General Effective Field Theory Research Articles

Indirect signs of the Peccei-Quinn mechanism

In the Standard Model, the renormalization of the QCD vacuum angle $\theta$ is extremely tiny, and small $\theta$ is technically natural. In the general Standard Model effective field theory (SMEFT), however, $\Delta\theta$ is quadratically divergent, reflecting the fact that new sources of hadronic CP-violation typically produce $\mathcal O(1)$ threshold corrections to $\theta$. The observation of such CP-violating interactions would therefore be in tension with solutions to the strong CP problem in which $\theta=0$ is an ultraviolet boundary condition, pointing to the Peccei-Quinn mechanism as the explanation for why $\theta$ is small in the infrared. We study the quadratic divergences in $\theta$ arising from dimension-6 SMEFT operators and discuss the discovery prospects for these operators at electric dipole moment experiments, the LHC, and future proton-proton colliders.

Limits on dark matter effective field theory parameters with CRESST-II

CRESST is a direct dark matter search experiment, aiming for an observation of nuclear recoils induced by the interaction of dark matter particles with cryogenic scintillating calcium tungstate crystals. Instead of confining ourselves to standard spin-independent and spin-dependent searches, we re-analyze data from CRESST-II using a more general effective field theory (EFT) framework. On many of the EFT coupling constants, improved exclusion limits in the low-mass region (< 3–4 GeV/c^2) are presented.

B-physics anomalies: a guide to combined explanations

Motivated by additional experimental hints of Lepton Flavour Universality violation in B decays, both in charged- and in neutral-current processes, we analyse the ingredients necessary to provide a combined description of these phenomena. By means of an Effective Field Theory (EFT) approach, based on the hypothesis of New Physics coupled predominantly to the third generation of left-handed quarks and leptons, we show how this is possible. We demonstrate, in particular, how to solve the problems posed by electroweak precision tests and direct searches with a rather natural choice of model parameters, within the context of a U(2)q ×U(2)ℓ flavour symmetry. We further exemplify the general EFT findings by means of simplified models with explicit mediators in the TeV range: coloured scalar or vector leptoquarks and colour-less vectors. Among these, the case of an SU(2)L-singlet vector leptoquark emerges as a particularly simple and successful framework.

On solar system dynamics in general relativity

Recent work in the literature has advocated using the Earth–Moon–planetoid Lagrangian points as observables, in order to test general relativity and effective field theories of gravity in the solar system. However, since the three-body problem of classical celestial mechanics is just an approximation of a much more complicated setting, where all celestial bodies in the solar system are subject to their mutual gravitational interactions, while solar radiation pressure and other sources of nongravitational perturbations also affect the dynamics, it is conceptually desirable to improve the current understanding of solar system dynamics in general relativity, as a first step towards a more accurate theoretical study of orbital motion in the weak-gravity regime. For this purpose, starting from the Einstein equations in the de Donder–Lanczos gauge, this paper arrives first at the Levi-Civita Lagrangian for the geodesic motion of planets, showing in detail under which conditions the effects of internal structure and finite extension get canceled in general relativity to first post-Newtonian order. The resulting nonlinear ordinary differential equations for the motion of planets and satellites are solved for the Earth’s orbit about the Sun, written down in detail for the Sun–Earth–Moon system, and investigated for the case of planar motion of a body immersed in the gravitational field produced by the other bodies (e.g. planets with their satellites). At this stage, we prove an exact property, according to which the fourth-order time derivative of the original system leads to a linear system of ordinary differential equations. This opens an interesting perspective on forthcoming research on planetary motions in general relativity within the solar system, although the resulting equations remain a challenge for numerical and qualitative studies. Last, the evaluation of quantum corrections to location of collinear and noncollinear Lagrangian points for the planar restricted three-body problem is revisited, and a new set of theoretical values of such corrections for the Earth–Moon–planetoid system is displayed and discussed. On the side of classical values, the general relativity corrections to Newtonian values for collinear and noncollinear Lagrangian points of the Sun–Earth–planetoid system are also obtained. A direction for future research will be the analysis of planetary motions within the relativistic celestial mechanics set up by Blanchet, Damour, Soffel and Xu.

