Standard Field Theory Research Articles

One-loop matching of the type-III seesaw model onto the Standard Model Effective Field Theory

In previous works [1, 2], we have performed the one-loop matching of both type-I and type-II seesaw models for neutrino masses onto the Standard Model Effective Field Theories (SMEFT). In the present paper, by matching the type-III seesaw model onto the SMEFT at the one-loop level, we complete this series of studies on the construction of low-energy effective field theories (EFTs) for the canonical seesaw models. After integrating out the heavy fermionic triplets in the type-III seesaw model via both functional and diagrammatic approaches, we find 33 dimension-six (dim-6) operators in the Warsaw basis and their Wilson coefficients, while the number of dim-6 operators is 31 (or 41) for the EFT of type-I (or type-II) seesaw model. Furthermore, we calculate the branching ratios of radiative decays of charged leptons in the EFT. Then, the relationship between the beta function of the quartic Higgs coupling λ in the full theory and that of λEFT in the EFT is clarified. Finally, we briefly discuss the phenomenological implications of three types of seesaw EFTs and propose working observables that are sensitive to the four-fermion operators, which could be used to distinguish among different seesaw models in collider experiments.

Conformal theory of central surface density for galactic dark halos

Numerous dark matter studies of galactic halo gravitation depend on models with core radius r0 and central density ρ0. Central surface density product ρ0r0 is found to be nearly a universal constant for a large range of galaxies. Standard variational field theory with Weyl conformal symmetry postulated for gravitation and the Higgs scalar field, without dark matter, implies nonclassical centripetal acceleration ∆a, for a = aN +∆a, where Newtonian acceleration aN is due to observable baryonic matter. Neglecting a halo cutoff at very large galactic radius, conformal ∆a is constant over the entire halo and a = aN + ∆a is a universal function, consistent with a recent study of galaxies, with independently measured mass, that constrains acceleration due to dark matter or to alternative theory. An equivalent dark matter source would be a pure cusp distribution with cutoff parameter determined by a halo boundary radius. This is shown to imply universal central surface density for any dark matter core model.

The general set of Noetherian energy-momentum tensors in linearized gravity: mathematical framework

Energy-momentum tensors are foundational objects which are uniquely defined in standard physical field theories such as electrodynamics and Yang-mills theory. In general relativity, and in particular linearized gravity where symmetries required for an energy-momentum tensor derived from Noether’s first theorem are well defined, there exists a long standing non-uniqueness problem; numerous distinct energy-momentum expressions exist in the literature, and there is not consensus which, if any, is the unique expressions for the theory. Recently, the viability of the superpotential ‘improvement’ method was shown to be insufficient for addressing the non-uniqueness problem of energy-momentum tensors in linearized gravity. In the present article, the mathematical framework for the general set of Noetherian energy-momentum tensors in linearized gravity is derived using Noether’s first theorem, which consists of all possible energy-momentum tensors from the Noether current which yield the linearized Einstein field equations in the corresponding Euler-Lagrange equation of the Noether identity without introducing any ‘improvement’ terms. This result has several advantages in addition to not requiring ‘improvements’, such as the ability to impact the Lagrangian proportional piece of the energy-momentum tensor. Numerous common published gravitational energy-momentum expressions are then compared to these general results to assess which can be classified as Noetherian, and which cannot. Standard physical criteria such as symmetry and tracelessness are then used to prove that it is possible to directly obtain an energy-momentum tensor which is simultaneously symmetric and traceless from the Noether current; such an expression is derived from the general results. Consequences of these results and their relation to the aforementioned non-uniqueness problem are discussed.

