The observation of a resonance structure in the opening angle of the electron-positron pairs in the $$^{7}$$ Li(p,e $$^+$$ e $$^-$$ ) $$^{8}$$ Be reaction was claimed and interpreted as the production and subsequent decay of a hypothetical particle (X17). Similar excesses, consistent with this particle, were later observed in processes involving $$^{4}$$ He and $$^{12}$$ C nuclei with the same experimental technique. The MEG II apparatus at PSI, designed to search for the $$\mu ^+ \rightarrow \textrm{e}^+ \gamma $$ decay, can be exploited to investigate the existence of this particle and study its nature. Protons from a Cockroft–Walton accelerator, with an energy up to 1.1 MeV, were delivered on a dedicated Li-based target. The $$\gamma $$ and the e $$^{+}$$ e $$^{-}$$ pair emerging from the $$^8\textrm{Be}^*$$ transitions were studied with calorimeters and a spectrometer, featuring a broader angular acceptance than previous experiments. We present in this paper the analysis of a four-week data-taking in 2023 with a beam energy of 1080 keV, resulting in the excitation of two different resonances with Q-value 17.6 and 18.1 MeV. No significant signal was found, and limits at 90% C.L. on the branching ratios (relative to the $$\gamma $$ emission) of the two resonances to X17 were set, $$R_{17.6} <{1.8}\,\times \,10^{-6}$$ and $$R_{18.1} < {1.2}\,\times \,10^{-5}$$ in the mass range between $${16.5}\hbox { MeV}/\hbox {c}^{2}$$ and $${17.1}\hbox { MeV}/\hbox {c}^{2}$$ .

Russia

K. Afanaciev

Italy

A. Baldini

Japan

S. Ban

H. Benmansour

G. Boca

P. Cattaneo

G. Cavoto

F. Cei

M. Chiappini

A. Corvaglia

Switzerland

G. Maso

A. Bari

M. Gerone

L. Barusso

M. Francesconi

L. Galli

G. Gallucci

F. Gatti

L. Gerritzen

F. Grancagnolo

E. Grandoni

M. Grassi

D. Grigoriev

M. Hildebrandt

United Kingdom

F. Ignatov

F. Ikeda

T. Iwamoto

S. Karpov

P. Kettle

N. Khomutov

A. Kolesnikov

N. Kravchuk

V. Krylov

N. Kuchinskiy

F. Leonetti

W. Li

V. Malyshev

A. Matsushita

M. Meucci

S. Mihara

United States

W. Molzon

T. Mori

D. Nicolò

H. Nishiguchi

A. Ochi

W. Ootani

A. Oya

D. Palo

M. Panareo

A. Papa

V. Pettinacci

A. Popov

F. Renga

S. Ritt

M. Rossella

A. Rozhdestvensky

S. Scarpellini

P. Schwendimann

G. Signorelli

M. Takahashi

Y. Uchiyama

A. Venturini

B. Vitali

C. Voena

K. Yamamoto

R. Yokota

T. Yonemoto

Search for the X17 particle in $$^{7}\textrm{Li}(\textrm{p},\textrm{e}^+ \textrm{e}^{-}) ^{8}\textrm{Be}$$ processes with the MEG II detector

