This paper discusses multi-particle production in QCD and in gravity at ultrarelativistic energies, their double-copy relations, and strong parallels in emergent shockwave dynamics. Dispersive techniques are applied to derive the BFKL equation for multi-gluon production in Regge asymptotics. Identical methods apply in gravity and are captured by a gravitational Lipatov equation. The building blocks in both cases are Lipatov vertices and reggeized propagators satisfying double-copy relations; in gravity, Weinberg’s soft theorem is recovered as a limit of the Lipatov framework. BFKL evolution in QCD generates wee parton states of maximal occupancy characterized by an emergent semi-hard saturation scale. Renormalization group equations in the Color Glass Condensate (CGC) EFT describe wee parton correlations and their rapidity evolution. A shockwave picture of deeply inelastic scattering and hadron–hadron collisions follows, with multi-particle production described by Cutkosky’s rules in strong time-dependent fields. Gluon radiation in the CGC EFT has a double copy in gravitational shockwave collisions, with a similar correspondence applicable between gluon and graviton shockwave propagators. Possible extensions of this semi-classical double copy are outlined for computing multi-particle production in gravitational shockwave collisions, self-force and tidal contributions, and classical and quantum noise in the focusing of geodesics. Abstract Published by the Jagiellonian University 2025 authors

United States

H. Raj

R. Venugopalan

QCD–Gravity Double Copy in Regge Asymptotics: From \(2\rightarrow n\) Amplitudes to Radiation in Shockwave Collisions

If a linear electron accelerator is installed into the SPPC (Super Proton–Proton Collider) complex, \(ep\) collision options will be available in addition to \(pp\) collisions. We consider the production of excited electrons with spin-1/2 at the future SPPC-based electron–proton colliders with center-of-mass energies of \(8.44\), \(11.66\), \(26.68\), and \(36.88\) TeV. In the \(ep\rightarrow e^{\star }X\rightarrow e\gamma X\) signal process, excited electrons are produced by contact interactions and decay into the photon channel by gauge interactions. Taking into account the corresponding background process, the pseudorapidity and transverse momentum distributions of the final-state particles are plotted. We reported on the discovery, observation, and exclusion mass limits of excited electrons by applying appropriate kinematical cuts best suited for amplifying the signal of the excited electron signature. We also investigated the highest achievable values of the compositeness scale for the discovery of excited electrons at these colliders. Abstract Published by the Jagiellonian University 2025 authors

Türkiye

A. Caliskan

Excited Electron Production at the SPPC-based \(ep\) Colliders via Contact Interactions

This review deals with measurements and future experiments of light pentaquark searches using hadron beams. Abstract Published by the Jagiellonian University 2025 authors

South Korea

J.K. Ahn

Light Pentaquark Searches with Hadron Beams

We present general features of the transverse densities of the stress-energy-momentum tensor \({\mit \Theta }^{\mu \nu }\) in the pion. We show positivity of the transverse density of \({\mit \Theta }^{++}\) (analogous to the positivity of the transverse density of the electromagnetic current \(J^+\)) and discuss its consequences in conjunction with analyticity and quark–hadron duality, as well as the connection to \(\pi \pi \) scattering at low energies. Our analysis takes into account the perturbative QCD effects, dominating at high momenta (or low transverse coordinate \(b\)), the effects of Chiral Perturbation Theory, dominating at low momenta (high \(b\)), and meson dominance in the intermediate region. We incorporate constraints form analyticity, leading to sum rules for the spectral densities of the corresponding form factors, which &lt;span class="it"&gt;ia.&lt;/span&gt; are relevant for the high-momentum (or the low-\(b\)) asymptotics. With the obtained high- and low-\(b\) behavior, we deduce that the scalar (trace-anomaly) gravitational transverse density \({\mit \Theta }^{\mu }_\mu (b)\) must change the sign, unlike the case of the positive definite \(J^+(b)\) or \({\mit \Theta }^{++}(b)\). We also discuss the transverse pressure in the pion, which is positive and singular at low \(b\), and negative at high \(b\), in harmony with the stability criterion. The results for the form factors for space-like momenta are compared to the recent lattice QCD data. Abstract Published by the Jagiellonian University 2025 authors

Poland

W. Broniowski

E. Ruiz Arriola

Transverse Densities of the~Energy-momentum Tensor and the~Gravitational Form Factors of the Pion

\({\mit \Theta }^+\) is a putative light pentaquark state of positive parity with minimal quark content \((uudd\bar {s})\). It naturally emerges in chiral models for baryons, but experimental evidence is uncertain. We review the theoretical foundations of chiral models and their phenomenological applications to exotic states. In particular, we discuss in detail the pentaquark widths with special emphasis on the cancellations occurring in the decay operator. We also discuss some experiments, mainly those whose positive evidence of \({\mit \Theta }^+\) persists to this day. This review is dedicated to Dmitry Diakonov, Victor Petrov, and Maxim Polyakov and their contribution to the \({\mit \Theta }^+\) story. Abstract Published by the Jagiellonian University 2025 authors

M. Praszałowicz

Odyssey of the Elusive \({\mit \Theta }^+\)

This brief review is dedicated to the memory of Maxim V. Polyakov and his pioneering contributions to pentaquark physics. We focus on his seminal 1997 work with Diakonov and Petrov that predicted the \({\mit \Theta }^+\) pentaquark, a breakthrough that initiated an intense period of research in hadron physics. The field faced a significant setback when the CLAS Collaboration at Jefferson Lab reported null results in 2006, leading to a dramatic decline in light-pentaquark research. Nevertheless, Maxim maintained his scientific conviction, supported by continued positive signals from the DIANA and LEPS collaborations. Through recent experimental findings on the \({\mit \Theta }^+\) and the nucleon-like resonance \(N^*(1685)\), we examine how Polyakov’s theoretical insights, particularly the prediction of a narrow width (\({\mit \Gamma } \approx 0.5\)–\(1.0\) MeV), remain relevant to our understanding of the \({\mit \Theta }^+\) light pentaquark. Abstract Published by the Jagiellonian University 2025 authors

