We constructed a four-Higgs-doublet model (4HDM) invariant under $\textit{D}$ $_{5}$ symmetry and investigated its complete neutral vacuum structure in detail. Assuming explicit CP conservation in the scalar potential, we examined whether CP symmetry can be spontaneously broken. We provided a complete list of all possible real and complex vacua, along with the constraints on the potential parameters required for each vacuum solution to exist. We also discussed the positive-definiteness conditions that the Hessian must satisfy for each vacuum to be a local minimum of the potential. The results show that, after spontaneous symmetry breaking, some complex vacua lead to spontaneous CP violation in the potential, whereas the remaining complex vacua still preserve CP conservation. Among these CP-violating complex vacua, one can be regarded as the most general form. Furthermore, we discussed the relationship between real and complex vacua.

China

Dong-Ping Fu

Michihisa Takeuchi

Spontaneous CP violation in the $\textit{D}$ $_{5}$-symmetric four-Higgs-doublet models * Supported by the Fundamental Research Funds for the Central Universities, the One Hundred Talent Program of Sun Yat-sen University, China, and the Guangdong Natural Science Foundation (2026A1515012641)

We investigate the vacuum-induced current density for a charged scalar field in a (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mo>+</mo><mn>1</mn></mrow></math>)-dimensional cosmic dispiration spacetime threaded by a magnetic flux. This background combines a cosmic string and a screw dislocation, yielding a nontrivial helical geometry. By constructing the normalized mode functions of the Klein-Gordon equation, we evaluate the Wightman function and obtain the vacuum expectation value of the current density. We show that, in addition to the azimuthal component describing a persistent current around the defect, a nonvanishing axial component is induced as a direct consequence of the helical structure of the spacetime. Both components are periodic functions of the magnetic flux depending only on its fractional part, reflecting the Aharonov-Bohm nature of the effect. Closed expressions are obtained for massive and massless fields in arbitrary dimensions. We demonstrate that the screw dislocation parameter plays a crucial role in the behavior of the induced currents, leading to the regularization of the components at the origin and controlling their magnitude. Their asymptotic behavior is also analyzed in detail. Our results reduce to known expressions in the absence of the screw dislocation, providing a consistency check. In particular, we examine the physically relevant (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional case, where numerical analysis reveals nontrivial features arising from the interplay between topology and gauge effects.

Brazil

Herondy Mota

Vacuum-induced current density from a magnetic flux threading a cosmic dispiration in (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo>+</mo><mn>1</mn></math>)-dimensional spacetime

We present a lattice quantum chromodynamics calculation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>x</mi></mrow></math>-dependent isovector quark helicity parton distribution function (PDF) of the proton in the large momentum effective theory (LaMET) framework. Through operator product expansion (OPE) we also extract the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>d</mi><mo stretchy="false">˜</mo></mover><mn>2</mn></msub></math> moment of the twist-3 PDF <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>T</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> for the first time in 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, which is proportional to the average color Lorentz force experienced by the quark in the proton. This calculation is performed on a lattice of spacing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>=</mo><mn>0.076</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> at physical quark masses. The quasi-PDF matrix elements are measured in proton states boosted to momenta <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>z</mi></msub><mo>=</mo><mo stretchy="false">{</mo><mn>0</mn><mo>,</mo><mn>0.25</mn><mo>,</mo><mn>1.02</mn><mo>,</mo><mn>1.53</mn><mo stretchy="false">}</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. We first extract the lowest few helicity PDF moments from the renormalization-group (RG) invariant ratios of the matrix elements with OPE. Combined with the matrix elements relevant for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>T</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math>, we obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>d</mi><mo stretchy="false">˜</mo></mover><mn>2</mn><mrow><mi>u</mi><mo>−</mo><mi>d</mi></mrow></msubsup><mo stretchy="false">(</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0.0024</mn><mo stretchy="false">(</mo><mn>46</mn><mo stretchy="false">)</mo></math> at next-to-leading order in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math>. Then, the helicity quasi-PDF matrix elements are renormalized in the hybrid scheme with linear renormalon resummation and Fourier transformed to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>-space after an asymptotic extrapolation. The quasi-PDF is perturbatively matched 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> PDF with RG and threshold resummations at next-to-leading power and next-to-next-to-leading logarithmic accuracies. After resummations, we determine the PDF in the region <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>∈</mo><mo stretchy="false">[</mo><mn>0.25</mn><mo>,</mo><mn>0.75</mn><mo stretchy="false">]</mo></math>. The end-point regions are then parametrized, combined with the LaMET prediction at moderate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>, and fitted to the short-distance matrix elements in coordinate space.

