GWTC-2.1: Deep extended catalog of compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run

GRB Coordinates Network

The long-duration GRB 240222A (Fermi/GBM detection: GCN 35769; Swift/BAT detection: GCN 35770; GECAM-B detection: GCN 35782; INTEGRAL/SPI-ACS peak detection at 2024-02-22~ 08: 51: 32 UT) was observed by the GRBAlpha 1U CubeSat (Pal et al. 2023, A&A, 677, 40; https://ui. adsabs. harvard. edu/abs/2023A% 26A... 677A.. 40P/abstract). The detection was confirmed at the peak time 2024-02-22 08: 51: 31 UTC. The T90 duration measured by GRBAlpha is 1.5 s and the overall significance during T90 reaches 6.3 sigma. The light curve obtained by GRBAlpha is available here: https://grbalpha. konkoly. hu/static/share/GRB240222A_GCN. pdf All GRBAlpha detections are listed at: https://monoceros. physics. muni. cz/hea/GRBAlpha/GRBAlpha, launched on 2021 March 22, is a demonstration mission for a future CubeSat constellation (Werner et al. Proc. SPIE 2018). The detector of GRBAlpha consists …

Among the various candidates for dark matter (DM), ultralight vector DM can be probed by laser interferometric gravitational wave detectors through the measurement of oscillating length changes in the arm cavities. In this context, KAGRA has a unique feature due to differing compositions of its mirrors, enhancing the signal of vector DM in the length change in the auxiliary channels. Here we present the result of a search for U (1) B− L gauge boson DM using the KAGRA data from auxiliary length channels during the first joint observation run together with GEO600. By applying our search pipeline, which takes into account the stochastic nature of ultralight DM, upper bounds on the coupling strength between the U (1) B− L gauge boson and ordinary matter are obtained for a range of DM masses. While our constraints are less stringent than those derived from previous experiments, this study demonstrates the applicability of our method to the lower-mass vector DM search, which is made difficult in this measurement by the short observation time compared to the auto-correlation time scale of DM.

Among the various candidates for dark matter (DM), ultralight vector DM can be probed by laser interferometric gravitational wave detectors through the measurement of oscillating length changes in the arm cavities. In this context, KAGRA has a unique feature due to differing compositions of its mirrors, enhancing the signal of vector DM in the length change in the auxiliary channels. Here we present the result of a search for U (1) B− L gauge boson DM using the KAGRA data from auxiliary length channels during the first joint observation run together with GEO600. By applying our search pipeline, which takes into account the stochastic nature of ultralight DM, upper bounds on the coupling strength between the U (1) B− L gauge boson and ordinary matter are obtained for a range of DM masses. While our constraints are less stringent than those derived from previous experiments, this study demonstrates the applicability of our method to the lower-mass vector DM search, which is made difficult in this measurement by the short observation time compared to the auto-correlation time scale of DM.

Bulletin of the American Physical Society

B05. 00001: General Relativistic Simulations of Gas Accretion onto Merging Supermassive Black Hole Binaries*

GRB Coordinates Network

We have conducted further analysis of the LIGO Hanford Observatory (H1), LIGO Livingston Observatory (L1), and Virgo Observatory (V1) data around the time of the compact binary merger (CBC) candidate S240422ed (GCN Circular 36236). Parameter estimation has been performed using Bilby [1] and a new sky map, Bilby. offline0. multiorder. fits, 0, distributed via GCN Notice, is available for retrieval from the GraceDB event page: https://gracedb. ligo. org/superevents/S240422ed Based on posterior support from parameter estimation [1], under the assumption that the candidate S240422ed is astrophysical in origin, the probability that the lighter compact object is consistent with a neutron star mass (HasNS) is> 99%.[2] Using the masses and spins inferred from the signal, the probability of matter outside the final compact object (HasRemnant) is> 99%.[2] Both HasNS and HasRemnant consider the support of …

Astronomy & Astrophysics

We report on radio timing observations of PSR J0210+5845 that reveal large deviations from typical pulsar spin-down behaviour. We interpret these deviations as being due to the binary motion around the V = 13.5 star 2MASS J02105640+5845176, which is coincident in terms of its celestial position and distance with the pulsar. Archival observations and new optical spectroscopy have identified this object as a B6 V star, with a temperature of Teff ≈ 14 000 K and a mass of Mc = 3.5 to 3.8 M⊙, making it the lowest mass for a main sequence star known to be orbiting a non-recycled pulsar. We find that the timing observations constrain the binary orbit to be wide and moderately eccentric, with an orbital period of yr and eccentricity of . We predict that the next periastron passage will occur between 2030 and 2034. Due to the low companion mass, we find that the probability for a system with the properties of …

