We present the first lattice result of the near threshold $ \Lambda_c\Lambda_c $ scattering with $ I(J^P) = 0(0^+) $ . The calculation is performed on two $ N_f = 2+1 $ Wilson-Clover ensembles with pion mass $ m_\pi \sim 303 $ MeV and lattice spacing $ a = 0.07746 $ fm. Lüscher's finite volume method is utilized to extract the scattering parameters from the finite-volume spectrum. The coupled channel $ \Xi_{cc}N $ is ignored in the scattering analysis based on the observation that the energy levels computed from the $ \Lambda_c\Lambda_c $ and $ \Xi_{cc}N $ operators do not mix. The $ \Sigma_c\Sigma_c $ channel is not included either since the energy range explored in this study is well below its threshold. Our results indicate that the interaction in the $ \Lambda_c\Lambda_c $ single channel is repulsive, and the scattering length is determined to be $ a_0 = -0.21(4)(8) $ fm, where the first error is statistical and the second is systematic.

China

Hanyang Xing

Yiqi Geng

Chuan Liu

Liuming Liu

Peng Sun

Jiajun Wu

Zhicheng Yan

Ruilin Zhu

Lattice QCD study of Λ $\textit{c}$ Λ $\textit{c}$ scattering * Supported by NSFC (12293060, 12293061, 12293063, 12175279, 12435002, 12322503, 12175239). L. Liu also acknowledges the Strategic Priority Research Program of the Chinese Academy of Sciences with (XDB34030301) and Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008). We also acknowledge the Science and Education Integration Young Faculty Project of University of Chinese Academy of Sciences (YSBR-101)

We construct the generalized  $$\beta $$  <math> <mi>β</mi> </math>   and (q, t)-deformed partition functions through W representations, where the expansions are respectively with respect to the generalized Jack and Macdonald polynomials labeled by N-tuple of Young diagrams. We find that there are the profound interrelations between our deformed partition functions and the 4d and 5d Nekrasov partition functions. Since the corresponding Nekrasov partition functions can be given by vertex operators, the remarkable connection between our  $$\beta $$  <math> <mi>β</mi> </math>   and (q, t)-deformed W-operators and vertex operators is revealed in this paper. In addition, we investigate the higher Hamiltonians for the generalized Jack and Macdonald polynomials.

Fan Liu

Rui Wang

Jie Yang

Wei-Zhong Zhao

Generalized  $$\beta $$  <math> <mi>β</mi> </math>   and (q, t)-deformed partition functions with W-representations and Nekrasov partition functions

In this letter we continue the development of W-representations. We propose several generalizations of the known models, such as the hypergeometric Hurwitz τ-functions. We construct W-representations for multi-character expansions, which involve a generic number of sets of time variables. We propose integral representations for such kind of partition functions which are given by tensor models and multi-matrix models with multi-trace couplings. We further propose the β-deformation of the discussed W-representation for the Hurwitz case for two sets of times as well as for the multi-character case.

Lu-Yao Wang

Russia

V. Mishnyakov

A. Popolitov

-representations for Multi-character Partition Functions and Their -deformations

Scattering amplitudes in planar   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super Yang-Mills theory exhibit singularities which reflect various aspects of the cluster algebras associated to the Grassmannians Gr(4, n) and their tropical counterparts. Here we investigate the potential origins of such structures and examine the extent to which they can be recovered from the Gröbner structure of the underlying Plücker ideals, focussing on the Grassmannians corresponding to finite cluster algebras.

Mexico

L. Bossinger

United Kingdom

J. Drummond

R. Glew

Adjacency for scattering amplitudes from the Gröbner fan

We construct the supersymmetric  $$\beta $$  <math> <mi>β</mi> </math>   and (q, t)-deformed Hurwitz–Kontsevich partition functions through W-representations and present the corresponding character expansions with respect to the Jack and Macdonald superpolynomials, respectively. Based on the constructed  $$\beta $$  <math> <mi>β</mi> </math>   and (q, t)-deformed superoperators, we further give the supersymmetric  $$\beta $$  <math> <mi>β</mi> </math>   and (q, t)-deformed partition function hierarchies through W-representations. We also present the generalized super Virasoro constraints, where the constraint operators obey the generalized super Virasoro algebra and null super 3-algebra. Moreover, the superintegrability for these (non-deformed) supersymmetric hierarchies is shown by their character expansions, i.e.,  $$&lt;character&gt;\sim character$$  <math> <mrow> <mo>&lt;</mo> <mi>c</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>a</mi> <mi>c</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> <mo>&gt;</mo> <mo>∼</mo> <mi>c</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>a</mi> <mi>c</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> </math>  .

