The roles of the $ \Delta (1232) $ , $ {N}^{*}(1520) $ , and $ {N}^{*}(1650) $ resonances in the $ \gamma p\to{\pi }^{0}{\pi }^{0}p $ reaction near threshold is investigated within an effective Lagrangian approach. The differential cross sections of the $ \gamma p\to{\pi }^{0}{\pi }^{0}p $ reaction was calculated including contributions from the $ \Delta (1232) $ , $ {N}^{*}(1520) $ , and $ {N}^{*}(1650) $ intermediate states decaying into $ \pi^0 p $ via the $\textit{s}$-channel nucleon pole and $\textit{t}$-channel $\textit{ρ}$ exchange. Current experimental measurements were well reproduced. The production of $ \Delta(1232) $ was mainly from the mechanism of the $\textit{s}$-channel nucleon pole, while the $ {N}^{*}(1520) $ and $ {N}^{*}(1650) $ were produced from the mechanism of the $\textit{t}$-channel $\textit{ρ}$ exchange. More experimental data on the $ \gamma p \to \pi^0 \pi^0 p $ reaction could be used to explore the properties of the low-lying excited baryon state.

China

Meng-Yuan Dai

Si-Wei Liu

Cheng Chen

De-Min Li

En Wang

Ju-Jun Xie

Roles of ${\boldsymbol\Delta(\bf 1232)}$ , ${\boldsymbol N^*(\bf 1520)}$ , and ${\boldsymbol N^*(\bf 1650)}$ resonances in ${\boldsymbol\gamma \boldsymbol p\to \boldsymbol\pi^{\bf 0} \boldsymbol\pi^{\bf 0}\boldsymbol p}$ reaction within an effective Lagrangian approach * Supported by the National Key R&D Program of China (2023YFA1606703, 2024YFE0105200), the Natural Science Foundation of Henan Province, China (232300421140, 222300420554), and the National Natural Science Foundation of China (12435007, 12361141819, 12475086, 12192263)

We investigate the process <math><msub><mi>η</mi><mi>c</mi></msub><mo>→</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> by taking into account the <math><mi>S</mi></math>-wave <math><msup><mi>K</mi><mo>*</mo></msup><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup></math> and <math><mi>ρ</mi><mi>ω</mi></math> interactions within the unitary coupled-channel approach, where the scalar meson <math><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>1710</mn><mo>)</mo></math> is dynamically generated. In addition, the contributions from the intermediate resonances <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>1430</mn><msup><mo>)</mo><mo>−</mo></msup><mo>→</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mo>−</mo></msup></math> and <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>1430</mn><msup><mo>)</mo><mn>0</mn></msup><mo>→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> are also considered. We find a significant dip structure around 1.8 GeV, associated to the <math><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>1710</mn><mo>)</mo></math>, in the <math><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup><msup><mi>K</mi><mo>+</mo></msup></math> invariant mass distribution, and the clear peaks of the <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>1430</mn><mo>)</mo></math> in the <math><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mo>−</mo></msup></math> and <math><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> invariant mass distributions, consistent with the BABAR measurements. We further estimate the branching fractions <math><mi>B</mi><mo>(</mo><msub><mi>η</mi><mi>c</mi></msub><mo>→</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mi>π</mi><mo>−</mo></msup><mo>)</mo><mo>=</mo><mn>5.5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> and <math><mi>B</mi><mo>(</mo><msub><mi>η</mi><mi>c</mi></msub><mo>→</mo><mi>ω</mi><msup><mi>ρ</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>)</mo><mo>=</mo><mn>7.9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>. Our predictions can be tested by the BESIII and Belle II experiments in the future.

Yan Ding

Xiao-Hui Zhang

Li-Sheng Geng

Theoretical study of scalar meson <math><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>1710</mn><mo>)</mo></math> in the <math><msub><mi>η</mi><mi>c</mi></msub><mo>→</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> reaction

When we impose discrete symmetries in the standard model we have Dai-Freed global anomalies. However, interestingly if we introduce three right-handed neutrinos we can have an anomaly-free discrete Z 4 gauge symmetry. This Z 4 symmetry should be spontaneously broken down to the Z 2 symmetry to generate the heavy Majorana masses for the right-handed neutrinos. We show that this symmetry breaking naturally generates topological inflation, which is consistent with the CMB observations at present and predicts a significant tensor mode with scalar-tensor ratio r &gt; 0.03. The right-handed neutrinos play an important role in reheating processes. The reheating temperature is as high as ∼ 108 GeV, and non-thermal leptogenesis successfully takes place.

