QFT Models Research Articles

A Laplacian to Compute Intersection Numbers on overline{{{mathcal {M}}}}_{g,n} and Correlation Functions in NCQFT

Let F_g(t) be the generating function of intersection numbers of psi -classes on the moduli spaces overline{{{mathcal {M}}}}_{g,n} of stable complex curves of genus g. As by-product of a complete solution of all non-planar correlation functions of the renormalised Phi ^3-matrical QFT model, we explicitly construct a Laplacian Delta _t on a space of formal parameters t_i which satisfies exp (sum _{gge 2} N^{2-2g}F_g(t))=exp ((-Delta _t+F_2(t))/N^2)1 as formal power series in 1/N^2. The result is achieved via Dyson-Schwinger equations from noncommutative quantum field theory combined with residue techniques from topological recursion. The genus-g correlation functions of the Phi ^3-matricial QFT model are obtained by repeated application of another differential operator to F_g(t) and taking for t_i the renormalised moments of a measure constructed from the covariance of the model.

A simple alternative to the relativistic Breit\u2013Wigner distribution

First, we discuss the conditions under which the non-relativistic and relativistic types of the Breit–Wigner energy distributions are obtained. Then, upon insisting on the correct normalization of the energy distribution, we introduce a Flatté-like relativistic distribution -denominated as Sill distribution- that (i) contains left-threshold effects, (ii) is properly normalized for any decay width, (iii) can be obtained as an appropriate limit in which the decay width is a constant, (iv) is easily generalized to the multi-channel case (v) as well as to a convoluted form in case of a decay chain and - last but not least - (vi) is simple to deal with. We compare the Sill distribution to spectral functions derived within specific QFT models and show that it fairs well in concrete examples that involve a fit to experimental data for the rho , a_1(1260), and K^*(982) mesons as well as the varDelta (1232) baryon. We also present a study of the f_2(1270) which has more than one possible decay channels. Finally, we discuss the limitations of the Sill distribution using the a_0(980)-a_0(1450) and the K_0^*(700)-K_0^*(1430) resonances as examples.

Feynman graph generation and propagator mixing, I

This paper discusses the algorithmic generation of Feynman graphs for QFT models that have some form of explicit propagator mixing, including some related theoretical background. Primarily, it is shown that an ordinary Feynman graph generator — ie one that is able to deal with models without mixed propagators — can be employed to simulate the former, more general type of graph generation.Most of the discussion occurs in the context of graph models — simplified versions of QFT models, that retain only the combinatorial features of the latter type of models. There is a single graph model, noted M(L), for each Lagrangian density L but, for each graph model M, there are infinitely many L such that M=M(L); hence, below, L¯ is not unique (that is not a critical issue, though, as L¯ is used mainly for explanatory purposes and the claims do not depend on the specific L¯ that may be chosen).The aforementioned simulation relies on the construction of an appropriate graph model M¯ from the original M(L)=M, such that (i) there is L¯ without mixed propagators which satisfies M¯=M(L¯) (ie M¯ is a type-SD⁎ model), (ii) the Feynman graphs for L can be easily obtained from those generated for L¯, and (iii) the symmetry factors computed for the graphs in L¯ need not be corrected (and, if some care is taken, the same applies to their signs).

From Feynman rules to conserved quantum numbers, III

The present article complements the earlier ones in this series. The first part contains various results on the constituent system Cκ(M) of a graph model M, and on its feasibility system Iη(M) (which comprises a number of identities that define the number conservation rules). Those results include the general form of the (particle) number conservation rules in models without explicit propagator mixing.A few types of graph models (including self-conjugate and quasi-normal models) are defined. Oversimplifying, a model M is self-conjugate if it has a certain (weak) combinatorial type of C-symmetry, and M is quasi-normal if Iη(M) fully determines for which multisets of coloured, unlinked half-edges there is a graph in M with that exact multiset. It is shown not only that every self-conjugate model is quasi-normal, but also that some extensions of self-conjugate models are still quasi-normal. Most conveniently, self-conjugate models (and even some extended models) may be recognized in polynomial time.These results seem to lead to the following conclusion: for many (possibly ‘most’ of the) consistent, relevant QFT models, a complete correlation function 〈F〉 is graphical — i.e. there exist Feynman diagram(s) for 〈F〉 — if and only if 〈F〉 is allowed by the number conservation rules (i.e. by a complete system of such rules). Since these rules can be computed in polynomial time then, for many QFT models, deciding whether 〈F〉 is graphical also takes polynomial time.

