Standard Model Effective Field Theory Research Articles

Moments for positivity: using Drell-Yan data to test positivity bounds and reverse-engineer new physics

Moments of the leptonic angular distribution in the Drell-Yan process have recently been shown to be sensitive probes of a specific class of dimension-8, four-fermion operators in the Standard Model Effective Field Theory, involving a pair of quarks and leptons. The same operators are also subject to positivity bounds, when requiring the associated (unknown) UV completion to obey basic principles of quantum field theory. We perform a phenomenological study to quantify the sensitivity of the high-luminosity LHC to this set of operators and, by extension, the positivity bounds. We further extend the angular basis of moments and consider double differential information to improve the ability to disentangle the different operators, leading to a sensitivity to new physics scales up to 3 TeV. We use this information to explore the violation of positivity at the LHC as a way to test the underlying principles of quantum field theory. Finally, we present a case study which combines our results with information from other (current and prospective) experiments, as well as the positivity cone to infer the properties of possible tree-level UV completions. The data lead to robust, model-independent lower bounds on the M/sqrt{g} combination of the particle mass and coupling, for states that couple to right-handed leptons and/or up quarks.

Adding Flavor to the SMEFT

We study the flavor structure of the lepton and baryon number-conserving dimension-6 operators in the Standard Model effective field theory (SMEFT). Building on the work of [1], we define several well-motivated flavor symmetries and symmetry-breaking patterns that serve as competing hypotheses about the ultraviolet (UV) dynamics beyond the SM, not far above the TeV scale. In particular, we consider four different structures in the quark sector and seven in the charged lepton sector. The set of flavor-breaking spurions is (almost) always taken to be the minimal one needed to reproduce the observed charged fermion masses and mixings. For each case, we explicitly construct and count the operators to the first few orders in the spurion expansion, providing ready-for-use setups for phenomenological studies and global fits. We provide a Mathematica package SMEFTflavor (https://github.com/aethomsen/SMEFTflavor) to facilitate similar analyses for flavor symmetries not covered in this work.

Beta-decay implications for the W -boson mass anomaly

We point out the necessity to consider $\beta$-decay observables in resolutions of the $W$-boson anomaly in the Standard Model Effective Field Theory that go beyond pure oblique corrections. We demonstrate that present global analyses that explain the $W$-boson mass anomaly predict a large, percent-level, violation of first-row CKM unitarity. We investigate what solutions to the $W$-boson mass anomaly survive after including $\beta$-decay constraints.

Probing top-quark operators with precision electroweak measurements* *Yiming Liu, Cen Zhang and Jiayin Gu are supported by National Natural Science Foundation of China (NSFC) (12035008), Yuhao Wang and Lei Zhang are supported by NSFC (12122507)

In the standard model effective field theory, operators involving the top quark are generally difficult to probe and can generate sizable loop contributions to electroweak precision observables measured by past and future lepton colliders. Could the high precision of electroweak measurements compensate for 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 performed? In this paper, we perform a detailed phenomenological study to address these two important questions. Focusing on eight dimension-6 operators that generate anomalous couplings between electroweak gauge bosons and third-generation quarks, we calculate their one loop contributions to processes, both on and off the Z-pole, and the process. A global analysis is performed with these eight operators and those that contribute to the above processes at tree level using measurements at the LEP, SLC, and several low energy experiments. We find that although current electroweak precision measurements are sensitive to the one-loop effects of top-quark operators, it is difficult to separate them from the operators that contribute at tree level, making a global analysis rather challenging. Under further assumptions (for instance, new physics contributes to only third generation quark operators and the S and T parameters), competitive reaches may be obtained in a global fit. Another important finding of our study is that the two operators that generate the dipole interactions of the bottom quark have a significant impact on the Z-pole measurements and should not be omitted. We also discuss the implications of the recently reported W-boson mass measurement at the CDF for our results. Finally, we estimate the reaches of future lepton colliders in probing top-quark operators with precision electroweak measurements.

