With the discovery of a Higgs boson with a mass of 125 gigaelectronvolts (GeV) at the Large Hadron Collider (LHC) at CERN in 2012, the Standard Model (SM) is complete, and despite intensive searches, no new fundamental particle has been observed since then. In fact, a discovery can be challenging without a predictive new physics model because different channels and observables cannot be combined directly and unambiguously. Furthermore, without supporting indirect hints, the signal space to be searched is huge, resulting in diluted significances owing to the look-elsewhere effect. Several LHC processes with multiple leptons in the final state point towards the existence of a new Higgs boson with a mass between 140 GeV to 160 GeV decaying mostly to $\textit{W}$ bosons. While the former strongly reduces the look-elsewhere effect, the latter indicates that it could be a Higgs triplet with zero hypercharge. Within this simple and predictive extension of the SM, we simulate and combine different channels of di-photon production in association with leptons, missing energy, jets, $\textit{etc}$... Using the full run-2 results by ATLAS, including those presented recently at the Moriond conference, an increased significance of 4 standard deviations is obtained for a $\approx$ 152 GeV Higgs. Due to the previously predicted mass range, the look-elsewhere effect is negligible, and this constitutes the highest statistical evidence for a new narrow resonance obtained at the LHC. Furthermore, the model predicts a heavier-than-expected $\textit{W}$ boson, as indicated by the global electroweak fit. If further substantiated, the discovery of a new Higgs would overthrow the SM, provide a compelling case for the construction of future particle colliders, and pave the way to a novel understanding of the known shortcomings of the SM. In particular, the triplet Higgs field can lead to a strong first-order phase transition and could thus be related to the matter anti-matter asymmetry in our Universe.

Switzerland

Andreas Crivellin

China

Saiyad Ashanujjaman

Sumit Banik

Guglielmo Coloretti

India

Siddharth P. Maharathy

South Africa

Bruce Mellado

Growing evidence for a Higgs triplet * The work of Andreas Crivellin is supported by a Professorship Grant from the Swiss National Science Foundation (PP00P21_76884). The work of Saiyad Ashanujjaman is partially supported by the National Natural Science Foundation of China (11835013). Siddharth P. Maharathy acknowledges using the SAMKHYA: High-Performance Computing Facility provided by the Institute of Physics, Bhubaneswar

We perform a lattice study of the (<math><mn>2</mn><mo>+</mo><mn>1</mn></math>)-dimensional Gross-Neveu model in a background magnetic field <math><mi>B</mi></math> and at nonzero chemical potential <math><mi>μ</mi></math>. The complex-action problem arising in our simulations using overlap fermions is under control. For <math><mi>B</mi><mo>=</mo><mn>0</mn></math>, we observe a first-order phase transition in <math><mi>μ</mi></math> even at nonvanishing temperatures. Our main finding, however, is that the rich phase structure found in the limit of infinite flavor number <math><msub><mi>N</mi><mi>f</mi></msub></math> is washed out by the fluctuations present at <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>1</mn></math>. We find no evidence for inverse magnetic catalysis, i.e., the decrease of the order parameter of chiral symmetry breaking with <math><mi>B</mi></math> for <math><mi>μ</mi></math> close to the chiral phase transition. Instead, the magnetic field tends to enhance the breakdown of chiral symmetry for all values of <math><mi>μ</mi></math> below the transition. Moreover, we find no trace of spatial inhomogeneities in the order parameter. We briefly comment on the potential relevance of our results for QCD.

