Generalized distribution amplitudes (GDAs) have attracted significant attention in recent years due to their connection with the energy-momentum tensor (EMT) form factors (FFs). The GDAs can be experimentally accessed through the study of amplitudes in <math altimg='si8.svg'><mrow><msup><mi>&#947;</mi><mo>*</mo></msup><mi>&#947;</mi><mo>&#8594;</mo><msub><mi>M</mi><mn>1</mn></msub><msub><mi>M</mi><mn>2</mn></msub></mrow></math> and <math altimg='si9.svg'><mrow><msup><mi>&#947;</mi><mo>*</mo></msup><mo>&#8594;</mo><msub><mi>M</mi><mn>1</mn></msub><msub><mi>M</mi><mn>2</mn></msub><mi>&#947;</mi></mrow></math>, where <math altimg='si10.svg'><mrow><msub><mi>M</mi><mn>1</mn></msub><msub><mi>M</mi><mn>2</mn></msub></mrow></math> is a pseudoscalar meson pair such as <math altimg='si1.svg'><mrow><mi>&#960;</mi><mi>&#951;</mi></mrow></math> and <math altimg='si11.svg'><mrow><mi>&#951;</mi><msup><mi>&#951;</mi><mo>&#8242;</mo></msup></mrow></math>. In this work, we calculate these amplitudes in the perturbative limit and express the extracted <math altimg='si10.svg'><mrow><msub><mi>M</mi><mn>1</mn></msub><msub><mi>M</mi><mn>2</mn></msub></mrow></math> GDAs in terms of meson distribution amplitudes that have been constrained by the previous experiments. Our explicit calculation verifies the existence of a new EMT FF that violates the conservation law of EMT when the hadronic matrix element of the EMT operator is considered separately for each quark flavor. In addition, our result shows that the <math altimg='si10.svg'><mrow><msub><mi>M</mi><mn>1</mn></msub><msub><mi>M</mi><mn>2</mn></msub></mrow></math> GDAs are identical in <math altimg='si8.svg'><mrow><msup><mi>&#947;</mi><mo>*</mo></msup><mi>&#947;</mi><mo>&#8594;</mo><msub><mi>M</mi><mn>1</mn></msub><msub><mi>M</mi><mn>2</mn></msub></mrow></math> and <math altimg='si9.svg'><mrow><msup><mi>&#947;</mi><mo>*</mo></msup><mo>&#8594;</mo><msub><mi>M</mi><mn>1</mn></msub><msub><mi>M</mi><mn>2</mn></msub><mi>&#947;</mi></mrow></math>, which confirms the universality of GDAs in the perturbative limit. In the future, the GDAs and the EMT FFs studied in this paper can be probed at Belle II. Our study enhances the accessibility to the <math altimg='si12.svg'><mi>P</mi></math>-wave GDAs in <math altimg='si8.svg'><mrow><msup><mi>&#947;</mi><mo>*</mo></msup><mi>&#947;</mi><mo>&#8594;</mo><msub><mi>M</mi><mn>1</mn></msub><msub><mi>M</mi><mn>2</mn></msub></mrow></math> and <math altimg='si9.svg'><mrow><msup><mi>&#947;</mi><mo>*</mo></msup><mo>&#8594;</mo><msub><mi>M</mi><mn>1</mn></msub><msub><mi>M</mi><mn>2</mn></msub><mi>&#947;</mi></mrow></math>, and provides a promising approach for searching for exotic hybrid mesons in future experiments.

China

Qin-Tao Song

Russia

O.V. Teryaev

Shinsuke Yoshida

Gravitational form factors in the perturbative limit

<p>Baryon-antibaryon generalized distribution amplitudes (GDAs) give an access to timelike gravitational form factors (GFFs), which are complementary to the spacelike ones, which can be deduced from the hadronic generalized parton distributions (GPDs) measured in deep exclusive electroproduction processes. They allow to probe the GFFs of unstable baryons in the baryon octet, since the second moments of hadronic GDAs lead to the timelike GFFs. These GDAs can be measured in the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>B</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>γ</mi></math>, in the generalized Bjorken regime where the invariant mass of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math> pair is near threshold at high energy facilities, such as BESIII, Belle II, and the proposed Super Tau-Charm Facility. In this work, we investigate this process using the QCD collinear factorization framework, where the scattering amplitudes are expressed in terms of the baryon timelike electromagnetic (EM) FFs and Compton FFs. We also provide a numerical estimate of the cross sections with a model for baryon-antibaryon GDAs. Our work provides us a possibility to extract the timelike baryon GFFs from near future experimental measurements, and these GFFs may be further used to study longstanding questions in hadronic physics such as the baryon spin decomposition and D-term.</p>

Jing Han

France

Bernard Pire

Baryon-antibaryon generalized distribution amplitudes and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">→</mo><mi>B</mi><mover accent="true"><mrow><mi>B</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>γ</mi></mrow></math>

