arXiv subjects

K. Azizi

Publications and source records attributed to K. Azizi.

At least 163 records · Page 9Linked to original sources

arXiv2020

The Scalar Hexaquark $uuddss$: a Candidate to Dark Matter?

It is conventionally argued that Dark Matter (DM) has a non-baryonic nature, but if we assume that DM was frozen out before primordial nucleosynthesis and could not significantly impact primordial abundances this argument may be evaded. Then a hypothetical $SU(3)$ flavor-singlet, highly symmetric, deeply bound neutral scalar hexaquark $\mathrm{S}=uuddss$, which due to its features has escaped from experimental detection so far, may be considered as a candidate for a baryonic DM. In the present work we calculate the mass and coupling constant of the scalar six-quark particle $\mathrm{S}$ by means of the QCD sum rule method. Our predictions for its mass are $ m_{S}=1180_{-26}^{+40}~\mathrm{MeV}$ ($m_s=95~\mathrm{MeV}$) and $ \widetilde {m}_{S}=1239_{-28}^{+42}~\mathrm{MeV}$ ($m_s=128~\mathrm{MeV}$). Although these values of mass would produce thermally the cosmological DM abundance, existence of this state may contradict to stability of the oxygen nuclei, which requires further thorough analysis.

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arXiv2020

Gravitational form factors of hyperons in light-cone QCD

The quark parts of the gravitational form factors of hyperons are calculated by means of the light-cone QCD sum rule. In the calculations, the distribution amplitudes (DAs) of $Σ$, $Ξ$ and $Λ$ together with the general forms of their interpolating currents as well as the quark part of the energy-momentum tensor current are used. These form factors can provide information on their mass and distributions of the angular momentum, energy and pressure inside the hyperons. It is obtained that the $Q^2$ dependencies of the hyperon gravitational form factors are nicely characterized by a multipole fit function. Using the fits of these form factors, some mechanical properties such as the mechanical radius of the hyperons and the pressure and energy distributions at the center of these particles are obtained. The obtained results can help us in better understanding of the internal structures of these baryons and the QCD as theory of the strong interaction.

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arXiv2020

Heavy exotic scalar meson $T_{bb;\bar{u}\bar{s}}^{-}$

The spectroscopic parameters and decay channels of the scalar tetraquark $ T_{bb;\overline{u}\overline{s}}^{-}$ (in what follows $T_{b:\overline{s} }^{-} $) are investigated. The mass and coupling of the $T_{b:s}^{-}$ are calculated using the two-point sum rules by taking into account quark, gluon and mixed vacuum condensates up to dimension 10. Our result for its mass $m=(10250 \pm 270)~\mathrm{MeV}$ demonstrates that $T_{b:\overline{s}}^{-} $ is stable against the strong and electromagnetic decays. Therefore to find the width and mean lifetime of the $T_{b:\overline{s}}^{-}$, we explore its dominant weak decays generated by the transition $b \to W^{-}c$. These channels embrace the semileptonic decay $T_{b:\overline{s}}^{-} \to Z_{bc;\overline{u}\overline{s}}^{0}l\overline{ ν}_{l}$ and nonleptonic modes $T_{b:\overline{s}}^{-} \to Z_{bc;\overline{ u}\overline{s}}^{0}π^{-}(K^{-}, D^{-}, D_s^{-})$, which at the final state contain the scalar tetraquark $Z_{bc;\overline{u}\overline{s}}^{0}$. Key quantities to compute partial widths of the weak decays are the form factors $G_1(q^2)$ and $G_2(q^2)$: they determine differential rate $dΓ/dq^2$ of the semileptonic and partial widths of the nonleptonic processes, respectively. These form factors are extracted from relevant three-point sum rules at momentum transfers $q^2$ accessible for such analysis. By means of the fit functions $F_{1(2)}(q^2)$ they are extrapolated to cover the whole integration region $m_l^{2}\leq q2\leq(m-\widetilde m)^2$, where $\widetilde m$ is the mass of $Z_{bc;\overline{u}\overline{s}}^{0}$. Predictions for the full width $Γ_{\mathrm{full}}=(15.21\pm 2.59)\times 10^{-10}~\mathrm{ MeV}$ and mean lifetime $4.33_{-0.63}^{+0.89}\times 10^{-13}~\mathrm{s}$ of the $T_{b:s}^{-} $ are useful for experimental and theoretical investigations of this exotic meson.