A bridge to new physics: proposing new — and reviving old — explanations of aμ

The 4.2 σ tension in the combined measurement of the anomalous magnetic moment of the muon, aμ, and the Standard Model prediction strongly suggests the existence of beyond the Standard Model physics. Following the Standard Model Effective Field Theory approach, we study a particular topology, the bridge diagram, which gives a chirally enhanced contribution to aμ. We classify all possible 2- and 3-field SM extensions that can generate this contribution and present the full aμ result for them. Within our approach, we find that several 2-field fermion-scalar extensions which had been previously discarded in the literature — when only the Yukawa-suppressed contribution was considered — can actually be viable models to explain the observed anomaly. Furthermore, the 3-field extensions which generate the bridge diagram represent a new class of models to account for aμ. We explore a particular 3-field extension which, beyond explaining aμ, can also account for the neutral B-meson anomalies and the Cabibbo angle anomaly. We present the full one-loop matching for this model and a one-loop phenomenological study.

Distinguishing electroweak EFTs with WLWL→n×h

The electroweak symmetry-breaking sector is one of the most promising and uncharted parts of the Standard Model (SM); but it seems likely that new electroweak physics may be out of reach of the present accelerator effort and the hope is to observe small deviations from the SM. Given that, effective field theory (EFT) becomes the logic method to use, and Standard Model effective field theory (SMEFT) has become the standard. However, the most general theory with the known particle content is Higgs effective field theory (HEFT), and whether SMEFT suffices should be investigated in future experimental efforts. Building on investigations by other groups that established geometric criteria to distinguish SMEFT from HEFT (useful for theorists examining specific beyond-SM completions), we seek more phenomenological understanding and present an analogous discussion aimed at a broader audience. We discuss various aspects of (multi)Higgs boson production from longitudinal electroweak gauge bosons ${W}_{L}{W}_{L}\ensuremath{\rightarrow}n\ifmmode\times\else\texttimes\fi{}h$ in the TeV region as the necessary information to characterize the flare function, $\mathcal{F}(h)$, that determines whether SMEFT or HEFT is needed. We also present tree-level amplitudes including contact and exchange channels, as well as a short discussion on accessing $\mathcal{F}$ from the statistical limit of many bosons. We also discuss the status of the coefficients of the series expansion of $\mathcal{F}(h)$, its validity, whether its complex-$h$ extension can be used to predict or not a tell-tale zero, and how they relate to the dimension-six and -eight SMEFT operators in the electroweak sector. We derive a set of new correlations among beyond the standard model corrections to the HEFT coefficients that help decide, from experimental data, whether we have a viable SMEFT. This analysis can be useful for machines beyond the LHC that could address the challenging final state with several Higgs bosons.

Monolepton production in SMEFT to mathcal{O} (1/Λ4) and beyond

We calculate pp → ℓ+ν, ℓ− overline{nu} to mathcal{O} (1/Λ4) within the Standard Model Effective Field Theory (SMEFT) framework. In particular, we calculate the four-fermion contribution from dimension six and eight operators, which dominates at large center of mass energy. We explore the relative size of the mathcal{O} (1/Λ4) and mathcal{O} (1/Λ2) results for various kinematic regimes and assumptions about the Wilson coefficients. Results for Drell-Yan production pp → ℓ+ℓ− at mathcal{O} (1/Λ4) are also provided. Additionally, we develop the form for four fermion contact term contributions to pp → ℓ+ν, ℓ− overline{nu} , pp → ℓ+ℓ− of arbitrary mass dimension. This allows us to estimate the effects from even higher dimensional (dimension > 8) terms in the SMEFT framework.

Measuring the anomalous quartic gauge couplings in the W+W−→ W+W− process at muon collider using artificial neural networks

The muon collider provides a unique opportunity to study the vector boson scattering processes and dimension-8 operators contributing to anomalous quartic gauge couplings (aQGCs). Because of the cleaner final state, it is easier to decode subprocess and certain operator couplings at a muon collider. We attempt to identify the anomalous WWWW coupling in the exclusive WW → WW scattering in this paper. Since one aQGC can be induced by multiple dimension-8 operators, the study of one coupling can help to confine different operators. Meanwhile, singling out the WW → WW process can help to study the unitarity bounds. The vector boson scattering process corresponding to the anomalous WWWW coupling is μ+μ− → nu nu overline{nu}overline{nu } ℓ+ℓ−, with four (anti-)neutrinos in the final state, which brings troubles in phenomenological studies. In this paper, the machine learning method is used to tackle this problem. We find that, the artificial neural network is helpful to extract the W+W− → W+W− contribution, and reconstruct the center of mass energy of the subprocess which is important in the study of the Standard Model effective field theory. The sensitivities and the expected constraints on the dimension-8 operators at the muon collider with sqrt{s} = 30 TeV are presented. We demonstrate that the artificial neural networks exhibit great potential in the phenomenological study of processes with multiple neutrinos in the final state.

