Recently, the BESIII Collaboration observed the three-body decays $ D_s^+\to \eta \omega\pi^+ $ , $ D^+\to K^0_S\pi^+\omega $ , and $ D^0\to K^-\pi^+\omega $ . In this study, we investigate the contributions of the subprocesses $ \rho^+\to \omega\pi^+ $ in these Cabibbo-favored decays $ D \to h\omega\pi $ , with $ \rho^+= \{\rho(770)^+, \rho(1450)^+, \rho(770)^+\&amp;\rho(1450)^+\} $ and $ h=\{ \eta, K^0_S, K^-\} $ , by introducing these subprocesses into the decay amplitudes of the relevant decay processes via the vector form factor $ F_{\omega\pi} $ , which has been measured in the related $\textit{τ}$ and $ e^+e^- $ processes. We provide the first theoretical predictions for the branching fractions of the quasi-two-body decays $ D_s^+\to\eta[\rho^+\to]\omega\pi^+ $ , $ D^+\to K^0_S[\rho^+\to]\omega\pi^+ $ , and $ D^0\to K^-[\rho^+\to]\omega\pi^+ $ . Our findings reveal that the contributions from the subprocess $ \rho(770)^+\to\omega\pi^+ $ are significant in these observed three-body decays $ D_s^+\to\eta \omega\pi^+ $ , $ D^+\to K^0_S \omega\pi^+ $ , and $ D^0\to K^- \omega\pi^+ $ , notwithstanding the contributions originating from the Breit-Wigner tail effect of $ \rho(770)^+ $ . The numerical results of this study suggest that the dominant resonance contributions for the three-body decays $ D_s^+\to\eta \omega\pi^+ $ and $ D^+\to K^0_S \omega\pi^+ $ originate from the $\textit{P}$-wave intermediate states $ \rho(770)^+ $ , $ \rho(1450)^+ $ and their interference effects.

China

Wen-Fei Wang

Jiao-Yuan Xu

Si-Hong Zhou

Spain

Pan-Pan Shi

Contributions of $\textit{ρ}$(770,1450)→$\textit{ωπ}$ to Cabibbo-favored $\textit{D}$→$\textit{hωπ}$ decays * Supported in part by the National Natural Science Foundation of China (12465017) and the Foundation of Shanxi '1331 Project' Key Subjects Construction

The decay of the Higgs boson and the nature of dark matter remain fundamental challenges in particle physics. We investigate the 95 GeV diphoton excess and dark matter within the framework of the triplet-extended minimal supersymmetric standard model (TMSSM). In this model, an additional hypercharge $ Y=0 $ , $ S U(2)_L $ triplet superfield is introduced. Mixing between the triplet and doublet Higgs states enhances the diphoton signal strength of the 95 GeV Higgs boson, resulting in $ \mu_{\gamma\gamma}^{{\rm{CMS+ATLAS}}} = 0.24_{-0.08}^{+0.09} $ , which is consistent with experimental observations. This enhancement arises primarily from charged Higgs and chargino loop contributions, together with an LEP excess in the $ Zb\bar{b} $ channel around the same mass within the $ 2\sigma $ range. Additionally, the model accommodates viable dark matter candidates in the form of a bino-dominated neutralino. The relic density is reduced to the observed value through resonance-enhanced annihilation via the Higgs portal or co-annihilation with the triplino or higgsino. This reduction remains consistent with constraints from direct and indirect detection experiments. A comprehensive parameter scan demonstrates that the TMSSM can simultaneously explain the 95 GeV diphoton excess, observed 125 GeV Higgs mass, and dark matter relic density, establishing a compelling and theoretically consistent framework.