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arXiv2020

Four-quark exotic mesons

We review our investigations devoted to the analysis of the resonances $ Z_{c}(3900)$, $Z_{c}(4430)$, $Z_{c}(4100)$, $X(4140)$, $X(4274)$, $a_1(1420)$ , $Y(4660)$, $X(2100)$, $X(2239)$ and $Y(2175)$ discovered in various processes by Belle, BaBar, BESIII, D0, CDF, CMS, LHCb and COMPASS collaborations. These resonances are considered as serious candidates to four-quark (tetraquark) exotic mesons. We treat all of them as diquark-antidiquark states with relevant spin-parities, find their masses and couplings, as well as explore their dominant strong decay channels. Calculations are performed in the context of the QCD sum rule method. Thus, the spectroscopic parameters of the tetraquarks are evaluated using the two-point sum rules. For computations of the strong couplings $G_{TM_1M_2}$, corresponding to the vertices $TM_1M_2$ and necessary to find the partial widths of the strong decays $T \to M_1M_2$, we employ either the three-point or full/approximate versions of the QCD light-cone sum rules methods. Obtained results are compared with available experimental data, and with predictions of other theoretical studies.

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arXiv2020

Properties of $Z_c(3900)$ tetraquark in a cold nuclear matter

The study of medium effects on properties of particles embedded in nuclear matter is of great importance for understanding the nature and internal quark-gluon organization as well as exact determination of the quantum numbers, especially of the exotic states. In this context, we study the physical properties of one of the famous charmonium-like states, $Z_c(3900)$, in a cold dense matter. We investigate the possible shifts in the mass and current-meson coupling of the $Z_c(3900)$ state due to the dense medium at saturation density, $ ρ^{sat} $, by means of the in-medium sum rules. We also estimate the vector self-energy of this state at saturation nuclear matter density. We discuss the behavior of the spectroscopic parameters of this state with respect to the density up to a high density corresponding to the core of neutron stars, $ρ\approx 5ρ^{sat}$. Both the mass and current-coupling of this state show nonlinear behavior and decrease with respect to the density of the medium: the mass reaches roughly $30\%$ of its vacuum value at $ ρ=5ρ^{sat} $, while the current-coupling approaches zero at $ ρ\approx2.1ρ^{sat} $, when the central values of the auxiliary and other input parameters are used.

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arXiv2020

$Λ_b(6146)^0$ state newly observed by LHCb

We study the bottom $Λ_b(6146)^0$ baryon, newly discovered by the LHCb Collaboration. By adopting an interpolating current of $(L_ρ, L_λ)=(0,2)$ type and $D$-wave nature with spin-parity quantum numbers $J^P=\frac{3}{2}^+$ for this heavy bottom baryon, we calculate its mass and residue. Using these spectroscopic parameters, we also investigate its dominant decays $Λ_b(6146)^0\rightarrowΣ_bπ$ and $Λ_b(6146)^0\rightarrowΣ^*_bπ$ and estimate the width of $Λ_b(6146)^0$ obtained via these channels. The obtained mass, $m_{Λ_b}=(6144\pm 68)$~MeV is in accord nicely with the experimental data. The width obtained via the dominant channels is also consistent with the experimental data of LHCb collaboration. We calculate the spectroscopic parameters and the same decay channels for the $c$-partner of $Λ_b(6146)^0$ state, namely $Λ_c(2860)^+$, as well. We compare the obtained results with the existing theoretical predictions as well as experimental data. The results indicate that the state $Λ_b(6146)^0$ and its charmed-partner $Λ_c(2860)^+$ can be considered as $1D$-wave baryons with $J^P=\frac{3}{2}^+$.

