arXiv subjects

Ramon Miravitllas

Publications and source records attributed to Ramon Miravitllas.

12 recordsLinked to original sources

arXiv2025

The complete trans-series for conserved charges in the Lieb-Liniger model

We determine the complete trans-series solution for the (non-relativistic) moments of the rapidity density in the Lieb-Liniger model. The trans-series is written explicitly in terms of a perturbative basis, which can be obtained from the already known perturbative expansion of the density by solving several ordinary differential equations. Unknown integration constants are fixed from Volin's method. We have checked that our solution satisfies the analytical consistency requirements including the newly derived resurgence relations and agrees with the high precision numerical solution. Our results also provides the full analytic trans-series for the capacitance of the coaxial circular plate capacitor.

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arXiv2024

Trans-series from condensates

The Shifman-Vainshtein-Zakharov (SVZ) sum rules provide a method to obtain trans-series expansions in many quantum field theories, in which exponentially small corrections are calculated by combining the operator product expansion with the assumption of vacuum condensates. In some solvable models, exact expressions for trans-series can be obtained from non-perturbative results, and this makes it possible to test the SVZ method by comparing its predictions to these exact trans-series. In this paper we perform such a precision test in the example of the fermion self-energy in the Gross-Neveu model. Its exact trans-series expansion can be extracted from the large $N$ solution, at the first non-trivial order in $1/N$. It is given by an infinite series of exponentially small corrections involving factorially divergent power series in the 't Hooft parameter. We show that the first two corrections are associated to two-quark and four-quark condensates, and we reproduce the corresponding power series exactly, and at all loops, by using the SVZ method. In addition, the numerical values of the condensates can be extracted from the exact result, up to order $1/N$.

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arXiv2023

Instantons, renormalons and the theta angle in integrable sigma models

Some sigma models which admit a theta angle are integrable at both $\vartheta=0$ and $\vartheta=π$. This includes the well-known $O(3)$ sigma model and two families of coset sigma models studied by Fendley. We consider the ground state energy of these models in the presence of a magnetic field, which can be computed with the Bethe ansatz. We obtain explicit results for its non-perturbative corrections and we study the effect of the theta angle on them. We show that imaginary, exponentially small corrections due to renormalons remain unchanged, while instanton corrections change sign, as expected. We find in addition corrections due to renormalons which also change sign as we turn on the theta angle. Based on these results we present an explicit non-perturbative formula for the topological susceptibility of the $O(3)$ sigma model in the presence of a magnetic field, in the weak coupling limit.

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arXiv2023

Large N instantons from topological strings

The $1/N$ expansion of matrix models is asymptotic, and it requires non-perturbative corrections due to large $N$ instantons. Explicit expressions for large $N$ instanton amplitudes are known in the case of Hermitian matrix models with one cut, but not in the multi-cut case. We show that the recent exact results on topological string instanton amplitudes provide the non-perturbative contributions of large $N$ instantons in generic multi-cut, Hermitian matrix models. We present a detailed test in the case of the cubic matrix model by considering the asymptotics of its $1/N$ expansion, which we obtain at relatively high genus for a generic two-cut background. These results can be extended to certain non-conventional matrix models which admit a topological string theory description. As an application, we determine the large $N$ instanton corrections for the free energy of ABJM theory on the three-sphere, which correspond to D-brane instanton corrections in superstring theory. We also illustrate the applications of topological string instantons in a more mathematical setting by considering orbifold Gromov-Witten invariants. By focusing on the example of $\mathbb{C}^3/\mathbb{Z}_3$, we show that they grow doubly-factorially with the genus and we obtain and test explicit asymptotic formulae for them.

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arXiv2023

New renormalons from analytic trans-series

We study the free energy of integrable, asymptotically free field theories in two dimensions coupled to a conserved charge. We develop methods to obtain analytic expressions for its trans-series expansion, directly from the Bethe ansatz equations, and we use this result to determine the structure of its Borel singularities. We find a new class of infrared renormalons which does not fit the traditional expectations of renormalon physics proposed long ago by 't Hooft and Parisi. We check the existence of these new singularities with detailed calculations based on the resurgent analysis of the perturbative expansion. Our results show that the structure of renormalons in asymptotically free theories is more subtle than previously thought, and that large $N$ estimates of their location might be misleading.

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arXiv2023

On the Structure of Trans-Series in Quantum Field Theory

Many observables in quantum field theory can be expressed in terms of trans-series, in which one adds to the perturbative series a typically infinite sum of exponentially small corrections, due to instantons or to renormalons. Even after Borel resummation of the series in the coupling constant, one has to sum this infinite series of small exponential corrections. It has been argued that this leads to a new divergence, which is sometimes called the divergence of the OPE. We show that, in some interesting examples in quantum field theory, the series of small exponential corrections is convergent, order by order in the coupling constant. In particular, we give numerical evidence for this convergence property in the case of the free energy of integrable asymptotically free theories, which has been intensively studied recently in the framework of resurgence. Our results indicate that, in these examples, the Borel resummed trans-series leads to a well defined function, and there are no further divergences.

