Renormalizable Theory Research Articles

Gauge and infrared properties of hadronic structure of nucleon in neutron beta decay to order O(α/π) in standard V − A effective theory with QED and linear sigma model of strong low-energy interactions

Within the standard [Formula: see text] theory of weak interactions, Quantum Electrodynamics (QED) and the linear [Formula: see text]-model [Formula: see text] of strong low-energy hadronic interactions we analyze gauge and infrared properties of hadronic structure of the neutron and proton in the neutron [Formula: see text]-decay to leading order in the large nucleon mass expansion. We show that the complete set of Feynman diagrams describing radiative corrections of order [Formula: see text], induced by hadronic structure of the nucleon, to the rate of the neutron [Formula: see text]-decay is gauge noninvariant and unrenormalizable. We show that a gauge noninvariant contribution does not depend on the electron energy in agreement with Sirlin’s analysis of contributions of strong low-energy interactions (Phys. Rev. 164, 1767 (1967)). We show that infrared divergent and dependent on the electron energy contributions from the neutron radiative [Formula: see text]-decay and neutron [Formula: see text]-decay, caused by hadronic structure of the nucleon, are canceled in the neutron lifetime. Nevertheless, we find that divergent contributions of virtual photon exchanges to the neutron lifetime, induced by hadronic structure of the nucleon, are unrenormalizable even formally. Such an unrenormalizability can be explained by the fact that the effective [Formula: see text] vertex of hadron–lepton current–current interactions is not a vertex of the combined quantum field theory including QED and [Formula: see text], which are renormalizable theories. We assert that for a consistent gauge invariant and renormalizable analysis of contributions of hadronic structure of the nucleon to the radiative corrections of any order to the neutron decays one has to use a gauge invariant and fully renormalizable quantum field theory including the Standard Electroweak Model (SEM) and the [Formula: see text], where the effective [Formula: see text] vertex of hadron–lepton current–current interactions is caused by the [Formula: see text]-electroweak-boson exchange.

Causality and Renormalization in Finite-Time-Path Out-of-Equilibrium ϕ3 QFT

Our aim is to contribute to quantum field theory (QFT) formalisms useful for descriptions of short time phenomena, dominant especially in heavy ion collisions. We formulate out-of-equilibrium QFT within the finite-time-path formalism (FTP) and renormalization theory (RT). The potential conflict of FTP and RT is investigated in g ϕ 3 QFT, by using the retarded/advanced ( R / A ) basis of Green functions and dimensional renormalization (DR). For example, vertices immediately after (in time) divergent self-energy loops do not conserve energy, as integrals diverge. We “repair” them, while keeping d < 4 , to obtain energy conservation at those vertices. Already in the S-matrix theory, the renormalized, finite part of Feynman self-energy Σ F ( p 0 ) does not vanish when | p 0 | → ∞ and cannot be split to retarded and advanced parts. In the Glaser–Epstein approach, the causality is repaired in the composite object G F ( p 0 ) Σ F ( p 0 ) . In the FTP approach, after repairing the vertices, the corresponding composite objects are G R ( p 0 ) Σ R ( p 0 ) and Σ A ( p 0 ) G A ( p 0 ) . In the limit d → 4 , one obtains causal QFT. The tadpole contribution splits into diverging and finite parts. The diverging, constant component is eliminated by the renormalization condition ⟨ 0 | ϕ | 0 ⟩ = 0 of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit t → ∞ .