Germany

United Kingdom

Julian J. Lenz

Michael Mandl

Andreas Wipf

Magnetized (<math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional Gross-Neveu model at finite density

We study the Gross-Neveu model in <math><mn>2</mn><mo>+</mo><mn>1</mn></math> dimensions in an external magnetic field <math><mi>B</mi></math>. We first summarize known mean-field results, obtained in the limit of large flavor number <math><msub><mi>N</mi><mi>f</mi></msub></math>, before presenting lattice results using the overlap discretization to study one reducible fermion flavor, <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>1</mn></math>. Our findings indicate that the magnetic catalysis phenomenon, i.e., an increase of the chiral condensate with the magnetic field, persists beyond the mean-field limit for temperatures below the chiral phase transition and that the critical temperature grows with increasing magnetic field. This is in contrast to the situation in QCD, where the broken phase shrinks with increasing <math><mi>B</mi></math> while the condensate exhibits a nonmonotonic <math><mi>B</mi></math> dependence close to the chiral crossover, and we comment on this discrepancy. We do not find any trace of inhomogeneous phases induced by the magnetic field.

Magnetic catalysis in the (<math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional Gross-Neveu model

We investigate the finite-temperature and -density chiral Gross-Neveu model with an axial <math><msub><mi>U</mi><mi>A</mi></msub><mo>(</mo><mn>1</mn><mo>)</mo></math> symmetry in <math><mn>1</mn><mo>+</mo><mn>1</mn></math> dimensions on the lattice. In the limit where the number of flavors <math><msub><mi>N</mi><mi>f</mi></msub></math> tends to infinity the continuum model has been solved analytically and shows two phases: a symmetric high-temperature phase with a vanishing condensate and a low-temperature phase in which the complex condensate forms a chiral spiral which breaks translation invariance. In the lattice simulations we employ chiral SLAC fermions with exact axial symmetry. Similarly to <math><msub><mi>N</mi><mi>f</mi></msub><mo>→</mo><mi>∞</mi></math>, we find for eight flavors, where quantum and thermal fluctuations are suppressed, two distinct regimes in the <math><mo>(</mo><mi>T</mi><mo>,</mo><mi>μ</mi><mo>)</mo></math> phase diagram, characterized by qualitatively different behavior of the two-point functions of the condensate fields. More surprisingly, at <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn></math>, where fluctuations are no longer suppressed, the model still behaves similarly to the <math><msub><mi>N</mi><mi>f</mi></msub><mo>→</mo><mi>∞</mi></math> model and we conclude that the chiral spiral leaves its footprints even on systems with a small number of flavors. For example, at low temperature the two-point functions are still dominated by chiral spirals with pitches proportional to the inverse chemical potential, although in contrast to large <math><msub><mi>N</mi><mi>f</mi></msub></math> their amplitudes decrease with distance. We argue that these results should not be interpreted as the spontaneous breaking of a continuous symmetry, which is forbidden in two dimensions. Finally, using Dyson-Schwinger equations we calculate the decay of the <math><msub><mi>U</mi><mi>A</mi></msub><mo>(</mo><mn>1</mn><mo>)</mo></math>-invariant fermion four-point function in search for a BKT phase at zero temperature.

Inhomogeneities in the two-flavor chiral Gross-Neveu model

Super-Yang-Mills theory (SYM) is a central building block for supersymmetric extensions of the Standard Model of particle physics. Whereas the weakly coupled subsector of the latter can be treated within a perturbative setting, the strongly coupled subsector must be dealt with a non-perturbative approach. Such an approach is provided by the lattice formulation. Unfortunately a lattice regularization breaks supersymmetry and consequently the mass degeneracy within a supermultiplet. In this article we investigate the properties of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supersymmetric SU(3) Yang-Mills theory with a lattice Wilson Dirac operator with an additional parity mass, similar as in twisted mass lattice QCD. We show that a special 45° twist effectively removes the mass splitting of the chiral partners. Thus, at finite lattice spacing both chiral and supersymmetry are enhanced resulting in an improved continuum extrapolation. Furthermore, we show that for the non-interacting theory at 45° twist discretization errors of order   <math> <mi>O</mi> <mfenced> <mi>a</mi> </mfenced> </math>  $$ \mathcal{O}(a) $$  are suppressed, suggesting that the same happens for the interacting theory as well. As an aside, we demonstrate that the DDαAMG multigrid algorithm accelerates the inversion of the Wilson Dirac operator considerably. On a 163 × 32 lattice, speed-up factors of up to 20 are reached if commonly used algorithms are replaced by the DDαAMG.

