<p>In this Letter, we advocate a set of novel azimuthal-angle-related observables associated with exclusive hadron production from two-photon fusion at <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></math> colliders, taking the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>γ</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi></math> as a benchmark process. As a direct consequence of the linearly polarized quasireal photons emitted off the electron and positron beams, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>cos</mi><mn>2</mn><mi>ϕ</mi></math> azimuthal asymmetry in dipion production is predicted within the transverse-momentum-dependent factorization framework. In numerical analysis, we take the helicity amplitudes of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>γ</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi></math> determined from the partial wave solutions in dispersion relation as input, and find that the predicted <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>cos</mi><mn>2</mn><mi>ϕ</mi></math> azimuthal modulation may reach 40% for the typical kinematical setup of Belle 2 and BESIII experiments. Future accurate measurement of this azimuthal asymmetry may facilitate the direct extraction of the relative phase between two helicity amplitudes with photon helicity configurations <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>+</mo><mo>+</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>+</mo><mo>−</mo></math>. This knowledge provides a valuable input for the dispersive determination of the hadronic light-by-light contributions.</p>

China

Yu Jia

Jian Zhou

Ya-jin Zhou

Novel Azimuthal Observables from Two-Photon Collision at <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></mrow></math> Colliders

We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

Germany

Jie Zhu

Canada

Xiang-Yu Wu

Guang-You Qin

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

The conventional wisdom in dealing with electromagnetic transition between heavy quarkonia is the multipole expansion, when the emitted photon has a typical energy of order quarkonium binding energy. Nevertheless, in the case when the energy carried by the photon is of order typical heavy quark momentum, the multipole expansion doctrine is expected to break down. In this work, we apply the “hard-scattering” approach originally developed to tackle the strongly hindered magnetic dipole (<math><mi>M</mi><mn>1</mn></math>) transition [Y. Jia et al., Phys. Rev. D 82, 014008 (2010)] to the strongly hindered electric dipole (<math><mi>E</mi><mn>1</mn></math>) transition between heavy quarkonia. We derive the factorization formula for the strongly hindered <math><mi>E</mi><mn>1</mn></math> transition rates at the lowest order in velocity and <math><msub><mi>α</mi><mi>s</mi></msub></math> in the context of the nonrelativistic QCD, and conduct a detailed numerical comparison with the standard predictions for various bottomonia and charmonia <math><mi>E</mi><mn>1</mn></math> transition processes.

Cai-Ping Jia

Junliang Lu

Zhewen Mo

United States

Jia-Yue Zhang

Hard-scattering approach to strongly hindered electric dipole transitions between heavy quarkonia

Inspired by the recent observation of the Higgs boson radiative decay into <math><msup><mi>Z</mi><mn>0</mn></msup></math> by ATLAS and CMS Collaborations, we investigate the next-to-leading-order (NLO) electroweak correction to this rare decay process in Standard Model (SM). Implementing the on shell renormalization scheme, we find that the magnitude of the NLO electroweak correction may reach 7% of the leading-order (LO) prediction, much more significant than that of the NLO QCD correction, which is merely about 0.3%. After incorporating the <math><mi>O</mi><mo>(</mo><mi>α</mi><mo>)</mo></math> correction, the predicted partial width from various <math><mi>α</mi></math> schemes tend to converge to each other. Including both NLO electroweak and QCD corrections, the SM prediction for the branching fraction shifts from the LO value of <math><mrow><mo>(</mo><mn>1.40</mn><mi>–</mi><mn>1.71</mn><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math> to <math><mo>(</mo><mn>1.55</mn><mo>±</mo><mn>0.06</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>, considerably lower than the measured value <math><msub><mi>B</mi><mi>exp</mi></msub><mo>[</mo><mi>H</mi><mo>→</mo><msup><mi>Z</mi><mn>0</mn></msup><mi>γ</mi><mo>]</mo><mo>=</mo><mo>(</mo><mn>3.4</mn><mo>±</mo><mn>1.1</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>. Resolving this discrepancy clearly calls for further theoretical investigations, and, more importantly, experimental efforts from HL-LHC and the prospective Higgs factories such as CEPC and FCC-ee.

Wen-Long Sang

Feng Feng

Next-to-leading-order electroweak correction to <math><mrow><mi>H</mi><mo>→</mo><msup><mrow><mi>Z</mi></mrow><mn>0</mn></msup><mi>γ</mi></mrow></math>

In this work, we investigate the inclusive photoproduction of the <math><mi>C</mi></math>-odd, <math><mi>S</mi></math>-wave fully charmed tetraquark at electron-ion colliders within the nonrelativistic QCD (NRQCD) factorization framework, at the lowest order in velocity and <math><msub><mi>α</mi><mi>s</mi></msub></math>. The value of the NRQCD long-distance matrix element is estimated from two phenomenological potential models. Our studies reveal that the photoproduction of the <math><msup><mn>1</mn><mrow><mo>+</mo><mo>−</mo></mrow></msup></math> fully charmed tetraquark may be difficult to observe at HERA and the EicC; nevertheless, its observation prospects at the EIC appear to be bright.

