Coefficients Of Effective Operators Research Articles

Electroweak constraints from the COHERENT experiment

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.

New physics in triboson event topologies

We present a study of the sensitivity to models of new physics of proton collisions resulting in three electroweak bosons. As a benchmark, we analyze models in which an exotic scalar field $\ensuremath{\phi}$ is produced in association with a gauge boson ($V=\ensuremath{\gamma}$ or $Z$). The scalar then decays to a pair of bosons, giving the process $pp\ensuremath{\rightarrow}\ensuremath{\phi}V\ensuremath{\rightarrow}{V}^{\ensuremath{'}}{V}^{\ensuremath{'}\ensuremath{'}}V$. We interpret our results in a set of effective field theories where the exotic scalar fields couple to the Standard Model through pairs of electroweak gauge bosons. We estimate the sensitivity of the LHC and HL-LHC datasets and find sensitivity to cross sections in the 10 fb--0.5 fb range, corresponding to scalar masses of 500 GeV to 2 TeV and effective operator coefficients up to 35 TeV.

Integrating out heavy fields in the path integral using the background-field method: general formalism

Building on an older method used to derive non-decoupling effects of a heavy Higgs boson in the Standard Model, we describe a general procedure to integrate out heavy fields in the path integral. The derivation of the corresponding effective Lagrangian including the one-loop contributions of the heavy particle(s) is particularly transparent, flexible, and algorithmic. The background-field formalism allows for a clear separation of tree-level and one-loop effects involving the heavy fields. Using expansion by regions the one-loop effects are further split into contributions from large and small momentum modes. The former are contained in Wilson coefficients of effective operators, the latter are reproduced by one-loop diagrams involving effective tree-level couplings. The method is illustrated by calculating potential non-decoupling effects of a heavy Higgs boson in a singlet Higgs extension of the Standard Model. In particular, we work in a field basis corresponding to mass eigenstates and properly take into account non-vanishing mixing between the two Higgs fields of the model. We also show that a proper choice of renormalization scheme for the non-standard sector of the underlying full theory is crucial for the construction of a consistent effective field theory.

Completing the scalar and fermionic universal one-loop effective action

We extend the known Universal One-Loop Effective Action (UOLEA) by all operators which involve scalars and fermions, not including contributions arising from open covariant derivatives. Our generic analytic expressions for the one-loop Wilson coefficients of effective operators up to dimension six allow for an application of the UOLEA to a broader class of UV-complete models. We apply our generic results to various effective theories of supersymmetric models, where different supersymmetric particles are integrated out at a high mass scale.

Radiative lepton flavor violating B , D , and K decays

We argue that radiative lepton flavor violating (RLFV) decays $P\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\ell}}_{1}{\overline{\ensuremath{\ell}}}_{2}$ of $P={B}_{q}^{0}$, ${\overline{D}}^{0}$, and ${K}^{0}$ meson states are robust probes of new physics models. In particular, they could be used to put constraints on the Wilson coefficients of effective operators describing lepton flavor-changing neutral current interactions at low energy scales. We set up a generic framework for describing these transitions and review new physics constraints from $P\ensuremath{\rightarrow}{\ensuremath{\ell}}_{1}{\overline{\ensuremath{\ell}}}_{2}$ decays. There is discussion of how RLFV transitions provide access to the operators that cannot be constrained in two-body decays and we in turn motivate further experimental searches via these channels.

Lepton flavor violating quarkonium decays

We argue that lepton flavor violating (LFV) decays $M \to \ell_1 \overline \ell_2$ of quarkonium states $M$ with different quantum numbers could be used to put constraints on the Wilson coefficients of effective operators describing LFV interactions at low energy scales. We note that restricted kinematics of the two-body quarkonium decays allows us to select operators with particular quantum numbers, significantly reducing the reliance on the single operator dominance assumption that is prevalent in constraining parameters of the effective LFV Lagrangian. We shall also argue that studies of radiative lepton flavor violating $M \to \gamma \ell_1 \overline \ell_2$ decays could provide important complementary access to those effective operators.

Effective theory of WIMP dark matter supplemented by simplified models: Singlet-like Majorana fermion case

We enumerate the set of simplified models which match onto the complete set of gauge invariant effective operators up to dimension six describing interactions of a singlet-like Majorana fermion dark matter with the standard model. Tree level matching conditions for each case are worked out in the large mediator mass limit, defining a one to one correspondence between the effective operator coefficients and the simplified model parameters for weakly interacting models. Utilizing such a mapping, we compute the dark matter annihilation rate in the early universe, as well as other low-energy observables like nuclear recoil rates using the effective operators, while the simplified models are used to compute the dark matter production rates at high energy colliders like LEP, LHC and future lepton colliders. Combining all relevant constraints with a profile likelihood analysis, we then discuss the currently allowed parameter regions and prospects for future searches in terms of the effective operator parameters, reducing the model dependence to a minimal level. In the parameter region where such a model-independent analysis is applicable, and leaving aside the special dark matter mass regions where the annihilation proceeds through an s-channel Z or Higgs boson pole, the current constraints allow effective operator suppression scales ($\Lambda$) of the order of a few hundred GeV for dark matter masses $m_\chi >$ 20 GeV at $95\%$ C.L., while the maximum allowed scale is around $3$ TeV for $m_\chi \sim \mathcal{O}(1\,{\rm TeV})$. An estimate of the future reach of ton-scale direct detection experiments and planned electron-positron colliders show that most of the remaining regions can be probed, apart from dark matter masses near half of the Z-boson mass (with $500\,{\rm GeV} < \Lambda < 2\,{\rm TeV} $) and those beyond the kinematic reach of the future lepton colliders.

