Session L06: Hadronic Physics - QCD II

The anomaly-driven breaking of chiral symmetry in the NJL and the instanton liquid models

We investigate an anomaly-driven breaking of chiral symmetry based on the Nambu-Jona-Lasinio(NJL) model and the interacting instanton liquid model(IILM). In the NJL model, an enough strong quark attraction induces the spontaneous breaking of chiral symmetry. Furthermore, if we take into account an axial U(1) breaking term, although the attraction is weaker than its critical strength, the chiral symmetry can be broken spontaneously due to the existence of the axial U(1) anomaly effect – we call such a breaking an anomaly-driven breaking of chiral symmetry. On the other hand, it is also known that the anomaly effect is induced by the instantons. In order to reveal the properties of the anomaly-driven breaking from the viewpoints of the instanton QCD vacuum with the quarks, we reconsidered the chiral symmetry breaking based on the IILM. From the analogy of the NJL model, particularly what we expect is that the anomaly-driven breaking can be characterized by a behavior of the vacuum energy density in the small quark condensate region. Therefore, we calculate the vacuum energy density and the quark condensate as a function of the instanton density by using numerical simulations and analyze the quark condensate dependence of the vacuum energy density. We will show our simulation results and discuss their interpretation. [1]S. Kono, et al., PTEP2021, 093D02 (2021).   

Casimir effect in dense QCD matter

The conventional Casimir effect is defined for photon fields, whereas various quasiparticle fields realized in condensed matter systems can lead to novel types of Casimir-effect-like phenomena [e.g., arXiv:2207.14078]. In QCD and nuclear physics, such a situation is rare, but there are some possibilities in dense QCD/nuclear matter. For example, the chiral density wave phase and the chiral soliton lattice phase are expected to be the ground states of finite-density QCD in a zero and a strong magnetic field, respectively. In this talk, we discuss the typical features of the Casimir effect in a small-size medium composed of such ground states. For example, the fermionic Casimir effect in the chiral density wave phase leads to oscillations of physical quantities as a function of system size. Also, the photonic Casimir effect is described based on the so-called axion electrodynamics, and anomalous behaviors of the Casimir effect can occur.   

Measurements of the Cosφ and Cos2φ Moments of the Unpolarized SIDIS π+ Cross-section at CLAS12

Semi-inclusive deep inelastic π⁺ electroproduction has been studied with the CLAS12 detector at Jefferson Laboratory. Data were taken by Run Group A at Hall B of the laboratory using a polarized 10.6 GeV electron beam, interacting with an unpolarized liquid hydrogen target. The collected statistics enable a high-precision study of the Cosφ and Cos2φ azimuthal moments of the unpolarized cross-sections. These azimuthal moments probe the Boer-Mulders function, which describes the net polarization of quarks inside an unpolarized proton, and the Cahn effect, which has a purely kinematic origin. The high statistics data will, for the first time, enable a multidimensional analysis of both moments over a large kinematic range of Q², y, z, and P_T. We will present the status of this ongoing analysis, including the multidimensional unfolding procedures used for acceptance corrections.   

Deep Neural Network-Based Reconstruction of SeaQuest E906 Data for Boer-Mulders Function Extraction

The Boer-Mulders function determines the distribution of transversely polarized quarks in an unpolarized proton. A non-zero Boer-Mulders function corresponds to a certain handedness of the nucleon and causes an azimuthal asymmetry in Drell-Yan scattering. To extract the unpolarized Drell-Yan Boer-Mulders function from the SeaQuest E906 data, we will utilize reconstruction techniques based on deep neural networks (DNN). This method has the potential to maximize statistics while minimizing systematic uncertainty in measuring the angular-dependence coefficients $lambda$, $mu$, and $ u$. Lower statistical errors enable an improved regression to obtain these coefficients across more bins, facilitating a broader extraction of the Boer-Mulders function with sensitivity to the $p_T$ dependence of $mu$. SeaQuest, located at Fermilab, was a fixed-target experiment devised to detect the Drell-Yan process in $p+p$ and $p+d$ reactions. We will discuss the process of developing the DNN-based reconstruction as well as present preliminary results.   

Partial restoration of chiral symmetry in nucleus observed in pionic atoms

We have quantitatively evaluated chiral condensate, the order parameter of the chiral symmetry, in nuclear matter and found that it is reduced to 77+-2% in the nuclear medium compared to vacuum. We have performed high-precision spectroscopy experiments of pion tin atoms at the RIKEN RI Beam Factory to derive chiral condensation. The obtained spectra were analyzed to determine the interaction between pions and nuclei. The results show that the s-wave interaction is stronger in the nucleus than in the vacuum. This enhancement is due to the wavefunction renormalization of the medium effect. From this, it is possible to estimate the medium effect inversely and link it to the partial recovery of the chiral symmetry. Taking into account the latest nuclear density distribution, spectroscopic factors, and residual interactions, the magnitude of chiral condensate in the nuclear medium is quantitatively evaluated and successfully estimated with errors for the first time in the world in a high-density medium. Future plans will also be discussed.   

Nucleon Polarizabilities and Elastic Compton Scattering on 3He at HIγS

The electric and magnetic polarizabilities (αE1 and βM1 ) are fundamental quantities encoding the internal structure of nucleons. They characterize the response of the nucleon to an external electromagnetic field and can be probed using Compton scattering processes. From chiral effective field theories ( χ EFTs) [1,2], the angular distributions of the Compton differential cross section for light nuclei (A=1-6) provide an important way of extracting the nucleon electromagnetic polarizabilities experimentally. However, due to the difficulties in experimental measurements, αE1 and βM1 of nucleons, particularly of the neutron, are still not precisely determined [3-5].

Compton scattering measurements using a liquid H3e target are planned for determining neutron electromagnetic polarizabilities. These measurements will be carried out using the nearly monoenergetic gamma-ray beam at the High Intensity Gamma-Ray Source (HIγS) facility at Triangle Universities Nuclear Laboratory (TUNL). This experiment will be the first Compton-scattering measurement performed on He 3, mainly because of limitations of cryogenic techniques, which have been recently overcome. Compared to Compton Scattering experiments on liquid deuterium [6] and He 4 [7,8], the elastic Compton cross section of He 3 arises from a different combination of the nucleon contributions. This can provide another way to extract the polarizabilities of the neutron and another test under the EFT formalism [9], although nuclear effects need to be taken into account. The proposed experiment will measure the angular differential cross section for Compton scattering from He 3 at 100 MeV using a circularly polarized photon beam at HIγS. In this talk, we will present the techniques and proposed setup of this experiment as well as the latest update about the research and development test.   

Operation of a new Longitudinally Polarized Solid Nuclear Target for experiments with CLAS12 at Jefferson Lab.

A large experimental program (dubbed "Run Group C”) to measure single- and double-spin observables in electron-proton and electron-deuteron scattering has recently been completed in Jefferson Lab’s Hall B. The experiments measured inclusive spin structure functions and spin observables in exclusive and semi-inclusive scattering using the 11 GeV, highly polarized electron beam scattering off a new, custom-built polarized target integrated into the CLAS12 spectrometer. Our report will cover the entire polarized target setup, operation, and its performance with different polarizable and unpolarizable materials.