We continue to explore the previously suggested dual regime of Yang-Baxter (YB) deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math> sigma models, which is a new one-parametric deformation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math> model. It can be obtained from the conventional YB deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo>+</mo><mn>2</mn><mo stretchy="false">)</mo></math> sigma model by freezing two isometries. The scattering matrix in the nondeformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></math> model is known to coincide with the rational <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi mathvariant="fraktur">so</mi></mrow><mi>n</mi></msub></math>-invariant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-matrix. For <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi><mo>=</mo><mn>2</mn><mi>N</mi></math> this rational solution allows for two trigonometric deformations: the usual <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>N</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msubsup></math> and the twisted <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>N</mi><mrow><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></msubsup></math>. The usual one is known to coincide with the scattering matrix of the conventional YB-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math> model. A natural question to ask is what sigma model corresponds to the twisted solution. In this work we claim that it is precisely our dual regime of YB-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math>. We find the corresponding unitarizing function <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>N</mi></msub><mo stretchy="false">(</mo><mi>θ</mi><mo stretchy="false">)</mo></math> explicitly, and, as a bonus, extract some physical properties of this system using the thermodynamic Bethe ansatz technique.

Russia

Alexey Bychkov

Boris Nekrasov

Scattering in the dual regime of Yang-Baxter deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></mrow></math> sigma models

It is believed that the theory of quantum gravity describing our universe is unitary. Nonetheless, if we only have access to a subsystem, its dynamics is described by nonequilibrium physics. Motivated by this, we investigate the planar limit of large $\textit{N}$ ungauged one-matrix quantum mechanics obeying the Lindblad master equation with dissipative jump terms, focusing on the existence, uniqueness, and properties of steady states that signal nonequilibrium phase transitions. In the first class of examples, where potentials are unbounded from below, we study nonequilibrium critical points above which strong dissipation allows for the existence of normalizable steady states that would otherwise not exist. In the second class of examples, termed matrix quantum optics, we find evidence of nonequilibrium phase transitions analogous to those recently reported in the quantum optics literature for driven-dissipative Kerr resonators. Preliminary results on two-matrix quantum mechanics are also presented. We implement bootstrap methods to obtain concrete and rigorous results for the nonequilibrium steady states of matrix quantum mechanics in the planar limit.

United States

Minjae Cho

Nonequilibrium phase transitions in Large $\textit{N}$ matrix quantum mechanics

In this work, we construct the <italic>D</italic>-wave isoscalar <math altimg='si1.svg'><mrow><mi>&#960;</mi><mi>&#960;</mi><mo linebreak='goodbreak'>/</mo><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> coupled-channel Omn&#232;s matrix, formulated to satisfy unitarity, analyticity, and the appropriate asymptotic behavior. We employ a two-channel <italic>K</italic>-matrix model containing poles associated with the <italic>f</italic> <inf>2</inf>(1270) and <math altimg='si7.svg'><mrow><msubsup><mi>f</mi><mrow><mn>2</mn></mrow><mo>&#8242;</mo></msubsup><mrow><mo>(</mo><mn>1525</mn><mo>)</mo></mrow></mrow></math> resonances. The resulting unitary scattering matrix, which reproduces the experimental <italic>&#960;&#960;</italic>&#8239;&#8594;&#8239; <italic>&#960;&#960;</italic> and <math altimg='si27.svg'><mrow><mi>&#960;</mi><mi>&#960;</mi><mo>&#8594;</mo><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> data and PDG information, serves as input to the homogeneous two-channel Muskhelishvili-Omn&#232;s equation. We compare our Omn&#232;s matrix with previous constructions based on <math altimg='si27.svg'><mrow><mi>&#960;</mi><mi>&#960;</mi><mo>&#8594;</mo><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> phases extracted from sums of Breit-Wigner amplitudes. The Omn&#232;s matrix developed here provides a reliable dispersive input for form-factor calculations and resonance studies in the tensor-meson sector. As an application, we show that it enables a simultaneous and accurate description of the BESIII <italic>J</italic>/ <italic>&#968;</italic>&#8239;&#8594;&#8239; <italic>&#960;</italic> 0 <italic>&#960;</italic> 0 <italic>&#947;</italic> and <italic>J</italic>/ <italic>&#968;</italic>&#8239;&#8594;&#8239; <italic>K<inf>S</inf>K<inf>S</inf>&#947;</italic> spectra in the <math altimg='si2.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math> electric-dipole (E1) partial wave.

