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Physics High Energy Physics (Phenomenology)

hep-ph Watch High Energy Physics (Phenomenology)

Saturday 8 August

High Energy Physics (Phenomenology)

Flavor–Kinetic Entanglement Production from Decay and Scattering at Finite Density

Zekun Li, Jia Liu, Xiao-Ping Wang et al. (+1 more)

We extend the scattering-entanglement dictionary to finite-density environments by investigating the flavor–kinetic bipartition of the Hilbert space. We show that tracing over kinematic degrees of freedom maps the total branch-changing transition probability directly onto the leading flavor–kinetic linear entanglement entropy. At finite density, the vacuum branch-changing probability is replaced by an occupation-weighted collision probability, built from the same directed reaction-density kernel that enters the integrated Boltzmann equation. The resulting observable is the bath-averaged flavor–kinetic entanglement entropy of a pair sampled from the medium. As a proof of principle, this framework is applied to an $O(N)$ singlet-scalar extended model to probe thermal phase transitions. In the examples studied, the resulting entanglement entropy serves as a collision-based phase-transition-type diagnostic, exhibiting a finite discontinuity across a first-order phase transition and a nonanalytic temperature derivative for continuous transitions. These examples suggest a novel way to characterize thermal phase structures, distinct from traditional thermodynamic order parameters.
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All authors Zekun Li, Jia Liu, Xiao-Ping Wang, Jing-Jun Zhang

High Energy Physics (Phenomenology)

Strong decays of the possible $D^{*}K$ and $\bar{D}^{*}K$ molecules

Zi-Li Yue, Dian-Yong Chen and Elena Santopinto

Inspired by the rich spectrum of structures near the $D^{(*)}K^{(*)}/\bar{D}^{(*)}K^{(*)}$ thresholds, we postulate the existence of $S$-wave $D^{*}K$ and $\bar{D}^{*}K$ molecules, denoted as $T_{c\bar{s}1}^{f}(2460)$ with $I=0$ (corresponding to $D_{s1}(2460)$), $T_{c\bar{s}1}^{a}(2470)$ with $I=1$, $T_{\bar{c}\bar{s}1}^{f}(2460)$ with $I=0$, and $T_{\bar{c}\bar{s}1}^{a}(2470)$ with $I=1$, respectively. Using an effective Lagrangian approach, we investigate the strong decays of these molecular states. Our estimates indicate that the width of $T_{c\bar{s}1}^{a}(2470)$ is roughly three orders of magnitude larger than that of $T_{c\bar{s}1}^{f}(2460)$, while the widths of $T_{\bar{c}\bar{s}1}^{a/f}(2470)$ are of the same orders as that of $T_{c\bar{s}1}^{f}(2460)$. The present study may provide valuable clues for the experimental search for these molecular candidates.
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Friday 7 August

High Energy Physics (Phenomenology)

Effective propagators of flavor neutrinos

Maxim Dvornikov

We analyze the possibility to construct propagators of flavor neutrinos, which are particles with indefinite masses. This kind of propagators was used previously while studying neutrino flavor oscillations in frames of the quantum field theory (QFT) based approach. Starting with the operator and the path integral formulations of the QFT, we obtain that the naive derivation of propagators for flavor neutrinos violates the basic principles of the QFT. Nevertheless, we can still construct the effective propagator of flavor neutrinos considering the mass mixing term as a perturbation. In this situation, the effective propagator arises from the solution of a Dyson-like equation. We use the derived effective propagator to rederive the quantum mechanical transition probability for neutrino oscillations in vacuum in frames of the QFT. The application of the obtained results to neutrino oscillations in background matter is also considered.
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High Energy Physics (Phenomenology) · Cross-listed from astro-ph.CO

Inflationary Axion Isocurvature in the CMB across All Ultralight Masses

Rayne Liu, Wayne Hu and Daniel Grin

If the Peccei-Quinn symmetry of an ultralight axion is broken before the end of inflation, axion quantum fluctuations seed isocurvature perturbations, linking them to the tensor-to-scalar ratio $r$. We extend the effective time average (ETA) approach of the Boltzmann code ${\rm AxiECAMB}$ to accurately evolve these perturbations across the full axion mass range from dark energy ($m_a \lesssim H_0$) to dark matter ($m_a \gg 10^{-28}$ eV) types. We provide analytic fitting formulae for the axion abundance given the initial field value $\phi_{\rm ini}$, accurate at sub-percent level for $m_a \gg H_0$ and allowed dark matter fraction $f_{\rm dm}$. In the dark matter regime, the Planck bound on CDM isocurvature requires $r\ f_{\rm dm} < 0.08\,(m_a/10^{-27}\,{\rm eV})^{-1/2}$, which becomes stronger than the current BICEP tensor bound for $m_a f_{\rm dm}^2 \gtrsim 10^{-26.4}\,{\rm eV}$. For $10^{-32} \lesssim m_a/{\rm eV} \lesssim 10^{-28}$, Jeans suppression breaks the degeneracy with CDM isocurvature, leaving unique signatures, and in the dark energy regime ($m_a \lesssim H_0$), the isocurvature signal is even more highly suppressed, peaking only at the CMB quadrupole. We provide analytic scalings for both signatures. Given the tensor bound, any primary CMB detection in these two lightest regimes would indicate a non-inflationary origin of the isocurvature modes or a breakdown of the standard frozen-field misalignment scenario. A window of coexistence opens near $m_a \sim 10^{-25}$ eV and $f_{\rm dm} \gtrsim 0.1$ where both axion isocurvature and tensor modes could be discovered just below current bounds while simultaneously alleviating the $S_8$ tension.
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High Energy Physics (Phenomenology) · Cross-listed from astro-ph.HE

Neutrino quantum kinetics for fast flavor conversion in a time-dependent environment