2, 84, 30, 993, 560, 15456, 11962, 261485, . . .: higher dimension operators in the SM EFT

In a companion paper [1], we show that operator bases for general effective field theories are controlled by the conformal algebra. Equations of motion and integration by parts identities can be systematically treated by organizing operators into irreducible representations of the conformal group. In the present work, we use this result to study the standard model effective field theory (SM EFT), determining the content and number of higher dimension operators up to dimension 12, for an arbitrary number of fermion generations. We find additional operators to those that have appeared in the literature at dimension 7 (specifically in the case of more than one fermion generation) and at dimension 8. (The title sequence is the total number of independent operators in the SM EFT with one fermion generation, including hermitian conjugates, ordered in mass dimension, starting at dimension 5.)

Erratum: Earth-moon Lagrangian points as a test bed for general relativity and effective field theories of gravity [Phys. Rev. D92, 064045 (2015)

Erratum: Earth-moon Lagrangian points as a test bed for general relativity and effective field theories of gravity [Phys. Rev. D<b>92</b>, 064045 (2015)

Five-body leptonic decays of muon and tau leptons

We study the five-body decays $\mu^- \to e^- e^+ e^- \nu_{\mu} \bar{\nu}_{e}$ and $\tau^- \to \ell^- \ell'^+\ell'^-\nu_{\tau}\bar{\nu}_{\ell}$ for $\ell, \ell'=e, \mu$ within the Standard Model (SM) and in a general effective field theory description of the weak interactions at low energies. We compute the branching ratios and compare our results with two previous, mutually discrepant, SM calculations. By assuming a general structure for the weak currents we derive the expressions for the energy and angular distributions of the three charged leptons when the decaying lepton is polarized, which will be useful in precise tests of the weak charged current at Belle II. In these decays, leptonic $\mathbf{T}$-odd correlations in triple products of spin and momenta --which may signal time reversal violation in the leptonic sector-- are suppressed by the tiny neutrino masses. Therefore, a measurement of such $\mathbf{T}$-violating observables would be associated to neutrinoless lepton flavor violating (LFV) decays, where this effect is not extremely suppressed. We also study the backgrounds that the SM five-lepton lepton decays constitute to searches of LFV $L^- \to \ell^- \ell'^+\ell'^-$ decays. Searches at high values of the invariant mass of the $\ell'^+\ell'^-$ pair look the most convenient way to overcome the background.

Earth-moon Lagrangian points as a test bed for general relativity and effective field theories of gravity

In the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid, we take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L4 and L5 both in the classical regime and in the context of effective field theories of gravity. We then evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L4 and L5, the corrections of coordinates are of order a few millimeters. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. By virtue of the effective-gravity correction to the longdistance form of the potential among two point masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order two millimeters, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. Finally, general relativity corrections to Newtonian position of collinear Lagrangian points turn out to be below the millimiter, whereas on stable equilibrium points they are of order of a few millimiters.

Dark matter effective field theory scattering in direct detection experiments

We examine the consequences of the effective field theory (EFT) of dark matter-nucleon scattering for current and proposed direct detection experiments. Exclusion limits on EFT coupling constants computed using the optimum interval method are presented for SuperCDMS Soudan, CDMS II, and LUX, and the necessity of combining results from multiple experiments in order to determine dark matter parameters is discussed. We demonstrate that spectral differences between the standard dark matter model and a general EFT interaction can produce a bias when calculating exclusion limits and when developing signal models for likelihood and machine learning techniques. We also discuss the implications of the EFT for the next-generation (G2) direct detection experiments and point out regions of complementarity in the EFT parameter space.

Strong interaction effects and criticality of bosons in shaken optical lattices.

We study the quantum phase transitions and identify a tricritical point between a normal Bose superfluid, a superfluid that breaks additional Z(2) Ising symmetry, and a Mott insulator in a recent shaken optical lattice experiment. We show that near the transition between normal and Z(2) symmetry breaking superfluids, bosons can condense into a momentum state with high or even locally maximum kinetic energies due to the interaction effect. We present a general low-energy effective field theory that treats both the superfluid transition and the Ising transition in a uniform framework. Using the perturbative renormalization group method, we find that the critical behavior of the quantum phase transition belongs to a universality class different from that of a dilute Bose gas.