GRB Coordinates Network

The long-duration GRB 240128A (MAXI/GSC detection: GCN 35646; CALET/CGBM detection: GCN 35647; INTEGRAL/SPI-ACS trigger no. 10493) was observed by the GRBAlpha 1U CubeSat (Pal et al. 2023, A&A, 677, 40; arXiv: 2302.10048). The detection was confirmed at the peak time 2024-01-28 15: 13: 46 UTC. The T90 duration measured by GRBAlpha is 13 s and the overall significance during T90 reaches 8 sigma. The light curve obtained by GRBAlpha is available here: https://grbalpha. konkoly. hu/static/share/GRB240128A_GCN. pdf All GRBAlpha detections are listed at: https://monoceros. physics. muni. cz/hea/GRBAlpha/GRBAlpha, launched on 2021 March 22, is a demonstration mission for a future CubeSat constellation (Werner et al. Proc. SPIE 2018). The detector of GRBAlpha consists of a 75 x 75 x 5 mm3 CsI scintillator read out by a SiPM array, covering the energy range from~ 50 keV to~ 1000 …

arXiv preprint arXiv:2308.13666

The detection of GW170817 (Abbott et al. 2017b) coincident with the short gamma-ray burst GRB 170817A (Goldstein et al. 2017; Savchenko et al. 2017) was a groundbreaking discovery for the multimessenger era. Not only was it the first binary neutron star (BNS) merger detected by the gravitational-wave (GW) instruments Advanced LIGO (Aasi et al. 2015) and Advanced Virgo (Acernese et al. 2014), it was also the first, and to date only, GW detection with a confirmed electromagnetic (EM) counterpart. Since then, the search for EM emission from more of these extreme events has been at the forefront of multimessenger astronomy, particularly in the gamma-ray energy band, since GRB 170817A demonstrated that BNS mergers are a progenitor of short gamma-ray bursts (GRBs; Abbott et al. 2017a). GWs have also been observed from the mergers of other compact objects, such as binary black hole (BBH) and …

Among the various candidates for dark matter (DM), ultralight vector DM can be probed by laser interferometric gravitational wave detectors through the measurement of oscillating length changes in the arm cavities. In this context, KAGRA has a unique feature due to differing compositions of its mirrors, enhancing the signal of vector DM in the length change in the auxiliary channels. Here we present the result of a search for U (1) B− L gauge boson DM using the KAGRA data from auxiliary length channels during the first joint observation run together with GEO600. By applying our search pipeline, which takes into account the stochastic nature of ultralight DM, upper bounds on the coupling strength between the U (1) B− L gauge boson and ordinary matter are obtained for a range of DM masses. While our constraints are less stringent than those derived from previous experiments, this study demonstrates the applicability of our method to the lower-mass vector DM search, which is made difficult in this measurement by the short observation time compared to the auto-correlation time scale of DM.

The Astrophysical Journal

Hierarchical Bayesian inference can simultaneously account for both measurement uncertainty and selection effects within astronomical catalogs. In particular, the imposed hierarchy encodes beliefs about the interdependence of the physical processes that generate the observed data. We show that several proposed approximations within the literature actually correspond to inferences that are incompatible with any physical detection process. This generically leads to biases and is associated with the assumption that detectability is independent of the observed data given the true source parameters. We show several examples of how this error can affect astrophysical inferences based on catalogs of coalescing binaries observed through gravitational waves, including misestimating the redshift evolution of the merger rate as well as incorrectly inferring that general relativity is the correct theory of gravity when it is …

arXiv preprint arXiv:2403.03004

Among the various candidates for dark matter (DM), ultralight vector DM can be probed by laser interferometric gravitational wave detectors through the measurement of oscillating length changes in the arm cavities. In this context, KAGRA has a unique feature due to differing compositions of its mirrors, enhancing the signal of vector DM in the length change in the auxiliary channels. Here we present the result of a search for gauge boson DM using the KAGRA data from auxiliary length channels during the first joint observation run together with GEO600. By applying our search pipeline, which takes into account the stochastic nature of ultralight DM, upper bounds on the coupling strength between the gauge boson and ordinary matter are obtained for a range of DM masses. While our constraints are less stringent than those derived from previous experiments, this study demonstrates the applicability of our method to the lower-mass vector DM search, which is made difficult in this measurement by the short observation time compared to the auto-correlation time scale of DM.

