The Efimov effect is an intriguing three-body quantum phenomenon. Searching for Efimov states within the realms of nuclear and hadronic physics presents a challenge due to the inherent inability of natural physical systems to exhibit adjustable two-body scattering lengths. In this study, we examine the potential existence of Efimov states in the $\textit{D}$ $\textit{D}$ $\textit{D}$ and $\textit{DD}$ $\textit{D}$ three-hadron systems. Utilizing a pionless effective field theory framework, we determine that the presence of Efimov states in the spectrum of the $\textit{D}$ $\textit{D}$ $\textit{D}$ system is contingent upon the existence of an ($\textit{I, J}$) = (1$\textit{,}$ 2) $\textit{D}$ $\textit{D}$ two-body bound system. If only the $$ {T}_{cc}^{+} $$ and its heavy quark spin partner $$ {T}_{cc}^{\ast +} $$ exist while there is no near-threshold pole in all other $\textit{S}$-wave $\textit{D}$ $\textit{D}$ scattering amplitudes, no Efimov effect is expected in the $\textit{D}$ $\textit{D}$ $\textit{D}$ systems.

China

Hai-Long Fu

Germany

Yong-Hui Lin

Feng-Kun Guo

Hans-Werner Hammer

Ulf-G. Meißner

Georgia

Akaki Rusetsky

Xu Zhang

Exploring Efimov states in $\textit{D}$

We investigate the feasibility of measuring the proton charge radius through dimuon photoproduction off a proton target. Our findings indicate that the Bethe-Heitler mechanism, which dominates at small momentum transfers, allows for an extraction of the proton electromagnetic form factors in the extremely low <math><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup></math> region below <math><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> GeV$^{2}$ in the spacelike region, when the incident photon beam energy exceeds several hundred MeV. The optimal kinematical region and a sensitivity study of the proton charge radius from dimuon photoproduction are presented. Such a measurement is expected to provide an alternative to the elastic muon-proton scattering measurements such as MUSE at PSI and AMBER at CERN.

The proton charge radius from dimuon photoproduction off the proton

We propose a novel method for measuring the charge radii of charged stable hadrons, with which the first measurement of the charge radii of the <math><msup><mrow><mi>Σ</mi></mrow><mrow><mo>+</mo></mrow></msup></math> and the <math><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> is foreseen. The method explores the facts that the Dalitz decay <math><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo><mo>→</mo><mi>Y</mi><mover><mrow><mi>Y</mi></mrow><mrow><mo>¯</mo></mrow></mover><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> contains the hyperon form factors and the lowest measurable four-momentum transfer squared can be as low as <math><mo>∼</mo><mn>4</mn><msubsup><mrow><mi>m</mi></mrow><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><mn>1.05</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup><mspace width="0.2em"></mspace><mrow><mi>Ge</mi><msup><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> in the time-like region. We identify a kinematic region where the hyperon form factors are essential and propose a method for subtracting the background from the data. It is estimated that the hyperon charge radii can be measured to a precision of about 0.2 fm with the BESIII experiment and one order of magnitude better at the future Super τ-Charm Facility. Moreover, the same method can be used to measure the charge radius of the proton, which provides an independent cross-check on the extraction of proton radius from elastic ep scattering or leptonic hydrogen spectroscopy.

Method for measuring the charge radii of charged hyperons from the time-like region

The electromagnetic form factors of the  $$\Lambda $$  <math> <mi>Λ</mi> </math>   hyperon in the time-like region are determined precisely through a dispersion-theoretical analysis of the world data for the cross section of the annihilation process  $$e^+e^-\rightarrow {\bar{\Lambda }}{\Lambda }$$  <math> <mrow> <msup> <mi>e</mi> <mo>+</mo> </msup> <msup> <mi>e</mi> <mo>-</mo> </msup> <mo>→</mo> <mover> <mrow> <mi>Λ</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>Λ</mi> </mrow> </math>  . The spectral function is represented by a superposition of narrow and broad vector meson poles. We test different scenarios for the spectral function and obtain a good description of the world data in the time-like region. The uncertainties in the extracted form factors are estimated by means of the bootstrap sampling method. The analytical continuation of the form factors to the space-like region introduces large errors due to the lack of data. When the electric  $$\Lambda $$  <math> <mi>Λ</mi> </math>   radius from chiral perturbation theory is taken as a constraint, the magnetic radius is predicted as  $$r_M = 0.681 \pm 0.002$$  <math> <mrow> <msub> <mi>r</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>0.681</mn> <mo>±</mo> <mn>0.002</mn> </mrow> </math>   fm. We also extract various vector meson to baryon coupling constants.