On the power counting in effective field theories

We discuss the systematics of power counting in general effective field theories, focusing on those that are nonrenormalizable at leading order. As an illuminating example we consider chiral perturbation theory gauged under the electromagnetic U(1) symmetry. This theory describes the low-energy interactions of the octet of pseudo-Goldstone bosons in QCD with photons and has been discussed extensively in the literature. Peculiarities of the standard approach are pointed out and it is shown how these are resolved within our scheme. The presentation follows closely our recent discussion of power counting for the electroweak chiral Lagrangian. The systematics of the latter is reviewed and shown to be consistent with the concept of chiral dimensions. The results imply that naive dimensional analysis (NDA) is incomplete in general effective field theories, while still reproducing the correct counting in special cases.

Conducting fixed points for inhomogeneous quantum wires: A conformally invariant boundary theory

Inhomogeneities and junctions in wires are natural sources of scattering, and hence resistance. A conducting fixed point usually requires an adiabatically smooth system. One notable exception is "healing", which has been predicted in systems with special symmetries, where the system is driven to the homogeneous fixed point. Here we present theoretical results for a different type of conducting fixed point which occurs in inhomogeneous wires with an abrupt jump in hopping and interaction strength. We show that it is always possible to tune the system to an unstable conducting fixed point which does not correspond to translational invariance. We analyze the temperature scaling of correlation functions at and near this fixed point and show that two distinct boundary exponents appear, which correspond to different effective Luttinger liquid parameters. Even though the system consists of two separate interacting parts, the fixed point is described by a single conformally invariant boundary theory. We present details of the general effective bosonic field theory including the mode expansion and the finite size spectrum. The results are confirmed by numerical quantum Monte Carlo simulations on spinless fermions. We predict characteristic experimental signatures of the local density of states near junctions.

Probing the nature of the Higgs-like boson via [formula omitted] decays

We give a general decomposition of the h→VF amplitude where V={W±,Z0} and F is a generic leptonic or hadronic final state, in the standard model (SM), and in the context of a general effective field theory. The differential distributions for F=ℓ+ℓ−, ℓν¯(ℓ=e,μ) are reported, and we show how such distributions can be used to determine modified Higgs couplings that cannot be directly extracted from a global fit to Higgs signal strengths. We also demonstrate how rare h→VP decays, where P is a pseudo-scalar meson, with SM rates in the 10−5 range, can be used to provide complementary information on the couplings of the newly discovered Higgs-like scalar and are an interesting probe of the vacuum structure of the theory.

Limits on Lorentz Violation from ForbiddenβDecays

Forbidden (slow) β decays offer new opportunities to test the invariance of the weak interaction under Lorentz transformations. Within a general effective field theory framework we analyze and reinterpret the only two relevant experiments, performed in the 1970s, dedicated to search for a preferred direction in space in first- and second-forbidden β decays. We show that the results of these experiments put strong and unique limits on Lorentz violation, and in particular on the presence of several interactions in the modern Lorentz-violating standard model extension. We discuss prospects to improve on these limits.

Naive dimensional analysis counting of gauge theory amplitudes and anomalous dimensions

We show that naive dimensional analysis (NDA) is equivalent to the result that L-loop scattering amplitudes have perturbative order N=L+Δ, with a shift Δ that depends on the NDA-weight of operator insertions. The NDA weight of an operator is defined in this Letter, and the general NDA formula for perturbative order N is derived. The formula is used to explain why the one-loop anomalous dimension matrix for dimension-six operators in the Standard Model effective field theory has entries with perturbative order ranging from 0 to 4. The results in this Letter are valid for an arbitrary effective field theory, and they constrain the coupling constant dependence of anomalous dimensions and scattering amplitudes in a general effective field theory.

