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Scalar bispectrum beyond slow-roll in the unified EFT of inflation
We introduce a complete formulation of the scalar bispectrum in the unified effective field theory(EFT) of inflation, which includes the Horndeski and beyond-Horndeski Gleyzes-Langlois-Piazza-Vernizzi classes, in terms of a set of simple one-dimensional integrals. These generalized slow-rollexpressions remain valid even when slow-roll is transiently violated and encompass all configurationsof the bispectrum. We demonstrate analytically that our expressions explicitly preserve the squeezed-limitconsistency relation beyond slow-roll. As an example application of our results, we compute thescalar bispectrum in a model in which potential-driven G-inflation at early times transitions tochaotic inflation at late times, showing that our expressions accurately track the bispectrum whenslow-roll is violated and conventional slow-roll approximations fail
Analytic prediction of baryonic effects from the EFT of large scale structures
We develop a method to describe analytically the effect of star formation physics on the clustering of galaxies at long distances.
Boost breaking in the EFT of inflation
If time-translations are spontaneously broken, so are boosts. This symmetry breaking pattern can be non-linearly realized by either just the Goldstone boson of time translations, or by four Goldstone bosons associated with time translations and boosts. Here in this paper we extend the Effective Field Theory of Multifield Inflation to consider the case in which the additional Goldstone bosons associated with boosts are light and coupled to the Goldstone boson of time translations. The symmetry breaking pattern forces a coupling to curvature so that the mass of the additional Goldstone bosons is predicted to be equal to √2H in the vast majority of the parameter space where they are light. This pattern therefore offers a natural way of generating self-interacting particles with Hubble mass during inflation. After constructing the general effective Lagrangian, we study how these particles mix and interact with the curvature fluctuations, generating potentially detectable non-Gaussian signals.
Efficient exploration of cosmology dependence in the EFT of LSS
The most effective use of data from current and upcoming large scale structure (LSS) and CMB observations requires the ability to predict the clustering of LSS with very high precision. The Effective Field Theory of Large Scale Structure (EFTofLSS) provides an instrument for performing analytical computations of LSS observables with the required precision in the mildly nonlinear regime. In this paper, we develop efficient implementations of these computations that allow for an exploration of their dependence on cosmological parameters. They are based on two ideas. First, once an observable has been computed with high precision for a reference cosmology, for a new cosmology the same can be easily obtained with comparable precision just by adding the difference in that observable, evaluated with much less precision. Second, most cosmologies of interest are sufficiently close to the Planck best-fit cosmology that observables can be obtained from a Taylor expansion around the reference cosmology. These ideas are implemented for the matter power spectrum at two loops and are released as public codes. When applied to cosmologies that are within 3σ of the Planck best-fit model, the first method evaluates the power spectrum in a few minutes on a laptop, with results that have 1% or better precision, while with the Taylor expansion the same quantity is instantly generated with similar precision. Finally, the ideas and codes we present may easily be extended for other applications or higher-precision results.
EFT of large scale structures in redshift space [On the EFT of large scale structures in redshift space]
Here, we further develop the description of redshift-space distortions within the effective field theory of large scale structures. First, we generalize the counterterms to include the effect of baryonic physics and primordial non-Gaussianity. Second, we evaluate the IR resummation of the dark matter power spectrum in redshift space. This requires us to identify a controlled approximation that makes the numerical evaluation straightforward and efficient. Third, we compare the predictions of the theory at one loop with the power spectrum from numerical simulations up to ℓ = 6. We find that the IR resummation allows us to correctly reproduce the baryon acoustic oscillation peak. The k reach—or, equivalently, the precision for a given k—depends on additional counterterms that need to be matched to simulations. Since the nonlinear scale for the velocity is expected to be longer than the one for the overdensity, we consider a minimal and a nonminimal set of counterterms. The quality of our numerical data makes it hard to firmly establish the performance of the theory at high wave numbers. Within this limitation, we find that the theory at redshift z = 0.56 and up to ℓ = 2 matches the data at the percent level approximately up to k~0.13 hMpc –1 or k~0.18 hMpc –1 , depending on the number of counterterms used, with a potentially large improvement over former analytical techniques.
Nonperturbative NN scattering in {sup 3}S{sub 1}–{sup 3}D{sub 1} channels of EFT(⁄π)
The closed-form T matrices in the {sup 3}S{sub 1}–{sup 3}D{sub 1} channels of EFT(⁄π) for NN scattering with the potentials truncated at order O(Q{sup 4}) are presented with the nonperturbative divergences parametrized in a general manner. The stringent constraints imposed by the closed form of the T matrices are exploited in the underlying theory perspective and turned into virtues in the implementation of subtractions and the manifestation of power counting rules in nonperturbative regimes, leading us to the concept of EFT scenario. A number of scenarios of the EFT description of NN scattering are compared with PSA data in terms of effective range expansion and {sup 3}S{sub 1} phase shifts, showing that it is favorable to proceed in a scenario with conventional EFT couplings and sophisticated renormalization in order to have large NN scattering lengths. The informative utilities of fine tuning are demonstrated in several examples and naturally interpreted in the underlying theory perspective. In addition, some of the approaches adopted in the recent literature are also addressed in the light of EFT scenario. -- Highlights: •Closed-form unitary T matrices for NN scattering are obtained in EFT(⁄π). •Nonperturbative properties inherent in such closed-form T matrices are explored. •Nonperturbative renormalization is implemented through exploiting these properties. •Unconventional power counting of couplings is shown to be less favored by PSA data. •The ideas about nonperturbative renormalization here might have wider applications.
