Effective Field Theory Approach Research Articles

Leading logs in QCD axion effective field theory

The axion is much lighter than all other degrees of freedom introduced by the Peccei-Quinn mechanism to solve the strong CP problem. It is therefore natural to use an effective field theory (EFT) to describe its interactions. Loop processes calculated in the EFT may however explicitly depend on the ultraviolet cutoff. In general, the UV cutoff is not uniquely defined, but the dimensionful couplings suggest to identify it with the Peccei-Quinn symmetry-breaking scale. An example are K+ → π+ + a decays that will soon be tested to improved precision in NA62 and KOTO and whose amplitude is dominated by the term logarithmically dependent on the cutoff. In this paper, we critically examine the adequacy of using such a naive EFT approach to study loop processes by comparing EFT calculations with ones performed in complete QCD axion models. In DFSZ models, for example, the cutoff is found to be set by additional Higgs degrees of freedom and to therefore be much closer to the electroweak scale than to the Peccei-Quinn scale. In fact, there are non-trivial requirements on axion models where the cutoff scale of loop processes is close to the Peccei-Quinn scale, such that the naive EFT result is reproduced. This suggests that the existence of a suitable UV embedding may impose restrictions on axion EFTs. We provide an explicit construction of a model with suitable fermion couplings and find promising prospects for NA62 and IAXO.

Effective field theory approach to lepton number violating τ decays * *Supported in part by the Grants No. NSFC-12035008, No. NSFC-11975130, by The National Key Research and Development Program of China under Grant No. 2017YFA0402200, by the CAS Center for Excellence in Particle Physics (CCEPP). XDM is supported by the MOST (109-2112-M-002-017-MY3, 109-2811-M-002-535)

We continue our endeavor to investigate lepton number violating (LNV) processes at low energies in the framework of effective field theory (EFT). In this work we study the LNV tau decays , where and denote the lowest-lying charged pseudoscalars . We analyze the dominant contributions in a series of EFTs from high to low energy scales, namely the standard model EFT (SMEFT), the low-energy EFT (LEFT), and the chiral perturbation theory ( ). The decay branching ratios are expressed in terms of the Wilson coefficients of dimension-five and -seven operators in SMEFT and the hadronic low-energy constants. These Wilson coefficients involve the first and second generations of quarks and all generations of leptons; thus, they cannot be explored in low-energy processes such as nuclear neutrinoless double beta decay or LNV kaon decays. Unfortunately, the current experimental upper bounds on the branching ratios are too weak to set useful constraints on these coefficients. Alternatively, if we assume the new physics scale is larger than 1 TeV, the branching ratios are well below the current experimental bounds. We also estimate the hadronic uncertainties incurred in applying to decays by computing one-loop chiral logarithms and attempt to improve the convergence of chiral perturbation by employing dispersion relations in the short-distance part of the decay amplitudes.

Probing effective field theory approach in the CP violating minimal linear sigma model

The Minimal Linear sigma Model is a useful theoretical laboratory. One can investigate in a perturbative renormalisable model the properties of the Higgs boson as a pseudo-Goldstone boson, the phenomenological effects of the radial mode of the field texttt {s} which spontaneously breaks the global SO(5) symmetry and the validity of conclusions based on the Effective Field Theory approach with the field texttt {s} in the spectrum, after the decoupling of heavy degrees of freedom. In this paper all those issues are discussed in the framework of the Minimal Linear sigma Model with CP violating phases leading to pseudoscalar components in the effective Standard Model Yukawa couplings. Also the character of the electroweak phase transition in the presence of the field texttt {s} is investigated.

Spin effects in the effective field theory approach to Post-Minkowskian conservative dynamics

Building upon the worldline effective field theory (EFT) formalism for spinning bodies developed for the Post-Newtonian regime, we generalize the EFT approach to Post-Minkowskian (PM) dynamics to include rotational degrees of freedom in a manifestly covariant framework. We introduce a systematic procedure to compute the total change in momentum and spin in the gravitational scattering of compact objects. For the special case of spins aligned with the orbital angular momentum, we show how to construct the radial action for elliptic-like orbits using the Boundary-to-Bound correspondence. As a paradigmatic example, we solve the scattering problem to next-to-leading PM order with linear and bilinear spin effects and arbitrary initial conditions, incorporating for the first time finite-size corrections. We obtain the aligned-spin radial action from the resulting scattering data, and derive the periastron advance and binding energy for circular orbits. We also provide the (square of the) center-of-mass momentum to mathcal{O}left({G}^2right) , which may be used to reconstruct a Hamiltonian. Our results are in perfect agreement with the existent literature, while at the same time extend the knowledge of the PM dynamics of compact binaries at quadratic order in spins.

