arXiv subjects

Antonio Vairo

Publications and source records attributed to Antonio Vairo.

At least 19 recordsLinked to original sources

arXiv2026

Long-distance hybrid spin-dependent and hybrid-quarkonium mixing potentials from lattice gauge theory

We present $SU(3)$ lattice gauge theory results for the $\mathcal{O}(1/m_Q)$ hybrid spin-dependent and hybrid-quarkonium mixing potentials. The only existing lattice computation of these potentials is limited to quark-antiquark separations smaller than approximately $0.5\,\text{fm}$. In this work, we extend the lattice results up to around $1.25 \, \text{fm}$ using large-volume, high-statistics simulations at several lattice spacings and gradient flow times, providing the first lattice data in this previously unexplored regime.

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arXiv2026

Inclusive P-wave Quarkonium Decay Widths from Lattice QCD and pNRQCD

Inclusive hadronic decay widths remain a long-standing challenge for first-principles QCD. We present a framework combining lattice QCD with strongly-coupled potential nonrelativistic QCD (pNRQCD) to compute inclusive P-wave heavy quarkonium decays to light hadrons. At leading order in the velocity expansion, all nonperturbative effects, apart from the square of the derivative of the wavefunction at the origin, are encoded in a single universal moment of the two-point chromoelectric correlator, which we determine for the first time from a quenched lattice QCD calculation matched to $\overline{\mathrm{MS}}$ via the gradient flow. Combined with perturbative short-distance coefficients and the square of the derivative of the wavefunction at the origin, our result reproduces the observed $\chi_{cJ}(1P)$ widths and, at the same time, provides predictions for the unmeasured $\chi_{bJ}(nP)$ widths. The framework extends naturally to inclusive decays and production of ordinary and exotic hadrons.

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arXiv2026

Extraction of charmonium branching fractions from $J/\psi\to\gamma\eta_c$ radiative decays

We assess the tension between theoretical predictions and the values quoted by the Particle Data Group (PDG) for the partial decay width and branching fraction associated with the radiative charmonium decay $J/\psi\to\gamma\eta_c$. A profile scan over the most recent PDG data depending on the branching fraction $\mathcal{B}(J/\psi\to\gamma\eta_c)$ suggests that the correlation between measured branching fractions is compatible with lattice QCD determinations of the partial decay widths $\Gamma(J/\psi\to\gamma\eta_c)$ and $\Gamma(\eta_c\to\gamma\gamma)$. We propose a theoretically grounded photon line shape for the radiative decay spectrum and a prescription for the extraction of (product) branching fractions involving the magnetic dipole (M1) transition $J/\psi\to\gamma\eta_c$. This approach obviates the need to modify the photon energy spectrum line shape using empirical damping functions, as done in the most recent experimental extractions of $\mathcal{B}(J/\psi\to\gamma\eta_c)$ from the photon line shape, thereby eliminating an inherent ambiguity in the determination of the derived observables.

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arXiv2026

Open-flavor threshold effects on quarkonium spectrum in the BOEFT

The impact of open-flavor thresholds on the quarkonium spectrum has been a subject of study since the introduction of the Cornell potential and has been quantified through various phenomenological approaches, most notably the $^3P_0$ model. We revisit this problem using the Born--Oppenheimer effective field theory (BOEFT), an effective field theory systematically derived from QCD by exploiting hierarchies of energy scales and symmetries. Within the BOEFT, open-flavor threshold effects emerge from the mixing between quarkonium and tetraquark static potentials sharing the same Born--Oppenheimer quantum numbers. The shapes of the static potentials are constrained by lattice QCD calculations. Furthermore, we account for the distinctive behavior of the BOEFT tetraquark static potentials at short and large distances: at short distances they are repulsive, reflecting the color-octet configuration of the heavy quark-antiquark pair, while at large distances they asymptotically approach heavy-light meson-antimeson thresholds. To quantify threshold effects on the quarkonium spectrum below threshold, we solve a set of coupled Schr\"{o}dinger equations dictated by the BOEFT, whose only free parameter, the adjoint meson mass, is fixed to the mass of the $\chi_{c1}(3872)$ state. These coupled equations are solved both in the spin-isospin averaged threshold limit and, for the first time, including the spin splittings of the physical thresholds. We validate our results by computing the same threshold effects as self-energy corrections to the quarkonium propagator. We compare our predictions with existing experimental data and previous literature. Finally, we provide a field-theoretical interpretation of the pair-creation constant $\gamma$ appearing in the $^3P_0$ model.