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arXiv2020

S-Wave Single Heavy Baryons with Spin-3/2 at Finite Temperature

The thermal behavior of the spectroscopic parameters of the S-wave single heavy baryons $ Σ_{Q}^{*}, Ξ_{Q}^{*}$ and $ Ω_{Q}^{*} $ with spin-3/2 are investigated in QCD at finite temperature. We analyze the variations of the mass and residue of these baryons taking into consideration the contributions of QCD thermal condensates up to dimension eight in Wilson expansion. At finite temperature, due to the breakdown of the Lorentz invariance by the choice of reference frame and presence of an extra $O(3)$ symmetry, some new four-dimensional operators come out in the form of the fermionic and gluonic parts of the energy momentum tensor that are taken into account in the calculations. Our analyses show that at lower temperatures, the parameters of baryons under consideration are not affected by the medium. These parameters, however, show rapid variations with respect to temperature at higher temperatures near to a pseudo-critical temperature, after which the baryons are melted. The results of the masses and residues at $ T\rightarrow 0 $ limit are compatible with the available experimental data and predictions of other theoretical studies.

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arXiv2020

Nature of the vector resonance $Y(2175)$

Spectroscopic parameters and decay channels of the vector resonance $Y(2175)$ are studied by considering it as a diquark-antidiquark state with the quark content $su\overline{s}\overline{u}$. The mass and coupling of the tetraquark $Y(2175)$ are calculated using the QCD two-point sum rules by taking into account various quark, gluon and mixed condensates up to dimension 15. Partial widths of its strong decays to $ϕf_{0}(980)$, $ ϕη$, and $ϕη^{\prime}$ are computed as well. To this end, we explore the vertices $Yϕf_{0}(980)$, $Yϕη$, and $Yϕη^{\prime}$, and calculate the corresponding strong couplings by means of the QCD light-cone sum rule method. The coupling $G_{Yϕf}$ of the vertex $Yϕf_{0}(980)$ is found using the full version of this method, and by treating the scalar meson $f_{0}(980)$ as a diquark-antidiquark tetraquark state. The couplings $g_{Yϕη}$ and $g_{Yϕη^{\prime}}$, however, are calculated by applying the soft-meson approximation to the light-cone sum rule method. Prediction for the mass of the resonance $m_{Y} =\left( 2173\pm 85\right)~\mathrm{MeV}$ is in excellent agreement with the data of the BaBar Collaboration \cite{Aubert:2006bu}, and within errors of calculations is compatible with the result reported by BESIII \cite {Ablikim:2014pfc}. The full width $Γ_{\mathrm{full}}=(91.1\pm 20.5)~ \mathrm{MeV}$ of the $Y(2175)$ saturated by its three strong decay channels is in a reasonable agreement with existing experimental data.

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arXiv2020

Gravitational transition form factors of $N(1535) \rightarrow N$

We employ the quark part of the symmetric energy-momentum tensor current to calculate the transition gravitational form factors of the $N(1535) \rightarrow N$ by means of the light cone QCD sum rule formalism. In numerical analysis, we use two different sets of the shape parameters in the distribution amplitudes of the $ N(1535) $ baryon and the general form of the nucleon's interpolating current. It is seen that the momentum squared dependence of the gravitational form factors can be well described by the p-pole fit function. The results obtained by using two sets of parameters are found to be quite different from each other and the $N(1535) \rightarrow N$ transition gravitational form factors depend highly on the shape parameters of the distribution amplitudes of the $N(1535)$ state that parametrize relative orbital angular momentum of the constituent quarks.