Yingsheng Huang

De-Shan Yang

Photoproduction of fully charmed tetraquark at electron-ion colliders

We calculate the next-to-next-to-leading-order (NNLO) QCD radiative correction to the pion electromagnetic form factor with large momentum transfer. We explicitly verify the validity of the collinear factorization to two-loop order for this observable and obtain the respective IR-finite two-loop hard-scattering kernel in the closed form. The NNLO QCD correction turns out to be positive and significant. Incorporating this new ingredient of correction, we then make a comprehensive comparison between the finest theoretical predictions and numerous data for both space- and timelike pion form factors. Our phenomenological analysis provides a strong constraint on the second Gegenbauer moment of the pion light-cone distribution amplitude obtained from recent lattice QCD studies.

Long-Bin Chen

Wen Chen

Next-to-Next-to-Leading-Order QCD Corrections to Pion Electromagnetic Form Factors

In this work we investigate the exclusive production of a pair of light neutral mesons in <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilation, where the final state bears an even <math><mi>C</mi></math>-parity. The production processes can be initiated via the photon fragmentation or the nonfragmentation mechanism. While the fragmentation contribution can be rigorously accounted, the nonfragmentation contributions are calculated within the framework of collinear factorization, where only the leading-twist light-cone distribution amplitudes (LCDAs) of mesons are considered. Mediately solely by the nonfragmentation mechanism, the production rates of double light neutral pseudoscalar mesons are too small to be observed at the commissioning <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> facilities. In contrast, the production rates of a pair of light neutral vector mesons are greatly amplified owing to the significant kinematic enhancement brought by the fragmentation mechanism. It is found that, at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>3.77</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, after including the destructive interference between the nonfragmentation and fragmentation contributions, the production rates for <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><msup><mi>ρ</mi><mn>0</mn></msup><msup><mi>ρ</mi><mn>0</mn></msup></math> and <math><msup><mi>ρ</mi><mn>0</mn></msup><mi>ω</mi></math> can be lowered by about 10% and 30% relative to the fragmentation predictions. Future precise measurement of these exclusive double neutral vector meson production channels at BESIII experiment may provide useful constraints on the LCDAs of light vector mesons.

Xiaonu Xiong

Exclusive production of double light neutral mesons at the <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> colliders

Within the nonrelativistic QCD (NRQCD) factorization framework, we compute the long-awaited <math><mi>O</mi><mo>(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></math> corrections for the exclusive double charmonium production process at B factories, i.e., <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>+</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub></math> at <math><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mn>10.58</mn></math> GeV. We confirm that NRQCD factorization does hold at next-to-next-to-leading-order (NNLO) for exclusive double charmonium production. It is found that including the NNLO QCD correction considerably reduces the renormalization scale dependence, and also implies the reasonable perturbative convergence behavior for this process. We also include both <math><mi>O</mi><mo>(</mo><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math> and <math><mi>O</mi><mo>(</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math> corrections for this process. With all the available corrections lumped together, our most comprehensive prediction is consistent with both the BaBar and Belle measurement within errors.

Next-to-next-to-leading-order QCD corrections to → / At Factories

We present a comprehensive study of the light-cone generalized parton distribution (GPD) and quasi-GPD of a flavor-neutral meson in the ’t Hooft model, i.e., two-dimensional QCD (<math><msub><mi>QCD</mi><mn>2</mn></msub></math>) in the <math><msub><mi>N</mi><mi>c</mi></msub><mo>→</mo><mi>∞</mi></math> limit. With the aid of the Hamiltonian approach, we construct the light-cone GPD in terms of the meson’s light-cone wave function in the framework of light-front quantization and express the quasi-GPD in terms of the meson’s Bars-Green wave functions and the chiral angle in the framework of equal-time quantization. We show that, both analytically and numerically, the quasi-GPD does approach the light-cone GPD when the meson is boosted to the infinite momentum frame, which justifies the tenet underlying the large momentum effective theory for the off-forward parton distribution. Upon taking the forward limit, the light-cone and quasi-GPDs reduce to the light-cone and quasi parton distribution functions (quasi-PDFs). As a bonus, we take this chance to correct the incomplete expression of the quasi-PDFs in the ’t Hooft model reported in our preceding work [Y. Jia , Phys. Rev. D 98, 054011 (2018)].

Rui Yu

Light-cone and quasigeneralized parton distributions in the ’t Hooft model

We carry out a comprehensive study of the quark-to-meson fragmentation function in the ’t Hooft model, i.e., the two-dimensional quantum chromodynamics (QCD) in  $$N_c\rightarrow \infty $$  <math> <mrow> <msub> <mi>N</mi> <mi>c</mi> </msub> <mo>→</mo> <mi>∞</mi> </mrow> </math>   limit, following the operator definition pioneered by Collins and Soper. We apply the Hamiltonian approach as well as the diagrammatic approach to construct the functional form of the quark-to-meson fragmentation function in terms of the meson’s light-cone wave function. For the sake of comparison, we also investigate the heavy quark fragmentation into quarkonium in two-dimensional QCD within the framework of the nonrelativistic QCD (NRQCD) factorization, at the lowest order in quark velocity. In the heavy quark limit, the quark fragmentation function obtained from the ab initio method agrees well, both analytically and numerically, with that obtained from the NRQCD approach. This agreement might be regarded as a nontrivial justification for the validity of both field-theoretical approaches to compute the heavy quark fragmentation function.

Heavy quark fragmentation function in two-dimensional QCD in  $$N_c\rightarrow \infty $$  <math> <mrow> <msub> <mi>N</mi> <mi>c</mi> </msub> <mo>→</mo> <mi>∞</mi> </mrow> </math>   limit