Study of Some (Non-)Conventional Mesons in the Framework of Effective Models

The main aim of our study is to understand the nature of some conventional and non-conventional mesonic states by applying effective QFT models. We start from the relativistic Lagrangians containing a unique $q\bar{q}$ seed state which is strongly coupled to the low-masses decay products of the original state. We find out that some states may appear as a dynamically generated companion poles of the heavier $q\bar{q}$ mesons. In particular we show that $K^*_0(700)$ is a companion pole of the well-known $K^*_0(1430)$ resonance, $X(3872)$ emerges as a (virtual) companion pole of $\chi_{c1}(2P)$, and the puzzling $Y(4008)$ is not a real state, but a spurious enhancement which appears when studying the state $\psi(4040)$.

Approximate symmetries and gravity

There are strong reasons to believe that global symmetries of quantum theories cannot be exact in the presence of gravity. While this has been argued at the qualitative level, establishing a quantitative statement is more challenging. In this work we take new steps towards quantifying symmetry violation in EFTs with gravity. First, we evaluate global charge violation by microscopic black holes present in a thermal system, which represents an irreducible, universal effect at finite temperature. Second, based on general QFT considerations, we propose that local symmetry-violating processes should be faster than black hole-induced processes at any sub-Planckian temperature. Such a proposal can be seen as part of the “swampland” program to constrain EFTs emerging from quantum gravity. Considering an EFT perspective, we formulate a con- jecture which requires the existence of operators violating global symmetry and places quantitative bounds on them. We study the interplay of our conjecture with emergent symmetries in QFT. In models where gauged U(1)’s enforce accidental symmetries, we find that constraints from the Weak Gravity Conjecture can ensure that our conjecture is satisfied. We also study the consistency of the conjecture with QFT models of emergent symmetries such as extradimensional localization, the Froggatt-Nielsen mechanism, and the clockwork mechanism.

Noncommutative 3-colour scalar quantum field theory model in 2D

We introduce the 3-colour noncommutative quantum field theory model in two dimensions. For this model we prove a generalised Ward–Takahashi identity, which is special to coloured noncommutative QFT models. It reduces to the usual Ward–Takahashi identity in a particular case. The Ward–Takahashi identity is used to simplify the Schwinger–Dyson equations for the 2-point function and the N-point function. The absence of any renormalisation conditions in the large (mathcal {N},V)-limit in 2D leads to a recursive integral equation for the 2-point function, which we solve perturbatively to sixth order in the coupling constant.

Weak Adiabatic Limit in Quantum Field Theories with Massless Particles

We construct the Wightman and Green functions in a large class of models of perturbative QFT in the four-dimensional Minkowski space in the Epstein–Glaser framework. To this end we prove the existence of the weak adiabatic limit, generalizing the results due to Blanchard and Seneor. Our proof is valid under the assumption that the time-ordered products satisfy certain normalization condition. We show that this normalization condition may be imposed in all models with interaction vertices of canonical dimension 4 as well as in all models with interaction vertices of canonical dimension 3 provided each of them contains at least one massive field. Moreover, we prove that it is compatible with all the standard normalization conditions which are usually imposed on the time-ordered products. The result applies, for example, to quantum electrodynamics and non-abelian Yang–Mills theories.

