arXiv subjects

Brigitte Hiller

Publications and source records attributed to Brigitte Hiller.

At least 19 recordsLinked to original sources

arXiv2024

An Implicit Regularization Approach to Chiral Models

The decays of the Z boson and CP-even or CP-odd scalar bosons into quark-antiquark pairs have been calculated at NLO in the framework of Implicit Regularization (IReg) , which operates strictly in the physical dimension and complies with the BPHZ procedure. The presence of the {\gamma}5 matrix is dealt without the need of gauge symmetry restoring counterterms and the Kinoshita-Lee-Nauenberg (KLN) theorem is verified. The results are compared to the ones obtained in the Dimensional Reduction scheme (DRed).

hep-ph↗

arXiv2024

Addressing $\gamma_5$ in Nondimensional Regularizations: A Case Study on the Bumblebee Model

We examine the subtleties of regularization schemes in four-dimensional space ($4S$), related in particular to the introduction of the $\gamma_5$ matrix. To illustrate we use a "Bumblebee" model featuring dynamically induced Lorentz symmetry violation. The analysis centers on how different regularization methods affect the solutions to the gap equation in this model. We highlight the resolution of ambiguities associated with the $\gamma_5$ matrix in ultraviolet divergent integrals by employing an enhanced Implicit Regularization (IREG) method. This method extends IREG to a quasi-four-dimensional space, $Q4S = 4S \oplus X$, drawing parallels with the consistent approach of Dimensional Reduction (DRED). Comparative analysis is conducted against results from the 't Hooft-Veltman regularization scheme, conventional IREG in strict $4S$, and sharp momentum cutoff techniques. Our results illustrate a scheme to compute $\gamma_5$ interactions in physical dimension of divergent amplitudes, confirming the approach in [1].

hep-ph↗

arXiv2023

Infrared Subtleties and Chiral Vertices at NLO: An Implicit Regularization Analysis

We employ implicit regularization (IReg) in quark-antiquark decays of the Z, or of a scalar (CP-even or odd) boson at NLO, and compare with dimensional schemes to reveal subtleties involving infrared divergence cancellation and $\gamma_5$-matrix issues. Besides the absence of evanescent fields in IReg, such as $\epsilon$-scalars required in certain schemes that operate partially in the physical dimension, we verify that our procedure preserves gauge invariance in the presence of the $\gamma_5$ matrix without requiring symmetry preserving counterterms while the amplitude is infrared finite as required by the KLN theorem.

hep-ph↗

arXiv2022

Higgs boson decay into gluons in a 4D regularization: IR cancellation without evanescent fields to NLO

Higgs decay using an effective Higgs-Yang-Mills interaction in terms of a dimension five operator as well as usual QCD interactions is revisited in the context of Implicit Regularization (IReg) and compared with conventional dimensional regularization (CDR), four dimensional helicity (FDH) and dimensional reduction (DRED) schemes. The decay rate for $H \rightarrow gg(g)$ is calculated in this strictly four-dimensional set-up to $\alpha_s^3$ order in the strong coupling. Moreover we include joint processes that contribute at the same perturbative order in the real emission channels consisting of 3 gluons as well as gluon quark-antiquark final states with light (zero mass) quarks. Unambiguous identification and separation of UV from IR divergences is achieved putting at work the renormalization group scale relation inherent to the method. UV singularities are removed as usual by renormalization, the IR divergences are cancelled due to the method's compliance with the Kinoshita-Lee-Nauenberg (KLN) theorem. Most importantly, we verify that no evanescent fields such as $\epsilon$-scalars need be introduced as required by some mixed regularizations that operate partially in the physical dimension.

hep-ph↗

arXiv2021

A brief review of Implicit Regularization and its connection with the BPHZ theorem

Quantum Field Theory, as the keystone of particle physics, has allowed great insights to deciphering the core of Nature. Despite its striking success, by adhering to local interactions, Quantum Field Theory suffers from the appearance of divergent quantities in intermediary steps of the calculation, which encompasses the need for some regularization/renormalization prescription. As an alternative to traditional methods, based on the analytic extension of space-time dimension, frameworks that stay in the physical dimension have emerged, Implicit Regularization is one among them. We briefly review the method, aiming to illustrate how Implicit Regularization complies with the BPHZ theorem, which implies that it respects unitarity and locality to arbitrary loop order.

hep-th↗

arXiv2020

Gouy phase of type-I SPDC-generated biphotons

We consider a double Gaussian approximation to describe the wavefunction of twin photons (also called a biphoton) created in a nonlinear crystal via a type-I spontaneous parametric downconversion (SPDC) process. We find that the wavefunction develops a Gouy phase while it propagates, being dependent of the two-photon correlation through the Rayleigh length. We evaluate the covariance matrix and show that the logarithmic negativity, useful in quantifying entanglement in Gaussian states, although Rayleigh-dependent, does not depend on the propagation distance. In addition, we show that the two-photon entanglement can be connected to the biphoton Gouy phase as these quantities are Rayleigh-length-related. Then, we focus the double Gaussian biphoton wavefunction using a thin lens and calculate a Gouy phase that is in reasonable agreement with the experimental data of D. Kawase et al. published in Ref. [1].