Global approach to top-quark flavor-changing interactions

We adopt a fully gauge-invariant effective-field-theory approach for parametrizing top-quark flavor-changing-neutral-current interactions. It allows for a global interpretation of experimental constraints (or measurements) and the systematic treatment of higher-order quantum corrections. We discuss some recent results obtained at next-to-leading-order accuracy in QCD and perform, at that order, a first global analysis of a subset of the available experimental limits in terms of effective operator coefficients. We encourage experimental collaborations to adopt this approach and extend the analysis by using all information they have prime access to.

Interpretation of precision tests in the Higgs sector in terms of physics beyond the standard model

We demonstrate how the measurements of the Higgs-fermion and Higgs-gauge boson couplings can be interpreted in terms of physics beyond the Standard Model in a model-independent way. That is, we describe deviations from the Standard Model by effective $d=6$ operators made of Higgs fields and gauge fields, under the hypothesis that the new physics may show up in the Higgs sector only and the effective operators are generated at tree level. While the effective operator coefficients are independent in general, the completion of the theory at high energies will lead to specific correlations which will be recovered between Higgs-fermion and Higgs-gauge boson couplings. We demonstrate that the current measurement of these couplings in terms of tree-level new physics requires several new mediators with specific relationships among different couplings. New insights in the effective theory and mediator spaces can be expected for improved measurements from the inclusive $H \rightarrow \tau \tau$ and the exclusive vector boson fusion-dominated $H \rightarrow \gamma \gamma$ search channels, as well as the measurement of the Higgs self-couplings, including higher order couplings which do not exist in the Standard Model.

Effective four-fermion operators in top physics: A roadmap

We write down a minimal basis for dimension-six gauge-invariant four-fermion operators, with some operator replacements with respect to previous ones which make it simpler for calculations. Using this basis we classify all four-fermion operator contributions involving one or two top quarks. Taking into account the different fermion chiralities, possible colour contractions and independent flavour combinations, a total number of 572 gauge-invariant operators are involved. We apply this to calculate all three-body top decay widths t → d k u i d ¯ j , t → d k e i + ν j , t → u k u i u ¯ j , t → u k e j + e i − , t → u k ν ¯ j ν i (with i , j , k generation indices) mediated by dimension-six four-fermion operators, including the interference with the Standard Model amplitudes when present. All single top production cross sections in pp, p p ¯ and e + e − collisions are calculated as well, namely u i d k → d j t , d ¯ j d k → u ¯ i t , u i d ¯ j → d ¯ k t , u i u k → u j t , u i u ¯ j → u ¯ k t , e + e − → u ¯ k t and the charge conjugate processes. We also compute all top pair production cross sections, u ¯ i u j → t t ¯ , d ¯ i d j → t t ¯ , u i u j → t t and e + e − → t t ¯ . Our results are completely general, without assuming any particular relation among effective operator coefficients.

A minimal set of top anomalous couplings

We simplify the general form of the fermion–fermion–gauge boson interactions generated by dimension-six gauge-invariant effective operators by using the equations of motion to remove redundant operators. It is found that the most general vertex for off-shell fermions f i , f j and an off-shell boson V = W , Z , γ , g only involves γ μ and σ μ ν q ν terms, with q = p i − p j . Examples are given for the Wtb, Ztt, γtt and gtt interactions, whose general expression is greatly simplified with respect to previous results in the literature. The same arguments apply to top flavour-changing neutral interactions with the Z boson, the photon or the gluon, which can also be parameterised in full generality with only γ μ and σ μ ν q ν couplings. Explicit expressions are given for these vertices in terms of dimension-six gauge-invariant operators. We also discuss how effective operator coefficients might be determined from eventual measurements of anomalous couplings.

How Magnetic is the Dirac Neutrino?

We derive model-independent, "naturalness" upper bounds on the magnetic moments munu of Dirac neutrinos generated by physics above the scale of electroweak symmetry breaking. In the absence of fine-tuning of effective operator coefficients, we find that current information on neutrino mass implies that[EQUATION: SEE TEXT] bohr magnetons. This bound is several orders of magnitude stronger than those obtained from analyses of solar and reactor neutrino data and astrophysical observations.

Comments on the origin of relativistic crystal fields

A re-examination has been made of the form and the role of equivalent operators which are used to represent the effects of intersite electron-electron interactions. The approach takes into account the relativistic character of both the interaction operator and the electronic wavefunctions. The calculations are based on procedures well known in atomic physics but they are applied here in the context of molecular complexes. New terms are found, in the form of the relativistic crystal field, which originate from the Breit-Pauli operator. Sample calculations of the effective operator coefficients for some terms in the relativistic crystal field have been provided. The role of the relativistic crystal fields has been discussed and illustrated with a number of important reduced matrix elements which involve these operators.