arXiv subjects

Halil Mutuk

Publications and source records attributed to Halil Mutuk.

At least 19 recordsLinked to original sources

arXiv2026

Doubly-strange hidden-charm pentaquarks from the Fermi statistics of the light-quark cloud

We extend the baryo-charmonium picture of pentaquarks -- a color-octet $c\bar c$ core bonded to a color-octet light-quark cloud -- to the doubly-strange sector $c\bar c ssq$. The mass splittings are set entirely by the light cloud, so the only new inputs are the strange-strange couplings $J^{ss}$, fixed by a second application of the chromomagnetic scaling, and an additive strange-mass increment taken from the observed $P_c\!\to\!P_{cs}$ shift. We obtain two negative-parity triplets, one produced with a kaon and one with an antiproton, the lowest kaon-associated $\tfrac12^-$ state near $4.60$~GeV and the antiproton-associated triplet some $120$~MeV below. The robust, distinctive prediction is that the upper two kaon-associated states form a near-degenerate doublet, in sharp contrast to the well-separated triplets of the lighter sectors -- a sparse, fixed-spacing pattern that sets the scheme apart from the molecular and diquark alternatives. The internal splittings follow without adjustment from the measured $P_c$ and $P_{cs}$ spectra; the absolute scale relies on the additive strange-mass ansatz, the main assumption of the extrapolation. The predicted masses agree with recent molecular coupled-channel and QCD sum-rule results.

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arXiv2026

The $T_{bc}$ tetraquarks near the $B\bar{D}$ threshold

We study the doubly heavy open-flavor tetraquarks $T_{bc}^{(0)}$ ($J^{P}=0^{+}$) and $T_{bc}^{(1)}$ ($J^{P}=1^{+}$) in the dynamical diquark model, describing the system as a heavy antidiquark--light diquark pair interacting through the lattice-QCD $\Sigma_g^+(1S)$ Born--Oppenheimer potential. Solving the radial Schr\"odinger equation yields $M(T_{bc}^{(0)}) = 7.143$--$7.158$ GeV and $M(T_{bc}^{(1)}) = 7.217$--$7.222$ GeV, with hyperfine splittings of $\Delta_{HF}\simeq 59$--$79$ MeV. The splitting is driven mainly by the mass difference between symmetric and antisymmetric heavy-antidiquark configurations, while the chromomagnetic interaction contributes linearly with $\partial\Delta_{HF}/\partial\kappa_{\bar b\bar c}=2$, consistent with heavy-antidiquark spin algebra. The mean separation, $\langle r\rangle\simeq 0.45$--$0.46$ fm, and inverse radius, $\langle 1/r\rangle^{-1}\simeq 0.33$--$0.34$ fm, exhibit weak parameter dependence and support a compact diquark--antidiquark interpretation. Relative to open-flavor thresholds, the scalar state lies essentially at the $B\bar D$ threshold and may appear either as a weakly decaying bound tetraquark or as a narrow near-threshold resonance. In contrast, the axial-vector state is consistently predicted as an $S$-wave resonance located $23$--$28$ MeV above $B^{*}\bar D$ and about $70$ MeV below $B\bar D^{*}$, implying a line shape strongly influenced by the nearby $B^{*}\bar D$ threshold.

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arXiv2026

Mass spectrum, magnetic moments and Regge trajectories of $\Omega_{ccb}$ and $\Omega_{cbb}$ baryons in the nonrelativistic quark--diquark model

In this work, we investigate the mass spectra, magnetic moments, and Regge trajectories of the triply heavy baryons $\Omega_{ccb}$ and $\Omega_{cbb}$ within a nonrelativistic constituent quark model based on the quark--diquark approximation, which reduces the three-body problem to an effective two-body system. For each baryon, all three possible diquark clusterings are considered, providing a qualitative indication of the sensitivity of the results to the quark--diquark decomposition. The model parameters are fixed by a fit to the measured $B_c$ meson spectrum, thereby anchoring the baryon predictions to experimentally constrained inputs and establishing a consistent link between the heavy meson and baryon sectors. We obtain ground-state masses of approximately $8.0$~GeV for $\Omega_{ccb}$ and $11.0$~GeV for $\Omega_{cbb}$, with radial and orbital excitation patterns in good agreement with the results reported in the literature. The computed magnetic moments of the spin-$\tfrac{1}{2}$ and spin-$\tfrac{3}{2}$ states are consistent with the results of various approaches. A radial Regge analysis in the $(n_r, M^2)$ plane reveals approximately linear $P$-wave trajectories and mildly curved $S$-wave trajectories, with slope and intercept parameters that scale systematically with the heavy-quark content of the baryon. These results suggest that the nonrelativistic quark--diquark framework provides a reliable description of triply heavy baryons and serves as a useful reference for future experimental searches, particularly at LHCb.

