We provide an extended lattice study of the SU(2) gauge theory coupled to one Dirac fermion flavor (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mn>1</mn></math>) transforming in the adjoint representation as the continuum limit is approached. This investigation is supplemented by results obtained for the SU(2) gauge theory with two Dirac fermion flavors (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mn>2</mn></math>) transforming in the adjoint representation, for which we perform numerical investigations at three values of the lattice spacing. The purpose of our study is to advance the characterization of the infrared properties of both theories, which previous investigations have concluded to be in the conformal window. For both, we determine the mass spectrum and the anomalous dimension of the fermion condensate using finite-size hyperscaling of the spectrum, mode number analysis of the Dirac operator (for which we improve on our previous proposal) and the ratio of masses of the lightest spin-2 particle over the lightest scalar. All methods provide a consistent picture, with the anomalous dimension of the condensate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>γ</mi><mo>*</mo></msub></math> decreasing significantly as one approaches the continuum limit for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mn>1</mn></math> theory towards a value consistent with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>γ</mi><mo>*</mo></msub><mo>=</mo><mn>0.170</mn><mo stretchy="false">(</mo><mn>6</mn><mo stretchy="false">)</mo></math>, while for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mn>2</mn></math> the anomalous dimension converges more rapidly with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>β</mi></math> to a value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>γ</mi><mo>*</mo></msub><mo>=</mo><mn>0.291</mn><mo stretchy="false">(</mo><mn>9</mn><mo stretchy="false">)</mo></math>. A chiral perturbation theory analysis shows that the infrared behavior of both theories is incompatible with the breaking of chiral symmetry.

Cyprus

Andreas Athenodorou

United Kingdom

Ed Bennett

Germany

Georg Bergner

Spain

Denmark

Pietro Butti

Julian Lenz

Biagio Lucini

SU(2) gauge theory with one and two adjoint fermions toward the continuum limit

We investigate static and dynamical aspects of string breaking in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></math> lattice gauge theory coupled to Kogut-Susskind staggered fermions. Using tensor network simulations, we demonstrate that the static potential as well as the site-resolved configuration of the matter sites and gauge links allows us to identify the regimes in which string breaking occurs. Furthermore, we develop a variational quantum eigensolver that allows for reliably preparing the ground state of the theory in both the absence and presence of static charges and to capture the static aspects of the phenomenon. Carrying out state preparation on real quantum hardware for up to 19 qubits, we demonstrate its suitability for current quantum devices. In addition, we study the real-time dynamics of a flux tube between two static charges using both tensor networks and quantum hardware. Using a trotterization for the time-evolution operator, we are able to show that the breaking process starts with the creation of charges inside the string. These eventually redistribute toward the static charges and screen them, which leads to the breaking of the flux tube.

Constantia Alexandrou

Kostas Blekos

Georgios Polykratis

Stefan Kühn

Realizing string breaking dynamics in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></math> lattice gauge theory on quantum hardware

In this study, we conduct a thorough examination of the spectrum of the open confining string in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math> dimensions, commonly referred to as the open flux tube, across various gauge groups of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><msub><mi>N</mi><mi>c</mi></msub><mo stretchy="false">)</mo></math>. Our primary objective is to explore its behavior as we approach the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> limit and the identification of possible world-sheet axion states. Specifically, we undertake a detailed analysis of the associated spectrum for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub><mo>=</mo><mn>3</mn></math>, 4, 5, 6. This marks the first systematic investigation of the open flux-tube spectrum within the context of the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> limit. More specifically, we analyze the spectra of flux tubes that form between a static quark-antiquark pair, considering a significant number of radial excitations and eight irreducible representations characterized by the quantum numbers of angular momentum <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math>, charge conjugation and parity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub></math>, and the reflection symmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ε</mi></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo>=</mo><mn>0</mn></math>. To this purpose we employ a diverse set of suitable operators, an anisotropic action, and smearing techniques, and solve the generalized eigenvalue problem. We compare our findings with predictions from the Nambu-Goto string model to assess potential tensions indicative of novel phenomena such as the existence of axionlike state along the flux-tube world sheet. Notably, we provide undoubted evidence of the existence of a massive axionlike particle with the same mass as the corresponding axion extracted within the context of closed flux tube. This strengthens the conjecture that the axion is a property of the world sheet of the QCD string.

Portugal

Alireza Sharifian

Pedro Bicudo

Spectrum of open confining strings in the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> limit

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

The 3d Ising model in the low temperature (ferromagnetic) phase describes dynamics of two-dimensional surfaces — domain walls between clusters of parallel spins. The Kramers-Wannier duality maps these surfaces into worldsheets of confining strings in the Wegner’s ℤ 2 gauge theory. We study the excitation spectrum of long Ising strings by simulating the ℤ 2 gauge theory on a lattice. We observe a strong mixing between string excitations and the lightest glueball state and do not find indications for light massive resonances on the string worldsheet.