One-loop structure of the photon propagator in the standard model extension

We study radiative corrections on the photon propagator from the electroweak sector of the minimal Lorentz- and $CPT$-violating Standard Model Extension. We derive the most general Lorentz-violating ghost sector from BRST symmetry and renormalization theory. We introduce a Lorentz-violating nonlinear gauge that simplifies both the Higgs and gauge-sector extensions, which can be helpful in radiative corrections. At one loop, these sectors contribute to the $CPT$-even part of the photon propagator, characterized by the Riemann-type tensor $(k_F)_{\alpha\beta\mu\nu}$. We give exact results for the contributions to the SO(1,3) irreducible parts of $(k_F)_{\alpha \beta \mu \nu}$, namely, the Weyl-type tensor $(\hat{k}_F)_{\alpha \beta \mu \nu}$, the Ricci-type tensor $(k_F)_{\alpha \beta}$, and the curvature-type scalar $k_F$. In the Yukawa sector, one-loop contributions are ultraviolet finite, but most of them are unobservable due to finite renormalization. The only observable effect is a contribution proportional to $(k_F)_{\alpha \beta}$ that emerges via a dimension-6 term that is observer and gauge invariant. In the Higgs and gauge sectors, all the irreducible parts of the corresponding Riemann-type tensors receive divergent contributions, so they are observable. The only finite contribution corresponds to the dimension-6 term. We think of these contributions as radiative corrections to the renormalized tensors and assume that both effects are of the same order of magnitude to find bounds from vacuum birefringence and compare with the literature. Bounds on $(k_F)_{\alpha \beta}$ contributions, innocuous to birefringence, are also derived using limits on the renormalized tensor from Laser-Interferometer-Gravitational-Wave-Observatory data. We compare these bounds with the literature. Beta functions associated with $(\hat{k}_F)_{\alpha \beta \mu \nu}$ and $(k_F)_{\alpha \beta}$ are derived.

Grüneisen parameter and thermal expansion near magnetic quantum critical points in itinerant electron systems

Complete expressions of the thermal-expansion coefficient $\alpha$ and the Gr\"{u}neisen parameter $\Gamma$ are derived on the basis of the self-consistent renormalization (SCR) theory. By considering zero-point as well as thermal spin fluctuation under the stationary condition, the specific heat for each class of the magnetic quantum critical point (QCP) specified by the dynamical exponent $z=3$ (FM) and $z=2$ (AFM) and the spatial dimension ($d=3$ and $2$) is shown to be expressed as $C_{V}=C_a-C_b$, where $C_a$ is dominant at low temperatures, reproducing the past SCR criticality endorsed by the renormalization group theory. Starting from the explicit form of the entropy and using the Maxwell relation, $\alpha=\alpha_a+\alpha_b$ (with $\alpha_a$ and $\alpha_b$ being related to $C_a$ and $C_b$, respectively) is derived, which is proven to be equivalent to $\alpha$ derived from the free energy. The temperature-dependent coefficient found to exist in $\alpha_b$, which is dominant at low temperatures, contributes to the crossover from the quantum-critical regime to the Curie-Weiss regime and even affects the quantum criticality at 2d AFM QCP. Based on these correctly calculated $C_{V}$ and $\alpha$, Gr\"{u}neisen parameter $\Gamma=\Gamma_a+\Gamma_b$ is derived, where $\Gamma_a$ and $\Gamma_b$ contain $\alpha_a$ and $\alpha_b$, respectively. The inverse susceptibility coupled to the volume $V$ in $\Gamma_b$ gives rise to divergence of $\Gamma$ at the QCP for each class even though characteristic energy scale of spin fluctuation $T_0$ is finite at the QCP, which gives a finite contribution in $\Gamma_a=-\frac{V}{T_0}\left(\frac{\partial T_0}{\partial V}\right)_{T=0}$. General properties of $\alpha$ and $\Gamma$ including their signs as well as the relation to $T_0$ and the Kondo temperature in temperature-pressure phase diagrams of Ce- and Yb-based heavy electron systems are discussed.

Z -boson polarization as a model-discrimination analyzer

Determining the spin of any new particle is critical in identifying the true theory among various extensions of the Standard Model (SM). The degree of $Z$-boson polarization in any two-body decay process $A\to B Z$ is sensitive to the spin assignments of two new particles $A$ and $B$. Considering all possible spin-0, 1/2 and 1 combinations in a renormalizable field theory, we demonstrate that $Z$-boson polarization can indeed play a role of a decisive and universal analyzer in distinguishing the different spin assignments.

Complete Lorentz-to-Galileo dictionary for direct dark matter detection

We determine the most general non-relativistic theory of DM-nucleon scattering complying with the sole requirement of Lorentz invariance, for spin-0 and spin-1/2 DM. To do so, we first classify a comprehensive list of amplitude terms encompassing the most general Lorentz-covariant 2-to-2 DM-nucleon scattering amplitude. We then match each term to a Galilean-invariant operator at leading-order in the non-relativistic expansion, for both elastic and inelastic (endothermic and exothermic) scattering. Our complete Lorentz-to-Galileo mapping can be used to promptly determine the non-relativistic DM-nucleon interaction and the associated nuclear form factor for any given Lorentz-invariant DM model. It applies to both renormalizable and non-renormalizable theories (such as effective field theories at all orders), at any order of a perturbative expansion. We use our results to prove that, at leading order, Lorentz invariance does not impose restrictions on the set of 16 Galilean-invariant operators commonly used to parametrize the non-relativistic DM-nucleon interaction. We also predict the lowest effective-operator dimension at which the non-relativistic operators appear in the effective field theory of a singlet DM particle.