Spacetime geometry of acoustics and electromagnetism

Both acoustics and electromagnetism represent measurable fields in terms of dynamical potential fields. Electromagnetic force-fields form a spacetime bivector that is represented by a dynamical energy–momentum 4-vector potential field. Acoustic pressure and velocity fields form an energy–momentum density 4-vector field that is represented by a dynamical action scalar potential field. Surprisingly, standard field theory analyses of spin angular momentum based on these traditional potential representations contradict recent experiments, which motivates a careful reassessment of both theories. We analyze extensions of both theories that use the full geometric structure of spacetime to respect essential symmetries enforced by vacuum wave propagation. The resulting extensions are geometrically complete and phase-invariant (i.e., dual-symmetric) formulations that span all five grades of spacetime, with dynamical potentials and measurable fields spanning complementary grades that are related by a spacetime vector derivative (i.e., the quantum Dirac operator). These complete representations correct the equations of motion, energy–momentum tensors, forces experienced by probes, Lagrangian densities, and allowed gauge freedoms, while making manifest the deep structural connections to relativistic quantum field theories. Finally, we discuss the implications of these corrections to experimental tests.

Abelian Constructivist Lagrangian

Constructivist lagrangian propiates a diverse approach to field theory. Introduce the set action. Consider fields families under a same symmetry group. The resulting fields set extends the standard atomist field theory to a whole field theory. An associative physics is proposed. The grouping physics. The relationship between the part and the whole is considered. A third quantum type beyond Planck granularity and quantum mechanics wave-particle is obtained. The quantum inserted in the whole. Differentiated energy packets are formed. A quantum system is constituted. The abelian grouping physics is considered. The simplest whole unity. Set action in terms of U(1) symmetry. The correspondent constructivist lagrangian is studied. A new type of individuation called whole quantum is derived.An abelian quantum system is constituted. The usual atomist gauge symmetry is preserved, but, constructivist properties are generated. Quantum system with own norm is a necessary theoretical argument. More is different, once time said P.W. Anderson. Physics is challenged to make the passage from an isolated particle to a quantum system. A theory to describe the physics of part in the whole. A challenge to be interpreted under gauge symmetry. A symmetry of difference is proposed. Quantum diversities enlarging the meanings of interaction, induction, connectivity. A quantum system is introduced. Its elementarity is identified as a third quantum type. It is called whole quantum or variety. This quantum of a many particles system appears with a new physicality. The correspondingset action derives antireductionist physical laws under gauge symmetry. Ruled by associativity, set transformation, evolution. Associativitity providing quantum under set, diversity, interdependence, nonlinearity, chance. Set transformations performing a whole determinism with directive conducted by gauge parameter and circumstances under lagrangian free coefficients. Generating a set physics with growth, evolution, emergence, complexity. An evolving quantum transforming their quantum numbers. The abelian constructivist lagrangian is explored. A quantum system assembled by fields families and gauge scalars is performed. It arises an environmental physics. Gauge scalars form substrutures with realities and potentialities. The volume of circumstances for each gauge scalar is calculated. Nonvirtual relationships are derived. Physical entities as masses, charges, coupling constants are expressed under constructivist properties. Functionalities will lead them to a physical behaviour beyond four interactions.

Generalization of Noether Theorem and action principle for non-Lagrangian theories

A non-Lagrangian field theory is a theory whose field equations cannot be derived from the action principle. The action principle is described by holonomic variational equations. These equations can be used only for standard field theories, equations of which can be represented as Euler–Lagrange equations for some Lagrangian density. In the general case, one should use non-holonomic variational equations to obtain a wider class of field equations. In this paper, it is proposed to use the Sedov non-holonomic variational equation as a generalization of action principle. Examples of application of non-holonomic variational equations to derive various field equations are suggested. The standard Noether theorem is formulated for the standard (Lagrangian) field theory with an action functional and expresses the invariance of the Lagrangian with respect to some continuous group of transformations. In this paper, a generalization of Noether’s theorem for non-Lagrangian field theories is proposed and proved by using the non-holonomic variational equation. The expression of Noether current is described in the general case of non-Lagrangian field theory. The energy–momentum tensor, orbital angular-momentum tensor and spin angular-momentum tensor are given for non-Lagrangian field theories. Examples of application of generalized first Noether’s theorem are suggested for scalar end vector fields of non-Lagrangian field theory. An important result of this paper is the proof of possibility of existence of some analogues of dissipative structures in non-Lagrangian field theories and some properties of such structures are suggested.

Is γKLS-generalized statistical field theory complete?