Germany

Igor Danilkin

Oleksandra Deineka

Spain

Emilie Passemar

Marc Vanderhaeghen

Coupled-channel Omnès matrix for the <italic>D</italic>-wave isoscalar <math altimg='si1.svg'><mrow><mi>&#960;</mi><mi>&#960;</mi><mo linebreak='goodbreak'>/</mo><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> system and its application to <italic>J</italic>/ <italic>&#968;</italic>&#8239;&#8594;&#8239; <italic>&#960;</italic> 0 <italic>&#960;</italic> 0 <italic>&#947;</italic>,&#8201; <italic>K<inf>S</inf>K<inf>S</inf>&#947;</italic>

By means of the zero-curvature equation and two sets of Lenard recursion sequences, we construct a nonisospectral generalized 3 × 3 Ablowitz–Kaup–Newell–Segur (AKNS) integrable hierarchy. The general inhomogeneous Dirac–Manakov equations with temporally and spatially modulated coefficients are derived. Under some special reductions, the two-component nonlinear Schrödinger (NLS) or Manakov equations with helicoidal spin-orbit (SO) coupling, Rabi coupling, and mixed helicoidal SO and Rabi couplings are obtained. In particular, we propose several novel inhomogeneous two-component NLS equations which have variable helicoidal SO and Rabi couplings as well as external potentials. The <italic>N</italic>-fold Darboux-dressing transformation related to the nonisospectral generalized 3&#8239;&#215;&#8239;3 AKNS matrix eigenvalue problem is established, and further the <italic>N</italic>-soliton solution represented in a compact determinant form is given. The classification of solitons for a two-component NLS equations with temporally modulated mixed helicoidal SO and Rabi couplings is discussed in detail. Specifically, three types of solitons including beating, bell-shaped and multi-peak solitons as well as their parabolic, periodic, exponential and kinked deformations, and some unconventional nonlinear superpositions are presented.

China

Jiao Wei

Xin Wang

Yanpei Zhen

Chendi Zhu

Tengjin Zhao

The general integrable inhomogeneous Dirac–Manakov equations: Darboux-dressing transformation and <italic>N</italic>-soliton solutions

We derive a parameter-free geometric constraint on residue phases dictated by the pole-threshold angle. Using the <italic>N</italic>(2190) anomaly as a test case, this constraint reveals a sign ambiguity in prior data; correcting the sign ambiguity yields a phase of <math altimg='si13.svg'><mrow><mo>&#8722;</mo><msup><mn>28</mn><mo>&#8728;</mo></msup><mo>&#177;</mo><msup><mn>10</mn><mo>&#8728;</mo></msup></mrow></math>, matching our prediction. This consistency validates the method as a model-independent diagnostic for distinguishing compact from molecular states, offering a rigorous tool for exotic spectroscopy.

Croatia

S. Ceci

Bosnia and Herzegovina

R. Omerović

H. Osmanović

M. Uroić

United Kingdom

M. Vukšić

B. Zauner

Geometric constraint on residue phases: resolving the <italic>N</italic>(2190) anomaly and implications for exotic states

We investigate low-energy <italic>N&#981;</italic> scattering driven by a pole-enhanced triangle-like diagram, in which the two-Kaon-exchange contribution is promoted by the near-threshold &#923;(1405) pole in the <math altimg='si3.svg'><mrow><mi>N</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> subsystem. Using an unphysical Kaon mass motivated by lattice simulations, we evaluate the <italic>N&#981;</italic> scattering length and find that this mechanism generates an attractive interaction with a magnitude of <math altimg='si7.svg'><mrow><mo>&#8722;</mo><mn>1.1</mn></mrow></math> to <math altimg='si8.svg'><mrow><mo>&#8722;</mo><mn>0.5</mn><mspace width='0.16em' /><mtext>fm</mtext></mrow></math>. Spin-dependent effects are not treated explicitly and are expected to provide subleading corrections in the near-threshold region. We further analyze the low-energy behavior of the triangle-like diagram amplitude and show that the scattering length depends on the parameter <italic>&#948;</italic>, defined as the mass difference between the <math altimg='si9.svg'><mrow><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> threshold and the <italic>&#981;</italic> meson, and the pole position of &#923;(1405), where the &#923;(1405) plays a crucial role to understand <italic>N&#981;</italic> interaction. Furthermore, by employing physical hadron masses, our calculated scattering length is found to be consistent with current experimental data, providing a unified description across both unphysical and physical mass regimes. This type of interaction differs from that associated with van der Waals-type forces or the long-range tail of two-pion exchange, highlighting the role of three-body dynamics encoded in the pole-enhanced triangle-like diagram in shaping the near-threshold <italic>N&#981;</italic> interaction.