Higher-spin particles at high-energy colliders

Using an effective field theory approach for higher-spin fields, we derive the interactions of colour singlet and electrically neutral particles with a spin higher than unity, concentrating on the spin-3/2, spin-2, spin-5/2 and spin-3 cases. We compute the decay rates and production cross sections in the main channels for spin-3/2 and spin-2 states at both electron-positron and hadron colliders, and identify the most promising novel experimental signatures for discovering such particles at the LHC. The discussion is qualitatively extended to the spin-5/2 and spin-3 cases. Higher-spin particles exhibit a rich phenomenology and have signatures that often resemble the ones of supersymmetric and extra-dimensional theories. To enable further studies of higher-spin particles at collider and beyond, we collect the relevant Feynman rules and other technical details.

First experimental constraints on WIMP couplings in the effective field theory framework from CDEX

We present weakly interacting massive particles (WIMPs) search results performed using two approaches of effective field theory from the China Dark Matter Experiment (CDEX), based on the data from both CDEX-1B and CDEX-10 stages. In the nonrelativistic effective field theory approach, both time-integrated and annual modulation analyses were used to set new limits for the coupling of WIMP-nucleon effective operators at 90% confidence level (C.L.) and improve over the current bounds in the low $m_{\chi}$ region. In the chiral effective field theory approach, data from CDEX-10 were used to set an upper limit on WIMP-pion coupling at 90% C.L. We for the first time extended the limit to the $m_{\chi}<$ 6 GeV/$c^2$ region.

Nambu-Goldstone modes in non-equilibrium systems from AdS/CFT correspondence

We investigate dispersion relation of Nambu-Goldstone modes in a dissipative system realized by the AdS/CFT correspondence. We employ the D3/D7 model which represents mathcal{N} = 4 supersymmetric Yang-Mills theory coupled to mathcal{N} = 2 flavor fields. If we consider massless quarks in the presence of an external magnetic field, the system exhibits the phase transition associated with the spontaneous symmetry breaking of the chiral symmetry. We find that the Nambu-Goldstone modes show a diffusive behavior in the dispersion relation, which agrees with that found with the effective field theory approach. We also study a non-equilibrium steady state which has a constant current flow in the presence of an external electric field. In a non-equilibrium steady state, we find that the Nambu-Goldstone modes show a linear dispersion in the real part of the frequency in addition to the diffusive behavior. Moreover, we analyze the linear dispersion of the Nambu-Goldstone modes in the hydrodynamic approximation. As a result, we find that the linear dispersion can be written as the analytic functions of quantities in the dual field theory. Our results imply that such a linear dispersion is a characteristic behavior of Nambu-Goldstone modes in a non-equilibrium steady state.

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.

Accessing large global charge via the \u03f5-expansion

We compute the lowest operator dimension ∆(J; D) at large global charge J in the O(2) Wilson-Fisher model in D = 4 − ϵ dimensions, to leading order in both 1/J and ϵ. While the effective field theory approach of [1] could only determine ∆(J; 3) as a series expansion in 1/J up to an undetermined constant in front of each term, this time we try to determine the coefficient in front of J3/2 in the ϵ-expansion. The final result for ∆(J; D) in the (resummed) ϵ-expansion, valid when J ≫ 1/ϵ ≫ 1, turns out to beΔJD=2D−13D−29D−2π5DD2D−15ΓD224π21D−1ϵD−12D−1×JDD−1+OJD−2D−1\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ \\Delta \\left(J;D\\right)=\\left[\\frac{2\\left(D-1\\right)}{3\\left(D-2\\right)}{\\left(\\frac{9\\left(D-2\\right)\\pi }{5D}\\right)}^{\\frac{D}{2\\left(D-1\\right)}}{\\left[\\frac{5\\Gamma \\left(\\frac{D}{2}\\right)}{24{\\pi}^2}\\right]}^{\\frac{1}{D-1}}{\\epsilon}^{\\frac{D-1}{2\\left(D-1\\right)}}\\right]\\times {J}^{\\frac{D}{D-1}}+O\\left({J}^{\\frac{D-2}{D-1}}\\right) $$\\end{document}where next-to-leading order onwards were not computed here due to technical cumbersomeness, despite there are no fundamental difficulties. We also compare the result at ϵ = 1,ΔJ=0.293×J3/2+⋯\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ \\Delta (J)=0.293\\times {J}^{3/2}+\\cdots $$\\end{document}to the actual data from the Monte-Carlo simulation in three dimensions [2], and the discrepancy of the coefficient 0.293 from the numerics turned out to be 13%. Additionally, we also find a crossover of ∆(J; D) from ∆(J) ∝ {J}^{frac{D}{D-1}} to ∆(J) ∝ J, at around J ∼ 1/ϵ, as one decreases J while fixing ϵ (or vice versa), reflecting the fact that there are no interacting fixed-point at ϵ = 0. Based on this behaviour, we propose an interesting double-scaling limit which fixes λ ≡ Jϵ, suitable for probing the region of the crossover. I will give ∆(J; D) to next-to-leading order in perturbation theory, either in 1/λ or in λ, valid when λ ≫ 1 and λ ≪ 1, respectively.