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arXiv2026

Magnetic moments of open bottom--charm molecular pentaquark octets

We present a comprehensive theoretical investigation of the magnetic moments of open heavy-flavor molecular pentaquarks with quark compositions $b\bar{c}qqq$ and $c\bar{b}qqq$ (where $q=u,d,s$). Employing a molecular picture in which the pentaquarks are treated as S-wave bound states of a heavy baryon and a meson, we systematically construct the complete spin--flavor wavefunctions for the two distinct SU(3)$_f$ octet representations, $8_{1f}$ and $8_{2f}$, arising from symmetric and antisymmetric light-diquark configurations, respectively. Within the framework of the constituent quark model, we calculate the magnetic moments of spin-parity configurations, $J^P = \frac{1}{2}^-(\frac{1}{2}^+\otimes 0^-)$ and $J^P = \frac{1}{2}^-, \frac{3}{2}^-(\frac{1}{2}^+\otimes 1^-)$, for each member of the $b\bar{c}$ and $c\bar{b}$ octets. Our results reveal a striking hierarchy: in the $8_{2f}$ representation, the $\frac{1}{2}^+\otimes 0^-$ states exhibit near-universal magnetic moments ($\mu \approx -0.062\,\mu_N$ for $b\bar{c}qqq$ and $\mu \approx +0.362\,\mu_N$ for $c\bar{b}qqq$), as a direct consequence of the spin-singlet light-diquark that suppresses light-quark contributions. In contrast, the $8_{1f}$ representation shows a broad spectrum of values with frequent sign changes, reflecting the active role of the symmetric light-diquark. The clear differences between the $b\bar{c}$ and $c\bar{b}$ families demonstrate explicit heavy-quark flavor symmetry breaking in electromagnetic observables. These predictions provide a detailed set of electromagnetic benchmarks that can serve as discriminants for the internal flavor structure and spin configuration of future experimentally observed open heavy-flavor pentaquarks, offering valuable guidance for ongoing and future searches at facilities such as LHCb and Belle II.

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arXiv2026

Bottom-charmed meson states in inverse problem of QCD

We present a comprehensive analysis of the bottom-charmed ($B_c$) meson spectrum within the inverse matrix QCD sum rules formalism. In this framework, conventional QCD sum rules are recast as an inverse problem, allowing for the direct reconstruction of hadronic spectral densities from first principles without invoking phenomenological continuum parametrizations or quark-hadron duality assumptions. We compute the masses and decay constants of conventional $B_c$ mesons with quantum numbers $J^P = 0^-$, $1^-$, $0^+$, and $1^+$. The obtained results are in close agreement with available experimental measurements and are consistent with predictions from various theoretical and phenomenological approaches. The inverse matrix formulation exhibits improved numerical stability and reduced systematic uncertainties relative to standard implementations, highlighting its suitability for precision spectroscopy of heavy quarkonium systems.

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arXiv2025

Exotic $T_{c\bar s0}^a(2900)^0$ and $T_{c\bar s0}^a(2900)^{++}$ states in Born-Oppenheimer approximation

We employ Born-Oppenheimer approximation to the $T_{c\bar s0}^a(2900)^0$ and $T_{c\bar s0}^a(2900)^{++}$ states observed by the LHCb Collaboration and study mass spectrum and root-mean-square radius values. For this purpose, we use dynamical diquark model. We assume that strange quark is a heavy for the usage of Born-Oppenheimer approximation. Our results strongly indicate that the $T_{c\overline{s}0}^{a}(2900)$ states are best described as composed of axial-vector (spin-1) diquark pairs. Furthermore, the calculated root-mean-square radius, $\langle r^{2}\rangle^{1/2} \approx 0.70-0.80$ fm, which is significantly less than 1 fm, provides compelling evidence that these are compact tetraquarks rather than loosely bound hadronic molecules.