Among the various candidates for dark matter (DM), ultralight vector DM can be probed by laser interferometric gravitational wave detectors through the measurement of oscillating length changes in the arm cavities. In this context, KAGRA has a unique feature due to differing compositions of its mirrors, enhancing the signal of vector DM in the length change in the auxiliary channels. Here we present the result of a search for U (1) B− L gauge boson DM using the KAGRA data from auxiliary length channels during the first joint observation run together with GEO600. By applying our search pipeline, which takes into account the stochastic nature of ultralight DM, upper bounds on the coupling strength between the U (1) B− L gauge boson and ordinary matter are obtained for a range of DM masses. While our constraints are less stringent than those derived from previous experiments, this study demonstrates the applicability of our method to the lower-mass vector DM search, which is made difficult in this measurement by the short observation time compared to the auto-correlation time scale of DM.

Bulletin of the American Physical Society

R17. 00007: Analytical Tests for U (1) Charge in Black Holes Using the Backwards One Body Model

Among the various candidates for dark matter (DM), ultralight vector DM can be probed by laser interferometric gravitational wave detectors through the measurement of oscillating length changes in the arm cavities. In this context, KAGRA has a unique feature due to differing compositions of its mirrors, enhancing the signal of vector DM in the length change in the auxiliary channels. Here we present the result of a search for U (1) B− L gauge boson DM using the KAGRA data from auxiliary length channels during the first joint observation run together with GEO600. By applying our search pipeline, which takes into account the stochastic nature of ultralight DM, upper bounds on the coupling strength between the U (1) B− L gauge boson and ordinary matter are obtained for a range of DM masses. While our constraints are less stringent than those derived from previous experiments, this study demonstrates the applicability of our method to the lower-mass vector DM search, which is made difficult in this measurement by the short observation time compared to the auto-correlation time scale of DM.

Bulletin of the American Physical Society

In this talk I report on the disappearance of a magnetic helical phase as it approaches a paramagnetic phase in thin film amorphous Fe51Ge49 (a-FeGe). a-FeGe hosts a randomized Dzyaloshinskii-Moriya interaction that competes with the exchange interaction to stabilize magnetic spin helices. By combining transmission resonant soft X-ray scattering and micromagnetic simulations, the phase transition was determined to be defect mediated with an accompanied reorientation of the helical propagation direction.

Physical Review D

The precision with which hadronic vacuum polarization (HVP) is obtained determines how accurately important observables, such as the muon anomalous magnetic moment a μ or the low-energy running of the electromagnetic coupling α, are predicted. The two most precise approaches for determining HVP are dispersive relations combined with e+ e−→ hadrons cross section data and lattice QCD. However, the results obtained in these two approaches display significant tensions, whose origins are not understood. Here we present a framework that sheds light on this issue and—if the two approaches can be reconciled—allows them to be combined. Via this framework, we test the hypothesis that the tensions can be explained by modifying the R-ratio in different intervals of center-of-mass energy s. As ingredients, we consider observables that have been precisely determined in both approaches. These are the …

Physical Review D

A search for quantum black holes in electron+ jet and muon+ jet invariant mass spectra is performed with 140 fb− 1 of data collected by the ATLAS detector in proton-proton collisions at s= 13 TeV at the Large Hadron Collider. The observed invariant mass spectrum of lepton+ jet pairs is consistent with Standard Model expectations. Upper limits are set at 95% confidence level on the production cross section times branching fractions for quantum black holes decaying into a lepton and a quark in a search region with invariant mass above 2.0 TeV. The resulting quantum black hole lower mass threshold limit is 9.2 TeV in the Arkani-Hamed-Dimopoulos-Dvali model, and 6.8 TeV in the Randall-Sundrum model.