Most general EFTs from spurion analysis Hilbert series and minimal lepton flavor violation
We derive a saturation theorem for general Effective Field Theories (EFTs) constructed using spurion analysis. Let S be a set of spurion fields introduced to organize the breaking of a global symmetry G f , and H S be the subgroup of G f that remains unbroken under a generic vacuum expectation value ⟨S⟩; we show that the EFT Lagrangian constructed from the spurion analysis saturates the EFT Lagrangian without the spurions but restricted to H S invariance, provided that arbitrary powers of the spurion fields are allowed. As examples, we study several implementations of the Minimal Lepton Flavor Violation (MLFV) principle, corresponding to various origins of the neutrino masses. In each scenario, we compute the Hilbert series to obtain the numbers of independent lepton flavor covariants that appear in the corresponding EFT at mass dimension 6. These numbers agree with the number of H S invariants in the EFT without the spurions, demonstrating the saturation theorem.
On the EFT validity for Drell–Yan tails at the LHC
Abstract In this article, we examine the validity range of the Effective Field Theory (EFT) description of high-energy Drell–Yan processes at the LHC. To this purpose, we consider explicit mediators that contribute to these processes in the s - and t -channels, comparing their effects in Drell–Yan distributions with the ones obtained by matching onto the corresponding EFT. We determine the conditions for the EFT results to accurately describe these scenarios. In particular, we explore the impact of including dimension-eight $$(d=8)$$ ( d = 8 ) operators in the faster convergence of the EFT series, at the analytical and numerical level, considering contributions to the cross section up to the square of $$d=8$$ d = 8 EFT operator insertions. Moreover, we discuss the possible implications of clipping LHC data and illustrate results for a specific New-Physics scenario motivated by low-energy flavor data.
Renormalization group improvement of the effective potential: an EFT approach
We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in powers of the mass ratio, as well as to sum large logarithms of mass ratios using renormalization group evolution. The effective potential is the sum of one-particle irreducible diagrams (1PI) but information about which diagrams are 1PI is lost after matching to the EFT, since heavy lines get shrunk to a point. We therefore introduce a tadpole condition in place of the 1PI condition, and use the renormalization group improved value of the tadpole in computing the effective potential. We explain why the effective potential computed using an EFT is not the same as the effective potential of the EFT. We illustrate our method using the O(N) model, a theory of two scalars in the unbroken and broken phases, and the Higgs-Yukawa model. Our leading-log result, obtained by integrating the one-loop β-functions, correctly reproduces the log-squared term in explicit two-loop calculations. Our method does not have a Goldstone boson infrared divergence problem.
The EFT-hedron
We re-examine the constraints imposed by causality and unitarity on the low-energy effective field theory expansion of four-particle scattering amplitudes, exposing a hidden “totally positive” structure strikingly similar to the positive geometries associated with grassmannians and amplituhedra. This forces the infinite tower of higher-dimension operators to lie inside a new geometry we call the “EFT-hedron”. We initiate a systematic investigation of the boundary structure of the EFT-hedron, giving infinitely many linear and non-linear inequalities that must be satisfied by the EFT expansion in any theory. We illustrate the EFT-hedron geometry and constraints in a wide variety of examples, including new consistency conditions on the scattering amplitudes of photons and gravitons in the real world.
Dilaton EFT framework for lattice data
We develop an effective-field-theory (EFT) framework to analyze the spectra emerging from lattice simulations of a large class of confining gauge theories. Simulations of these theories, for which the light-fermion count is not far below the critical value for transition to infrared conformal behavior, have indicated the presence of a remarkably light singlet scalar particle. We incorporate this particle by including a scalar field in the EFT along with the Nambu-Goldstone bosons (NGB’s), and discuss the application of this EFT to lattice data. We highlight the feature that data on the NGB’s alone can tightly restrict the form of the scalar interactions. As an example, we apply the framework to lattice data for an SU(3) gauge theory with eight fermion flavors, concluding that the EFT can describe the data well.