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arXiv2025

Mass spectrum and magnetic moments of singly-charmed baryons: a quark-diquark model analysis of $\Omega_{c}(3185)^0$ and $\Omega_c(3327)^0$

Research on singly-heavy baryons, especially those with a charm quark, offers a distinct perspective on the non-perturbative behavior of Quantum Chromodynamics (QCD). In this work, we investigate the recently observed $\Omega_{c}(3185)^{0}$ and $\Omega_{c}(3327)^{0}$ as singly-charmed baryons within the framework of the quark-diquark model. By employing a non-relativistic method with a Cornell-like potential, we systematically determine magnetic moments and mass spectra. Our analysis reveals that the $\Omega_{c}(3185)^{0}$ can be effectively described as a $2S$ state with quantum numbers $J^{P}=\frac{1}{2}^{+}$ or $\frac{3}{2}^{+}$, or alternatively as a $1P$ state with $J^{P}=\frac{1}{2}^{-}$ or $\frac{3}{2}^{-}$, depending on the diquark configuration. Similarly, the $\Omega_{c}(3327)^{0}$ is consistent with a $2S$ configuration. We also investigate their magnetic moments, emphasizing the critical role of diquark correlations in shaping the electromagnetic properties of these states. Our results not only validate existing theoretical models but also offer new insights into the nature of singly-heavy baryons, setting the stage for future experimental and theoretical investigations in heavy baryon spectroscopy. This paper emphasizes the importance of diquark configurations in elucidating the mass spectrum and electromagnetic characteristics of singly-charmed baryons, aiding in the broader effort to decipher QCD intricacies.

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arXiv2025

Reappraisal of rho meson in nuclear matter by inverse QCD sum rules method

We present a comprehensive reappraisal of the in-medium properties of the rho meson using the inverse QCD sum rules (QCDSR) formalism, offering a novel, model-independent approach to studying hadronic modifications in nuclear matter. Unlike conventional QCDSR, which rely on a predefined pole+continuum structure, the inverse method reconstructs the spectral function directly from the operator product expansion (OPE), eliminating assumptions about the spectral ansatz. To the best of our knowledge, this is the first application of the inverse QCDSR method to the rho meson in nuclear matter. Our analysis reveals a significant reduction in the rho meson mass, consistent with previous theoretical predictions, and highlights the crucial role of medium-induced modifications, including condensate suppression and factorization-breaking effects. Furthermore, we assess the sensitivity of our results to the factorization assumption and higher-dimensional condensates, demonstrating the necessity of refining nonperturbative contributions for an accurate description of in-medium hadron properties. Our findings establish the inverse QCDSR method as a robust alternative to conventional spectral analysis techniques, providing a systematically controlled framework for exploring strongly interacting matter under extreme conditions. These results offer important theoretical benchmarks for lattice QCD simulations and heavy-ion collision experiments, shedding light on the restoration of chiral symmetry and the evolution of hadronic matter in dense environments.

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arXiv2024

Revisiting light-flavor diquarks in the inverse matrix method of QCD sum rules

This study reexamines the spectroscopic parameters of light-flavor diquarks within the framework of quantum chromodynamics sum rules (QCDSR) using the inverse matrix method. Conventional QCDSR analyses are based on assumptions such as quark-hadron duality and continuum models, which introduce a degree of systematic uncertainty. The inverse matrix method circumvents these assumptions by reformulating the problem as an inverse integral equation and expanding the unknown spectral density using orthogonal Laguerre polynomials. This method allows for a direct determination of spectral densities, thereby enhancing the precision of predictions regarding resonance masses and decay constants. By employing this methodology with regard to light-flavor diquarks ($sq$ and $ud$), it is possible to extract the associated masses and decay constants. The results indicate that the masses of diquarks with quantum numbers $J^P = 0^+$ and $J^P = 0^-$ are nearly degenerate. We compare our results regarding masses and decay constants with those of other theoretical predictions, which could prove a useful complementary tool in interpretation. Our results are consistent with those in the literature and can be shown as evidence for the consistency of the method. The results achieved in this study highlight the potential of the inverse matrix method as a robust tool for exploring nonperturbative QCD phenomena and elucidating the internal structure of exotic hadronic systems.