Zewei Xiong and Meng-Ru Wu

Fast flavor conversions (FFCs) of neutrinos, driven by the fast flavor instability (FFI), can reshape the neutrino flavor content in dense astrophysical environments such as core-collapse supernovae and neutron star mergers. Most studies of FFCs adopt a two-step approach, in which a flavor-unstable state containing deep electron-minus-heavy-flavor lepton number (E-XLN) angular crossings is first constructed and subsequently evolved. Because realistic crossings should instead develop gradually through neutrino transport, the validity of such setups has been called into question. We investigate this issue by solving the neutrino quantum kinetic equations with self-consistent collisional rates in a spherically symmetric supernova background whose electron fraction evolves in time through a sequence of stages, starting from a configuration free of E-XLN crossings. We find that the evolution proceeds through three characteristic episodes. In the shallow-crossing episode, FFCs develop from marginally unstable, shallow crossings, carrying small-scale structures consistent with linear stability analysis. In the near-crossing-elimination episode, the balance between collisions and FFCs keeps the system in a near-quasistationary state in which the emerging crossings are continuously eliminated, so that the strongly unstable regime is never reached. In the swapping episodes, the E-XLN reverses sign and a dynamically propagating flavor-swap E-XLN zero surface forms. We find that the evolved flavor content at the end of different time stages broadly agrees with the quasistationary solutions obtained in the corresponding two-step models adopting fixed matter backgrounds. In addition, we investigate the robustness of the effective classical transport (ECT) framework that adopts subgrid flavor redistribution using different parametrized prescriptions. Notably, except during the swapping [abridged]
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High Energy Physics (Phenomenology)

Quest for an Understanding of Pion and Kaon Structure

Zhen-Ni Xu, Daniele Binosi, Craig D. Roberts et al. (+1 more)

The emergence of massless (Nambu-Goldstone) bosons in association with a dynamically global broken symmetry is a long known and widespread phenomenon in physics. However, practically nothing is known about the expressions of Nambu–Goldstone boson character on the internal structure of these bound states. Indeed, their structure is often ignored. In strong interactions, pions and kaons are the (would-be) Nambu-Goldstone bosons and experiments underway or planned at existing or anticipated high-energy, high-luminosity facilities will gather data that it is hoped will enable maps to be drawn of their internal structure. Meanwhile, theory and phenomenology find themselves in something of a quagmire. Herein, we provide a snapshot of the current status, highlighting issues under debate and identifying areas that deserve greater attention so that best use can be made of what is likely to be a huge volume of data delivered in the next decade or so.
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All authors Zhen-Ni Xu, Daniele Binosi, Craig D. Roberts, José Rodríguez-Quintero

High Energy Physics (Phenomenology)

Neutrinoless Double-Beta Decays from Operator Mixing

J. de Vries, S. Fajfer, L. P. S. Leal et al. (+2 more)

We perform a complete one-loop Renormalization Group (RG) analysis of neutrinoless double-beta decays within the Standard Model Effective Field Theory (SMEFT). Although several effective operators do not contribute to these processes at tree level, we show that they can generate sizable contributions through operator mixing. By accounting for the full one-loop RG evolution within the SMEFT, we find that the resulting constraints provide the most stringent bounds on numerous dimension-seven operators, improving upon limits derived from meson decays. We also highlight the importance of contributions beyond the first leading logarithm, which can provide the leading effects for specific operators and flavor combinations.
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All authors J. de Vries, S. Fajfer, L. P. S. Leal, O. Sumensari, R. Zukanovich Funchal

High Energy Physics (Phenomenology)

Testing Antimatter Couplings with Spectroscopy

Joerg Jaeckel and Lucas Puetter

We investigate how scalar-mediated potentials with Lorentz-violating couplings to Standard Model fermions affect spectroscopic observables in atoms and highly charged ions. Suitable combinations of an ordinary scalar and a time-like component of a Lorentz violating vector coupling allow for a split into "matter" and "antimatter" couplings, at least in the non-relativistic limit. By considering hydrogen and antihydrogen spectra, we access both matter and antimatter couplings. While relativistic effects alone lift degeneracies in ordinary hydrogen, providing indirect access to antimatter couplings, comparisons with antihydrogen measurements lead to significantly improved sensitivity to the antimatter couplings. In highly charged ions, enhanced relativistic effects further amplify the sensitivity, compensating for reduced experimental precision and larger theoretical uncertainties. We obtain the strongest bounds to date for scalar masses $m_\phi \gtrsim 400\:\mathrm{keV}$. For comparison, we estimate astrophysical constraints on the same parameter space, providing strong bounds even on antimatter couplings, despite stars being predominantly composed of matter.
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High Energy Physics (Phenomenology) · Cross-listed from astro-ph.HE

Constraints on magnetic monopoles from X-ray observations of neutron stars

Mainak Mukhopadhyay, Daniele Perri and Edward W. Kolb

Magnetic monopoles are captured efficiently by neutron stars, and if they catalyze nucleon decay, the decay products would thermalize and generate observable X-ray surface emission. We use archival Chandra, XMM-Newton, and Swift-XRT data for old isolated millisecond pulsars to place conservative limits on the Galactic monopole flux ($F_M$). For a benchmark cross-section of $\sigma_{\Delta \rm B} \sim 10^{-27}\ {\rm cm^2}$, our constraint as a function of monopole mass $m_M$ is given by $F_{\rm M}(m_M) \lesssim 6 \times 10^{-19}~\mathrm{cm^{-2}s^{-1}sr^{-1}} \times \max \big(4 \times 10^{-6}, \min (2 \times 10^{11}~\mathrm{(GeV/c^2)}/m_{\rm M} , 1 ) \big)$. These limits improve previous neutron-star bounds, provide the strongest constraints to date on $F_M$ for $m_M$ between $10^{11} - 10^{13}\ {\rm GeV/c^2}$, and are competitive to existing constraints for this scenario. We also derive complementary constraints from the measured thermal emission of the Magnificent Seven. Our results demonstrate that neutron star X-ray observations provide a powerful probe of magnetic monopoles and motivate dedicated X-ray searches for old neutron stars as a means to test monopole-induced heating.
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High Energy Physics (Phenomenology)

A $\Gamma_{3}$ modular symmetric approach for two-zero textures in left-right symmetric model

Ankita Kakoti and Happy Borgohain

The observed pattern for neutrino masses and mixing provides compelling evidence for Beyond Standard Model physics which further motivates the search for predictive frameworks that can simultaneously address flavor structure and its phenomenological consequences. This work particularly investigates the realization of all possible seven two-zero neutrino mass textures within the generic left-right symmetric model with $A_{4}$ modular symmetry. By considering modular weights 4,8 and 10, we systematically construct all the possible classes of 2-0 textures without the introduction of any flavon fields which enhances the predictive power of the framework. In this work, we also identify the texture classes capable of simultaneously accommodating current neutrino data, reproducing the observed baryon asymmetry and also yielding experimentally testable results for the effective Majorana neutrino mass for new physics contributions of neutrinoless double beta decay.
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High Energy Physics (Phenomenology)

Probing Dark Matter and Phantom Field Effects on Neutrino Oscillations around Black Holes