hep-ph↗

arXiv2026

Strong coupling constant from the 1-loop improved static energy

The static energy is an excellent observable for extracting the strong coupling $\alpha_s$ on the lattice. For short distances, the static energy can be calculated both on the lattice using Wilson line correlators, and with perturbation theory up to three loop accuracy with leading ultrasoft log resummation. Comparing the perturbative expression and lattice data allows for precise determination of $\alpha_s$. We present early results for 1-loop lattice perturbation theory improvement of the Wilson loop and show how it improves the $\alpha_s$ extraction. We present a preliminary reanalysis of the TUMQCD (2+1)-flavor QCD data.

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arXiv2026

Inclusive hadroproduction of $\chi_{c1}(3872)$, $X_b$ and pentaquarks

We use the Born--Oppenheimer effective field theory factorization to compute the inclusive production cross sections of the $\chi_{c1}(3872)$ and its partner in the bottomonium sector. In the same framework, we compute the production cross sections of the pentaquark states $P_{c\bar{c}}(4312)^+$, $P_{c\bar{c}}(4457)^+$, $P_{c\bar{c}}(4380)^+$ and $P_{c\bar{c}}(4440)^+$ within two possible scenarios for the Born--Oppenheimer potentials. Also for pentaquarks, we extend the results to the bottomonium sector. All our results are genuine predictions that do not involve fits to prompt hadroproduction data.

hep-ph↗

arXiv2025

Born-Oppenheimer EFT: a unified description of ordinary and exotic quarkonia

We show how the Born-Oppenheimer effective field theory (BOEFT) provides a unified description of ordinary and exotic quarkonia grounded on the non-relativistic expansions of QCD and supplemented with lattice QCD inputs. We apply BOEFT to tetraquarks, pentaquarks, quarkonium hybrids and to assess threshold effects in the quarkonium spectrum.

hep-ph↗

arXiv2025

Unravelling Pentaquarks with Born--Oppenheimer effective theory

The hidden-charm pentaquark states $P_{c\bar{c}}\left(4312\right)^+$, $P_{c\bar{c}}\left(4380\right)^+$, $P_{c\bar{c}}\left(4440\right)^+$, and $P_{c\bar{c}}\left(4457\right)^+$, all with isospin $I = 1/2$, were discovered by the LHCb collaboration in the decay process $\Lambda_b^0 \to J/\psi p K^-$. Although their quantum numbers remain undetermined, these states have generated significant theoretical interest. We analyze their spectrum and decay patterns-including those of their spin partners-within the Born--Oppenheimer effective field theory (BOEFT), a framework grounded in QCD. At leading order in BOEFT, we identify these pentaquark states as bound states in BO potentials that exhibit at short-distance a repulsive octet behavior and a nonperturbative shift due to the adjoint baryons masses, while asymptotically approaching the $\Sigma_c\bar{D}$ threshold. We further incorporate ${\cal O}(1/m_Q)$ spin-dependent corrections to compute pentaquark multiplet spin splittings. Based on the spectrum, semi-inclusive decay widths to $J/\psi$ and $\eta_c$, and the decay width ratios to $\Lambda_c\bar{D}$ and $\Lambda_c\bar{D}^*$, we provide the first theoretical predictions for the adjoint baryon masses, which can be confirmed by future lattice QCD studies. Moreover, our analysis supports the quantum number assignments: $J^{P} = (1/2)^-$ for $P_{c\bar{c}}\left(4312\right)^+$, $(3/2)^-$ for $P_{c\bar{c}}\left(4380\right)^+$, $(1/2)^-$ for $P_{c\bar{c}}\left(4457\right)^+$, and $(3/2)^-$ for $P_{c\bar{c}}\left(4440\right)^+$. We also present results for the lowest bottom pentaquarks.

