The proximity of the narrow <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>4312</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>4440</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>4457</mn><mo stretchy="false">)</mo></math> structures to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> thresholds motivates their interpretation as hadronic molecules. We treat the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>4312</mn><mo stretchy="false">)</mo></math> as an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> state with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and examine both <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mtext> </mtext><mtext> </mtext><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> assignments for each heavier peak. The selected <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave open-charm transitions to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> are calculated at Born order in the quark-interchange model, including the prior and post rearrangement diagrams and their color, flavor, spin, and spatial matrix elements. Across the input variations considered, the quark-interchange widths robustly favor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> over <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> for every <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> assignment. At either heavier peak mass, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> width for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> is suppressed by approximately one order of magnitude relative to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>, providing a potential decay-based discriminator of the spin assignments. The large channel hierarchies arise from spatial overlaps and interference between spin-independent and hyperfine contributions and are not universal heavy-quark-spin-symmetry ratios. We also explore a retarded one-pion-exchange transition at first Born order. It affects <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>4312</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> most strongly, while the coherent widths remain sensitive to the cutoff, energy-transfer prescription, short-distance subtraction, and unresolved relative matching sign. The quark-interchange hierarchies are therefore the central predictions, whereas the pion-exchange results quantify matching sensitivity. Measurements of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> modes can directly test these patterns.

India

Vandan Patel

Ajay Kumar Rai

Selected open-charm decays of the narrow <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>c</mi></msub></math> states: Quark-interchange predictions and pion-exchange sensitivity

In the present work, we study the radiative decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> molecular state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>G</mi><mn>0</mn></msub></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>I</mi><mi>G</mi></msup><mo stretchy="false">(</mo><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><msup><mn>0</mn><mo>+</mo></msup><mo stretchy="false">(</mo><msup><mn>0</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo stretchy="false">)</mo></math> using a phenomenological Lagrangian approach. The molecular coupling is fixed by the compositeness condition with a Gaussian form factor. The partial widths for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>G</mi><mn>0</mn></msub><mo stretchy="false">→</mo><mi>γ</mi><mi>γ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><msub><mi>h</mi><mi>c</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>ρ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>ω</mi></math> are evaluated. Our results show that the two-photon and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><msub><mi>h</mi><mi>c</mi></msub></math> channels are highly suppressed, while <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>ρ</mi></math> are of the order of a few keV, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>ω</mi></math> reaches several tens of keV, making it the dominant radiative mode. The ratios <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><msub><mi>G</mi><mn>0</mn></msub><mo stretchy="false">→</mo><mi>γ</mi><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><msub><mi>G</mi><mn>0</mn></msub><mo stretchy="false">→</mo><mi>γ</mi><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><msub><mi>G</mi><mn>0</mn></msub><mo stretchy="false">→</mo><mi>γ</mi><mi>ω</mi><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><msub><mi>G</mi><mn>0</mn></msub><mo stretchy="false">→</mo><mi>γ</mi><mi>ρ</mi><mo stretchy="false">)</mo></math> are predicted to be 1–2.6 and 3.4–5.4, respectively, with mild parameter dependence. We also compare with hadronic decays and find that the total radiative decay width is lower than the hadronic decay widths by about one order of magnitude. We propose searching for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>G</mi><mn>0</mn></msub></math> in the sequential decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4230</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>G</mi><mn>0</mn></msub><mo stretchy="false">→</mo><mi>γ</mi><mi>ω</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, which is accessible to further experimental measurements by the BESIII, Belle II, and LHCb Collaborations.

China

Qi Wu

Ming-Qi Cui

Zi-Li Yue

Dian-Yong Chen

Shi-Dong Liu

Gang Li

Radiative decays of the predicted <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> molecular state: The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> case