Ikrom Ergashov, Bakhtiyor Narzilloev, Ibrar Hussain et al. (+1 more)

This study investigates how dark matter in the background of the phantom field (DMPF) near a black hole influences neutrino flavor oscillations using a two-flavor model. It is found that gravitational effects are cancelled for radially moving neutrinos, causing the oscillation phase to increase with distance and mass-splitting, similar to flat spacetime. However, deflected neutrinos experience additional phase shifts due to dark matter, which slightly alters the mass-difference term and the total phase. Numerical analysis supports these findings and reveals a degeneracy between lens mass and dark matter parameters, affecting the transition probability curves based on source angle changes. Neutrinos modeled as Gaussian wave packets show that decoherence in a gravitational field is minimally influenced by dark matter, with the absolute neutrino mass determining the oscillation duration. Our findings imply that curved spacetime and dark matter significantly impact neutrino oscillations, offering potential insights into dark matter through neutrino astronomy in extreme environments.
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All authors Ikrom Ergashov, Bakhtiyor Narzilloev, Ibrar Hussain, Bobomurat Ahmedov

High Energy Physics (Phenomenology) · Cross-listed from hep-th

Quantum de Sitter and Analytically Continued Chern Simons Theory

Stephon Alexander and Kenneth Blakey

We give a Lefschetz thimble definition of the Chern–Simons–Kodama wavefunctional in Lorentzian self-dual gravity with positive cosmological constant. By complexifying the connection and choosing the Lefschetz thimble attached to the self-dual de~Sitter saddle, Witten's analytic continuation of Chern–Simons theory replaces the real contour, on which the defining integral is at best conditionally convergent, by an absolutely convergent integration cycle and yields a controlled semiclassical expansion. The relevant integrand is the full holomorphic exponential $e^{I}$, with $I=\kappa Y_{\rm CS}+(\text{source})$, and the steepest descent flow is governed by the Morse function $h=\operatorname{Re} I$. In the homogeneous isotropic de Sitter reduction, the construction reproduces the Hartle–Hawking Airy wavefunction. In the Bianchi~IX truncation, we take the Lefschetz thimble attached to the expanding de~Sitter saddle (the contracting branch defines a conjugate Lefschetz thimble); within this sector, the symmetric configuration is the only critical point for $\Lambda>0$. The corresponding Lefschetz thimble contains one trace direction with the FRW Airy structure and two anisotropic shear directions that are real-Gaussian damped at leading quadratic order. This gives a finite Bianchi~IX wavefunction which, to leading order, is the FRW Airy factor multiplied by a real anisotropy Gaussian. Thus, the Airy behavior is not an artifact of the one-dimensional minisuperspace reduction, but the leading form of the wavefunction on the Lefschetz thimble. We also discuss how the Lefschetz thimble prescription interfaces with Lorentzian reality conditions.
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High Energy Physics (Phenomenology)

Optimal Calibration-Free Observable for the Nucleon-Coupling Ratio in a Dual-Alkali Comagnetometer for Dark Matter Searches

Yossi Rosenzweig, Yevgeny Kats, Eli Sarid et al. (+3 more)

A dual-alkali single-cell $^{87}$Rb-$^{39}$K-$^{3}$He comagnetometer can read an axion-like dark matter signal through two optical rotation channels, encoding the ratio $\mathcal{R}=\xi_n/\xi_p$ of the field's neutron and proton spin couplings in their relative response. The inter-species phase difference $\Delta\varphi$ has been proposed as a calibration-free readout that is sensitive to $\mathcal{R}$. Treating the extraction of $\mathcal{R}$ as a statistical estimation problem, we show that the estimate of $\mathcal{R}$ depends on the two channels only through their complex ratio, which splits into $\Delta\varphi$ and an amplitude ratio, of which only $\Delta\varphi$ is insensitive to the relative gain and hence calibration free. For our choice of comagnetometer parameters, above $\sim\!100$ Hz the phase difference alone captures most of the coupling-ratio information. At lower frequencies $\Delta\varphi$ is no longer near-sufficient. Below $\sim\!40$ Hz, the amplitude ratio would improve the precision on $\mathcal{R}$ by a factor of $\gtrsim2$. Recovering that information, however, requires the relative gain to be known sufficiently accurately, so $\Delta\varphi$ remains the robust observable even where it is not the most informative one.
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All authors Yossi Rosenzweig, Yevgeny Kats, Eli Sarid, Menachem Givon, Yonathan Japha, Ron Folman

High Energy Physics (Phenomenology) · Cross-listed from astro-ph.CO

Sensitivity of Next-Generation CMB Surveys to Neutrinos and Other Light Relics

Cynthia Trendafilova, Srinivasan Raghunathan, Benjamin Wallisch et al. (+33 more)

Neutrinos and other light relics leave characteristic imprints in the cosmic microwave background anisotropies, making their observation a sensitive probe of the particle content and thermal history of the early universe. The energy density in these relativistic species is parameterized by their effective number $N_\mathrm{eff}$. Measuring this parameter at the percent level, which is a long-standing science goal of CMB-S4 and other experiments, would test a wide range of well-motivated physics within and beyond the Standard Model of particle physics. In this paper, we present Fisher-matrix forecasts of the projected sensitivity to $N_\mathrm{eff}$ of several CMB-S4 survey configurations considered during its extensive design phase. The conceptual design reaches $\sigma(N_\mathrm{eff}) < 0.03$ over its seven-year observing period, while the revised configuration achieves the same precision over a longer timescale. We complement these results with a cosmic-variance-limited survey over the same multipole range to quantify the room for improvement accessible with additional instrumental, observational, and theoretical efforts. Finally, we discuss the broad implications of precise $N_\mathrm{eff}$ measurements for the radiation sector, big bang nucleosynthesis, light thermal relics, and other early-universe physics. The forecasts presented in this work are performed with the publicly released DRAFT (Dark Radiation Anisotropy Flowdown Team) tool. It provides an end-to-end pipeline from simulated foreground maps and component separation to delensing and projected sensitivities for any cosmological parameter, and it can be directly applied to other cosmic microwave background survey designs.
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All authors Cynthia Trendafilova, Srinivasan Raghunathan, Benjamin Wallisch, Joel Meyers, Kevork N. Abazajian, Edoardo Altamura, Carlo Baccigalupi, Kimberly K. Boddy, Thejs Brinckmann, Yuji Chinone, Gabriele Coppi, Francis-Yan Cyr-Racine, Jacques Delabrouille, Katherine Freese, Helena García Escudero, Martina Gerbino, Shamik Ghosh, Vera Gluscevic, Daniel Green, Daniel Grin, Kevin M. Huffenberger, Mudit Jain, Lloyd Knox, Anto I. Lonappan, Marilena Loverde, Philip Lubin, Gabriele Montefalcone, Valentine Novosad, Marco Raveri, Christian L. Reichardt, Sayan Saha, Murali M. Saravanan, Emmanuel Schaan, Sara M. Simon, Julien Tang, Scott Watson