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arXiv2024

Magnetic Moments of Hidden-Charm Pentaquarks in the Diquark-Diquark-Antiquark Scheme

The magnetic moment of a hadron is an important spectroscopic parameter that encodes valuable information about its internal structure. In this work, we systematically investigate the magnetic moments of hidden-charm pentaquark states, including the experimentally observed $P_c(4457)$ and related configurations with and without strangeness. The analysis is performed within the diquark-diquark-antiquark framework for spin-parity quantum numbers $J^P = \frac{1}{2}^-$, $\frac{3}{2}^-$, and $\frac{5}{2}^-$. Magnetic moment values are computed for different spin and flavor configurations, and the results are compared with existing predictions in the literature. These predictions may offer insight into the inner structure and quantum numbers of these exotic states, and potentially help distinguish between different theoretical models.

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arXiv2024

Unveiling the Structure of Hidden-Bottom Strange Pentaquarks via Magnetic Moments

Motivated by the discovery of hidden-charm strange pentaquarks, we conduct a systematic study of the magnetic moments of the hidden-bottom strange pentaquarks in molecular picture. We calculate magnetic moments of hidden-bottom strange pentaquarks with strangeness-1 and 2. Magnetic moment gives valuable information about the inner structure and shape of the hadron. The obtained results may be helpful to determine the inner structure of these new yet hypothetical states.

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arXiv2024

Magnetic Moments of Hidden-Bottom Pentaquark States

We study systematically magnetic moments of hiddden-bottom pentaquark states with quantum numbers $J^P=\frac{1}{2}^{\pm}$, $J^P=\frac{3}{2}^{\pm}$, and $J^P=\frac{5}{2}^{\pm}$ with molecular, diquark-diquark-antiquark, and diquark-triquark models. The numerical results show that magnetic moments are different within the same model according to same quantum numbers and spin-orbit couplings. The results are also different when different models are taken into account with the same angular momentum. The magnetic moments encode valuable information about inner structures. We believe that our results may be helpful for experimental studies.

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arXiv2024

Magnetic Moment of $\Xi_b(6227)$ as Molecular Pentaquark State

Motivated by the observation of $\Xi_b(6227)$ state, in this study considering $\Xi_b(6227)$ has a molecular structure, we calculate magnetic moment of this state in quark model. The magnetic moment of a hadron gives valuable information about the internal structure and shape deformations. We observe that orbital excitation of $\Xi_b(6227)$ molecular state change the results of magnetic moment significantly. We also observe that light quarks in $\Xi_b(6227)$ molecular state determine magnetic moment. Measurement of the magnetic moment of $\Xi_b(6227)$ can clarify the nature of this state and be useful to identify the quantum numbers.

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arXiv2024

Doubly-Charged $T_{cc}^{++}$ States in the Dynamical Diquark Model

One of the celebrated tools in explaining the Hydrogen atom is Born-Oppenheimer approximation. The resemblance of $QQ\bar{q}\bar{q}$ tetraquarks to Hydrogen atom within Quantum chromodynamics (QCD) implies usage of Born-Oppenheimer approximation for these multiquark states. In this work, we use dynamical diquark model to calculate mass spectra and sizes of doubly charmed and charged tetraquark states denoted as $T_{cc}^{++}$. Our results for mass spectra indicate some bound state candidates with respect to corresponding two-meson thresholds. Calculation of expectation values of $\sqrt{\langle r^2 \rangle}$ reflects that doubly charmed and charged tetraquark states are compact.

