We present a study of the central exclusive production (CEP) of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><mo stretchy="false">(</mo><mn>958</mn><mo stretchy="false">)</mo></mrow></math> mesons in diffractive proton-proton collisions at high energies. The amplitudes, including pomeron and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mrow><mn>2</mn><mi mathvariant="double-struck">R</mi></mrow></msub></math> reggeon exchanges, are calculated within the tensor-pomeron model. Absorption effects are also taken into account at the amplitude level. We fit some undetermined model parameters (coupling constants and cutoff parameters in form factors) to the WA102 experimental data and then make predictions for the LHC energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math>. Both total cross sections and several differential distributions are presented. For <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><mi>p</mi><mi>p</mi><mi>η</mi></math>, we find an upper limit for the total cross section of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2.5</mn><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">μ</mi><mi mathvariant="normal">b</mi></mrow></math> for pseudorapidity of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">|</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>M</mi></mrow></msub><mo stretchy="false">|</mo><mo>&lt;</mo><mn>1</mn></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>5.6</mn><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">μ</mi><mi mathvariant="normal">b</mi></mrow></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>&lt;</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>M</mi></mrow></msub><mo>&lt;</mo><mn>5</mn></mrow></math>. For <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><mi>p</mi><mi>p</mi><msup><mi>η</mi><mo>′</mo></msup></math>, we predict the cross section to be in the range of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0.3</mn><mi>–</mi><mn>0.7</mn><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">μ</mi><mi mathvariant="normal">b</mi></mrow></math> for pseudorapidity of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>η</mi><mi>M</mi></msub><mo stretchy="false">|</mo><mo>&lt;</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0.9</mn><mi>–</mi><mn>2.1</mn><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">μ</mi><mi mathvariant="normal">b</mi></mrow></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo>&lt;</mo><msub><mi>η</mi><mi>M</mi></msub><mo>&lt;</mo><mn>5</mn></math>. This opens the possibility to study diffractive production of pseudoscalar mesons in experiments at the LHC. We discuss if there are arguments from SU(3)-flavor symmetry which would forbid pomeron-pomeron fusion giving an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> meson. In our opinion such arguments do not exist. We also consider CEP of the pseudoscalars <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mn>958</mn><mo stretchy="false">)</mo></math> and the pseudovector meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1285</mn><mo stretchy="false">)</mo></math> in diffractive proton-proton collisions in a theory with a scalar pomeron. We show that none of these particles can be produced in this way in the scalar-pomeron theory. Thus, experimental observation of any of these particles in the above CEP processes at the LHC would give striking evidence against a scalar character of the pomeron.

Poland

Piotr Lebiedowicz

Germany

Otto Nachtmann

Antoni Szczurek

Central exclusive production of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> mesons in diffractive proton-proton collisions at the LHC within the tensor-pomeron approach

A comprehensive analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi><mo stretchy="false">→</mo><mi>π</mi><mi>K</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mo stretchy="false">→</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> amplitudes at large unphysical pion mass for all important partial waves is presented. A set of crossing-symmetric partial-wave hyperbolic dispersion relations is used to describe lattice quantum chromodynamics (QCD) data at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>391</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. In the present analysis, the amplitudes for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-waves are formulated by combining the constraints of analyticity, unitarity, and crossing symmetry, fulfilling Roy-Steiner-type equations. We use these results to investigate the low-lying strange-meson resonances and resolve the instability problem tied to analytic continuation in prior lattice QCD studies based on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>-matrix formalism. At <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>391</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, the rigorous Roy-Steiner-type equation approach allows us to determine the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave scattering lengths, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><msubsup><mi>a</mi><mn>0</mn><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msubsup><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>0.9</mn><msubsup><mn>2</mn><mrow><mo>−</mo><mn>0.28</mn></mrow><mrow><mo>+</mo><mn>0.06</mn></mrow></msubsup><mo stretchy="false">)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><msubsup><mi>a</mi><mn>0</mn><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msubsup><mo>=</mo><mo>−</mo><mrow><mo stretchy="false">(</mo><mn>0.3</mn><msubsup><mn>2</mn><mrow><mo>−</mo><mn>0.02</mn></mrow><mrow><mo>+</mo><mn>0.05</mn></mrow></msubsup><mo stretchy="false">)</mo></mrow></math>, and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi></math> [also known as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></math>] pole position, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><msub><mi>s</mi><mi>κ</mi></msub></msqrt><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>96</mn><msubsup><mn>6</mn><mrow><mo>−</mo><mn>24</mn></mrow><mrow><mo>+</mo><mn>41</mn></mrow></msubsup><mo>−</mo><mi>i</mi><mn>19</mn><msubsup><mn>8</mn><mrow><mo>−</mo><mn>17</mn></mrow><mrow><mo>+</mo><mn>38</mn></mrow></msubsup><mo stretchy="false">)</mo></mrow><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. We also provide a detailed analysis of the complex validity domain of the Roy-Steiner-type equations.