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arXiv2020

Nucleon's energy-momentum tensor form factors in light-cone QCD

We use the energy-momentum tensor (EMT) current to compute the EMT form factors of the nucleon in the framework of the light cone QCD sum rule formalism. In the calculations, we employ the most general form of the nucleon's interpolating field and use the distribution amplitudes (DAs) of the nucleon with two sets of the numerical values of the main input parameters entering the expressions of the DAs. The directly obtained results from the sum rules for the form factors are reliable at $ Q^2\geq1~GeV^2 $: To extrapolate the results to include the zero momentum transfer squared with the aim of estimation of the related static physical quantities, we use some fit functions for the form factors. The numerical computations show that the energy-momentum tensor form factors of the nucleon can be well fitted to the multipole fit form. We compare the results obtained for the form factors at $ Q^2=0 $ with the existing theoretical predictions as well as experimental data on the gravitational form factor d$_1^q(0)$. For the form factors M$_2^q (0)$ and J$^q(0)$ a consistency among the theoretical predictions is seen within the errors: Our results are nicely consistent with the Lattice QCD and chiral perturbation theory predictions. However, there are large discrepancies among the theoretical predictions on d$_1^q(0)$. Nevertheless, our prediction is in accord with the JLab data as well as with the results of the Lattice QCD, chiral perturbation theory and KM15-fit. Our fit functions well define most of the JLab data in the interval $ Q^2\in[0,0.4]~GeV^2 $, while the Lattice results suffer from large uncertainties in this region. As a by-product, some mechanical properties of the nucleon like the pressure and energy density at the center of nucleon as well as its mechanical radius are also calculated and their results are compared with other existing theoretical predictions.

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arXiv2019

Light scalar $K_{0}^{*}(700)$ meson in vacuum and a hot medium

The $K_{0}^{*}(700)$ meson appears as the lightest strange scalar meson in PDG. Although there were a lot of experimental and theoretical efforts to establish this particle and determine its properties and nature, it still needs confirmation in an experiment and its internal quark-gluon organization needs to be clarified. In this connection, we study some spectroscopic properties of this state in a hot medium as well as a vacuum by modeling it as a usual meson of a quark and an aniquark. In particular, we investigate its mass and coupling or decay constant in terms of the temperature of a hot medium by including the medium effects by the fermionic and gluonic parts of the energy momentum tensor as well as the temperature-dependent continuum threshold, quark, gluon and mixed condensates. We observe that the mass of $K_{0}^{*}(700)$ remains unchanged up to $T \simeq 0.6 ~ T_c$ with $ T_c $ being the critical temperature, but it starts to diminish after this point and approaches zero near to the critical temperature referring to the melting of the meson. The coupling of $K_{0}^{*}(700)$ is also sensitive to $ T $ at higher temperatures. It starts to grow rapidly after $T \simeq 0.85 ~ T_c$. We turn off the medium effects and calculate the mass and coupling of the $K_{0}^{*}(700)$ state at zero temperature. The obtained mass is in accord with the average Breit-Wigner mass value reported by PDG.