Dispersion-theoretical analysis of the electromagnetic form factors of the  $$\Lambda $$  <math> <mi>Λ</mi> </math>   hyperon

We present a high-precision calculation of the recoil–finite-size correction to the hyperfine splitting (HFS) in muonic and electronic hydrogen based on nucleon electromagnetic form factors obtained from dispersion theory. This will help guide the upcoming searches of the HFS transition in muonic hydrogen, and will allow a precise determination of the sum of the polarizability and Zemach radius contributions when this transition is found.

Switzerland

Aldo Antognini

Precision calculation of the recoil–finite-size correction for the hyperfine splitting in muonic and electronic hydrogen

We systematically calculate the radiative corrections of order <math><mi>α</mi><mo>/</mo><mi>π</mi></math> to elastic muon-proton scattering at low momentum transfers. These include vacuum polarization, photon-loop form factors of the muon and the proton, two-photon exchange corrections and soft photon radiation. In particular, we discuss these corrections for the kinematics of the upcoming AMBER experiment with a 100 GeV muon beam. It is found that for the ratio to the Born cross section, only the minor terms from the photon-loop form factors of the proton and two-photon exchange depend on the proton structure as predetermined by the strong interactions. The inclusion of soft photon radiation (below 20 MeV), which as such is mandatory to cancel the infrared divergences arising from virtual photon loops, points to a prominent role of bremsstrahlung among the radiative corrections of order <math><mi>α</mi><mo>/</mo><mi>π</mi></math>. Therefore, the calculation of the process <math><msup><mi>μ</mi><mo>∓</mo></msup><mi>p</mi><mo>→</mo><msup><mi>μ</mi><mo>∓</mo></msup><mi>p</mi><mi>γ</mi></math> must be extended beyond the soft photon approximation and tailored to the specific experimental conditions for a proper analysis of the upcoming AMBER data.

Norbert Kaiser

Radiative corrections to elastic muon-proton scattering at low momentum transfers

We predict the differential cross sections for <math><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>p</mi></math> and <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><mi>p</mi></math> elastic scattering in the PRad-II energy region. The prediction is based on form factors obtained in our previous high-precision analysis of space- and time-like data from dispersion theory and different sets of two-photon exchange corrections. We investigate the sensitivity of the cross sections to two-photon exchange effects and find that the differences between model calculations and phenomenological extractions of two-photon corrections can not be resolved if the uncertainty in the form factors is taken into account.

Differential cross section predictions for PRad-II from dispersion theory

We present a combined analysis of the electromagnetic form factors of the nucleon in the space- and timelike regions using dispersion theory. Our framework provides a consistent description of the experimental data over the full range of momentum transfer, in line with the strictures from analyticity and unitarity. The statistical uncertainties of the extracted form factors are estimated using the bootstrap method, while systematic errors are determined from variations of the spectral functions. We also perform a high-precision extraction of the nucleon radii and find good agreement with previous analyses of spacelike data alone. For the proton charge radius, we find <math><mrow><msubsup><mrow><mi>r</mi></mrow><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>=</mo><mn>0.84</mn><msubsup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>0.002</mn></mrow><mrow><mo>+</mo><mn>0.003</mn></mrow></msubsup><msubsup><mrow><mtext> </mtext></mrow><mrow><mo>−</mo><mn>0.002</mn></mrow><mrow><mo>+</mo><mn>0.002</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math>, where the first error is statistical and the second one is systematic. The Zemach radius and third moment are in agreement with Lamb shift measurements and hyperfine splittings. The combined dataset of space- and timelike data disfavors a zero crossing of <math><msub><mi>μ</mi><mi>p</mi></msub><msubsup><mi>G</mi><mi>E</mi><mi>p</mi></msubsup><mo>/</mo><msubsup><mi>G</mi><mi>M</mi><mi>p</mi></msubsup></math> in the spacelike region. Finally, we discuss the status and perspectives of modulus and phase of the form factors in the timelike region in the context of future experiments, as well as the onset of perturbative QCD.