China

Xiong-Hui Cao

Feng-Kun Guo

Zhi-Hui Guo

Qu-Zhi Li

Revisiting Roy-Steiner-equation analysis of pion-kaon scattering from lattice QCD data

Metastable cosmic strings (MSCSs) are among the best-fitting explanations of the 2023 pulsar timing array (PTA) signal for gravitational waves at nanohertz frequencies. We propose the novel possibility that a network of MSCSs generating this signal originates from the multistep spontaneous breaking of a gauged flavor symmetry. As a specific example, we construct a model of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math> flavor symmetry in the context of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo></math> grand unification, where the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math> acts exclusively on the first two generations of the matter 10-plet, such that it is “right for leptons” and allows for large lepton mixing. The model explains the mass hierarchies of the Standard Model fermions, and predicts the string scale of the MSCSs in a range compatible with the 2023 PTA signal. Cosmic inflation is associated with the latter step of (two-step) family symmetry breaking, and the phase transition ending inflation generates the cosmic string network.

Switzerland

Stefan Antusch

Kevin Hinze

Slovenia

Shaikh Saad

Metastable cosmic strings and gravitational waves from flavor symmetry breaking

We perform a rigorous analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering at an unphysical pion mass 391 MeV using the Roy-Steiner equations, which satisfy unitarity, analyticity, and crossing symmetry, for the first time. Stable solutions of the Roy-Steiner equations with different quantum numbers of isospin and angular momentum are obtained in the elastic energy region, by taking inputs from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> lattice data in the inelastic region, the lattice data from the crossed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mo stretchy="false">→</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> channels, the masses of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math> at the same pion mass from previous study, and the Regge model. Predictions on the elastic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering phase shifts and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></math> pole content are made. Contrary to the virtual pole scenario obtained using the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>-matrix method in the literature, we find that lightest strange scalar meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></mrow></math> remains a broad resonance at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>391</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The cross-channel dynamics is found to play a crucial role in deriving the proper pole position.

Rigorous Roy-Steiner equation analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering at unphysical quark masses

Recently, a number of exotic hadrons have been reported in the experiments, and most of these states lie slightly below the threshold. Therefore, these states are considered to be hadronic molecules composed of mesons or baryons. In 2022, the doubly charmed tetraquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> was reported by the LHCb experiment, which is considered to be composed of two heavy quarks and two light antiquarks, and located slightly below the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> threshold. The observation motivates us to study the bound and resonant states of the doubly heavy tetraquarks as two meson systems. We employ the one boson exchange potential as an interaction between two mesons, where one free parameter has been determined to reproduce <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> reported by the LHCb experiment. In our previous work, bound states of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mi>B</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> molecules were studied, where we respected the heavy quark spin symmetry (HQS). Using the same framework, we study not only bound but also resonant states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>≤</mo><mn>2</mn></math> in this paper. Furthermore, we discuss the HQS partner structures of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> obtained in our study by introducing the light cloud basis.