Zetian Li

Ning Liu

Bin Zhu

Interplay of 95 GeV diphoton excess and dark matter in supersymmetric triplet model * Supported by the National Natural Science Foundation of China (NNSFC) (12275232, 12335005) and Bin Zhu is also supported by the Natural Science Foundation of Shandong Province (ZR2025QA20)

In this study, we investigate the isospin-violating decays of $ B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0} $ , which may provide additional information for the determination of the properties of $ B_{c}(1P)^{+} $ , the first orbital excitation states of the $B_c $ meson. By assuming a dual relation between the $\textit{U}$(1) anomaly soft-gluon coupling for $ B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0} $ and the intermediate meson loop transitions, we can quantify the isospin-violating decay effects for these four $\textit{P}$-wave states. We observe that the partial decay width of $ B_{c0}^{*+}\to B_{c}^{+}\pi^{0} $ is approximately three orders of magnitude larger than that for $ B_{c2}^{*+}\to B_{c}^{+}\pi^{0} $ . This indicates that $ B_{c0}^{*+} $ can be established in the $ B_{c}^{+}\pi^{0} $ decay channel as a single state. Meanwhile, the two axial-vector states $ B_{c1}^{+}/B_{c1}'^{+} $ can be possibly identified in $ B_{c1}^{+}/B_{c1}'^{+}\to B_{c}^{*+}\pi^{0} $ with comparable strengths. Although these isospin-violating decays are observed to be small, the theoretical predictions should be useful for guiding future experimental efforts.

Jun Wang

Qiang Zhao

Predictions for the isospin-violating decays of ${{\boldsymbol B}_{\boldsymbol c}({\boldsymbol{1P}})^{\bf +}{\bf\to}{\boldsymbol B}_{\boldsymbol c}^{({\bf *})+}\boldsymbol\pi^{\bf 0}}$ * Supported, in part, by the National Natural Science Foundation of China (12235018), DFG and NSFC funds to the Sino-German CRC 110 'Symmetries and the Emergence of Structure in QCD' (12070131001, DFG Project-ID 196253076), National Key Basic Research Program of China (2020YFA0406300) and Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030302)

In this work, we investigate the resonance structures in the $ \Sigma(1/2^-) $ system from both three-quark and five-quark perspectives within the framework of the chiral quark model. An accurate few-body computational approach, the Gaussian expansion method, is employed to construct the orbital wave functions of multiquark states. To reduce the model dependence on parameters, we fit two sets of parameters to check the stability of the results. The calculations show that our results remain stable despite changes in the parameters. In the three-quark calculations, two $ \Sigma(1/2^-) $ states are obtained with energies around 1.8 GeV, which are good candidates for the experimentally observed $ \Sigma(1750) $ and $ \Sigma(1900) $ . In the five-quark configuration, several stable resonance states are identified, including $ \Sigma \pi $ , $ N \bar{K} $ , and $ N \bar{K}^{*} $ . These resonance states survive the channel-coupling calculations under the complex-scaling framework and manifest as stable structures. Our results support the existence of a two-pole structure for the $ \Sigma(1/2^-) $ system, predominantly composed of $ \Sigma \pi $ and $ N \bar{K} $ configurations, analogous to the well-known $ \Lambda(1380) $ - $ \Lambda(1405) $ ( $ \Sigma \pi $ - $ N \bar{K} $ ) system. On the other hand, although the energy of the $ N \bar{K}^{*} $ configuration is close to that of $ \Sigma(1750) $ and $ \Sigma(1900) $ , the obtained width is not consistent with the experimental values. This suggests that the $ N \bar{K}^{*} $ state needs to mix with three-quark components to better explain the experimental $ \Sigma(1750) $ and $ \Sigma(1900) $ states. According to our decay width calculations, the predicted two resonance states are primarily composed of $ \Sigma \pi $ and $ N \bar{K} $ , with their main decay channel being $ \Lambda \pi $ . Therefore, we encourage experimental groups to search for the predicted two-pole structure of the $ \Sigma(1/2^-) $ system in the invariant mass spectrum of $ \Lambda \pi $ .