Japan

Masahiro Kawasaki

Tsutomu Yanagida

Dai-Freed anomaly in the standard model and topological inflation

We extend on-shell bootstrap methods from spacetime amplitudes to the world sheet objects of the Cachazo-He-Yuan formalism. We observe that the integrands corresponding to tree-level nonlinear sigma model, Yang-Mills and <math><mo>(</mo><mi>D</mi><mi>F</mi><msup><mo>)</mo><mn>2</mn></msup></math> theory are determined by demanding enhanced UV scaling under Britto-Cachazo-Feng-Witten shifts. Back in spacetime, we also find that <math><mo>(</mo><mi>D</mi><mi>F</mi><msup><mo>)</mo><mn>2</mn></msup></math> theory is fixed by gauge invariance/UV scaling and simple locality assumptions.

France

Laurentiu Rodina

UV consistency conditions for Cachazo-He-Yuan integrands

The Cachazo-He-Yuan formula was originally proposed to describe on-shell scattering of particles from a single massless field. We present a method to modify it to include several interacting scalar fields, all possessing different masses and possibly off-shell momenta. The method is applied to Yukawa interactions between a number of scalar nucleons and pions, and to the <math><msub><mi>ϕ</mi><mn>1</mn></msub><msub><mi>ϕ</mi><mn>2</mn></msub><msub><mi>ϕ</mi><mn>3</mn></msub></math> coupling of three different scalar fields. Composite models constructed from existing theories can be used to broaden the scope of the method. The modification is applied to describe Compton scattering from a massive particle and to photon bremsstrahlung. It is also employed to generalize the disk function <math><mi>Z</mi></math> and the sphere function <math><mi>J</mi></math>.

Canada

C. S. Lam

Cachazo-He-Yuan theory for several fields

Anomalies can be elegantly analyzed by means of the Dai-Freed theorem. In this framework it is natural to consider a refinement of traditional anomaly cancellation conditions, which sometimes leads to nontrivial extra constraints in the fermion spectrum. We analyze these more refined anomaly cancellation conditions in a variety of theories of physical interest, including the Standard Model and the SU(5) and Spin(10) GUTs, which we find to be anomaly free. Turning to discrete symmetries, we find that baryon triality has a ℤ9 anomaly that only cancels if the number of generations is a multiple of 3. Assuming the existence of certain anomaly-free ℤ4 symmetry we relate the fact that there are 16 fermions per generation of the Standard model — including right-handed neutrinos — to anomalies under time-reversal of boundary states in four-dimensional topological superconductors. A similar relation exists for the MSSM, only this time involving the number of gauginos and Higgsinos, and it is non-trivially, and remarkably, satisfied for the SU(3) × SU(2) × U(1) gauge group with two Higgs doublets. We relate the constraints we find to the well-known Ibañez-Ross ones, and discuss the dependence on UV data of the construction. Finally, we comment on the (non-)existence of K-theoretic θ angles in four dimensions.

United Kingdom

Germany

Iñaki García-Etxebarria

Belgium

Netherlands

Miguel Montero

Dai-Freed anomalies in particle physics

Möbius invariance is used to construct gluon tree amplitudes in the Cachazo, He, and Yuan (CHY) formalism. If it is equally effective in steering the construction of off-shell tree amplitudes, then the S-matrix CHY theory can be used to replace the Lagrangian Yang-Mills theory. Unfortunately that is not possible. We find that the CHY formula can indeed be modified to obtain a Möbius-invariant off-shell amplitude <math><msub><mi>M</mi><mi>P</mi></msub></math>, but this modified amplitude lacks local gauge invariance, which can be restored to give the correct Yang-Mills amplitude only by the addition of a complementary amplitude <math><msub><mi>M</mi><mi>Q</mi></msub></math>. Although neither <math><msub><mi>M</mi><mi>P</mi></msub></math> nor <math><msub><mi>M</mi><mi>Q</mi></msub></math> is fully gauge invariant, both are partially gauge invariant in a sense to be explained.