Role of dimension-eight operators in an EFT for the 2HDM

The Standard Model effective field theory (SMEFT) is the tool of choice for studying deviations of Higgs couplings from the Standard Model predictions. The SMEFT is an expansion in an infinite tower of higher dimension operators, which is typically truncated at dimension-six. We consider the effective theory including dimension-eight operators and examine the matching to the 2 Higgs doublet model (2HDM) that is assumed to be valid at some high scale. Both the limits from the direct production of single Higgs bosons and the indirect limits on the Higgs trilinear coupling are considered in the context of the SMEFT matched to the 2HDM, and the importance of the assumptions about the expansions in powers of the high scale are examined numerically.

SMEFT analysis of mW

We use the Fitmaker tool to incorporate the recent CDF measurement of mW in a global fit to electroweak, Higgs, and diboson data in the Standard Model Effective Field Theory (SMEFT) including dimension-6 operators at linear order. We find that including any one of the SMEFT operators mathcal{O} HWB, mathcal{O} HD, mathcal{O} ℓℓ or {mathcal{O}}_{Hell}^{(3)} with a non-zero coefficient could provide a better fit than the Standard Model, with the strongest pull for mathcal{O} HD and no tension with other electroweak precision data. We then analyse which tree-level single-field extensions of the Standard Model could generate such operator coefficients with the appropriate sign, and discuss the masses and couplings of these fields that best fit the CDF measurement and other data. In particular, the global fit favours either a singlet Z′ vector boson, a scalar electroweak triplet with zero hypercharge, or a vector electroweak triplet with unit hypercharge, followed by a singlet heavy neutral lepton, all with masses in the multi-TeV range for unit coupling.

Towards the renormalisation of the Standard Model effective field theory to dimension eight: bosonic interactions II

We calculate the renormalisation group running of the bosonic Standard Model (SM) effective operators at one loop and to order v^4/Lambda ^4, with vsim 246 GeV being the electroweak scale and Lambda the unknown new physics threshold. We focus on contributions driven by one dimension-eight term and SM couplings, thus extending (and completing) the effort initiated in Chala et al. (SciPost Phys 11:065, 2021). arXiv:2106.05291, in which quantum corrections from pairs of dimension-six interactions were considered. We highlight some interesting consequences, including the renormalisation of loop-induced interactions by tree-level generated terms and, more importantly, the validity of positivity bounds on different operators inducing anomalous gauge quartic couplings.

Large t→cZ as a sign of vectorlike quarks in light of the W mass

The rare flavor-changing top quark decay $t\ensuremath{\rightarrow}cZ$ is a clear sign of new physics and experimentally very interesting due to the huge number of top quarks produced at the LHC. However, there are few (viable) models which can generate a sizable branching ratio for $t\ensuremath{\rightarrow}cZ$---in fact vectorlike quarks seem to be the only realistic option. In this paper, we investigate all three representations (under the Standard Model gauge group) of vectorlike quarks ($U$, ${Q}_{1}$ and ${Q}_{7}$) that can generate a sizable branching ratio for $t\ensuremath{\rightarrow}cZ$ without violating bounds from $B$ physics. Importantly, these are exactly the three vectorlike quarks which can lead to a sizable positive shift in the prediction for $W$ mass, via the couplings to the top quark also needed for a sizable $\mathrm{Br}(t\ensuremath{\rightarrow}cZ)$. Calculating and using the one-loop matching of vectorlike quarks on the Standard Model effective field theory, we find that $\mathrm{Br}(t\ensuremath{\rightarrow}cZ)$ can be of the order of ${10}^{\ensuremath{-}6}$, ${10}^{\ensuremath{-}5}$ and ${10}^{\ensuremath{-}4}$ for $U$, ${Q}_{1}$ and ${Q}_{7}$, respectively, and that in all three cases the large $W$ mass measurement can be accommodated.

