We investigate the effects of D-instantons on a holographic Weyl semimetal in a top-down approach. We find that the presence of D-instantons induces a novel phase transition from a Weyl semimetal to a gapped phase, providing a new mechanism for gap formation in strongly coupled systems. By analyzing the free energy of probe D7-brane embeddings, we construct the phase diagram in terms of the fermion mass, instanton density, and temperature, measured in units of the Weyl parameter. We show that, in addition to the conventional mass-driven transition associated with band inversion, the instanton density gives rise to a qualitatively different transition whose mechanism cannot be understood within the standard Dirac picture. We compute nonlinear electric conductivities from the regularity condition at the black hole horizon and demonstrate that the two types of transitions exhibit distinct transport behavior. In particular, the instanton-induced transition leads to a gapped phase with properties that differ from the conventional insulating phase. We also discuss possible interpretations of this phase in the boundary theory and comment on its relation to nonperturbative effects in strongly interacting systems.

South Korea

Hwajin Eom

Yunseok Seo

D-instanton effects on the holographic Weyl semimetals

Understanding flux string dynamics can provide insight into quark confinement and hadronization. First-principles quantum and numerical simulations have mostly focused on toy-model Abelian lattice gauge theories (LGTs). With the advent of state-of-the-art quantum simulation experiments, it is timely to study string dynamics in non-Abelian LGTs beyond one spatial dimension. Using tensor network methods, we simulate the real-time string dynamics of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn><mi mathvariant="normal">D</mi></mrow></math> SU(2) Yang-Mills LGT with dynamical matter. In the strong-coupling regime and at resonance, string breaking occurs via a sharp Casimir reduction, along with meson and baryon-antibaryon formation, a distinctively non-Abelian feature. At finite baryon density, we discover a baryon blockade mechanism that delays string breaking. Away from resonance, the magnetic term drives purely non-Abelian fluctuations: glueball-like excitations and self-crossed strings that resolve two SU(2) intertwiners with distinct dynamics. For higher-energy strings, we uncover representation-dependent tension-reduction resonances. Our findings serve as a guide for upcoming quantum simulators of non-Abelian LGTs.

Germany

Giovanni Cataldi

Italy

Simone Orlando

Jad C. Halimeh

Real-Time String Dynamics in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn><mi mathvariant="normal">D</mi></mrow></math> Non-Abelian Lattice Gauge Theory: String Breaking, Glueball Formation, Baryon Blockade, and Tension Reduction

We derive the pertinent chiral potentials for charmed vector meson interactions with light pseudoscalar bosons in a relativistic U(3) chiral effective field theory up to next-to-leading order. Predictions 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>-wave scattering lengths are obtained for all the relevant elastic channels. A comparison with the most recent—and currently the sole—lattice QCD data on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mi>π</mi></math> scattering length at a pion mass of 391 MeV reveals good agreement, thereby validating the estimation of low-energy constants via heavy quark spin symmetry. Within the relativistic formalism, we confirm that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo></math> can be identified with a bound-state pole, while the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>2430</mn><mo stretchy="false">)</mo></math> corresponds to the interplay of two poles: a lower one on the second Riemann sheet and a higher one on the third Riemann sheet. We show that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo></math> and the lower <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>2430</mn><mo stretchy="false">)</mo></math> pole originate from the same flavor SU(3) triplet, whereas the higher <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>2430</mn><mo stretchy="false">)</mo></math> pole belongs to the SU(3) sextet. All these states are not of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>q</mi></math> nature, as they flow to complex infinity in the large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>C</mi></msub></math> limit. Our results provide quantitative benchmarks for future lattice QCD and experimental studies, particularly those using femtoscopy.

China

Ze-Rui Liang

Qi-Chao Xiao

Zhi-Hui Guo

De-Liang Yao

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo></math> and other open-charm <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mo>+</mo></msup></math> states in relativistic chiral effective field theory

