Motivated by two new states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1911</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2300</mn><mo stretchy="false">)</mo></math> observed by BESIII, we have investigated the mass spectrum and the strong decay properties of the strangeonium mesons within the modified Godfrey-Isgur model by considering the screening effects. We have determined the free parameters using the masses and widths of the well-established <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mo stretchy="false">(</mo><mn>1020</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mo stretchy="false">(</mo><mn>1680</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1415</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>f</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">(</mo><mn>1525</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ϕ</mi><mn>3</mn></msub><mo stretchy="false">(</mo><mn>1850</mn><mo stretchy="false">)</mo></math>. According to our results, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1911</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2300</mn><mo stretchy="false">)</mo></math> could be well explained as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><msup><mn>2</mn><mn>1</mn></msup><msub><mi>P</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><msup><mn>3</mn><mn>1</mn></msup><msub><mi>P</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> states, respectively. Meanwhile, the possible assignments of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2000</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1870</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mo stretchy="false">(</mo><mn>2170</mn><mo stretchy="false">)</mo></math> as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>3</mn><mn>3</mn></msup><msub><mi>S</mi><mn>1</mn></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mn>1</mn></msup><msub><mi>D</mi><mn>2</mn></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>2</mn><mn>3</mn></msup><msub><mi>D</mi><mn>1</mn></msub></math> are also discussed. Furthermore, the masses and widths of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>S</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mi>S</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>P</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mi>P</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>D</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>D</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> states are also given and compared with various theoretical predictions, which will be helpful for the observations and confirmations of these states in the future.

China

Wei Hao

Pakistan

M. Atif Sultan

Li-Juan Liu

En Wang

Strangeonium spectrum with screening effects and interpretation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1911</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2300</mn><mo stretchy="false">)</mo></math> observed by BESIII

Axionlike particles (ALPs) are hypothetical particles that serve as promising candidates for cold dark matter. Portals like inelastic axion scattering and axion propagated force have been employed to search for the upper limit of the ALPs’ coupling with standard model particles. Other methods, like the axion-fermion interaction in the CASPEr experiment, integrate the dark matter motion into the measurement. We suggest a new method for detecting dark matter axions based on axion-electron elastic scattering. In the pseudoscalar axion model, this interaction can be seen as an effective magnetic field, so high-sensitivity atomic magnetometers can be utilized to measure this interaction. The scattering cross section of this process is significantly amplified by the high number density and occupation number of axion dark matter. The upper limit of the electron-axion coupling coefficient obtained from this process can reach two orders of magnitude higher than previous results at low axion mass, and will exceed the astrophysics limits by using a developing magnetometer. This scattering process also provides an efficient way to detect local structures of dark matter.

Dongyi Yang

Chenxi Sun

Jianwei Zhang

Constraints on axion dark matter by spin-dependent macroscopic force

Parton distribution functions (PDFs) form an essential part of particle physics calculations. Currently, the most precise predictions for these nonperturbative functions are generated through fits to global data. A problem that several PDF fitting groups encounter is the presence of tension in datasets that appear to pull the fits in different directions. In other words, the best fit depends on the choice of dataset. Several methods to capture the uncertainty in PDFs in presence of seemingly inconsistent fits have been proposed and are currently in use. These methods are important to ensure that uncertainty in PDFs are not underestimated. Here we propose a novel method for estimating the uncertainty by introducing a generalized statistical model based on Bayesian hierarchical models, which is implemented via the Gaussian Mixture Model (GMM). The methodology is inspired by unsupervised machine learning techniques and is closely related to the statistical methods of ensemble learning and Bayesian model averaging. Using a toy model of PDFs, we demonstrate how the GMM can be used to faithfully reconstruct the likelihood associated with PDF fits, which can in turn be used to accurately determine the uncertainty on PDFs, especially in the presence of tension in the fitted datasets. We further show how this statistical model reduces to the usual <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>χ</mi><mn>2</mn></msup></math> likelihood function for a consistent dataset and provide measures to optimize the number of Gaussians in the GMM.