The STAR experiment has recently reported data on the <math altimg='si13.svg'><mrow><msqrt><mrow><mo>&#9001;</mo><mstyle mathvariant='normal'><mi>&#916;</mi></mstyle><msub><mi>p</mi><mrow><mi>T</mi><mo>,</mo><mi>i</mi></mrow></msub><mstyle mathvariant='normal'><mi>&#916;</mi></mstyle><msub><mi>p</mi><mrow><mi>T</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>&#9002;</mo></mrow></msqrt><mo linebreak='goodbreak'>/</mo><mrow><mo>&#9001;</mo><mrow><mo>&#9001;</mo><msub><mi>p</mi><mi>T</mi></msub><mo>&#9002;</mo></mrow><mo>&#9002;</mo></mrow></mrow></math> charged hadron correlation in Au+Au reactions from <math altimg='si14.svg'><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo linebreak='goodbreak'>=</mo><mn>3</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>200</mn></mrow></math> GeV. The beam energy dependence of this quantity is non-monotonic, showing a pronounced minimum at <math altimg='si15.svg'><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>&#8776;</mo><mn>7.7</mn></mrow></math> GeV, while being essentially flat at lower and higher energies. It has been proposed that such a non-monotonicity would be consistent with increased momentum correlations due to a critical point of QCD. In the present work it is shown, using a simplified model, that the observed structure can be consistently explained by the transition from a baryon dominated system to a meson dominated system and is therefore not a good observable for the critical point of QCD.

Switzerland

Tom Reichert

Germany

Jan Steinheimer

Marcus Bleicher

Non-monotonicity of <italic>p<inf>T</inf></italic> correlations from meson-baryon mixing

We searched for proton decay via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> in 0.401 megaton-years of data collected in all pure water detector phases of Super-Kamiokande (SK) I-V. A theoretical study predicts proton decay rates without assuming a particular grand unified theory and suggests that three-body proton decays involving two pions can have decay rates comparable to those of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math>. This is the first search for proton decay into a charged antilepton and two neutral pions in SK. One data candidate event was found for each of the two decay modes, which is compatible with the expected atmospheric neutrino background. We set lower limits on the lifetime of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>τ</mi><mo>/</mo><mi>B</mi><mo stretchy="false">(</mo><mi>p</mi><mo stretchy="false">→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">)</mo><mo>&gt;</mo><mn>7.2</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>33</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>τ</mi><mo>/</mo><mi>B</mi><mo stretchy="false">(</mo><mi>p</mi><mo stretchy="false">→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">)</mo><mo>&gt;</mo><mn>4.5</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>33</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>year</mi></mrow></math> at 90% confidence level. These limits are more than one order of magnitude better than those of the previous experiment.

Japan

K. Abe

S. Abe

Y. Asaoka

M. Harada

Y. Hayato

K. Hiraide

T.H. Hung

K. Hosokawa

K. Ieki

M. Ikeda

J. Kameda

Y. Kanemura

R. Kaneshima

Y. Kashiwagi

Y. Kataoka

S. Miki

United States

S. Mine

M. Miura

S. Moriyama

K. Nakagiri

M. Nakahata

S. Nakayama

Y. Noguchi

G. Pronost

K. Okamoto

K. Sato

H. Sekiya

H. Shiba

K. Shimizu

R. Shinoda

M. Shiozawa

Y. Sonoda

Y. Suzuki

A. Takeda

Y. Takemoto

A. Takenaka

H. Tanaka

T. Yano

S. Chen

Y. Itow

T. Kajita

R. Nishijima

K. Okumura

T. Tashiro

T. Tomiya

X. Wang

S. Yoshida

Spain

P. Fernandez

L. Labarga

D. Samudio

B. Zaldivar

F.G. Garay

Canada

B.W. Pointon

C. Yanagisawa

B. Jargowsky

E. Kearns

J. Mirabito

J.L. Raaf

L. Wan

T. Wester

J. Bian

B. Cortez

N.J. Griskevich

Y. Jiang

S. Locke

M.B. Smy

H.W. Sobel

V. Takhistov

H.G. Berns

J. Hill

South Korea

M.C. Jang

S.H. Lee

D.H. Moon

R.G. Park

B.S. Yang

B. Bodur

K. Scholberg

C.W. Walter

France

A. Beauchêne

O. Drapier

A. Ershova

M. Ferey

A. Giampaolo

Z. Hu

E. Le Blévec

Th. A. Mueller

A.D. Santos

P. Paganini

C. Quach

R. Rogly

T. Nakamura

J.S. Jang

United Kingdom

R.P. Litchfield

L.N. Machado

F.J.P. Soler

J.G. Learned

K. Choi

N. Iovine

Vietnam

S. Cao

L.H.V. Anthony

Search for proton decay via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>p</mi><mo stretchy="false">→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>p</mi><mo stretchy="false">→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> in 0.401 megaton-years exposure of Super-Kamiokande I-V

