynamically break the electroweak symmetry of the standard model. For the two-index symmetric representation of the gauge group the lowest number of techniflavors needed to render the underlying gauge theory quasi conformal is two. We confront the models with the recent electroweak precision measurements and demonstrate that the two technicolor theory is a valid candidate for a dynamical breaking of the electroweak symmetry. The electroweak precision measurements provide use…
We propose a framework where a phase transition associated with a gauge symmetry breaking that occurs (not far) above the electroweak scale sets a stage for baryogenesis similar to the electroweak baryogenesis in the Standard Model. A concrete realization utilizes the breaking of $SU(2)_R \times U(1)_X \rightarrow U(1)_Y$. New chiral fermions charged under the extended gauge symmetry have nonzero lepton numbers, which makes the $B-L$ symmetry anomalous. The new lepton sector contains a large flavor-dependent CP violation, similar to the Cabibbo-Kobayashi-Maskawa phase, without inducing sizable…
We study constraints on the Minimal Supersymmetric Standard Model from electroweak experiments. We find that the light sfermions always make the fit worse than the Standard Model, while the light chargino generally make the fit slightly better through the oblique corrections. The best overall fit to the precision measurements are found when the mass of lighter chargino is about 100 GeV and the SU(2)_L doublet sfermions are all much heavier. We find the slight improvement of the fit over the SM, where the total χ^2 of the fit decreases by about one unit.
In this article we propose a simple model which can provide a combined explanation of the $Z\to b\bar b$ forward-backward asymmetry, the Cabibbo Angle Anomaly (CAA), $τ\toμνν$ and $b\to s\ell^+\ell^-$ data. This model is obtained by extending the Standard Model (SM) by two heavy vector-like quarks (an $SU(2)_L$ doublet (singlet) with hypercharge $-5/6$ (-1/3)), two new scalars (a neutral and a singly charged one) and a gauged $L_μ-L_τ$ symmetry. The mixing of the new quarks with the SM ones, after electroweak symmetry breaking, does not only explain $Z\to b\bar b$ data but also generates a lep…
This series of five lectures describes aspects of CP violation, emphasizing its description within the standard electroweak model. After discussing the kaon system, the only place in which CP violation has been seen so far, we turn to the leading contender for the effect, complex phases in the Cabibbo-Kobayashi-Maskawa (CKM) matrix. A number of suggestions are made for improved tests of the standard picture. Hadrons containing $b$ quarks play a key role in this program, and are discussed separately. We also mention a number of non-standard and speculative aspects of CP violation, including alt…
We present a mechanism that addresses the electroweak, the strong CP, and the flavor hierarchies of the Standard Model (including neutrino masses) in a unified way. The naturalness of the electroweak scale is solved together with the strong CP problem by the Nelson-Barr relaxion: the relaxion field is identified with the pseudo-Nambu-Goldstone boson of an abelian symmetry with no QCD anomaly. The Nelson-Barr sector generates the "rolling" potential and the relaxion vacuum expectation value at the stopping point is mapped to the Cabibbo-Kobayashi-Maskawa phase. An abelian symmetry accounts for …
Electroweak radiative corrections to e+e- scattering processes typically amount to O(10%) at LEP energies. Their logarithmic increase with energy renders them even more important at future colliders. Although the bulk of these corrections is due to universal process-independent effects, the remaining non-universal corrections are nevertheless phenomenologically important. We describe the structure of the universal corrections to e+e- --> WW --> 4f in detail and discuss the numerical size of universal and non-universal effects using the Monte Carlo generator RACOONWW.
We show that the Standard Model electroweak interaction of ultrarelativistic electrons with nucleons ($eN$ interaction) in a neutron star (NS) permeated by a seed large-scale helical magnetic field provides its growth up to $\gtrsim 10^{15}\thinspace\text{G}$ during a time comparable with the ages of young magnetars $\sim 10^4\thinspace\text{yr}$. The magnetic field instability originates from the parity violation in the $eN$ interaction entering the generalized Dirac equation for right and left massless electrons in an external uniform magnetic field. We calculate the averaged electric curren…
Cutoff Scales in the Type-I 2HDM with Strongly First-Order Electroweak Phase Transitions: One-Step versus Multistep
National Institute for Mathematical Sciences（韩国数学科学研究院）；Department of Physics, Konkuk University（建国大学物理系）；School of Physics, Korea Institute for Advanced Study（韩国高等研究院物理学院）
本文研究 Type-I 2HDM 中强一阶电弱相变的紫外可行性，发现一步相变中强度与截断能标存在张力，而两步相变（主要在 IS 中）可同时达到高截断能标和强相变，并锐化了对撞机搜索参数空间。
Hadronic vacuum polarization (HVP) is not only a critical part of the Standard Model (SM) prediction for the anomalous magnetic moment of the muon $(g-2)_μ$, but also a crucial ingredient for global fits to electroweak (EW) precision observables due to its contribution to the running of the fine-structure constant encoded in $Δα^{(5)}_\text{had}$. We find that with modern EW precision data, including the measurement of the Higgs mass, the global fit alone provides a competitive, independent determination of $Δα^{(5)}_\text{had}\big|_\text{EW}=270.2(3.0)\times 10^{-4}$. This value actually lies…
Results from the global Standard Model fit to electroweak precision data, including newest Tevatron measurements, are reviewed and discussed. The complete fit using also the constraints from the direct Higgs boson searches yields an upper limit on the Higgs mass of 153 GeV at 95% CL. The top mass is indirectly determined to be (177.2 +10.5 -7.8) GeV and (179.5 +8.8 -5.2) GeV for fits including or not the constraints from the direct Higgs searches, respectively. Using the 3NLO perturbative prediction of the massless QCD Adler function, the strong coupling constant at the Z-mass scale is determi…
