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)

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)

In this paper we study a complete set of scalar and pseudoscalar four-quark operators, with a particular emphasis on their renormalization within a gauge-invariant renormalization scheme (GIRS). We focus on operators that do not mix with lower-dimensional operators by virtue of their transformation properties under the flavor-symmetry group. This class includes all <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>F</mi><mo>=</mo><mn>2</mn></math> operators, as well as their partners that transform under the same irreducible representations of the flavor group. These encompass a substantial subset of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>F</mi><mo>=</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>F</mi><mo>=</mo><mn>0</mn></math> operators. The present analysis provides a detailed classification of all four-quark operators, exploring their Fierz identities, symmetry properties, and mixing patterns. Different variants of GIRS are explored, including a “democratic” version that treats all mixing operators uniformly. For selected variants, which exhibit smaller mixing effects, we present the conversion matrices from GIRS to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math> scheme at next-to-leading order.

Cyprus

G. Spanoudes

M. Costa

K. Mitsidi

H. Panagopoulos

Classification of four-quark operators with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>F</mi><mo>≤</mo><mn>2</mn></math> under flavor symmetry and their renormalization in a gauge-invariant scheme

The method of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Q</mi></mrow></math> cumulants has been shown as a powerful tool to study the fine details of the azimuthal anisotropies in high-energy nucleus-nucleus collisions. A new method for the fast calculation of arbitrary order <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Q</mi></mrow></math>-cumulant <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>v</mi><mi>n</mi></msub><mrow><mo>{</mo><mn>2</mn><mi>k</mi><mo>}</mo></mrow></mrow></math> values, based on the partition of a non-negative integer <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>l</mi><mo>≤</mo><mi>m</mi></mrow></math> for calculation of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><mi>m</mi></mrow></math>-particle azimuthal correlations is presented in this paper. Unlike the standard <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Q</mi></mrow></math>-cumulants method in which the calculation of high-order multiparticle calculations is impractical, the newly proposed method enables easy calculation. The validity of the method is proven via a toy model that uses the elliptic power distribution to simulate anisotropic emission of particles. The method enables the study of fine details of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> distribution, such as higher-order central moments of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> distribution, as well as the hydrodynamic behavior of the quark-gluon plasma.

Serbia

L. Nađđerđ

J. Milošević

D. Devetak

F. Wang

X. Zhu

Novel approach to a fast calculation of high-order <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Q</mi></mrow></math> cumulants

A systematic investigation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave triply heavy tetraquark systems with quark content <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mi>b</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>b</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>q</mi><mo>=</mo><mi>u</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>d</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>s</mi></mrow></math>), spin-parity quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>+</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mo>+</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>2</mn><mo>+</mo></msup></math>, and isospin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math> is carried out within the constituent quark model framework. The four-body bound and resonance states are determined by solving the Schrödinger equation employing the high-precision and efficient Gaussian expansion method in conjunction with the powerful complex scaling method. Besides, a comprehensive coupled-channel analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave tetraquark systems is performed, taking into account meson-meson, diquark-antidiquark, and K-type configurations, as well as all allowed color structures. Several narrow resonant states are identified in each <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo></math> channel. In particular, resonances for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></math> system are found in the mass range of 8.87–9.36 GeV, while those for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mi>b</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>b</mi></math> system lie between 12.13–12.45 GeV. Most of the predicted resonances are compact tetraquark states with sizes smaller than 1.0 fm, although four states exhibit more extended structures with sizes around 1.3 fm, suggesting a more loosely bound nature. Magnetic moments and dominant wave function components of these exotic states are also analyzed. The results indicate that K-type configurations play a major role in the structure of the observed resonances. Finally, possible strong decay channels (golden modes) for these states are theoretically proposed.

Gang Yang

Jialun Ping

Spain

Jorge Segovia

Triply heavy tetraquarks <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mi>b</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>b</mi></math> in a constituent quark model

The Neutrinos from Stored Muons (nuSTORM) facility will generate neutrino beams from both muon and meson decays in a storage ring, providing a neutrino flux known to the percent level. This unprecedented precision enables a rich physics programme, including high-precision tests of the Standard Model and searches for new phenomena. In this paper we demonstrate nuSTORM’s sensitivity to key Standard Model processes such as, measurements of the weak mixing angle at low $\textit{Q}$ and the rare process of neutrino trident production. We also show its powerful reach for a diverse range of beyond-the-Standard-Model scenarios, including eV-scale sterile neutrinos, Kaluza-Klein excitations from large extra dimensions and lepton flavour violation. Furthermore, nuSTORM can place significant constraints on heavy QCD axions and other axion-like particles produced in rare kaon decays. These capabilities establish nuSTORM as a powerful and complementary probe to long baseline experiments and collider searches.

United Kingdom

Jack Franklin

Rohan Kamath

Dhruv Pasari

Yuber Perez-Gonzalez

Jessica Turner

Maria Vogiatzi

nuSTORM as a Precision Probe of the Standard Model and New Physics

We derive a factorization formula for boosted double resonant top-antitop pair production in $\textit{e}$ $\textit{e}$ annihilation with a semileptonic top quark decay in the phase space region where the $\textit{b}$-jet invariant mass is small. The decaying top quark state is defined through invariant mass measurements on the final states in the top and antitop hemispheres, and the $\textit{b}$-jet is defined from clustering all hadrons in the top hemisphere. The factorization does not rely on the narrow width limit and accounts for the QCD off-shell and interference effects. The approach employs Soft-Collinear-Effective Theory and boosted Heavy-Quark-Effective-Theory and relies on a combination of factorization theorems known from $\textit{e}$ $\textit{e}$ dijet production and inclusive semileptonic heavy meson endpoint decays. The result provides a first principles treatment of the dominant hadronization effects, which can be determined from $\textit{e}$ $\textit{e}$ event shapes. In the factorization a new distribution function arises, called the ultra-collinear-soft (ucs) function, which encodes the Fermi motion of the decaying top quark within the state defined from the invariant mass measurement. The ucs function is a differential generalization of the inclusive bHQET jet function and shares properties of the shape function in semileptonic heavy meson decays. In frames where the top quark is very slow, it describes the coherent soft radiation arising from top production, propagation and decay, and encodes all effects that are non-factorizable from the perspective of the NW limit. Its form and renormalization depend on two light-cone momenta related to the top-jet and $\textit{b}$-jet directions and their relative angle. Due to the large top quark width, the ucs function can be computed perturbatively, and we determine the QCD corrections at 𝒪($\textit{α}$ ). The anomalous dimension is known to three loops.

Austria

André Hoang

Christoph Regner

Endpoint factorization for semileptonic decays of boosted and resonant off-shell top quarks with a large-radius bottom jet