Fri·Dec 24, 2021Friday·December 24, 2021

1. 01*

   The Higgs phase as a spin glass phase in D=5 dimensional SU(2) gauge Higgs theory

   David Ward🇺🇸

   According to recent work of Greensite and Matsuyama, the Higgs phase of a gauge Higgs theory is distinguished from the confinement and massless phases by the spontaneous breaking of a global center subgroup of the gauge group, and by confinement type. This is contrary to the notion that there is no essential distinction between the Higgs and confinement phases when the Higgs field is in the fundamental representation of the gauge group. Although this new symmetry breaking order parameter has been investigated in $D=4$ dimensions, there is so far no check in a non-abelian gauge theory containing a massless as well as confinement/Higgs phases, where the prediction is that the symmetry breaking order parameter will show transition lines separating the massless to Higgs and confinement to Higgs phases, but not the massless to confinement phase. In this work we map out the phase structure of the $D=5$ dimensional model, according to both the symmetry breaking parameter and thermodynamic observables, and check the assertion regarding the massless to confinement phase.

   hep-latPRD(2022)·5 citations
2. 02*

   Generalization capabilities of neural networks in lattice applications

   Srinath Bulusu🇦🇹 · Matteo Favoni🇦🇹 · Andreas Ipp🇦🇹 · David I. Müller🇦🇹 · Daniel Schuh🇦🇹

   In recent years, the use of machine learning has become increasingly popular in the context of lattice field theories. An essential element of such theories is represented by symmetries, whose inclusion in the neural network properties can lead to high reward in terms of performance and generalizability. A fundamental symmetry that usually characterizes physical systems on a lattice with periodic boundary conditions is equivariance under spacetime translations. Here we investigate the advantages of adopting translationally equivariant neural networks in favor of non-equivariant ones. The system we consider is a complex scalar field with quartic interaction on a two-dimensional lattice in the flux representation, on which the networks carry out various regression and classification tasks. Promising equivariant and non-equivariant architectures are identified with a systematic search. We demonstrate that in most of these tasks our best equivariant architectures can perform and generalize significantly better than their non-equivariant counterparts, which applies not only to physical parameters beyond those represented in the training set, but also to different lattice sizes.

   hep-latcs.LGhep-phstat.MLPoS(2022)·0 citations
3. 03*

   Equivariance and generalization in neural networks

   Srinath Bulusu🇦🇹 · Matteo Favoni🇦🇹 · Andreas Ipp🇦🇹 · David I. Müller🇦🇹 · Daniel Schuh🇦🇹

   The crucial role played by the underlying symmetries of high energy physics and lattice field theories calls for the implementation of such symmetries in the neural network architectures that are applied to the physical system under consideration. In these proceedings, we focus on the consequences of incorporating translational equivariance among the network properties, particularly in terms of performance and generalization. The benefits of equivariant networks are exemplified by studying a complex scalar field theory, on which various regression and classification tasks are examined. For a meaningful comparison, promising equivariant and non-equivariant architectures are identified by means of a systematic search. The results indicate that in most of the tasks our best equivariant architectures can perform and generalize significantly better than their non-equivariant counterparts, which applies not only to physical parameters beyond those represented in the training set, but also to different lattice sizes.

   hep-latcs.LGhep-phstat.MLEPJ Web Conf.(2022)·6 citations
4. 04*

   Baryon masses from full QCD+QED${}_{\text{C}}$ simulations

   Lucius Bushnaq🇮🇪 · Isabel Campos🇪🇸 · Marco Catillo🇨🇭 · Alessandro Cotellucci🇩🇪 · Madeleine Dale🇮🇹 · Patrick Fritzsch🇮🇪 · Jens Lücke🇩🇪 · Marina Krstić Marinković🇨🇭 · Agostino Patella🇩🇪 · Nazario Tantalo🇮🇹

   In these proceedings we present preliminary results for the masses of the proton, neutron and ${\Omega }^{-}$ baryons obtained from QCD+QED lattice simulations performed with four dynamical quarks using C${}^{\ast }$ boundary conditions. These results are part of the ongoing effort of the RC${}^{\ast }$ collaboration discussed in the companion proceedings, and have been obtained on a single ensemble in which the renormalised electromagnetic coupling is ${\alpha }_{\text{em}}\sim 0.04$, the physical volume is $L\sim 1.7$ fm and the masses of the four dynamical quarks have been tuned at the $U$--spin symmetric point $m_d=m_s$. We demonstrate on this unphysical ensemble that baryon masses can be calculated with satisfactory precision when including QED without the need for gauge--fixing and perturbation theory. This makes us confident in the effectiveness of the strategy presented here also in the case of simulations closer to the physical point.

