We investigated the effect of an isospin chemical potential ( $ \mu_{I} $ ) within the quark-meson model, which approximates quantum chromodynamics (QCD) by modeling low-energy phenomena such as chiral symmetry breaking and phase structure under varying conditions of temperature and chemical potential. Using the functional renormalization group (FRG) flow equations, we calculated the phase diagram in the chiral limit within the two-flavor quark-meson model in a finite $ \mu_{I} $ with $\textit{ρ}$ vector meson interactions. Fluctuation effects significantly decrease the critical chemical potential from the mean-field (MF) value $\mu_{I,{\rm MF}} \gt m_\rho$ to a lower value at which the $\textit{ρ}$ vector meson condensates alongside the chiral condensate once the isospin chemical potential exceeds the critical value $ \mu_{I}^{{\rm{crit}}} $ . This $\textit{ρ}$ condensation was investigated numerically for different meson coupling strengths. The $\textit{ρ}$ meson dominated region is delineated from other phases by a second-order phase transition at lower $ \mu_{I} $ and a first-order transition at slightly higher $ \mu_{I} $ .

China

Mohammed Osman

Defu Hou

Wentao Wang

United States

Hui Zhang

Functional renormalization group study of $\textit{ρ}$ meson condensate at a finite isospin chemical potential in the quark meson model * Supported in part by the National Key Research and Development Program of China (2022YFA1604900). This work is also partly supported by the National Natural Science Foundation of China (NSFC) (12435009, 12275104). Hui Zhang acknowledges the financial support from the Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008) and the National Natural Science Foundation of China (12047523, 12105107)

In this study, we investigate a scenario based on the effects of the Loop Quantum Gravity (LQG) on the electromagnetic sector of the Standard Model of Fundamental Interactions and Particle Physics (SM). Starting from a post-Maxwellian version of electromagnetism that includes LQG effects, we derive and discuss the influence of LQG parameters on classical quantities such as the components of the stress-tensor. Furthermore, we inspect the propagation of electromagnetic waves and examine the optical properties of the QED vacuum in this scenario. Among these, we contemplate the combined effect of the LQG parameters and a homogeneous background magnetic field on the propagation of electromagnetic waves by considering issues such as group velocities and refractive indices of the QED vacuum, in detail. Finally, with the aid of the previously analyzed LQG-extended photonic dispersion relations, we re-discuss the kinematics of the Compton effect and conclude that an interesting nonlinear profile emerges in the wavelengths of the incoming and deflected photons.

Brazil

P.A.L. Mourão

G.L.L.W. Levy

J.A. Helayël-Neto

Reassessing aspects of LQG-modified dispersion relations of photons * P. A. L. Mourão is support by CAPES. G. L. L. W. L. Levy is support by the Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ), Grant No. E-26/202.437/2024.

Several possible excesses around $ 95 $ GeV hint at an additional light scalar beyond the Standard Model. We examine the capability of the Circular Electron-Positron Collider (CEPC) to test this hypothesis in the Higgs-strahlung channel $ e^{+}e^{-} \to ZS $ with $ Z \to\mu^{+}\mu^{-} $ and $ S \to\tau^{+}\tau^{-} $ . A full detector simulation shows that the optimal center-of-mass energy for studying the 95 GeV light scalar is 210 GeV. A deep neural network classifier reduces the luminosity required for discovery by half. At $ L = 20\; \mathrm{ab}^{-1} $ , the $ 5\sigma $ sensitivity of the CEPC to the signal strength $ \mu_{\tau\tau}^{ZS} $ reaches 0.016 and 0.020 for $ \sqrt{s} = 210 $ GeV and 240 GeV, respectively. The corresponding thresholds for a 5% precision measurement are $ \mu_{\tau\tau}^{ZS} \gt 0.10 $ and $ \gt 0.12 $ . At $ \sqrt{s}=210 $ GeV (240 GeV), the $ 5\sigma $ coverage of all N2HDM-Flipped samples with $ \chi^2_{h_{95}} \lt 7.82 $ requires $ L=800\ \mathrm{fb}^{-1} $ (1.22 $ \mathrm{ab}^{-1} $ ). These results establish a 210 GeV run, augmented by machine-learning selection, as the most efficient strategy to confirm or refute the 95 GeV excess at future lepton colliders.

Yabo Dong

Manqi Ruan

Kun Wang

Haijun Yang

Jingya Zhu

Testing a 95 GeV Scalar at the CEPC with Machine Learning * This work was supported by the National Natural Science Foundation of China under Grant No. 12275066 and by the startup research funds of Henan University. The work of K. Wang was also supported by the Open Project of the Shanghai Key Laboratory of Particle Physics and Cosmology under Grant No. 22DZ2229013-3. The work of M. Ruan was also supported by the National Key Program for S&T Research and Development under Contract No. 2024YFA1610603. The work of H. Yang was also supported by the National Natural Science Foundation of China under Grant No. W2441004.

