Focusing on the recent measurements of the scattering processes <math altimg='si1.svg'><mover accent='true'><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover><mi>p</mi><mo stretchy='false'>&#8594;</mo><mover accent='true'><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover><mi>p</mi></math> and <math altimg='si2.svg'><mi mathvariant='normal'>&#923;</mi><mi>p</mi><mo stretchy='false'>&#8594;</mo><mi mathvariant='normal'>&#923;</mi><mi>p</mi></math> reported by BESIII, we offer a dynamical interpretation of the differences in the measured total and differential cross sections for both processes. This discrepancy arises because the <italic>u</italic>-channel contribution is forbidden for <math altimg='si1.svg'><mover accent='true'><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover><mi>p</mi><mo stretchy='false'>&#8594;</mo><mover accent='true'><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover><mi>p</mi></math> but allowed for <math altimg='si2.svg'><mi mathvariant='normal'>&#923;</mi><mi>p</mi><mo stretchy='false'>&#8594;</mo><mi mathvariant='normal'>&#923;</mi><mi>p</mi></math>. Additionally, we examine the enhancement effect in the forward angle region of the differential cross section for <math altimg='si3.svg'><mover accent='true'><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover><mi>p</mi></math> elastic scattering, attributed to the <italic>t</italic>-channel contribution. This work serves as a test to the scattering mechanism involved in these reactions.

China

Xiao-Yun Wang

Yuan Gao

Xiang Liu

Understanding of the BESIII measurement of (anti)hyperon-nucleon scattering

<p>In this study, applying the effective Lagrangian approach, we investigate the reaction <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>p</mi><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mi mathvariant="normal">Σ</mi></mrow></math> to explore the production of the hidden-strange molecular pentaquarks <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math>. Specifically, we analyze two scenarios, where the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup></math> quantum numbers of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>s</mi><mover accent="true"><mrow><mi>s</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></msub></mrow></math> are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>. Our results show that the contribution from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> exchange dominates the total cross section, surpassing those from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> exchange and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi></math> exchange. Additionally, we present predictions for the differential cross section of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>p</mi><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mi mathvariant="normal">Σ</mi></mrow></math> process. Finally, we extend the 2-to-2 scattering process to the 2-to-3 Dalitz process and provide theoretical predictions for this scenario. Our findings suggest that the cross section for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>p</mi><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mi mathvariant="normal">Σ</mi><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> process can reach several tens of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mi>b</mi></math> near the threshold, making it highly favorable for experimental measurement. However, the current scarcity of experimental data for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>p</mi><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mi mathvariant="normal">Σ</mi></mrow></math> reaction at threshold energy limits our ability to determine the properties of the hidden-strange molecular pentaquarks <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> and related physical quantities. Therefore, additional experimental measurements of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mi mathvariant="normal">Σ</mi></math> reaction at threshold are strongly encouraged, and correlation studies could be pursued at facilities such as J-PARC, AMBER, and upcoming HIKE and HIAF meson beam experiments.</p>

Production potential of hidden-strange molecular pentaquarks through the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>p</mi><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo mathvariant="bold">*</mo></mrow></msup><mi mathvariant="normal">Σ</mi></mrow></math> process

The Gao-Wald theorem says that the Penrose diagram of de Sitter spacetime reacts to a positive energy perturbation by getting “taller”. How does this change in the presence of timelike boundaries? We study this question in two-dimensional de Sitter JT gravity coupled to conformal matter. The effect of the boundaries has its roots in quantum corrections to the vacuum energy of the CFT due to Casimir-like effects. We consider two different kinds of timelike boundaries, and for each kind we compute the vacuum expectation value of the matter CFT stress tensor. The stress tensor violates the null energy condition in the first case and saturates it in the second case, with each case exhibiting a negative energy density in the vacuum state. We then compute the semiclassical backreaction of this energy density and show how it can make the spacetime “fatter” or “taller” or a combination of both, depending on the regime. The spacetime getting fatter corresponds to an increase in the value of the dilaton at the horizon and hence also in the static patch horizon area in the higher-dimensional solution. We comment on the implications of our results for the quantum theories living on the timelike boundaries.

United States

Gauri Batra

Timelike boundaries in de Sitter JT gravity and the Gao-Wald theorem

Double strangeness <math><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> production in Au+Au collisions at 2, 4, and 6 GeV/nucleon incident beam energies is studied with the pure hadron cascade version of a multi-phase transport model. It is found that due to larger nuclear compression, the model with the soft equation of state (EoS) gives larger yields of both single strangeness (<math><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></math> and <math><mi>Λ</mi><mo>+</mo><msup><mrow><mi>Σ</mi></mrow><mrow><mn>0</mn></mrow></msup></math>) and double strangeness <math><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>−</mo></mrow></msup></math>. The sensitivity of the double strangeness <math><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> to the EoS is evidently larger than that of <math><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></math> or <math><mi>Λ</mi><mo>+</mo><msup><mrow><mi>Σ</mi></mrow><mrow><mn>0</mn></mrow></msup></math> since the phase-space distribution of produced <math><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> is more compact compared to those of the single strangeness. The larger sensitivity of the yields ratio of <math><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> to the EoS from heavy and light systems is kept compared to that of the single strangeness. The study of <math><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> production in relativistic heavy-ion collisions provides an alternative for the ongoing heavy-ion collision program at facilities worldwide for identifying the EoS at high densities, which is relevant to the investigation of the phase boundary and onset of deconfinement of dense nuclear matter.

Gao-Chan Yong

Zhi-Gang Xiao

Zi-Wei Lin

Double strangeness Ξ Production as a Probe of Nuclear Equation of State at High Densities

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

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

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.

R.A. Briceño

T.D. Cohen

S. Coito

J.J. Dudek

E. Eichten

Germany

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).

A proof is given of the formula, recently proposed by Cachazo, He and Yuan (CHY) for gluon tree amplitudes in pure Yang-Mills theory in arbitrary dimension. The approach is to first establish the corresponding result for massless ϕ 3 theory using the BCFW recurrence relation and then to extend this to the gauge theory case. Additionally, it is shown that the scattering equations introduced by CHY can be generalized to massive particles, enabling the description of tree amplitudes for massive ϕ 3 theory.

Louise Dolan

Peter Goddard

Proof of the formula of Cachazo, He and Yuan for Yang-Mills tree amplitudes in arbitrary dimension