We investigate Λ production in the ( <math altimg='si146.svg'><msup><mrow><mi>&#960;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math>, <math altimg='si3.svg'><msup><mrow><mi>K</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math>) reaction on a 6Li target at <math altimg='si4.svg'><msub><mrow><mi>p</mi></mrow><mrow><msup><mrow><mi>&#960;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1.05</mn></math> GeV/ <italic>c</italic>, using the distorted-wave impulse approximation (DWIA) with the Fermi-averaged <math altimg='si5.svg'><msup><mrow><mi>&#960;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup><mi>n</mi><mo stretchy='false'>&#8594;</mo><msup><mrow><mi>K</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup><mi mathvariant='normal'>&#923;</mi></math> amplitudes. The calculated spectrum is in good agreement with the experimental data, suggesting that <math altimg='si1.svg'><mmultiscripts><mrow><mi mathvariant='normal'>He</mi></mrow><mprescripts /><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mn>4</mn></mrow></mmultiscripts></math>- <italic>d</italic> configurations play a key role in describing the &#923; continuum states of <math altimg='si23.svg'><msubsup><mrow /><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mn>6</mn></mrow></msubsup></math>Li near and above the <math altimg='si8.svg'><mmultiscripts><mrow><mi mathvariant='normal'>He</mi></mrow><mprescripts /><none /><mrow><mn>3</mn></mrow></mmultiscripts><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mi>d</mi><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mi mathvariant='normal'>&#923;</mi></math> threshold. Our analysis shows that the <math altimg='si1.svg'><mmultiscripts><mrow><mi mathvariant='normal'>He</mi></mrow><mprescripts /><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mn>4</mn></mrow></mmultiscripts></math> hypernucleus as a hyperfragment is prominently produced through <italic>D</italic>-wave resonances with <math altimg='si9.svg'><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msup><mrow><mn>3</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math>, <math altimg='si10.svg'><msup><mrow><mn>2</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math>, and <math altimg='si11.svg'><msup><mrow><mn>1</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math> in the <math altimg='si108.svg'><mmultiscripts><mrow><mi mathvariant='normal'>He</mi></mrow><mprescripts /><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mn>4</mn></mrow></mmultiscripts><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mi>d</mi></math> channel at a large momentum transfer <math altimg='si13.svg'><mi>q</mi><mo>&#8771;</mo><mn>360</mn></math>&#8211;400 MeV/ <italic>c</italic>. These findings provide theoretical evidence for the production of a <math altimg='si1.svg'><mmultiscripts><mrow><mi mathvariant='normal'>He</mi></mrow><mprescripts /><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mn>4</mn></mrow></mmultiscripts></math> hyperfragment via a cluster-like mechanism in the 6Li( <math altimg='si146.svg'><msup><mrow><mi>&#960;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math>, <math altimg='si3.svg'><msup><mrow><mi>K</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math>) reaction.

Toru Harada

Yoshiharu Hirabayashi

Evidence for <math altimg='si1.svg'><mmultiscripts><mrow><mi mathvariant='normal'>He</mi></mrow><mprescripts /><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mn>4</mn></mrow></mmultiscripts></math> hyperfragment production in the 6Li( <italic>&#960;</italic> +, <italic>K</italic> +) reaction

In this study, we propose using the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> pole position to constrain the existence of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> three-body bound state within the one-boson-exchange (OBE) model. The existence of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> bound state remains uncertain due to significant variations in the OBE interaction, particularly in the strength of scalar-meson-exchange interactions, which can differ by a factor about 20 between two commonly used OBE models. This discrepancy renders the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> system highly model-dependent. To address this issue, we constrain the scalar-meson-exchange interaction using the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> pole position, where the pseudoscalar-meson coupling is well-determined, and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi></math>-exchange interactions nearly cancel each other out, leaving the coupling constant of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math>-exchange as the only unknown parameter. Our results indicate that the isospin-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mfrac><mn>1</mn><mn>2</mn></mfrac></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> bound states exist when <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> is a virtual state of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><msup><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup><mo>/</mo><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> located within approximately <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>15</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> of the threshold. However, the three-body bound state is gone when the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> virtual state pole is more than 20 MeV away from the threshold. Each experimental progress, either on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> state or the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, can shed light on the nature of the other state. Another significant outcome is a refined set of OBE model parameters calibrated using the pole positions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>3875</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, rigorously addressing the cutoff dependence. These parameters provide a valuable resource for more accurate calculations of systems involving few-body <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup></math>, and their antiparticles. Additionally, we find no evidence of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> three-body resonances after extensive search using a combination of the Gaussian expansion method and the complex scaling method.

China

Hai-Xiang Zhu

Germany

Lu Meng

Yao Ma

Ning Li

Wei Chen

Shi-Lin Zhu

Constraining the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> three-body bound state via the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> pole

The hadronic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msup><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Σ</mi><mi>c</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> interactions are revisited, with a focus on their short-range parts, motivated by a tension between the interpretations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow></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><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow></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><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow></msub><mo stretchy="false">(</mo><mn>4457</mn><mo stretchy="false">)</mo></math> in effective field theory (EFT) frameworks and the one-boson-exchange (OBE) model. While the three states can be interpreted as <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> molecular states within EFT frameworks, this is not feasible in the single-channel OBE model with consistent cutoff. In this work, the possibility to reconcile OBE model with EFTs by refitting the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi></math>-, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math>-exchange interaction is explored and ruled out. It is pointed out that the problem in OBE arises from the strong short-range spin-dependent one-pion-exchange (OPE) interaction and the fixed signs of other short-range interactions in OBE model also prevent the cancellation. To address this issue, the short-range subtraction strategies within the OBE model are revisited. Two subtraction schemes are explored: removing the delta-function from all interactions and eliminating it only from the pseudoscalar-meson-exchange component. These schemes favor different spin assignments for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow></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><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow></msub><mo stretchy="false">(</mo><mn>4457</mn><mo stretchy="false">)</mo></math>. Though solving the problem, there is no clear dynamical picture to support the subtraction schemes. We propose a new quark-exchange mechanism motivated by the Pauli principle. Different from the two subtraction schemes in OBE, the quark-exchange mechanism offers an explanation grounded in microscopic dynamics. It is shown that the spin-dependent quark-exchange interaction cancels those from OPE. The differences in the predictions for the spin, isospin, and open-charm partner states of the experimental <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states offer a way to distinguish between the subtracted OBE model and the OBE model with quark-exchange contributions.