Japan

Manato Sakai

Yasuhiro Yamaguchi

Analysis of bound and resonant states of doubly heavy tetraquarks with spin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>≤</mo><mn>2</mn></math>

We evaluate the pion and kaon transverse momentum dependent parton distribution functions in the instanton liquid model, a model of the QCD vacuum at low resolution. The relevant transverse momentum distributions (TMDs) are factored into a constituent quark distribution times a rapidity dependent soft factor from staple-shaped Wilson lines, for fixed parton longitudinal momentum and transverse separation. The results are evolved to higher rapidities using the Collins-Soper kernel and higher resolution using renormalization group evolution. The comparison to existing extractions of pion TMDs from Drell-Yan data is briefly discussed.

United States

Wei-Yang Liu

Ismail Zahed

Tomography of pions and kaons in the QCD vacuum: Transverse momentum dependent parton distribution functions

We analyze the pole expansion of the two-hadron imaginary-time correlation function. We first explain the general idea that the imaginary-time correlation function is expressed as a sum of the pole terms, the Mittag-Leffler expansion, in terms of the uniformization variable, which makes the S-matrix single-valued. We then derive explicit expressions of the pole expansion for the single-channel (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> meson) and two-channel [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></math>] examples and demonstrate that the pole expansion actually holds employing phenomenological models, the vector-dominance model for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> meson and the chiral unitary model for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></math>. From this observation we propose the pole expansion as a method to extract information of unstable states such as masses and widths from the two-hadron imaginary-time correlation functions obtained by lattice quantum chromodynamics (QCD) simulations.

Wren Yamada

Osamu Morimatsu

Toru Sato

Koichi Yazaki

Pole-expansion of two-hadron imaginary-time correlation function: A new analysis method for unstable states in lattice QCD

Building upon the success of optimal transport metrics defined for single collinear jets, we develop a multiscale framework that models entire collider events as distributions on the manifold of their constituent jets, which are themselves distributions on the ground space of the calorimeter. This hierarchical structure of optimal transport effectively captures relevant physics at different scales. We demonstrate the versatility of our method in two event classification tasks, which respectively emphasize intrajet substructure and interjet spatial correlations. Our results highlight the importance of a nested structure of manifolds in the treatment of full collider events, broadening the applicability of optimal transport methods in collider analyses.

Tianji Cai

Nathaniel Craig

Katy Craig

Xinyuan Lin

Multiscale optimal transport for complete collider events

Based on the studies of pseudoentropy in de Sitter, there have been recent proposals for a timelike entanglement in AdS/CFT. In this work, we explore this proposal in the context of a holographic CFT undergoing a global quench. We study various cases in which the timelike intervals are anchored at various boundary times, sometimes straddling the infalling shell. The early and late time behaviors reproduce the known results coming from the pure AdS and the black hole geometry dual to the thermal CFT state respectively. However when the infalling shock straddles the timelike interval, the dynamics drastically differs from how the entanglement entropy evolves.

India

Gaurav Katoch

Debajyoti Sarkar

Bhim Sen

Holographic timelike entanglement in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> Vaidya

The hadron physics community has been actively debating the interpretation of so-called mechanical properties of hadrons. Nonrelativistic quantum-mechanical systems like the hydrogen atom have been appealed to in these debates as analogies. Since such appeals are likely to continue, it is important to have Galilei-covariant expressions for matrix elements of the energy-momentum tensor. In this work, I obtain Galilei-covariant breakdowns of such matrix elements into mechanical form factors, with a special focus on spin-half states. I additionally study the spatial densities associated with these form factors, using the pilot wave interpretation to guide their breakdown into contributions from internal structure and from quantum-mechanical effects such as wave packet dispersion. For completeness, I also obtain nonrelativistic Breit frame densities.

Adam Freese

Mechanical form factors and densities of nonrelativistic fermions