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First Observation of an Exotic Reggeon

This paper reports the first high-significance observation of an exotic Reggeon, likely associated with the $\pi_1(1600)$ , in the peripheral production of $\eta\pi^-$ and $\eta^\prime\pi^-$ pairs based on new high-statistics COMPASS measurements and an unbinned high-mass analysis.

Original authors: G. D. Alexeev (for JPAC Collaboration), M. G. Alexeev (for JPAC Collaboration), C. Alice (for JPAC Collaboration), A. Amoroso (for JPAC Collaboration), V. Andrieux (for JPAC Collaboration), V. Anosov G. D. Alexeev (for JPAC Collaboration), M. G. Alexeev (for JPAC Collaboration), C. Alice (for JPAC Collaboration), A. Amoroso (for JPAC Collaboration), V. Andrieux (for JPAC Collaboration), V. Anosov (for JPAC Collaboration), K. Augsten (for JPAC Collaboration), W. Augustyniak (for JPAC Collaboration), C. D. R. Azevedo (for JPAC Collaboration), B. Badelek (for JPAC Collaboration), R. Beck (for JPAC Collaboration), J. Beckers (for JPAC Collaboration), Y. Bedfer (for JPAC Collaboration), J. Bernhard (for JPAC Collaboration), F. Bradamante (for JPAC Collaboration), A. Bressan (for JPAC Collaboration), W. -C. Chang (for JPAC Collaboration), C. Chatterjee (for JPAC Collaboration), M. Chiosso (for JPAC Collaboration), S. -U. Chung (for JPAC Collaboration), A. Cicuttin (for JPAC Collaboration), M. L. Crespo (for JPAC Collaboration), D. D'Ago (for JPAC Collaboration), S. Dalla Torre (for JPAC Collaboration), S. S. Dasgupta (for JPAC Collaboration), S. Dasgupta (for JPAC Collaboration), F. Delcarro (for JPAC Collaboration), I. Denisenko (for JPAC Collaboration), O. Yu. Denisov (for JPAC Collaboration), S. V. Donskov (for JPAC Collaboration), N. Doshita (for JPAC Collaboration), Ch. Dreisbach (for JPAC Collaboration), W. Dunnweber (for JPAC Collaboration), R. R. Dusaev (for JPAC Collaboration), D. Ecker (for JPAC Collaboration), P. Faccioli (for JPAC Collaboration), M. Faessler (for JPAC Collaboration), M. Finger (for JPAC Collaboration), M. jr Finger (for JPAC Collaboration), H. Fischer (for JPAC Collaboration), K. J. Flothner (for JPAC Collaboration), W. Florian (for JPAC Collaboration), J. M. Friedrich (for JPAC Collaboration), V. Frolov (for JPAC Collaboration), L. G. Garcia Ordonez (for JPAC Collaboration), O. P. Gavrichtchouk (for JPAC Collaboration), S. Gerassimov (for JPAC Collaboration), J. Giarra (for JPAC Collaboration), D. Giordano (for JPAC Collaboration), A. Grasso (for JPAC Collaboration), A. Gridin (for JPAC Collaboration), M. Grosse Perdekamp (for JPAC Collaboration), B. Grube (for JPAC Collaboration), M. Gruner (for JPAC Collaboration), A. Guskov (for JPAC Collaboration), P. Haas (for JPAC Collaboration), D. von Harrach (for JPAC Collaboration), M. Hoffmann (for JPAC Collaboration), N. d'Hose (for JPAC Collaboration), C. -Y. Hsieh (for JPAC Collaboration), S. Ishimoto (for JPAC Collaboration), A. Ivanov (for JPAC Collaboration), T. Iwata (for JPAC Collaboration), V. Jary (for JPAC Collaboration), R. Joosten (for JPAC Collaboration), E. Kabuss (for JPAC Collaboration), F. Kaspar (for JPAC Collaboration), A. Kerbizi (for JPAC Collaboration), B. Ketzer (for JPAC Collaboration), G. V. Khaustov (for JPAC Collaboration), J. H. Koivuniemi (for JPAC Collaboration), V. N. Kolosov (for JPAC Collaboration), K. Kondo Horikawa (for JPAC Collaboration), I. Konorov (for JPAC Collaboration), A. Yu. Korzenev (for JPAC Collaboration), A. M. Kotzinian (for JPAC Collaboration), O. M. Kouznetsov (for JPAC Collaboration), A. Koval (for JPAC Collaboration), F. Kunne (for JPAC Collaboration), K. Kurek (for JPAC Collaboration), R. P. Kurjata (for JPAC Collaboration), G. Kurten (for JPAC