Fri·Sep 17, 2021Friday·September 17, 2021

1. 01*

   Universality of a truncated sigma-model

   Andrei Alexandru🇺🇸 · Paulo F. Bedaque🇺🇸 · Andrea Carosso🇺🇸 · Andy Sheng🇺🇸

   Bosonic quantum field theories, even when regularized using a finite lattice, possess an infinite dimensional Hilbert space and, therefore, cannot be simulated in quantum computers with a finite number of qubits. A truncation of the Hilbert space is then needed and the physical results are obtained after a double limit: one to remove the truncation and another to remove the regulator (the continuum limit). A simpler alternative is to find a model with a finite dimensional Hilbert space belonging to the same universality class as the continuum model (a "qubitization"), so only the space continuum limit is required. A qubitization of the $1+1$ dimensional asymptotically free $O(3)$ nonlinear $\sigma$-model based on ideas of non-commutative geometry was previously proposed arXiv:1903.06577 and, in this paper, we provide evidence that it reproduces the physics of the $\sigma$-model both in the infrared and the ultraviolet regimes.

   hep-lathep-thnucl-thquant-phPLB(2022)·11 citations
2. 02*

   Derivative expansion in the HAL QCD method for a separable potential

   Sinya Aoki🇯🇵 · Koichi Yazaki🇯🇵

   We investigate how the derivative expansion in the HAL QCD method works to extract physical observables, using a separable potential in quantum mechanics, which is solvable but highly non-local in the coordinate system. We consider three cases for inputs to determine the HAL QCD potential in the derivative expansion, (1) energy eigenfunctions (2) time-dependent wave functions as solutions to the time dependent Schrödinger equation with some boundary conditions (3) time-dependent wave function made by a linear combination of finite number of eigenfunctions at low energy to mimic the finite volume effect. We have found that, for all three cases, the potentials provide reasonable scattering phase shifts even at the leading order of the derivative expansion, and they give more accurate results as the order of the expansion increases. By comparing the above results with those from the formal derivative expansion for the separable potential, we conclude that the derivative expansion is not a way to obtain the potential but a method to extract physical observables such as phase shifts and binding energies, and that the scattering phase shifts from the derivative expansion in the HAL QCD method converge to the exact ones much faster than those from the formal derivative expansion of the separable potential.

   hep-latPTEP(2022)·5 citations
3. 03*

   On the chiral anomaly and the Yang-Mills gradient flow

   Martin Lüscher🇨🇭

   There are currently two singularity-free universal expressions for the topological susceptibility in QCD, one based on the Yang-Mills gradient flow and the other on density-chain correlation functions. While the latter link the susceptibility to the anomalous chiral Ward identities, the gradient flow permits the emergence of the topological sectors in lattice QCD to be understood. Here the two expressions are shown to coincide in the continuum theory, for any number of quark flavours in the range where the theory is asymptotically free.

   hep-latPLB(2021)·4 citations
4. 04*

   Different faces of confinement

   Roman Pasechnik🇸🇪 · Michal Šumbera🇨🇿

   In this review, we provide a short outlook of some of the currently most popular pictures and promising approaches to non-perturbative physics and confinement in gauge theories. A qualitative and by no means exhaustive discussion presented here covers such key topics as the phases of QCD matter, the order parameters for confinement, the central vortex and monopole pictures of the QCD vacuum structure, fundamental properties of the string tension, confinement realisations in gauge-Higgs and Yang-Mills theories, magnetic order/disorder phase transition among others.

   ↳ hep-phhep-lathep-thUniverse(2021)·17 citations
5. 05*

   Machine learning with quantum field theories

   Dimitrios Bachtis🇬🇧 · Gert Aarts🇬🇧 · Biagio Lucini🇬🇧

   The precise equivalence between discretized Euclidean field theories and a certain class of probabilistic graphical models, namely the mathematical framework of Markov random fields, opens up the opportunity to investigate machine learning from the perspective of quantum field theory. In this contribution we will demonstrate, through the Hammersley-Clifford theorem, that the ${\varphi }^4$ scalar field theory on a square lattice satisfies the local Markov property and can therefore be recast as a Markov random field. We will then derive from the ${\varphi }^4$ theory machine learning algorithms and neural networks which can be viewed as generalizations of conventional neural network architectures. Finally, we will conclude by presenting applications based on the minimization of an asymmetric distance between the probability distribution of the ${\varphi }^4$ machine learning algorithms and target probability distributions.

   ↳ cs.LGhep-lathep-thmath-ph+2PoS(2022)·4 citations
6. 06*

   Bootstrap Method in Harmonic Oscillator

   Yu Aikawa🇯🇵 · Takeshi Morita🇯🇵 · Kota Yoshimura🇺🇸

   Recently, an application of the numerical bootstrap method to quantum mechanics was proposed, and it successfully reproduces the eigenstates of various systems. However, it is unclear why this method works. In order to understand this question, we study the bootstrap method in harmonic oscillators. We find that the problem reduces to the Dirac's ladder operator problem and is exactly solvable analytically. Our result suggests that the bootstrap method may be regarded as a numerical version of the Dirac's approach and it may explain why it works in various systems.

   ↳ hep-thhep-latquant-phPLB(2022)·30 citations
7. 07*

   Heavy-meson chiral Lagrangians, effective flavored couplings, SU(4) flavor breaking and their consequences

   Bruno El-Bennich🇧🇷 · Fernando E. Serna🇧🇷

   We review heavy quark flavor and spin symmetries, their exploitation in heavy meson effective theories and the flavored couplings of charmed and light mesons in the definition of their effective Lagrangians. We point out how nonperturbative continuum QCD approaches based on Dyson-Schwinger and Bethe-Salpeter equations can be used to calculate strong and leptonic decays of open-charm mesons and heavy quarkonia. The strong decay $D^{\ast }\to D\pi$ serves as a benchmark, as it is the only physical open-charm observable that can be related to the effective Lagrangian's couplings. Nonetheless, a quantitative comparison of $D^{\ast }D\pi$, $\rho DD$, $\rho D^{\ast }D$ and $\rho D^{\ast }{D}^{\ast }$ couplings for a range of off-shell momenta of the $\rho$-meson invalidates SU(4)${}_F$ symmetry relations between these couplings. Thus, besides the breaking of flavor symmetry by mass terms in the Lagrangians, the flavor-symmetry breaching in couplings and their dependence on the $\rho$-meson virtuality cannot be ignored. We also take the opportunity to present new results for the effective $J/\psi DD$ and $J/\psi D^{\ast }D$ couplings. We conclude this contribution with a discussion on how the description of pseudoscalar and vector $D$, $D_s$, $B$ and $B_s$ meson properties can be drastically improved with a modest modification of the flavor-dependence in the Bethe-Salpeter equation.

   ↳ hep-phhep-exhep-latnucl-thPoS(2021)·4 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.