Yu Yao

Xuejie Liu

Xiaoyun Chen

Yuheng Wu

Jialun Ping

Yue Tan

Qi Huang

Investigation of resonances in the Σ(1/2$^{–}$) system based on the chiral quark model * Supported partly by the National Science Foundation of China (12205249, 12305087). Yue Tan is supported by the Funding for School-Level Research Projects of Yancheng Institute of Technology (xjr2022039) and the Qinglan Project Fund of Jiangsu Province. Qi Huang is supported by the Start-up Funds of Nanjing Normal University (184080H201B20)

Recent studies have shown that observing entangled particle states at a particle collider, such as the Large Hadron Collider (LHC), and testing the violation of Bell inequality in them can open up new research areas for studying high energy physics. We examine the presence of quantum entanglement in the $ pp\to ZZ\to 4\ell $ process at leading order. We apply a generally recognized method, quantum state tomography, to reconstruct the spin density matrix of the joint $\textit{ZZ}$ system, through which all the relevant observables can be obtained. The angular distribution of the final leptons is obtained from simulated events using a Monte-Carlo program, which is used to reconstruct the spin density matrix. A non-zero value of the lower bound of the concurrence is measured with the simulated data. The numerical analysis shows that, with the luminosity corresponding to LHC Run 2+3, entanglement can be probed at the 2 $ \sigma $ level and up to the 3.75 $ \sigma $ level for High-Luminosity LHC data (3ab$^{-1}$), revealing the possibility of finding quantum entanglement in real collider experiments.

Alim Ruzi

Youpeng Wu

Ran Ding

Qiang Li

Searching quantum entanglement in the $\textit{pp}$ → $\textit{ZZ}$ process * Supported by National Natural Science Foundation of China (NSFC) (12325504, 120611410), and by MOST (2023YFA1605800). This work is supported in part by the National Natural Science Foundation of China (12325504, 12150005, 12075004)

Geometric phases can manifest when a relativistic quantum particle moves cyclically along a loop in parameter space. The phase can be affected by the presence of a background field and can be accompanied by nontrivial topological features. The appearance of adiabatic geometric phases in momentum space is demonstrated for a Lorentz-violating Weyl fermion, where the role of the background is played by the coefficients for Lorentz violation. As explicit examples, the Berry curvature and the first Chern number are derived for two cases with large Lorentz violation, one incorporating <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi><mi>T</mi></mrow></math> violation and one preserving <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi><mi>T</mi></mrow></math> symmetry. Some alternative topological invariants are also obtained. In certain scenarios with large Lorentz violation, the physical vacuum is associated with a topological phase.

United States

V. Alan Kostelecký

Ralf Lehnert

Brazil

Marco Schreck

Babak Seradjeh

Lorentz violation and momentum-space geometric phases

We consider the double parton scattering (DPS) initiated by direct photons in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>A</mi></math> collisions. We extend the previously known results for photoproduction to the case of electroproduction with nonzero photon virtuality <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup></math>, and then consider the DPS for both photo and electroproduction for HERA and EIC (electron ion collider) kinematics. The number of DPS events at the EIC is shown to be of the same order as in HERA and is even larger, with increase in luminosity compensating the decrease of the center-of-mass energy.

Israel

B. Blok

R. Segev

Double parton interactions initiated by direct photons in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>A</mi></math> collisions revisited