We present a systematic study of the magnetic dipole and electric quadrupole moments of compact <math altimg='si3.svg'><mrow><mrow><mo>[</mo><msub><mi>q</mi><mn>1</mn></msub><msub><mi>q</mi><mn>2</mn></msub><mo>]</mo></mrow><mrow><mo>[</mo><msub><mover accent='true'><mi>q</mi><mo>&#175;</mo></mover><mn>3</mn></msub><mover accent='true'><mi>c</mi><mo>&#175;</mo></mover><mo>]</mo></mrow></mrow></math> tetraquark states with quantum numbers <math altimg='si22.svg'><mrow><msup><mi>J</mi><mi>P</mi></msup><mo linebreak='goodbreak'>=</mo><msup><mn>1</mn><mo>+</mo></msup></mrow></math>, in the diquark&#8211;antidiquark picture and within the light-cone QCD sum rule framework. By performing a flavor decomposition across all admissible <italic>u</italic>/ <italic>d</italic> configurations, we show that the charm-quark contribution to the electromagnetic moments vanishes algebraically at the operator level &#8211; a structural feature of the specific spin organization adopted here, in which the heavy antiquark resides in a pseudoscalar antidiquark, distinct from the dynamical 1/ <italic>m<inf>c</inf></italic> suppression operative in alternative compact constructions and in hadronic molecules. The magnetic moments follow a coherent light-flavor pattern &#8211; positive for <italic>uu</italic>-, negative for <italic>dd</italic>-, and suppressed for mixed-flavor diquarks &#8211; and the quadrupole moments are non-zero throughout, corresponding, in the customary geometrical interpretation, to intrinsically deformed charge distributions. We further identify the dimensionless multipole ratio <math altimg='si39.svg'><mrow><mi mathvariant='script'>D</mi><mo linebreak='goodbreak'>/</mo><mi>&#956;</mi></mrow></math> as a structural observable, independent of the normalization of the interpolating current, which probes the relative geometry of the spin-current and charge distributions complementary to the absolute moments. Taken together, the algebraic decoupling of the charm contribution and the operator-level distinction it implies among different singly-heavy tetraquark architectures constitute methodological signatures that discriminate among the corresponding internal organizations and, to the extent that a physical candidate is dominated by one of them, among compact and molecular interpretations.

Türkiye

Ulaş Özdem

Flavor decomposition of electromagnetic multipole moments in <math altimg='si3.svg'><mrow><mrow><mo>[</mo><msub><mi>q</mi><mn>1</mn></msub><msub><mi>q</mi><mn>2</mn></msub><mo>]</mo></mrow><mrow><mo>[</mo><msub><mover accent='true'><mi>q</mi><mo>&#175;</mo></mover><mn>3</mn></msub><mover accent='true'><mi>c</mi><mo>&#175;</mo></mover><mo>]</mo></mrow></mrow></math> tetraquarks: Light-quark analogs of <italic>T</italic> <inf><italic>cs</italic>1</inf>(2900) 0 with <math altimg='si22.svg'><mrow><msup><mi>J</mi><mi>P</mi></msup><mo linebreak='goodbreak'>=</mo><msup><mn>1</mn><mo>+</mo></msup></mrow></math>

We investigate the exclusive semileptonic decays of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi><mo>→</mo><mi>p</mi><msup><mi>ℓ</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo>¯</mo></mover><mi>ℓ</mi></msub><mspace width="4pt"></mspace><mrow><mo>(</mo><mi>ℓ</mi><mo>=</mo><mi>e</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></mrow></math> within the standard model using the light-front quark model. The transition form factor behaviors of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi><mo>→</mo><mi>p</mi></mrow></math> are obtained from the effective treatment of nonvalence contributions in addition to the valence ones in the Drell-Yan-West frame due to the Bethe-Salpeter formalism. Based on these form factors, we obtain that the branching ratios of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi><mo>→</mo><mi>p</mi><msup><mi>e</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo>¯</mo></mover><mi>e</mi></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><msup><mi>μ</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo>¯</mo></mover><mi>μ</mi></msub></mrow></math>, including nonvalence contributions, are around <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>8.32</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1.31</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math>, which are consistent with the latest measurements from the BESIII Collaboration, respectively. Our results indicate that nonvalence contributions can play a non-negligible role in the semileptonic baryon decays within the light-front framework.

