Nonlocal Form Factors Research Articles

Anomalous thresholds in B → (P, V)γ* form factors

We study the effects of anomalous thresholds on the non-local form factors describing the hadronization of the light-quark contribution to B → (P, V)γ* transitions. Starting from a comprehensive discussion of anomalous thresholds in the triangle loop function for different mass configurations, we detail how the dispersion relation for ππ intermediate states is affected by contour deformations mandated by the anomalous branch points. Phenomenological estimates of the size of the anomalous contributions to the form factors are provided with couplings determined from measured branching fractions and Dalitz plot distributions. Our key finding is that anomalous effects are suppressed on the ρ(770) resonance, while off-peak the effects can become as large as O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(10%) of the full (light-quark-loop induced) non-local form factors. We comment on future generalizations towards higher intermediate states and the charm loop, outlining how the dispersive framework established in this work could help improve the non-local form factors needed as input for a robust interpretation of B → (P, V)ℓ+ℓ− decays.

Non-factorisable contributions of strong-penguin operators in Λb→ Λℓ+ℓ− decays

We investigate for the first time a certain class of non-factorisable contributions of the four-quark operators O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}3−6 in the weak effective Hamiltonian to the Λb → Λℓ+ℓ− decay amplitude. We focus on the case where a virtual photon is radiated from one of the light constituents of the Λb baryon, in the kinematic situation of large hadronic recoil with an energetic Λ baryon in the final state. The effect on the suitably defined “non-local form factors” is calculated using the light-cone sum rule approach for a correlator with an interpolating current for the light Λ baryon. We find that this approach requires the introduction of new soft functions that generalise the standard light-cone distribution amplitudes (LCDAs) for the heavy Λb baryon. We give a heuristic discussion of their properties and a model that relates them to the standard LCDAs. Within this framework, we provide numerical results for the size of the non-local form factors considered.

Magnetogenesis in Non-Local Models during Inflation

The generation of magnetic fields during the inflation in an electromagnetic model with a non-local form factor in Maxwell’s action is studied. The equations of motion for the electromagnetic field are derived and solved. It is found that the conformal symmetry breaking due to the non-local form factor does not lead to the generation of magnetic fields during the inflation in the absence of an interaction with the inflaton field. If such a coupling takes place, then the presence of the form factor inhibits the generation of primordial magnetic fields compared to the case where the non-local form factor is absent.

Reduced QED with Few Planes and Fermion Gap Generation.

The formalism of reduced quantum electrodynamics is generalized to the case of heterostructures composed of a few atomically thick layers, and the corresponding effective (2+1)-dimensional gauge theory is formulated. This dimensionally reduced theory describes charged fermions confined to N planes and contains N vector fields with Maxwell's action modified by non-local form factors whose explicit form is determined. Taking into account the polarization function, the explicit formulae for the screened electromagnetic interaction are presented in the case of two and three layers. For a heterostructure with two atomically thick layers and charged fermions described by the massless Dirac equation, the dynamical gap generation of the excitonic type is studied. It is found that additional screening due to the second layer increases the value of the critical coupling constant for the gap generation compared to that in graphene.

Effective approach to the Antoniadis-Mottola model: quantum decoupling of the higher derivative terms

We explore the decoupling of massive ghost mode in the 4D (four-dimensional) theory of the conformal factor of the metric. The model was introduced by Antoniadis and Mottola in [1] and can be regarded as a close analog of the fourth-derivative quantum gravity. The analysis of the derived one-loop nonlocal form factors includes their asymptotic behavior in the UV and IR limits. In the UV (high energy) domain, our results reproduce the Minimal Subtraction scheme-based beta functions of [1]. In the IR (i.e., at low energies), the diagrams with massive ghost internal lines collapse into tadpole-type graphs without nonlocal contributions and become irrelevant. On the other hand, those structures that contribute to the running of parameters of the action and survive in the IR, are well-correlated with the divergent part (or the leading in UV contributions to the form factors), coming from the effective low-energy theory of the conformal factor. This effective theory describes only the light propagating mode. Finally, we discuss whether these results may shed light on the possible running of the cosmological constant at low energies.