It is customary to identify <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>ψ</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>=</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>+</mo><mi>C</mi><msup><mrow><mover accent="true"><mrow><msub><mrow><mi>ν</mi></mrow><mrow><mi>R</mi></mrow></msub></mrow><mrow><mo stretchy="true">¯</mo></mrow></mover></mrow><mrow><mi>T</mi></mrow></msup></mrow></math> with a Majorana fermion on the basis of chirality changing charge conjugation <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mover accent="true"><mrow><mi>C</mi></mrow><mrow><mo stretchy="false">˜</mo></mrow></mover><mo>:</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>R</mi></mrow></msub><mo stretchy="false">→</mo><mi>C</mi><msup><mrow><mover accent="true"><mrow><msub><mrow><mi>ν</mi></mrow><mrow><mi>R</mi></mrow></msub></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>T</mi></mrow></msup></mrow></math> and parity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mover accent="true"><mrow><mi>P</mi></mrow><mrow><mo stretchy="false">˜</mo></mrow></mover><mo>:</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>R</mi></mrow></msub><mo stretchy="false">→</mo><mi>i</mi><msub><mrow><mi>γ</mi></mrow><mrow><mn>4</mn></mrow></msub><msub><mrow><mi>ν</mi></mrow><mrow><mi>R</mi></mrow></msub></mrow></math>. The theorem on the absence of a Majorana-Weyl fermion in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>4</mn></math> states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>C</mi><mo stretchy="false">˜</mo></mover><msub><mi>γ</mi><mn>5</mn></msub><msup><mover accent="true"><mi>C</mi><mo stretchy="false">˜</mo></mover><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo><mo>−</mo><msub><mi>γ</mi><mn>5</mn></msub></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>C</mi><mo stretchy="false">˜</mo></mover><mo>=</mo><mi>C</mi><msubsup><mi>γ</mi><mn>4</mn><mi>T</mi></msubsup></math>, and, thus, the charge conjugation of the equivalent Majorana <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ψ</mi><mo>+</mo></msub><mo>=</mo><mo stretchy="false">(</mo><mfrac><mrow><mn>1</mn><mo stretchy="false">+</mo><msub><mi>γ</mi><mn>5</mn></msub></mrow><mn>2</mn></mfrac><mo stretchy="false">)</mo><msub><mi>ν</mi><mi>R</mi></msub><mo>+</mo><mo stretchy="false">(</mo><mfrac><mrow><mn>1</mn><mo stretchy="false">−</mo><msub><mi>γ</mi><mn>5</mn></msub></mrow><mn>2</mn></mfrac><mo stretchy="false">)</mo><mi>C</mi><msup><mover accent="true"><msub><mi>ν</mi><mi>R</mi></msub><mo stretchy="true">¯</mo></mover><mi>T</mi></msup></math> vanishes without subsidiary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">→</mo><mo>−</mo><msub><mi>γ</mi><mn>5</mn></msub></math>, namely, not defined in field theory. To be consistent with the theorem, it is common to use a doublet representation of chirality preserving charge conjugation <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>C</mi><mo stretchy="false">^</mo></mover><mo>:</mo><msub><mi>ν</mi><mrow><mi>R</mi><mo>,</mo><mi>L</mi></mrow></msub><mo stretchy="false">→</mo><mi>C</mi><msup><mover accent="true"><msub><mi>ν</mi><mrow><mi>L</mi><mo>,</mo><mi>R</mi></mrow></msub><mo stretchy="true">¯</mo></mover><mi>T</mi></msup></math> and parity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mover accent="true"><mrow><mi>P</mi></mrow><mrow><mo stretchy="false">^</mo></mrow></mover><mo>:</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>R</mi><mo>,</mo><mi>L</mi></mrow></msub><mo stretchy="false">→</mo><mi>i</mi><msub><mrow><mi>γ</mi></mrow><mrow><mn>4</mn></mrow></msub><msub><mrow><mi>ν</mi></mrow><mrow><mi>L</mi><mo>,</mo><mi>R</mi></mrow></msub></mrow></math> in theory containing both <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mrow><mi>R</mi><mo>,</mo><mi>L</mi></mrow></msub></math>. In the type I seesaw model, the latter formulation is applicable but <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ψ</mi><mo>+</mo></msub><mo>=</mo><msub><mi>ν</mi><mi>R</mi></msub><mo>+</mo><mi>C</mi><msup><mover accent="true"><msub><mi>ν</mi><mi>R</mi></msub><mo stretchy="true">¯</mo></mover><mi>T</mi></msup></math> is not a Majorana fermion. An analog of the Bogoliubov transformation converts <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ψ</mi><mo>±</mo></msub><mo>=</mo><msub><mi>ν</mi><mrow><mi>R</mi><mo>,</mo><mi>L</mi></mrow></msub><mo>±</mo><mi>C</mi><msup><mover accent="true"><msub><mi>ν</mi><mrow><mi>R</mi><mo>,</mo><mi>L</mi></mrow></msub><mo stretchy="true">¯</mo></mover><mi>T</mi></msup></math>, which are obtained by a precise diagonalization of the seesaw model, to Majorana fermions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ψ</mi><msub><mi>M</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></msub><mo>=</mo><mo stretchy="false">(</mo><mi>ψ</mi><mo>±</mo><mi>C</mi><msup><mover accent="true"><mi>ψ</mi><mo stretchy="false">¯</mo></mover><mi>T</mi></msup><mo stretchy="false">)</mo><mo>/</mo><msqrt><mn>2</mn></msqrt></math> with a Dirac-type fermion <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi></math>, as originally defined by Majorana. A chiral projection <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">[</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo><mo>/</mo><mn>2</mn><mo stretchy="false">]</mo><msub><mi>ψ</mi><msub><mi>M</mi><mn>1</mn></msub></msub></math> of a Majorana fermion is not a chiral fermion, which ensures the presence of the neutrinoless double beta decay.