Xuewei Liu

Wei Dou

Japan

Benda Xu

Hanwen Wang

Guofu Cao

Erratum to: First-principle event reconstruction by time-charge readouts for TAO

The Taishan Antineutrino Observatory (TAO) is a liquid-scintillator satellite experiment of the Jiangmen Underground Neutrino Observatory (JUNO) to measure the reference reactor neutrino spectrum with unprecedented energy resolution. We use inhomogeneous Poisson process and Tweedie generalized linear model (GLM) to characterize the detector response and the charge distribution of a SiPM. We develop a pure probabilistic model for time and charge of SiPMs from first principles to reconstruct point-like events in the TAO central detector. Thanks to our precise model and the high photo-coverage and quantum efficiency of the SiPM tiles at TAO, we achieve vertex position resolution better than $$20\,\hbox {mm}$$ , energy resolution of about $$2\%$$ at $$1\,\hbox {MeV}$$ and $$<0.5\%$$ non-uniformity, marking the world’s best performance of liquid scintillator detectors. With such resolution, we perceive $$\hbox {MeV}$$ events to exhibit track effects. It opens up an exciting possibility of computed tracking calorimeter for unsegmented liquid scintillator detector like TAO. Our methodology is applicable to other experiments that utilize PMTs for time and charge readouts.

First-principle event reconstruction by time-charge readouts for TAO

The spin-orbit correlation in spin-0 hadrons can be investigated through the kinetic energy-momentum tensor form factor <math altimg='si1.svg'><msup><mrow><mover accent='true'><mrow><mi>F</mi></mrow><mrow><mo stretchy='false'>&#732;</mo></mrow></mover></mrow><mrow><mi>q</mi></mrow></msup><mo stretchy='false'>(</mo><mi>t</mi><mo stretchy='false'>)</mo></math>. We observe that the latter is also related to a torque about the radial direction, which we interpret as a chiral stress. If we neglect the quark mass contribution, then <math altimg='si1.svg'><msup><mrow><mover accent='true'><mrow><mi>F</mi></mrow><mrow><mo stretchy='false'>&#732;</mo></mrow></mover></mrow><mrow><mi>q</mi></mrow></msup><mo stretchy='false'>(</mo><mi>t</mi><mo stretchy='false'>)</mo></math> is simply proportional to the electromagnetic form factor for spin-0 hadrons, and the spin-orbit correlation is equal to minus half of the valence quark number. Given the extensive studies on the electromagnetic form factor for spin-0 hadrons such as pions, kaons, and the <italic>&#945;</italic> particle, we present the spatial distributions of chiral stress and kinetic spin-orbit correlation based on current parametrizations of the pion electromagnetic form factor.

Cédric Lorcé

Spin-orbit correlation and spatial distributions for spin-0 hadrons

<p>The tensor-polarized structures of the deuteron can be probed through the proton-deuteron Drell-Yan process, where the proton is unpolarized and the deuteron is tensor polarized. This measurement will be conducted at Fermilab in the near future. In this reaction, the twist-3 contribution is not negligible compared to the twist-2 contribution due to the limited invariant mass of the dilepton pair. We calculate the twist-3 contribution for the Drell-Yan cross section with a tensor-polarized deuteron target, preserving the U(1)-gauge invariance of the hadronic tensor. The cross sections and weighted cross sections are expressed in terms of the tensor-polarized parton distribution functions (PDFs); thus, one can extract the PDFs <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mrow><mn>1</mn><mrow><mi>L</mi><mi>L</mi></mrow></mrow></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mrow><mi>L</mi><mi>T</mi></mrow></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>f</mi><mrow><mn>1</mn><mi>L</mi><mi>T</mi></mrow><mrow><mrow><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msubsup></math> from the experimental measurements of Drell-Yan process. Our study should be helpful to solve the puzzle in the tensor-polarized structures of the deuteron.</p>

