We present a new method for numerically computing generic multi-loop Feynman integrals. The method relies on an iterative application of Feynman’s trick for combining two propagators. Each application of Feynman’s trick introduces a simplified Feynman integral topology which depends on a Feynman parameter that should be integrated over. For each integral family, we set up a system of differential equations which we solve in terms of a piecewise collection of generalized series expansions in the Feynman parameter. These generalized series expansions can be efficiently integrated term by term, and segment by segment. This approach leads to a fully algorithmic method for computing Feynman integrals from differential equations, which does not require the manual determination of boundary conditions. Furthermore, the most complicated topology that appears in the method often has less master integrals than the original one. We illustrate the strength of our method with a five-point two-loop integral family.

We study the impact of the ambient fluid on the evolution of collapsing false vacuum bubbles by simulating the dynamics of a coupled bubble-particle system. A significant increase in the mass of the particles across the bubble wall leads to a buildup of those particles inside the false vacuum bubble. We show that the backreaction of the particles on the bubble slows or even reverses the collapse. Consequently, if the particles in the true vacuum become heavier than in the false vacuum, the particle-wall interactions always decrease the compactness that the false vacuum bubbles can reach, making their collapse to black holes less likely.

The Gross-Neveu model in the $N\to \infty$ limit in $d=1$ spatial dimensions exhibits a chiral inhomogeneous phase (IP), where the chiral condensate has a spatial dependence that spontaneously breaks translational invariance and the ${\mathbb{Z}}_2$ chiral symmetry. This phase is absent in $d=2$, while in $d=3$ its existence and extent strongly depends on the regularization and the value of the finite regulator. This work connects these three results smoothly by extending the analysis to noninteger spatial dimensions $1\le d<3$, where the model is fully renormalizable. To this end, we adapt the stability analysis, which probes the stability of the homogeneous ground state under inhomogeneous perturbations, to noninteger spatial dimensions. We find that the IP is present for all $d<2$ and vanishes exactly at $d=2$. Moreover, we find no instability toward an IP for $2\le d<3$, which suggests that the IP in $d=3$ is solely generated by the presence of a regulator.

In previous work on Schwinger pair creation in purely time-dependent fields, it was shown how to construct “solitonic” electric fields that do not create scalar pairs with an arbitrary fixed momentum. We show that this construction can be adapted to the fermionic case in two inequivalent ways, both closely related to supersymmetric quantum mechanics for reflectionless potentials, and both leading to the vanishing of the density of created pairs at certain values of the Pöschl-Teller like index $p$ of the associated Schrödinger equation. For one of them, we are able to demonstrate that the pair noncreation can be interpreted as a quantum interference effect using the phase-integral formalism. Asymptotically for large $p$, here scalar particles are not created for integer $p$ and fermions are not created for half-integer $p$. Thus, for any given momentum we can construct electric fields that create scalar particles but not spinor particles, and vice versa. In the scalar QED case, the solitonic fields had originally been found using the Gelfand-Dikii equation, which is related to the resolvent of the mode equation, and through it to the (generalized) KdV equation [I. M. Gelfand and L. A. Dikii, Asymptotic behavior of the resolvent of Sturm-Liouville equations and the Algebra of the Korteweg-De Vries equations, Russ. Math. Surv. 30, 5 (1975)]. This motivates us to develop for the spinor QED case, too, an evolution equation that can be considered as a fermionic generalization of the Gelfand-Dikii equation.

The Higgs mass is not protected by any symmetry in the Standard Model. Hence, the self-energy corrections to the Higgs mass become large due to the quadratic divergence terms. The Veltman condition (V.C.) ensures that the coefficient of the quadratic divergent term either vanishes or becomes negligible. The nonobservation of new physics has pushed the new physics scale to be larger than 1 TeV, making it impossible to satisfy the Veltman condition in the Standard Model without a very large fine-tuning. Many attempts are made to satisfy the V.C. in beyond the Standard Model theories, but the V.C. is hard to achieve at a very large scale ($\mathrm{\Lambda }$). Alternatively, it is possible that the new physics appears much above the electroweak scale, and the effect of the new physics is observed in terms of the Wilson coefficients of the Standard Model effective field theory (SMEFT) operators. The V.C. can be addressed in the SMEFT framework. In this paper, some specific new physics scenarios are considered at a very large scale. Below that scale, the effect of the new physics is observed as beyond the SMEFT. We particularly study the type-II seesaw model with the complex scalar triplet ($Y=1$) in the context of V.C. We found that this particular model is the minimal model to generate all SMEFT operators that appear in V.C. and satisfies V.C. We also examine the model parameter dependence of the Wilson coefficients in detail and show how the cancellation of the Wilson coefficients is highly dependent on some specific values of the model parameters.