United States

Xiang Gao

Andrew D. Hanlon

Swagato Mukherjee

Peter Petreczky

Hai-Tao Shu

Fei Yao

Rui Zhang

Yong Zhao

Proton isovector helicity PDF at NNLO and the twist-3 moment <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mover accent="true"><mrow><mi>d</mi></mrow><mrow><mo stretchy="false">˜</mo></mrow></mover></mrow><mn>2</mn></msub></mrow></math> from lattice QCD at physical quark masses

We investigate the reaction mechanism of strangeness production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><mi>ϕ</mi><mi mathvariant="normal">Λ</mi></math> within a hybrid Regge framework, taking into account <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math>-Reggeon exchanges. We present results for the total cross section, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-dependent differential cross sections, and spin-density matrix elements (SDMEs), and compare them with the available experimental data. We find that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math>-Reggeon exchange provides the dominant contribution, while <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>-Reggeon exchange remains non-negligible, particularly in describing the SDMEs. In contrast, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi></math>-channel nucleon exchanges are negligible. To obtain reliable predictions for the open-charm production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>−</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup></math>, we employ a quark-gluon-string-model-motivated Regge prescription that incorporates both pseudoscalar- and vector-Reggeon exchanges. Within this prescription, the Regge trajectories <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> and energy-scale parameters <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>s</mi><mn>0</mn></msub></math> are determined consistently, thereby constraining the model and reducing theoretical ambiguities. For the hidden-charm production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math>, we use the same quark-level diagrammatic correspondence. The total cross sections for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>−</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math> are suppressed by approximately 4–6 and 8–9 orders of magnitude, respectively, compared with that for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><mi>ϕ</mi><mi mathvariant="normal">Λ</mi></math>. We also examine possible <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>-channel contributions from the hidden-charm pentaquark states with strangeness, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4338</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math>, to both <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>−</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math> production.

South Korea

Sang-Ho Kim

Production of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mi mathvariant="normal">Λ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>−</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math> in kaon-induced reactions off the nucleon

We investigate how the temperature influences the threshold cusps in meson-meson scatterings, i.e., <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi><mi>π</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></mrow></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>D</mi><mo>*</mo></msup><mover accent="true"><mi>D</mi><mo>¯</mo></mover></mrow></math>) scatterings, using the production rates and propagators obtained at finite temperature. The line shape of production rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi><mi>π</mi></mrow></math> at different temperatures demonstrates that the cusp structure in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi><mi>π</mi></mrow></math> scattering is mildly enhanced as the temperature increases. For the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi><mi>π</mi></mrow></math> propagator, which includes isospin symmetry breaking, the line shape displays a unique plateaulike structure, and this structure will also be enhanced as the temperature increases. For comparison, the line shape of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></mrow></math> propagator including isospin symmetry breaking is also investigated at different temperatures. As the temperature increases, its line shape shows a similar plateaulike structure but with some different properties when the temperature modifications to the masses and widths of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mover accent="true"><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> are considered.

Japan

Ying Zhang

Atsushi Hosaka

Qian Wang

Shigehiro Yasui

Finite-temperature effects on the threshold cusps in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi><mi>π</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></mrow></math> scatterings from relativistic heavy-ion collisions

We investigate a non-Abelian SU(2) quantum link model in $$2+1$$ dimensions on a hexagonal lattice using tensor network methods. We determine the static quark potential for a wide range of bare coupling values and find that the theory is confining. We also probe the existence of a Lüscher term and find a clear signal with a $$g^2$$ dependent coefficient, in qualitative agreement with a strong coupling expansion. Correspondingly, the width of the strings scales logarithmically with the string length again for all $$g^2$$ -values, providing evidence for a rough string, with no indication for a roughening transition.

