Renormalizable Theory Research Articles

Gravitational waves as a probe of extended scalar sectors with the first order electroweak phase transition

We discuss spectra of gravitational waves which are originated by the strongly first order phase transition at the electroweak symmetry breaking, which is required for a successful scenario of electroweak baryogenesis. Such spectra are numerically evaluated without high temperature expansion in a set of extended scalar sectors with additional N isospin-singlet fields as a concrete example of renormalizable theories. We find that the produced gravitational waves can be significant, so that they are detectable at future gravitational wave interferometers such as DECIGO and BBO. Furthermore, since the spectra strongly depend on N and the mass of the singlet fields, our results indicate that future detailed observation of gravitational waves can be in general a useful probe of extended scalar sectors with the first order phase transition.

Extending theories on muon-specific interactions

The proton radius puzzle, the discrepancy between the proton radius measured in muonic hydrogen and electronic hydrogen, has yet to be resolved. There are suggestions that beyond the standard model (BSM) physics could resolve both this puzzle and the muon anomalous magnetic moment discrepancy. Karshenboim et al. point out that simple, nonrenormalizable, models in this direction involving new vector bosons have serious problems when confronting high energy data. The prime example is radiative corrections to W to mu nu decay which exceed experimental bounds. We show how embedding the model in a larger and arguably renormalizable theory restores gauge invariance of the vector particle interactions and controls the high energy behavior of decay and scattering amplitudes. Thus BSM explanations of the proton radius puzzle can still be viable.

W' Boson near 2 TeV: Predictions for Run 2 of the LHC.

We present a renormalizable theory that includes a W' boson of mass in the 1.8-2 TeV range, which may explain the excess events reported by the ATLAS Collaboration in a WZ final state, and by the CMS Collaboration in e(+)e(-)jj, Wh(0), and jj final states. The W' boson couples to right-handed quarks and leptons, including Dirac neutrinos with TeV-scale masses. This theory predicts a Z' boson of mass in the 3.4-4.5 TeV range. The cross section times branching fractions for the narrow Z' dijet and dilepton peaks at the 13 TeV LHC are 10 and 0.6 fb, respectively, for M_(Z')=3.4 TeV, and an order of magnitude smaller for M_(Z')=4.5 TeV.

No scale SUGRA SO(10) derived Starobinsky model of inflation

We show that a supersymmetric renormalizable theory based on gauge group SO(10) and Higgs system 10⊕210⊕126⊕126‾ with no scale supergravity can lead to a Starobinsky kind of potential for inflation. Successful inflation is possible in the cases where the potential during inflation corresponds to SU(3)C×SU(2)L×SU(2)R×U(1)B-L, SU(5)×U(1) and flipped SU(5)×U(1) intermediate symmetry with a suitable choice of superpotential parameters. The reheating in such a scenario can occur via non-perturbative decay of inflaton i.e. through “preheating”. After the end of reheating, when universe cools down, the finite temperature potential can have a minimum which corresponds to MSSM.

Spin and chirality effects in antler-topology processes at high energy $$\varvec{e^+e^-}$$ colliders

We perform a model-independent investigation of spin and chirality correlation effects in the antler-topology processes $e^+e^-\to\mathcal{P}^+\mathcal{P}^-\to (\ell^+ \mathcal{D}^0) (\ell^-\mathcal{\bar{D}}^0)$ at high energy $e^+e^-$ colliders with polarized beams. Generally the production process $e^+e^-\to\mathcal{P}^+\mathcal{P}^-$ can occur not only through the $s$-channel exchange of vector bosons, $\mathcal{V}^0$, including the neutral Standard Model (SM) gauge bosons, $\gamma$ and $Z$, but also through the $s$- and $t$-channel exchanges of new neutral states, $\mathcal{S}^0$ and $\mathcal{T}^0$, and the $u$-channel exchange of new doubly-charged states, $\mathcal{U}^{--}$. The general set of (non-chiral) three-point couplings of the new particles and leptons allowed in a renormalizable quantum field theory is considered. The general spin and chirality analysis is based on the threshold behavior of the excitation curves for $\mathcal{P}^+\mathcal{P}^-$ pair production in $e^+e^-$ collisions with longitudinal and transverse polarized beams, the angular distributions in the production process and also the production-decay angular correlations. In the first step, we present the observables in the helicity formalism. Subsequently, we show how a set of observables can be designed for determining the spins and chiral structures of the new particles without any model assumptions. Finally, taking into account a typical set of approximately chiral invariant scenarios, we demonstrate how the spin and chirality effects can be probed experimentally at a high energy $e^+e^-$ collider.

