Recently, Ai, Cruz, Garbrecht, and Tamarit (ACGT) [1–3] claimed that the strong CP problem can be avoided by adopting a particular order of limits in the Euclidean path integral, in which the spacetime volume is taken to infinity before summing over all topological sectors. We critically examine this proposal using exactly solvable examples of one-dimensional quantum mechanics on a ring, namely the quantum rotor and the quantum pendulum. These systems provide fully controlled settings with known $\textit{θ}$-dependent spectra. We find that the ACGT procedure fails to reproduce the correct energy spectrum. Since the spectrum is a direct physical observable, this result demonstrates that the proposed order of limits cannot be justified and conclusions about CP conservation in QCD cannot be based on this prescription alone.

Japan

Mohammad Aghaie

Ryosuke Sato

A particle on a ring or: how I learned to stop worrying and love $\textit{θ}$-vacua

Long-range attractive interactions between dark matter particles can significantly enhance their annihilation, particularly at low velocities. This “Sommerfeld enhancement” is typically computed by evaluating the deformation of the two-particle wavefunction due to the long-range potential, while ignoring the physics associated with the annihilation, and then scaling the appropriate annihilation matrix elements by factors that depend on the wavefunction in the limit where the particles approach zero relative separation. It has long been recognized that this approach is a valid approximation only in the limit where the annihilation rate is small, and breaks down in the regime where the enhanced annihilation rate approaches the unitarity bound, in which case ignoring the impact of the annihilation physics on the two-particle wavefunction cannot be justified and leads to apparent violations of unitarity. In the case where the physics relevant to annihilation occurs at a parametrically shorter distance scale (higher energy scale) compared with the long-range potential, we provide a simple prescription for correcting the Sommerfeld enhancement for the effects of the short-range physics, valid for all partial waves and for systems where multiple states are coupled by the long-range potential.

United States

Aditya Parikh

Tracy Slatyer

Regulating Sommerfeld resonances for multi-state systems and higher partial waves

<p>We discuss a novel mechanism for generating dark matter from a fast-rolling scalar field, relevant for both inflation and rotating axion models, and apply it specifically to the (QCD) axion. Dark matter comes from scalar field fluctuations generated by the product of the curvature perturbation and the fast-rolling background field. These fluctuations can explain the totality of dark matter in a vast axion parameter space, particularly for the QCD axion, which will be targeted by upcoming experiments. We review the constraints on this mechanism and potential gravitational-wave signatures.</p>

Türkiye

Cem Eröncel

Israel

Germany

Yann Gouttenoire

Géraldine Servant

Spain

Thailand

Peera Simakachorn

New Source for QCD Axion Dark Matter Production: Curvature Induced

<p>We show that primordial adiabatic curvature fluctuations generate an instability of the scalar field sourcing a kination era. We demonstrate that the generated higher Fourier modes constitute a radiationlike component dominating over the kination background after about 11 e-folds of cosmic expansion. Current constraints on the extra number of neutrino flavors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>N</mi><mi>eff</mi></msub></math> thus imply the observational bound of approximately 10 e-folds, representing the most stringent bound to date on the stiffness of the equation of state of the pre–Big Bang–nucleosynthesis universe.</p>

Universal Bound on the Duration of a Kination Era

A dark matter model based on QCD-like SU(N  c ) gauge theory with electroweakly interacting dark quarks is discussed. Assuming the dark quark mass m is smaller than the dynamical scale Λ d  ~ 4πf  d , the main component of the dark matter is the lightest G-parity odd dark pion associated with chiral symmetry breaking in the dark sector. We show that nonzero dark quark mass induces the universal mass contribution to both G-parity odd and even pions, and their masses tend to be degenerate. As a result, dark pion annihilation into heavier G-parity even dark pion also affects the dark matter relic abundance. Thus, our setup naturally accommodates forbidden dark matter scenario and realizes heavy dark matter whose mass is   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (1–100) TeV, which is different from conventional electroweakly interacting dark matter such as minimal dark matter. We also discuss CP-violation from the θ-term in the dark gauge sector and find that the predicted size of the electron electric dipole moment can be as large as ∼ 10 −32 e cm.

Tomohiro Abe

Takumu Yamanaka

Composite dark matter with forbidden annihilation

We investigate cosmological phase transitions in various composite Higgs models consisting of four-dimensional asymptotically-free gauge field theories. Each model may lead to a confinement-deconfinement transition and a phase transition associated with the spontaneous breaking of a global symmetry that realizes the Standard Model Higgs field as a pseudo-Nambu-Goldstone boson. Based on the argument of universality, we discuss the order of the phase transition associated with the global symmetry breaking by studying the renormalization group flow of the corresponding linear sigma model at finite temperature, which is calculated by utilizing the ϵ-expansion technique at the one-loop order. Our analysis indicates that some composite Higgs models accommodate phenomenologically interesting first-order phase transitions. We also explore the confinement-deconfinement transition in a UV-completed composite Higgs model based on a Sp(2N  c ) gauge theory. It is found that the first-order phase transition is favored when the number of degrees of freedom for the Sp(2N  c ) gauge field is much larger than that of matter fields in the fundamental representation of Sp(2N  c ). We comment on the gravitational wave signal generated by the confinement-deconfinement transition and its detectability at future observations. Our discussions motivate further studies on phase transitions in composite Higgs models with the use of lattice simulations.