Formation and evaporation of quantum black holes from the decoupling mechanism in quantum gravity

We propose a new method to account for quantum-gravitational effects in cosmological and black hole spacetimes. At the core of our construction is the “decoupling mechanism”: when a physical infrared scale overcomes the effect of the regulator implementing the Wilsonian integration of fluctuating modes, the renormalization group flow of the scale-dependent effective action freezes out, so that at the decoupling scale the latter approximates the standard quantum effective action. Identifying the decoupling scale allows to access terms in the effective action that were not part of the original truncation and thus to study leading-order quantum corrections to field equations and their solutions. Starting from the Einstein-Hilbert truncation, we exploit for the first time the decoupling mechanism in quantum gravity to investigate the dynamics of quantum-corrected black holes from formation to evaporation. Our findings are in qualitative agreement with previous results in the context of renormalization group improved black holes, but additionally feature novel properties reminiscent of higher-derivative operators with specific non-local form factors.

Improved theory predictions and global analysis of exclusive b → sμ+μ− processes

We provide improved Standard Model theory predictions for the exclusive rare semimuonic processes B → K(*)μ+μ− and Bs → ϕμ+μ−. Our results are based on a novel parametrization of the non-local form factors, which manifestly respects a recently developed dispersive bound. We critically compare our predictions to those obtained in the framework of QCD factorization. Our predictions provide, for the first time, parametric estimates of the systematic uncertainties due to non-local contributions. Comparing our predictions within the Standard Model to available experimental data, we find a large tension for B → Kμ+μ−. A simple model-independent analysis of potential effects beyond the Standard Model yields results compatible with other approaches, albeit with larger uncertainties for the B → K*μ+μ− and Bs → ϕμ+μ− decays. Our approach yields systematically improvable predictions, and we look forward to its application in further analyses beyond the Standard Model.

Nonlocality of quantum matter corrections and cosmological constant running

Semiclassical loop corrections to the gravitational action include various terms with zero, two, and four derivatives of the metric as well as nonlocal form factors for these terms. Contributions to some of these terms could be confused with others on a specific metric background or for a particular gauge fixing. We present a critical analysis of the recent works where the tensor structure and the number of derivatives in the action of gravity were not properly taken into account. Taking these relevant aspects into account, we show that although some contributions owing to the quantum fluctuations of massive or massless scalar as well as fermion and vector fields may be attributed to the “running” of the cosmological constant, in reality they correspond to the fourth derivative terms of the action.

New nonsingular cosmological solution of nonlocal gravity

We present a new bouncing cosmological solution of the non-local theory known as infinite derivative gravity, which goes beyond the recursive ansatz, ${\Box R = r_1 R +r_2}$. The non-local field equations are evaluated using the spectral decomposition with respect to the eigenfunctions of the wave operator. The energy-momentum tensor computed for this geometry turns out to be much more sensitive to the choice of the non-local form-factor, since it depends on the value of the function on a continuous infinite interval. We show that this stronger dependence on the form-factor allows us to source the geometry by the perfect fluid with the non-negative energy density satisfying the strong energy condition. We show that this bouncing behaviour is not possible in the local theories of gravity such as in general relativity or $R+R^2$ gravity sourced by a fluid which meets the non-negative energy and strong energy conditions.

Directly probing the Higgs-top coupling at high scales

We explore the sensitivity to new physics for the coupling of the Higgs boson (h) and top quark (t) at high energy scales with the process pp→tt¯h at the high-luminosity LHC. This process probes the coupling in both the space-like and time-like domains at a high scale, complementary to the off-shell Higgs processes in the time-like domain. The effects from physics beyond the Standard Model are parametrized in terms of the effective field theory framework and a non-local Higgs-top form factor. Focusing on the boosted Higgs regime in association with jet substructure techniques, we show that the present search can directly probe the Higgs-top coupling to good precision, providing a strong sensitivity to the new physics scale.