hep-ph↗

arXiv2025

Thermalization of Bottomonium in the Quark-Gluon Plasma

We study the approach to equilibrium of bottomonium in the quark-gluon plasma within the open quantum system framework. We perform large-scale simulations of the long-time behavior in three dimensions using the quantum trajectory method to observe the emergence of steady states and determine the timescale of thermalization in position-, angular-momentum-, and color-space. We find that the thermalization timescale increases with decreasing temperature and decreasing coupling to the medium, which is given by transport coefficients of the medium. Additionally, we observe that the steady states exhibit small corrections to the Gibbs state due to medium interactions and show that these corrections diminish for weaker medium coupling and higher temperature. At a temperature of $450\,$MeV, quarkonium relaxes to a state that is approximately thermal, with the most significant correction being a smaller overlap of the $1S$ state with respect to the Gibbs state. We compare these findings with the master equation obtained at leading order in the expansion of the binding energy over the temperature, which we find to have a trivial steady state.

hep-ph↗

arXiv2025

Lattice study of correlators for quarkonium decay

While there has been a lot of progress in developing a formalism for the study of quarkonia in QGP, a nonperturbative study is still difficult. For bottomonia, where the system size is much less than the inverse temperature, the interaction of the system with the medium can be approximated by a dipole interaction with the color electric field. The decay of the quarkonia can be connected to a correlation function of the color electric field. We present preliminary results from a lattice study of the relevant color electric field correlator. The structure of the correlator, and its difference from the corresponding correlator studied for heavy quark diffusion, is discussed.

hep-lat↗

arXiv2025

Lattice study of correlators of chromoelectric fields for heavy quarkonium dynamics in the quark-gluon plasma

We perform a lattice calculation of the correlators of two chromoelectric fields in the adjoint representation connected by adjoint Wilson lines at non-zero temperature. These correlators arise in the study of quarkonium dynamics and of adjoint heavy quark diffusion in deconfined matter. We work in SU(3) gauge theory using either gradient flow or multi-level algorithms for noise reduction, and discuss the renormalization of the correlators on the lattice. We find that a Casimir factor rescaling relates the adjoint correlators corresponding to the diffusion of an adjoint heavy quark and the octet-octet quarkonium transitions to the chromoelectric correlator in the fundamental representation describing the diffusion of a heavy quark.

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arXiv2025

The chromoelectric adjoint correlators in Euclidean space at next-to-leading order

The physics of quarkonium created in heavy-ion collisions is intrinsically connected to the correlation functions of adjoint chromoelectric fields in quantum chromodynamics. We study such correlation functions in a weak-coupling expansion in a thermal medium. We identify three distinct gauge-invariant correlators, and evaluate them to next-to-leading order. Two of the resulting correlators turn out to be asymmetric. We pinpoint the source of this asymmetry to Matsubara zero modes associated with Wilson lines. The results are shown to agree well with recent lattice calculations at high temperatures.

hep-ph↗

arXiv2025

Bottomonium suppression in pNRQCD and open quantum system approach

By employing the potential non-relativistic quantum chromodynamics (pNRQCD) effective field theory within an open quantum system framework, we derive a Lindblad equation governing the evolution of the heavy-quarkonium reduced density matrix, accurate to next-to-leading order (NLO) in the ratio of the state's binding energy to the medium's temperature [1]. The derived NLO Lindblad equation provides a more reliable description of heavy-quarkonium evolution in the quark-gluon plasma at low temperatures compared to the leading-order truncation. For phenomenological applications, we numerically solve this equation using the quantum trajectories algorithm. By averaging over Monte Carlo-sampled quantum jumps, we obtain solutions without truncation in the angular momentum quantum number of the considered states. Our analysis highlights the importance of quantum jumps in the nonequilibrium evolution of bottomonium states within the quark-gluon plasma [2]. Additionally, we demonstrate that the quantum regeneration of singlet states from octet configurations is essential to explain experimental observations of bottomonium suppression. The heavy-quarkonium transport coefficients used in our study align with recent lattice QCD determinations.

hep-ph↗

arXiv2025

Strong coupling in (2+1+1)-flavor QCD

The strong coupling $\alpha_\mathrm{s}$ can be obtained from the static energy as shown in previous lattices studies. For short distances, the static energy can be calculated both on the lattice with the use of Wilson line correlators, and with the perturbation theory up to three loop accuracy with leading ultrasoft log resummation. Comparing the perturbative expression and lattice data allows for precise determination of $\alpha_\mathrm{s}(m_Z)$. We will present preliminary results for the determination of $\alpha_\mathrm{s} {(M_Z)}$ in (2+1+1)-flavor QCD using the configurations made availableby the MILC-collaboration with smallest lattice spacing reaching 0.0321fm.