Marc Steinhauser

André Sternbeck

Björn Wellegehausen

<math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 Super-Yang-Mills theory on the lattice with twisted mass fermions

In a recent work [J. Lenz et al., Phys. Rev. D 101, 094512 (2020)] we studied the phase structure of the Gross-Neveu (GN) model in <math><mn>1</mn><mo>+</mo><mn>1</mn></math> dimensions at finite number of fermion flavors <math><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>16</mn></mrow></math>, finite temperature and finite chemical potential using lattice field theory. Most importantly, we found an inhomogeneous phase at low temperature and large chemical potential, quite similar to the analytically solvable <math><msub><mi>N</mi><mi>f</mi></msub><mo>→</mo><mi>∞</mi></math> limit. In the present work we continue our lattice field theory investigation of the finite-<math><msub><mi>N</mi><mi>f</mi></msub></math> GN model by studying the formation of baryons, their spatial distribution and their relation to the chiral condensate. As a preparatory step we also discuss a linear coupling of lattice fermions to the chemical potential.

Laurin Pannullo

Marc Wagner

Björn H. Wellegehausen

Baryons in the Gross-Neveu model in <math><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math> dimensions at finite number of flavors

We construct a nonunitary transformation that relates a given “asymptotically free” conformal quantum mechanical system <math><msub><mi>H</mi><mi>f</mi></msub></math> with its confined, harmonically trapped version <math><msub><mi>H</mi><mi>c</mi></msub></math>. In our construction, Jordan states corresponding to the zero eigenvalue of <math><msub><mi>H</mi><mi>f</mi></msub></math>, as well as its eigenstates and Gaussian packets, are mapped into the eigenstates, coherent states, and squeezed states of <math><msub><mi>H</mi><mi>c</mi></msub></math>, respectively. The transformation is an automorphism of the conformal <math><mrow><mrow><mi>s</mi><mi>l</mi></mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo>)</mo></mrow></math> algebra of the nature of the fourth-order root of the identity transformation, to which a complex canonical transformation corresponds on the classical level being the fourth-order root of the spatial reflection. We investigate the one- and two-dimensional examples that reveal, in particular, a curious relation between the two-dimensional free particle and the Landau problem.

Chile

Luis Inzunza

Mikhail S. Plyushchay

Conformal bridge between asymptotic freedom and confinement

We explore the thermodynamics of the <math><mn>1</mn><mo>+</mo><mn>1</mn></math>-dimensional Gross-Neveu (GN) model at a finite number of fermion flavors <math><msub><mi>N</mi><mi>f</mi></msub></math>, finite temperature, and finite chemical potential using lattice field theory. In the limit <math><msub><mi>N</mi><mi>f</mi></msub><mo>→</mo><mi>∞</mi></math> the model has been solved analytically in the continuum. In this limit three phases exist: a massive phase, in which a homogeneous chiral condensate breaks chiral symmetry spontaneously; a massless symmetric phase with vanishing condensate; and most interestingly an inhomogeneous phase with a condensate, which oscillates in the spatial direction. In the present work we use chiral lattice fermions (naive fermions and SLAC fermions) to simulate the GN model with 2, 8, and 16 flavors. The results obtained with both discretizations are in agreement. Similarly as for <math><msub><mi>N</mi><mi>f</mi></msub><mo>→</mo><mi>∞</mi></math> we find three distinct regimes in the phase diagram, characterized by a qualitatively different behavior of the two-point function of the condensate field. For <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>8</mn></math> we map out the phase diagram in detail and obtain an inhomogeneous region smaller as in the limit <math><msub><mi>N</mi><mi>f</mi></msub><mo>→</mo><mi>∞</mi></math>, where quantum fluctuations are suppressed. We also comment on the existence or absence of Goldstone bosons related to the breaking of translation invariance in <math><mn>1</mn><mo>+</mo><mn>1</mn></math> dimensions.