In this Letter we introduce some field-theoretic approach for computing the critical properties of γKLS-generalized systems undergoing continuous phase transitions, namely γKLS-statistical field theory. From this new approach emerges the new generalized O(N)γKLS universality class, which is capable of encompassing nonconventional critical exponents for real imperfect systems known as manganites not described by standard statistical field theory. We compare the generalized results with those obtained from measurements in manganites. The agreement was satisfactory, where the relative errors are <5% for the most of manganites used. Although the present approach describes the aforementioned nonconventional critical indices, we show that it is not complete. For example, it does not explain the results for some other manganites, being explained only for nonextensive statistical field theory recently introduced in literature. So, γKLS-statistical field theory has to be discarded for statistical mechanics generalization purposes.

Towards the non-perturbative cosmological bootstrap

We study quantum field theory on a de Sitter spacetime dSd+1 background. Our main tool is the Hilbert space decomposition in irreducible unitary representations of its isometry group SO(d + 1, 1). As the first application of the Hilbert space formalism, we recover the Källen-Lehmann spectral decomposition of the scalar bulk two-point function. In the process, we exhibit a relation between poles in the corresponding spectral densities and the boundary CFT data. Moreover, we derive an inversion formula for the spectral density through analytical continuation from the sphere and use it to find the spectral decompisiton for a few examples. Next, we study the conformal partial wave decomposition of the four-point functions of boundary operators. These correlation functions are very similar to the ones of standard conformal field theory, but have different positivity proper- ties that follow from unitarity in de Sitter. We conclude by proposing a non-perturbative conformal bootstrap approach to the study of these late-time four-point functions, and we illustrate our proposal with a concrete example for QFT in dS2.

Quintessence dark energy from strongly-coupled higgs mass gap: local and non-local higher-derivative non-perturbative scenarios

We entertain the possibility that dark energy arises from the Higgs field of quintessence type in the non-perturbative regimes. For this purpose we utilize a set of exact solutions of Higgs field theory recently devised, in terms of Jacobi elliptical function for a massless quartic scalar field, that satisfy a massive dispersion relation. In certain regions of the parameter space, determined by the quartic coupling value, we show that such solutions have the property to give the correct behavior for the equation of state of the dark energy depending on the initial theta value of periodicity of the Jacobi elliptical function solution. It is seen that on a time scale determined by the Hubble constant and the strength of the self-interaction of the scalar field, when conformal invariance is restored, the equation of state for the dark energy becomes manifest. Further we investigate scenarios within standard field theory framework and also extending to higher-derivative theories, namely infinite-derivative theory, motivated from p-adic string field theory, and Lee–Wick theories and in all cases, we find suitable choices of the parameter space leads to dark energy behavior of the Higgs field, which we compare.

Spacetime instability and quantum gravity as low energy effective field theory

We discuss spacetime instability for effective field theories of quantum gravity. The effective action of gravity introduces infinite higher derivative curvature terms $R^{2}, { R }_{ \mu \nu }{ R }^{ \mu \nu }, R_{\mu\nu\kappa\lambda} R^{\mu\nu\kappa\lambda}\dots$. Although these higher derivative curvature terms are indispensable to construct the self-consistent renormalizable theory of quantum gravity, they lead to several pathologies. We clearly show that even if they are written as the Planck-suppressed operators they lead to serious consequences and and de Sitter or radiation-dominated Universe is highly unstable. We show that the couplings of these higher derivative curvatures must satisfy $\left|a_{1,2,3}\right|\gtrsim 10^{118}$ to be consistent with the cosmological observations. Thus, the standard effective field theories of quantum gravity fail to describe the observed Universe unless introducing a specific technique dealing with the higher derivative curvature terms.