Ru Xu

Toward modeling the short-range interactions of hidden and open charm pentaquark molecular states

The ultralight dark photon is an intriguing dark matter candidate. The interaction between visible and dark photons is introduced by the gauge kinetic mixing between the field strength tensors of the Abelian gauge groups in the Standard Model and dark sector. Relativistic electrodynamics was generalized to quantum electromagnetodynamics (QEMD) in the presence of both electric and magnetic charges. The photon is described by two four-potentials corresponding to two $ U(1) $ gauge groups and satisfying non-trivial commutation relations. In this work, we construct low-energy dark photon-photon interactions in the QEMD framework and obtain new dark photon-photon kinetic mixings. Then, we derive the consequent field and Maxwell's equations. We also investigate the detection strategies of dark photons as light dark matter and generic kinetic mixings at haloscope experiments.

Chang-Jie Dai

Tong Li

Rui-Jia Zhang

Dark photon dark matter in quantum electromagnetodynamics and detection at haloscope experiments * Li Tong is supported by the National Natural Science Foundation of China (12375096, 12035008, 11975129)

Cryogenic calorimetric experiments to search for neutrinoless double-beta decay ( $$0\nu \beta \beta $$ ) are highly competitive, scalable and versatile in isotope. The largest planned detector array, CUPID, is comprised of about 1500 individual Li $$_{2}$$ $$^{100}$$ MoO $$_4$$ detector modules with a further scale up envisioned for a follow up experiment (CUPID-1T). In this article, we present a novel detector concept targeting this second stage with a low impedance TES based readout for the Li $$_2$$ MoO $$_4$$ absorber that is easily mass-produced and lends itself to a multiplexed readout. We present the detector design and results from a first prototype detector operated at the NEXUS shallow underground facility at Fermilab. The detector is a 2-cm-side cube with 21 g mass that is strongly thermally coupled to its readout chip to allow rise-times of $$\sim $$ 0.5 ms. This design is more than one order of magnitude faster than present NTD based detectors and is hence expected to effectively mitigate backgrounds generated through the pile-up of two independent two neutrino decay events coinciding close in time. Together with a baseline resolution of 1.95 keV (FWHM) these performance parameters extrapolate to a background index from pile-up as low as $$5\cdot 10^{-6}$$ counts/keV/kg/yr in CUPID size crystals. The detector was calibrated up to the MeV region showing sufficient dynamic range for $$0\nu \beta \beta $$ searches. In combination with a SuperCDMS HVeV detector this setup also allowed us to perform a precision measurement of the scintillation time constants of Li $$_2$$ MoO $$_4$$ , which showed a primary component with a fast O(20 $$\upmu $$ s) time scale.

G. Bratrud

C. Chang

R. Chen

Canada

E. Cudmore

E. Figueroa-Feliciano

Z. Hong

K. Kennard

S. Lewis

M. Lisovenko

L. Mateo

V. Novati

V. Novosad

France

E. Oliveri

R. Ren

J. Scarpaci

B. Schmidt

G. Wang

L. Winslow

V. Yefremenko

J. Zhang

D. Baxter

M. Hollister

C. James

P. Lukens

D. Temples

First demonstration of a TES based cryogenic Li $$_2$$ MoO $$_4$$ detector for neutrinoless double beta decay search