High Energy Physics (Phenomenology) · Cross-listed from gr-qc

Inflation with Nieh-Yan-like terms in metric-affine gravity

Ilaria Andrei, Christian Dioguardi, Damianos Iosifidis et al. (+3 more)

We study single-field slow-roll inflation in metric-affine gravity with a scalar field non-minimally coupled to the non-Riemannian Ricci scalar and to the divergences of the torsion and nonmetricity vectors, a structure that generalizes the well-known Nieh-Yan term. By imposing projective coherence of the matter sector and solving the connection field equations, we integrate out torsion and nonmetricity and obtain an equivalent Einstein-frame formulation in which the metric-affine couplings are encoded in a modified kinetic function and potential. For the choice of coupling functions $\mathcal{A}(\phi) = M_P^2 + \xi \phi^2$ to the non-Riemannian Ricci scalar, $\mathcal{C}_i(\phi) = \xi_i \phi$ to the Nieh-Yan-like terms and a monomial Jordan-frame potential $\mathcal{V} \propto \phi^k$, we show that in the limit of a large positive effective Nieh-Yan-like coupling $\bar{\xi}$ the canonical field satisfies $\chi \sim \phi^2$, the Jordan-frame field values during inflation become sub-Planckian, and the Einstein-frame potential reduces to $U \sim \chi^{k/2}$. We compute the slow-roll predictions numerically for quartic and quadratic Jordan-frame potentials and compare them with the current CMB constraints from Planck, BICEP/Keck, ACT, and SPT. We find that intermediate values of $\bar{\xi}$ can restore the compatibility of non-minimally coupled Palatini inflation with observations: in the quartic case, the model predicts a tensor-to-scalar ratio within reach of next-generation CMB experiments for $\bar{\xi}\lesssim10^4$, while in the quadratic case the coupling cures the $\eta$-problem arising for $\xi \gtrsim 10^{-2}$ and yields viable predictions for $10^{-2}\lesssim\bar{\xi}\lesssim 10^2$. In the negative $\bar{\xi}$ regime, the model does not improve upon standard Palatini inflation, though it can still produce distinct, testable predictions.
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All authors Ilaria Andrei, Christian Dioguardi, Damianos Iosifidis, Laur Järv, Antonio Racioppi, Margus Saal

High Energy Physics (Phenomenology) · Cross-listed from hep-th

Critical dynamics of a scalar field near four spatial dimensions

Laura Batini and Eduardo Grossi

The critical dynamics of a non-conserved order parameter is generally expected to become overdamped at long distances, even when propagating modes occur at microscopic or intermediate scales. We investigate the critical dynamics of a scalar field theory in thermal equilibrium which, in addition to local friction and noise, also contains a time-dependent second-order kinetic term. We show how to build a supersymmetric field-theory formulation. Using a two-loop expansion about four spatial dimensions, we show that the propagating and strictly overdamped limits share the same static Gaussian and Wilson-Fisher fixed points but realize distinct dynamical scaling regimes. The overdamped limit reproduces Model A. On the surface where local friction and noise vanish, the theory instead supports an interacting propagating fixed point whose dynamic exponent receives corrections at two loops. We demonstrate that coarse-graining does not generate a local dissipative operator on this surface, which therefore remains invariant under the RG flow. Local dissipation is nevertheless relevant at the propagating fixed point: an arbitrarily small equilibrium friction-noise perturbation drives the flow away from propagating scaling. Propagating critical dynamics thus defines a consistent but fine-tuned regime that is unstable to local equilibrium dissipation.
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High Energy Physics (Phenomenology) · Cross-listed from hep-th

Magnetic Catalysis and Fermion Mass Generation in de Sitter Spacetime

Kohei Fujikura, Toshifumi Noumi and Shintetsu Yamazaki

We consider the dynamics of a charged fermion in de Sitter space in the presence of a uniform background magnetic field, and discuss magnetic catalysis of chiral symmetry breaking using the Nambu–Jona-Lasinio (NJL) model. We evaluate the mode functions of the charged fermion field in this background by imposing the Bunch–Davies vacuum condition. The gap equation is solved in the mean-field approximation. We derive analytic expressions for the gap in several limiting regimes, such as the large-magnetic-field and large-curvature limits. We find that the curvature effect restores chiral symmetry, whereas the magnetic field enhances chiral symmetry breaking through the conventional mechanism of magnetic catalysis. The phase structure associated with chiral symmetry breaking is revealed by numerical calculations.
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High Energy Physics (Phenomenology)

Chiral Doubling of Heavy-Light Hadrons and the New Beauty–Strange $B_{s0}^*(5700)^0$ Candidate

Maciej A. Nowak and Ismail Zahed

The recent observation by the LHCb Collaboration of a new beauty–strange meson $B_{s0}^*(5700)^0$~\cite{LHCb:2026Bs0star}, under the conditional assignment $J^P=0^+$ provides an important new test of the chiral organization of heavy-light hadrons. More than three decades ago it was proposed that the coexistence of heavy-quark spin symmetry and spontaneously broken chiral symmetry implies that every heavy-light spin multiplet should possess an opposite-parity partner separated by a nearly universal mass gap determined primarily by the dynamics of the light degrees of freedom~\cite{Nowak:1993vc,Bardeen:1993ae}. This chiral doubling scenario was later developed into a quantitative heavy-hadron effective theory and extended to the complete charm and beauty spectra. In particular, the strange beauty sector was predicted to exhibit a parity splitting closely related to that of the strange charm sector, with only small $1/m_Q$ corrections. We briefly review the symmetry origin of chiral doubling, derive the universal parity splitting through the heavy-hadron chiral effective theory, and discuss the new LHCb observation in the context of the original theoretical predictions. Taken together with the established charm spectrum, if the new beauty-strange state is confirmed to have $J^P=0^+$, its mass is consistent with its interpretation as the chiral partner of the ground state $B_s^0$. Finally, we stress that the above confirmation of the spin and parity imposes in the chiral doubling scenario an existence of yet unobserved, very narrow beauty-strange meson with assignment $1^+$ at 5747 $\pm$ 2 MeV. This work is dedicated to the memory of our friend and collaborator Mannque Rho (1936–2026).
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High Energy Physics (Phenomenology)

