The gauged <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math> model is well motivated to explain the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly and dark matter in previous studies. However, the latest <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>NA</mi><mrow><mn>64</mn><mi>μ</mi></mrow></mrow></math> experiment has almost excluded all the parameter space for the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math>, which indicates that the light dark matter benchmark scenarios interpreting muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math> in previous studies are under significant pressure at present. In light of many recent and future experimental results, we revisit the minimal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> portal dark matter in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math>. Focusing on the phenomenology of dark matter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>χ</mi></math>, we first explore the viable parameter space for light dark matter under various tight constraints. Around the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> resonance, we find that there is still a large parameter space for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>χ</mi></msub><mo>≳</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> via thermal freeze-out. On the other hand, the constraints on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> above the electroweak scale are quite loose, but are less studied for dark matter. We also investigate the heavy dark matter around the TeV scale and corresponding constraints. A large part of the parameter space for dark matter is within the reach of future experiments.

China

Zhen-Wei Wang

Zhi-Long Han

Fei Huang

Yi Jin

Honglei Li

Prospects of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> portal dark matter in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mrow><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>L</mi><mi>μ</mi><mo>−</mo><mi>L</mi><mi>τ</mi></mrow></msub></mrow></mrow></math>

A comprehensive analysis of all available data on cross sections and spin-dependent observables for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>p</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi mathvariant="normal">Σ</mi><mn>0</mn></msup><mo stretchy="false">(</mo><mn>1385</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>n</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi mathvariant="normal">Σ</mi><mo>−</mo></msup><mo stretchy="false">(</mo><mn>1385</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><mi>p</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup><mo stretchy="false">(</mo><mn>1385</mn><mo stretchy="false">)</mo></math> reactions is performed within an effective Lagrangian framework. In addition to 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>N</mi></math> exchange, <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> exchanges, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Σ</mi><mo>*</mo></msup></math> exchanges, and the interaction current, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>-channel contributions from a minimal set of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi></math> resonances are included in constructing the reaction amplitudes to describe the data. The analysis reveals that all available data for both photon- and hadron-induced <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mi mathvariant="normal">Σ</mi><mo stretchy="false">(</mo><mn>1385</mn><mo stretchy="false">)</mo></math> production reactions can be simultaneously and satisfactorily reproduced when the contribution of 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">Δ</mi><mo stretchy="false">(</mo><mn>1930</mn><mo stretchy="false">)</mo><msup><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow><mo>−</mo></msup></math> resonance is taken into account. The reaction mechanisms, particularly the resonance contributions in each considered reaction, are thoroughly analyzed and discussed in detail.

Ai-Chao Wang

Neng-Chang Wei

Analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>p</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi mathvariant="normal">Σ</mi><mn>0</mn></msup><mo stretchy="false">(</mo><mn>1385</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>n</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi mathvariant="normal">Σ</mi><mo>−</mo></msup><mo stretchy="false">(</mo><mn>1385</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><mi>p</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup><mo stretchy="false">(</mo><mn>1385</mn><mo stretchy="false">)</mo></math> reactions

The newly published data on spin density matrix elements from the GlueX Collaboration, along with the previously released differential cross-section data from the CLAS Collaboration and the other two experiments for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>ρ</mi><mn>0</mn></msup><mi>p</mi></mrow></math> reaction, are systematically investigated using an effective Lagrangian approach within the tree-level Born approximation. The model combines contributions from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>-channel meson exchanges (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi><mo>,</mo><mo> </mo><mi>η</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mn>2</mn></msub></math>), <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math>-channel nucleon (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>) and nucleon resonance (<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>N</mi><mo>*</mo></msup></math>) exchanges, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math> exchange, and a generalized contact term to construct the scattering amplitudes. Regge propagators are employed for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>-channel amplitudes to incorporate the contributions from mesons with various spins lying on the same trajectories. The analysis shows that the background contributions, dominated by the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mn>2</mn></msub></math>-trajectory exchange, provide a satisfactory description of the data in the high-energy and forward-angle regions. The inclusion of specific nucleon resonances, such as <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mrow><mo>(</mo><mn>2100</mn><mo>)</mo></mrow><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow><mo>,</mo><mo> </mo><mrow><mi>N</mi><mrow><mo>(</mo><mn>2060</mn><mo>)</mo></mrow><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></math>, or <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Δ</mi><mrow><mo>(</mo><mn>2000</mn><mo>)</mo></mrow><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></math>, significantly improves the description of the differential cross-section data at near-perpendicular scattering angles in the low-energy region. Predictions of photon beam and target nucleon asymmetries are provided, offering valuable insights to discriminate reaction mechanisms when corresponding data become available in the future.