Julian Lenz

Inhomogeneous phases in the Gross-Neveu model in <math><mn>1</mn><mo>+</mo><mn>1</mn></math> dimensions at finite number of flavors

We study classical and quantum hidden symmetries of a particle with electric charge in the background of a Dirac monopole of magnetic charge subjected to an additional central potential ( ) = ( ) + ( ) with ( ) = $$ \frac{1}{2} $$ , similar to that in the one-dimensional conformal mechanics model of de Alfaro, Fubini and Furlan (AFF). By means of a non-unitary conformal bridge transformation, we establish a relation of the quantum states and of all symmetries of the system with those of the system without harmonic trap, ( ) = 0. Introducing spin degrees of freedom via a very special spin-orbit coupling, we construct the $$ \mathfrak{sop} $$ (2 2) superconformal extension of the system with unbroken $$ \mathcal{N} $$ = 2 Poincaré supersymmetry and show that two different superconformal extensions of the one-dimensional AFF model with unbroken and spontaneously broken supersymmetry have a common origin. We also show a universal relationship between the dynamics of a Euclidean particle in an arbitrary central potential ( ) and the dynamics of a charged particle in a monopole background subjected to the potential ( ).

Mikhail Plyushchay

Hidden symmetry and (super)conformal mechanics in a monopole background

The Thirring model is an interacting fermion theory with current-current interaction. The model in <math><mn>1</mn><mo>+</mo><mn>2</mn></math> dimensions has applications in condensed-matter physics to describe the electronic excitations of Dirac materials. Earlier investigations with Schwinger-Dyson equations, the functional renormalization group and lattice simulations with staggered fermions suggest that a critical number of (reducible) flavors <math><msup><mi>N</mi><mi>c</mi></msup></math> exists, below which chiral symmetry can be broken spontaneously. Values for <math><msup><mi>N</mi><mi>c</mi></msup></math> found in the literature vary between 2 and 7. Recent lattice studies with chirally invariant SLAC fermions have indicated that chiral symmetry is unbroken for all integer flavor numbers [B. H. Wellegehausen, D. Schmidt, and A. Wipf, Phys. Rev. D 96, 094504 (2017); D. Schmidt, Three-dimensional four-Fermi theories with exact chiral symmetry on the lattice, Ph.D. thesis, TPI, FS-University Jena, 2018, https://doi.org/10.22032/dbt.34148]. An independent simulation based on domain wall fermions seems to favor a critical flavor-number that satisfies <math><mn>1</mn><mo>&lt;</mo><msup><mi>N</mi><mi>c</mi></msup><mo>&lt;</mo><mn>2</mn></math> [S. Hands, Phys. Rev. D 99, 034504 (2019)]. However, in the latter simulations difficulties in reaching the massless limit in the broken phase (at strong coupling and after the <math><msub><mi>L</mi><mi>s</mi></msub><mo>→</mo><mi>∞</mi></math> limit has been taken) are encountered. To find an accurate value <math><msup><mi>N</mi><mi>c</mi></msup></math> we study the Thirring model (by using an analytic continuation of the parity even theory to arbitrary real <math><mi>N</mi></math>) for <math><mi>N</mi></math> between 0.5 and 1.1. We investigate the chiral condensate, the spectral density of the Dirac operator, the spectrum of (would-be) Goldstone bosons and the variation of the filling-factor and conclude that the critical flavor number is <math><msup><mi>N</mi><mi>c</mi></msup><mo>=</mo><mn>0.80</mn><mo>(</mo><mn>4</mn><mo>)</mo></math>. Thus we see no chiral symmetry breaking in all Thirring models with 1 or more flavors of (4-component) fermions. Besides the transition to the unphysical lattice artifact phase we find strong evidence for a hitherto unknown phase transition that exists for <math><mi>N</mi><mo>&gt;</mo><msup><mi>N</mi><mi>c</mi></msup></math> and should answer the question of where to construct a continuum limit.