A Cohomological Perspective on Algebraic Quantum Field Theory

Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of constructing interacting QFT models. Symmetry is the primary tool for understanding the structure and properties of a QFT model.This perspective leads to a generalization of the algebraic quantum field theory framework, as well as a more general definition of symmetry. This means that some models may have symmetries that were not previously recognized or exploited.To first order, a deformation of a QFT model is described by a Hochschild cohomology class. A deformation could, for example, correspond to adding an interaction term to a Lagrangian. The cohomology class for such an interaction is computed here. However, the result is more general and does not require the undeformed model to be constructed from a Lagrangian. This computation leads to a more concrete version of the construction of perturbative algebraic quantum field theory.

The [formula omitted] and [formula omitted] matricial QFT models have reflection positive two-point function

We extend our previous work (on D=2) to give an exact solution of the ΦD3 large-N matrix model (or renormalised Kontsevich model) in D=4 and D=6 dimensions. Induction proofs and the difficult combinatorics are unchanged compared with D=2, but the renormalisation – performed according to Zimmermann – is much more involved. As main result we prove that the Schwinger 2-point function resulting from the ΦD3-QFT model on Moyal space satisfies, for real coupling constant, reflection positivity in D=4 and D=6 dimensions. The Källén–Lehmann mass spectrum of the associated Wightman 2-point function describes a scattering part |p|2≥2μ2 and an isolated broadened mass shell around |p|2=μ2.

A model of adaptive decision-making from representation of information environment by quantum fields.

We present the mathematical model of decision-making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioural and geopolitical factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are a purely informational nature. The QFT model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism. We demonstrate the quantum-like interference effect in DM, which is exhibited as a violation of the formula of total probability, and hence the classical Bayesian inference scheme.This article is part of the themed issue 'Second quantum revolution: foundational questions'.

Strong and radiative decays of excited vector mesons and predictions for a new ϕ(1930) resonance

We study the phenomenology of two nonets of excited vector mesons, $\{\rho(1450)$, $K^{\ast}(1410)$, $\omega(1420)$, $\phi(1680)\}$ and $\{\rho(1700),$ $K^{\ast}(1680),\omega(1650),$ $\phi(???)\},$ which (roughly) correspond to radially excited $2^{3}S_{1}$ and to orbitally excited $1^{3}D_{1}$ vector mesons. We evaluate the strong and radiative decays of these mesons into pseudoscalar and ground-state vector mesons by using an effective relativistic QFT model based on flavour symmetry. We compare decay widths and branching ratios with various experimental results listed in the PDG. An overall agreement of theory with experiment reinforces the standard quark-antiquark assignment of the resonances mentioned above. Predictions for not yet measured quantities are also made. In particular, we shall also make predictions for the not-yet discovered $s\bar{s}$ state of the $1^{3}D_{1}$ nonet, denoted as $\phi(???)$. Its mass can be estimated to be about $1930$ MeV, hence we shall call this putative state $\phi(1930).$ Its main decays are into $KK^{\ast}(892)$ (about $200$ MeV) and $KK$ (about $100$ MeV). Since this state couples also to $\gamma\eta,$ it can be searched in the near future in the photoproduction-based experiments GlueX and CLAS12 at Jefferson Lab.

Long-range nonlocality in six-point string scattering: Simulation of black hole infallers

We set up a tree-level six point scattering process in which two strings are separated longitudinally such that they could only interact directly via a non-local spreading effect such as that predicted by light cone gauge calculations and the Gross-Mende saddle point. One string, the `detector', is produced at a finite time with energy $E$ by an auxiliary $2\to 2$ sub-process, with kinematics such that it has sufficient resolution to detect the longitudinal spreading of an additional incoming string, the `source'. We test this hypothesis in a gauge-invariant S-matrix calculation convolved with an appropriate wavepacket peaked at a separation $X$ between the central trajectories of the source and produced detector. The amplitude exhibits support for scattering at the predicted longitudinal separation $X\sim\alpha' E$, in sharp contrast to the analogous quantum field theory amplitude (whose support manifestly traces out a tail of the position-space wavefunction). The effect arises in a regime in which the string amplitude is not obtained as a convergent sum of such QFT amplitudes, and has larger amplitude than similar QFT models (with the same auxiliary four point amplitude). In a linear dilaton background, the amplitude depends on the string coupling as expected if the scattering is not simply occuring on the wavepacket tail in string theory. This manifests the scale of longitudinal spreading in a gauge-invariant S-matrix amplitude, in a calculable process with significant amplitude. It simulates a key feature of the dynamics of time-translated horizon infallers.