Analysis of the data on differential cross sections and spin density matrix elements for <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>ρ</mi><mn>0</mn></msup><mi>p</mi></mrow></math>

The spin correlation of final-state hadrons provides a novel platform to explore the hadronization mechanism of polarized partons in unpolarized high-energy collisions. In this work, we investigate the helicity correlation of two hadrons originating from the same single parton. The production of such a dihadron system is formally described by the dihadron fragmentation function, in which the helicity correlation between the two hadrons arise from both the long-distance nonperturbative physics and the perturbative QCD evolution. Beyond the extraction of the dihadron fragmentation function, we demonstrate that it is also a sensitive observable to the longitudinal spin transfer, characterized by the single hadron fragmentation function <math altimg='si1.svg'><msub><mrow><mi>G</mi></mrow><mrow><mn>1</mn><mi>L</mi></mrow></msub></math>. This intriguing connection opens up new opportunities for understanding the spin dynamics of hadronization and provides a complementary approach to corresponding studies using polarized beams and targets.

Tianbo Liu

Yu-Kun Song

Shu-Yi Wei

Helicity correlation of neighboring dihadron

In this paper, we study the single production of doubly charged Higgs <math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mo>±</mo><mo>±</mo></mrow></msup></mrow></math> in the type-II seesaw at the high energy muon collider. Compared with the pair production channel <math><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup><mo>→</mo><msup><mi>H</mi><mrow><mo>+</mo><mo>+</mo></mrow></msup><msup><mi>H</mi><mrow><mo>−</mo><mo>−</mo></mrow></msup></math>, the single production channel <math><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup><mo>→</mo><msup><mi>μ</mi><mo>∓</mo></msup><msup><mo>ℓ</mo><mo>∓</mo></msup><msup><mi>H</mi><mrow><mo>±</mo><mo>±</mo></mrow></msup></math> in principle could probe the mass region above the threshold <math><msub><mi>m</mi><msup><mi>H</mi><mrow><mo>±</mo><mo>±</mo></mrow></msup></msub><mo>&gt;</mo><msqrt><mi>s</mi></msqrt><mo>/</mo><mn>2</mn></math>. The single production channel depends on the Yukawa coupling <math><mi>h</mi></math>, which is related to the neutrino oscillation parameters. We show that the Majorana phases <math><msub><mi>ϕ</mi><mn>1</mn></msub></math> and <math><msub><mi>ϕ</mi><mn>2</mn></msub></math> have great impact on the individual cross section of the single production. We find that the same sign dilepton signature from <math><msup><mi>H</mi><mrow><mo>±</mo><mo>±</mo></mrow></msup><mo>→</mo><msup><mo>ℓ</mo><mo>±</mo></msup><msup><mo>ℓ</mo><mo>±</mo></msup></math> could probe <math><msub><mi>m</mi><msup><mi>H</mi><mrow><mo>±</mo><mo>±</mo></mrow></msup></msub><mo>≲</mo><mn>2.6</mn><mo>(</mo><mn>7.1</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> at the 3 (10) TeV muon collider when the triplet VEV <math><msub><mi>v</mi><mi>Δ</mi></msub><mo>≲</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></math>.

