arXiv subjects

Nora Brambilla

Publications and source records attributed to Nora Brambilla.

At least 19 recordsLinked to original sources

arXiv2026

Quarkoniumlike states above open-flavor thresholds in Born-Oppenheimer EFT

Many quarkoniumlike states have been observed above open-flavor thresholds, but their organization and internal structure remain unsettled. We study the isoscalar hidden-charm and hidden-bottom sectors in Born--Oppenheimer effective field theory (BOEFT), between the spin--isospin averaged $S+S$ and $S+P$ thresholds. At leading order, heavy-quark spin decouples, and the quarkonium static potential mixes through string breaking with the lowest tetraquark/open-flavor BO potentials of the same quantum numbers. These potentials are constrained by QCD symmetries, their short- and long-distance behavior, and lattice-QCD data. The only calibrated parameter is the lowest $1^{--}$ adjoint meson mass, fixed from the shallow multiplet associated with the $\chi_{c1}(3872)$. Using $T$-matrix, $K$-matrix, and complex-scaling methods, we determine bound states and resonance poles, their masses, pole widths from the included nonstrange $S+S$ channels, normalized pole couplings, and prescription-dependent quarkonium--open-flavor composition measures. Uncoupled hybrid BOEFT multiplets are included as reference levels. The spectrum exhibits a common heavy-quark-spin-symmetry multiplet organization. Most poles are predominantly quarkonium resonances localized at short distances, with the largest open-flavor components closest to threshold. The same equations also generate shallow, spatially extended, open-flavor-dominated states with molecular long-distance characteristics. Their binding energies, radii, and small quarkonium components are highly sensitive to the adjoint meson mass, whereas the higher spectrum is more stable. Together with the hybrid reference levels, the spectrum provides multiplet assignments for most candidates. States not naturally accommodated point to the need for hidden-strange and $S+P$ tetraquark/open-flavor BO sectors and for hybrid--tetraquark and hybrid--quarkonium mixings.

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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

Imprint of the adjoint meson spectrum in the decay patterns of hidden-bottom tetraquarks

We aim to clarify the experimentally observed near-degeneracy and decay patterns of the isospin, $I=1$, hidden-bottom tetraquarks $Z_b(10610)$ and $Z_b(10650)$ with quantum numbers $J^{P}=1^{+}$.We refer to them as $Z_b$ and $Z_b^{'}$, respectively. In particular, we find first evidence that the suppression of the decay of $Z_b^{'}$ to $B\bar{B^*}$ can be understood in the context of the Born-Oppenheimer Effective Field Theory (BOEFT). BOEFT enables writing both $Z_b$ and $Z_b^{'}$ as superpositions of $Z_1$ and $Z_2$ tetraquark configurations. This decomposition naturally relates the decay patterns of $Z_b$ and $Z_b^{'}$ to the degeneracy of the light degrees of freedom associated with $Z_1$ and $Z_2$ tetraquarks, {\it i.e.,} $1^{--}$and $0^{-+}$ adjoint mesons, respectively. By calculating the adjoint meson correlators within the framework of lattice QCD, we get good indications that these adjoint mesons are degenerate.

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arXiv2026

Wilson loops with neural networks

Wilson loops are essential objects in QCD and have been pivotal in scale setting and demonstrating confinement. Various generalizations are crucial for computations needed in effective field theories. In lattice gauge theory, Wilson loop calculations face challenges, including excited-state contamination at short times and the signal-to-noise ratio issue at longer times. To address these problems, we develop a new method by using neural networks to parametrize interpolators for the static quark-antiquark pair. We construct gauge-equivariant layers for the network and train it to find the ground state of the system. The trained network itself is then treated as our new observable for the inference. Our results demonstrate a significant improvement in the signal compared to traditional Wilson loops, performing as well as Coulomb-gauge Wilson-line correlators while maintaining gauge invariance. Additionally, we present an example where the optimized ground state is used to measure the static force directly, as well as another example combining this method with the multilevel algorithm. Finally, we extend the formalism to find excited-state interpolators for static quark-antiquark systems. To our knowledge, this work is the first study of neural networks with a physically motivated loss function for Wilson loops.

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arXiv2026

Strong coupling constant from the 1-loop improved static energy

The static energy is an excellent observable for extracting the strong coupling $α_s$ 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 $α_s$. We present early results for 1-loop lattice perturbation theory improvement of the Wilson loop and show how it improves the $α_s$ extraction. We present a preliminary reanalysis of the TUMQCD (2+1)-flavor QCD data.