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arXiv2019

Decay modes of the scalar exotic meson $T_{bs;\overline{u}\overline{d}}^{-}$

We investigate the semileptonic decay of the scalar tetraquark $T_{bs; \overline{u}\overline{d}}^{-}$ to final state $T_{cs;\overline{u}\overline{d} }^{0} l \overlineν_l$, which proceeds due to the weak transition $b \to c l \overlineν_l$. For these purposes, we calculate the spectroscopic parameters of the final-state scalar tetraquark $T_{cs;\overline{u}\overline{ d}}^{0}$. In calculations we use the QCD sum rule method by taking into account the quark, gluon, and mixed condensates up to dimension 10. The mass of the $T_{cs;\overline{u}\overline{d}}^{0}$ obtained in the present work $( 2878 \pm 128 )~\mathrm{MeV}$ indicates that it is unstable against the strong interactions, and can decay to the mesons $D^{0}\overline{K}^{0}$ and $D^{+}K^{-}$. Partial widths of these $S$-wave modes as well as the full width of the tetraquark $T_{cs;\overline{u}\overline{d}}^{0}$ are found by means of the QCD light-cone sum rule method and technical tools of the soft-meson approximation. The partial widths of the main semileptonic processes $T_{bs;\overline{u}\overline{d}}^{-} \to T_{cs;\overline{u} \overline{d}}^{0}l\overlineν_l$, $l=e, μ$, and $τ$ are computed by employing the weak form factors $G_{1}(q^2)$ and $G_{2}(q^2)$, which are extracted from the QCD three-point sum rules. We also trace back the weak transformations of the stable tetraquark $T_{bb;\overline{u}\overline{d} }^{-} $ to conventional mesons. The obtained results for the full width $ Γ_{\mathrm{full}}=(3.28\pm 0.60) \times 10^{-10}~\mathrm{MeV} $ and mean lifetime $τ=2.01_{-0.31}^{+0.44}~\mathrm{ps}$ of $T_{bs;\overline{u} \overline{d}}^{-}$, as well as predictions for decay channels of the tetraquark $T_{bb;\overline{u}\overline{d}}^{-}$ can be used in experimental studies of these exotic states. \end{abstract}

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arXiv2019

Effects of a dense medium on parameters of doubly heavy baryons

The spectroscopic properties of the doubly heavy spin-$1/2$ baryons $Ξ_{QQ'}$, $Ξ'_{QQ'}$, $Ω_{QQ'}$ and $Ω'_{QQ'}$, with heavy quarks $Q$ and $Q'$ being $b$ or/and $c$, are investigated in cold nuclear matter. In particular, the behavior of the mass of these particles with respect to the density of the medium in the range $ρ\in [0,1.4] ~ρ_{sat}$, with $ρ_{sat}=0.11^3 ~GeV^3$ being the saturation density of nuclear matter, is investigated. From the shifts in the mass and vector self energy of the states under consideration, it is obtained that $Ξ_{QQ'}$ and $Ξ'_{QQ'}$ baryons with two heavy quarks and one $u$ or $d$ quark are affected by the medium, considerably. It is also seen that the $Ω_{QQ'}$ and $Ω'_{QQ'}$ states, containing two heavy quarks and one $s$ quark do not see the dense medium, at all. The value of mass for the $Ξ_{cc}$ state obtained at $ρ\rightarrow 0$ limit is nicely consistent with the experimental data. Our results on parameters of other members can be useful in the search for these states. The obtained results may also shed light on the future in-medium experiments aiming to search for the behavior of the doubly heavy baryons under extreme conditions.