A model for the nuclear medium modification of parton densities is presented. The approach is based on a global analysis of available deep inelastic scattering data for different nuclear targets within the rescaling model, combined with the effects of Fermi motion. The scale dependence is implemented through the DGLAP-evolved quark and gluon densities in a proton derived analytically at the leading order of QCD coupling. By fitting the rescaling parameters to experimental data on the ratio $F_2^A(x,Q^2)/F_2^{A^\prime}(x,Q^2) $ for several nuclear targets $\textit{A}$ and $\textit{A}$', we obtain predictions for nuclear parton distributions, even for unmeasured nuclei. The effects of nuclear modifications are investigated with respect to the mass number $\textit{A}$. We highlight distinct shadowing and antishadowing behaviors for gluons and quarks.

Russia

A.V. Kotikov

A.V. Lipatov

A simple model for nuclear modification of parton distribution functions * This research has been carried out at the expense of the Russian Science Foundation grant 25-22-00066, https://rscf.ru/en/project/25-22-00066/

We investigate the discovery prospects of a leptophilic gauge boson $ Z_\ell $ at future $ e^+e^- $ colliders, focusing on a comparative study of the Circular Electron–Positron Collider (CEPC) and the International Linear Collider (ILC). Such a state naturally arises from an additional $ U(1)'_\ell $ gauge symmetry, under which quarks remain neutral while all leptons carry a universal charge, motivated by neutrino oscillations and scenarios of physics beyond the Standard Model. As a clean benchmark, we study the process $ e^+e^- \to \mu^+\mu^- $ , including realistic effects of initial-state radiation and beamstrahlung. Our results indicate that the CEPC, with its very high luminosity at $ \sqrt{s}=240 $ GeV, can probe couplings down to $ g_\ell \approx 10^{-3} $ for $ Z_\ell $ masses up to about 220 GeV. The ILC extends the sensitivity to heavier states in the multi-hundred GeV range through its higher $ \sqrt{s} $ stages. These findings demonstrate the strong complementarity of circular and linear colliders in exploring purely leptophilic interactions.

S.O. Kara

Discovery prospects for a leptophilic gauge boson Z$_{ℓ}$ at CEPC and ILC

An analytical and numerical systematic study of the neutrino mass matrix with one texture zero is presented in a basis where the charged leptons are diagonal. Under the assumption that neutrinos are Dirac particles, the analysis is conducted in detail for the normal and inverted hierarchy mass spectra. Our study is performed without any approximations, first analytically and then numerically, using current neutrino oscillation data. The analysis constrains the parameter space in such a way that, among the six possible one-texture-zero patterns, only four are favored in the normal hierarchy and one in the inverted hierarchy by current oscillation data at the $3 \sigma$ level. Phenomenological implications for the lepton CP-violating phase and neutrino masses are also explored.

Colombia

Richard H. Benavides

Yessica Lenis

John D. Gómez

William A. Ponce

One texture zero for Dirac neutrinos in a diagonal charged lepton basis * Richard H. Benavides acknowledges additional financial support from Minciencias (CD82315 CT ICETEX 2021-1080)

Heavy Majorana neutrinos ($\textit{N}$) are predicted in many models of physics beyond the Standard Model. In this work, we explore the production and detection prospects of TeV-scale heavy neutrinos ( $ m_N \gtrsim 1 $ TeV) at a future 3 TeV Compact Linear Collider (CLIC). We focus on two distinct decay topologies: (i) $ N \to \ell^\pm W^\mp $ with hadronic $\textit{W}$ boson decay, leading to a final state with one charged lepton and a hadronic fat jet $ J_W $ ; and (ii) $ N \to \nu h $ with subsequent Higgs decay $ h \to b\bar{b} $ , yielding a Higgs-tagged fat jet $ J_h $ and $\not {E}_T$ . Based on comprehensive detector-level simulations and background analysis, we present both $ 2\sigma $ exclusion limits and $ 5\sigma $ discovery reaches in the $ m_N $ – $ |V_{\ell N}|^2 $ plane. We further extract 95% confidence level upper limits on the mixing parameter $ |V_{\ell N}|^2 $ and perform a detailed comparison with existing constraints from direct searches at future colliders and indirect global fits. Our findings demonstrate that a 3 TeV CLIC can improve the sensitivity to $ |V_{\ell N}|^2 $ by about two orders of magnitude compared with the projected reaches of future hadron colliders while remaining competitive with other CLIC search channels.

Yao-Bei Liu

Jing-Wei Lian

Searches for heavy neutrinos at a 3 TeV CLIC in fat jet final states * Yao-Bei Liu is supported by the Natural Science Foundation of Henan Province, China (252300421988), Jing-Wei Lian is supported by the National Natural Science Foundation of China (12447140) and the Natural Science Foundation of Henan Province, China (252300421771)

A wide range of scintillating bolometers are under investigation for applications in the search for rare events and processes beyond the Standard Model. In this work, we report the first measurement of a natural, non-molybdenum-doped, lithium tungstate (Li $$_2$$ WO $$_4$$ ) crystal operated underground as a scintillating cryogenic calorimeter. The detector achieved a baseline energy resolution of 0.5 keV RMS with a low-energy threshold of about 1.5 keV. The simultaneous readout of heat and light enabled particle identification, revealing a clear separation between $$\beta /\gamma ,$$ $$\alpha ,$$ and nuclear recoil populations above 300 keV, with a light-yield-based particle discrimination better than $$6\sigma .$$ These results, fully comparable with those achieved with other compounds in the field, demonstrate that Li $$_2$$ WO $$_4$$ is a promising candidate for rare-event searches. In particular, the combination of excellent radio-purity (with U/Th levels below 0.5 mBq/kg) and sensitivity to neutron interactions via the $$^6$$ Li(n, $$\alpha )$$ $$^3$$ H reaction makes this material an attractive option for next-generation experiments in dark matter, coherent elastic neutrino-nucleus scattering, and spin-dependent interactions.