Kohei Fujikura

China

Yuichiro Nakai

Yaoduo Wang

Cosmological phase transitions in composite Higgs models

We explore a model of dark matter (DM) that can explain the reported discrepancy in the muon anomalous magnetic moment and predict a large electric dipole moment (EDM) of the muon. The model contains a DM fermion and new scalars whose exclusive interactions with the muon radiatively generate the observed muon mass. Constraints from DM direct and indirect detection experiments as well as collider searches are safely evaded. The model parameter space that gives the observed DM abundance and explains the muon g – 2 anomaly leads to the muon EDM of d  μ  ≃ (4-5) × 10 −22 e cm that can be probed by the projected PSI muEDM experiment. Another viable parameter space even achieves   <math> <msub> <mi>d</mi> <mi>μ</mi> </msub> <mo>=</mo> <mi>O</mi> <mfenced> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>21</mn> </mrow> </msup> </mfenced> </math>  $$ {d}_{\mu }=\mathcal{O}\left({10}^{-21}\right) $$  e cm reachable by the ongoing Fermilab Muon g − 2 experiment and the future J-PARC Muon g − 2/EDM experiment.

Kim Khaw

Yoshihiro Shigekami

Zhihao Zhang

A large muon EDM from dark matter

Abstract We discuss spontaneous chiral symmetry breaking and the quark bilinear condensate in large-N$_{c}$ quantum chromodynamics (QCD). It is known that the existence of the η′ meson is implied in large-N$_{c}$ QCD, as pointed out by Witten[27] and Veneziano[28]. First, we show that the existence of η′ and the Ward–Takahashi identities implies the existence of Nambu–Goldstone bosons from chiral symmetry breaking SU(N$_{f}$)$_{L}$ × SU(N$_{f}$)$_{R}$ → SU(N$_{f}$)$_{V}$. Second, we show that a QCD inequality implies a non-zero lower bound on the quark bilinear condensate.

Chiral symmetry breaking and the quark bilinear condensate in large- Qcd La Rivista del Nuovo Cimento Quarks and strings on a lattice

Electric dipole moments (EDMs) of elementary particles are powerful probes of new physics with flavor-diagonal CP violation. The reported discrepancy in the muon anomalous magnetic moment motivates us to explore to what extent new physics with flavor-diagonal CP violation to address the discrepancy is probed by searches for the muon EDM. As a benchmark, we focus on a CP-violating two-Higgs-doublet model to explain the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly where the muon exclusively couples to one Higgs doublet. Since contributions to flavor violating processes as well as the electron EDM are suppressed, the muon EDM becomes an essential probe of the model. Our result shows that some viable parameter space leads to the muon EDM of around <math><msub><mrow><mi>d</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>≃</mo><mn>6</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>23</mn></mrow></msup><mspace width="0.2em"></mspace><mi>e</mi><mtext> cm</mtext></math> probed by the PSI experiment and most of the parameter space is covered by the proposed J-PARC experiment.

Muon electric dipole moment as a probe of flavor-diagonal CP violation

Spontaneous CP violation, such as the Nelson-Barr (NB) mechanism, is an attractive scenario for addressing the strong CP problem while realizing the observed phase of the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix. However, not only the CKM phase but also the baryon asymmetric Universe requires sources of CP violation. In this study, we show that a supersymmetric NB mechanism can naturally accommodate the Affleck-Dine (AD) baryogenesis within a CP-invariant Lagrangian. The model provides flat directions associated with new heavy quarks. Focusing on one of the directions, we find that the correct baryon asymmetry is obtained with a sufficiently low reheating temperature which does not cause the gravitino problem. Some parameter space is consistent with the gravitino dark matter. We assess radiative corrections to the strong CP phase induced by gauge-mediated supersymmetry breaking and CP-violating heavy fields and show that the strong CP problem is solved in a viable parameter space where the visible sector supersymmetric particles must be lighter than   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (100) TeV. Even in the case that they are heavier than the TeV scale, our model predicts the neutron electric dipole moment within the reach of the near future experiments. Our model addresses the electroweak naturalness problem, strong CP problem, baryon asymmetric Universe, and dark matter. Then, the model may give a new compelling paradigm of physics beyond the Standard Model.