Unitarity violation and the geometry of Higgs EFTs
We derive the scale of unitarity violation from the geometry of Effective Field Theory (EFT) extensions of the Standard Model Higgs sector. The high-energy behavior of amplitudes with more than four scalar legs depends on derivatives of geometric invariants with respect to the physical Higgs field h, such that higher-point amplitudes begin to reconstruct the scalar manifold away from our vacuum. In theories whose low-energy limit can be described by the Higgs EFT (HEFT) but not the Standard Model EFT (SMEFT), non-analyticities in the vicinity of our vacuum limit the radius of convergence of geometric invariants, leading to unitarity violation at energies below 4πv. Our results unify approaches to the HEFT/SMEFT dichotomy based on unitarity, analyticity, and geometry, and more broadly illustrate the sense in which observables probe the geometry of an EFT. Along the way, we provide novel basis-independent results for Goldstone/Higgs boson scattering amplitudes expressed in terms of geometric covariant quantities.
Search for New Physics via EFT in collisions containing a top quark and a boosted Z or Higgs boson
We present a generator-level sensitivity study of physics beyond the Standard Model within the framework of Effective Field Theory (EFT). The targeted signal processes are single top quark production in association with a Lorentz-boosted Higgs or Z boson (tHq and tZq) in proton-proton collisions at a center-of-mass energy of 13.6 TeV. Event selection requires one electron or muon, a high-transverse-momentum, large-radius (AK8) jet reconstructing hadronic H → b̄b or Z → b̄b decays, at least two distinct, non-overlapping small-radius (AK4) jets with one originating from a b quark, and a missing transverse energy greater than 30 GeV. Signal and background samples are generated via Monte Carlo simulation using MadGraph with MadJax to perform EFT matrix-element calculations. Deviations from the Standard Model are parametrized through dimension-six EFT operators that probe modified top quark interactions. This generator-level study identifies kinematic observables with enhanced sensitivity to EFT operators and motivates future reconstruction-level analyses of tHq and tZq channels.
Search for New Physics via EFT in collisions containing a top quark and a boosted Z or Higgs boson
We present a generator-level sensitivity study of physics beyond the Standard Model within the framework of Effective Field Theory (EFT). The targeted signal processes are single top quark production in association with a Lorentz-boosted Higgs or Z boson (tHq and tZq) in proton-proton collisions at a center-of-mass energy of 13.6 TeV. Event selection requires one electron or muon, a high-transverse-momentum, large-radius (AK8) jet reconstructing hadronic H → b̄b or Z → b̄b decays, at least two distinct, non-overlapping small-radius (AK4) jets with one originating from a b quark, and a missing transverse energy greater than 30 GeV. Signal and background samples are generated via Monte Carlo simulation using MadGraph with MadJax to perform EFT matrix-element calculations. Deviations from the Standard Model are parametrized through dimension-six EFT operators that probe modified top quark interactions. This generator-level study identifies kinematic observables with enhanced sensitivity to EFT operators and motivates future reconstruction-level analyses of tHq and tZq channels.
EFT validity issues in Vector Boson Scattering processes
Vector Boson Scattering (VBS) processes are regarded as the best lab to study the $VVVV$ quartic couplings, where $V = W, Z$. Such studies are carried in the framework of Effective Field Theories (EFT), but the EFT formalism is often not used in a fully consistent way. We discuss the limitations of the EFT approach to describe New Physics effects in VBS data. We argue that the "clipping" technique is the most theory-motivated way to do data analysis in the EFT language and discuss first results from an analysis of CMS Run 2 data on the $WZ$ and same-sign $WW$ process, with and without "clipping" implemented.
Loops and trees in generic EFTs
We consider aspects of tree and one-loop behavior in a generic 4d EFT of massless scalars, fermions, and vectors, with a particular eye to the high-energy limit of the Standard Model EFT at operator dimensions 6 and 8. First, we classify the possible Lorentz structures of operators and the subset of these that can arise at tree-level in a weakly coupled UV completion, extending the tree/loop classification through dimension 8 using functional methods. Second, we investigate how operators contribute to tree and one-loop helicity amplitudes, exploring the impact of non-renormalization theorems through dimension 8. We further observe that many dimension 6 contributions to helicity amplitudes, including rational parts, vanish exactly at one-loop level. This suggests the impact of helicity selection rules extends beyond one loop in non-supersymmetric EFTs.
Validity of standard model EFT studies of V H and V V production at NLO
The production of $W^±H, ZH, W^+W^-$, and $W^±Z$ pairs probes non-Standard-Model interactions of quarks, gauge bosons, and the Higgs boson. New effects can be parameterized in terms of an effective field theory (EFT) where the Lagrangian is expanded in terms of higher-dimension operators suppressed by increasing powers of a high scale Λ. We examine the importance of including next-to-leading-order QCD corrections in global fits to the coefficients of the EFT. The numerical implications on the fits due to different approaches to enforcing the validity of the EFT are quantified. We pay particular attention to the dependence of the fits on the ex-pansion in 1/Λ 2 since the differences between results calculated at $\mathcal{O}$(1/Λ 2 ) and $\mathcal{O}$(1/Λ 4 ) may give insight into the possible significance of dimension-8 effects.