Jie-Cheng Jia

Production of single doubly charged Higgs bosons at muon colliders

The <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math> <math><msup><mi>Z</mi><mo>′</mo></msup></math> model has emerged as a promising candidate to address the longstanding muon <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo>)</mo><mi>μ</mi></msub></math> anomaly. Flavor-conserving <math><msup><mi>Z</mi><mo>′</mo></msup></math> interactions are subject to stringent constraints from the neutrino trident process and <math><mrow><mi>NA</mi><mrow><mn>64</mn><mi>μ</mi></mrow></mrow></math> experiments, which limit the <math><msup><mi>Z</mi><mo>′</mo></msup></math> mass to <math><msub><mi>m</mi><msup><mi>Z</mi><mo>′</mo></msup></msub><mo>&lt;</mo><mn>40</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. To circumvent these constraints, flavor-conserving <math><msup><mi>Z</mi><mo>′</mo></msup></math> interactions can be converted into maximal flavor-violating interactions through a discrete exchange symmetry. Maximal flavor-violating <math><msup><mi>Z</mi><mo>′</mo></msup></math> interactions contribute to <math><mi>τ</mi><mo>→</mo><mi>μ</mi><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover></math> via the neutral current, yet the parameter space for this process conflicts with the <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo>)</mo><mi>μ</mi></msub></math> allowed regions. To resolve this conflict, we propose introducing a singly charged scalar that mediates via charged current interactions. This scalar is anticipated to produce a negative contribution to the lepton <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo>)</mo><mi>l</mi></msub></math> while concurrently inducing the tau decay <math><mi>τ</mi><mo>→</mo><mi>μ</mi><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover></math>. Three distinct scenarios arise from the introduction of singly charged scalars: the <math><msub><mi>O</mi><mrow><mi>L</mi><mi>L</mi></mrow></msub></math> operator, driven by weak singlet and triplet, and the <math><msub><mi>O</mi><mrow><mi>L</mi><mi>R</mi></mrow></msub></math> operator, driven by weak doublet. Our analysis of the phenomenology in these three cases reveals that the tension between the muon <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo>)</mo><mi>μ</mi></msub></math> anomaly and <math><mi>τ</mi><mo>→</mo><mi>μ</mi><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover></math> for large <math><msup><mi>Z</mi><mo>′</mo></msup></math> masses can be effectively alleviated only by the singly charged scalars from the weak triplet, whereas the singlet and doublet scenarios fall short. Furthermore, the singly charged scalars from the weak triplet offer an additional explanation for the electron <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo>)</mo><mi>e</mi></msub></math> anomaly. Our findings indicate that weak triplets could play a crucial role in <math><msup><mi>Z</mi><mo>′</mo></msup></math> models, potentially providing valuable insights for future research into <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> frameworks.

South Korea

Jin Sun

Maximal flavor violating <math><mrow><mi>U</mi><mo>(</mo><mn>1</mn><msub><mrow><mo>)</mo></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>−</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>τ</mi></mrow></msub></mrow></msub></mrow></math> model with a singly charged scalar

In this work, we investigate the resonance production in <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><mi>γ</mi><msup><mi>π</mi><mo>+</mo></msup><mi>Λ</mi></math> decay through the triangle singularity (TS) mechanism, within an effective Lagrangian approach. We find that the appropriate loop decay process could develop a triangle singularity in the invariant mass <math><msub><mi>M</mi><mrow><mi>π</mi><mi>Λ</mi></mrow></msub></math> around 1.35 GeV, with the shape depending on the quantum numbers of <math><msup><mi>Σ</mi><mo>*</mo></msup></math> states that couple to the final <math><mi>π</mi><mi>Λ</mi></math> system. Especially, the <math><mi>Σ</mi><mo>(</mo><mn>1380</mn><mo>)</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> state newly predicted in the pentaquark model, if exists, significantly enhances the TS contribution and sharpens the TS peak due to the <math><mi>S</mi></math>-wave <math><msup><mi>Σ</mi><mo>*</mo></msup><mi>π</mi><mi>Σ</mi></math> vertex in the loop. Therefore, the existence of the <math><mi>Σ</mi><mo>(</mo><mn>1380</mn><mo>)</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> state can be examined by measuring the TS signal in <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><mi>γ</mi><msup><mi>π</mi><mo>+</mo></msup><mi>Λ</mi></math>. Considering also possible tree-level diagrams, we additionally obtain the branching ratio <math><mrow><mtext>Br</mtext><mo>(</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><mi>γ</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mi>Λ</mi><mo>)</mo><mo>≃</mo><mn>1.5</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup></mrow></math>. We suggest the investigation of this reaction by future BESIII, LHCb, and Belle experiments.

Ke Wang

Yu-Fei Wang

Bo-Chao Liu

Search for the <math><mi>Σ</mi><mo>(</mo><mn>1380</mn><mo>)</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> state in <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><mi>γ</mi><msup><mi>π</mi><mo>+</mo></msup><mi>Λ</mi></math> decay by triangle singularity