Mengshi Yan

Tie-Jiun Hou

Zhao Li

United States

Kirtimaan Mohan

C.P. Yuan

Generalized statistical model for fits to parton distributions

The singlet-doublet model is an economical model of weakly interacting dark matter. We revisit it in light of improved dark matter direct detection limits. We characterize the now well-defined regions of remaining parameter space with suppressed direct detection cross sections and discuss features of the spectrum accessible at the Large Hadron Collider. We discuss when and how parameters in these special regions might be realized as the result of renormalization group evolution when starting with generic ultraviolet initial conditions.

Italy

Prudhvi N. Bhattiprolu

Evan Petrosky

Aaron Pierce

Singlet-doublet dark matter revisited

We investigate the sensitivity of future high-energy muon colliders to heavy Majorana neutrinos, considering both opposite-sign (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math>) and same-sign (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup></math>) collision modes. We focus on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> colliders operating at center-of-mass energies of 1, 3, and 10 TeV, as well as the proposed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mi>TRISTAN</mi></math> facility at 2 TeV, and we analyze the production of heavy neutrinos via vector boson fusion in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel, a mechanism that becomes dominant in the multi-TeV regime. We evaluate its exclusion potential in terms of the heavy neutrino mass and the mixing of the heavy neutrino with its Standard Model counterparts, using both cut-based selections and boosted decision trees trained to exploit the distinct kinematic signatures of heavy Majorana neutrino exchanges. Our results demonstrate the complementarity between collider configurations and show that active-sterile mixing angles as small as 0.001 could be probed for neutrino masses up to 100 TeV, an experimentally inaccessible region of the parameter space at current facilities. Altogether, this work establishes the discovery potential of muon colliders for testing super-heavy Majorana neutrinos, complementary to conventional probes, and provides compelling motivation for the next generation of high-energy lepton colliders.

Canada

Parham Dehghani

Mariana Frank

France

Benjamin Fuks

Vector boson fusion signatures of superheavy Majorana neutrinos at muon colliders

In this work we compute the branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mi>τ</mi><msub><mi>ν</mi><mi>τ</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>s</mi></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><mi>τ</mi><msub><mi>ν</mi><mi>τ</mi></msub></math> within the relativistic independent quark model, emphasizing the harmonic potential model-dependent analysis of these decay channels in the precision flavor physics era. Considering the experimental observation of longitudinal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math>-polarization and fraction of longitudinal polarization at LHCb and Belle, we have also investigated these observables within our model framework which are aligning well with the standard model expectations. We perform a comprehensive analysis of the form factors across the whole accessible kinematic range of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math>. Our results are consistent and compatible with other theoretical approaches as well as with the experimental measurements. Furthermore, we evaluated the clean ratios of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>s</mi></msub></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mn>0</mn></msub></math> in the semimuonic mode that are in accordance with the LHCb measurements, and support the validity of the SU(3) flavor symmetry. Although the concept of new physics is facing a significant challenge at the current TeV scale, semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays, nevertheless, always serve as a valuable probe to study the decay dynamics.

India

Sonali Patnaik

Lopamudra Nayak

Sanjay Kumar Swain

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mi>τ</mi><msub><mi>ν</mi><mi>τ</mi></msub></math> decay properties with the relativistic independent quark model