Enlightening dark moments of neutrino with superradiance

Indra Kumar Banerjee, Ujjal Kumar Dey and Anna John

Neutrinos can acquire electromagnetic moments either within the Standard Model through higher order radiative corrections or within the domain of new physics. In this study we focus on probing these beyond the standard model neutrino moments through quenched superradiance of black holes where fermionic pairs can be produced from the superradiant bosonic cloud. We consider the production of dark photons from black hole superradiance and quenching occurs through the production of neutrino-antineutrino pairs from the dark photons. The efficiency of the pair production depends on the effective coupling between the dark photons and neutrinos, i.e., the dark electromagnetic moments. We also discuss bounds on primordial black hole abundance from neutrino background arising from this quenched superradiance mechanism.
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High Energy Physics (Phenomenology)

Axion Dark Matter Modulated Spin Wave Interferometry

Jiayi Liu, Chen-Hui Xie, Runyu Lei et al. (+3 more)

We propose a novel asymmetric spin wave interferometer to detect ultralight axion dark matter. The axion modulates spin-wave properties via a weak effective magnetic field in ferromagnets. The interferometer splits a spin-wave source into two paths of different lengths and sets them to interfere destructively. The system then converts the axion-induced phase shift into a measurable magnetization oscillation that can radiate electromagnetic waves and generate electrical signals via Faraday induction. The signal-to-noise ratios have been evaluated for three detection schemes: the linear amplifier, the single-photon detector, and the electrical signal detection approach, accounting for both magnetization fluctuation and thermal noise. The accessible axion mass range is approximately $10^{-8}$ eV to $10^{-6}$ eV, set by the spin wave propagation length and the relaxation time.
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All authors Jiayi Liu, Chen-Hui Xie, Runyu Lei, Sichun Sun, Yu Gao, Jinxing Zhang

High Energy Physics (Phenomenology)

Extraction of Pion Unpolarized Quark and Gluon Generalized Parton Distributions using Deep Neural-Networks

Satyajit Puhan, Shubham Sharma and Narinder Kumar

We present a deep neural-network (DNN) extraction of the pion unpolarized quark and gluon generalized parton distributions (GPDs) using the corresponding parton distribution functions (PDFs) from the JAM21 and xFitter analysis, together with experimental measurements of the pion electromagnetic form factor (EMFF) and lattice quantum chromodynamics (QCD) results. The GPDs are parameterized using a physics-informed neural-network (PINN) that incorporates the known PDF behavior, an exponential momentum-transfer dependence, and a trainable neural network (NN) component. The network parameters are determined by minimizing a $\chi^2$-based loss function. For the valence-quark GPDs, the loss function includes contributions from the EMFF, squared EMFF, charge-normalization constraints, and regularization terms. For the gluon GPDs, it incorporates constraints from the gluon gravitational form factors together with regularization. This framework enables a flexible, nonparametric extraction while preserving the essential theoretical and phenomenological constraints. By employing the full ensemble of available PDF replicas, we quantify the uncertainties of the extracted GPDs over a broad kinematic range in the longitudinal momentum fraction and momentum transfer, with the uncertainty bands corresponding to the $1\sigma$ confidence interval. The extracted valence-quark GPDs are found to be in good agreement with available lattice-QCD calculations. Our study demonstrates that DNN-based methods provide a flexible and robust framework for extracting pion GPDs and probing the multidimensional internal structure of the pion, offering a promising avenue for future investigations of hadron tomography.
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High Energy Physics (Phenomenology)

Leptogenesis via Resonant Sequential Dominance and TBC3 Mixing in a Type-I Seesaw Model

Michael Fodroci and Teruyuki Kitabayashi

We demonstrate how phenomenological model construction assuming Sequential Dominance can be extended to cases with degenerate right-handed neutrino masses. Because this framework accommodates resonant leptogenesis, we designate it as Resonant Sequential Dominance. We then investigate Dirac mass matrix textures compatible with current neutrino data within Resonant Sequential Dominance, utilizing a novel neutrino mixing matrix ansatz termed TBC3, proposed in this work. Additionally, we present an $A_4 \times (Z_3)^4 \times (Z_2)^2$-symmetric Lagrangian that is consistent with neutrino oscillation data and successfully drives resonant leptogenesis. Lastly, we find that accounting for the observed baryon asymmetry of the Universe requires the lightest right-handed neutrino mass to lie in the range $0.13\text{ TeV} \le m_{N_1} \le 230\text{ TeV}$.
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High Energy Physics (Phenomenology)

Probing dark matter through charged Higgs pair production at future multi-TeV muon colliders: A machine-learning analysis

Khiem Hong Phan and Quang Hoang-Minh Pham

Probing dark matter (DM) via charged Higgs pair production at future multi-TeV muon colliders is investigated within the Inert Doublet Model (IDM). The viable parameter space of the IDM is first updated by incorporating theoretical constraints and current experimental data. Based on the allowed parameter space, we evaluate DM relic density and compare the results with the latest constraints from direct DM detection experiments. The resulting parameter points consistent with all DM constraints are subsequently employed to study charged Higgs pair production at future multi-TeV muon colliders, including the subsequent decays of the charged Higgs bosons into Standard Model (SM) particles in association with DM candidate. In particular, we study the following production processes: $\mu^- \mu^+ \to \nu_{\mu} \bar{\nu}_{\mu} H^{\pm} H^{\mp} \to \ell^+ \ell^- + \nu_{\mu} \bar{\nu}_{\mu} \nu_{\ell} \bar{\nu}_{\ell} HH$, $\mu^- \mu^+ \to \nu_{\mu} \bar{\nu}_{\mu} H^{\pm} H^{\mp} \to \ell^\pm + 2\,\text{jets} + \nu_{\mu} \bar{\nu}_{\mu} \nu_{\ell} HH$ and $\mu^- \mu^+ \to \nu_{\mu} \bar{\nu}_{\mu} H^{\pm} H^{\mp} \to 4\,\text{jets} + \nu_{\mu} \bar{\nu}_{\mu} HH$ for $\ell =e, \mu$. The signal significance is evaluated against the corresponding SM backgrounds using both cut-based and machine-learning (ML) approaches. We find that ML framework substantially enhances the sensitivity to the signal processes compared with the conventional cut-based analysis. Furthermore, our results indicate that the DM signals through charged Higgs pair production can be indirectly probed with a statistical significance exceeding $5\sigma$ for several viable benchmark points at future multi-TeV muon colliders.
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High Energy Physics (Phenomenology)