We study a simple model of vector dark matter that couples to Standard Model particles via magnetic dipole interactions. In this scenario, the cosmological abundance arises through the freeze-in mechanism and depends on the dipole coupling, the vector mass, and the reheat temperature. To ensure cosmological metastability, the vector must be lighter than the fermions to which it couples, but rare decays can still produce observable $3\gamma$ final states; two-body decays can also occur at one loop with additional weak suppression, but are subdominant if the vector couples mainly to light fermions. For sufficiently heavy vectors, induced kinetic mixing with the photon can also yield additional two-body decays to lighter fermions and predict indirect detection signals through final-state radiation. We explore the implications of couplings to various flavors of visible particles and emphasize leptophilic dipoles involving electrons, muons, and taus, which offer the most promising indirect detection signatures through $3\gamma$, $e^{+}{e}^{-}\gamma$, and ${\mu }^{+}{\mu }^{-}\gamma$ decay channels. We also present constraints from current and past telescopes, and sensitivity projections for future missions including e-ASTROGAM and AMEGO.

We suggest a common origin for dark matter, neutrino mass and family symmetry within the orbifold theory proposed in [Phys. Lett. B 801, 135195 (2020); Phys. Rev. D 101, 116012 (2020)]. Flavor physics is described by an $A_4$ family symmetry that results naturally from compactification. Weakly interacting massive particle dark matter emerges from the first Kaluza-Klein excitation of the same scalar that drives family symmetry breaking and neutrino masses through the inverse seesaw mechanism. In addition to the “golden” quark-lepton mass relation and predictions for $0\nu \beta \beta$ decay, the model provides a good global description of all flavor observables.

We consider the embedding of Higgs inflation with a nonminimal coupling into the Weyl gravity. In this model, the effective current-current interactions from the heavy Weyl gauge field cancel the noncanonical Higgs kinetic term in Einstein frame, so the unitarity problem of the original Higgs inflation becomes less severe. For a simple case where the couplings of the heavy Weyl gauge field appears from the nonminimal couplings to the Ricci curvature scalar in Weyl gravity, we find that the resultant model for Higgs inflation is the same as in the Palatini formulation for Higgs inflation. The crucial difference of our model from the Palatini formulation for Higgs inflation is that there is a light Weyl gauge field coupled to the Higgs fields. We also generalize the unitarization of Higgs inflation with general covariant kinetic terms for the dilaton and the Higgs fields and realize a successful Higgs inflation, interpolating between the Palatini formulation for Higgs inflation and a Higgs-like inflation. We also discuss the Higgs mechanism for the light Weyl gauge field with an extra singlet scalar and show some interesting signatures for Higgs physics, such as the overall suppression of Higgs couplings and the direct couplings of the light Weyl gauge field to the Higgs boson.

We consider a model of dark photon which appears as a result of the successive symmetry breaking $\mathrm{SU}(2)\to \mathrm{U}(1)\to {\mathbb{Z}}_2$, where various types of topological defects appear in the dark sector. In this paper, we study the interactions between quantum electrodynamics (QED) charges and the dark topological defects through mixing between QED photon and dark photon. In particular, we extend our previous analysis by incorporating the magnetic mixing and $\theta$-terms. We also consider the dyons and dyonic beads in the dark sector. Notably, dark magnetic/dyonic beads are found to induce a QED Coulomb potential through the magnetic mixing despite finite mass of the dark photon.