Galileon radiation from binary systems

We calculate the power emitted in scalar modes for a binary system, including binary pulsars, with a conformal coupling to the most general Galileon effective field theory by considering perturbations around a static, spherical background. While this method is effective for calculating the power in the cubic Galileon case, here we find that if the quartic or quintic Galileon dominate, for realistic pulsar systems the classical perturbative expansion about spherically symmetric backgrounds breaks down (although the quantum effective theory is well defined). The basic reason is that the equations of motion for the fluctuations are then effectively one dimensional. This leads to many multipoles radiating with equal strength, as opposed to the normal Minkowski spacetime and cubic Galileon cases, where increasing multipoles are suppressed by increasing powers of the orbital velocity. We consider the following two cases where perturbation theory gives trustworthy results: (1) when there is a large hierarchy between the masses of two orbiting objects and (2) when we choose scales such that the quartic Galileon only begins to dominate at distances smaller than the inverse pulsar frequency. Implications for future calculations with the full Galileon that account for the Vainshtein mechanism are considered.

Flavour physics from an approximate U(2)3 symmetry

The quark sector of the Standard Model exhibits an approximate U(2)^3 flavour symmetry. This symmetry, broken in specific directions dictated by minimality, can explain the success of the Cabibbo-Kobayashi-Maskawa picture of flavour mixing and CP violation, confirmed by the data so far, while allowing for observable deviations from it, as expected in most models of ElectroWeak Symmetry Breaking. Building on previous work in the specific context of supersymmetry, we analyze the expected effects and we quantify the current bounds in a general Effective Field Theory framework. As a further relevant example we then show how the U(2)^3 symmetry and its breaking can be implemented in a generic composite Higgs model and we make a first analysis of its peculiar consequences. We also discuss how some partial extension of U(2)^3 to the lepton sector can arise, both in general and in composite Higgs models. An optimistic though conceivable interpretation of the considerations developed in this paper gives reasons to think that new physics searches in the flavour sector may be about to explore an interesting realm of phenomena.

LHC predictions from a tevatron anomaly in the top quark forward-backward asymmetry

We examine the implications of the recent CDF measurement of the top-quark forward-backward asymmetry, focusing on a scenario with a new color octet vector boson at 1-3 TeV. We study several models, as well as a general effective field theory, and determine the parameter space which provides the best simultaneous fit to the CDF asymmetry, the Tevatron top pair production cross section, and the exclusion regions from LHC dijet resonance and contact interaction searches. Flavor constraints on these models are more subtle and less severe than the literature indicates. We find a large region of allowed parameter space at high axigluon mass and a smaller region at low mass; we match the latter to an SU(3)xSU(3)/SU(3) coset model with a heavy vector-like fermion. Our scenario produces discoverable effects at the LHC with only 1-2 inverse femtobarns of luminosity at 7-8 TeV. Lastly, we point out that a Tevatron measurement of the b-quark forward-backward asymmetry would be very helpful in characterizing the physics underlying the top-quark asymmetry.

Effective theory approach to the spontaneous breakdown of Lorentz invariance

We generalize the coset construction of Callan, Coleman, Wess and Zumino to theories in which the Lorentz group is spontaneously broken down to one of its subgroups. This allows us to write down the most general low-energy effective Lagrangian in which Lorentz invariance is non-linearly realized, and to explore the consequences of broken Lorentz symmetry without having to make any assumptions about the mechanism that triggers the breaking. We carry out the construction both in flat space, in which the Lorentz group is a global spacetime symmetry, and in a generally covariant theory, in which the Lorentz group can be treated as a local internal symmetry. As an illustration of this formalism, we construct the most general effective field theory in which the rotation group remains unbroken, and show that the latter is just the Einstein-aether theory.

Perturbative Lorentz andCPTviolation for neutrino and antineutrino oscillations

The effects of perturbative Lorentz and CPT violation on neutrino oscillations are studied. Features include neutrino-antineutrino oscillations, direction dependence, and unconventional energy behavior. Leading-order corrections arising from renormalizable operators are derived in the general three-flavor effective field theory. The results are applied to neutrino-beam experiments with long baselines, which offer excellent sensitivity to the accompanying effects. Key signatures of Lorentz and CPT violation using neutrino beams include sidereal variations in the oscillation probabilities arising from the breakdown of rotational symmetry, and CPT asymmetries comparing neutrino and antineutrino modes. Attainable sensitivities to coefficients for Lorentz violation are estimated for several existing and future experiments.