Physical Review D

A search for quantum black holes in electron+ jet and muon+ jet invariant mass spectra is performed with 140 fb− 1 of data collected by the ATLAS detector in proton-proton collisions at s= 13 TeV at the Large Hadron Collider. The observed invariant mass spectrum of lepton+ jet pairs is consistent with Standard Model expectations. Upper limits are set at 95% confidence level on the production cross section times branching fractions for quantum black holes decaying into a lepton and a quark in a search region with invariant mass above 2.0 TeV. The resulting quantum black hole lower mass threshold limit is 9.2 TeV in the Arkani-Hamed-Dimopoulos-Dvali model, and 6.8 TeV in the Randall-Sundrum model.

Physical Review D

In this work we analyze the motion of charged particles in the background of the Kiselev geometry, which is considered here as an exact solution in the context of power-Maxwell electrodynamics. As it is well known, one can use either an electric ansatz or a magnetic one for the nonlinear electromagnetic field. We study the motion of an electrically charged particle for an electrically charged black hole and also for a magnetically charged black hole. In the second case the motion is restricted to Poincaré cones of various angles, as expected.

Physical Review D

Ultracold atomic gases can undergo phase transitions that mimic relativistic vacuum decay, allowing us to empirically test early Universe physics in tabletop experiments. We investigate the physics of these analog systems, going beyond previous analyses of the classical equations of motion to study quantum fluctuations in the cold-atom false vacuum. We show that the fluctuation spectrum of this vacuum state agrees with the usual relativistic result in the regime where the classical analogy holds, providing further evidence for the suitability of these systems for studying vacuum decay. Using a suite of semiclassical lattice simulations, we simulate bubble nucleation from this analog vacuum state in a 1D homonuclear potassium-41 mixture, finding qualitative agreement with instanton predictions. We identify realistic parameters for this system that will allow us to study vacuum decay with current experimental …

Physical Review D

The evolution of linear initial conditions present in the early Universe into extended halos of dark matter at late times can be computed using cosmological simulations. However, a theoretical understanding of this complex process remains elusive; in particular, the role of anisotropic information in the initial conditions in establishing the final mass of dark matter halos remains a long-standing puzzle. Here, we build a deep learning framework to investigate this question. We train a three-dimensional convolutional neural network to predict the mass of dark matter halos from the initial conditions, and quantify in full generality the amounts of information in the isotropic and anisotropic aspects of the initial density field about final halo masses. We find that anisotropies add a small, albeit statistically significant amount of information over that contained within spherical averages of the density field about final halo mass …

Physical Review D

We investigate the hypothetical X17 boson on neutron stars and quark stars (QSs) using various hadronic equation of states (EoSs) with phenomenological or microscopic origin. Our aim is to set realistic constraints on its coupling constant and the mass scaling, with respect to causality and various possible upper mass limits and the dimensionless tidal deformability Λ 1.4. In particular, we pay special attention to two main phenomenological parameters of the X17, one is related to the coupling constant g that it has with hadrons or quarks and the other with the in-medium effects through regulator C. Both are very crucial concerning the contribution on the total energy density and pressure. In the case of considering the X17 as a carrier of nuclear force in relativistic mean field theory, an admixture into the vector boson segment was constrained by 20% and 30%. In our investigation, we came to the general conclusion …

Physical Review D

The recent analysis on the central compact object in the HESS J1731-347 remnant suggests interestingly small values for its mass and radius. Such an observation favors soft nuclear models that may be challenged by the observation of massive compact stars. In contrast, the recent PREX-II experiment, concerning the neutron skin thickness of Pb 208, points toward stiff equations of state that favor larger compact star radii. In the present study, we aim to explore the compatibility between stiff hadronic equations of state (favored by PREX-II) and the HESS J1731-347 remnant in the context of hybrid stars. For the construction of hybrid equations of state we use three widely employed Skyrme models combined with the well-known vector MIT bag model. Furthermore we consider two different scenarios concerning the energy density of the bag. In the first case, that of a constant bag parameter, we find that the resulting …

Physical Review D

The second Gravitational-Wave Transient Catalog, GWTC-2, reported on 39 compact binary coalescences observed by the Advanced LIGO and Advanced Virgo detectors between 1 April 2019 15∶ 00 UTC and 1 October 2019 15∶ 00 UTC. Here, we present GWTC-2.1, which reports on a deeper list of candidate events observed over the same period. We analyze the final version of the strain data over this period with improved calibration and better subtraction of excess noise, which has been publicly released. We employ three matched-filter search pipelines for candidate identification, and estimate the probability of astrophysical origin for each candidate event. While GWTC-2 used a false alarm rate threshold of 2 per year, we include in GWTC-2.1, 1201 candidates that pass a false alarm rate threshold of 2 per day. We calculate the source properties of a subset of 44 high-significance candidates that have a …

