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Antonio Pineda

Publications and source records attributed to Antonio Pineda.

At least 19 recordsLinked to original sources
arXiv2026

Hyperasymptotic Expansions in QCD: The Lightest Gluelump Mass Case

In these proceedings, we provide a summary of our recent advancements in determining the mass of the lightest gluelump using hyperasymptotic expansions in Quantum Chromodynamics (QCD) \cite{Ayala2025}. This paper details our methodology, our precise determination of leading renormalon normalization constants, and our extraction of the gluelump mass from two independent physical systems, yielding a final combined, renormalization-group-invariant and scheme-independent result of $Λ_{B}^{\rm PV} = 2.44(7) r_0^{-1}$.

hep-ph↗
arXiv2026

The ultrafine splitting of heavy quarkonium with next-to-next-to-next-to-next-to-leading-order accuracy

We compute the hyperfine splitting of P-wave heavy quarkonium states with next-to-next-to-next-to-next-to-leading-order accuracy. The resummation of logarithms with next-to-next-to-next-to-next-to-leading-logarithmic accuracy is also addressed. A phenomenological analysis of these results is performed for bottomonium, charmonium and the $B_c$ system. We also apply these results to positronium, muonium, hydrogen and muonic hydrogen.

hep-ph↗
arXiv2026

Relativity: A matter of causality

We take causality and uniqueness of events observation as our driving forces. They are built in in the way we define distinct observers, which then require a finite time to communicate between each other. This unavoidably leads to the existence of maximal transfer-information velocity between arbitrary (not necessarily inertial) reference frames. Inertial reference frames are defined by fixing the geometrical properties of (spatial) distance without any reference to relativity, electromagnetism, or laws of physics in general. For these inertial reference frames, the causality condition fixes the causal group to be the orthochronous inhomogeneous Lorentz group times dilatations. The mathematics we will use are quite basic.

physics.gen-ph↗
arXiv2026

The chromomagnetic moment of a heavy quark with hyperasymptotic precision

We determine the normalization of the leading infrared renormalon of the chromomagnetic moment of a heavy quark. Estimates of higher order coefficients of the perturbative series are given. We compute the hyperfine splitting of the $B$ and $D$ mesons for the ground state with hyperasymptotic precision by including the leading terminant, associated with the first infrared renormalon. We fit the experimental data to the operator product expansion theoretical prediction with $\hat μ^2_{G,\rm PV}$ as the free parameter. We obtain $\hat μ^2_{G,\rm PV}=0.507(7)$ GeV$^2$ for the ground state.

hep-ph↗
arXiv2025

The mass of the lightest gluelump

We give the most up-to-date determinations of the normalization of the leading renormalons of the pole mass, the singlet static potential, the octet static potential, and the gluelump energy. They read $Z^{\rm MS}_m=-Z^{\rm MS}_{V_s}/2=\{0.604(17),0.551(20)\}$, $Z^{\rm MS}_{V_o}=\{0.136(8),0.121(13)\}$, and $Z^{\rm MS}_A=\{-1.343(36),-1.224(43)\}$, for $n_f=0$ and $n_f=3$ respectively. We obtain two independent renormalization group invariant and renormalization scale independent determinations of the energy of the ground state gluelump in the principal value summation scheme: $Λ_{B}^{\rm PV}=2.47(9)r_0^{-1}$ and $Λ_{B}^{\rm PV}=2.38(11)r_0^{-1}$. They combine in $Λ_{B}^{\rm PV}=2.44(7)r_0^{-1}$.

hep-ph↗
arXiv2022

Bjorken sum rule with hyperasymptotic precision

We obtain an improved determination of the normalization of the leading infrared renormalon of the Bjorken sum rule: $Z_B (n_f=3)= -0.407\pm 0.119 $. Estimates of higher order terms of the perturbative series are given. We compute the Bjorken sum rule with hyperasymptotic precision by including the leading terminant, associated with the first infrared renormalon. We fit the experimental data to the operator product expansion theoretical prediction with $\hat f_{3}^{\rm PV}$ as the free parameter. We obtain a good agreement with the experiment with $\hat f_{3}^{\rm PV}\times 10^3=32^{+187}_{-196}\;{\rm GeV}^{2}$ for $Q^2 \geq 1$ GeV$^2$.