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arXiv2019

Double-heavy axial-vector tetraquark $T_{bc;\bar{u}\bar{d}}^{0}$

The mass and coupling of the axial-vector tetraquark $T_{bc;\bar{u}\bar{d} }^{0}$ (in a short form $T_{bc}^{0}$) are calculated by means of the QCD two-point sum rule method. In computations we take into account contributions arising from various quark, gluon and mixed vacuum condensates up to dimension 10. The central value of the mass $m=(7105 \pm 155)~\mathrm{ MeV}$ lies below the thresholds for the strong and electromagnetic decays of $T_{bc}^{0}$ state, and hence it transforms to conventional mesons only through the weak decays. In the case of $m=7260~\mathrm{MeV}$ the tetraquark $T_{bc}^{0}$ becomes the strong- and electromagnetic-interaction unstable particle. In the first case, we find the full width and mean lifetime of $ T_{bc}^{0}$ using its dominant semileptonic decays $T_{bc}^{0}\to T_{cc;\bar{ u}\bar{d}}^{+}l\overline{ν}_{l}$ ($l=e,\ μ, τ$), where the final-state tetraquark is a scalar state. We compute also partial widths of the nonleptonic weak decays $T_{bc}^{0}\to T_{cc;\bar{u}\bar{d} }^{+}π^{-}(K^{-}, D^{-}, D_{s}^{-})$, and take into account their effects on the full width of $T_{bc}^{0}$. In the context of the second scenario we calculate partial widths of $S$-wave strong decays $T_{bc}^{0}\to B^{\ast -}D^{+}$ and $T_{bc}^{0}\to \overline{B}^{\ast 0}D^{0}$, and using these channels evaluate the full width of $T_{bc}^{0}$. Predictions for $Γ_{ \mathrm{full}} =(3.98\pm 0.51)\times 10^{-10}~\mathrm{MeV}$ and mean lifetime $τ=1.65_{-0.18}^{+0.25}~\mathrm{ps}$ of $T_{bc}^{0}$ obtained in the context of the first option, as well as the full width $Γ_{\mathrm{ full}}=(63.5\pm 8.9)~\mathrm{MeV}$ extracted in the second scenario may be useful for experimental and theoretical exploration of double-heavy exotic mesons.

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arXiv2019

Semileptonic decays of the scalar tetraquark $Z_{bc;\overline{u} \overline{d}}^{0}$

We study semileptonic decays of the scalar tetraquark $Z_{bc;\overline{u} \overline{d}}^{0}$ to final states $T_{bs;\overline{u}\overline{d} }^{-}e^{+}ν_{e}$ and $T_{bs;\overline{u}\overline{d}}^{-}μ^{+}ν_μ$ , which run through the weak transitions $c\to se^{+}ν_{e}$ and $c\to sμ^{+}ν_μ$, respectively. To this end, we calculate the mass and coupling of the final-state scalar tetraquark $T_{bs;\overline{u}\overline{d} }^{-} $ by means of the QCD two-point sum rule method: these spectroscopic parameters are used in our following investigations. In calculations we take into account the vacuum expectation values of the quark, gluon, and mixed operators up to dimension ten. We use also three-point sum rules to evaluate the weak form factors $G_{i}(q^2)$ ($i=1,~2$) that describe these decays. The sum rule predictions for $G_{i}(q^2)$ are employed to construct fit functions $F_{i}(q^2)$, which allow us to extrapolate the form factors to the whole region of kinematically accessible $q^2$. These functions are required to get partial widths of the semileptonic decays $Γ\left( Z_{bc}^{0}\rightarrow Te^{+}ν_{e}\right) $ and $Γ\left( Z_{bc}^{0}\rightarrow Tμ^{+}ν_{μ}\right)$ by integrating corresponding differential rates. We analyze also the two-body nonleptonic decays $Z_{bc;\overline{u}\overline{d}}^{0} \to T_{bs;\overline{u}\overline{d }}^{-}π^{+}$ and $Z_{bc;\overline{u}\overline{d}}^{0} \to T_{bs;\overline{u }\overline{d}}^{-}K^{+}$, which are necessary to evaluate the full width of the $Z_{bc;\overline{u}\overline{d}}^{0}$. The obtained results for $Γ_{ \mathrm{full}}=(3.18\pm 0.39)\times 10^{-11}~\mathrm{MeV}$ and mean lifetime $20.7_{-2.3}^{+2.9}~\mathrm{ps}$ of the tetraquark $Z_{bc;\overline{u} \overline{d}}^{0}$ can be used in experimental investigations of this exotic state.