Japan

Kazuo Fujikawa

Absence of Majorana-Weyl fermions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>4</mn></math> and the theory of Majorana fermions

Through symmetry of the action under global spacetime translations, Noether’s first theorem infamously entails an energy-momentum tensor (EMT) that is neither symmetric nor gauge-invariant. In a prior work [<a href="http://dx.doi.org/10.1103/PhysRevD.106.125012">Phys. Rev. D 106, 125012 (2022)</a>], I had obtained a symmetric and gauge-invariant EMT by using Noether’s second theorem instead, with local spacetime translations as the symmetry group. However, the derivation therein was flawed, containing a faulty assumption about the transformation rule for spinor fields. In this work, I revisit the derivation of the previous work, both correcting the faulty step and simplifying the derivation for broader accessibility. The end result is an EMT for quantum chromodynamics that is gauge-invariant, but not symmetric.

Adam Freese

Reflections on Noether’s second theorem and the energy-momentum tensor

We study the collider phenomenology of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math> extension of the Standard Model (BLSM), focusing on the production and decay of a heavy neutral gauge boson (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math>) at the Large Hadron Collider (LHC). In this framework, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> can decay into pairs of heavy right-handed neutrinos (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>R</mi></msub></math>), which subsequently decay into charged leptons and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math> bosons. These processes give rise to three distinctive final states: (i) two leptons plus four jets (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo>ℓ</mo><mo>+</mo><mn>4</mn><mi>j</mi></math>), (ii) four leptons plus missing transverse energy (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mo>ℓ</mo><mo>+</mo><mi>MET</mi></math>), and (iii) three leptons plus two jets and MET (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mo>ℓ</mo><mo>+</mo><mn>2</mn><mi>j</mi><mo>+</mo><mi>MET</mi></math>). To enhance signal sensitivity and suppress Standard Model backgrounds, we employ multivariate analysis techniques based on boosted decision trees (BDTs), as well as selection optimizations using the xgboost framework. The classifiers are trained on kinematic observables sensitive to the masses of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>R</mi></msub></math>. We demonstrate that all three final states offer significant discovery potential for both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> and heavy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>R</mi></msub></math> at the High-Luminosity LHC. Our results highlight the testability of the BLSM at current and future collider experiments, and provide a promising avenue for probing the origin of neutrino masses and the baryon asymmetry of the Universe.

Egypt

Kareem Ezzat

Syria

Germany

Nidal Chamoun

Shaaban Khalil

Rhitaja Sengupta

Exploring <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> and right-handed neutrinos in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math> symmetric SM at the Large Hadron Collider