hep-ph↗
arXiv2021

The proton radius (puzzle?) and its relatives

We review determinations of the electric proton charge radius from a diverse set of low-energy observables. We explore under which conditions it can be related to Wilson coefficients of appropriate effective field theories. This discussion is generalized to other low-energy constants. This provides us with a unified framework to deal with a set of low-energy constants of the proton associated with its electromagnetic interactions. Unambiguous definitions of these objects are given, as well as their relation with expectation values of QCD operators. We show that the proton radius obtained from spectroscopy and lepton-proton scattering (when both the lepton and proton move with nonrelativistic velocities) is related to the same object of the underlying field theory with ${\cal O}(α)$ precision. The model dependence of these analyses is discussed. The prospects of constructing effective field theories valid for the kinematic configuration of present, or near-future, lepton-proton scattering experiments are discussed.

hep-ph↗
arXiv2021

Theoretical description of the plaquette with exponential accuracy

We review recent studies of the operator product expansion of the plaquette and of the associated determination of the gluon condensate. One first needs the perturbative expansion to orders high enough to reach the asymptotic regime where the renormalon behavior sets in. The divergent perturbative series is formally regulated using the principal value prescription for its Borel integral. Subtracting the perturbative series truncated at the minimal term, we obtain the leading non-perturbative correction of the operator product expansion, i.e. the gluon condensate, with superasymptotic accuracy. It is then explored how to increase such precision within the context of the hyperasymptotic expansion. The results fully confirm expectations from renormalons and the operator product expansion.

hep-ph↗
arXiv2020

Hyperasymptotic approximation to the plaquette and determination of the gluon condensate

We give the hyperasymptotic expansion of the plaquette with a precision that includes the terminant associated to the leading renormalon. Subleading effects are also considered. The perturbative series is regulated using the principal value prescription for its Borel integral. We use this analysis to give a determination of the gluon condensate in SU(3) pure gluodynamics that is independent of the scale and renormalization scheme used for the coupling constant: $\langle G^2 \rangle_{\rm PV} (n_f=0)=3.15(18)\; r_0^{-4}$.

hep-ph↗
arXiv2020

Determination of $α(M_z)$ from an hyperasymptotic approximation to the energy of a static quark-antiquark pair

We give the hyperasymptotic expansion of the energy of a static quark-antiquark pair with a precision that includes the effects of the subleading renormalon. The terminants associated to the first and second renormalon are incorporated in the analysis when necessary. In particular, we determine the normalization of the leading renormalon of the force and, consequently, of the subleading renormalon of the static potential. We obtain $Z_3^F(n_f=3)=2Z_3^V(n_f=3)=0.37(17)$. The precision we reach in strict perturbation theory is next-to-next-to-next-to-leading logarithmic resummed order both for the static potential and for the force. We find that the resummation of large logarithms and the inclusion of the leading terminants associated to the renormalons are compulsory to get accurate determinations of $Λ_{\overline{\rm MS}}$ when fitting to short-distance lattice data of the static energy. We obtain $Λ_{\overline{\rm MS}}^{(n_f=3)}=338(12)$ MeV and $α(M_z)=0.1181(9)$. We have also found strong consistency checks that the ultrasoft correction to the static energy can be computed at weak coupling in the energy range we have studied.

hep-ph↗
arXiv2020

Hyperasymptotic approximation to the top, bottom and charm pole mass

We construct hyperasymptotic expansions for the heavy quark pole mass regulated using the principal value (PV) prescription. We apply such hyperasymptotic expansions to the $B/D$ meson masses, and $\bar Λ$ computed in the lattice. The issue of the uncertainty of the (top) pole mass is critically reexamined. The present theoretical uncertainty in the relation between ${\bar m}_t$, the $\bar{\rm MS}$ top mass, and $m_{t, \rm PV}$, the top pole mass regulated using the PV prescription, is numerically assessed to be $δm_{t,\rm PV}= 28\;{\rm MeV}$ for ${\bar m}_t =163$ GeV.

hep-ph↗
arXiv2019

Novel implementation of the multipole expansion to quarkonium hadronic transitions