On the development of effective field theory

Editor’s note: One of the most important developments in theoretical particle physics at the end of the 20th century and beginning of the twenty-first century has been the development of effective field theories (EFTs). Pursuing an effective field theory approach is a methodology for constructing theories, where a set of core principles is agreed upon, such as Lorentz symmetry and unitarity, and all possible interactions consistent with them are then compulsory in the theory. The utility of this approach to particle physics (and beyond) is wide ranging and undisputed, as evidenced by the recent formation of the international seminar series All Things EFT (Talks in the series can be viewed at https://www.youtube.com/channel/UC1_KF6kdJFoDEcLgpcegwCQ (accessed 21 December 2020).) which brings together each week the worldwide community of EFT practitioners. The text below is a lightly edited version of the talk given by Prof. Weinberg on September 30, 2020, which inaugurated the series. The talk reviews some of the early history of EFTs from the perspective of its pioneer and concludes with a discussion of EFT implications for future discovery.

The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: Potential contributions

We calculate the potential contributions of the motion of binary mass systems in gravity to the fifth post–Newtonian order ab initio using coupling and velocity expansions within an effective field theory approach based on Feynman amplitudes starting with harmonic coordinates and using dimensional regularization. Furthermore, the singular and logarithmic tail contributions are calculated. We also consider the non–local tail contributions. Further steps towards the complete calculation are discussed. We calculate all but the rational O(ν2) contributions to the bound state energy for circular motion and periastron advance K(Eˆ,j). Comparisons are given to results in the literature.

Effective response theory for Floquet topological systems

We present an effective field theory approach to the topological response of Floquet systems with symmetry group $G$. This is achieved by introducing a background $G$ gauge field in the Schwinger-Keldysh formalism, which is suitable for far from equilibrium systems. We carry out this program for chiral topological Floquet systems (anomalous Floquet-Anderson insulators) in two spatial dimensions, and the group cohomology models of topological Floquet unitaries. These response actions serve as many-body topological invariants for topological Floquet unitaries. The effective action approach also leads us to propose novel topological response functions.

Precision Higgs couplings in neutral naturalness models: an effective field theory approach

The Higgs sector in neutral naturalness models provides a portal to the hidden sectors, and thus measurements of Higgs couplings at current and future colliders play a central role in constraining the parameter space of the model. We investigate a class of neutral naturalness models, in which the Higgs boson is a pseudo-Goldstone boson from the universal SO(N)/SO(N − 1) coset structure. Integrating out the radial mode from the spontaneous global symmetry breaking, we obtain various dimension-six operators in the Standard Model effective field theory, and calculate the low energy Higgs effective potential with radiative corrections included. We perform a χ2 fit to the Higgs coupling precision measurements at current and future colliders and show that the new physics scale could be explored up to 2.3 (2.4) TeV without (with) the Higgs invisible decay channels at future Higgs factories. The limits are comparable to the indirect constraints obtained via electroweak precision measurements.

Efficient resummation of high post-Newtonian contributions to the binding energy

A factorisation property of Feynman diagrams in the context the Effective Field Theory approach to the compact binary problem has been recently employed to efficiently determine the static sector of the potential at fifth post-Newtonian (5PN) order. We extend this procedure to the case of non-static diagrams and we use it to fix, by means of elementary algebraic manipulations, the value of more than one thousand diagrams at 5PN order, that is a substantial fraction of the diagrams needed to fully determine the dynamics at 5PN. This procedure addresses the redundancy problem that plagues the computation of the binding energy with respect to more “efficient” observables like the scattering angle, thus making the EFT approach in harmonic gauge at least as scalable as the others methods.