SMEFT predictions for gg → hh at full NLO QCD and truncation uncertainties

We present a calculation of the NLO QCD corrections for Higgs-boson pair production in gluon fusion including effects of anomalous couplings within Standard Model Effective Field Theory (SMEFT). We study effects of different truncation options of the EFT expansion in 1/Λ and of double operator insertions, both at total cross-section level as well as for the distribution of the invariant mass of the Higgs-boson pair, at sqrt{s} = 13 TeV. The NLO corrections are implemented in the generator ggHH_SMEFT in the Powheg-Box-V2 framework.

Measurements of the Higgs boson inclusive and differential fiducial cross-sections in the diphoton decay channel with pp collisions at sqrt{s} = 13 TeV with the ATLAS detector

A measurement of inclusive and differential fiducial cross-sections for the production of the Higgs boson decaying into two photons is performed using 139 fb−1 of proton-proton collision data recorded at sqrt{s} = 13 TeV by the ATLAS experiment at the Large Hadron Collider. The inclusive cross-section times branching ratio, in a fiducial region closely matching the experimental selection, is measured to be 67 ± 6 fb, which is in agreement with the state-of-the-art Standard Model prediction of 64 ± 4 fb. Extrapolating this result to the full phase space and correcting for the branching ratio, the total cross-section for Higgs boson production is estimated to be 58 ± 6 pb. In addition, the cross-sections in four fiducial regions sensitive to various Higgs boson production modes and differential cross-sections as a function of either one or two of several observables are measured. All the measurements are found to be in agreement with the Standard Model predictions. The measured transverse momentum distribution of the Higgs boson is used as an indirect probe of the Yukawa coupling of the Higgs boson to the bottom and charm quarks. In addition, five differential cross-section measurements are used to constrain anomalous Higgs boson couplings to vector bosons in the Standard Model effective field theory framework.

NLO QCD renormalization group evolution for nonleptonic ΔF=2 transitions in the SMEFT

We present for the first time Next-to-Leading (NLO) QCD renormalization group (RG) evolution matrices for nonleptonic $\mathrm{\ensuremath{\Delta}}F=2$ transitions in the Standard Model effective field theory (SMEFT). To this end we transform first the known two-loop QCD anomalous dimension matrices (ADMs) of the BSM (Beyond the SM) operators in the so-called Buras Misiak Urban basis into the ones in the common weak effective theory (WET) basis (the so-called Jenkins Manohar Stoffer basis) for which tree-level and one-loop matching to the SMEFT are already known. This subsequently allows us to find the two-loop QCD ADMs for the SMEFT nonleptonic $\mathrm{\ensuremath{\Delta}}F=2$ operators in the Warsaw basis. Having all these ingredients we investigate the impact of these NLO QCD effects on the QCD RG evolution of SMEFT Wilson coefficients for nonleptonic $\mathrm{\ensuremath{\Delta}}F=2$ transitions from the new physics scale $\mathrm{\ensuremath{\Lambda}}$ down to the electroweak scale ${\ensuremath{\mu}}_{\mathrm{ew}}$. The main benefit of these new contributions is that they allow one to remove renormalization scheme dependences present in the one-loop matchings both between the WET and SMEFT and also between SMEFT and a chosen UV completion. But the Next-to-Leading (NLO) QCD effects, calculated here in the Naive dimensional regularisation minimal subtraction scheme, turn out to be small, in the ballpark of a few percent but larger than one-loop Yukawa top effects when only the $\mathrm{\ensuremath{\Delta}}F=2$ operators are considered. The more complicated class of nonleptonic $\mathrm{\ensuremath{\Delta}}F=1$ decays will be presented soon in another publication.

Lepton flavor violation, lepton (g − 2)μ, e and electron EDM in the modular symmetry

We study the lepton flavor violation (LFV), the leptonic magnetic moments (g − 2)μ, e and the electric dipole moment (EDM) of the electron in the Standard-Model Effective Field Theory with the ΓN modular flavor symmetry. We employ the stringy Ansatz on coupling structure that 4-point couplings of matter fields are written by a product of 3-point couplings of matter fields. We take the level 3 finite modular group, Γ3 for the flavor symmetry, and discuss the dipole operators at nearby fixed point τ = i, where observed lepton masses and mixing angles are well reproduced. Suppose the anomaly of the anomalous magnetic moment of the muon to be evidence of the new physics (NP), we have related it with (g − 2)e, LFV decays, and the electron EDM. It is found that the NP contribution to (g − 2)e is proportional to the lepton masses squared likewise the naive scaling. We also discuss the correlations among the LFV processes μ → eγ, τ → μγ and τ → eγ, which are testable in the future. The electron EDM requires the tiny imaginary part of the relevant Wilson coefficient in the basis of real positive charged lepton masses, which is related to the μ → eγ transition in our framework.