hep-lat↗

arXiv2025

Effective field theories for dark matter pairs in the early universe: Debye mass effects

In some scenarios for the early universe, non-relativistic thermal dark matter chemically decouples from the thermal environment once the temperature drops well below the dark matter mass. The value at which the energy density freezes out depends on the underlying model. In a simple setting, we provide a comprehensive study of heavy fermionic dark matter interacting with the light degrees of freedom of a dark thermal sector whose temperature $T$ decreases from an initial value close to the freeze-out temperature. Different temperatures imply different hierarchies of energy scales. By exploiting the methods of non-relativistic effective field theories at finite $T$, we systematically determine the thermal and in-vacuum interaction rates. In particular, we address the impact of the Debye mass on the observables and ultimately on the dark matter relic abundance. We numerically compare the corrections to the present energy density originating from the resummation of Debye mass effects with the corrections coming from a next-to-leading order treatment of the bath-particle interactions. We observe that the fixed-order calculation of the inelastic heavy-light scattering at high temperatures provides a larger dark matter depletion, and hence an undersized yield for given benchmark points in the parameter space, with respect to the calculation where Debye mass effects are resummed.

hep-ph↗

arXiv2024

The nature of $\chi_{c1}\left(3872\right)$ and $T_{cc}^+\left(3875\right)$

Two decades ago the $\chi_{c1}\left(3872\right)$ was discovered in the hadron spectrum with two heavy quarks. The discovery fueled a surge in experimental research, uncovering dozens of so called XYZ exotics states lying outside the conventional quark model, as well as theoretical investigations into new forms of matter, such as quark-gluon hybrids, tetraquarks, pentaquarks, with the potential of disclosing new information about the fundamental strong force. Among the XYZs, the $\chi_{c1}\left(3872\right)$ and $T_{cc}^+\left(3875\right)$ stand out for their striking characteristics and unlashed many discussions about their nature. Here, we address this question using the Born--Oppenheimer Effective Field Theory (BOEFT) and show how QCD settles the issue of their composition. Not only we describe well the main features of the $\chi_{c1}\left(3872\right)$ and $T_{cc}^+\left(3875\right)$ but obtain also predictions in the bottomonium sector. This opens the way to systematic applications of BOEFT to all XYZs.

hep-ph↗

arXiv2024

One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium

The discovery of XYZ exotic states in the hadronic sector with two heavy quarks, represents a significant challenge in particle theory. Understanding and predicting their nature remains an open problem. In this work, we demonstrate how the Born$-$Oppenheimer (BO) effective field theory (BOEFT), derived from Quantum Chromodynamics (QCD) on the basis of scale separation and symmetries, can address XYZ exotics of any composition. We derive the Schr\"odinger coupled equations that describe hybrids, tetraquarks, pentaquarks, doubly heavy baryons, and quarkonia at leading order, incorporating nonadiabatic terms, and present the predicted multiples. We define the static potentials in terms of the QCD static energies for all relevant cases. We provide the precise form of the nonperturbative low-energy gauge-invariant correlators required for the BOEFT: static energies, generalized Wilson loops, gluelumps, and adjoint mesons. These are to be calculated on the lattice and we calculate here their short-distance behavior. Furthermore, we outline how spin-dependent corrections and mixing terms can be incorporated using matching computations. Lastly, we discuss how static energies with the same BO quantum numbers mix at large distances leading to the phenomenon of avoided level crossing. This effect is crucial to understand the emergence of exotics with molecular characteristics, such as the $\chi_{c1}(3872)$. With BOEFT both the tetraquark and the molecular picture appear as part of the same description.

hep-ph↗

arXiv2024

Bottomonium suppression from the three-loop QCD potential

We compute the suppression of bottomonium in the quark-gluon plasma using the three-loop QCD static potential. The potential describes the spin-averaged bottomonium spectrum below threshold with a less than 1% error. Within potential nonrelativistic quantum chromodynamics and an open quantum systems framework, we compute the evolution of the bottomonium density matrix. The values of the quarkonium transport coefficients are obtained from lattice QCD measurements of the bottomonium in-medium width and thermal mass shift; we additionally include for the first time a vacuum contribution to the dispersive coefficient $γ$. Using the three-loop potential and the values of the heavy quarkonium transport coefficients, we find that the resulting bottomonium nuclear modification factor is consistent with experimental observations, while at the same time reproducing the lattice measurements of the in-medium width.

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