Collaboration), A. Kveton (for JPAC Collaboration), K. Lavickova (for JPAC Collaboration), S. Levorato (for JPAC Collaboration), Y. -S. Lian (for JPAC Collaboration), J. Lichtenstadt (for JPAC Collaboration), P. -J. Lin (for JPAC Collaboration), R. Longo (for JPAC Collaboration), V. E. Lyubovitskij (for JPAC Collaboration), A. Maggiora (for JPAC Collaboration), N. Makke (for JPAC Collaboration), G. K. Mallot (for JPAC Collaboration), A. Maltsev (for JPAC Collaboration), A. Martin (for JPAC Collaboration), J. Marzec (for JPAC Collaboration), J. Matousek (for JPAC Collaboration), T. Matsuda (for JPAC Collaboration), C. Menezes Pires (for JPAC Collaboration), F. Metzger (for JPAC Collaboration), W. Meyer (for JPAC Collaboration), M. Mikhasenko (for JPAC Collaboration), E. Mitrofanov (for JPAC Collaboration), D. Miura (for JPAC Collaboration), Y. Miyachi (for JPAC Collaboration), R. Molina (for JPAC Collaboration), A. Moretti (for JPAC Collaboration), A. Nagaytsev (for JPAC Collaboration), D. Neyret (for JPAC Collaboration), M. Niemiec (for JPAC Collaboration), J. Novy (for JPAC Collaboration), W. -D. Nowak (for JPAC Collaboration), G. Nukazuka (for JPAC Collaboration), A. G. Olshevsky (for JPAC Collaboration), M. Ostrick (for JPAC Collaboration), D. Panzieri (for JPAC Collaboration), B. Parsamyan (for JPAC Collaboration), S. Paul (for JPAC Collaboration), H. Pekeler (for JPAC Collaboration), J. -C. Peng (for JPAC Collaboration), M. Pesek (for JPAC Collaboration), D. V. Peshekhonov (for JPAC Collaboration), M. Peskova (for JPAC Collaboration), S. Platchkov (for JPAC Collaboration), J. Pochodzalla (for JPAC Collaboration), V. A. Polyakov (for JPAC Collaboration), C. Quintans (for JPAC Collaboration), G. Reicherz (for JPAC Collaboration), C. Riedl (for JPAC Collaboration), D. I. Ryabchikov (for JPAC Collaboration), A. Rychter (for JPAC Collaboration), A. Rymbekova (for JPAC Collaboration), V. D. Samoylenko (for JPAC Collaboration), A. Sandacz (for JPAC Collaboration), S. Sarkar (for JPAC Collaboration), I. A. Savin (for JPAC Collaboration), G. Sbrizzai (for JPAC Collaboration), H. Schmieden (for JPAC Collaboration), A. Selyunin (for JPAC Collaboration), S. Seriubin (for JPAC Collaboration), L. Sinha (for JPAC Collaboration), D. Spulbeck (for JPAC Collaboration), A. Srnka (for JPAC Collaboration), M. Stolarski (for JPAC Collaboration), M. Sulc (for JPAC Collaboration), H. Suzuki (for JPAC Collaboration), S. Tessaro (for JPAC Collaboration), F. Tessarotto (for JPAC Collaboration), A. Thiel (for JPAC Collaboration), F. Tosello (for JPAC Collaboration), A. Townsend (for JPAC Collaboration), V. Tskhay (for JPAC Collaboration), B. Valinoti (for JPAC Collaboration), B. M. Veit (for JPAC Collaboration), J. F. C. A. Veloso (for JPAC Collaboration), A. Vijayakumar (for JPAC Collaboration), M. Virius (for JPAC Collaboration), M. Wagner (for JPAC Collaboration), S. Wallner (for JPAC Collaboration), K. Zaremba (for JPAC Collaboration), M. Zavertyaev (for JPAC Collaboration), M. Zemko (for JPAC Collaboration), E. Zemlyanichkina (for JPAC Collaboration), M. Ziembicki (for JPAC Collaboration), for the COMPASS Collaboration (for JPAC Collaboration), C. Fernandez-Ramirez (for JPAC Collaboration), M. Mikhasenko (for JPAC Collaboration), L. Bibrzycki (for JPAC Collaboration), G. Foti (for JPAC Collaboration), N. Hammoud (for JPAC Collaboration), V. Mathieu (for JPAC Collaboration), G. Montana (for JPAC Collaboration), R. J. Perry (for JPAC Collaboration), A. Pilloni (for JPAC Collaboration), A. Rodas (for JPAC Collaboration), V. Shastry (for JPAC Collaboration), W. A. Smith (for JPAC Collaboration), A. P. Szczepaniak (for JPAC Collaboration), D. Winney (for JPAC Collaboration)