Physical Review D

We study the compact binary dynamics in the post-Newtonian approach implemented to the Einstein-Hilbert action adding the cosmological constant Λ at first post-Newtonian (1PN) order. We consider very small values of Λ finding that it plays the role of a PN factor to derive the Lagrangian of a compact two-body system at the center of mass frame at 1PN. Furthermore, the phase function ϕ (t) is obtained from the balance equation, and the two polarizations h+ and h× are also calculated. We observe changes due to Λ only at very low frequencies, and we notice that it plays the role of “stretch” the spacetime such that both amplitudes become smaller. However, given its nearly negligible value, Λ has no relevance at higher frequencies whatsoever.

Physical Review D

The nuclear reaction network within the interior of the Sun is an efficient MeV physics factory and can produce long-lived particles generic to dark sector models. In this work we consider the sensitivity of satellite instruments, primarily the RHESSI spectrometer, that observe the quiet Sun in the MeV regime where backgrounds are low. We find that quiet Sun observations offer a powerful and complementary probe in regions of parameter space, where the long-lived particle decay length is longer than the radius of the Sun and shorter than the distance between the Sun and Earth. We comment on connections to recent model-building work on heavy neutral leptons coupled to neutrinos and high-quality axions from mirror symmetries.

Physical Review D

Within the framework of relative and absolute quantum field theories (QFTs), we present a general formalism for understanding polarizations of the intermediate defect group and constructing noninvertible duality defects in theories in 2 k spacetime dimensions with self-dual gauge fields. We introduce the polarization pair, which fully specifies absolute QFTs as far as their (k− 1)-form defect groups are concerned, including their (k− 1)-form symmetries, global structures (including discrete θ-angle), and local counterterms. Using the associated symmetry topological field theory (TFT), we show that the polarization pair is capable of succinctly describing topological manipulations, eg, gauging (k− 1)-form global symmetries and stacking counterterms, of absolute QFTs. Furthermore, automorphisms of the (k− 1)-form charge lattice naturally act on polarization pairs via their action on the defect group; they can be viewed as …

Physical Review D

Recent measurements of charm-baryon production in hadronic collisions have questioned the universality of charm-quark fragmentation across different collision systems. In this work the fragmentation of charm quarks into charm baryons is probed, by presenting the first measurement of the longitudinal jet momentum fraction carried by Λ c+ baryons, z∥ ch, in hadronic collisions. The results are obtained in proton-proton (p p) collisions at s= 13 TeV at the LHC, with Λ c+ baryons and charged (track-based) jets reconstructed in the transverse momentum intervals of 3≤ p T Λ c+< 15 GeV/c and 7≤ p T jet ch< 15 GeV/c, respectively. The z∥ ch distribution is compared to a measurement of D 0-tagged charged jets in p p collisions as well as to pythia 8 simulations. The data hints that the fragmentation of charm quarks into charm baryons is softer with respect to charm mesons, in the measured kinematic interval, as …

Physical Review D

The second Gravitational-Wave Transient Catalog, GWTC-2, reported on 39 compact binary coalescences observed by the Advanced LIGO and Advanced Virgo detectors between 1 April 2019 15∶ 00 UTC and 1 October 2019 15∶ 00 UTC. Here, we present GWTC-2.1, which reports on a deeper list of candidate events observed over the same period. We analyze the final version of the strain data over this period with improved calibration and better subtraction of excess noise, which has been publicly released. We employ three matched-filter search pipelines for candidate identification, and estimate the probability of astrophysical origin for each candidate event. While GWTC-2 used a false alarm rate threshold of 2 per year, we include in GWTC-2.1, 1201 candidates that pass a false alarm rate threshold of 2 per day. We calculate the source properties of a subset of 44 high-significance candidates that have a …

