We introduce a robust numerical method for determining intersection numbers of Lefschetz thimbles in multivariable settings. Our approach employs the multiple shooting method to solve the upward flow equations from the saddle points to the original integration cycle, which also enables us to determine the signs of the intersection numbers. The method demonstrates stable and reliable performance, and has been tested for systems with up to 20 variables, which can be further extended by adopting quadruple-precision arithmetic. We determine intersection numbers for several complex saddle points in a discretized path integral, providing new insights into the structure of real-time path integrals. The proposed method is broadly applicable to a wide range of problems involving oscillatory integrals in physics and mathematics. <inter-ref xmlns:ns0='http://www.w3.org/1999/xlink' id='intrrf0001' ns0:href='https://github.com/KTrailovic/Lefschetz_Thimble_Intersection_Numbers'>https://github.com/KTrailovic/Lefschetz_Thimble_Intersection_Numbers</inter-ref>

Slovenia

India

Yutaro Shoji

Katarina Trailović

Stable evaluation of Lefschetz thimble intersection numbers:Towards real-time path integrals

<p>We propose an efficient regularization method for functional determinants of radial operators using heat kernel coefficients. Our key finding is a systematic way to identify heat kernel coefficients in the angular momentum space. We explicitly obtain the formulas up to sixth order in the heat kernel expansion, which suffice to regularize up to 13-dimensional functional determinants. We find that the heat kernel coefficients accurately approximate the large angular momentum dependence of functional determinants, and make numerical computations more efficient. In the limit of a large angular momentum, our formulas reduce to the Wentzel-Kramers-Brillouin formulas in previous studies, but are extended to higher orders. All the results are available in both the zeta function regularization and the dimensional regularization.</p>

Masahide Yamaguchi

Regularization of functional determinants of radial operators via heat kernel coefficients

We derive simple expressions to regularise functional determinants from fluctuations of fields with spin 0, 1/2, and 1. These are important for the precise dimensionful determination of false vacuum decay rates. We work in $\textit{D}$ = 4 Euclidean dimensions and use familiar Feynman diagrammatic techniques with a double expansion in interactions and masses, together with dimensional regularisation in momentum space. We Fourier transform to coordinate space and end up with a simple regularisation prescription in terms of single integrals over the Euclidean radius of field-dependent masses and their derivatives. Our results apply to models with an arbitrary scalar potential and with any number of scalars, fermions, gauge bosons and associated ghosts. We exemplify this approach on the Standard Model with a streamlined calculation of the renormalisation and isolation of divergences in fluctuation determinants.

Pietro Baratella

Miha Nemevšek

Lorenzo Ubaldi

Functional determinants for false vacuum decay

We consider a single real scalar field in flat spacetime with a polynomial potential up to $\textit{ϕ}$ , that has a local minimum, the false vacuum, and a deeper global minimum, the true vacuum. When the vacua are almost degenerate we are in the thin wall regime, while as their difference in potential energy increases, we approach the thick wall regime. We give explicit simple formulae for the decay rate of the false vacuum in 3 and 4 spacetime dimensions. Our results include a careful treatment both of the bounce action, which enters at the exponent of the decay rate, and of the functional determinant at one loop, which determines the prefactor. The bounce action is computed analytically as an expansion in the thin wall parameter in generic $\textit{D}$ dimensions. We find that truncating such an expansion at second order we obtain a remarkably accurate bounce action also deep into thick wall regimes. We calculate the functional determinant numerically in 3 and 4 dimensions and fit the results with simple polynomials of the same thin wall parameter. This allows us to write the complete one-loop decay rate as a compact expression, which works accurately from thin to thick wall regimes.

Marco Matteini

False vacuum decay rate from thin to thick walls

We revisit the decay rate of the electroweak vacuum in the standard model with the full one-loop prefactor. We focus on the gauge degrees of freedom and derive the degeneracy factors appearing in the functional determinant using group theoretical arguments. Our treatment shows that the transverse modes were previously overcounted, so we revise the calculation of that part of the prefactor. The new result modifies the gauge fields’ contribution by 6% and slightly decreases the previously predicted lifetime of the electroweak vacuum, which remains much longer than the age of the Universe. Our discussion of the transverse mode degeneracy applies to any calculation of functional determinants involving gauge fields in four dimensions.

