We unveil the impact of the $\textit{θ}$-angle on the QCD phase diagram at nonzero isospin and strangeness chemical potentials for three light flavors and different quark mass ratios. We establish the phase boundaries as well as the nature of the associated phase transitions. The order parameters and the physical spectrum in the different phases are determined. We further elucidate the physics around $\textit{θ}$ = $\textit{π}$ where we discover a novel parity-preserving superfluid phase. Finally, we comment on Dashen’s phenomenon in the superfluid phases when varying the number of light flavors.

Japan

Jahmall Bersini

Italy

Denmark

Alessandra D’Alise

Clelia Gambardella

Francesco Sannino

On the $\textit{θ}$-angle physics of QCD under pressure: the strange and isospin phase diagram

We systematically analyze the impact of dilatonic dynamics on Skyrme spheres, crystals, and branes. The effects of the dilatonic model parameters, encompassing different underlying near-conformal dynamics, on the macroscopic properties of skyrmions such as their mass and radius are discussed. For spheres and crystals we identify special values of the ratio of the decay constants for which the second order differential equations reduce to a solvable first order system. Additionally, in the case of the crystals, the dilaton presence spatially separates the baryon and isospin charge distributions. For branes, we show how the dilaton smooths out their configurations. Our results are expected to have wide implications from the study of near-conformal dynamics stemming from QCD-like theories to phenomenological investigations of nuclear matter in extreme regimes.

Belgium

Matías Torres

Dilatonic dynamics of baryonic crystals, branes, and spheres

We provide the leading near conformal corrections on a cylinder to the scaling dimension of the lowest-lying fixed isospin charge <math><mi>Q</mi></math> operators defined at the lower boundary of the quantum chromodynamics conformal window, <math><mrow><msub><mrow><mover><mrow><mi>Δ</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>Q</mi></mrow></msub><mo>=</mo><msubsup><mrow><mover><mrow><mi>Δ</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>Q</mi></mrow><mrow><mo>*</mo></mrow></msubsup><mo>+</mo><msup><mrow><mo>(</mo><mfrac><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>σ</mi></mrow></msub></mrow><mrow><mn>4</mn><mi>π</mi><mi>ν</mi></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>Q</mi></mrow><mrow><mfrac><mrow><mi>Δ</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><msup><mrow><mo>(</mo><mfrac><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mrow><mn>4</mn><mi>π</mi><mi>ν</mi></mrow></mfrac><mo>)</mo></mrow><mrow><mn>4</mn></mrow></msup><msup><mrow><mi>Q</mi></mrow><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>(</mo><mn>1</mn><mo>−</mo><mi>γ</mi><mo>)</mo></mrow></msup><msub><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>+</mo><mi>O</mi><mrow><mo>(</mo><msubsup><mrow><mi>m</mi></mrow><mrow><mi>σ</mi></mrow><mrow><mn>4</mn></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow><mrow><mn>8</mn></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>m</mi></mrow><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msubsup><msubsup><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow><mrow><mn>4</mn></mrow></msubsup><mo>)</mo></mrow><mo>.</mo></mrow></math> Here, <math><mrow><msub><mrow><mover><mrow><mi>Δ</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>Q</mi></mrow></msub><mo>/</mo><mi>r</mi></mrow></math> is the classical ground state energy of the theory on <math><mi>R</mi><mo>×</mo><msubsup><mi>S</mi><mi>r</mi><mn>3</mn></msubsup></math> at fixed isospin charge while <math><mrow><msubsup><mrow><mover><mrow><mi>Δ</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>Q</mi></mrow><mrow><mo>*</mo></mrow></msubsup></mrow></math> is the scaling dimension at the leading order in the large charge expansion. In the conformal limit <math><msub><mi>m</mi><mi>σ</mi></msub><mo>=</mo><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>0</mn></math>, the state-operator correspondence implies <math><mrow><msub><mrow><mover><mrow><mi>Δ</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>Q</mi></mrow></msub><mo>=</mo><msubsup><mrow><mover><mrow><mi>Δ</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>Q</mi></mrow><mrow><mo>*</mo></mrow></msubsup></mrow></math>. The near-conformal corrections are expressed in powers of the dilaton and pion masses in units of the chiral symmetry breaking scale <math><mn>4</mn><mi>π</mi><mi>ν</mi></math> with the <math><mi>θ</mi></math>-angle dependence encoded directly in the pion mass. The characteristic <math><mi>Q</mi></math>-scaling is dictated by the quark mass operator anomalous dimension <math><mi>γ</mi></math> and the one characterizing the dilaton potential <math><mi>Δ</mi></math>. The coefficients <math><msub><mi>B</mi><mi>i</mi></msub></math> with <math><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math> depend on the geometry of the cylinder and properties of the nearby conformal field theory.