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arXiv2019

Light axial-vector and vector resonances $X(2100)$ and $X(2239)$

We study features of the resonances $X(2100)$ and $X(2239)$ by treating them as the axial-vector and vector tetraquarks with the quark content $ss \overline{s}\overline{s}$, respectively. The spectroscopic parameters of these exotic mesons are calculated in the framework of the QCD two-point sum rule method. Obtained prediction for the mass $m=(2067 \pm 84)~\mathrm{MeV}$ of the axial-vector state is in excellent agreement with the mass of the structure $X(2100)$ recently observed by the BESIII Collaboration in the decay $J/ψ\to ϕηη^{\prime}$ as the resonance in the $ϕη^{\prime}$ mass spectrum. We explore also the $S$-wave decays $X(2100) \to ϕη^{\prime}$ and $X(2100) \to ϕη$ using the QCD light-cone sum rule approach and technical methods of the soft-meson approximation. The width of the axial-vector tetraquark, $Γ=(130.2\pm 30.1)~\mathrm{MeV}$, saturated by these two decays is comparable with the measured full width of the resonance $X(2100)$. Our prediction for the vector $ss\overline{s}\overline{s }$ tetraquark's mass $\widetilde{m}=(2283\pm 114)~\mathrm{MeV}$ is consistent with the experimental result $2239.2 \pm 7.1 \pm 11.3~\mathrm{MeV}$ of the BESIII Collaboration for the mass of the resonance $X(2239)$.

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arXiv2019

Lepton flavor universality violation in semileptonic tree level weak transitions

The recent deviations of the experimental data on some parameters of the tree-level semileptonic $B$ and $B_c$ mesons decays from the standard model (SM) predictions indicate considerable violations of the lepton flavor universality, and as a result possible new physics (NP) effects. To better understand the possible NP effects it is necessary to study deeply the physical quantities defining these decays from many aspects. The calculations of the physical quantities require the determinations of the hadronic form factors entering the matrix elements of the considered transitions as the main inputs. We calculate the form factors governing the tree-level $B_c\rightarrow J/ψl ν$ and $B_c \rightarrow η_c l ν$ transitions within the QCD sum rules method. The obtained form factors are used in the calculations of the branching ratios ($BR$s) of the $B_c \rightarrow J/ψl ν$ and $B_c \rightarrow η_cl ν$ transitions as well as $R(J/ψ)$ and $R(η_c)$. Our result on $R(J/ψ)$ supports the present tension between the SM theory prediction and the experimental data. Our result on $R(η_c)$ can be checked in future experiments.

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arXiv2019

Strong decays of double-charmed pseudoscalar and scalar $cc\overline{u}\overline{d}$ tetraquarks

The strong decays of the pseudoscalar and scalar double-charmed tetraquarks $ T_{cc;\overline{u}\overline{d}}^{+}$ and $\widetilde{T}_{cc;\overline{u} \overline{d}}^{+}$ are investigated in the framework of the QCD sum rule method. The mass and coupling of these exotic four-quark mesons are calculated in the framework of the QCD two-point sum rule approach by taking into account vacuum condensates of the quark, gluon, and mixed local operators up to dimension 10. Our results for masses $m_{T}=(4130~\pm 170)~ \mathrm{MeV} $ and $m_{\widetilde{T}}=(3845~\pm 175)~\mathrm{MeV}$ demonstrate that these tetraquarks are strong-interaction unstable resonances and decay to conventional mesons through the channels $T_{cc; \overline{u}\overline{d}}^{+} \to D^{+}D^{\ast }(2007)^{0},~D^{0}D^{\ast }(2010)^{+}$ and $\widetilde{T}_{cc;\overline{u}\overline{d}}^{+}\to D^{+}D^{0}$. Key quantities necessary to compute the partial width of these decay modes, i.e., the strong couplings of two $D$ mesons and a corresponding tetraquark $g_i,~i=1,2$, and $G$ are extracted from the QCD three-point sum rules. The full width $Γ_{T}=(129.9\pm 23.5)~\mathrm{ MeV}$ demonstrates that the tetraquark $T_{cc;\overline{u}\overline{d}}^{+}$ is a broad resonance, whereas the scalar exotic meson with $Γ_{ \widetilde{T}}=(12.4\pm 3.1)~\mathrm{MeV}$ can be classified as a relatively narrow state.

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