Quantum field theory in generalised Snyder spaces

We discuss the generalisation of the Snyder model that includes all possible deformations of the Heisenberg algebra compatible with Lorentz invariance and investigate its properties. We calculate perturbatively the law of addition of momenta and the star product in the general case. We also undertake the construction of a scalar field theory on these noncommutative spaces showing that the free theory is equivalent to the commutative one, like in other models of noncommutative QFT.

The search for Physics Beyond the SM: Wins and Losses

In this paper we review briefly the motivations for physics Beyond the Standard Model, which generate many possible signals that can be searched at the LHC. To get some perspective on the current affairs, we discuss some landmark success in the sub-fields of theoretical particle physics: formal QFT developments, Model Building and Phenomenology. By studying how these developments were done, we can learn some lessons about how to be cautious and optimistic at the same time, when looking at potential signals of new physics. We conclude by considering the case of the 750 GeV state and what we have learned from the theoretical activity that tried to reproduce this signal.

Convergent perturbation theory for lattice models with fermions

The standard perturbation theory in QFT and lattice models leads to the asymptotic expansions. However, an appropriate regularization of the path or lattice integrals allows one to construct convergent series with an infinite radius of the convergence. In the earlier studies, this approach was applied to the purely bosonic systems. Here, using bosonization, we develop the convergent perturbation theory for a toy lattice model with interacting fermionic and bosonic fields.

On the Fixed Point Equation of a Solvable 4D QFT Model

The regularisation of the \({\lambda {\upphi }^{4}_{4}}\)-model on noncommutative Moyal space gives rise to a solvable QFT model in which all correlation functions are expressed in terms of the solution of a fixed point problem. We prove that the non-linear operator for the logarithm of the original problem satisfies the assumptions of the Schauder fixed point theorem, thereby completing the solution of the QFT model.

Mapping between the Heisenberg XX Spin Chain and Low-Energy QCD

By using random matrix models we uncover a connection between the low energy sector of four dimensional QCD at finite volume and the Heisenberg XX model in a 1d spin chain. This connection allows to relate crucial properties of QCD with physically meaningful properties of the spin chain, establishing a dictionary between both worlds. We predict for the spin chain a third-order phase transition and a Tracy-Widom law in the transition region. We postulate that this dictionary goes beyond the particular example analyzed here and can be applied to other QFT and spin chain models. We finally comment on possible numerical implications of the connection as well as on possible experimental implementations.

Entanglement in a QFT Model of Neutrino Oscillations

Tools of quantum information theory can be exploited to provide a convenient description of the phenomena of particle mixing and flavor oscillations in terms of entanglement, a fundamental quantum resource. We extend such a picture to the domain of quantum field theory where, due to the nontrivial nature of flavor neutrino states, the presence of antiparticles provides additional contributions to flavor entanglement. We use a suitable entanglement measure, the concurrence, that allows extracting the two-mode (flavor) entanglement from the full multimode, multiparticle flavor neutrino states.

NEW MASSIVE GRAVITY HOLOGRAPHY

We investigate the holographic renormalization group flows and the classical phase transitions that occur in two-dimensional QFT model dual to the New Massive 3D Gravity coupled to scalar matter. Specific matter self-interactions generated by quadratic superpotential are considered. The off-critical AdS3/CFT2 correspondence determines the exact form of the QFT2's β-function and the singular part of the reduced free energy. The corresponding scaling laws and critical exponents characterizing the RG fixed points as well as the values of the mass gaps in the massive phases are obtained.