A Compatibility Check: Low-Scale Chiral $U(1)_X$ Theories Vs. $(g-2)_e$ Anomaly

Bibhabasu De

Chiral Abelian extensions of the Standard Model (SM) gauge group may offer significant new possibilities for explaining various Beyond the Standard Model (BSM) phenomena within a common framework. The models being less explored in the literature only a few experimental constraints have been reported to date, leaving a major portion of the parameter space available for the New Physics (NP) phenomenology. The present paper considers three anomaly-free chiral Abelian extensions and examines the compatibility of the corresponding low-scale parameter spaces with the observed $(g-2)_e$ anomaly. The analysis results in stringent exclusion limits, completely ruling out the considered chiral models when used in complementarity with the existing experimental bounds.
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High Energy Physics (Phenomenology)

$q\bar{q}$ scattering phase shift in the $\pi^0$ channel and ${\pi}^0$ meson spectral function under external magnetic field and finite meson momentum

Min Zhou, Zhiyang Liu, Yvming Tian et al. (+3 more)

$q\bar{q}$ scattering phase shift in the $\pi^0$ channel $\Phi_{\pi^0}(\omega^2,\mathbf{k}_\perp^2,k^2_3)$ and ${\pi}^0$ meson spectral function $\rho_{\pi^0}(\omega^2,\mathbf{k}_\perp^2,k^2_3)$ under external magnetic field $eB$ and finite meson momentum $\mathbf{k}_\perp^2,k^2_3$ are studied in the framework of a two-flavor Nambu-Jona-Lasinio (NJL) model. The $q\bar{q}$ scattering phase shift in the $\pi^0$ channel $\Phi_{\pi^0}$ is closely related to $\pi^0$ spectral function $\rho_{\pi^0}$. We consider three situations, chiral broken phase ($T=\mu=0$), chiral restoration phase ($T>T_{pc},\ \mu=0$) and chiral restoration phase ($T=0,\ \mu>\mu_{pc}$). For $T=\mu=0$ and $T>T_{pc},\ \mu=0$ cases, ${\pi}^0$ meson spectral function $\rho_{\pi^0}$ shows a delta peak, several Breit-Wigner peaks and several non-Breit-Wigner peaks. The delta peak indicates the bound state of $\pi^0$ meson, and the Breit-Wigner peak means the resonant state of $\pi^0$ meson. For $T=0,\ \mu>\mu_{pc}$ case, Pauli blocking effect plays a role, which changes the inner structure of these Breit-Wigner peaks and non-Breit-Wigner peaks. Such multiple peak structure is caused by the external magnetic field. The $q\bar{q}$ scattering phase shift in the $\pi^0$ channel $\Phi_{\pi^0}$ shows a jump from $0$ to $\pi$ when $\pi^0$ meson is in bound state. When $\pi^0$ meson is in resonant state, $\Phi_{\pi^0}$ has the value $\pi/2$ and changes continuously. In large $\omega$ region, at the starting and end points of wide peaks of spectral function, $\Phi_{\pi^0}$ jumps abruptly (from $\pi$ to finite value or from finite value to $0$), and such jumps are caused by the external magnetic field. Finite momentum $\mathbf{k}_\perp^2$ or $k^2_3$ modifies the spectral function $\rho_{\pi^0}$ and scattering phase shift $\Phi_{\pi^0}$, which demonstrates the anisotropy in the system induced by external magnetic field.
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All authors Min Zhou, Zhiyang Liu, Yvming Tian, Chonglong Xie, Guoyun Shao, Shijun Mao

High Energy Physics (Phenomenology) · Cross-listed from nucl-th

Laboratory-frame $T$-matrix and heavy quark drag in the quark-gluon plasma

Anurag Tiwari and Min He

Non-perturbative scattering $T$-matrix is a core input for the evaluation of transport phenomena in a strongly-coupled medium. Existing in-medium $T$-matrix calculations are typically formulated in the two-particle center-of-mass frame, where the scattering equation can be reduced to a lower-dimensional problem. However, a medium explicitly breaks Lorentz invariance and defines a preferred reference frame, entailing that physical observables be constructed from scattering amplitudes evaluated in the medium rest (laboratory) frame. In this work, by exploiting the rotational symmetry about the scattering-pair-momentum axis, we develop a practical framework for solving the in-medium two-body $T$-matrix directly in the laboratory frame while retaining the full dependence on the total pair-momentum and scattering geometry. We demonstrate that the resulting amplitudes differ significantly from conventional center-of-mass-frame results and, when applied to heavy-light quark scattering in the quark-gluon plasma (QGP), lead to 25-40% corrections to heavy-quark drag coefficients at low momenta, thereby removing a significant source of theoretical uncertainty in extracting the QGP transport properties with heavy-quark probes.
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Thursday 6 August

High Energy Physics (Phenomenology)

Ultraviolet Flavor Transmission to T-Violating Neutrino Oscillation Observables in a Seesaw Framework with Sterile Mixing and Planck-Suppressed Corrections

Poulastya Kar, Bipin Singh Koranga and Vivek Nautiyal

We construct, numerically validate, and phenomenologically constrain a pipeline connecting a spontaneously CP-violating ultraviolet Type-I seesaw boundary condition to Planck-suppressed corrections of the T-violating oscillation asymmetry and the CP asymmetry in a minimal 3+1 sterile-neutrino framework. The ultraviolet Yukawa structure is reconstructed via Casas-Ibarra parameterization, matched onto the Weinberg operator at seesaw thresholds, and evolved to the electroweak scale using one-loop RGEs. The renormalized operator is combined with a 3+1 sterile sector to build the oscillation Hamiltonian, with Planck-suppressed terms treated perturbatively to yield closed-form first-order corrections. We report three substantive implementation errors identified and corrected during independent module validation. Running transports ultraviolet flavor structure with high fidelity distorting mixing angles and phases at or below the per-mille level despite an overall flavor-blind operator normalization run of about fifty percent. Subjecting the ultraviolet texture to a four-channel phenomenological suite (muon to electron gamma, tau to muon gamma, tau to electron gamma, non-unitarity, and perturbativity) confines the correction to the range between three in one hundred million and three in ten million at the natural scale. We prove the asymmetry correction is exactly independent of Casas-Ibarra angles at all allowed points, affecting the correction only indirectly via allowed heavy spectra. Sterile sector effects are strongly texture-dependent, ranging from suppression to a forty-fold enhancement. Evaluating the corresponding antineutrino Hamiltonian for the CP asymmetry, we find the Planck-induced correction lies two to three orders of magnitude below DUNE's published CP-phase sensitivity floor. We present this as a checked, reproducible negative phenomenological result.
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High Energy Physics (Phenomenology) · Cross-listed from hep-ex