Revisiting RGEs for general gauge theories

We revisit the renormalisation group equations (RGE) for general renormalisable gauge theories at one- and two-loop accuracy. We identify and correct various mistakes in the literature for the β-functions of the dimensionful Lagrangian parameters (the fermion mass, the bilinear and trilinear scalar couplings) as well as the dimensionless quartic scalar couplings. There are two sources for these discrepancies. Firstly, the known expressions for the scalar couplings assume a diagonal wave-function renormalisation which is not appropriate for models with mixing in the scalar sector. Secondly, the dimensionful parameters have been derived in the literature using a dummy field method which we critically re-examine, obtaining revised expressions for the β-function of the fermion mass. We perform an independent cross-check using well-tested supersymmetric RGEs which confirms our results. The numerical impact of the changes in the β-function for the fermion mass terms is illustrated using a toy model with a heavy vector-like fermion pair coupled to a scalar gauge singlet. Unsurprisingly, the correction to the running of the fermion mass becomes sizeable for large Yukawa couplings of the order of O(1). Furthermore, we demonstrate the importance of the correction to the β-functions of the scalar quartic couplings using a general type-III Two-Higgs-Doublet-Model. All the corrected expressions have been implemented in updated versions of the Mathematica package SARAH and the Python package PyR@TE.

A flavorful factoring of the strong CP problem

Motivated by the intimate connection between the strong CP problem and the flavor structure of the Standard Model, we present a flavor model that revives and extends the classic mu = 0 solution to the strong CP problem. QCD is embedded into a SU(3)1 × SU(3)2 × SU(3)3 gauge group, with each generation of quarks charged under the respective SU(3). The non-zero value of the up-quark Yukawa coupling (along with the strange quark and bottom-quark Yukawas) is generated by contributions from small instantons at a new scale M ≫ ΛQCD. The Higgsing of SU(3)3 → SU(3)c allows dimension-5 operators that generate the Standard Model flavor structure and can be completed in a simple renormalizable theory. The smallness of the third generation mixing angles can naturally emerge in this picture, and is connected to the smallness of threshold corrections to overline{theta} . Remarkably, overline{theta} is essentially fixed by the measured quark masses and mixings, and is estimated to be close to the current experimental bound and well within reach of the next generation of neutron and proton EDM experiments.

Temperatures of renormalizable quantum field theories in curved spacetime

In this paper we compute the temperature registered by an Unruh–DeWitt detector coupled to a Hadamard renormalizable quantum field in an arbitrary state, moving along an accelerated trajectory in a curved spacetime. For a massless and conformally invariant field, the generalized expression for the temperature is given by the quadratic sum of the 4-acceleration, Raychaudhuri scalar, and renormalized field polarization. We can further find a novel constraint on the renormalized quantum field polarization in relativistic systems that are in global thermal equilibrium.

Three-loop effective potential of general scalar theory via differential equations

We consider the scalar sector of a general renormalizable theory and evaluate the effective potential through three loops analytically. We encounter three-loop vacuum bubble diagrams with up to two masses and six lines, which we solve using differential equations transformed into the favorable ϵ form of dimensional regularization. The master integrals of the canonical basis thus obtained are expressed in terms of cyclotomic polylogarithms up to weight four. We also introduce an algorithm for the numerical evaluation of cyclotomic polylogarithms with multiple-precision arithmetic, which is implemented in the Mathematica package cyclogpl.m supplied here.

Massless and quantized modes of kinks in the phase space of superconducting gaps

We investigated quantized modes of kinks in the phase space of superconducting gaps in a superconductor with multiple gaps. The kink is described by the sine-Gordon model in a two-gap superconductor and by the double sine-Gordon model in a three-gap superconductor. A fractional-flux vortex exists at the edge of the kink, and a fractional-flux vortex will be stable in a three-gap superconductor with time-reversal symmetry breaking. The kink and fractional-flux vortex exhibit massless modes as a sliding motion. We show further that there are one zero-energy mode (massless mode) and quantized excitation modes in kinks, which are characteristic features of multi-gap superconductors. The equation of quantized modes for the double sine-Gordon model is solved numerically. The correction to the ground-state energy is calculated based on the renormalization theory.