Published 2026-07-21

📖 5 min read🧠 Deep dive

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Original authors: G. D. Alexeev (for JPAC Collaboration), M. G. Alexeev (for JPAC Collaboration), C. Alice (for JPAC Collaboration), A. Amoroso (for JPAC Collaboration), V. Andrieux (for JPAC Collaboration), V. Anosov (for JPAC Collaboration), K. Augsten (for JPAC Collaboration), W. Augustyniak (for JPAC Collaboration), C. D. R. Azevedo (for JPAC Collaboration), B. Badelek (for JPAC Collaboration), R. Beck (for JPAC Collaboration), J. Beckers (for JPAC Collaboration), Y. Bedfer (for JPAC Collaboration), J. Bernhard (for JPAC Collaboration), F. Bradamante (for JPAC Collaboration), A. Bressan (for JPAC Collaboration), W. -C. Chang (for JPAC Collaboration), C. Chatterjee (for JPAC Collaboration), M. Chiosso (for JPAC Collaboration), S. -U. Chung (for JPAC Collaboration), A. Cicuttin (for JPAC Collaboration), M. L. Crespo (for JPAC Collaboration), D. D'Ago (for JPAC Collaboration), S. Dalla Torre (for JPAC Collaboration), S. S. Dasgupta (for JPAC Collaboration), S. Dasgupta (for JPAC Collaboration), F. Delcarro (for JPAC Collaboration), I. Denisenko (for JPAC Collaboration), O. Yu. Denisov (for JPAC Collaboration), S. V. Donskov (for JPAC Collaboration), N. Doshita (for JPAC Collaboration), Ch. Dreisbach (for JPAC Collaboration), W. Dunnweber (for JPAC Collaboration), R. R. Dusaev (for JPAC Collaboration), D. Ecker (for JPAC Collaboration), P. Faccioli (for JPAC Collaboration), M. Faessler (for JPAC Collaboration), M. Finger (for JPAC Collaboration), M. jr Finger (for JPAC Collaboration), H. Fischer (for JPAC Collaboration), K. J. Flothner (for JPAC Collaboration), W. Florian (for JPAC Collaboration), J. M. Friedrich (for JPAC Collaboration), V. Frolov (for JPAC Collaboration), L. G. Garcia Ordonez (for JPAC Collaboration), O. P. Gavrichtchouk (for JPAC Collaboration), S. Gerassimov (for JPAC Collaboration), J. Giarra (for JPAC Collaboration), D. Giordano (for JPAC Collaboration), A. Grasso (for JPAC Collaboration), A. Gridin (for JPAC Collaboration), M. Grosse Perdekamp (for JPAC Collaboration), B. Grube (for JPAC Collaboration), M. Gruner (for JPAC Collaboration), A. Guskov (for JPAC Collaboration), P. Haas (for JPAC Collaboration), D. von Harrach (for JPAC Collaboration), M. Hoffmann (for JPAC Collaboration), N. d'Hose (for JPAC Collaboration), C. -Y. Hsieh (for JPAC Collaboration), S. Ishimoto (for JPAC Collaboration), A. Ivanov (for JPAC Collaboration), T. Iwata (for JPAC Collaboration), V. Jary (for JPAC Collaboration), R. Joosten (for JPAC Collaboration), E. Kabuss (for JPAC Collaboration), F. Kaspar (for JPAC Collaboration), A. Kerbizi (for JPAC Collaboration), B. Ketzer (for JPAC Collaboration), G. V. Khaustov (for JPAC Collaboration), J. H. Koivuniemi (for JPAC Collaboration), V. N. Kolosov (for JPAC Collaboration), K. Kondo Horikawa (for JPAC Collaboration), I. Konorov (for JPAC Collaboration), A. Yu. Korzenev (for JPAC Collaboration), A. M. Kotzinian (for JPAC Collaboration), O. M. Kouznetsov (for JPAC Collaboration), A. Koval (for JPAC Collaboration), F. Kunne (for JPAC Collaboration), K. Kurek (for JPAC Collaboration), R. P. Kurjata (for JPAC Collaboration), G. Kurten (for JPAC Collaboration), A. Kveton (for JPAC Collaboration), K. Lavickova (for JPAC Collaboration), S. Levorato (for JPAC Collaboration), Y. -S. Lian (for JPAC Collaboration), J. Lichtenstadt (for JPAC Collaboration), P. -J. Lin (for JPAC