We present a lattice QCD calculation of the pion scalar form factor and associated radii with fully controlled systematics. Lattice results are computed on a large set of 17 gauge ensembles with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></math> Wilson Clover-improved sea quarks. These ensembles cover four values of the lattice spacing between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>=</mo><mn>0.049</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>=</mo><mn>0.086</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>, a pion mass range of 130–350 MeV, and various physical volumes. A precise determination of the notorious quark-disconnected contributions facilitates an unprecedented momentum resolution for the form factor, particularly on large and fine ensembles in the vicinity of physical quark mass. A large range of source-sink separations <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1.0</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi><mo>≲</mo><msub><mi>t</mi><mi>sep</mi></msub><mo>≲</mo><mn>3.25</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> is used to reliably extract the relevant ground state matrix elements at vanishing and nonvanishing momentum transfer. This allows us for the first time to obtain the scalar radii from a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>z</mi></math>-expansion parametrization of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup></math> dependence of the resulting form factors rather than a simple, linear approximation at small momentum transfer. The physical extrapolation for the radii is carried out using three-flavor NLO chiral perturbation theory to parametrize the quark mass dependence in terms of three low-energy constants, including the first lattice determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>L</mi><mn>4</mn><mi>r</mi></msubsup></math>. Systematic uncertainties on the final results related to the ground state extraction, form factor parametrization as well as the physical extrapolation are accounted for via model averages based on the Akaike information criterion. Our physical results for the pion singlet and octet scalar radii are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">⟨</mo><msubsup><mrow><mi>r</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msubsup><msubsup><mrow><mo stretchy="false">⟩</mo></mrow><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>=</mo><mn>0.550</mn><mo stretchy="false">(</mo><mn>32</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo stretchy="false">(</mo><mn>39</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>sys</mi></mrow></msub><mo stretchy="false">[</mo><mn>50</mn><msub><mrow><mo stretchy="false">]</mo></mrow><mrow><mtext>total</mtext></mrow></msub><mtext> </mtext><mtext> </mtext><msup><mrow><mi>fm</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">⟨</mo><msubsup><mrow><mi>r</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msubsup><msubsup><mrow><mo stretchy="false">⟩</mo></mrow><mrow><mi>π</mi></mrow><mrow><mn>8</mn></mrow></msubsup><mo>=</mo><mn>0.443</mn><mo stretchy="false">(</mo><mn>16</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo stretchy="false">(</mo><mn>45</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>sys</mi></mrow></msub><mo stretchy="false">[</mo><mn>47</mn><msub><mrow><mo stretchy="false">]</mo></mrow><mrow><mtext>total</mtext></mrow></msub><mtext> </mtext><mtext> </mtext><msup><mrow><mi>fm</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, respectively. The values of the relevant low energy constants are given by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mspace linebreak="goodbreak"></mspace><mn>116.5</mn><mo stretchy="false">(</mo><mn>5.5</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo stretchy="false">(</mo><mn>13.7</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>sys</mi></mrow></msub><mo stretchy="false">[</mo><mn>14.8</mn><msub><mrow><mo stretchy="false">]</mo></mrow><mrow><mtext>total</mtext></mrow></msub><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>L</mi><mn>4</mn><mi>r</mi></msubsup><mo stretchy="false">(</mo><mi>μ</mi><mo>=</mo><mn>770</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo stretchy="false">)</mo><mo>=</mo><mo>+</mo><mn>0.38</mn><mo stretchy="false">(</mo><mn>09</mn><msub><mo stretchy="false">)</mo><mrow><mi>stat</mi></mrow></msub><mo stretchy="false">(</mo><mn>15</mn><msub><mo stretchy="false">)</mo><mi>sys</mi></msub><mo stretchy="false">[</mo><mn>18</mn><msub><mo stretchy="false">]</mo><mtext>total</mtext></msub><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>L</mi><mn>5</mn><mi>r</mi></msubsup><mo stretchy="false">(</mo><mi>μ</mi><mo>=</mo><mn>770</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo stretchy="false">)</mo><mo>=</mo><mo>+</mo><mn>0.58</mn><mo stretchy="false">(</mo><mn>0.38</mn><msub><mo stretchy="false">)</mo><mrow><mi>stat</mi></mrow></msub><mo stretchy="false">(</mo><mn>1.08</mn><msub><mo stretchy="false">)</mo><mi>sys</mi></msub><mo stretchy="false">[</mo><mn>1.14</mn><msub><mo stretchy="false">]</mo><mtext>total</mtext></msub><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>. For the light quark contribution to the pion scalar radius, we obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">⟨</mo><msubsup><mrow><mi>r</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msubsup><msubsup><mrow><mo stretchy="false">⟩</mo></mrow><mrow><mi>π</mi></mrow><mrow><mi>l</mi></mrow></msubsup><mo>=</mo><mn>0.515</mn><mo stretchy="false">(</mo><mn>28</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo stretchy="false">(</mo><mn>32</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>sys</mi></mrow></msub><mo stretchy="false">[</mo><mn>43</mn><msub><mrow><mo stretchy="false">]</mo></mrow><mrow><mtext>total</mtext></mrow></msub><mtext> </mtext><mtext> </mtext><msup><mrow><mi>fm</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, resulting in a value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mo>ℓ</mo><mo stretchy="true">¯</mo></mover><mn>4</mn></msub><mo>=</mo><mn>3.99</mn><mo stretchy="false">(</mo><mn>15</mn><msub><mo stretchy="false">)</mo><mrow><mi>stat</mi></mrow></msub><mo stretchy="false">(</mo><mn>17</mn><msub><mo stretchy="false">)</mo><mi>sys</mi></msub><mo stretchy="false">[</mo><mn>23</mn><msub><mo stretchy="false">]</mo><mtext>total</mtext></msub></math> for the pertinent low-energy constant in two-flavor chiral perturbation theory.