Inspired by the recent measurements of the muon and electron anomalous magnetic moments, the rapid progress of the LHC search for supersymmetry, and the significantly improved sensitivities of dark matter direct detection experiments, we studied the supersymmetric contribution to the electron $g-2$, $a_e^{\mathrm{SUSY}}$, in the Next-to-Minimal Supersymmetric Standard Model with a discrete ${\mathbb{Z}}_3$ symmetry. We concluded that $a_e^{\mathrm{SUSY}}$ was mainly correlated with $a_{\mu }^{\mathrm{SUSY}}$ by the formula $a_e^{\mathrm{SUSY}}/m_e^2\simeq a_{\mu }^{\mathrm{SUSY}}/m_{\mu }^2$, and significant violations of this correlation might occur only in rare cases. As a result, $a_e^{\mathrm{SUSY}}$ was typically around $5\times {10}^{-14}$ when $a_{\mu }^{\mathrm{SUSY}}\simeq 2.5\times {10}^{-9}$. We also concluded that the dark matter direct detection and LHC experiments played crucial roles in determining the maximum reach of $a_e^{\mathrm{SUSY}}$. Concretely, $a_e^{\mathrm{SUSY}}$ might be around $3\times {10}^{-13}$ in the optimum cases if one used the XENON-1T experiment to limit the supersymmetry parameter space. This prediction, however, was reduced to $1.5\times {10}^{-13}$ after implementing the LZ restrictions and $1.0\times {10}^{-13}$ when further considering the LHC restrictions.

We propose a novel experiment to search for dark matter, based on the application of an electric field inside a microwave cavity and electrometry using Rydberg atoms. We show that this kind of experiment could be extremely useful for detecting specific dark matter candidates, namely massive vector fields coupled to the photon field, more commonly known as dark photons. Such a massive vector field is a good candidate for dark matter. Using realistic experimental parameters we show that such an experiment could improve the current constraint on the coupling constant of the dark photons to Standard Model photons in the $1\mathrm{\mu }\mathrm{eV}$ to $10\mathrm{\mu }\mathrm{eV}$ mass range, with the possibility of tuning the maximum sensitivity via the cavity size. The main limiting factors on the sensitivity of the experiment are the amplitude stability of the applied field and the measurement uncertainty of the electric field by the atoms.

Recently, it has been shown that the presence of a noninstantaneous era of reheating can significantly alter the charged lepton(s) equilibration temperature(s) which plays an important role in flavor leptogenesis. In this work, we extend the analysis to a more general situation where right-handed neutrinos (RHNs) are also produced from the decay of the inflaton. The presence of these RHNs along with the thermally generated ones (above its mass equivalent temperature only) redistributes different components of the energy density of the Universe during this reheating era, thereby affecting the charged lepton equilibration temperature (in addition to the Hubble effect) as well as the final reheating temperature $T_{\mathrm{RH}}$. Taking both the effects into account, we find that the decay of the lightest RHN in the setup not only provides a platform to study flavor leptogenesis during reheating, but also an interesting framework of $quasi$-thermal leptogenesis emerges.

We describe data on elastic $pp$ scattering at ISR and LHC energies using the analytical representation of the amplitude as the sum of three exponentials equipped with complex phases. In addition, we take into account the Coulomb and Coulomb-nuclear contributions in the entire transfer region and strong “perturbative” contributions in the large transfer region. Refined values of basic scattering characteristics are obtained. Significant changes in the behavior of the amplitude are detected at the transition from ISR to LHC energies. The results obtained indicate a two-layer structure of the colliding protons. In the transition to 13 TeV, a sharp increase in the size of the inner layer and its activity in the scattering is observed. A possible interpretation of this effect is discussed.

Deriving a comprehensive set of reduction rules for Feynman integrals has been a long-standing challenge. In this paper, we present a proposed solution to this problem utilizing generating functions of Feynman integrals. By establishing and solving differential equations of these generating functions, we are able to derive a system of reduction rules that effectively reduce any associated Feynman integrals to their bases. We illustrate this method through various examples and observe its potential value in numerous scenarios.

We compute the pressure, chiral condensate and strange quark number susceptibility from first principles within perturbative QCD at finite temperature and very high magnetic fields up to two-loop and physical quark masses. The region of validity for our framework is given by $m_s\ll T\ll \sqrt{eB}$, where $m_s$ is the strange quark mass, $e$ is the fundamental electric charge, $T$ is the temperature, and $B$ is the magnetic field strength. We study the convergence of the perturbative series for the pressure for different choices of renormalization scale in the running coupling, ${\alpha }_s(T,B)$. Our results for the chiral condensate and strange quark number susceptibility can be directly compared to recent lattice QCD data away from the chiral transition. Even though current lattice results do not overlap with the region of validity above, perturbative results seem to be in the same ballpark.