Germany

Paul Ludwig

Timo Jakobs

Carsten Urbach

Scaling and Lüscher term in a non-Abelian (2+1)d SU(2) quantum link model

Auxiliary field techniques have recently gained interest in four-dimensional non-linear electrodynamics and two-dimensional integrable sigma models. In these settings, coupling a suitable “seed” theory to auxiliary fields provides a powerful mechanism to generate infinite families of models while preserving key dynamical properties, such as electromagnetic duality invariance in four dimensions and classical integrability in two dimensions. Deformations induced through auxiliary fields are closely related to $$ T\overline{T} $$ -like deformations and, in two dimensions, also to their higher-spin generalisations. In this paper, we analyse and clarify the relations between different auxiliary field formulations in two and four dimensions, showing how they are governed by Legendre transformations of the interaction functions combined with appropriate field redefinitions. In four-dimensional electrodynamics, we establish a correspondence between the auxiliary field model of Russo and Townsend and the Ivanov-Zupnik formalism. In two dimensions, we develop the analogue of the Ivanov-Zupnik $\textit{μ}$-frame to deform Principal Chiral, symmetric-space, non-Abelian T-dual, and (bi-)Yang-Baxter sigma models. We discuss how integrability is preserved and use properties of the $\textit{μ}$-frame to further extend known families of integrable deformations.

Australia

Nicola Baglioni

Thailand

Daniele Bielli

Michele Galli

Gabriele Tartaglino-Mazzucchelli

Relating auxiliary field formulations of 4$\textit{d}$ duality-invariant and 2$\textit{d}$ integrable field theories

For the worldline theory of an extremal black hole, extremality amounts to vanishing ground state energy. In light of recent gravity results one would expect much like the ground-state degeneracy, this fine tuned condition too will not be satisfied. It is unclear, however, whether this should be a quantum artefact or classical effect. In this paper we consider a non-BPS extremal four-charge Reissner Nordström black hole in 𝒩 = 8 String theory. It is shown that the microscopic D-brane description fails to admit any extremal state, even classically. This positive energy is expected to destabilize the near-horizon $\textit{AdS}$ . The positive minimum energy is a direct consequence of the pattern of supersymmetry breaking by the D-branes. The black hole entropy is found to be the logarithm of the number of isolated minima and hence is related to the configurational entropy of the microscopic potential. We also find multiple continua of local minima corresponding to marginally bound states of the constituent D-branes.

India

Pranav Kumar

Swapnamay Mondal

Classical unattainability of extremality in non-BPS D-brane systems

In this paper, we explore <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math> quantum electrodynamics at finite density on a quantum computer, including two fermion flavors. Our method employs an established gauge-invariant Ansatz together with a quantum circuit structure that enforces Gauss’s law. As a proof of principle, we benchmark our simulation protocol on a small lattice system of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo>×</mo><mn>2</mn></math>, demonstrating the identification of density-induced level crossings in terms of the particle number of the fermion flavors. Classical simulations are used to obtain optimized variational parameters, which are then deployed in inference runs on IBM quantum hardware. We conclude by discussing hardware limitations and prospects for scaling this method to larger systems.

Emil Otis Rosanowski

Arianna Crippa

Lena Funcke

Cyprus

Paulo Vitor Itaboraí

Karl Jansen

Simran Singh

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math> quantum electrodynamics at finite density on a quantum computer

In this work, we investigate the production and decay of molecular states with quark content $cc\bar c\bar q$ and $J^P=1^+$ using a phenomenological analysis and an effective Lagrangian approach. Based on an $\textit{SU}$(3) flavor-symmetry analysis to identify golden channels, we further explore the dynamics of these processes under the molecular assumptions of ${\eta_c D^*}$ and ${J/\psi D^*}$ . Our results indicate that the production branching ratio in $B_c$ decays is sizable: it can be of order $10^{-4}$ for the molecular configuration ${{\eta}_cD^*}$ and $10^{-5}$ for the molecule ${J/\psi D^*}$ . In addition, we find that the decay widths of the two molecular configurations ${{\eta}_cD^*}$ and ${J/\psi D^*}$ are not significant, at the level of ${\cal{O}}$ ( $\text{MeV}$ ).

Na Li

Ye Xing

Jing-Rui Shi

Analysis of molecular state $\textit{η$_{c}$D}$ $^{*}$ and $\textit{J}$/$\textit{ψD}$ $^{*}$ in the effective Lagrangian approach * Supported by the National Natural Science Foundation of China (NSFC) (12005294)