Off-shell Yang-Mills amplitude in the Cachazo-He-Yuan formalism

We show that the use of Sudakov variables greatly simplifies the study of the solutions to the scattering equations in the Cachazo-He-Yuan formalism. We work in the center-of-mass frame for the two incoming particles, which partially fixes the SL(2, ℂ) redundancy in the integrand defining the scattering amplitudes, the remaining freedom translates into a global shift in the azimuthal angle of the outgoing particles. Studying four- and five-particle amplitudes, we see how an appropriate choice of this phase allows for algebraic simplifications when finding solutions to the scattering equations, as well as in the expression of the scattering amplitudes in terms of the locations of the punctures in the sphere. These punctures themselves are remarkably simple functions of the Sudakov parameters.

Spain

Grigorios Chachamis

Diego Jiménez

Agustín Vera

Miguel Vázquez-Mozo

Sudakov representation of the Cachazo-He-Yuan scattering equations formalism

We describe a physics derivation of theorems due to Dai and Freed about the Atiyah-Patodi-Singer eta-invariant which is important for anomalies and topological phases of matter. This is done by studying a massive fermion. The key role is played by the wave function of the ground state in the Hilbert space of the fermion in the large mass limit. The ground state takes values in the determinant line bundle and has nontrivial Berry phases which characterize the low energy topological phases.

Kazuya Yonekura

Dai-Freed theorem and topological phases of matter

The last few years have been witness to a proliferation of new results concerning heavy exotic hadrons. Experimentally, many new signals have been discovered that could be pointing towards the existence of tetraquarks, pentaquarks, and other exotic configurations of quarks and gluons. Theoretically, advances in lattice field theory techniques place us at the cusp of understanding complex coupled-channel phenomena, modelling grows more sophisticated, and effective field theories are being applied to an ever greater range of situations. It is thus an opportune time to evaluate the status of the field. In the following, a series of high priority experimental and theoretical issues concerning heavy exotic hadrons is presented.

United States

R.A. Briceño

T.D. Cohen

S. Coito

J.J. Dudek

E. Eichten

C.S. Fischer

M. Fritsch

W. Gradl

A. Jackura

M. Kornicer

Brazil

G. Krein

R. F. Lebed

F. A. Machado

R. E. Mitchell

C.J. Morningstar

Ireland

M. Peardon

M. R. Pennington

K. Peters

J. M. Richard

C. P. Shen

M.R. Shepherd

T. Skwarnicki

E. S. Swanson

A. P. Szczepaniak

C. Z. Yuan

Issues and Opportunities in Exotic HadronsSupported by U.S. Department of Energy (Cohen); the Institute of Modern Physics and Chinese Academy of Sciences under contract Y104160YQ0 and agreement No. 2015-BH-02 (Coito); the U.S. Department of Energy, for grant DE-AC05-06OR23177, under which Jefferson Science Associates, LLC, manages and operates Jefferson Laboratory and DE-SC0006765, Early Career award (Dudek); Fermilab, operated by the Fermi Research Alliance under contract number DEAC02-07CH11359 with the U.S. Department of Energy (Eichten); BMBF, under contract No. 06GI7121, and the DAAD under contract No. 56889822 and by the Helmholtz International Center for FAIR within the LOEWE program of the State of Hesse (Fischer); the German Research Foundation DFG under contract number Collaborative Research Centre CRC-1044 (Gradl); the Conselho Nacional de Desenvolvimento CientÃ­fico e TecnolÃ³gico - CNPq, Grant No. 305894/2009-9 and FundaÃ§Ã£o de Amparo Ã Pesquisa do Estado de SÃ£o Paulo - FAPESP, Grant No. 2013/01907-0 (Krein); U.S. National Science Foundation, under grants PHY-1068286 and PHY-1403891 (Lebed); the Brazilian National Council for Scientific and Technological Development under grant CNPq/CAPES-208188/2014-2 (Machado); U.S. Department of Energy under grant DE-FG02-05ER41374 (Mitchell); U.S. National Science Foundation under grant PHY-1306805 (Morningstar); U.S. Department of Energy, supported by Jefferson Science Associates, LLC under contract No. DE-AC05-06OR23177 (Pennington); the National Natural Science Foundation of China (NSFC) under contract No. 11575017, the Ministry of Science and Technology of China under Contract No. 2015CB856701 (Shen); U.S. Department of Energy, under grant DE-FG02-05ER41374 (Shepherd); U.S. National Science Foundation under grant PHY-1507572 (Skwarnicki); U.S. Department of Energy, under contract DE-AC05-06OR23177 and grant DE-FG0287ER40365 (Szczepaniak); the National Natural Science Foundation of China (NSFC) under contract numbers 11235011 and 11475187 (Yuan).