quant-ph↗

arXiv2018

Supercurrent anomaly and gauge invariance in N=1 supersymmetric Yang-Mills theory

We analyse Feynman diagram calculational issues related to the quantum breaking of supercurrent conservation in a supersymmetric non-abelian Yang-Mills theory. For the sake of simplicity, we take a zero mass gauge field multiplet interacting with a massless Majorana spin-$1/2$ field in the adjoint representation of $SU(2)$. We shed light on a long-standing controversy regarding the perturbative evaluation of the supercurrent anomaly in connection with gauge and superconformal symmetry in different frameworks. We find that only superconformal symmetry is unambiguously broken using an invariant four dimensional regularization and compare with the triangle AVV anomaly. Subtleties related to momentum routing invariance in the loops of diagrams and Clifford algebra evaluation inside divergent integrals are also discussed in connection with finite and undetermined quantities in Feynman amplitudes.

hep-th↗

arXiv2018

On the Bose symmetry and the left- and right-chiral anomalies

It is generally assumed that in order to preserve Bose symmetry in the left- (or right-chiral) current it is necessary to equally distribute the chiral anomaly between the vectorial and the axial Ward identities, requiring the use of counterterms to restore consistency. In this work, we show how to calculate the quantum breaking of the left- and right-chiral currents in a way that allows to preserve Bose symmetry independently of the chiral anomaly, using the Implicit Regularization method.

hep-th↗

arXiv2017

The effects of explicit chiral symmetry breaking multiquark interactions on the spin 0 and 1 meson nonets: the ruling of the vector mesons

We have recently extended the scalar-pseudoscalar sector of a generalized NJL Lagrangian that includes all NLO non derivative interactions in Nc counting (including explicit symmetry breaking ones) in order to incorporate the spin 1 mesons in the low-lying ground state of QCD [1]. Upon bosonization, the well known mixing of the scalar-vector and of the pseudoscalar- axial-vector fields occurs in the quadratic part of the Lagrangian. We show that a linearized diagonalization of these terms can be effected in a completely general way without compromising the underlying symmetries of the Lagrangian [2]. The resulting spin 1 mass spectra evidence a relation involving only the vector and axial-vector meson masses and the constituent quark masses. We discuss the dominant role of this relation in the fits and we show that the model may be fitted to accommodate to a very good accuracy the 4 low-lying meson spectra.

hep-ph↗

arXiv2017

A general framework to diagonalize vector--scalar and axial-vector--pseudoscalar transitions in the effective meson Lagrangian

A new mathematical framework for the diagonalization of the nondiagonal vector--scalar and axial-vector--pseudoscalar mixing in the effective meson Lagrangian is described. This procedure has unexpected connections with the Hadamard product of $n\times n$ matrices describing the couplings, masses, and fields involved. The approach is shown to be much more efficient as compared with the standard methods employed previously. The difference is especially noticeable if the chiral symmetry is broken explicitly. The paper ends with an illustrative application to the chiral model with broken $SU(3)_L\times SU(3)_R$ symmetry.

hep-ph↗

arXiv2017

Spin 1 low lying meson spectra and the subtle link to the spin 0 mesons

An NJL-type three-flavor quark model with a complete set of explicit chiral symmetry breaking terms is extended to include vector and axial vector effective interaction terms. The bosonized Lagrangian is written up to quadratic order in the bosonic fields and the role of the new interactions is analysed in detail. The model's parameters are fitted to yield reasonable values to the four low-lying spin 0 and spin 1 meson nonets' masses.

hep-ph↗

arXiv2017

Masses of the lowest spin-0 and spin-1 meson nonets: explicit symmetry breaking effects

We extend a known multi-quark three-flavor Lagrangian of the Nambu-Jona-Lasinio type, which includes a set of effective interactions proportional to the current quark masses, to include the multi-quark interactions of vector and axial-vector types. It is shown that the mass spectrum of the four low-lying meson nonets are in agreement with current phenomenological expectations. The role of the new interactions is analyzed in detail.

hep-ph↗

arXiv2016

$γ_{5}$ algebra ambiguities in Feynman amplitudes: momentum routing invariance and anomalies in $D=4$ and $D=2$