Estimating the sensitivity of the IceCube Upgrade to probe the interior of the Earth using atmospheric neutrino oscillations

The IceCube Collaboration: R. Abbasi, M. Ackermann, J. Adams et al. (+420 more)

The IceCube Upgrade is a densely instrumented central region of the IceCube Neutrino Observatory, deployed during the 2025-26 polar season. It will reduce the detector's energy threshold and improve overall reconstruction capabilities for multi-GeV atmospheric neutrinos, which in turn enhance their sensitivity to Earth matter effects as they traverse through the deep Earth. In this study, we describe the potential of the IceCube Upgrade to observe Earth matter effects on atmospheric neutrinos and estimate the detector's sensitivity to probe key features of the Preliminary Reference Earth Model by utilizing these observations. We highlight the IceCube Upgrade's capability to estimate the mass of the Earth and verify the non-homogeneous distribution of matter density within the Earth. We also estimate the IceCube Upgrade sensitivity to measure the correlated densities of the Earth layers while incorporating constraints from the mass and moment of inertia of the Earth. Neutrino-based results would be independent and complementary to the seismic and gravitational measurements.
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All authors The IceCube Collaboration: R. Abbasi, M. Ackermann, J. Adams, S. K. Agarwalla, J. A. Aguilar, M. Ahlers, J.M. Alameddine, S. Ali, N. M. Amin, K. Andeen, C. Argüelles, S. Athanasiadou, S. N. Axani, R. Babu, X. Bai, A. Balagopal V., S. W. Barwick, V. Basu, R. Bay, J. J. Beatty, J. Becker Tjus, P. Behrens, J. Beise, C. Bellenghi, S. Benkel, S. BenZvi, D. Berley, E. Bernardini, D. Z. Besson, E. Blaufuss, L. Bloom, S. Blot, F. Bontempo, J. Y. Book Motzkin, C. Boscolo Meneguolo, S. Böser, O. Botner, J. Böttcher, J. Braun, B. Brinson, Z. Brisson-Tsavoussis, L. Brusa, R. T. Burley, D. Butterfield, K. Carloni, J. Carpio, S. Chattopadhyay, N. Chau, Y. C. Chen, Z. Chen, D. Chirkin, S. Choi, A. Chubarov, B. A. Clark, D. A. Coloma Borja, A. Connolly, J. M. Conrad, D. F. Cowen, C. De Clercq, J. J. DeLaunay, D. Delgado, T. Delmeulle, S. Deng, P. Desiati, K. D. de Vries, G. de Wasseige, T. DeYoung, J. C. Díaz-Vélez, S. DiKerby, T. Ding, M. Dittmer, A. Domi, L. Draper, L. Dueser, D. Durnford, K. Dutta, M. A. DuVernois, T. Ehrhardt, L. Eidenschink, A. Eimer, C. Eldridge, P. Eller, E. Ellinger, D. Elsässer, R. Engel, H. Erpenbeck, W. Esmail, S. Eulig, J. Evans, P. A. Evenson, K. L. Fan, K. Fang, K. Farrag, A. Fattorini, A. R. Fazely, A. Fedynitch, N. Feigl, C. Finley, D. Fox, A. Franckowiak, S. Fukami, P. Fürst, J. Gallagher, E. Ganster, A. Garcia, M. Garcia, E. Genton, L. Gerhardt, A. Ghadimi, C. Glaser, T. Glüsenkamp, J. G. Gonzalez, S. Goswami, A. Granados, D. Grant, S. J. Gray, S. Griffin, S. Griswold, K. M. Groth, D. Guevel, C. Günther, P. Gutjahr, C. Ha, A. Hallgren, L. Halve, F. Halzen, L. Hamacher, M. Handt, K. Hanson, J. Hardin, A. A. Harnisch, P. Hatch, A. Haungs, J. Häußler, K. Helbing, J. Hellrung, B. Henke, L. Hennig, F. Henningsen, L. Heuermann, R. Hewett, N. Heyer, S. Hickford, A. Hidvegi, C. Hill, G. C. Hill, R. Hmaid, K. D. Hoffman, A. Hollnagel, D. Hooper, S. Hori, K. Hoshina, M. Hostert, W. Hou, M. Hrywniak, T. Huber, K. Hultqvist, K. Hymon, A. Ishihara, W. Iwakiri, M. Jacquart, S. Jain, O. Janik, M. Jansson, M. Jin, N. Kamp, D. Kang, W. Kang, A. Kappes, L. Kardum, T. Karg, A. Karle, A. Katil, M. Kauer, J. L. Kelley, M. Khanal, A. Khatee Zathul, A. Kheirandish, T. Kim, H. Kimku, F. Kirchner, J. Kiryluk, C. Klein, Y. Kobayashi, S. Koch, A. Kochocki, R. Koirala, H. Kolanoski, T. Kontrimas, L. Köpke, C. Kopper, D. J. Koskinen, P. Koundal, M. Kowalski, T. Kozynets, A. Kravka, N. Krieger, J. Krishnamoorthi, T. Krishnan, K. Kruiswijk, E. Krupczak, A. Kumar, E. Kun, N. Kurahashi, C. Lagunas Gualda, L. Lallement Arnaud, M. J. Larson, F. Lauber, J. P. Lazar, K. Leonard DeHolton, A. Leszczyńska, C. Li, J. Liao, C. Lin, Q. R. Liu, Y. T. Liu, M. Liubarska, C. Love, L. Lu, F. Lucarelli, W. Luszczak, Y. Lyu, M. Macdonald, E. Magnus, Y. Makino, E. Manao, S. Mancina, A. Mand, I. C. Mariş, S. Marka, Z. Marka, L. Marten, I. Martinez-Soler, R. Maruyama, J. Mauro, F. Mayhew, F. McNally, K. Meagher, A. Medina, M. Meier, Y. Merckx, L. Merten, J. Mitchell, L. Molchany, S. Mondal, T. Montaruli, R. W. Moore, Y. Morii, A. Mosbrugger, D. Mousadi, E. Moyaux, T. Mukherjee, M. Nakos, U. Naumann, R. Neshat, L. Neste, M. Neumann, H. Niederhausen, M. U. Nisa, K. Noda, A. Noell, A. Novikov, A. Obertacke, V. O'Dell, A. Olivas, R. Orsoe, J. Osborn, E. O'Sullivan, B. Owens, V. Palusova, H. Pandya, A. Parenti, C. Parisel, N. Park, V. Parrish, E. N. Paudel, L. Paul, T. Pernice, T. C. Petersen, J. Peterson, S. Pick, M. Plum, A. Pontén, V. Poojyam, B. Pries, R. Procter-Murphy, G. T. Przybylski, L. Pyras, C. Raab, J. Rack-Helleis, N. Rad, M. Ravn, K. Rawlins, Z. Rechav, A. Rehman, I. Reistroffer, E. Resconi, C. D. Rho, W. Rhode, L. Ricca, B. Riedel, A. Rifaie, E. J. Roberts, S. Rodan, M. Rongen, A. Rosted, C. Rott, T. Ruhe, L. Ruohan, D. Ryckbosch, J. Saffer, D. Salazar-Gallegos, P. Sampathkumar, A. Sandrock, G. Sanger-Johnson, M. Santander, S. Sarkar, M. Scarnera, M. Schaufel, H. Schieler, S. Schindler, L. Schlickmann, B. Schlüter, F. Schlüter, N. Schmeisser, T. Schmidt, F. Schmitt, A. Scholz, F. G. Schröder, S. Schwirn, S. Sclafani, D. Seckel, L. Seen, M. Seikh, S. Seunarine, P. A. Sevle Myhr, R. Shah, S. Shah, S. Shefali, N. Shimizu, M. Shin, B. Skrzypek, R. Snihur, J. Soedingrekso, D. Soldin, P. Soldin, G. Sommani, D. Song, C. Spannfellner, G. M. Spiczak, C. Spiering, J. Stachurska, M. Stamatikos, T. Stanev, T. Stezelberger, T. Stürwald, T. Stuttard, G. W. Sullivan, I. Taboada, S. Ter-Antonyan, A. Terliuk, A. Thakuri, M. Thiesmeyer, W. G. Thompson, J. Thwaites, W. Tian, S. Tilav, K. Tollefson, J. A. Torres, S. Toscano, D. Tosi, A. K. Upadhyay, K. Upshaw, A. Vaidyanathan, N. Valtonen-Mattila, J. Valverde, J. Vandenbroucke, T. Van Eeden, N. van Eijndhoven, L. Van Rootselaar, J. van Santen, J. Vara, F. Varsi, M. Velazquez, M. Venugopal, M. Vereecken, S. Vergara Carrasco, S. Verpoest, D. Veske, A. Vijai, J. Villarreal, C. Walck, A. Wang, E. H. S. Warrick, C. Weaver, A. Weindl, J. Weldert, A. Y. Wen, C. Wendt, J. Werthebach, M. Weyrauch, N. Whitehorn, C. H. Wiebusch, D. R. Williams, L. Witthaus, J. Woodward, G. Wrede, X. W. Xu, J. P. Yanez, Y. Yao, E. Yildizci, S. Yoshida, F. Yu, S. Yu, T. Yuan, S. Yun-Cárcamo, A. Zander Jurowitzki, A. Zegarelli, S. Zhang, Z. Zhang, P. Zhelnin, P. Zilberman, C. Zilleruelo Cañas