A chaotic lattice field theory in one dimension* *Dedicated to Fritz Haake 1941–2019 [

Motivated by Gutzwiller’s semiclassical quantization, in which unstable periodic orbits of low-dimensional deterministic dynamics serve as a WKB ‘skeleton’ for chaotic quantum mechanics, we construct the corresponding deterministic skeleton for infinite-dimensional lattice-discretized scalar field theories. In the field-theoretical formulation, there is no evolution in time, and there is no ‘Lyapunov horizon’; there is only an enumeration of lattice states that contribute to the theory’s partition sum, each a global spatiotemporal solution of system’s deterministic Euler–Lagrange equations. The reformulation aligns ‘chaos theory’ with the standard solid state, field theory, and statistical mechanics. In a spatiotemporal, crystallographer formulation, the time-periodic orbits of dynamical systems theory are replaced by periodic d-dimensional Bravais cell tilings of spacetime, each weighted by the inverse of its instability, its Hill determinant. Hyperbolic shadowing of large cells by smaller ones ensures that the predictions of the theory are dominated by the smallest Bravais cells. The form of the partition function of a given field theory is determined by the group of its spatiotemporal symmetries, that is, by the space group of its lattice discretization, best studied on its reciprocal lattice. Already one-dimensional lattice discretization is of sufficient interest to be the focus of this paper. In particular, from a spatiotemporal field theory perspective, ‘time’-reversal is a purely crystallographic notion, a reflection point group, leading to a novel, symmetry quotienting perspective of time-reversible theories and associated topological zeta functions.

Electroweak phase transition in the nearly aligned Higgs effective field theory

We investigate the strongly first-order electroweak phase transition using an effective field theoretical approach. The standard effective field theory with finite number truncation of higher dimensional operators fails in the typical parameter space where the strongly first-order phase transition is realized because it cannot describe the non-decoupling quantum effect of new physics beyond the standard model. To parameterize the non-decoupling quantum effect, we employ the nearly aligned Higgs effective theory in which the Higgs potential is parameterized by a Coleman-Weinberg like form. Extending this framework with finite temperature corrections, we study the parameter space for realizing the strongly first-order phase transition, and estimate the gravitational wave produced at the phase transition.

Constructing chiral effective field theory around unnatural leading-order interactions

A momentum-dependent formulation based on a stationary spin-0 and isospin-1 dibaryon field is proposed to improve convergence of chiral effective field theory in the ${}^{1}{S}_{0}$ channel of $NN$ scattering. Although the two-parameter leading-order interaction appears to be unnatural, it nevertheless has the necessary features of an effective field theory. A rapid order-by-order convergence is found in ${}^{1}{S}_{0}$. As an application beyond the two-body level, the triton binding energy is studied and compared to standard chiral effective field theory with partly perturbative pions. The consistency of the chiral Lagrangian for the new formulation is examined by working out the pionic radiative corrections, and consequences of nontrivial chiral-connection terms are discussed.

Time Series Path Integral Expansions for Stochastic Processes

A form of time series path integral expansion is provided that enables both analytic and numerical temporal effect calculations for a range of stochastic processes. All methods rely on finding a suitable reproducing kernel associated with an underlying representative algebra to perform the expansion. Birth–death processes can be analysed with these techniques, using either standard Doi-Peliti coherent states, or the {mathfrak {s}}{mathfrak {u}}(1,1) Lie algebra. These result in simplest expansions for processes with linear or quadratic rates, respectively. The techniques are also adapted to diffusion processes. The resulting series differ from those found in standard Dyson time series field theory techniques.

A new Higgs effective field theory and the new no-lose theorem

Non-decoupling effects of heavy new particles cannot be described by the standard effective field theory with finite truncation of higher dimensional operators. We propose a new effective field theory in which non-decoupling quantum effects of new physics are correctly described. We discuss vacuum stability and perturbative unitarity in our effective field theory, and we find that the scale of new physics can be estimated if we will observe the Higgs coupling deviation via non-decoupling effects in future collider experiments.

Standard Model EFTs via on-shell methods

We present the Standard Model Effective Field Theories (SMEFT) from purely on-shell arguments. Starting from few basics assumptions such as Poincaré invariance and locality, we classify all the renormalisable and non-renormalisable interactions at lowest order in the couplings. From these building blocks, we review how locality and unitarity enforce Lie algebra structures to appear in the S-matrix elements together with relations among couplings (and hypercharges). Furthermore, we give a fully on-shell algorithm to compute any higher-point tree-level amplitude (or form factor) in generic EFTs, bypassing BCFW-like recursion relations which are known to be problematic when non-renormalisable interactions are involved. Finally, using known amplitudes techniques we compute the mixing matrix of SMEFT marginal interactions up to mass dimension 8, to linear order in the effective interactions.