B¯→D(*)ℓX¯ decays in effective field theory with massive right-handed neutrinos

We calculate the complete differential decay distributions for the $B$ meson decays, $\bar B \to D^{(*)} \ell \bar{X}$, to a massive right-handed (RH) neutrino in the low-energy effective field theory (LEFT) framework. We find that a massive RH neutrino does not introduce any new angular structures compared to the massless case, but can cause significant distortions in angular observables. We study the phenomenology of low-energy four-fermion operators permitted by the standard model effective field theory (SMEFT) extended with RH neutrinos (SMNEFT). We show that to explain the positive value of the difference in forward-backward asymmetries, $\Delta A_{\text{FB}}\equiv A_{\text{FB}}^\mu-A_{\text{FB}}^e$, tentatively inferred from Belle data, the RH neutrino must be massive. We also make predictions for $q^2$ dependent angular observables to motivate future measurements.

Violation of custodial symmetry from W -boson mass measurements

The new measurement of the $W$-boson mass from the CDF collaboration shows a significant tension with the Standard Model prediction. We quantify this discrepancy within a state-of-the-art analysis of electroweak precision data and scrutinize the leading deformations of the Standard Model Effective Field Theory arising at dimension six. We find evidence for a non-zero value of the $T$ parameter, i.e. for a novel source of violation of custodial symmetry, pointing to physics beyond the Standard Model at the 4.5$\sigma$ level. We contextualize the implications of our findings in light of other present anomalies in Particle Physics.

Light-by-light scattering at future e^+e^- colliders

We study the sensitivity of possible CLIC and FCC-ee measurements of light-by-light scattering to old and new physics, including the Heisenberg–Euler Lagrangian in the Standard Model with possible contributions from loops of additional charged particles or magnetic monopoles, the Born–Infeld extension of QED, and effective dimension-8 operators involving four electromagnetic field strengths as could appear in the Standard Model Effective Field Theory. We find that FCC-ee measurements at 365 GeV and CLIC measurements at 350 GeV would be sensitive to new physics scales of half a TeV in the dimension-8 operator coefficients, and that CLIC measurements at 1.4 TeV or 3 TeV would be sensitive to new physics scales sim 2 TeV or 5 TeV at 95% CL, corresponding to probing loops of new particles with masses up to sim 3.7 TeV for large charges and/or multiple species. Within Born–Infeld theory, the 95% CL sensitivities would range from sim 300 GeV to 1.3 or 2.8 TeV for the high-energy CLIC options. Measurements of light-by-light scattering would not exclude monopole production at FCC-hh, except in the context of Born–Infeld theory.

Measurements of μ → 3e decay with polarised muons as a probe of new physics

Working within the Standard Model effective field theory approach, we examine the possibility to test charged lepton flavour violating (cLFV) new physics (NP) by angular measurements of the outgoing electron and positrons in the polarised μ+→e+e+e− decay. This decay is planned to be studied with a sensitivity to the branching ratio of Bμ→3e∼10−15 by the Mu3e experiment at PSI. To illustrate the potential of these measurements, we consider a set of eight effective operators generating the decay at the tree level, including dimension-five dipole operators and dimension-six scalar and vector four-fermion operators of different chiralities. We show that if the polarised μ+→e+e+e− decay is observed and is induced by a single operator, data from three angular observables – two P-odd asymmetries and one T-odd asymmetry – can allow to discriminate between all considered operators with the exception of scalar and vector operators of opposite chirality. For these two types of operators, the P-odd asymmetry is maximal in magnitude; they can be distinguished, in principle, by measuring the helicities of the outgoing positrons. The observation of a non-zero T-odd asymmetry would indicate the presence in the decay rate of a dipole and vector operator interference term that is T (CP) violating.