H.-Ch. Kim

Pentaquarks and Maxim V. Polyakov

In the search for the pentaquark \({\mit \Theta }^+\) baryon, the world data on \(K^+n\to K^+n\) and \(K^+n\to K^0p\) reactions on the deuteron target and \(K^0p\to K^+n\) and \(K^0_{\mathrm {L}}\,p\to K^0_{\mathrm {S}}\,p\) reactions on the hydrogen target are revisited to study the isoscalar component of the scattering amplitudes. The determination of the \(s\)- and \(p\)-wave phase shifts for the two former channels on the deuteron target is presented in the low-momentum region with the uncertainty due to the deuteron form factors at forward angles discussed. For the reactions on hydrogen targets, a similarity expected from time reversal between the charge exchange processes \(K^+n\to K^0p\) and \(K^0p\to K^+n\) is exploited, while we present the analysis of the \(K_{\mathrm {L}}^0\,p\to K_{\mathrm {S}}^0\,p\) scattering based on the \(s\)-wave phase shift for low momenta combined with the \(t\)-channel \(\rho ^0(775)+\omega (782)+\phi (1020)\) vector meson exchange at high momenta. With the mass of 1535 MeV and decay width of 5 MeV, the possibility of the \({\mit \Theta }^+\) in the Breit–Wigner (BW) form is tested in the differential cross section measured by Damerell &lt;span class="it"&gt;et al.&lt;/span&gt; [&lt;span class="it"&gt;Nucl. Phys. B&lt;/span&gt; &lt;span class="bf"&gt;94&lt;/span&gt;, 374 (1075)] at \({P_\mathrm {Lab}}=434\) MeV/\(c\) and polarization. Our analysis suggests measuring the polarization observable rather than the differential cross section, which has sufficient sensitivity to distinguish the \({\mit \Theta }^+\) baryon among all spin and parity states \(J^P = 1/2^\pm \) and \(3/2^\pm \). Abstract Published by the Jagiellonian University 2025 authors

B.G. Yu

K.J. Kong

T.K. Choi

Revisiting \(KN\) Elastic and Charge Exchange Reactions in Search of the Pentaquark \({\mit \Theta }^+\) Baryon

This paper describes my personal appreciation for some of the great research achievements of Mitya Diakonov, Vitya Petrov, and Maxim Polyakov, and how my own research career has followed the paths they opened. Among the topics where they have been the most influential have been the pursuit and study of the exotic pentaquark. The search for exotics may require a complementary approach, such as experimental and theoretical activity. Here, I would like to focus on a story of \(N(1680)\), a non-strange unitary partner of \({\mit \Theta }^+\), in which I was involved. Abstract Published by the Jagiellonian University 2025 authors

I. Strakovsky

History of \(N(1680)\)

One method for deriving a factorization for QCD processes is to use successive integration over fields in the functional integral. In this approach, we separate the fields into two categories: dynamical fields with momenta above a relevant cutoff, and background fields with momenta below the cutoff. The dynamical fields are then integrated out in the background of the low-momentum background fields. This strategy works well at tree level, allowing us to quickly derive QCD factorization formulas at leading order. However, to extend the approach to higher loops, it is necessary to rigorously define the functional integral over dynamical fields in an arbitrary background field. This framework was carefully developed for the calculation of the effective action in a background field at the two-loop level in the classic paper by Abbott «The Background Field Method Beyond One Loop», &lt;span class="it"&gt;Nucl. Phys. B&lt;/span&gt; &lt;span class="bf"&gt;185&lt;/span&gt;, 189 (1981). Building on this work, I specify the renormalized background-field Lagrangian and define the notion of the quantum average of an operator in a background field, consistent with the “separation of scales” scheme mentioned earlier. As examples, I discuss the evolution of the twist-2 gluon light-ray operator and the one-loop gluon propagator in a background field near the light cone. Abstract Published by the Jagiellonian University 2025 authors

I. Balitsky

Background-field Method and QCD Factorization

The instanton vacuum provides an effective description of chiral symmetry breaking by local topological fluctuations of the gauge fields, as observed in lattice QCD simulations. The resulting effective dynamics at momenta below \(1/\bar \rho \approx 0.6\) GeV explains the basic features of light-quark correlation functions and is used extensively in studies of hadron structure. The instanton fields also make definite contributions to the gluonic structure of light hadrons, as expressed in the matrix elements of composite quark–gluon or gluon operators. The article reviews the gluonic structure of light hadrons (nucleon, pion) induced by instantons. This includes: &lt;span class="it"&gt;(i)&lt;/span&gt; twist-2 parton distributions and momentum sum rule; &lt;span class="it"&gt;(ii)&lt;/span&gt; twist-3 angular momentum and spin-orbit interactions; &lt;span class="it"&gt;(iii)&lt;/span&gt; twist-3 and twist-4 quark–gluon correlations and power corrections; &lt;span class="it"&gt;(iv)&lt;/span&gt; trace anomaly and hadron mass decomposition; &lt;span class="it"&gt;(v)&lt;/span&gt; scalar gluon form factors and mechanical properties; &lt;span class="it"&gt;(vi)&lt;/span&gt; axial anomaly and pseudoscalar gluon form factors. It also discusses possible further applications of the methods and recent developments including gauge field configurations beyond instantons. Abstract Published by the Jagiellonian University 2025 authors