Generalized abelian gauge field theory under rotor model

Gauge field theory with rank-one field [Formula: see text] is a quantum field theory that describes the interaction of elementary spin-1 particles, of which being massless to preserve gauge symmetry. In this paper, we give a generalized, extended study of abelian gauge field theory under successive rotor model in general [Formula: see text]-dimensional flat spacetime for spin-1 particles in the context of higher-order derivatives. We establish a theorem that [Formula: see text] rotor contributes to the [Formula: see text] fields in the integration-by-parts formalism of the action. This corresponds to the transformation of gauge field [Formula: see text] and gauge field strength [Formula: see text] in the action. The [Formula: see text] case restores back to the standard abelian gauge field theory. The equation of motion and Noether’s conserved current of the theory are also studied.

The unequal-time matter power spectrum: impact on weak lensing observables

We investigate the impact of a common approximation of weak lensing power spectra: the use of single-epoch matter power spectra in integrals over redshift. We disentangle this from the closely connected Limber's approximation. We derive the unequal-time matter power spectrum at one-loop in standard perturbation theory and effective field theory to deal with non-linear physics. We compare these formalisms and conclude that the unequal-time power spectrum using effective field theory breaks for larger scales. As an alternative we introduce the midpoint approximation. We also provide, for the first time, a fitting function for the time evolution of the effective field theory counterterms based on the Quijote simulations. Then we compute the angular power spectrum using a range of approaches: the Limber approximation, and the geometric and midpoint approximations. We compare our results with the exact calculation at all angular scales using the unequal-time power spectrum. We use DES Y1 and LSST-like redshift distributions for our analysis. We find that the use of the Limber's approximation in weak lensing diverges from the exact calculation of the angular power spectrum on large-angle separations, ℓ < 10. Even though this deviation is of order 2% maximum for cosmic lensing, we find the biggest effect for galaxy clustering and galaxy-galaxy lensing. We show that not only is this true for upcoming galaxy surveys, but also for current data such as DES Y1. Finally, we make our pipeline and analysis publicly available as a Python package called unequalpy.

TwInflation

The general structure of Hybrid Inflation remains a very well-motivated mechanism for lower-scale cosmic inflation in the face of improving constraints on the tensor-to-scalar ratio. However, as originally modeled, the “waterfall” field in this mechanism gives rise to a hierarchy problem (η−problem) for the inflaton after demanding standard effective field theory (EFT) control. We modify the hybrid mechanism and incorporate a discrete “twin” symmetry, thereby yielding a viable, natural and EFT-controlled model of non-supersymmetric low-scale inflation, “Twinflation”. Analogously to Twin Higgs models, the discrete exchange-symmetry with a “twin” sector reduces quadratic sensitivity in the inflationary potential to ultra-violet physics, at the root of the hierarchy problem. The observed phase of inflation takes place on a hilltop-like potential but without fine-tuning of the initial inflaton position in field-space. We also show that all parameters of the model can take natural values, below any associated EFT-cutoff mass scales and field values, thus ensuring straightforward theoretical control. We discuss the basic phenomenological considerations and constraints, as well as possible future directions.

Anomalous dimensions from Yukawa couplings in SMNEFT: four-fermion operators

The Standard Model Neutrino Effective Field Theory (SMNEFT) is the Standard Model Effective Field Theory (SMEFT) augmented with right-handed neutrinos. Building on our previous work, arXiv:2010.12109, we calculate the Yukawa coupling contributions to the one-loop anomalous dimension matrix for the 11 dimension-six four-fermion SMNEFT operators. We also present the new contributions to the anomalous dimension matrix for the 14 four-fermion SMEFT operators that mix with the SMNEFT operators through the Yukawa couplings of the right-handed neutrinos.