Collaboration), R. Longo (for JPAC Collaboration), V. E. Lyubovitskij (for JPAC Collaboration), A. Maggiora (for JPAC Collaboration), N. Makke (for JPAC Collaboration), G. K. Mallot (for JPAC Collaboration), A. Maltsev (for JPAC Collaboration), A. Martin (for JPAC Collaboration), J. Marzec (for JPAC Collaboration), J. Matousek (for JPAC Collaboration), T. Matsuda (for JPAC Collaboration), C. Menezes Pires (for JPAC Collaboration), F. Metzger (for JPAC Collaboration), W. Meyer (for JPAC Collaboration), M. Mikhasenko (for JPAC Collaboration), E. Mitrofanov (for JPAC Collaboration), D. Miura (for JPAC Collaboration), Y. Miyachi (for JPAC Collaboration), R. Molina (for JPAC Collaboration), A. Moretti (for JPAC Collaboration), A. Nagaytsev (for JPAC Collaboration), D. Neyret (for JPAC Collaboration), M. Niemiec (for JPAC Collaboration), J. Novy (for JPAC Collaboration), W. -D. Nowak (for JPAC Collaboration), G. Nukazuka (for JPAC Collaboration), A. G. Olshevsky (for JPAC Collaboration), M. Ostrick (for JPAC Collaboration), D. Panzieri (for JPAC Collaboration), B. Parsamyan (for JPAC Collaboration), S. Paul (for JPAC Collaboration), H. Pekeler (for JPAC Collaboration), J. -C. Peng (for JPAC Collaboration), M. Pesek (for JPAC Collaboration), D. V. Peshekhonov (for JPAC Collaboration), M. Peskova (for JPAC Collaboration), S. Platchkov (for JPAC Collaboration), J. Pochodzalla (for JPAC Collaboration), V. A. Polyakov (for JPAC Collaboration), C. Quintans (for JPAC Collaboration), G. Reicherz (for JPAC Collaboration), C. Riedl (for JPAC Collaboration), D. I. Ryabchikov (for JPAC Collaboration), A. Rychter (for JPAC Collaboration), A. Rymbekova (for JPAC Collaboration), V. D. Samoylenko (for JPAC Collaboration), A. Sandacz (for JPAC Collaboration), S. Sarkar (for JPAC Collaboration), I. A. Savin (for JPAC Collaboration), G. Sbrizzai (for JPAC Collaboration), H. Schmieden (for JPAC Collaboration), A. Selyunin (for JPAC Collaboration), S. Seriubin (for JPAC Collaboration), L. Sinha (for JPAC Collaboration), D. Spulbeck (for JPAC Collaboration), A. Srnka (for JPAC Collaboration), M. Stolarski (for JPAC Collaboration), M. Sulc (for JPAC Collaboration), H. Suzuki (for JPAC Collaboration), S. Tessaro (for JPAC Collaboration), F. Tessarotto (for JPAC Collaboration), A. Thiel (for JPAC Collaboration), F. Tosello (for JPAC Collaboration), A. Townsend (for JPAC Collaboration), V. Tskhay (for JPAC Collaboration), B. Valinoti (for JPAC Collaboration), B. M. Veit (for JPAC Collaboration), J. F. C. A. Veloso (for JPAC Collaboration), A. Vijayakumar (for JPAC Collaboration), M. Virius (for JPAC Collaboration), M. Wagner (for JPAC Collaboration), S. Wallner (for JPAC Collaboration), K. Zaremba (for JPAC Collaboration), M. Zavertyaev (for JPAC Collaboration), M. Zemko (for JPAC Collaboration), E. Zemlyanichkina (for JPAC Collaboration), M. Ziembicki (for JPAC Collaboration), for the COMPASS Collaboration (for JPAC Collaboration), C. Fernandez-Ramirez (for JPAC Collaboration), M. Mikhasenko (for JPAC Collaboration), L. Bibrzycki (for JPAC Collaboration), G. Foti (for JPAC Collaboration), N. Hammoud (for JPAC Collaboration), V. Mathieu (for JPAC Collaboration), G. Montana (for JPAC Collaboration), R. J. Perry (for JPAC Collaboration), A. Pilloni (for JPAC Collaboration), A. Rodas (for JPAC Collaboration), V. Shastry (for JPAC Collaboration), W. A. Smith (for JPAC Collaboration), A. P. Szczepaniak (for JPAC Collaboration), D. Winney (for JPAC Collaboration)