   hep-latPoS(2022)·3 citations
5. 05*

   Consecutive level spacings in the chiral Gaussian unitary ensemble: From the hard and soft edge to the bulk

   G. Akemann🇩🇪 · V. Gorski🇩🇪 · M. Kieburg🇦🇺

   The local spectral statistics of random matrices forms distinct universality classes, strongly depending on the position in the spectrum. Surprisingly, the spacing between consecutive eigenvalues at the spectral edges has received little attention, where the density diverges or vanishes, respectively. This different behaviour is called hard or soft edge. We show that the spacings at the edges are almost indistinguishable from the spacing in the bulk of the spectrum. We present analytical results for consecutive spacings between the $k$th and $(k+1)$st smallest eigenvalues in the chiral Gaussian unitary ensemble, both for finite- and large-$n$. The result depends on the number of the generic zero modes $\nu$ and the number of flavours $N_{\mathrm{f}}$, which are given in terms of characteristic polynomials, as motivated by Quantum Chromodynamics (QCD). We find that the convergence in $n$ is very rapid. The same can be said separately about the limit $k\to \infty$ (limit to the bulk) and $\nu \to \infty$ (limit to the soft edge). Interestingly, the Wigner surmise is a very good approximation for all these cases and, apart from $k=1$, shows a deviation below one percent. These findings are corroborated with Monte-Carlo simulations. We finally compare for $k=1$ with data from QCD on the lattice, being in this symmetry class.

   ↳ math-phcond-mat.stat-mechhep-latmath.MPJ.Phys.A(2022)·3 citations
6. 06*

   $T_{cc}^{+}$ and its partners

   Chengrong Deng🇨🇳 · Shi-Lin Zhu🇨🇳

   Inspired by the $T_{cc}^{+}$ signal discovered by the LHCb Collaboration, we systematically investigate the doubly heavy tetraquark states with the molecule configuration $[Q_1{\bar{q}}_2][Q_3{\bar{q}}_4]$ ($Q=c$ and $b$, $q=u$, $d$ and $s$) in a nonrelativistic quark model. The model involves a color screening confinement potential, meson-exchange interactions and one-gluon-exchange interactions. The $T_{cc}^{+}$ state with $I{J}^P=01^{+}$ is a very loosely bound deuteron-like state with a binding energy around 0.34 MeV and a huge size of 4.32 fm. Both the meson exchange force and the coupled channel effect play a pivotal role. Without the meson exchange force, there does not exist the $T_{cc}^{+}$ molecular state. In strong contrast, the QCD valence bond forms clearly in the $T_{bb}^{+}$ system when we turn off the meson-exchange force, which is very similar to the hydrogen molecule in QED. Moreover, the $T_{bb}^{+}$ becomes a helium-like QCD-atom if we increase the bottom quark mass by a factor of three. Especially, the $T_{bb}^{+}$ states with $01^{+}$, $T_{bc}^{+}$ with $00^{+}$ and $01^{+}$ and the $V$-spin antisymmetric states $T_{bbs}^{+}$ with $\frac{1}{2}{1}^{+}$, $T_{bcs}^{+}$ with $\frac{1}{2}{0}^{+}$ and $\frac{1}{2}{1}^{+}$ can form a compact, hydrogen molecule-like or deuteron-like bound state with different binding dynamics. The high-spin states $T_{bc}^{+}$ with $02^{+}$ and $T_{bcs}^{+}$ with $\frac{1}{2}{2}^{+}$ can decay into $D$-wave $\bar{B}D$ and ${\bar{B}}_{s}D$ although they are below the thresholds ${\bar{B}}^{\ast }{D}^{\ast }$ and ${\bar{B}}_s^{\ast }{D}^{\ast }$, respectively. The isospin and $V$-spin symmetric states are unbound. We also calculate their magnetic moments and axial charges.

   ↳ hep-phhep-exhep-latnucl-thPRD(2022)·99 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.