High Energy Physics (Phenomenology)

Quantum Computers will constrain the Equation of State of Neutron Stars

Adrián Castaño-García, Nahia J. Dios-Bilbao, J. J. Gálvez-Viruet et al. (+4 more)

The Equation of State (EoS) of Nuclear Matter at high densities, and particularly that of neutron stars, resists $\mathit{ab}$ $\mathit{initio}$ Quantum Chromodynamics (QCD) computations due to the notorious sign problem of Lattice Gauge Theory at finite chemical potential. A quantum computer deploying QCD in canonical quantization should be able to make substantial progress. We set some basic goals for a future quantum computer to predict the EoS, and thus the basic static observables of the star (mass, radius and Tidal deformability, for example). We then develop the basic theory to address the canonical Hamiltonian in Weyl (time-axial) gauge expressed in normal modes, together with the squared Gauss operator $\mathcal{G}^2$ necessary to execute energy minimization algorithms restricted to the physical Fock subspace. Finally, we deploy our particle-quantum register encoding of a generic field theory to demonstrate QCD at finite chemical potential for a few (three-four) particles with a modest number of momentum modes, by simulating the quantum computer on a classical cluster. This opens the possibility for effective quantum computers to constrain the microscopic physics of neutron stars simultaneously to the operation of third–generation gravitational wave detectors such as the Einstein Telescope, providing more detailed predictions than has been possible until now.
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All authors Adrián Castaño-García, Nahia J. Dios-Bilbao, J. J. Gálvez-Viruet, Felipe J. Llanes-Estrada, Marío Logrosán-Álvarez, Nicolás M. Arenaza, María Gómez-Rocha

High Energy Physics (Phenomenology) · Cross-listed from astro-ph.CO

Cosmic birefringence from a joint analysis of ACT and Planck

Johannes R. Eskilt

Dark matter and dark energy could be ultra-light pseudoscalar fields that couple to electromagnetism through a Chern-Simons term. This would cause a parity-breaking rotation of the plane of linearly polarized light from the cosmic microwave background, known as cosmic birefringence, which is not predicted by $\Lambda$CDM. Recent hints of a non-zero cosmic birefringence angle have been found in both the Planck Data Release 4 and ACT Data Release 6 datasets independently. This work jointly analyzes the polarized maps of both, leveraging the cross-power spectra between the two telescopes. Taking the reported instrumental priors at face value, the joint analysis yields $\beta = 0.277^{\circ} \pm 0.057^{\circ}$, which is non-zero with a statistical significance of $4.8\sigma$. A robustness test mitigating contamination from dust emission excludes $\beta = 0^{\circ}$ at $3.5\sigma$, and retrieving $\beta=0^{\circ}$ would require both the dust $EB$ modeling and instrumental priors to fail simultaneously. However, unresolved systematics in the data must be understood before we can draw strong cosmological conclusions.
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