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe is a giant, invisible LEGO set, but instead of plastic bricks, the pieces are made of pure energy and rules. For decades, physicists have been trying to figure out how these pieces snap together to build the stuff we see around us, like protons and neutrons. They have a rulebook called the "Standard Model," which says that most particles are built from smaller bits called quarks, glued together by a force called the strong interaction. But here's the twist: the rulebook also hints that there might be "exotic" LEGO creations—structures that don't just use the standard bricks but include the glue itself as a building block. These are called "hybrid mesons." Finding them is like finding a secret level in a video game that no one knew existed; it would prove that the "glue" holding the universe together can actually act like a piece of the puzzle itself.

For a long time, scientists have been hunting for these exotic hybrids, mostly by smashing particles together and looking for specific patterns in the debris. They know exactly what to look for: particles with "exotic quantum numbers," which is a fancy way of saying they have a weird combination of properties that a normal quark-and-antiquark pair just can't have. It's like trying to build a red cube out of only blue and yellow blocks; if you see a red cube, you know you must have used a special, hidden ingredient. The big question has been: do these exotic hybrids exist as short-lived particles that pop into existence and vanish, or do they behave differently?

This is where the new paper comes in. A massive international team of scientists, known as the COMPASS Collaboration, decided to look at this problem from a completely different angle. Instead of just looking for the hybrids as things that are created and then break apart, they looked at them as things that are exchanged during a collision. Think of it like a game of catch. Usually, you throw a ball (a particle) from one person to another. But in this experiment, the scientists realized that sometimes, the "throw" itself involves a secret, exotic object passing between the players that isn't a ball at all, but a ghostly wave of force.