Quantum gravity with torsion and non-metricity

We study the renormalization of theories of gravity with an arbitrary (torsional and non-metric) connection. The class of actions we consider is of the Palatini type, including the most general terms with up to two derivatives of the metric, but no derivatives of the connection. It contains 19 independent parameters. We calculate the one-loop beta functions of these parameters and find their fixed points. The Holst subspace is discussed in some detail and found not to be stable under renormalization. Some possible implications for ultraviolet and infrared gravity are discussed.

Yu. V. Novozhilov: Creative path

The scientific activity of Yu. V. Novozhilov started under the influence of two outstanding physicists of that time: Corresponding Member of the Academy Ya. I. Frenkel and Academician V. A. Fock. From these two leading scientists, so different from each other, Novozhilov inherited a devotion to science, a taste for research at the frontier, a true understanding of the relevance of the studied questions, and a rigorous mathematical approach combined with physical intuition. The initial stage of Novozhilov’s scientific work coincided with the period of explosive development of quantum field theory and the theory of elementary particles in the 1940s and 1950s, with the creation of renormalization theory and relativistic scattering theory. The plenitude of new ideas and methods and the extremely rapid pace of research characteristic of that period determined Novozhilov’s direction and style of work. At this time, Novozhilov published papers on the functional method in quantum field theory. In them, he developed the theory of renormalization in the framework of Fock’s functional method and studied the problem of the variation of functionals in Fermi fields. The keen interest of Novozhilov in the functional method was somewhat ahead of its time: later, in the 1970s, this method became the base for analyzing gauge fields, which underlie the modern theory of fundamental interactions. The review paper “Functional method in quantum field theory” [1] by Novozhilov and A. V. Tulub, published as a separate book in the USA, was long the only handbook on the functional method and is still relevant today. In 1953, Novozhilov was awarded a first-degree university prize for the paper “Application of Fock’s functional method to the problem of self-energy” [2]. We briefly discuss this first paper by Novozhilov. In the abstract, he wrote: “Fock’s functional method is used to obtain the Dirac equation with electromagnetic mass and radiative corrections.” In the functional method, a state is described by an analytic functional Ω{α(x)} of the complex function α(x). The creation and annihilation operators a † (x )a nda(x) correspond to multiplication by α(x )a nd the functional derivative of that function. In application to the Dirac equation in quantum electrodynamics, we start from the equation for the state functional [ ˆ

Gradient flows in three dimensions

The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the β- functions via a gradient flow equation involving a positive definite metric. We demonstrate the existence of a candidate a-function for renormalisable Chern-Simons theories in three dimensions, involving scalar and fermion fields, in both non-supersymmetric and super-symmetric cases.

Efficient and accurate treatment of electron correlations with Correlation Matrix Renormalization theory.

We present an efficient method for calculating the electronic structure and total energy of strongly correlated electron systems. The method extends the traditional Gutzwiller approximation for one-particle operators to the evaluation of the expectation values of two particle operators in the many-electron Hamiltonian. The method is free of adjustable Coulomb parameters, and has no double counting issues in the calculation of total energy, and has the correct atomic limit. We demonstrate that the method describes well the bonding and dissociation behaviors of the hydrogen and nitrogen clusters, as well as the ammonia composed of hydrogen and nitrogen atoms. We also show that the method can satisfactorily tackle great challenging problems faced by the density functional theory recently discussed in the literature. The computational workload of our method is similar to the Hartree-Fock approach while the results are comparable to high-level quantum chemistry calculations.

Renormalization of gauge theories on general anisotropic lattices and high-energy scattering in QCD

We study the renormalisation of $SU(N_c)$ gauge theories on general anisotropic lattices, to one-loop order in perturbation theory, employing the background field method. The results are then applied in the context of two different approaches to hadronic high-energy scattering. In the context of the Euclidean nonperturbative approach to soft high-energy scattering based on Wilson loops, we refine the nonperturbative justification of the analytic continuation relations of the relevant Wilson-loop correlators, required to obtain physical results. In the context of longitudinally-rescaled actions, we study the consequences of one-loop corrections on the relation between the $SU(N_c)$ gauge theory and its effective description in terms of two-dimensional principal chiral models.

One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory

We elaborate in this paper a translation-invariant model for fermions in 4-dimensional noncommutative Euclidean space. The construction is done on the basis of the renormalizable noncommutative translation-invariant theory introduced by Gurau et al. 2009 Commun. Math. Phys. 287 275–90. We combine our model with a scalar model, in order to study the noncommutative pseudo-scalar Yukawa theory. After we derive the Feynman rules of the theory, we perform an explicit calculation of the quantum corrections at one loop level for the propagators and vertices.