We present results of a search for bosonic super-weakly interacting massive particles (BSW) as keV scale dark matter candidates that is based on an exposure of $97.7\mathrm{kg}·\mathrm{year}$ from the COSINE experiment. In this search, we employ, for the first time, Compton-like as well as absorption processes for pseudoscalar and vector BSWs. No evidence for BSWs is found in the mass range from $10{\mathrm{keV}/\mathrm{c}}^2$ to $1{\mathrm{MeV}/\mathrm{c}}^2$, and we present the exclusion limits on the dimensionless coupling constants to electrons $g_{ae}$ for pseudoscalar and $\kappa$ for vector BSWs at 90% confidence level. Our results show that these limits are improved by including the Compton-like process in masses of BSW, above $\mathcal{O}(100{\mathrm{keV}/\mathrm{c}}^2)$.

Leptogenesis typically requires the introduction of heavy particles whose out-of-equilibrium decays are essential for generating a matter-antimatter asymmetry, according to one of Sakharov’s conditions. We show that, in Dirac leptogenesis, scatterings between the light degrees of freedom—Standard Model particles plus Dirac neutrinos—suffice to generate the asymmetry. Sakharov’s conditions are satisfied because the right-handed neutrino partners are out of equilibrium. Consequently, heavy degrees of freedom never needed to be produced in the early Universe, allowing for a reheating temperature below their mass scale. We solve the Boltzmann equations and discuss the viable parameter space together with observational signatures such as an increased number of effective neutrinos in the early Universe as well as proton decay for some realizations.

The $SU(2{)}_L$ triplet scalar with hypercharge $Y=0$ predicts a positive definite shift in the $W$ mass, with respect to the Standard Model prediction, if it acquires a vacuum expectation value. As this new field cannot couple directly to Standard Model fermions (on its own), it has no significant impact on other low-energy precision observables and is weakly constrained by collider searches. In fact, the multilepton anomalies at the LHC even point toward new scalars that decay dominantly to $W$ bosons, as the neutral component of the triplet naturally does. In this article, we show that with a minimal extension of the scalar triplet model by a heavy vectorlike lepton, being either (I) an $SU(2{)}_L$ doublet with $Y=-1/2$ or (II) an $SU(2{)}_L$ triplet with $Y=-1$, couplings of the triplet to Standard Model leptons are possible. This minimal extension can then provide, in addition to the desired positive shift in the $W$ mass, a chirally enhanced contribution to $(g-2{)}_{\mu }$. In addition, versions (I) and (II) can improve on $Z\to {\mu }^{+}{\mu }^{-}$ and alleviate the tension in first-row Cabibbo-Kobayashi-Maskawa unitarity (known as the Cabibbo angle anomaly), respectively. Finally, both options, in general, predict sizable changes of $h\to {\mu }^{+}{\mu }^{-}$, i.e., much larger than most other $(g-2{)}_{\mu }$ explanations where only $O(\%)$ effects are expected, making this channel a smoking gun signature of our model.

We study the high-energy limit of projectable Hořava gravity using on-shell graviton scattering amplitudes. We compute the tree-level amplitudes using symbolic computer algebra and analyze their properties in the case of collisions with zero total momentum. The amplitudes grow with collision energy in the way consistent with tree-level unitarity. We discuss their angular dependence and derive the expression for the differential cross section that happens to depend only on the essential combinations of the couplings. One of our key results is that the amplitudes for arbitrary kinematics are finite when the coupling $\lambda$ in the kinetic Lagrangian is taken to infinity—the value corresponding to candidate asymptotically free ultraviolet fixed points of the theory. We formulate a modified action which reproduces the same amplitudes and is directly applicable at $\lambda =\infty$, thereby establishing that the limit $\lambda \to \infty$ of projectable Hořava gravity is regular. As an auxiliary result, we derive the generalized Ward identities for the amplitudes in nonrelativistic gauge theories.

We set up the computation of correlation functions for operators that are dual to semiclassical string states in strongly coupled defect conformal field theories (dCFTs). In the dCFT that is dual to the D3-D5 probe-brane system, we calculate the correlation function of two heavy operators perturbatively, in powers of the conformal ratio. We find that the leading term agrees with the prediction of the operator product expansion (OPE). In the case of two heavy Berenstein-Maldacena-Nastase operators, we find agreement in subleading orders as well.