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arXiv2021

Testing the Bethe ansatz with large N renormalons

The ground state energy of integrable asymptotically free theories can be conjecturally computed by using the Bethe ansatz, once the theory has been coupled to an external potential through a conserved charge. This leads to a precise prediction for the perturbative expansion of the energy. We provide a non-trivial test of this prediction in the non-linear sigma model and its supersymmetric extension, by calculating analytically the associated Feynman diagrams at next-to-leading order in the $1/N$ expansion, and at all loops. By investigating the large order behaviour of the diagrams, we locate the position of the renormalons of the theory and we obtain an analytic expression for the large $N$ trans-series associated to each. As a spin-off of our calculation, we provide a direct derivation of the beta function of these theories, at next-to-leading order in the $1/N$ expansion.

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arXiv2018

Absence of even-integer $ζ$-function values in Euclidean physical quantities in QCD

At order $α_s^4$ in perturbative quantum chromodynamics, even-integer $ζ$-function values are present in Euclidean physical correlation functions like the scalar quark correlation function or the scalar gluonium correlator. We demonstrate that these contributions cancel when the perturbative expansion is expressed in terms of the so-called $C$-scheme coupling $\hatα_s$ which has recently been introduced in Ref. [1]. It is furthermore conjectured that a $ζ_4$ term should arise in the Adler function at order $α_s^5$ in the $\overline{\rm MS}$-scheme, and that this term is expected to disappear in the $C$-scheme as well.

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arXiv2016

Scheme variations of the QCD coupling and tau decays

The QCD coupling, $α_s$, is not a physical observable since it depends on conventions related to the renormalization procedure. Here we discuss a redefinition of the coupling where changes of scheme are parametrised by a single parameter $C$. The new coupling is denoted $\hat α_s$ and its running is scheme independent. Moreover, scheme variations become completely analogous to renormalization scale variations. We discuss how the coupling $\hat α_s$ can be used in order to optimize predictions for the inclusive hadronic decays of the tau lepton. Preliminary investigations of the $C$-scheme in the presence of higher-order terms of the perturbative series are discussed here for the first time.

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arXiv2016

Scheme variations of the QCD coupling

The Quantum Chromodynamics (QCD) coupling $α_s$ is a central parameter in the Standard Model of particle physics. However, it depends on theoretical conventions related to renormalisation and hence is not an observable quantity. In order to capture this dependence in a transparent way, a novel definition of the QCD coupling, denoted by $\hat a$, is introduced, whose running is explicitly renormalisation scheme invariant. The remaining renormalisation scheme dependence is related to transformations of the QCD scale $Λ$, and can be parametrised by a single parameter $C$. Hence, we call $\hat a$ the $C$-scheme coupling. The dependence on $C$ can be exploited to study and improve perturbative predictions of physical observables. This is demonstrated for the QCD Adler function and hadronic decays of the $τ$ lepton.

hep-ph↗

arXiv2016

Scalar correlator, Higgs decay into quarks, and scheme variations of the QCD coupling

In this work, the perturbative QCD series of the scalar correlation function $Ψ(s)$ is investigated. Besides ${\rm Im}Ψ(s)$, which is relevant for Higgs decay into quarks, two other physical correlators, $Ψ^{"}(s)$ and $D^L(s)$, have been employed in QCD applications like quark mass determinations or hadronic $τ$ decays. $D^L(s)$ suffers from large higher-order corrections and, by resorting to the large-$β_0$ approximation, it is shown that this is related to a spurious renormalon ambiguity at $u=1$. Hence, this correlator should be avoided in phenomenological analyses. Moreover, it turns out advantageous to express the quark mass factor, introduced to make the scalar current renormalisation group invariant, in terms of the renormalisation invariant quark mass $\hat m_q$. To further study the behaviour of the perturbative expansion, we introduce a QCD coupling $\hatα_s$, whose running is explicitly renormalisation scheme independent. The scheme dependence of $\hatα_s$ is parametrised by a single parameter $C$, being related to transformations of the QCD scale parameter $Λ$. It is demonstrated that appropriate choices of $C$ lead to a substantial improvement in the behaviour of the perturbative series for $Ψ^{"}(s)$ and ${\rm Im}Ψ(s)$.

hep-ph↗

arXiv2016

Scheme variations of the QCD coupling and hadronic $τ$ decays

The Quantum Chromodynamics (QCD) coupling, $α_s$, is not a physical observable of the theory since it depends on conventions related to the renormalization procedure. We introduce a definition of the QCD coupling, denoted by $\hatα_s$, whose running is explicitly renormalization scheme invariant. The scheme dependence of the new coupling $\hatα_s$ is parameterized by a single parameter $C$, related to transformations of the QCD scale $Λ$. It is demonstrated that appropriate choices of $C$ can lead to substantial improvements in the perturbative prediction of physical observables. As phenomenological applications, we study $e^+e^-$ scattering and decays of the $τ$ lepton into hadrons, both being governed by the QCD Adler function.

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