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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 Schrödinger equations dictated by the BOEFT, whose only free parameter, the adjoint meson mass, is fixed to the mass of the $χ_{c1}(3872)$ 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 $γ$ appearing in the $^3P_0$ model.

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arXiv2026

Schwinger Model with a Dynamical Axion

One of the major open puzzles in the Standard Model of particle physics is the strong CP problem: although Quantum Chromodynamics allows a CP-violating topological $θ$-term, experiments constrain its value to be extremely small. The Peccei--Quinn mechanism resolves this problem by promoting the $θ$-angle to a dynamical field-introducing the axion -- whose dynamics relax the effective angle $θ_\text{eff}$ to a CP-conserving minimum. Here, we investigate the resulting axion physics in a Hamiltonian lattice gauge theory (LGT) by coupling a quantized axion field to the massive Schwinger model with a topological $θ$-term. Using infinite matrix product state techniques, we compute the ground-state properties of the resulting theory and demonstrate that the axion dynamically relaxes $θ_\text{eff}$ to the minimum of the vacuum energy. Consequently, the ground-state energy becomes independent of $θ$, demonstrating the axion-mediated solution to the strong CP problem within a fully dynamical LGT. We further analyze CP restoration and extract the axion mass from the topological susceptibility and excitation spectrum. Our results provide a nonperturbative demonstration of axion dynamics in a quantum LGT amenable to investigation on modern quantum hardware.

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arXiv2026

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

We use the Born--Oppenheimer effective field theory factorization to compute the inclusive production cross sections of the $χ_{c1}(3872)$ 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.

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arXiv2025

Heavy quarkonium dynamics at next-to-leading order in the binding energy over temperature

Using the potential non-relativistic quantum chromodynamics (pNRQCD) effective field theory, we derive a Lindblad equation for the evolution of the heavy-quarkonium reduced density matrix that is accurate to next-to-leading order (NLO) in the ratio of the binding energy of the state to the temperature of the medium. The resulting NLO Lindblad equation can be used to more reliably describe heavy-quarkonium evolution in the quark-gluon plasma at low temperatures compared to the leading-order truncation. For phenomenological application, we numerically solve the resulting NLO Lindblad equation using the quantum trajectories algorithm. To achieve this, we map the solution of the three-dimensional Lindblad equation to the solution of an ensemble of one-dimensional Schrödinger evolutions with Monte-Carlo sampled quantum jumps. Averaging over the Monte-Carlo sampled quantum jumps, we obtain the solution to the NLO Lindblad equation without truncation in the angular momentum quantum number of the states considered. We also consider the evolution of the system using only the complex effective Hamiltonian without stochastic jumps and find that this provides a reliable approximation for the ground state survival probability at LO and NLO. Finally, we make comparisons with our prior leading-order pNRQCD results and experimental data available from the ATLAS, ALICE, and CMS collaborations.

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arXiv2025

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

Two decades ago the $χ_{c1}\left(3872\right)$ 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 $χ_{c1}\left(3872\right)$ 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 $χ_{c1}\left(3872\right)$ 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.

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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.

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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.

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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.

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arXiv2025

How well does nonrelativistic QCD factorization work at next-to-leading order?

We perform a thorough investigation of the universality of the long distance matrix elements (LDMEs) of nonrelativistic QCD factorization based on a next-to-leading order (NLO) fit of $J/ψ$ color octet (CO) LDMEs to high transverse momentum $p_T$ $J/ψ$ and $η_c$ production data at the LHC. We thereby apply a novel fit-and-predict procedure to systematically take into account scale variations, and predict various observables never studied in this context before. In particular, the LDMEs can well describe $J/ψ$ hadroproduction up to the highest measured values of $p_T$, as well as $Υ(nS)$ production via potential NRQCD based relations. Furthermore, $J/ψ$ production in $γγ$ and $γp$ collisions is surprisingly reproduced down to $p_T=1$ GeV, as long as the region of large inelasticity $z$ is excluded, which may be of significance in future quarkonium studies, in particular at the EIC and the high-luminosity LHC. In addition, our summary reveals an interesting pattern as to which observables still evade a consistent description.

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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.

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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

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 $α_\mathrm{s}$ 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 $α_\mathrm{s}(m_Z)$. We will present preliminary results for the determination of $α_\mathrm{s} {(M_Z)}$ in (2+1+1)-flavor QCD using the configurations made availableby the MILC-collaboration with smallest lattice spacing reaching 0.0321fm.

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