We address the subject of chiral anomalies in two and four dimensional theories. Ambiguities associated with the $γ_5$ algebra within divergent integrals are identified, even though the physical dimension is not altered in the process of regularization. We present a minimal prescription that leads to unique results and apply it to a series of examples. For the particular case of abelian theories with effective chiral vertices, we show: 1- Its implication on the way to display the anomalies democratically in the Ward identities. 2- The possibility to fix an arbitrary surface term in such a way that a momentum routing independent result emerges. This leads to a reinterpretation of the role of momentum routing in the process of choosing the Ward identity to be satisfied in an anomalous process. 3- Momentum Routing Invariance (MRI) is a necessary and sufficient condition to assure vectorial gauge invariance of effective chiral Abelian gauge theories. We also briefly discuss the case of complete chiral theories, using the Chiral Schwinger Model as an example.

hep-th↗

arXiv2016

Entanglement of Vacuum States With the de Sitter Horizon: Consequences on Holographic Dark Energy

The aim of this article is to study the effect of an Event Horizon on the entanglement of the Quantum Vacuum and how entanglement, together with the Holographic Principle, may explain the current value of the Cosmological Constant, in light of recent theories. Entanglement is tested for vacuum states very near and very far from the Horizon of a de Sitter Universe, using the Peres-Horodecki (PPT) criterion. A scalar vacuum field ($\hatϕ$) is averaged inside two boxes of volume $V$ in different spatial positions such that it acquires the structure of a bipartite Quantum Harmonic Oscillator, for which the PPT criterion is a necessary but not sufficient condition of separability. Entanglement is found between states obtained from boxes shaped as spherical shells with thickness of the order of one Planck distance ($l_p$), when one of the states is near the Horizon, and the other state is anywhere in the Universe. Entanglement disappears when the distance of the state near the horizon and the Horizon increases to around $5l_p$. If we consider the Horizon not as a surface but as a spherical shell of thickness $l_p$, then this means that there is entanglement between the states in the Horizon and the rest of the Universe. When both states are at distances larger than $\sim 5 l_p$ from the Horizon, no entanglement is found.

gr-qc↗

arXiv2016

Momentum correlations of scattered particles in quantum field theory: one-loop entanglement generation

We compute the entanglement entropy variation between initial (separable or entangled in the momenta) and final states $ΔS_E$ in an elastic scattering of a bipartite system composed by two interacting scalar particles. We perform a quantum field theoretical calculation to one loop order and verify that $ΔS_E $ changes as we vary the energy of incoming particles and the coupling strength in a non-trivial way.

hep-ph↗

arXiv2016

The $π^0-η-η'$ mixing in a generalized multi-quark interaction scheme

We investigate the isospin symmetry breaking effects within a recently derived Nambu-Jona-Lasinio related model by fitting the measured pseudoscalar meson masses and weak decay couplings $f_π$, $f_K$. Our model contains the next to leading order terms in the $1/N_c$ expansion of the effective multi-quark Lagrangian, including the ones that break the chiral symmetry explicitly. We show the important phenomenological role of these interactions: (1) they lead to an accurate fit of the low-lying pseudoscalar nonet characteristics; (2) they account for a very good agreement of the current quark masses with the present PDG values; (3) they reduce by $40\%$ the ratio $ε/ε'$ of the $π_0-η$ and $π_0-η'$ mixing angles, as compared to the case that contemplates explicit breaking only in the leading order, bringing it in consonance with the quoted values in the literature. The conventional NJL-type models fail in the joint description of these parameters.

hep-ph↗

arXiv2014

Guises and Disguises of Quadratic Divergences

In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale $λ$. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

hep-ph↗

arXiv2013

Naturalness and theoretical constraints on the Higgs boson mass

Arbitrary regularization dependent parameters in Quantum Field Theory are usually fixed on symmetry or phenomenology grounds. We verify that the quadratically divergent behavior responsible for the lack of naturalness in the Standard Model (SM) is intrinsically arbitrary and regularization dependent. While quadratic divergences are welcome for instance in effective models of low energy QCD, they pose a problem in the SM treated as an effective theory in the Higgs sector. Being the very existence of quadratic divergences a matter of debate, a plausible scenario is to search for a symmetry requirement that could fix the arbitrary coefficient of the leading quadratic behavior to the Higgs boson mass to zero. We show that this is possible employing consistency of scale symmetry breaking by quantum corrections. Besides eliminating a fine-tuning problem and restoring validity of perturbation theory, this requirement allows to construct bounds for the Higgs boson mass in terms of $δm^2/m^2_H$ (where $m_H$ is the renormalized Higgs mass and $δm^2$ is the 1-loop Higgs mass correction). Whereas $δm^2/m^2_H<1$ (perturbative regime) in this scenario allows the Higgs boson mass around the current accepted value, the inclusion of the quadratic divergence demands $δm^2/m^2_H$ arbitrarily large to reach that experimental value.

hep-ph↗