The decay of the D meson into multibody final states is a complex process that provides valuable insights into the fundamental interactions within the Standard Model of particle physics. This study focuses on the decay cascade $$D^{+}\rightarrow K^{*}_{J} \ell ^{+}\nu \rightarrow K^{\pm }\pi ^{\mp } \ell ^{+}\nu $$ <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <mmultiscripts> <mi>K</mi> <mi>J</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </mmultiscripts> <msup> <mi>ℓ</mi> <mo>+</mo> </msup> <mi>ν</mi> <mo>→</mo> <msup> <mi>K</mi> <mo>±</mo> </msup> <msup> <mi>π</mi> <mo>∓</mo> </msup> <msup> <mi>ℓ</mi> <mo>+</mo> </msup> <mi>ν</mi> </mrow> </math> where the $$K^*_J$$ <math> <msubsup> <mi>K</mi> <mi>J</mi> <mo>∗</mo> </msubsup> </math> resonance encompasses the $$K^*(892),K^{*}(1410),K^{*}_0(1430)$$ <math> <mrow> <msup> <mi>K</mi> <mo>∗</mo> </msup> <mrow> <mo>(</mo> <mn>892</mn> <mo>)</mo> </mrow> <mo>,</mo> <mmultiscripts> <mi>K</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </mmultiscripts> <mrow> <mo>(</mo> <mn>1410</mn> <mo>)</mo> </mrow> <mo>,</mo> <mmultiscripts> <mi>K</mi> <mn>0</mn> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </mmultiscripts> <mrow> <mo>(</mo> <mn>1430</mn> <mo>)</mo> </mrow> </mrow> </math> states. We employ the helicity amplitude technique to derive the angular distributions for the decay chain, enabling the extraction of one-dimensional and two-dimensional distributions. Utilizing form factors for the $$D\rightarrow K^*$$ <math> <mrow> <mi>D</mi> <mo>→</mo> <msup> <mi>K</mi> <mo>∗</mo> </msup> </mrow> </math> transition derived from the quark model, we calculate the differential and integrated partial decay widths, explicitly considering the electron and muon masses. Decay branching fractions are calculated, the ratios of the branching fractions are found to be $$\frac{\mathcal {B}r(D^{+}\rightarrow K^{*}(892)(\rightarrow K ^{-}\pi ^{+}) \, \mu ^{+}\nu _{\mu })}{\mathcal {B}r(D^{+}\rightarrow K^{*}(892)(\rightarrow K ^{-}\pi ^{+}) \, e^{+}\nu _{e})} = 0.975$$ <math> <mrow> <mfrac> <mrow> <mi>B</mi> <mi>r</mi> <mo>(</mo> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <mmultiscripts> <mi>K</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </mmultiscripts> <mrow> <mo>(</mo> <mn>892</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mo>→</mo> <msup> <mi>K</mi> <mo>-</mo> </msup> <msup> <mi>π</mi> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mspace width="0.166667em"></mspace> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msub> <mi>ν</mi> <mi>μ</mi> </msub> <mo>)</mo> </mrow> <mrow> <mi>B</mi> <mi>r</mi> <mo>(</mo> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <mmultiscripts> <mi>K</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </mmultiscripts> <mrow> <mo>(</mo> <mn>892</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mo>→</mo> <msup> <mi>K</mi> <mo>-</mo> </msup> <msup> <mi>π</mi> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mspace width="0.166667em"></mspace> <msup> <mi>e</mi> <mo>+</mo> </msup> <msub> <mi>ν</mi> <mi>e</mi> </msub> <mo>)</mo> </mrow> </mfrac> <mo>=</mo> <mn>0.975</mn> </mrow> </math> , $$\frac{\mathcal {B}r(D^{+}\rightarrow K^{*}(1410)(\rightarrow K ^{-}\pi ^{+}) \, \mu ^{+}\nu _{\mu })}{\mathcal {B}r(D^{+}\rightarrow K^{*}(1410)(\rightarrow K ^{-}\pi ^{+}) \, e^{+}\nu _{e})} = 0.714$$ <math> <mrow> <mfrac> <mrow> <mi>B</mi> <mi>r</mi> <mo>(</mo> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <mmultiscripts> <mi>K</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </mmultiscripts> <mrow> <mo>(</mo> <mn>1410</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mo>→</mo> <msup> <mi>K</mi> <mo>-</mo> </msup> <msup> <mi>π</mi> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mspace width="0.166667em"></mspace> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msub> <mi>ν</mi> <mi>μ</mi> </msub> <mo>)</mo> </mrow> <mrow> <mi>B</mi> <mi>r</mi> <mo>(</mo> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <mmultiscripts> <mi>K</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </mmultiscripts> <mrow> <mo>(</mo> <mn>1410</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mo>→</mo> <msup> <mi>K</mi> <mo>-</mo> </msup> <msup> <mi>π</mi> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mspace width="0.166667em"></mspace> <msup> <mi>e</mi> <mo>+</mo> </msup> <msub> <mi>ν</mi> <mi>e</mi> </msub> <mo>)</mo> </mrow> </mfrac> <mo>=</mo> <mn>0.714</mn> </mrow> </math> and $$\frac{\mathcal {B}r(D^{+}\rightarrow K^{*}_{0}(1430)(\rightarrow K ^{+}\pi ^{-}) \, \mu ^{+}\nu _{\mu })}{\mathcal {B}r(D^{+}\rightarrow K^{*}_{0}(1430)(\rightarrow K ^{+}\pi ^{-}) \, e^{+}\nu _{e})} = 0.774$$ <math> <mrow> <mfrac> <mrow> <mi>B</mi> <mi>r</mi> <mo>(</mo> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <mmultiscripts> <mi>K</mi> <mn>0</mn> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </mmultiscripts> <mrow> <mo>(</mo> <mn>1430</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mo>→</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <msup> <mi>π</mi> <mo>-</mo> </msup> <mo>)</mo> </mrow> <mspace width="0.166667em"></mspace> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msub> <mi>ν</mi> <mi>μ</mi> </msub> <mo>)</mo> </mrow> <mrow> <mi>B</mi> <mi>r</mi> <mo>(</mo> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <mmultiscripts> <mi>K</mi> <mn>0</mn> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </mmultiscripts> <mrow> <mo>(</mo> <mn>1430</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mo>→</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <msup> <mi>π</mi> <mo>-</mo> </msup> <mo>)</mo> </mrow> <mspace width="0.166667em"></mspace> <msup> <mi>e</mi> <mo>+</mo> </msup> <msub> <mi>ν</mi> <mi>e</mi> </msub> <mo>)</mo> </mrow> </mfrac> <mo>=</mo> <mn>0.774</mn> </mrow> </math> . Results in this work will serve a calibration for the study of $$c \rightarrow s $$ <math> <mrow> <mi>c</mi> <mo>→</mo> <mi>s</mi> </mrow> </math> in D meson decays in future and provide useful information towards the understanding of the properties of the $$K^{*}$$ <math> <mmultiscripts> <mi>K</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </mmultiscripts> </math> meson, as well as $$K \pi $$ <math> <mrow> <mi>K</mi> <mi>π</mi> </mrow> </math> system.