The team analyzed data from smashing a beam of negative pions (a type of particle) into a proton target. They were specifically looking at the debris that came out: a mix of an eta meson and a pion. They focused on the high-energy crashes, where the particles fly off at very high speeds. By using a super-precise, un-binned analysis (which means they looked at every single event individually rather than grouping them into buckets), they were able to separate the different ways the particles could interact.

Here is the big discovery: The data showed a clear, undeniable signal of an "exotic Reggeon." In the world of high-energy physics, a "Reggeon" is like a ladder of particles that get heavier and spin faster as you go up the rungs. Most of these ladders are made of "normal" particles. But the scientists found a ladder that is made of "exotic" particles. They identified this exotic ladder with a specific, previously suspected particle called the $\pi_1(1600)$ .

The evidence is incredibly strong. The team calculated that the chance of this signal being a random fluke is less than one in a billion. In scientific terms, they have a significance of $9.9\sigma$ for one type of collision and $5.5\sigma$ for another. To put that in perspective, in science, a "5 sigma" result is the gold standard for claiming a discovery; this team has gone way beyond that.

What does this actually mean? It means that the exotic $\pi_1(1600)$ isn't just a particle that gets made and breaks apart; it is also a fundamental "exchange" that happens when particles collide. It's as if the scientists found that the "glue" holding the universe together doesn't just hold things in place, but can also be thrown back and forth like a baton in a relay race. This confirms that the dynamics of the strong force are even richer and more complex than we thought. The paper explicitly rules out the idea that the data can be explained by just the "normal" exchanges we already knew about; the exotic exchange is absolutely necessary to make the math work.

The researchers are careful to note that while they have found this exotic exchange, they haven't necessarily "solved" the entire mystery of hybrid mesons. Instead, they have opened a new window. They found that this exotic trajectory contributes right alongside the famous "Pomeron" (which is the standard, vacuum-like exchange in these collisions). This discovery suggests that future experiments, like the GlueX experiment, might be able to see even more of these exotic effects, especially in different types of collisions where the normal exchanges are forbidden.

In short, the paper reports the first observation of an exotic Reggeon exchange in high-energy scattering. It proves that the exotic $\pi_1(1600)$ plays a leading role in how particles interact at high speeds, not just as a fleeting resonance, but as a fundamental part of the force that drives the collision. It's a massive step forward in understanding how the "glue" of the universe behaves, confirming that the exotic stuff we've been hunting for is real, and it's right there in the middle of the action.

Technical Summary: First Observation of an Exotic Reggeon

Problem and Motivation
Understanding the hadron spectrum through the degrees of freedom of Quantum Chromodynamics (QCD) is a central objective in non-perturbative strong-interaction physics. While many exotic states beyond the naive quark model have been identified, particularly those involving heavy quarks, candidates involving light quarks remain a focus of investigation. A primary class of such candidates is hybrid mesons—hadrons with explicit gluonic excitations. These are often sought in final states with odd angular momentum, such as $\eta\pi$ and $\eta'\pi$ , which carry exotic quantum numbers ( $J^{PC}$ ) inaccessible to simple quark-antiquark pairs.

Previous high-statistics measurements by the COMPASS collaboration established the existence of structures near 1.4 GeV/ $c^2$ in $\eta\pi^-$ and 1.6 GeV/ $c^2$ in $\eta'\pi^-$ . A coupled-channel analysis by the Joint Physics Analysis Center (JPAC) resolved the nature of these peaks, identifying them as manifestations of a single spin-exotic resonance, the $\pi_1(1600)$ . However, the dynamics of these states at high energies, specifically in the context of Regge theory, had not been fully disentangled. High-energy reactions are typically parametrized by the exchange of Reggeons (trajectories of increasing-spin states). While the Pomeron (vacuum quantum numbers) and ordinary meson trajectories (e.g., $a_2$ , $f_2$ ) are well-established, the existence and role of an exotic Reggeon trajectory in peripheral production processes remained to be experimentally confirmed in this kinematic regime.