Min-Li Li

Supersymmetric partition function hierarchies and character expansions

We follow the general recipe for constructing commutative families of W-operators, which provides Hurwitz-like expansions in symmetric functions (Macdonald polynomials), in order to obtain a difference operator example that gives rise to a <math><mo>(</mo><mi>q</mi><mo>,</mo><mi>t</mi><mo>)</mo></math>-deformation of the earlier studied models. As before, a key role is played by an appropriate deformation of the cut-and-join rotation operator. We outline its expression both in terms of generators of the quantum toroidal algebra and in terms of the Macdonald difference operators.

A. Mironov

A. Morozov

( , )-deformed (skew) Hurwitz -functions

We construct the ( $$\beta $$  <math> <mi>β</mi> </math>  -deformed) partition function hierarchies with W-representations. Based on the W-representations, we analyze the superintegrability property and derive their character expansions with respect to the Schur functions and Jack polynomials, respectively. Some well known superintegrable matrix models such as the Gaussian hermitian one-matrix model (in the external field),  $$N\times N$$  <math> <mrow> <mi>N</mi> <mo>×</mo> <mi>N</mi> </mrow> </math>   complex matrix model,  $$\beta $$  <math> <mi>β</mi> </math>  -deformed Gaussian hermitian and rectangular complex matrix models are contained in the constructed hierarchies.

Chun-Hong Zhang

Superintegrability for ( $$\beta $$  <math> <mi>β</mi> </math>  -deformed) partition function hierarchies with W-representations

This exploratory study computes two-photon decay widths of pseudo-scalar (
					) and scalar (
					) charmonium using two ensembles of 
					 twisted mass lattice QCD gauge configurations. The simulation is performed using two lattice ensembles with lattice spacings 
					 fm with size 
					 and 
					 fm with size 
					. The decay widths for the two charmonia are obtained within the expected ballpark, but are however smaller than the experimental ones. Possible reasons for these discrepancies are discussed.
				

Ying Chen

Ming Gong

Ning Li

Yu-Bin Liu

Zhaofeng Liu

Jian-Ping Ma

Yu Meng

Chao Xiong

Ke-Long Zhang

Lattice study of two-photon decay widths for scalar and pseudo-scalar charmonium This work is supported in part by the National Science Foundation of China (NSFC) (11335001, 11275169, 11405178, 11935017, 11575196, 11875169, 11775229). It is also supported in part by the DFG and the NSFC (11261130311) through funds provided to the Sino-Germen CRC 110 symmetries and the Emergence of Structure in QCD. This work is also funded in part by National Basic Research Program of China (973 Program) (2015CB856700). M. Gong and Z. Liu are partially supported by the Youth Innovation Promotion Association of CAS (2013013). This work is also supported by the Scientific Research Program Funded by Shaanxi Provincial Education Department (19JK0391) andNatural Science Basic Research Plan in Shaanxi Province of China (2019JM-001)

Within QCD reggeon field theory we study the formation of two subsequent triple pomeron vertices in the process P→PP→PPP. We make use of an earlier investigation [1] of the six-reggeon amplitude in deep inelastic scattering and show that in the large-N  c  limit pomeron fan diagrams emerge with the same triple pomeron vertex in all places. We thus confirm the BK-equation, but we also find additional terms related to the reggeization of the gluon, and we discuss their potential significance. Our analysis also includes the general pomeron → two odderon vertex: a particular version of this vertex has been included into earlier generalizations the BK equation.

Germany

J. Bartels

M. Braun

Pomeron fan diagrams in perturbative QCD

Using the one-boson-exchange model, we investigate the , , , , , and interactions by considering the one-eta-exchange and/or one-pion-exchange contributions. We further predict the existence of hidden-charm molecular pentaquarks. Promising candidates for hidden-charm molecular pentaquarks include a state with and the states with and . Experimental searches for these predicted hidden-charm molecular pentaquarks are an interesting future research topic for experiments like LHCb.

Rui Chen

Jun He

Xiang Liu

Possible strange hidden-charm pentaquarks from and interactionsSupported by National Natural Science Foundation of China (11222547, 11175073, 11675228), Major State Basic Research Development Program in China (2014CB845405) and Fundamental Research Funds for the Central Universities. Xiang Liu is also supported by the National Program for Support of Top-notch Young Professionals