We perform a systematic QCD sum rule study of light tetraquark states with <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>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> in the diquark-antidiquark picture. A complete set of local interpolating currents is constructed and projected onto six flavor-isospin configurations (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mo>=</mo><mi>u</mi><mo>/</mo><mi>d</mi></math>): the isoscalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>s</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> sectors, the isovector <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>s</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> sectors, and the isotensor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> sector. From the nonderivative currents studied in the present work, the extracted masses of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>s</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> configurations lie in the ranges 1.53–2.37 GeV, 1.86–2.51 GeV, and 2.46–2.60 GeV, respectively. For the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> vector sector, we also quote the previous derivative-current result <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>2.34</mn><mrow><mo>−</mo><mn>0.30</mn></mrow><mrow><mo>+</mo><mn>0.23</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> as a complementary benchmark. We further compare the present <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> tetraquark spectrum with previous QCD sum rule results for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> tetraquark and hybrid states [N. Su, E.-L. Cui, Y.-W. Jiang, and H.-X. Chen, <a href="http://dx.doi.org/10.1140/epjc/s10052-026-15939-y">Eur. Phys. J. C 86, 724 (2026)</a>.], aiming to provide useful information for distinguishing tetraquark and hybrid configurations in the light hadron spectrum. As an additional improvement, we complete the previously missing isotensor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> tetraquark entry and obtain its lowest mass to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi><mo>=</mo><mn>2.1</mn><msubsup><mn>9</mn><mrow><mo>−</mo><mn>0.24</mn></mrow><mrow><mo>+</mo><mn>0.26</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, which is included in the spectral comparison.

Yi-Wei Jiang

Hua-Xing Chen

Er-Liang Cui

Ding-Kun Lian

Wen-Ying Liu

Niu Su

Light tetraquark states with <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>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> from QCD sum rules

The topological susceptibility of the QCD vacuum provides an understanding of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi></math> vacua as vacua of a Chern-Simons gauge theory. In this way, it gives an immediate proof of the physicality of the boundary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi></math>-term. This makes the essence of the strong-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> puzzle very transparent and offers a solution in form of the gauge axion, which has exact quality. This axion represents an intrinsic part of the QCD gauge redundancy without any reference to an anomalous global symmetry. It is a two-form transforming under the QCD gauge symmetry. Because of its pure-gauge nature, the gauge axion represents a powerful tool to monitor physics of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi></math> vacua in various regimes. Unlike the ordinary Peccei-Quinn axion, which is UV completed into a Goldstone phase of a complex scalar and thereby suffers from the quality problem, the gauge axion is UV completed directly into a fundamental theory of gravity. We study the domain wall and string structure of the gauge axion and show that the strings sourcing it must be a part of this fundamental theory. We thus observe that the absence of the axion quality problem motivates the presence of fundamental strings. This provides a new argument for a connection between the axion and gravity.

Gia Dvali

Lucy Komisel

Otari Sakhelashvili

United States

Anja Wachowitz

Strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> problem and its gauge axion solution as evidence for fundamental strings

New binning schemes for the Dalitz plots of $$D\to {K}_{\text{S}}^{0}{\pi }^{+}{\pi }^{-}$$ and $$D\to {K}_{\text{S}}^{0}{K}^{+}{K}^{-}$$ decays are presented. These are determined using a new figure of merit for optimisation that better represents the sensitivity to $\textit{γ}$ than previous metrics. Further augmentation comes from including consideration of degeneracy with other physics parameters determined simultaneously and a more accurate treatment of relevant backgrounds. The overall expected improvement in the precision of $\textit{γ}$ measurements using $\textit{B}$ → $\textit{DK}$ decays, followed by $$D\to {K}_{\text{S}}^{0}{\pi }^{+}{\pi }^{-}$$ , is estimated at around 5%. In addition, the first dedicated optimisation is performed for the observables relevant to charm mixing, $\textit{x}$ and ∆$\textit{x}$, in $$D\to {K}_{\text{S}}^{0}{\pi }^{+}{\pi }^{-}$$ decays. This procedure accounts for both statistical sensitivity and the migration of events between bins due to detector resolution. The resulting binning scheme leads to an estimated gain of approximately 20% in statistical sensitivity, while maintaining the bias due to bin migration at a level comparable to the currently used scheme.

United Kingdom

M. Bovill

Switzerland

N. Jurik

S. Malde

Optimal binning of $$D\to {K}_{\text{S}}^{0}{\pi }^{+}{\pi }^{-}$$ and $$D\to {K}_{\text{S}}^{0}{K}^{+}{K}^{-}$$ phase space for experimental measurements

Motivated by the observation of numerous charmed-strange hadrons lying close to the $$K^{(*)}\bar{D}^{(*)}$$ and $$K^{(*)}D^{(*)}$$ thresholds, we systematically investigate their mass spectra and electromagnetic characteristics, explicitly incorporating the $\textit{S}$-$\textit{D}$ wave mixing and coupled-channel effects. For the mass spectra, we employ the one-boson-exchange model and obtain several promising $$K^{(*)}\bar{D}^{(*)}$$ and $$K^{(*)}D^{(*)}$$ molecular candidates awaiting future experimental confirmation. The coupled-channel dynamics is found to play an essential role: it not only enhances binding in existing channels but also generates new loosely bound states that are absent in the single-channel approximation. Regarding the electromagnetic characteristics, we discuss the M1 radiative decay widths and magnetic moments of these charmed-strange molecular tetraquarks based on our obtained mass spectra and spatial wave functions within the constituent quark model. Our results demonstrate that the electromagnetic observables serve as valuable discriminants for clarifying the nature of these hadronic molecules. We encourage experimental collaborations to focus on such predicted charmed-strange molecular tetraquark candidates, especially the genuinely exotic $$K^{(*)}\bar{D}^{(*)}$$ states comprising four different flavors with valence quark content $$\bar{c} \bar{s} u d$$ .