Germany

Konstantin Ottnad

Georg von Hippel

Scalar size of the pion from lattice QCD

The radiative seesaw model with gauged <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub><mo>×</mo><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></math> extension is a well-motivated scenario that gives consistent predictions of active neutrino masses and the abundance of dark matter. Majorana masses of right-handed neutrinos, the lightest of which can be identified as dark matter, are given by the spontaneous breaking of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> gauge symmetry. We revisit this model with the latest constraints from dark-matter searches, neutrino oscillations, flavor experiments, and collider experiments. We examine several benchmark scenarios and identify the valid parameter space of this model, finding that there are still allowed regions under the latest experimental constraints. We present new viable benchmark scenarios for this model, i.e., the right-handed neutrino dark-matter scenario and the scalar dark-matter scenario. We also mention the testability of these benchmark scenarios in future experiments.

Japan

Shinya Kanemura

Yushi Mura

Guohao Ying

Revisiting the model for radiative neutrino masses with dark matter in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mstyle mathvariant="normal"><mi>U</mi></mstyle><mo stretchy="false">(</mo><mn>1</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></mrow></math> gauge theory

Coupled dark sector models have gained significant attention, motivated by recent advances in cosmology and the pressing need to address unresolved puzzles. In this work, we study coupled scalar dark sector models inspired by ultraviolet-complete frameworks such as supergravity and string theory. These models involve scalar couplings arising either from their kinetic terms, through a nontrivial field space metric, or from their scalar potential. We demonstrate how these couplings can be elegantly formulated in terms of an interacting vector, a standard tool in coupled dark sector studies, and analyse their distinct cosmological effects using a dynamical systems approach. Using this framework, we further investigate an axio-dilaton system recently explored in the literature, where the dilaton also couples to baryons. Intriguingly, we show that certain kinetic and potential interactions may mimic one another or even cancel out, making them observationally indistinguishable. If such a distinction becomes possible through observational constraints, it could provide valuable insights into the underlying field space metric and its connection to fundamental physics.

United Kingdom

Saba Rahimy

Elsa M. Teixeira

Ivonne Zavala

Deciphering coupled scalar dark sectors

In this work, we systematically study the interactions of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> systems within the framework of chiral effective field theory in heavy hadron formalism. We calculate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> effective potentials up to next-to-leading order, explore the bound state formations, and investigate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> scattering properties, such as scattering rate, scattering length, and effective range. Our results show that all <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>1</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> potentials are repulsive, preventing the formation of bound states, while the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math> potentials are generally attractive. Specifically, we get two important observations: first, the shallow bound state is more likely to exist in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">[</mo><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>0</mn><mo>+</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">]</mo></math> system than in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><mo stretchy="false">[</mo><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>+</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">]</mo></math> system; second, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><mo stretchy="false">[</mo><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>0</mn><mo>+</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">]</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><mo stretchy="false">[</mo><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>+</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">]</mo></math> systems possess relatively large binding energies and positive scattering lengths, which suggests strong bound state formations in these channels. So, the attractions in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><mo stretchy="false">[</mo><mi>I</mi><mo>=</mo><mn>0</mn><mo stretchy="false">]</mo></math> systems are deeper than those in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">[</mo><mi>I</mi><mo>=</mo><mn>0</mn><mo stretchy="false">]</mo></math> systems, thus we strongly recommend the future experiment to search for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><mo stretchy="false">[</mo><mi>I</mi><mo>=</mo><mn>0</mn><mo stretchy="false">]</mo></math> tetraquark systems. We also investigate the coupled-channel effects on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn></mrow></math> systems and conclude that the inclusion of the coupled channels introduces small but visible influences. In addition, we also investigate the dependencies of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> binding energies on the contact low-energy coupling constants.

Zhe Liu

Hao Xu

Xiang Liu

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mrow><mover accent="true"><mrow><mi>B</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></mrow></math> dynamics in chiral effective field theory