Italy

D. Helis

A. Melchiorre

S. Nagorny

Switzerland

M. Noia

L. Pagnanini

S. Pirro

A. Puiu

G. Benato

P. Carniti

R. Elleboro

P. Gambacorta

C. Gotti

V. Grigorieva

S. Nisi

France

E. Olivieri

G. Pessina

S. Piacentini

Kazakhstan

M. Shafiee

V. Shlegel

Characterization of the Li $$_2$$ WO $$_4$$ crystal as a cryogenic scintillating calorimeter

<p>The MAGNETO-<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ν</mi></math> experiment searches for keV-scale heavy neutral leptons (HNLs) through precise measurements of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>β</mi><mo>−</mo></msup></math>-decay spectrum of <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi>Pu</mi><mprescripts></mprescripts><none></none><mn>241</mn></mmultiscripts></math>. We present spectra comprising a total of 194 million <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>β</mi><mo>−</mo></msup></math> decays recorded using decay energy spectrometry with metallic magnetic calorimeters, representing the most statistically precise measurement of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mmultiscripts><mi>Pu</mi><mprescripts></mprescripts><none></none><mn>241</mn></mmultiscripts><mspace width="0.16em"></mspace><msup><mi>β</mi><mo>−</mo></msup></mrow></math> decay to date. The <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi></math>-endpoint energy was determined using <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi></math> rays and x-rays from an external <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi>Ba</mi><mprescripts></mprescripts><none></none><mn>133</mn></mmultiscripts></math> calibration source, yielding <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>Q</mi><mi>β</mi></msub><mo>=</mo><mn>22.273</mn><mspace width="0.16em"></mspace><mrow><mo>(</mo><mn>33</mn><mo>)</mo></mrow><mspace width="0.28em"></mspace><mi>keV</mi></mrow></math>. The measured spectrum shows no statistically significant deviation from the allowed <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi></math>-decay model. From a subset of the high-statistics data, we set an upper limit on the mixing of an 11.5-keV HNL with the electron neutrino, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>|</mo></mrow><msub><mi>U</mi><mrow><mi>e</mi><mn>4</mn></mrow></msub><msup><mrow><mo>|</mo></mrow><mn>2</mn></msup><mo>&lt;</mo><mn>1.31</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math> at the 95% confidence level.</p>

C. Lee

X. Zhang

A. Kavner

T. Parsons-Davis

D. Lee

N. Hines

S.T.P. Boyd

M. Loidl

X. Mougeot

M. Rodrigues

South Korea

M.K. Lee

J.W. Song

R. Wood

I. Jovanovic

G.B. Kim

Search for a heavy neutral lepton with the MAGNETO-<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ν</mi></math> experiment using <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mmultiscripts><mi>Pu</mi><mprescripts></mprescripts><none></none><mn>241</mn></mmultiscripts><mspace width="0.16em"></mspace><msup><mi>β</mi><mo>−</mo></msup></mrow></math> decays

<p>We calculate the binding energies of the hypothetical mesonic atom, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> (kaonium), using the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> elastic scattering amplitude. Our findings are in line with previously reported results, which involve solving an eigenvalue equation of the Kudryavtsev-Popov type. Using chiral perturbation theory, we show that kaonium manifests itself as a sharp resonance around 992 MeV accompanying <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> in cross sections for processes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>γ</mi><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>γ</mi><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><mi>η</mi></math>. The latter process is particularly striking: the peak at the kaonium resonance energy is highly pronounced, with the ratio of the cross sections <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi><mo stretchy="false">(</mo><mi>γ</mi><mi>γ</mi><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><mi>η</mi><mo stretchy="false">)</mo><mo>/</mo><mi>σ</mi><mo stretchy="false">(</mo><mi>γ</mi><mi>γ</mi><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><mo stretchy="false">)</mo><mo>≈</mo><mn>9</mn></math>. Due to the short lifetime of kaonium (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>18</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">s</mi></math>) and its small decay width (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>0.4</mn><mtext> </mtext><mtext> </mtext><mi>keV</mi></math>), direct detection of this exotic atom poses a significant challenge and requires high experimental resolution. However, we show that once the formation of kaonium is considered in the cross section, a better fit to the available experimental data is obtained.</p>

Germany

Alireza Beygi

S.P. Klevansky

South Africa

R.H. Lemmer

Emergence of kaonium as a sharp resonance in photon-photon to meson-meson cross sections