Owing to the SU(3) symmetry breaking effect, the axial-vector kaons <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>1270</mn><mo>)</mo></math> and <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>1400</mn><mo>)</mo></math> are established to be mixtures of two P-wave <math><mrow><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn><mi>A</mi></mrow></msub><mo>(</mo><mrow><msub><mrow><mmultiscripts><mrow><mi>P</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow></mrow></math> and <math><msub><mi>K</mi><mrow><mn>1</mn><mi>B</mi></mrow></msub><mrow><mo>(</mo><msub><mrow><mmultiscripts><mrow><mi>P</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>1</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow></math> states. In QCD sum rules, we propose a new construction of the <math><msub><mi>K</mi><mn>1</mn></msub></math> current operators and calculate the two-point correlation functions by including the next-to-leading order four-quark condensates. The mixing angle is determined as <math><mrow><mi>θ</mi><mo>=</mo><mo>(</mo><msubsup><mrow><mn>46.95</mn></mrow><mrow><mo>−</mo><mn>0.23</mn></mrow><mrow><mo>+</mo><mn>0.25</mn></mrow></msubsup><mo>)</mo><mo>°</mo></mrow></math> by reproducing the masses of <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>1270</mn><mo>)</mo></math> and <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>1400</mn><mo>)</mo></math>. We further compose the <math><mi>K</mi><msub><mover><mi>K</mi><mo>¯</mo></mover><mn>1</mn></msub><mrow><mo>(</mo><mn>1270</mn><mo>)</mo></mrow></math> and <math><mi>K</mi><msub><mover><mi>K</mi><mo>¯</mo></mover><mn>1</mn></msub><mrow><mo>(</mo><mn>1400</mn><mo>)</mo></mrow></math> interpolating currents with exotic quantum numbers <math><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> to investigate the possible molecular interpretation of the recently observed <math><msub><mi>η</mi><mn>1</mn></msub><mo>(</mo><mn>1855</mn><mo>)</mo></math> state. We calculate the correlation functions and perform the QCD sum rule analyses for these two molecular systems. However, the spectral functions are found to be negative in physical regions so that they are not able to provide reliable investigations of the <math><mi>K</mi><msub><mover><mi>K</mi><mo>¯</mo></mover><mn>1</mn></msub></math> molecular states.

Zheng-Shu Liu

Xu-Liang Chen

Ding-Kun Lian

Mixing angle of <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>1270</mn><mo>/</mo><mn>1400</mn><mo>)</mo></math> and the <math><mi>K</mi><msub><mover><mi>K</mi><mo>¯</mo></mover><mn>1</mn></msub><mo>(</mo><mn>1400</mn><mo>)</mo></math> molecular interpretation of <math><msub><mi>η</mi><mn>1</mn></msub><mo>(</mo><mn>1855</mn><mo>)</mo></math>

In this work, we make a study of the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> state observed by the LHCb collaboration in 2021. In obtaining the effective potentials using the one-boson-exchange potential model we use an exponential form factor and find that, in the short and medium range, the contributions of the <math><mi>π</mi></math>, <math><mi>ρ</mi></math>, and <math><mi>ω</mi></math> exchanges are comparable while in the long range the pion-exchange contribution is dominant. Based on the assumption that <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> is a loosely bound state of <math><msup><mi>D</mi><mo>*</mo></msup><mi>D</mi></math>, we focus on its three-body decay using the meson-exchange method. Considering that the difference between the thresholds of <math><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mi>D</mi><mn>0</mn></msup></math> and <math><msup><mi>D</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mi>D</mi><mo>+</mo></msup></math> is even larger than the binding energy of <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>, the isospin-breaking effect is amplified by the small binding energy of <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>. Explicitly including such an isospin-breaking effect we obtain, by solving the Schrödinger equation, that the probability of the isoscalar component is about 91% while that of the isovector component is around 9% for <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>. Using the experimental value of the mass of <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> as an input, we obtain the wave function of <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> and further obtain its width via the three-body hadronic as well as the radiative decays. The total width we obtain is in agreement with the experimental value of the LHCb measurement with a unitarized Breit-Wigner profile. Conversely, the current results support the conclusion that <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> is a hadronic molecule of <math><msup><mi>D</mi><mo>*</mo></msup><mi>D</mi></math>.

Zhi-Feng Sun

Xiang Liu

Isospin violation effect and three-body decays of the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> state

In this work we investigate the two-neutron decay of $^{13}$Li and of the excited states of $^{11}$Li populated via one-proton removal from $^{14}$Be and $^{12}$Be, respectively. A phenomenological model is used to describe the decay of $^{11}$Li and $^{13}$Li. While the first one displays important sequential components, the second one appears dominated by the direct two-neutron decay. A microscopic three-body model is used to extract information on the spatial configuration of the emitted neutrons before the decay and shows that the average distance between the neutrons increases going from $^{11}$Li to $^{13}$Li.