Scaling results for charged sectors of near conformal QCD

We consider sets of states in conformal quantum mechanics associated to generators of time evolution whose orbits cover different regions of the time domain. States labelled by a continuous global time variable define the two-point correlation functions of the theory seen as a one-dimensional conformal field theory. Such states exhibit the structure of a thermofield double built on bipartite eigenstates of generators of non-global time evolution. In terms of the correspondence between radial conformal symmetries in Minkowski space-time and time evolution in conformal quantum mechanics proposed in [1, 2] these generators coincide with conformal Killing vectors tangent to worldlines of Milne and diamond observers at constant radius. The temperature of the thermofield double states in conformal quantum mechanics reproduces the temperatures perceived by such diamond and Milne observers. We calculate the entanglement entropy associated to the thermofield double states and obtain a UV divergent logarithmic behaviour analogous to known results in two-dimensional conformal field theory in which the entangling boundary is point-like.

Michele Arzano

Domenico Frattulillo

Entanglement entropy in conformal quantum mechanics

We determine the impact of the <math><mi>θ</mi></math> angle and axion physics on the near conformal dynamics of the large-charge baryon sector of <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> gauge theories with <math><msub><mi>N</mi><mi>f</mi></msub></math> fermions in the fundamental representation. We employ an effective approach featuring Goldstone and dilaton degrees of freedom augmented by the topological terms in the theory. We investigate how different dilaton potentials, including the ones for which a systematic counting scheme can be established, affect the results. Via state-operator correspondence we compute the corrections to the would-be conformal dimensions of the lowest large-charge operators as a function of the <math><mi>θ</mi></math> term and dilaton potential.

Croatia

CERN

Charging the conformal window at nonzero <math><mi>θ</mi></math> angle

We analyze the impact of the θ-angle and axion dynamics for two-color (in fact any Sp(2N )) QCD at nonzero baryon charge and as a function of the number of matter fields on the vacuum properties, the pattern of chiral symmetry breaking as well as the spectrum of the theory. We show that the vacuum acquires a rich structure when the underlying CP violating topological operator is added to the theory. We discover novel phases and analyse the order of their transitions characterizing the dynamics of the odd and even number of flavours. We further determine the critical chemical potential as function of the θ angle separating the normal from the superfluid phase of the theory. Our results will guide numerical simulations and novel tests of the model’s dynamics. The results are also expected to better inform phenomenological applications of the model ranging from composite Higgs physics to strongly interacting massive dark matter models featuring number changing interactions. In the companion work [1] we repurpose and upgrade the approach to determine the impact of the θ-angle and axion physics on non-perturbative near conformal dynamics related to the fixed baryon charge sector.

The θ-angle and axion physics of two-color QCD at fixed baryon charge

We critically analyze the body of results that hints to the existence of New Physics from possible violations of lepton universality observed by the LHCb experiment in the μ/e ratios R  K  and   <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mo>∗</mo> </msup> </msub> </math>  $$ {R}_{K^{\ast }} $$  to the g − 2 lepton anomalies. The analysis begins with a theoretical, in depth, study of the μ/e ratios R  K  and   <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mo>∗</mo> </msup> </msub> </math>  $$ {R}_{K^{\ast }} $$  as well as the process B  s  → μ + μ  − . Here we consider the impact of complex Wilson coefficients and derive constraints on their imaginary and real parts. We then move to a comprehensive comparison with experimental results. We show that, by fitting a single Wilson coefficient, the deviations from the Standard Model are at the 4.7σ level when including only the hadronic insensitive observables while it increases to 6.1σ when including also the hadronic sensitive ones. When switching on all relevant Wilson coefficients and combining both hadronic sensitive and insensitive data into the fit, the deviation from the Standard Model peaks at 7.2σ and decreases at the 4.9σ level if we assume that the central values of R  K  and   <math> <msubsup> <mi>R</mi> <mi>K</mi> <mo>∗</mo> </msubsup> </math>  $$ {R}_K^{\ast } $$  are taken to be unity. We further estimate other unaccounted for SM contributions and show that their inclusion still requires New Physics to fit the data. We then introduce the g − 2 lepton anomalies as well as the most recent W-mass results. Different theoretical models are considered that can explain the discrepancies from the Standard Model. In the final part of our work we estimate the impact of the forthcoming data from LHCb (coming from LHC Run3) and Belle II, when it will have accumulated about 5 ab  −1.