Mao-Jun Yan

Chun-Sheng An

Cheng-Rong Deng

Low-energy <italic>N&#981;</italic> scattering from a pole-enhanced triangle diagram

We compute the next-to-leading-power corrections in the $\textit{N}$-jettiness variable to the production of a prompt photon and a jet at next-to-leading order in perturbative QCD in the $$ q\overline{q} $$ annihilation channel. We employ the $\textit{k}$ jet algorithm and assume that the $\textit{N}$-jettiness value divided by the jet transverse momentum is the smallest parameter in the problem; in particular it should be small compared to the jet radius $\textit{R}$.

Prem Agarwal

Kirill Melnikov

Ivan Pedron

Power corrections to the production of a prompt photon in association with a jet in the $\textit{N}$-jettiness slicing scheme at NLO QCD

Motivated by the interpretation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></mrow></math> as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> molecular state, heavy-quark spin symmetry predicts a spin-2 partner, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math>, which can be regarded as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> molecule with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>. Its experimental confirmation, however, remains elusive. In this work, we investigate the production mechanisms of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> in the reactions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>p</mi><mo stretchy="false">→</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msub><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> within an effective Lagrangian framework. The production processes are modeled via <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"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mo>/</mo><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> meson exchanges, while initial-state interactions (ISIs) mediated by Pomeron and Reggeon exchanges are also taken into account. Our calculations indicate that the total cross sections can reach the pb level, suggesting that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> may be accessible at current and future experiments such as AMBER@CERN and LHCb. Inclusion of ISIs enhances the cross sections by nearly 1 order of magnitude. The differential distributions show distinct angular behaviors for the two reactions: the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi></math> reaction exhibits a forward-peaked distribution, whereas the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> reaction shows a dip near central angles. This study provides a quantitative theoretical benchmark for future experimental searches of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> and highlights the importance of ISIs in high-energy particle investigations.

Min Yuan

Bo Nan Zhang

Yin Huang

Search for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> molecular state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions

We revisit type <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>II</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math> limits in the vector multiplet moduli space of compactifications of type IIB string theory on Calabi-Yau threefolds. These limits are special because they cannot be described using mirror symmetry. While we showed in previous work that the gravitational duality sector emerging in such limits corresponds to a weakly coupled heterotic string compactified on K3 times a string-sized torus, our focus here is on the additional field theory sectors that decouple from gravity in these asymptotic regimes. Concretely, we argue that, in the dual heterotic description, these field theory sectors correspond to spacetime-filling NS5-branes wrapping the heterotic torus. The existence of such nonperturbative field theory sectors manifests itself in an exponential dependence of the prepotential on the heterotic dilaton at leading order. Applied to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>-point limits in one-parameter moduli spaces, our results imply that these limits are in perfect agreement with the distance and emergent string conjectures. More precisely, the light tower of states predicted by the distance conjecture arises from excitations of a weakly coupled heterotic string compactified to four dimensions on a background containing spacetime-filling NS5-branes.

Jeroen Monnee

Timo Weigand

Max Wiesner

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math> points and type IIB/heterotic duality with NS5-branes

We define two new indecomposable (not fully reducible) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>8</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>1</mn></math> off-shell multiplets and consider the corresponding models of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>8</mn></math> supersymmetric mechanics with spin variables. Each multiplet is described off shell by a scalar superfield which is a nonlinear deformation of the standard scalar superfield <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi></math> carrying the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>1</mn></math> multiplet (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn mathvariant="bold">1</mn><mo>,</mo><mn mathvariant="bold">8</mn><mo>,</mo><mn mathvariant="bold">7</mn></mrow></math>). Deformed systems involve, as invariant subsets, two different off-shell versions of the irreducible multiplet (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn mathvariant="bold">8</mn><mo>,</mo><mn mathvariant="bold">8</mn><mo>,</mo><mn mathvariant="bold">0</mn></mrow></math>). For both systems we present the manifestly <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>8</mn></math> supersymmetric superfield constraints, as well as the component off- and on-shell invariant actions, which for one version exactly match those given in <a href="http://arXiv.org/abs/2402.00539">arXiv:2402.00539</a>. The two models differ off shell, but prove to be equivalent to each other on shell, with the spin variables sitting in the adjoint representation of the maximal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-symmetry group <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SO</mi></mrow><mo stretchy="false">(</mo><mn>8</mn><mo stretchy="false">)</mo></math>.

JINR

Evgeny Ivanov

Stepan Sidorov

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>8</mn></math> supersymmetric mechanics with spin variables from indecomposable multiplets