Two-loop effective potential for generalized gauge fixing

We obtain the two-loop effective potential for general renormalizable theories, using a generalized gauge-fixing scheme that includes as special cases the background-field $R_\xi$ gauges, the Fermi gauges, and the familiar Landau gauge, and using dimensional regularization in the bare and \MSbar renormalization schemes. As examples, the results are then specialized to the Abelian Higgs model and to the Standard Model. In the case of the Standard Model, we study how the vacuum expectation value and the minimum vacuum energy depend numerically on the gauge-fixing parameters. The results at fixed two-loop order exhibit non-convergent behavior for sufficiently large gauge-fixing parameters; this can presumably be addressed by a resummation of higher-order contributions.

New infra-red enhancements in 4-derivative gravity

4-Derivative gravity provides a renormalizable theory of quantum gravity at the price of introducing a physical ghost, which could admit a sensible positive-energy quantization. To understand its physics, we compute ghost-mediated scatterings among matter particles at tree-level, finding a new power-like infra-red enhancement typical of 4-derivative theories, that we dub ‘ghostrahlung’. Super-Planckian scatterings get downgraded to Planckian by radiating hard gravitons and ghosts, which are weakly coupled and carry away the energy.

Renormalizing gravity: A new insight into an old problem

It is well known that perturbative quantum gravity is nonrenormalizable. The metric or vierbein has generally been used as the variable to quantize in perturbative quantum gravity. In this paper, we show that one can use the spin connection instead, in which case it is possible to obtain a ghost-free renormalizable theory of quantum gravity. Furthermore in this approach, gravitational analogs of particle physics phenomena can be studied. In particular, we study the gravitational Higgs mechanism using spin connection as a gauge field, and show that this provides a mechanism for the effective reduction in the dimensionality of spacetime.

Perturbatively renormalizable quantum gravity

The Wilsonian renormalization group (RG) requires Euclidean signature. The conformal factor of the metric then has a wrong-sign kinetic term, which has a profound effect on its RG properties. In particular, around the Gaussian fixed point, it supports a Hilbert space of renormalizable interactions involving arbitrarily high powers of the gravitational fluctuations. These interactions are characterized by being exponentially suppressed for large field amplitude, perturbative in Newton’s constant but nonperturbative in Planck’s constant. By taking a limit to the boundary of the Hilbert space, diffeomorphism invariance is recovered whilst retaining renormalizability. Thus the so-called conformal factor instability points the way to constructing a perturbatively renormalizable theory of quantum gravity.

Taming the Beast: Diffusion Method in Nonlocal Gravity

We present a method to solve the nonlinear dynamical equations of motion in gravitational theories with fundamental nonlocalities of a certain type. For these specific form factors, which appear in some renormalizable theories, the number of field degrees of freedom and of initial conditions is finite.

Unitary symmetry constraints on tensorial group field theory renormalization group flow

Renormalization group methods are an essential ingredient in the study of nonperturbative problems of quantum field theory. This paper deal with the symmetry constraints on the renormalization group flow for quartic melonic tensorial group field theories. Using the unitary invariance of the interactions, we provide a set of Ward–Takahashi identities which leads to relations between correlation functions. There are numerous reasons to consider such Ward identities in the functional renormalization group. Their compatibility along the flow provides a non-trivial constraint on the reliability of the approximation schemes used in the non-perturbative regime, especially on the truncation and the choice of the regulator. We establish the so-called structure equations in the melonic sector and in the symmetric phase. As an example we consider the TGFT model without gauge constraint. The Wetterich flow equation is given and the way to improve the truncation on the effective action is also scrutinized.