Off-shell Higgs couplings in H⁎ → ZZ → ℓℓνν

We explore the new physics reach for the off-shell Higgs boson measurement in the pp→H⁎→Z(ℓ+ℓ−)Z(νν¯) channel at the high-luminosity LHC. The new physics sensitivity is parametrized in terms of the Higgs boson width, effective field theory framework, and a non-local Higgs-top coupling form factor. Adopting Machine-learning techniques, we demonstrate that the combination of a large signal rate and a precise phenomenological probe for the process energy scale, due to the transverse ZZ mass, leads to significant sensitivities beyond the existing results in the literature for the new physics scenarios considered.

One-Loop Effective Action: Nonlocal Form Factors and Renormalization Group

We review and present full detail of the Feynman diagram - based and heat-kernel method - based calculations of the simplest nonlocal form factors in the one-loop contributions of a massive scalar field. The paper has a pedagogical and introductory purposes and is intended to help the reader in better understanding the existing literature on the subject. The functional calculations are based on the solution by Avramidi and Barvinsky \& Vilkovisky for the heat kernel and are performed in curved spacetime. One of the important points is that the main structure of non-localities is the same as in the flat background.

Ultrarelativistic spinning objects in nonlocal ghost-free gravity

We study the gravitational field of ultrarelativistic spinning objects (gyratons) in a modified gravity theory with higher derivatives. In particular, we focus on a special class of such theories with an infinite number of derivatives known as "ghost-free gravity" that include a non-local form factor such as $\exp(-\Box\ell^2)$, where $\ell$ is the scale of non-locality. First, we obtain solutions of the linearized ghost-free equations for stationary spinning objects. To obtain gyraton solutions we boost these metrics and take their Penrose limit. This approach allows us to perform calculations for any number of spacetime dimensions. All solutions are regular at the gyraton axis. In four dimensions, when the scale non-locality $\ell$ tends to zero, the obtained gyraton solutions correctly reproduce the Aichelburg--Sexl metric and its generalization to spinning sources found earlier by Bonnor. We also study the properties of the obtained four-dimensional and higher-dimensional ghost-free gyraton metrics and briefly discuss their possible applications.

Exact NLO matching and analyticity in b\u2009\u2192\u2009s\u2113\u2113

Exclusive rare decays mediated by b → sℓℓ transitions receive contributions from four-quark operators that cannot be naively expressed in terms of local form factors. Instead, one needs to calculate a matrix element of a bilocal operator. In certain kinematic regions, this bilocal operator obeys some type of Operator Product Expansion, with coefficients that can be calculated in perturbation theory. We review the formalism and, focusing on the dominant SM operators O1,2, we perform an improved calculation of the NLO matching for the leading dimension-three operators. This calculation is performed completely analytically in the two relevant mass scales (charm-quark mass mc and dilepton squared mass q2), and we pay particular attention to the analytic continuation in the complex q2 plane. This allows for the first time to study the analytic structure of the non-local form factors at NLO, and to calculate the OPE coefficients far below q2 = 0, say {q}^2underset{sim }{<}-10{mathrm{GeV}}^2 . We also provide explicitly the contributions proportional to different charge factors, which obey separate dispersion relations.