Neutrino masses and mixing in models with large extra dimensions and localized fermions

Using a low-energy effective field theory approach, we study some properties of models with large extra dimensions, in which quarks and leptons have localized wave functions in the extra dimensions. We consider models with two types of gauge groups: (i) the Standard-Model gauge group, and (ii) the left-right symmetric (LRS) gauge group. Our main focus is on the lepton sector of models with $n=2$ extra dimensions, in particular, neutrino masses and mixing. We analyze the requisite conditions that the models must satisfy to be in accord with data and present a solution for lepton wave functions in the extra dimensions that fulfills these conditions. As part of our work, we also present a new solution for quark wave function centers. Issues with flavor-changing neutral current effects are assessed. Finally, we remark on baryogenesis and dark matter in these models.

Precise calibration of the one-loop bispectrum in the effective field theory of large scale structure

The large-scale structure (LSS) provides a three-dimensional cosmological probe containing significantly more information than the CMB, but its small-scale non-linearities render standard perturbation theory unreliable beyond tree-level. The authors study the bispectrum of the LSS, an important cosmological observable for non-Gaussianity, in the effective field theory approach up to 1-loop order, while taking the full $\mathrm{\ensuremath{\Lambda}}$CDM time-dependence into account, and show that this is essential for the next loop-level.

Low-energy phenomenology of scalar leptoquarks at one-loop accuracy

We perform a complete study of the low-energy phenomenology of S1 and S3 leptoquarks, aimed at addressing the observed deviations in B-meson decays and the muon magnetic dipole moment. Leptoquark contributions to observables are computed at one-loop accuracy in an effective field theory approach, using the recently published complete one-loop matching of these leptoquarks to the Standard Model effective field theory. We present several scenarios, discussing in each case the preferred parameter space and the most relevant observables.

EFT approach of inelastic dark matter for Xenon electron recoil detection

Measuring dark matter (DM) signals via electron recoil provides an important means for direct detection of light DM particles. The recent XENON1T anomaly with electron recoil energy around ER = (2–3) keV can be naturally explained by DM inelastic scattering which injects energy to the recoiled electrons and gives a narrow peak structure in the recoil spectrum. We present an effective field theory (EFT) approach to exothermic inelastic DM signals for the Xenon electron recoil detection. For relatively heavy mediator, we fairly formulate the DM-lepton interactions by effective contact operators with two DM fields (X, X′) and two leptons. Using the XENON1T data, we fit the electron recoil spectrum and constrain the allowed scalar DM mass-splitting as 2.1 keV < Δm < 3.3 keV (95% C.L.), with the best fit Δm = 2.8 keV . We analyze the relic abundance produced by such effective DM-electron contact interaction. To provide both the DM relic abundance and the XENON1T excess, we derive new constraints on the DM mass and the UV cutoff scale of DM effective interactions. Finally, we study possible UV completions for the effective DM-lepton contact interactions.

Effective field theory approach to lepto-philic self-conjugate dark matter

We study self-conjugate dark matter (DM) particles interacting primarily with Standard Model (SM) leptons in an effective field theoretical framework. We consider SM gauge-invariant effective contact interactions between Majorana fermion, real scalar and real vector DM with leptons by evaluating the Wilson coefficients appropriate for interaction terms up to dimension 8, and obtain constraints on the parameters of the theory from the observed relic density, indirect detection observations and from the DM-electron scattering cross-sections in direct detection experiments. Low energy LEP data has been used to study sensitivity in the pair production of low mass ( 80 GeV) DM particles. Pair production of DM particles of mass 50 GeV in association with mono-photons at the proposed ILC has rich potential to probe such effective operators.

Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach.

We derive the conservative dynamics of nonspinning binaries to third post-Minkowskian order, using the effective field theory (EFT) approach introduced in [G. Kälin and R. A. Porto, J. High Energy Phys. 11 (2020) 106JHEPFG1029-847910.1007/JHEP11(2020)106] together with the boundary-to-bound dictionary developed in [G. Kälin and R. A. Porto, J. High Energy Phys. 01 (2020) 072JHEPFG1029-847910.1007/JHEP01(2020)072; J. High Energy Phys. 02 (2020) 120.JHEPFG1029-847910.1007/JHEP02(2020)120]. The main ingredient is the scattering angle, which we compute to O(G^{3}) via Feynman diagrams. Adapting to the EFT framework powerful tools from the amplitudes program, we show how the associated (master) integrals are bootstrapped to all orders in velocities via differential equations. Remarkably, the boundary conditions can be reduced to the same integrals that appear in the EFT with post-Newtonian sources. For the sake of comparison, we reconstruct the Hamiltonian and the classical limit of the scattering amplitude. Our results are in perfect agreement with those in Bern etal. [Phys. Rev. Lett. 122, 201603 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.201603; J. High Energy Phys. 10 (2019) 206JHEPFG1029-847910.1007/JHEP10(2019)206].