Methodology
The paper presents an unbinned, event-by-event analysis of high-statistics COMPASS data from the reaction $\pi^- p \to \eta^{(\prime)}\pi^- p$ . The dataset comprises approximately 270,000 $\eta\pi^-$ events and 85,000 $\eta'\pi^-$ events, covering an invariant mass range up to 6 GeV/ $c^2$ . The analysis focuses on the peripheral production region (small four-momentum transfer to the target proton, $t_p \in [-1, -0.1]$ GeV $^2/c^2$ ) and high-mass region ( $m_{\eta\pi} > 2.4$ GeV/ $c^2$ ), where the double-Regge (DR) exchange mechanism is expected to dominate.

The production amplitude is modeled using the double-Regge formalism, involving a top Reggeon ( $R_t$ ) exchanged between the produced mesons and a bottom Reggeon ( $R_b$ ) exchanged between the proton and the meson system. The model includes:

Leading ordinary exchanges: $a_2 f_2$ , $a_2 P$ , $f_2 f_2$ , $f_2 P$ , $P f_2$ , and $P P$ .
Subleading ordinary exchanges: The $a'_2$ trajectory.
Exotic exchange: The $\pi_1$ trajectory (negative signature, odd spin).

The analysis utilizes an extended negative log-likelihood (ENLL) fit to the event distributions in the Gottfried-Jackson frame. Acceptance effects are corrected using Monte Carlo simulations propagated through the TGEANT framework. The fit parameters include the strength coefficients ( $c_i$ ) for each amplitude and slope parameters ( $b_i$ ) for the form factors at the vertices. The significance of including the exotic $\pi_1$ trajectory is determined by comparing nested models using Wilks' theorem.

Key Contributions and Results
The primary contribution of this work is the first observation of an exotic Reggeon exchange in high-energy scattering. The analysis demonstrates that a model containing only leading ordinary Regge exchanges fails to describe the data, particularly the forward-peak events in the $\eta\pi^-$ channel.

Necessity of Exotic Exchange: When the base model (leading ordinary exchanges) is extended to include the subleading $a'_2$ trajectory, the description of the data improves but remains insufficient. The inclusion of the exotic $\pi_1$ trajectory is required to reproduce the observed forward-backward asymmetry and intensity distributions.
Statistical Significance: The significance of the $\pi_1$ exchange is quantified by comparing the likelihoods of models with and without the $\pi_1$ trajectory. The results show a significance of 9.9 $\sigma$ for the $\eta\pi^-$ channel and 5.5 $\sigma$ for the $\eta'\pi^-$ channel. These significances exceed the standard 5 $\sigma$ threshold for discovery.
Trajectory Identification: The observed exotic exchange is most plausibly identified with the $\pi_1(1600)$ trajectory. The analysis confirms that this trajectory contributes at leading order alongside the Pomeron in the high-mass region.
Bottom Exchange Dynamics: The study also quantifies the contribution of bottom exchanges, finding that while the Pomeron ( $P$ ) dominates, the $f_2$ exchange contributes significantly over a wide angular range, particularly at small $t_p$ .
Asymmetry: The forward-backward asymmetry ( $A(m_{\eta\pi})$ ) is found to be significantly non-zero, providing direct evidence of odd-exotic waves beyond the resonance region. The DR amplitude successfully reproduces this asymmetry, confirming the dominance of the double-Regge mechanism in the selected kinematic region.

Significance
The paper claims that these findings establish the first observation of an exotic Reggeon exchange. This result implies that the dynamics generating exotic waves are richer than previously recognized: hybrid mesons appear not only as produced resonances but also as exchanged trajectories. This provides a complementary window into gluonic excitations in QCD.

The authors note that these findings motivate analogous measurements at the GlueX experiment, where the polarized photon beam and access to $\eta^{(\prime)}\pi^0$ final states could isolate the exotic contribution by forbidding Pomeron exchange. Furthermore, the analysis opens the way for incorporating analyticity constraints in low-energy partial-wave extractions, potentially sharpening the determination of hybrid-meson parameters. The quantification of subdominant exchanges, such as the $f_2$ bottom exchange, is also highlighted as essential for diffractive parton distribution functions and future searches for the Odderon.

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