We compute hadronic transitions between heavy quarkonium states with two, or one, pion/eta particles in the final state. We use the multipole expansion but not the twist expansion. The latter cannot be justified for the energy release of hadronic transitions between heavy quarkonium states with different principal quantum numbers. Instead, we use a counting based on the dimension of the interpolating field of the hybrid. This alternative counting allows us to still use chiral low-energy theorems to compute the pion production by local gluonic operators. We explore the phenomenological impact of this counting. Remarkably enough, for the two-pion transitions, we obtain the same predictions for the normalized differential decay rate as those obtained assuming the twist expansion. We implement this computational scheme using the hadronic representation of the effective theory potential NRQCD. We assume that the inverse Bohr radius of the heavy quarkonium is much larger than $Λ_{\rm QCD}$ but do not impose any constraint on the relative size of $Λ_{\rm QCD}$ and the typical kinetic energy of the bound state.

hep-ph↗
arXiv2019

Superasymptotic and hyperasymptotic approximation to the operator product expansion

Given an observable and its operator product expansion (OPE), we present expressions that carefully disentangle truncated sums of the perturbative series in powers of $α$ from the non-perturbative (NP) corrections. This splitting is done with NP power accuracy. Analytic control of the splitting is achieved and the organization of the different terms is done along an super/hyper-asymptotic expansion. As a test we apply the methods to the static potential in the large $β_0$ approximation. We see the superasymptotic and hyperasymptotic structure of the observable in full glory.

hep-th↗
arXiv2018

P-wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy

We compute the heavy quarkonium mass of $l\not= 0$ (angular momentum) states, with otherwise arbitrary quantum numbers, with next-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. This constitutes the first observable in heavy quarkonium for which two orders of the weak-coupling expansion sensitive to the ultrasoft scale are known and the resummation of ultrasoft logarithms is made. We also obtain, for the first time, resummed N$^3$LL expressions for the different fine and hyperfine energy splittings of these states, which are not sensitive to the ultrasoft scale but still require resummation of (hard) logarithms. We do this analysis for the equal and non-equal mass cases. We also study an alternative computational scheme that treats the static potential exactly. We then perform a comprehensive phenomenological analysis: we apply these results to the $n=2$, $l=1$ bottomonium, $B_c$ and charmonium systems and study their convergence.

hep-ph↗
arXiv2018

Potential NRQCD for unequal masses and the $B_c$ spectrum at NNNLO

We determine the $1/m$ and $1/m^2$ spin-independent heavy quarkonium potentials in the unequal mass case with $\mathcal O(α^3)$ and $\mathcal O(α^2)$ accuracy, respectively. We discuss in detail different methods to calculate the potentials, and show the equivalence among them. In particular we obtain, for the first time, the manifestly gauge invariant $1/m$ and $1/m^2$ potentials in terms of Wilson loops with next-to-leading order (NLO) precision. As an application of our results we derive the theoretical expression for the $B_c$ spectrum in the weak-coupling limit through next-to-next-to-next-to-leading order (N$^3$LO).

hep-ph↗
arXiv2018

The charm/bottom quark mass from heavy quarkonium at N$^3$LO

We determine the charm and bottom quark masses using the N$^3$LO perturbative expression of the ground state (pseudoscalar) energy of the bottomonium, charmonium and $B_c$ systems: the $η_b$, $η_c$ and $B_c$ masses. We work in the renormalon subtracted scheme, which allows us to control the divergence of the perturbation series due to the pole mass renormalon. Our result for the $\overline{\rm MS}$ masses reads ${\overline m}_{c}({\overline m}_{c})=1223(33)$ MeV and ${\overline m}_{b}({\overline m}_{b})=4186(37)$ MeV. We also extract a value of $α_s$ from a renormalon-free combination of the $η_b$, $η_c$ and $B_c$ masses: $α_s(M_z)=0.1195(53)$. We explore the applicability of the weak coupling approximation to bottomonium $n=2$ states. Finally, we consider an alternative computational scheme that treats the static potential exactly and study its convergence properties.

hep-ph↗
arXiv2018

The chromo-polarizabilities of a heavy quark at weak coupling

We obtain the renormalization group improved expressions of the Wilson coefficients of the HQET Lagrangian with leading logarithmic approximation to ${\cal O}(1/m^3)$ for the spin-independent sector, which includes the heavy quark chromo-polarizabilites. Our analysis includes the effects induced by spectator quarks. We observe that the numerical impact of these logarithms is very large in most cases.

hep-ph↗