Italy

United States

Sergei Dubovsky

Conghuan Luo

Michael Teper

Excitations of Ising strings on a lattice

We compute the topological susceptibility of N  f  = 2 + 1 QCD with physical quark masses in the high-temperature phase, using numerical simulations of the theory discretized on a space-time lattice. More precisely we estimate the topological susceptibility for five temperatures in the range from ∼ 200 MeV up to ∼ 600 MeV, adopting the spectral projectors definition of the topological charge based on the staggered Dirac operator. This strategy turns out to be effective in reducing the large lattice artifacts which affect the standard gluonic definition, making it possible to perform a reliable continuum extrapolation. Our results for the susceptibility in the explored temperature range are found to be partially in tension with previous determinations in the literature.

Claudio Bonanno

Claudio Bonati

Giuseppe Clemente

Francesco D’Angelo

Massimo D’Elia

Lorenzo Maio

Guido Martinelli

Francesco Sanfilippo

Antonino Todaro

Topological susceptibility of N  f  = 2 + 1 QCD from staggered fermions spectral projectors at high temperatures

We calculate the low-lying glueball spectrum, several string tensions and some properties of topology and the running coupling for SU(N) lattice gauge theories in 3 + 1 dimensions. We do so for 2 ≤ N ≤ 12, using lattice simulations with the Wilson plaquette action, and for glueball states in all the representations of the cubic rotation group, for both values of parity and charge conjugation. We extrapolate these results to the continuum limit of each theory and then to N = ∞. For a number of these states we are able to identify their continuum spins with very little ambiguity. We calculate the fundamental string tension and k = 2 string tension and investigate the N dependence of the ratio. Using the string tension as the scale, we calculate the running of a lattice coupling and confirm that g 2(a) ∝ 1/N for constant physics as N → ∞. We fit our calculated values of a√σ with the 3-loop β-function, and extract a value for <math> <msub> <mi>Λ</mi> <mover> <mi>MS</mi> <mo>¯</mo> </mover> </msub> </math> $$ {\Lambda}_{\overline{MS}} $$ , in units of the string tension, for all our values of N, including SU(3). We use these fits to provide analytic formulae for estimating the string tension at a given lattice coupling. We calculate the topological charge Q for N ≤ 6 where it fluctuates sufficiently for a plausible estimate of the continuum topological susceptibility. We also calculate the renormalisation of the lattice topological charge, Z Q (β), for all our SU(N) gauge theories, using a standard definition of the charge, and we provide interpolating formulae, which may be useful in estimating the renormalisation of the lattice θ parameter. We provide quantitative results for how the topological charge ‘freezes’ with decreasing lattice spacing and with increasing N. Although we are able to show that within our typical errors our glueball and string tension results are insensitive to the freezing of Q at larger N and β, we choose to perform our calculations with a typical distribution of Q imposed upon the fields so as to further reduce any potential systematic errors.

SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology

We present a major update on our investigations of SU(2) gauge theory with one Dirac flavor in the adjoint representation on the lattice. In particular, we consider larger volumes as well as four different values of the gauge coupling. We provide results for the spectrum including gluonic, fermionic, and hybrid observables; Polyakov loops; and the anomalous dimension of the fermionic condensate from the Dirac mode number. These data confirm that the theory is close to the lower boundary of the conformal window for adjoint fermions. Our investigations provide important insights regarding the realization of different infrared scenarios that have been conjectured for this theory.

Investigating the conformal behavior of SU(2) with one adjoint Dirac flavor

In this paper we study, by means of numerical simulations, the behavior of the scalar glueball mass and the ground state of the torelon for trace deformed Yang-Mills theory defined on <math><msup><mi>R</mi><mn>3</mn></msup><mo>×</mo><msup><mi>S</mi><mn>1</mn></msup></math>, in which center symmetry is recovered even at small compactification radii. We find, by investigating both <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> and <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>4</mn><mo>)</mo></math> pure gauge theories, that the glueball mass computed in the deformed theory, when center symmetry is recovered, is compatible with its value at zero temperature and does not show any significant dependence on the compactification radius; moreover, we establish a connection between the deformation parameter and an effective compactification size, which works well at least for small deformations. In addition, we observe that the ground state of the torelon which winds around the small traced deformed circle with size <math><mi>l</mi></math> acquires a plateau for large values of the strength <math><mi>h</mi></math>, with values which are compatible with a <math><mn>1</mn><mo>/</mo><mi>l</mi></math> behavior but, on the other hand, are still not in complete agreement with the asymptotic semiclassical large-<math><mi>N</mi></math> predictions.

Marco Cardinali

Spectrum of trace deformed Yang-Mills theories

We calculate the low-lying glueball spectrum of the SU(3) lattice gauge theory in 3 + 1 dimensions for the range β ≤ 6.50 using the standard plaquette action. We do so for states in all the representations R of the cubic rotation group, and for both values of parity P and charge conjugation C . We extrapolate these results to the continuum limit of the theory using the confining string tension σ as our energy scale. We also present our results in units of the r0 scale and, from that, in terms of physical ‘GeV’ units. For a number of these states we are able to identify their continuum spins J with very little ambiguity. We also calculate the topological charge Q of the lattice gauge fields so as to show that we have sufficient ergodicity throughout our range of β, and we calculate the multiplicative renormalisation of Q as a function of β. We also obtain the continuum limit of the SU(3) topological susceptibility.

The glueball spectrum of SU(3) gauge theory in 3 + 1 dimensions