Scattering amplitudes in super-renormalizable gravity

We explicitly compute the tree-level on-shell four-graviton amplitudes in four, five and six dimensions for local and weakly nonlocal gravitational theories that are quadratic in both, the Ricci and scalar curvature with form factors of the d'Alembertian operator inserted between. More specifically we are interested in renormalizable, super-renormalizable or finite theories. The scattering amplitudes for these theories turn out to be the same as the ones of Einstein gravity regardless of the explicit form of the form factors. As a special case the four-graviton scattering amplitudes in Weyl conformal gravity are identically zero. Using a field redefinition, we prove that the outcome is correct for any number of external gravitons (on-shell $n-$point functions) and in any dimension for a large class of theories. However, when an operator quadratic in the Riemann tensor is added in any dimension (with the exception of the Gauss-Bonnet term in four dimensions) the result is completely altered, and the scattering amplitudes depend on all the form factors introduced in the action.

Accidental composite dark matter

We build models where Dark Matter candidates arise as composite states of a new conning gauge force, stable thanks to accidental symmetries. Restricting to renormalizable theories compatible with SU(5) unication, wend 13 models based on SU(N) gauge theories and 9 based on SO(N). We also describe other models that require non-renormalizable interactions. The two gauge groups lead to distinctive phenomenolo- gies: SU(N) theories give complex DM, with potentially observable electric and magnetic dipole moments that lead to peculiar spin-independent cross sections; SO(N) theories give real DM, with challenging spin-dependent cross sections or inelastic scatterings. Models with Yukawa couplings also give rise to spin-independent direct detection mediated by the Higgs boson and to electric dipole moments for the electron. In some models DM has higher spin. Each model predicts a specic set of lighter composite scalars, possibly observable at colliders.

Simple recursion relations for general field theories

On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-line constructibility of all gauge theories with fermions and complex scalars in arbitrary representations, all supersymmetric theories, and the standard model. Moreover, all amplitudes in non-renormalizable theories without derivative interactions are constructible; with derivative interactions, a subset of amplitudes is constructible. We illustrate our results with examples from both renormalizable and non-renormalizable theories. Our study demonstrates both the power and limitations of recursion relations as a self-contained formulation of quantum field theory.

The dynamical composite Higgs

We present a simple microscopic realization of a pseudo-Nambu-Goldstone (pNGB) boson Higgs scenario arising from the breaking of SO(5) → SO(4). The Higgs constituents are explicitly identified as well as the interactions responsible for forming the bound state and breaking the electroweak symmetry. This outcome follows from the presence of four-fermion interactions with a super-critical coupling, and uses the Nambu-Jona-Lasinio mechanism to break the global SO(5) symmetry. The Higgs potential is found to be insensitive to high energy scales due to the existence of an approximate infrared fixed point. The appearance of vector resonances is described and the correspondence with other proposals in the literature established. The model described here is significantly simpler than other recent ultraviolet completions of pNGB scenarios. The observed Higgs mass can be accommodated, and agreement with electroweak precision tests achieved in certain regions of parameter space. There are also new vector-like fermions, some of which may lie within reach of the LHC. In addition, we predict a heavy standard model singlet scalar in the multi-TeV range. The amount of fine-tuning required in the model is studied. Finally, we show that such a scheme can be completed in the ultraviolet by a renormalizable theory.

Recursion relation for boundary contribution

It is well known that under a BCFW-deformation, there is a boundary contribution when the amplitude scales as $$ \mathcal{O}\left({z}^0\right) $$ or worse. We show that boundary contributions have a similar recursion relation as scattering amplitude. Just like the BCFW recursion relation, where scattering amplitudes are expressed as the products of two on-shell subamplitudes (plus possible boundary contributions), our new recursion relation expresses boundary contributions as products of sub-amplitudes and boundary contributions with less legs, plus yet another possible boundary contribution. In other words, the complete scattering amplitude, including boundary contributions, can be obtained by multiple steps of recursions, unless the boundary contributions are still non-zero when all possible deformations are exploited. We demonstrate this algorithm by several examples. Especially, we show that for standard model like renormalizable theory in 4D, i.e., the theory including only gauge boson, fermions and scalars, the complete amplitude can always be computed by at most four recursive steps using our algorithm.