Si-Yi Qiao

Twist-3 contribution in the Drell-Yan process with tensor-polarized deuteron

Generalized distribution amplitudes (GDAs) of mesons can be probed by the reactions <math><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><mo>→</mo><msub><mi>M</mi><mn>1</mn></msub><msub><mi>M</mi><mn>2</mn></msub><mi>γ</mi></math>, which are accessible at electron-positron colliders such as BESIII and Belle II. After discussing the neutral meson production case in our previous paper, we discuss here the complementary case of the charged meson (<math><msup><mi>M</mi><mo>+</mo></msup><msup><mi>M</mi><mo>−</mo></msup></math>) production, where one can extract the complete information on GDAs from the interference of the amplitudes of the two competing processes where the photon is emitted either in the initial or in the final state. Considering the importance of the charged meson production, we present a complete expression for the interference term of the cross section, which is experimentally accessible thanks to its charge conjugation specific property. We adopt two types of models for leading-twist <math><mi>π</mi><mi>π</mi></math> GDAs to estimate the size of the interference term in the process <math><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mi>γ</mi></math> numerically, namely, a model extracted from previous experimental results on <math><msup><mi>γ</mi><mo>*</mo></msup><mi>γ</mi><mo>→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> at Belle and the asymptotic form predicted by QCD evolution equations. We include in the calculation the kinematical power suppressed (sometimes called kinematical higher-twist) corrections up to <math><mn>1</mn><mo>/</mo><msup><mi>Q</mi><mn>2</mn></msup></math> for the helicity amplitudes. Both models of GDAs indicate that the kinematical corrections are not negligible for the interference term of the cross section measured at BESIII, thus it is necessary to include them if we try to extract the GDAs precisely. On the other side, the kinematical corrections are very tiny for the measurements at Belle II, and the leading twist-two formula of the interference term will be good enough to describe the charge conjugation odd part of the differential cross section.

Kinematical higher-twist corrections in <math><msup><mi>γ</mi><mo>*</mo></msup><mo>→</mo><msub><mi>M</mi><mn>1</mn></msub><msub><mi>M</mi><mn>2</mn></msub><mi>γ</mi></math>: Charged meson production

We study the energy-momentum tensor of spin-0 and spin-<math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math> hadrons in momentum space. We parametrize this object in terms of so-called gravitational transverse-momentum distributions, and we identify in the quark sector the relations between the latter and the usual transverse-momentum distributions. Focusing on particular components of the energy-momentum tensor, we study momentum densities, flux of inertia and stress distribution in momentum space, revealing part of the wealth of physical information that can be gained from higher-twist transverse-momentum distributions.

Gravitational transverse-momentum distributions

There are three types of fragmentation functions (FFs) which are used to describe the twist-3 cross sections of the hard semi-inclusive processes under QCD collinear factorization, and they are called intrinsic, kinematical, and dynamical FFs. In this work, we investigate the theoretical relations among these FFs for a tensor-polarized spin-1 hadron. Three Lorentz-invariance relations are derived by using the identities between the nonlocal quark-quark and quark-gluon-quark operators, which guarantee the frame independence of the twist-3 spin observables. The QCD equation of motion relations are also presented for the tensor-polarized FFs. In addition, we show that the intrinsic and kinematical twist-3 FFs can be decomposed into the contributions of twist-2 FFs and twist-3 three-parton FFs, and the latter are also called dynamical FFs. If one neglects the dynamical FFs, we can obtain relations which are analogous to the Wandzura-Wilczek relation. Then, the intrinsic and kinematical twist-3 FFs are expressed in terms of the leading-twist ones. Since the FFs of a spin-1 hadron can be measured at various experimental facilities in the near future, these theoretical relations will play an important role in the analysis of the collinear tensor-polarized FFs.

Novel relations for twist-3 tensor-polarized fragmentation functions in spin-1 hadrons

We carry out the calculation of kinematical higher-twist corrections to the cross section of <math><msup><mi>γ</mi><mo>*</mo></msup><mo>→</mo><msub><mi>M</mi><mn>1</mn></msub><msub><mi>M</mi><mn>2</mn></msub><mi>γ</mi></math> up to twist 4, where <math><msub><mi>M</mi><mi>i</mi></msub></math> is a scalar or pseudoscalar neutral meson. The three independent helicity amplitudes are presented in terms of the twist-2 generalized distribution amplitudes (GDAs), which are important nonperturbative quantities for understanding the 3D structure of hadrons. Since this process can be measured by BESIII in <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> collisions, we perform the numerical estimate of the kinematical higher-twist corrections by using the kinematics of BESIII. We adopt the <math><mi>π</mi><mi>π</mi></math> GDA extracted from Belle measurements and the asymptotic <math><mi>π</mi><mi>π</mi></math> GDA to study the size of the kinematical corrections in the case of pion meson pair, and a model <math><mi>η</mi><mi>η</mi></math> GDA is used to see the impact of target mass corrections <math><mi>O</mi><mo>(</mo><msup><mi>m</mi><mn>2</mn></msup><mo>/</mo><mi>s</mi><mo>)</mo></math> for <math><msup><mi>γ</mi><mo>*</mo></msup><mo>→</mo><mi>η</mi><mi>η</mi><mi>γ</mi></math>. Our results show that the kinematical higher-twist corrections account for <math><mo>∼</mo><mn>20</mn><mo>%</mo></math> of the cross sections at BESIII on the average, and it is necessary to include them if one tries to extract GDAs from experimental measurements precisely. We also comment the case of <math><msup><mi>π</mi><mn>0</mn></msup><mi>η</mi></math> production which is important for the search of hybrid mesons.

Kinematical higher-twist corrections in <math><mrow><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup><mo>→</mo><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>γ</mi></mrow></math>: Neutral meson production