Physical Review D

The second Gravitational-Wave Transient Catalog, GWTC-2, reported on 39 compact binary coalescences observed by the Advanced LIGO and Advanced Virgo detectors between 1 April 2019 15∶ 00 UTC and 1 October 2019 15∶ 00 UTC. Here, we present GWTC-2.1, which reports on a deeper list of candidate events observed over the same period. We analyze the final version of the strain data over this period with improved calibration and better subtraction of excess noise, which has been publicly released. We employ three matched-filter search pipelines for candidate identification, and estimate the probability of astrophysical origin for each candidate event. While GWTC-2 used a false alarm rate threshold of 2 per year, we include in GWTC-2.1, 1201 candidates that pass a false alarm rate threshold of 2 per day. We calculate the source properties of a subset of 44 high-significance candidates that have a …

Physical Review D

A search for quantum black holes in electron+ jet and muon+ jet invariant mass spectra is performed with 140 fb− 1 of data collected by the ATLAS detector in proton-proton collisions at s= 13 TeV at the Large Hadron Collider. The observed invariant mass spectrum of lepton+ jet pairs is consistent with Standard Model expectations. Upper limits are set at 95% confidence level on the production cross section times branching fractions for quantum black holes decaying into a lepton and a quark in a search region with invariant mass above 2.0 TeV. The resulting quantum black hole lower mass threshold limit is 9.2 TeV in the Arkani-Hamed-Dimopoulos-Dvali model, and 6.8 TeV in the Randall-Sundrum model.

Physical Review D

Recent measurements of charm-baryon production in hadronic collisions have questioned the universality of charm-quark fragmentation across different collision systems. In this work the fragmentation of charm quarks into charm baryons is probed, by presenting the first measurement of the longitudinal jet momentum fraction carried by Λ c+ baryons, z∥ ch, in hadronic collisions. The results are obtained in proton-proton (p p) collisions at s= 13 TeV at the LHC, with Λ c+ baryons and charged (track-based) jets reconstructed in the transverse momentum intervals of 3≤ p T Λ c+< 15 GeV/c and 7≤ p T jet ch< 15 GeV/c, respectively. The z∥ ch distribution is compared to a measurement of D 0-tagged charged jets in p p collisions as well as to pythia 8 simulations. The data hints that the fragmentation of charm quarks into charm baryons is softer with respect to charm mesons, in the measured kinematic interval, as …

Physical Review D

A search for quantum black holes in electron+ jet and muon+ jet invariant mass spectra is performed with 140 fb− 1 of data collected by the ATLAS detector in proton-proton collisions at s= 13 TeV at the Large Hadron Collider. The observed invariant mass spectrum of lepton+ jet pairs is consistent with Standard Model expectations. Upper limits are set at 95% confidence level on the production cross section times branching fractions for quantum black holes decaying into a lepton and a quark in a search region with invariant mass above 2.0 TeV. The resulting quantum black hole lower mass threshold limit is 9.2 TeV in the Arkani-Hamed-Dimopoulos-Dvali model, and 6.8 TeV in the Randall-Sundrum model.

Physical Review D

We use data from the Atacama Cosmology Telescope (ACT) DR4 to search for the presence of neutrino self-interaction in the cosmic microwave background. Consistent with prior works, the posterior distributions we find are bimodal, with one mode consistent with Λ CDM and one where neutrinos strongly self-interact. By combining ACT data with large-scale information from WMAP, we find that a delayed onset of neutrino free streaming caused by significantly strong neutrino self-interaction is compatible with these data at the 2− 3 σ level. As seen in the past, the preference shifts to Λ CDM with the inclusion of Planck data. We determine that the preference for strong neutrino self-interaction is largely driven by angular scales corresponding to 700≲ ℓ≲ 1000 in the ACT E-mode polarization data. This region is expected to be key to discriminate between neutrino self-interacting modes and will soon be probed with …

Physical Review D

We determine the fine-tuning of the Yukawa couplings of supersymmetric QCD, discretized on a lattice. We use perturbation theory at one-loop level. The modified minimal subtraction scheme (MS) is employed; by its definition, this scheme requires perturbative calculations, in the continuum and/or on the lattice. On the lattice, we utilize the Wilson formulation for gluon, quark, and gluino fields; for squark fields we use naive discretization. The sheer difficulties of this study lie in the fact that different components of squark fields mix among themselves at the quantum level and the action’s symmetries, such as parity and charge conjugation, allow an additional Yukawa coupling. Consequently, for an appropriate fine-tuning of the Yukawa terms, these mixings must be taken into account in the renormalization conditions. All Green’s functions and renormalization factors are analytic expressions depending on the number of …