New Insights into the Nucleon’s Electromagnetic Structure

The effects of the <math><msub><mi>Σ</mi><mi>c</mi></msub><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><mo>−</mo><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><mo>)</mo><mover><mi>D</mi><mo>¯</mo></mover></math> coupled-channel dynamics and various one-boson-exchange (OBE) forces for the LHCb pentaquark states, <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math> and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math>, are reinvestigated. Both the pion and <math><mi>ρ</mi></math>-meson exchanges are considered for the <math><msub><mi>Σ</mi><mi>c</mi></msub><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><mtext>−</mtext><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><mo>)</mo><mover><mi>D</mi><mo>¯</mo></mover></math> coupled-channel dynamics. It is found that the role of the <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><mo>)</mo><mover><mi>D</mi><mo>¯</mo></mover></math> channel in the descriptions of the <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math> and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math> states is not significant with the OBE parameters constrained by other experimental sources. The naive OBE models with the short-distance <math><mi>δ</mi><mo>(</mo><mover><mi>r</mi><mo>→</mo></mover><mo>)</mo></math> term of the one-pion exchange (OPE) keep failing to reproduce the <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math> and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math> states simultaneously. The OPE potential with the full <math><mi>δ</mi><mo>(</mo><mover><mi>r</mi><mo>→</mo></mover><mo>)</mo></math> term results in a too large mass splitting for the <math><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><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mtext> </mtext><mtext> </mtext><msub><mi>Σ</mi><mi>c</mi></msub><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> bound states with total isospin <math><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math>. The OBE model with only the OPE <math><mi>δ</mi><mo>(</mo><mover><mi>r</mi><mo>→</mo></mover><mo>)</mo></math> term dropped may fit the splitting much better but somewhat underestimates the splitting. Since the <math><mi>δ</mi><mo>(</mo><mover><mi>r</mi><mo>→</mo></mover><mo>)</mo></math> potential is from short-distance physics, which also contains contributions from the exchange of mesons heavier than those considered explicitly, we vary the strength of the <math><mi>δ</mi><mo>(</mo><mover><mi>r</mi><mo>→</mo></mover><mo>)</mo></math> potential and find that the masses of the <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4312</mn><mo>)</mo></math>, <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math>, and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math> can be reproduced simultaneously with the <math><mi>δ</mi><mo>(</mo><mover><mi>r</mi><mo>→</mo></mover><mo>)</mo></math> term in the OBE model reduced by about 80%. While two different spin assignments are possible to produce their masses, in the preferred description, the spin parities of the <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math> and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math> are <math><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and <math><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>, respectively.

Nijiati Yalikun

Yuki Kamiya

Bing-Song Zou

Coupled-channel effects of the <math><msubsup><mi>Σ</mi><mi>c</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msup><mover><mi>D</mi><mo>¯</mo></mover><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mo>−</mo><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><mo>)</mo><mover><mi>D</mi><mo>¯</mo></mover></math> system and molecular nature of the <math><msub><mi>P</mi><mi>c</mi></msub></math> pentaquark states from one-boson exchange model

Using dispersion theory with an improved description of the two-pion continuum based on the precise Roy-Steiner analysis of pion-nucleon scattering, we analyze recent data from electron-proton scattering. This allows for a high-precision determination of the electric and magnetic radius of the proton, <math><msub><mrow><mi>r</mi></mrow><mrow><mi>E</mi></mrow></msub><mo>=</mo><mo>(</mo><msubsup><mrow><mn>0.838</mn></mrow><mrow><mo>−</mo><mn>0.004</mn></mrow><mrow><mo>+</mo><mn>0.005</mn></mrow></msubsup><msubsup><mrow></mrow><mrow><mo>−</mo><mn>0.003</mn></mrow><mrow><mo>+</mo><mn>0.004</mn></mrow></msubsup><mo>)</mo></math>fm and <math><msub><mrow><mi>r</mi></mrow><mrow><mi>M</mi></mrow></msub><mo>=</mo><mo>(</mo><mn>0.847</mn><mo>±</mo><mn>0.004</mn><mo>±</mo><mn>0.004</mn><mo>)</mo></math>fm, where the first error refers to the fitting procedure using bootstrap and the data while the second one refers to the systematic uncertainty related to the underlying spectral functions.