Static and dynamical magnetic properties of the itinerant ferromagnetLaCo2P2

We synthesized single crystals of an itinerant ferromagnet ${\mathrm{LaCo}}_{2}{\mathrm{P}}_{2}$ with ${\mathrm{ThCr}}_{2}{\mathrm{Si}}_{2}$-type structure and studied their magnetism by magnetization and ${}^{31}\mathrm{P}$ NMR measurements. We measured Knight shift $K$ and spin-lattice relaxation rate divided by temperature $1/{T}_{1}T$ with the applied fields parallel to the $a$ and $c$ axes, and estimated spin fluctuations in the $ab$ plane and $c$. In addition, we evaluated spin fluctuations from the result of magnetization data with a three-dimensional ferromagnetic model. There is little anisotropy in evaluated spin fluctuations in the $ab$ plane and $c$. Spin fluctuations of ${\mathrm{LaCo}}_{2}{\mathrm{P}}_{2}$ have a three-dimensional character and can be understood in the framework of the self-consistent renormalization theory of spin fluctuations.

Perturbative and non-perturbative renormalization results of the Chromomagnetic Operator on the Lattice

The Chromomagnetic operator (CMO) mixes with a large number of operators under renormalization. We identify which operators can mix with the CMO, at the quantum level. Even in dimensional regularization (DR), which has the simplest mixing pattern, the CMO mixes with a total of 9 other operators, forming a basis of dimension-five, Lorentz scalar operators with the same flavor content as the CMO. Among them, there are also gauge noninvariant operators; these are BRST invariant and vanish by the equations of motion, as required by renormalization theory. On the other hand using a lattice regularization further operators with d 5 will mix; choosing the lattice action in a manner as to preserve certain discrete symmetries, a minimul set of 3 additional operators (all with d < 5) will appear. In order to compute all relevant mixing coefficients, we calculate the quark-antiquark (2-pt) and the quark-antiquark-gluon (3-pt) Green’s functions of the CMO at nonzero quark masses. These calculations were performed in the continuum (dimensional regularization) and on the lattice using the maximally twisted mass fermion action and the Symanzik improved gluon action. In parallel, non-perturbative measurements of the K p matrix element are being performed in simulations with 4 dynamical (Nf = 2+ 1+ 1) twisted mass fermions and the Iwasaki improved gluon action.

Filtrations in Dyson–Schwinger equations: Next-to[formula omitted]-leading log expansions systematically

Dyson–Schwinger equations determine the Green functions Gr(α,L) in quantum field theory. Their solutions are triangular series in a coupling constant α and an external scale parameter L for a chosen amplitude r, with the order in L bounded by the order in the coupling.Perturbation theory calculates the first few orders in α. On the other hand, Dyson–Schwinger equations determine next-to{j}-leading log expansions, Gr(α,L)=1+∑j=0∞∑MpjMαjM(u). ∑M sums for any finite j a finite number of functions M in u. Here, u is the one-loop approximation to Gr, for example, for the (inverse) propagator in massless Yukawa theory, u=αL/2.The leading logs come then from the trivial representation, e.g. M(u)=1−1−2u in massless Yukawa theory. The respective period at j=0 is p0M(u)=1. All non-leading logs are organized by corresponding suppressions in powers αj.We describe an algebraic method to derive all next-to{j}-leading log terms from the knowledge of the first (j+1) terms in perturbation theory and their filtrations. This implies the calculation of the functions M(u) and periods pjM.In the first part of our paper, we investigate the structure of Dyson–Schwinger equations and develop a method to filter their solutions. Applying renormalized Feynman rules maps each filtered term to a certain power of α and L in the log-expansion.Based on this, the second part derives the next-to{j}-leading log expansions. Our method is general. Here, we exemplify it using the examples of the propagator in Yukawa theory and the photon self-energy in quantum electrodynamics. In particular, we give explicit formulas for the leading log, next-to-leading log and next-to-next-to-leading log orders in terms of at most three-loop Feynman integrals. The reader may apply our method to any (set of) Dyson–Schwinger equation(s) appearing in renormalizable quantum field theories.

Perturbative search for dead-end CFTs

To explore the possibility of self-organized criticality, we look for CFTs without any relevant scalar deformations (a.k.a dead-end CFTs) within power-counting renormalizable quantum field theories with a weakly coupled Lagrangian description. In three dimensions, the only candidates are pure (Abelian) gauge theories, which may be further deformed by Chern-Simons terms. In four dimensions, we show that there are infinitely many non-trivial candidates based on chiral gauge theories. Using the three-loop beta functions, we compute the gap of scaling dimensions above the marginal value, and it can be as small as $\mathcal{O}(10^{-5})$ and robust against the perturbative corrections. These classes of candidates are very weakly coupled and our perturbative conclusion seems difficult to refute. Thus, the hypothesis that non-trivial dead-end CFTs do not exist is likely to be false in four dimensions.