We investigate the Ward-Takahashi identity at one-loop in the light-front (LF) formalism for a bound state of fermions. We consider a spinless bound state made up of two fermions in which the Ward-Takahashi identity is satisfied in the covariant formulation. Considering the same system in the light-front formalism, we investigate the proof of Ward-Takahashi identity by integrating the light-front energy component through the identification of the relevant ranges of the longitudinal LF momentum. We elucidate that the pair production diagram plays a crucial role in establishing the Ward-Takahashi identity. We also point out the necessity of taking into account the corresponding zero modes for truly establishing the Ward-Takahashi identity in the LF formalism.

Brazil

Deepesh Bhamre

J.P.B.C. de Melo

Ward-Takahashi identity in the light-front formalism for a bound state of fermions

We propose two novel solutions to the domain wall problem of the QCD axion by introducing a massless or light axion that also couples to gluons. The first solution applies when the new axion forms strings after inflation. Due to its mixing with the QCD axion, domain walls of the QCD axion are bounded by these strings and confined into cosmologically safe string bundles. This scenario predicts the existence of such string bundles, which may survive until today and leave observable signatures, such as gravitational waves, cosmic birefringence, and CMB anisotropies. The simultaneous detection of the QCD axion and any of these cosmological signatures would serve as a smoking-gun signal. The second solution assumes a homogeneous initial condition for the new axion. If it is sufficiently light, its potential temporarily induces a bias in the QCD axion potential before the onset of oscillations, rendering the domain walls unstable. In both scenarios, the Peccei-Quinn mechanism remains effective, and the strong CP problem is not reintroduced. We identify the viable parameter regions and discuss the resulting dark matter abundance.

Japan

Junseok Lee

Kai Murai

Fuminobu Takahashi

Wen Yin

Resolving the QCD axion domain wall problem with a light axion

We study a dark energy model composed of a bare negative cosmological constant and a single ultralight axion, motivated by the string axiverse. Assuming that intelligent observers arise and observe, as in our Universe, the onset of dark-energy-driven acceleration following matter domination, and that this acceleration persists to the present, we derive nontrivial constraints on both the axion mass and the bare cosmological constant. The axion mass is bounded from above to avoid fine-tuning of the initial misalignment angle near the hilltop, and from below because too light axions cannot achieve accelerated expansion due to their limited energy budget. As a result, the anthropically allowed axion mass range typically lies around <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi><mo>=</mo><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo><msub><mi>H</mi><mn>0</mn></msub></math> for a decay constant close to the Planck scale, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>H</mi><mn>0</mn></msub></math> is the observed value of the Hubble constant. In this framework, the dark energy equation-of-state parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>w</mi><mn>0</mn></msub></math> generically deviates from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>1</mn></math> by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>0.1</mn><mo stretchy="false">)</mo></math>, providing a natural explanation for why <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>w</mi><mo>≠</mo><mo>−</mo><mn>1</mn></math> may be expected. We also find that, for a decay constant slightly smaller than the Planck scale, the peak value of dark energy density is significantly smaller than the anthropic bound on the cosmological constant and can be close to the observed value. These outcomes are intriguingly consistent with recent DESI hints of time-varying dark energy, and offer a compelling anthropic explanation within the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo>+</mo></math> axion framework.

Anthropic selection in a model with negative <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> plus axion dark energy

Recently, results from the Atacama Cosmology Telescope (ACT) DR6 have shown a preference for isotropic cosmic birefringence, consistent with previous analyses based on Planck and WMAP data. Separately, the Dark Energy Spectroscopic Instrument (DESI) DR2 results suggest that dark energy evolves over cosmic history, pointing to new physics in the late-time universe. In this paper, we propose that domain walls associated with the string axion can naturally explain the isotropic cosmic birefringence, focusing on the case in which the axion starts near a hilltop. Interestingly, to avoid the domain wall problem, these walls must form well after recombination. The predicted rotation angle, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>β</mi><mo>≈</mo><mn>0.21</mn><msub><mrow><mi>c</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow></math> degrees (with anomaly coefficient <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>c</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>≈</mo><mn>1</mn></mrow></math>), is in excellent agreement with observations. This scenario can be further tested by probing anisotropic birefringence of photons emitted long after recombination, as well as gravitational waves. Moreover, starting the axion oscillation from a hilltop naturally enhances its abundance via anharmonic effects, thus contributing to the dark energy component. We discuss how this hilltop axion scenario may connect with the DESI results.