Jia-Ning Cui

Fu-Lai Wang

Mass spectra and electromagnetic characteristics of the $$K^{(*)}\bar{D}^{(*)}$$ and $$K^{(*)}{D}^{(*)}$$ molecular tetraquarks from the coupled-channel dynamics

According to the formulation of the charged large $\textit{D}$ membrane paradigm, an arbitrary dynamic black hole solution to a theory of gravity with a U(1) gauge field is dual to the dynamics of a membrane in a non-gravitational background. This membrane is endowed with a stress-energy tensor and a charge current, whose conservation equations govern its dynamics. In this work, we demonstrate that the dynamics of these membrane configurations (at the leading nontrivial order in 1/$\textit{D}$) can be mapped to a relativistic charged fluid, establishing a correspondence for asymptotically flat black holes with a particular class of fluid systems. Unlike the standard AdS/Hydrodynamics correspondence, this dual fluid does not reside on an asymptotic boundary, but is localised strictly on the non-gravitational membrane worldvolume. By evaluating the system in both the Eckart and Landau frames, we systematically extract the out-of-equilibrium transport coefficients. We find that the fluid is governed by a negative effective thermal conductivity and a negative heat capacity. This mechanism provides a hydrodynamic interpretation of thermodynamic stability, effectively translating the previously established quasinormal mode damping of the large-$\textit{D}$ Reissner-Nordström geometry into the language of fluid dynamics.

India

Supratim Halder

Manu Kurian

Mangesh Mandlik

A fluid dual to the charged large $\textit{D}$ membrane paradigm

We consider the photon-energy spectrum of the inclusive radiative decay $\textit{B}$ → $\textit{X}$ $\textit{γ}$, induced by the electromagnetic dipole operator $\textit{O}$ , to next-to-next-to-next-to-leading order and calculate the complete corrections for light fermions, for the contributions with two closed massive fermion loops, and for the limit of large QCD colour factors $\textit{N}$ in the remaining part. We discuss the integrated decay rate both without and with a cut on the photon energy. In addition to the on-shell renormalization of the bottom-quark mass, we also consider the kinetic mass and the MSR mass schemes. The latter two lead to an improved perturbative behaviour of the decay rate.

Matteo Fael

Fabian Lange

Kay Schönwald

Matthias Steinhauser

The photon-energy spectrum in $\textit{B}$ → $\textit{X}$ $\textit{s}$ $\textit{γ}$ to N3LO: light-fermion and large-$\textit{N}$ c corrections

We perform a theoretical study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><mi mathvariant="normal">Λ</mi></math> reactions by looking at the production mechanisms, with special emphasis in the final state interaction of the charmed mesons, which gives rise to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3930</mn><mo stretchy="false">)</mo></math>, coupling strongly to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub></math>, and another state that we call <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3700</mn><mo stretchy="false">)</mo></math>, coupling strongly to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> that qualifies as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> bound state. The combined study of all these reactions shows that the final state interaction responsible for the production of these resonances is more important in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup></math> reaction than in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><mi mathvariant="normal">Λ</mi></math> one. We have taken this into account and shown that normalizing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup></math> mass distributions to the same value at the peak of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math> production, the two mass distributions are quite different in a range of 10 MeV above the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup></math> threshold, with a value about an order of magnitude bigger for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup></math> reaction than for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><mi mathvariant="normal">Λ</mi></math> one. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup></math> mass distribution by itself also shows an enhancement of about one order of magnitude in the presence of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3700</mn><mo stretchy="false">)</mo></math> with respect to a calculation where this resonance is absent. We make a call to measure these magnitudes in the coming LHCb upgrades, which would bring great support to the existence of the bound <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup></math> state.

Xiu-Lei Ren

Hai-Peng Li

Wei-Hong Liang

Chu-Wen Xiao

Spain

Eulogio Oset

Search for signals of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> bound state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3700</mn><mo stretchy="false">)</mo></math> from study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><mi mathvariant="normal">Λ</mi></math> reactions