Rearrangement term in the folding model of the nucleon optical potential

Based on the mean-field determination of the single-particle energy in nuclear matter that contains naturally a rearrangement term (RT) implied by the Hugenholtz–van Hove theorem, the folding model of the nucleon optical potential (OP) is extended to take into account the RT using the effective, density dependent CDM3Yn interaction. With the exchange part of the nucleon folded OP treated exactly in the Hartree–Fock manner, a compact nonlocal version of the folding model is suggested in the present work to determine explicitly the isospin-dependent, nonlocal central term of the nucleon OP. To solve the optical model (OM) equation with a complex nonlocal OP, the calculable R-matrix method is used to analyse the elastic neutron and proton scattering on 40,48Ca, 90Zr, and 208Pb targets at low energies. The inclusion of the RT into the folding model calculation of the nonlocal nucleon OP was shown to be essential for the overall good OM description of elastic nucleon scattering. To validate the nonlocal version of the folding model, the OM results given by the nonlocal folded nucleon OP are also compared with those given by the global parametrization of the nonlocal OP using the analytical nonlocal form factor suggested by Perey and Buck.

Ghost-free modification of the Polyakov action and Hawking radiation

In this paper we discuss possible effects of non-locality in black hole spacetimes. We consider a two-dimensional theory in which the action describing matter is a ghost-free modification of the Polyakov action. For this purpose we write the Polyakov action in a local form by using an auxiliary scalar field and modify its kinetic term by including into it a non-local ghost-free form factor. We demonstrate that the effective stress-energy tensor is modified and we study its properties in a background of a two-dimensional black hole. We obtain the expression for the contribution of the ghost-free auxiliary field to the entropy of the black hole. We also demonstrate that if the back-reaction effects are not taken into account, such a ghost-free modification of the theory does not change the energy flux of the Hawking radiation measured at infinity. We illustrate the discussed properties for black hole solution of a 2D dilaton gravity model which admits a rather complete analytical study.

Lagrangian formulation of an infinite derivative real scalar field theory in the framework of the covariant Kempf–Mangano algebra in a [formula omitted]-dimensional Minkowski space–time

In 2017, G. P. de Brito and co-workers suggested a covariant generalization of the Kempf–Mangano algebra in a (D+1)-dimensional Minkowski space–time (Kempf and Mangano, 1997; de Brito et al., 2017). It is shown that reformulation of a real scalar field theory from the viewpoint of the covariant Kempf–Mangano algebra leads to an infinite derivative Klein–Gordon wave equation which describes two bosonic particles in the free space (a usual particle and a ghostlike particle). We show that in the low-energy (large-distance) limit our infinite derivative scalar field theory behaves like a Pais–Uhlenbeck oscillator for a spatially homogeneous field configuration ϕ(t,x→)=ϕ(t). Our calculations show that there is a characteristic length scale δ in our model whose upper limit in a four-dimensional Minkowski space–time is close to the nuclear scale, i.e., δmax∼δnuclearscale∼10−15m. Finally, we show that there is an equivalence between a non-local real scalar field theory with a non-local form factor K(x−y)=−□x(1−δ22□x)2δ(D+1)(x−y) and an infinite derivative real scalar field theory from the viewpoint of the covariant Kempf–Mangano algebra.

On thermal field fluctuations in ghost-free theories

We study the response of a scalar thermal field to a δ-probe in the context of non-local ghost-free theories. In these theories a non-local form factor is inserted into the kinetic part of the action which does not introduce new poles. For the case of a static δ-potential we obtain an explicit expression for the thermal Hadamard function and use it for the calculation of the thermal fluctuations. We then demonstrate how the presence of non-locality modifies the amplitude of these fluctuations. Finally, we also discuss the fluctuation-dissipation theorem in the context of ghost-free quantum field theories at finite temperature.

Vacuum Effective Actions and Mass-Dependent Renormalization in Curved Space

We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss the importance of these form-factors in the construction of mass-dependent beta functions for the Newton’s constant and the other gravitational couplings.

Form factors and decoupling of matter fields in four-dimensional gravity

We extend previous calculations of the non-local form factors of semiclassical gravity in 4D to include the Einstein–Hilbert term. The quantized fields are massive scalar, fermion and vector fields. The non-local form factor in this case can be seen as the sum of a power series of total derivatives, but it enables us to derive the beta function of Newton's constant and formally evaluate the decoupling law in the new sector, which turns out to be the standard quadratic one.