The decay h \u2192 \u03b3\u03b3 in the Standard-Model Effective Field Theory

Assuming that new physics effects are parametrized by the Standard-Model Effective Field Theory (SMEFT) written in a complete basis of up to dimension-6 operators, we calculate the CP-conserving one-loop amplitude for the decay h → γγ in general Rξ - gauges. We employ a simple renormalisation scheme that is hybrid between on-shell overline{mathrm{SM}} -like renormalised parameters and running MS Wilson coefficients. The resulting amplitude is then finite, renormalisation scale invariant, independent of the gauge choice (ξ) and respects SM Ward identities. Remarkably, the S-matrix amplitude calculation resembles very closely the one usually known from renormalisable theories and can be automatised to a high degree. We use this gauge invariant amplitude and recent LHC data to check upon sensitivity to various Wilson coefficients entering from a more complete theory at the matching energy scale. We present a closed expression for the ratio ℛh→ γγ , of the Beyond the SM versus the SM contributions as appeared in LHC h → γγ searches. The most important contributions arise at tree level from the operators QφB, QφW, QφW B , and at one-loop level from the dipole operators QuB, QuW. Our calculation shows also that, for operators that appear at tree level in SMEFT, one-loop corrections can modify their contributions by less than 10%. Wilson coefficients corresponding to these five operators are bounded from current LHC h → γγ data — in some cases an order of magnitude stronger than from other searches. Finally, we correct results that appeared previously in the literature.

Correlation of individual differences in audiovisual asynchrony across stimuli and tasks: New constraints on temporal renormalization theory.

Sight and sound are out of synch in different people by different amounts for different tasks. But surprisingly, different concurrent measures of perceptual asynchrony correlate negatively (Freeman et al., 2013). Thus, if vision subjectively leads audition in one individual, the same individual might show a visual lag in other measures of audiovisual integration (e.g., McGurk illusion, Stream-Bounce illusion). This curious negative correlation was first observed between explicit temporal order judgments and implicit phoneme identification tasks, performed concurrently as a dual task, using incongruent McGurk stimuli. Here we used a new set of explicit and implicit tasks and congruent stimuli, to test whether this negative correlation persists across testing sessions, and whether it might be an artifact of using specific incongruent stimuli. None of these manipulations eliminated the negative correlation between explicit and implicit measures. This supports the generalizability and validity of the phenomenon, and offers new theoretical insights into its explanation. Our previously proposed "temporal renormalization" theory assumes that the timings of sensory events registered within the brain's different multimodal subnetworks are each perceived relative to a representation of the typical average timing of such events across the wider network. Our new data suggest that this representation is stable and generic, rather than dependent on specific stimuli or task contexts, and that it may be acquired through experience with a variety of simultaneous stimuli. Our results also add further evidence that speech comprehension may be improved in some individuals by artificially delaying voices relative to lip-movements. (PsycINFO Database Record

Renormalization in large-N QCD is incompatible with open/closed string duality

Solving by a canonical string theory, of closed strings for the glueballs and open strings for the mesons, the 't Hooft large-N expansion of QCD is a long-standing problem that resisted all the attempts despite the advent of the celebrated gauge/gravity duality in the framework of string theory. We demonstrate that in the canonical string framework such a solution does not actually exist because an inconsistency arises between the renormalization properties of the QCD S matrix at large N, recently worked out in Bochicchio (2017) [5], and the open/closed duality of the would-be string solution. Specifically, the would-be open-string one-loop corrections to the tree glueball amplitudes must be ultraviolet (UV) divergent by the aforementioned renormalization properties, which follow from the QCD asymptotic freedom (AF) and renormalization group. Hence, naively, the inconsistency arises because these amplitudes are dual to tree closed-string diagrams, which are universally believed to be both UV finite – since they are closed-string tree diagrams – and infrared (IR) finite because of the glueball mass gap. In fact, the inconsistency follows from a low-energy theorem of the Novikov–Shifman–Vainshtein–Zakharov (NSVZ) type derived in Bochicchio (2017) [5] that controls the renormalization in QCD-like theories. The aforementioned inconsistency extends to the would-be canonical string for a vast class of 't Hooft large-N confining asymptotically free QCD-like theories including N=1 SUSY QCD. We also demonstrate that the presently existing SUSY string models with a mass gap based on the gauge/gravity duality– such as Klebanov–Strassler, Polchinski–Strassler (PS) and certain PS variants – cannot contradict the above-mentioned results, not even potentially, since they are not asymptotically free. Moreover, we shed light on the way the open/closed string duality may be perturbatively realized in these string models compatibly with a mass gap in the 't Hooft-planar closed-string sector and the aforementioned low-energy theorem because of the lack of AF. Finally, we suggest a noncanonical way-out for asymptotically free QCD-like theories based on topological strings on noncommutative twistor space.