Isotropic cosmic birefringence from string axion domain walls without cosmic strings and DESI results

We propose a novel mechanism of primordial black hole (PBH) formation through inverted bubble collapse. In this scenario, bubbles nucleate sparsely in an incomplete first-order phase transition, such that they remain isolated and do not percolate or collide with each other due to the extremely low nucleation rate. This is followed by a bulk phase transition in the rest of the universe that inverts these pre-existing bubbles into false vacuum regions. These spherically symmetric false-vacuum bubbles subsequently collapse to form PBHs. Unlike conventional PBH formation mechanisms associated with domain wall collapse or bubble coalescence, our inverted bubble collapse mechanism naturally ensures spherical collapse. We demonstrate that, when applied to the singlet extension of the Standard Model, this mechanism can produce highly monochromatic PBHs with masses up to $$ \mathcal{O} $$ (10 – 10 )$\textit{M}$ , which potentially explain the microlensing events observed in the OGLE and Subaru HSC data.

Kodai Sakurai

Primordial black hole formation via inverted bubble collapse

We study the evolution of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-balls under a spontaneously broken global U(1) symmetry. <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-balls are stabilized by the conservation of U(1) charge, but when the symmetry is spontaneously broken, the resulting Nambu-Goldstone boson can carry charge away from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-ball, potentially leading to charge leakage. To study this process in a controlled setting, we consider a scenario where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-balls first form under an unbroken U(1) symmetry, which is then spontaneously broken. We introduce two complex scalar fields: one responsible for forming the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-ball, and the other for spontaneously breaking the U(1) symmetry, allowing us to clearly separate the formation and symmetry-breaking phases. Using numerical simulations in a spherically symmetric system, we find that the evolution of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-balls depends sensitively on the structure of the interaction between the two fields and the magnitude of symmetry breaking. Depending on parameters, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-balls can completely decay, evaporate into smaller, stable <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-balls, or transition into oscillons/I-balls. In particular, we find that stable, localized remnants often survive the evolution over long timescales, especially when the symmetry-breaking scale is small. These results demonstrate that, even though spontaneous U(1) breaking can lead to significant energy and charge loss from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-balls, stable localized objects with reduced or no charge can frequently survive and potentially contribute to cosmological relics.

Masahiro Kawasaki

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math>-balls under a spontaneously broken U(1) symmetry

We discuss the thermal production of axions in renormalizable models involving two Higgs doublet fields and a complex singlet field with a global U(1) Peccei-Quinn symmetry, i.e., DFSZ type axion models. We demonstrate that, when the reheating temperature exceeds the mass scale of heavy Higgs bosons, axions are efficiently produced through heavy Higgs boson decays and scatterings at temperatures comparable to the heavy Higgs boson mass scale. As a result, the abundance of thermally produced axions is independent of the reheating temperature, which should be contrasted with the KSVZ axion model. This is because thermal productions via renormalizable interactions are IR-dominated processes. We demonstrate that the heavy Higgs boson decays are the main channels for axion thermal productions among various processes in the DFSZ-type axion models, which were missed in the literature. Our results apply to the original DFSZ QCD axion model since the production mechanism does not depend on the axion mass. As an application of axion productions from the heavy Higgs boson decays, we calculate the contributions to ∆$\textit{N}$ for axions with a mass smaller than $$ \mathcal{O}(0.1)\textrm{eV} $$ . Future measurements of ∆$\textit{N}$ could constrain model parameters in both axion and Higgs sectors. Focusing on axions with masses from keV to sub-GeV scale, we then discuss how cosmological observations such as X-ray and cosmic microwave background constrain the produced axion. We show that a large portion of the parameter space of the models can be explored even if the amount of the axion produced from the heavy Higgs bosons is much smaller than the observed cold dark matter abundance.