Revising the Full One-Loop Gauge Prefactor in Electroweak Vacuum Stability

Low-energy Compton scattering is an important background for sub-GeV dark matter direct-detection and other experiments. Current Compton scattering calculations typically rely on assumptions that are not valid in the low-energy region of interest, beneath <math><mrow><mo>∼</mo><mn>50</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></mrow></math>. Here we relate the low-energy Compton scattering differential cross section to the dielectric response of the material. Our new approach can be used for a wide range of materials and includes all-electron, band-structure, and collective effects, which can be particularly relevant at low energies. We demonstrate the strength of our approach in several solid-state systems, in particular, Si, Ge, GaAs, and SiC, which are relevant for current and proposed experiments searching for dark matter, neutrinos, and millicharged particles.

United States

Rouven Essig

Israel

Yonit Hochberg

Aman Singal

Gregory Suczewski

Low-energy Compton scattering in materials

Abstract We use the anti-de Sitter/conformal field theory (AdS/CFT) correspondence to find the least bounce action in an AdS false vacuum state, i.e. the most probable decay process of the metastable AdS vacuum within the Euclidean formalism by Callan and Coleman. It was shown that the O(4) symmetric bounce solution leads to the action minimum in the absence of gravity, but it is nontrivial in the presence of gravity. The AdS/CFT duality is used to evade the difficulties particular to a metastable gravitational system. To this end, we show that the Fubini bounce solution in CFT, corresponding to the Coleman–de Luccia (CdL) bounce in AdS, gives the least action among all finite bounce solutions in a conformal scalar field theory. Thus, we prove that the CdL action is the least action among all possible large and thin-wall configurations under certain conditions.

Japan

Naritaka Oshita

South Korea

Is the Coleman–de Luccia Action Minimum?: An AdS/CFT Approach

We study the stability of the electroweak vacuum in the supersymmetric (SUSY) standard model (SM), paying particular attention to its relation to the SUSY contribution to the muon anomalous magnetic moment a  μ . If the SUSY contribution to a  μ  is sizable, the electroweak vacuum may become unstable because of enhanced trilinear scalar interactions. With a  μ  being fixed, larger slepton masses require more enhanced trilinear couplings, which make the electroweak vacuum more unstable. Thus, assuming SUSY contribution to a  μ  being sizable, an upper bound on the slepton masses is obtained. We give a detailed prescription to perform a full one-loop calculation of the decay rate of the electroweak vacuum for the case that the SUSY contribution to a  μ  is enhanced. We also give an upper bound on the slepton masses as a function of the SUSY contribution to a  μ .

So Chigusa

Takeo Moroi

Stability of electroweak vacuum and supersymmetric contribution to muon g − 2

We discuss new possible tunneling processes in the presence of gravity. We formulate quantum tunneling using the Wheeler-deWitt canonical quantization and the WKB approximation. The distinctive feature of our formulation is that it accommodates the coexistence of Euclidean and Lorentzian evolution. It opens up a new possibility of quantum tunneling; e.g. a bubble wall itself tunnels the potential barrier pulling the field nearby, where the wall region experiences the Euclidean evolution while the other regions experience the Lorentzian evolution simultaneously. We execute numerical analysis and find that such a process can have a much higher tunneling rate than that of the Coleman-De Luccia bounce. We also find that the new tunneling processes exist even in the decoupling regime of gravity and affect low energy phenomenology.

Polychronic tunneling: New tunneling processes experiencing Euclidean and Lorentzian evolution simultaneously

Abstract We study SU(4)$_{C}$ × SU(2)$_{L}$ × U(1)$_{R}$ models with modular A$_{4}$ symmetry that provide a unified description of the quark and lepton sectors including the flavor structures. The models are distinguished by the assignments of the modular weight to matter superfields. We carry out numerical χ$^{2}$ analysis and search for parameter sets that accommodate the experimental results. We provide a benchmark point for each model to illustrate the implications of our models.

China

Takaaki Nomura

Hiroshi Okada

(4) × (2) × (1) Models With Modular Symmetry Dark matter stability at fixed points in a modular A4 symmetry A linear seesaw model with A modular flavor and local symmetries Broken scaling neutrino mass matrix and leptogenesis based on modular invariance Modulus linking leptonic CP violation to baryon asymmetry in modular invariant flavor model SO models with A modular symmetry Modular symmetry in the SMEFT Modular flavor symmetry and vector-valued modular forms Lepton flavor violation, lepton and electron EDM in the modular symmetry 4D modular flavor symmetric models inspired by a higher-dimensional theory