Ji Xu

Study of lepton flavor universality and angular distributions in $$D\rightarrow K^*_{J} (\rightarrow K\pi )\ell \nu _{\ell }$$ <math> <mrow> <mi>D</mi> <mo>→</mo> <msubsup> <mi>K</mi> <mi>J</mi> <mo>∗</mo> </msubsup> <mrow> <mo>(</mo> <mo>→</mo> <mi>K</mi> <mi>π</mi> <mo>)</mo> </mrow> <mi>ℓ</mi> <msub> <mi>ν</mi> <mi>ℓ</mi> </msub> </mrow> </math>

The most recent data on differential cross sections and photon beam asymmetries <math><mi>Σ</mi></math> from the LEPS2/BGOegg Collaboration for the <math><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msub><mi>f</mi><mn>0</mn></msub><mrow><mo>(</mo><mn>980</mn><mo>)</mo></mrow><mi>p</mi></mrow></math> reaction are analyzed within a tree-level effective Lagrangian approach. The <math><mi>t</mi></math>-channel <math><mi>ρ</mi></math> and <math><mi>ω</mi></math> exchanges, the <math><mi>u</mi></math>- and <math><mi>s</mi></math>-channel <math><mi>N</mi></math> exchanges, the interaction current, and the possible <math><mi>s</mi></math>-channel <math><msup><mi>N</mi><mo>*</mo></msup></math> exchanges are taken into account in constructing the reaction amplitudes to reproduce the data. The results show that the contributions from either the <math><mrow><mi>N</mi><mrow><mo>(</mo><mn>2040</mn><mo>)</mo></mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></math> or the <math><mrow><mi>N</mi><mrow><mo>(</mo><mn>2100</mn><mo>)</mo></mrow><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></math> resonance exchange in the <math><mi>s</mi></math> channel are necessarily required to describe the LEPS2/BGOegg data and they dominate the differential cross sections of <math><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msub><mi>f</mi><mn>0</mn></msub><mrow><mo>(</mo><mn>980</mn><mo>)</mo></mrow><mi>p</mi></mrow></math>. Further analysis shows that the contributions from the <math><mi>t</mi></math>-channel <math><mi>ρ</mi></math> and <math><mi>ω</mi></math> exchanges and the interaction current are rather small to both differential cross sections and photo beam asymmetries, and the contributions from <math><mi>u</mi></math>-channel <math><mi>N</mi></math> exchange are considerable in the case of including <math><mrow><mi>N</mi><mrow><mo>(</mo><mn>2040</mn><mo>)</mo></mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></math> in the model while negligible in the case of including <math><mrow><mi>N</mi><mrow><mo>(</mo><mn>2100</mn><mo>)</mo></mrow><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></math> in the model. Predictions of target asymmetries <math><mi>T</mi></math> for <math><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msub><mi>f</mi><mn>0</mn></msub><mrow><mo>(</mo><mn>980</mn><mo>)</mo></mrow><mi>p</mi></mrow></math> are given, which can be examined by future experiments.