Poland

Thermal production of axions from heavy Higgs bosons

We investigate the level-crossing phenomenon in two-axion systems, where the mass eigenvalues intersect as the mass of one axion increases with the cooling of the universe. This phenomenon can significantly alter the abundance of axions in the early universe. Our study focuses on its impact on the QCD axion and an axion-like particle, identifying viable regions of axion mass and decay constant that explain the observed dark matter. We demonstrate the equivalence of two different bases for describing the axion system in the existing literature. Furthermore, we derive an improved expression for the adiabatic condition that overcomes limitations in earlier formulations. This new formulation is basis-independent, and we numerically validate its effectiveness. Our analysis reveals specific relations between axion masses and axion-photon couplings within the viable region. These relations could potentially serve as a smoking gun signal for this scenario if confirmed experimentally. We also find that, using the chiral perturbation model, the thermal friction on the QCD axion might be significantly larger than previously estimated. Additionally, we show that a simple model with axion mixing can naturally realize either a heavier or lighter QCD axion.

Yuma Narita

QCD axion dark matter from level crossing with refined adiabatic condition

We derive a bound on dark photon dark matter scenarios where the dark photon mass is generated through the Higgs mechanism, based on the requirement that symmetry breaking must occur sufficiently early in the universe. We emphasize that dark photon production occurs successfully when the dark Higgs field remains in the symmetric phase due to non-thermal trapping effects. For renormalizable Higgs potentials, our bound reads <display><formula id='fm0010'><math altimg='si1.svg'><mfrac><mrow><msub><mrow><mi>m</mi></mrow><mrow><msup><mrow><mi>&#947;</mi></mrow><mrow><mo>&#8242;</mo></mrow></msup></mrow></msub></mrow><mrow><msub><mrow><mi>q</mi></mrow><mrow><mi>H</mi></mrow></msub><msub><mrow><mi>e</mi></mrow><mrow><mi>H</mi></mrow></msub></mrow></mfrac><mspace width='0.25em' /><mo>&#8811;</mo><mspace width='0.25em' /><mn>60</mn><mspace width='0.2em' /><mrow><mi mathvariant='normal'>eV</mi></mrow><msup><mrow><mo stretchy='true'>(</mo><mfrac><mrow><mn>2</mn><mi>&#960;</mi></mrow><mrow><mi>&#955;</mi></mrow></mfrac><mo stretchy='true'>)</mo></mrow><mrow><mn>1</mn><mo stretchy='false'>/</mo><mn>4</mn></mrow></msup></math></formula></display> where <math altimg='si2.svg'><msub><mrow><mi>m</mi></mrow><mrow><msup><mrow><mi>&#947;</mi></mrow><mrow><mo>&#8242;</mo></mrow></msup></mrow></msub></math> is the dark photon mass, <math altimg='si3.svg'><msub><mrow><mi>e</mi></mrow><mrow><mi>H</mi></mrow></msub></math> is the gauge coupling, <math altimg='si4.svg'><msub><mrow><mi>q</mi></mrow><mrow><mi>H</mi></mrow></msub></math> is the charge of the dark Higgs boson, and <italic>&#955;</italic> is the Higgs quartic coupling. This constraint holds independently of any complications arising from the Schwinger effect and vortex formation in the Higgsed phase. For more general Higgs potentials such as the Coleman-Weinberg type potential, our bound yields different forms. We argue that late-time symmetry breaking of the dark U(1) symmetry satisfying our bound has only a mild impact on both the abundance and momentum distribution of dark photon dark matter, and therefore does not pose any serious problem for the dark photon dark matter scenario.

Naoya Kitajima

China

Shota Nakagawa

A bound on light dark photon dark matter

We derive the new identity in homotopy algebras which directly corresponds to the Schwinger-Dyson equations in quantum field theory. As an application, we derive the Ward-Takahashi identities. We demonstrate that the Ward-Takahashi identities are reproduced in several examples. In general, our formula contains divergence. We mediate this problem by introducing stubs known in the context of string field theory. With the regularization, we can calculate the anomaly such as axial U(1) anomaly in vector-like U(1) gauge theory.