We study sensitivity of low-energy experiments to the scale of supersymmetry breaking $\sqrt{F}$ in models with light sgoldstinos --- superpartners of goldstino. The limits on $\sqrt{F}$ may be obtained from direct and indirect measurements of sgoldstino coupling to photons, leptons, mesons and nucleons. There are three sources of constraints: ($i$) astrophysics and cosmology; ($ii$) precision laboratory experiments at low energies; ($iii$) rare decays. We discuss only processes with real sgoldstinos. For sgoldstino lighter than a few MeV and superpartner masses of the order of electroweak sca…
There are now two single measurements of precision observables that have major anomalies in the Standard Model: the recent CDF measurement of the $W$ mass shows a $7σ$ deviation and the Muon $g-2$ experiment at FNAL confirmed a long-standing anomaly, implying a $4.2 σ$ deviation. Doubts regarding new physics interpretations of these anomalies could stem from uncertainties in the common hadronic contributions. We demonstrate that these two anomalies pull the hadronic contributions in opposite directions by performing electroweak fits in which the hadronic contribution was allowed to float. The …
We quantify and examine the uncertainties in predictions of the lightest $CP$ even Higgs boson pole mass $M_h$ in the Minimal Supersymmetric Standard Model (MSSM), utilising current spectrum generators and including some three-loop corrections. There are two broadly different approximations being used: effective field theory (EFT) where an effective Standard Model (SM) is used below a supersymmetric mass scale, and a fixed order calculation, where the MSSM is matched to QCD$\times$QED at the electroweak scale. The uncertainties on the $M_h$ prediction in each approach are broken down into loga…
Exotic self-interactions among the Standard-Model neutrinos have been proposed as a potential reason behind the tension in the expansion rate, H0, of the universe inferred from different observations. We constrain this proposal using electroweak precision observables, rare meson decays, and neutrinoless double-\{beta} decay. In contrast to previous works, we emphasize the importance of carrying out this study in a framework with full Standard-Model gauge invariance. We implement this first by working with a relevant set of Standard- Model-Effective-Field-Theory operators and subsequently by co…
We perform a comprehensive SU(3)-flavor analysis of charmed mesons decaying to two pseudoscalar SU(3)-octet mesons. Taking into account SU(3)-breaking effects induced by the splitting of the quark masses, m_s != m_{u,d}, we find that existing data can be described by SU(3)-breaking of the order 30%. The requisite penguin enhancement to accomodate all data on CP violation tends to be even larger than the one extracted from Delta a_{CP}^{dir}(K^+K^-,pi^+pi^-) alone, strengthening explanations beyond the standard model. Despite the large number of matrix elements, correlations between CP asymmetr…
We study constraints on the supersymmetric standard model from the updated electroweak precision measurements --- the Z-pole experiments and the $W$-boson mass measurements. The supersymmetric-particle contributions to the universal gauge-boson-propagator corrections are parametrized by the three oblique parameters Sz, Tz and mw. The oblique corrections, the Zqq and Zll vertex corrections, and the vertex and box corrections to the μ-decay width are separately studied in detail. We first study individual contribution from the four sectors of the model, the squarks, the sleptons, the supersymmet…
The tension among measurements of $V_{us}$ from different channels, the so-called Cabibbo Angle Anomaly, can be interpreted as a signal of lepton flavor universality (LFU) violation in the $W$ boson couplings. We investigate this issue in the framework of effective field theory, keeping the gauge structure of the Standard Model (SM) unchanged. We introduce gauge-invariant dimension-6 effective operators that couple the Higgs doublet to leptons, thereby giving non-universal tree-level contributions to the couplings of electroweak gauge bosons. Due to the $SU(2)_L$ gauge symmetry, a tension aris…
Standard Model $CP$ violation associated with the phase of the Cabibbo-Kobayashi-Maskawa quark mixing matrix is known to give small answers for the EDM observables. Moreover, predictions for the EDMs of neutrons and diamagnetic atoms suffer from considerable uncertainties. We point out that the $CP$-violating observables associated with the electron spin (paramagnetic EDMs) are dominated by the combination of the electroweak penguin diagrams and $ΔI =1/2$ weak transitions in the baryon sector, and are calculable within chiral perturbation theory. The predicted size of the semileptonic operator…
We study the possible gravitational wave signal and the viability of baryogenesis arising from the electroweak phase transition in an extension of the Standard Model (SM) by a scalar singlet field without a $\mathbb{Z}_2$ symmetry. We first analyze the velocity of the expanding true-vacuum bubbles during the phase transition, confirming our previous finding in the unbroken $\mathbb{Z}_2$ symmetry scenario, where the bubble wall velocity can be computed from first principles only for weak transitions with strength parameters $α\lesssim 0.05$, and the Chapman-Jouguet velocity defines the maximum…
We study the exclusive semileptonic $B$-meson decays $B\to K(π)\ell^+\ell^-$, $B\to K(π)ν\barν$, and $B\toπτν$, computing observables in the Standard model using the recent lattice-QCD results for the underlying form factors from the Fermilab Lattice and MILC Collaborations. These processes provide theoretically clean windows into physics beyond the Standard Model because the hadronic uncertainties are now under good control for suitably binned observables. For example, the resulting partially integrated branching fractions for $B\toπμ^+μ^-$ and $B\to Kμ^+μ^-$ outside the charmonium resonance …