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arXiv2023

Masses and Magnetic Moments of Doubly Heavy Tetraquarks via Diffusion Monte Carlo Method

We present mass spectrum and magnetic moments of the $\bar{n}\bar{n}QQ$ states, where $n=u,d,s$ and $Q=c,b$. We solve four-body Schr\"odinger equation with a quark potential model by using diffusion Monte Carlo (DMC) method. The quark potential is based on the Coulomb, confinement and spin-spin interaction terms. We find mass and magnetic moment of the $T_{cc}^+$ state as $M_{T_{cc}^+}=3892 ~\text{MeV}$ and $\mu=0.28 \mu_N$, respectively. We also find the mass and magnetic moment of $T_{bb}^-$ as $M_{T_{bb}^-}=10338 ~\text{MeV}$ and $\mu=-0.32 \mu_N$, respectively. We find some bound state candidates of doubly heavy tetraquark systems with $I(J^P)=0(1)^+$ $nn \bar b \bar b$, $I(J^P)=0(0)^+$ $nn \bar c \bar b$, $I(J^P)=0(1)^+$ $nn \bar c \bar b$, and $I(J^P)=1/2(1)^+$ $ns \bar b \bar b$. We compare our results with other approaches in the literature.

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arXiv2023

Flavor Exotic Triply-Heavy Tetraquark States in AdS/QCD Potential

We study the $S$-wave mass spectra of flavor exotic triply-heavy tetraquark states $cc\bar{c}\bar{q}$, $cc\bar{b}\bar{q}$, $bb\bar{c}\bar{q}$ and $bb\bar{b}\bar{q}$. We adopt a diquark-antidiquark scheme to solve Schr\"{o}dinger equation. The calculations are carried out in a nonrelativistic quark model with a color interaction described by a potential computed in AdS/QCD. The AdS/QCD potential model consists of a central potential which reflects short distance and large distance behaviour of QCD, spin dependent term for hyperfine splitting and a constant term. We find stable state candidates in the $cc\bar{c}\bar{q}$ sector whereas in the $cc\bar{b}\bar{q}$, $bb\bar{c}\bar{q}$ and $bb\bar{b}\bar{q}$ sectors all the states lie above corresponding $S$-wave meson-meson thresholds. \end{abstract}

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arXiv2022

Molecular Interpretation of $X(3960)$ as $D_s^+ D_s^-$ State

We study $D_s^+ D_s^-$ and $D \bar D$ states assuming that they are hadronic molecules with $J^{PC}=0^{++}$ quantum number. We use two-point QCD sum rule formalism and extract the mass and decay constant values of these states. We take into account contributions of various quark, gluon, and mixed vacuum condensates up to dimension eight. The extracted mass and decay constant values of $D \bar D$ and $D_s^+ D_s^-$ states read as $M_{D \bar D} = 3795^{+85}_{-82} ~\mathrm{MeV} $, $f_{D \bar D} = 1.70^{+0.33}_{-0.29} \times 10^{-2} ~\mathrm{GeV}^5$, and $M_{D_s^+ D_s^-} = 3983^{+93}_{-88} ~\mathrm{MeV}$, $f_{D_s^+ D_s^-} = 2.52^{+0.64}_{-0.54} \times 10^{-2} ~\mathrm{GeV}^5$, respectively. The predicted mass of $D_s^+ D_s^-$ state is in good agreement with the recent LHCb observation and supports quantum number and molecular picture assignments. A possible observation of $D \bar D$ state would help for establishing the lowest four-quark state in charmonium sector.

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arXiv2022

Spectrum of $cc\bar{b}\bar{b}$, $bc\bar{c}\bar{c}$, and $bc\bar{b}\bar{b}$ Tetraquark States in the Dynamical Diquark Model

The dynamical diquark model assumes that exotic hadrons can be formed from colored diquarks. This model asserts a multiquark exotic state composed of a compact diquark $\delta$ and antidiquark $\bar{\delta}$ for a tetraquark interacting through a gluonic field of finite extent. Using Born-Oppenheimer (BO) approximation and BO potential calculated numerically on the lattice, we study mass spectra of $S-$wave $cc\bar{b}\bar{b}$, $bc\bar{c}\bar{c}$, and $bc\bar{b}\bar{b}$ tetraquark systems in the basis of diquark spins. We assume that colour-antitriple diquark and colour-triplet antidiquark form tetraquark state. The predicted mass spectrum for ground state of $cc\bar{b}\bar{b}$ is found to be lower then their corresponding two-meson thresholds. This system may be a candidate for bound state. Masses of $bc\bar{c}\bar{c}$ and $bc\bar{b}\bar{b}$ tetraquark states are found to be above than the corresponding two-meson thresholds.

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