Photoproduction of <math><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msub><mi>f</mi><mn>0</mn></msub><mrow><mo>(</mo><mn>980</mn><mo>)</mo></mrow><mi>p</mi></mrow></math> in an effective Lagrangian approach

Inspired by the resonance <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo>(</mo><mn>3875</mn><mo>)</mo></math> recently observed by the LHCb Collaboration, we systematically explore the <math><mi>S</mi></math>- and <math><mi>P</mi></math>-wave <math><mi>c</mi><mi>c</mi><mover><mi>q</mi><mo>¯</mo></mover><msup><mover><mi>q</mi><mo>¯</mo></mover><mo>′</mo></msup></math> <math><mo>(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><msup><mover><mi>q</mi><mo>¯</mo></mover><mo>′</mo></msup><mo>=</mo><mover><mi>u</mi><mo>¯</mo></mover><mo>,</mo><mover><mi>d</mi><mo>¯</mo></mover><mo>,</mo><mover><mi>s</mi><mo>¯</mo></mover><mo>)</mo></math> systems in a chiral SU(3) quark model. The Hamiltonian contains the kinetic energy, the one-gluon-exchange (OGE) potential, the confinement potential, and the one-boson-exchange (OBE) potential stemming from the coupling of quark and chiral fields. The Schrödinger equation is solved by use of the variational method with the spacial trial wave functions chosen as Gaussian functions. It is found that the lowest state has a mass 3879 MeV, isospin and spin-parity <math><mi>I</mi><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>0</mn><msup><mn>1</mn><mo>+</mo></msup></math>, and quark constituent <math><mi>c</mi><mi>c</mi><mover><mi>u</mi><mo>¯</mo></mover><mover><mi>d</mi><mo>¯</mo></mover></math>, in agreement with the experimentally observed <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo>(</mo><mn>3875</mn><mo>)</mo></math>. This state is approximately at the calculated <math><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> threshold and has a root-mean-square radius of about 0.48 fm. These demonstrate that the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo>(</mo><mn>3875</mn><mo>)</mo></math> can be accommodated as a stable and compact tetraquark sate in the chiral SU(3) quark model. All the other <math><mi>S</mi></math>- and <math><mi>P</mi></math>-wave <math><mi>c</mi><mi>c</mi><mover><mi>q</mi><mo>¯</mo></mover><msup><mover><mi>q</mi><mo>¯</mo></mover><mo>′</mo></msup></math> <math><mo>(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><msup><mover><mi>q</mi><mo>¯</mo></mover><mo>′</mo></msup><mo>=</mo><mover><mi>u</mi><mo>¯</mo></mover><mo>,</mo><mover><mi>d</mi><mo>¯</mo></mover><mo>,</mo><mover><mi>s</mi><mo>¯</mo></mover><mo>)</mo></math> states lie about 100 to a few hundreds MeV higher than the corresponding meson-meson thresholds and thus are not suggested to be candidates of stable and compact tetraquark states due to their fall-apart decays to two mesons.

Du Wang

Ke-Rang Song

Wen-Ling Wang

Spectrum of <math><mi>S</mi></math>- and <math><mi>P</mi></math>-wave <math><mi>c</mi><mi>c</mi><mover><mi>q</mi><mo>¯</mo></mover><msup><mover><mi>q</mi><mo>¯</mo></mover><mo>′</mo></msup></math> <math><mo>(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><msup><mover><mi>q</mi><mo>¯</mo></mover><mo>′</mo></msup><mo>=</mo><mover><mi>u</mi><mo>¯</mo></mover><mo>,</mo><mover><mi>d</mi><mo>¯</mo></mover><mo>,</mo><mover><mi>s</mi><mo>¯</mo></mover><mo>)</mo></math> systems in a chiral SU(3) quark model