Chong-Chung Lih

Chao-Qiang Geng

Semileptonic decays of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi><mo>→</mo><mi>p</mi><msup><mi>ℓ</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo>¯</mo></mover><mi>ℓ</mi></msub></mrow></math> in light-front dynamics

Hao Xu

Ju-Jun Xie

Xiang Liu

Correction to: Implication of the observed $$e^+e^-\rightarrow p\bar{p}\pi ^0$$ for studying the $$p\bar{p}\rightarrow \psi (3770)\pi ^0$$ process

We perform a systematic QCD sum rule study of light tetraquark states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> in the diquark-antidiquark picture. A complete set of local interpolating currents is constructed and projected onto six flavor-isospin configurations (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mo>=</mo><mi>u</mi><mo>/</mo><mi>d</mi></math>): the isoscalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>s</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> sectors, the isovector <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>s</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> sectors, and the isotensor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> sector. From the nonderivative currents studied in the present work, the extracted masses of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>s</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> configurations lie in the ranges 1.53–2.37 GeV, 1.86–2.51 GeV, and 2.46–2.60 GeV, respectively. For the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> vector sector, we also quote the previous derivative-current result <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>2.34</mn><mrow><mo>−</mo><mn>0.30</mn></mrow><mrow><mo>+</mo><mn>0.23</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> as a complementary benchmark. We further compare the present <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> tetraquark spectrum with previous QCD sum rule results for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> tetraquark and hybrid states [N. Su, E.-L. Cui, Y.-W. Jiang, and H.-X. Chen, <a href="http://dx.doi.org/10.1140/epjc/s10052-026-15939-y">Eur. Phys. J. C 86, 724 (2026)</a>.], aiming to provide useful information for distinguishing tetraquark and hybrid configurations in the light hadron spectrum. As an additional improvement, we complete the previously missing isotensor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> tetraquark entry and obtain its lowest mass to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi><mo>=</mo><mn>2.1</mn><msubsup><mn>9</mn><mrow><mo>−</mo><mn>0.24</mn></mrow><mrow><mo>+</mo><mn>0.26</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, which is included in the spectral comparison.

Yi-Wei Jiang

Hua-Xing Chen

Er-Liang Cui

Ding-Kun Lian

Wen-Ying Liu

Niu Su

Light tetraquark states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> from QCD sum rules

The topological susceptibility of the QCD vacuum provides an understanding of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi></math> vacua as vacua of a Chern-Simons gauge theory. In this way, it gives an immediate proof of the physicality of the boundary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi></math>-term. This makes the essence of the strong-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> puzzle very transparent and offers a solution in form of the gauge axion, which has exact quality. This axion represents an intrinsic part of the QCD gauge redundancy without any reference to an anomalous global symmetry. It is a two-form transforming under the QCD gauge symmetry. Because of its pure-gauge nature, the gauge axion represents a powerful tool to monitor physics of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi></math> vacua in various regimes. Unlike the ordinary Peccei-Quinn axion, which is UV completed into a Goldstone phase of a complex scalar and thereby suffers from the quality problem, the gauge axion is UV completed directly into a fundamental theory of gravity. We study the domain wall and string structure of the gauge axion and show that the strings sourcing it must be a part of this fundamental theory. We thus observe that the absence of the axion quality problem motivates the presence of fundamental strings. This provides a new argument for a connection between the axion and gravity.

Gia Dvali

Lucy Komisel

Otari Sakhelashvili

Anja Wachowitz

Strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> problem and its gauge axion solution as evidence for fundamental strings

The masses of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> P-wave charmoniumlike and bottomoniumlike tetraquark states are calculated in a constituent quark model where the Cornell-like potential and Breit-Fermi interaction are employed. All model parameters were imported from previous work, and predetermined by studying the low-lying conventional S- and P-wave light, charmed, bottom, charmonium, and bottomonium meson mass spectra. The lowest <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> tetraquark mass is predicted to be around 4.15 GeV. The decay widths of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> P-wave tetraquark states are calculated for possible two-body strong decay channels within the rearrangement mechanism, including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math> for charmoniumlike tetraquarks, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><msub><mi>χ</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub></math> for bottomoniumlike tetraquarks. The theoretical results are compared with the selected exotic states, also known as Y states, and tentative assignments are suggested. This study suggests that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>4230</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>4360</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>4660</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>10753</mn><mo stretchy="false">)</mo></math> may be P-wave tetraquark states and that multiple states might exist around 4.36 GeV.

Thailand

Zheng Zhao

Attaphon Kaewsnod

Kai Xu

Nattapat Tagsinsit

Xuyang Liu

Ayut Limphirat

Yupeng Yan

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup><mtext> </mtext><mtext> </mtext><mi>P</mi></math>-wave charmoniumlike and bottomoniumlike tetraquark spectroscopy