arXiv subjects

S. Narison

Publications and source records attributed to S. Narison.

At least 19 recordsLinked to original sources

arXiv2026

Next-to-Leading-Order Calculation of the Light Tensor $(J^P=2^+)$ Hybrid Correlation Function

We report on the QCD calculations underlying a next-to-leading-order (NLO) QCD Laplace sum-rule analysis of the light tensor $(J^P = 2^+)$ hybrid meson mass and coupling. This article focuses on the calculation of the NLO perturbative and leading-log NLO non-perturbative contributions. The diagrammatic renormalization method is employed, and a renormalization-group approach is used to determine the leading-log NLO corrections to condensate contributions, including the dimension-six gluon condensate, whose renormalization we extend to $n_f$ quark flavors. The NLO contributions provide a systematically improved theoretical description of the light tensor hybrid correlation function, leading to more reliable determinations of its mass and coupling. The phenomenological implications of our results are discussed separately in these proceedings.

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arXiv2025

Light scalar quarkonia from QCD Laplace sum rule at higher order

We review our estimations on the light scalar $\bar{q}q$, $(\bar{q}q')(\bar{q'}q)$ and $\overline{qq'}qq'$ ($q,q'\equiv u,d,s$) states from relativistic Laplace sum rule (LSR) within stability criteria and including higher order perturbative (PT) corrections up to the (estimated) N5LO. We evaluate the QCD spectral functions at Lowest Order (LO) of PT QCD and up to the $D=6$ dimension of quark and gluon condensates. Using stability criteria and the constraint: Pole contribution is larger than the QCD continuum one ($R_{P/C}\geqslant 1$) our results exclude an on-shell mass around $(500-600)$ MeV obtained for values of the QCD continuum threshold $t_c \leqslant(1\sim 1.5)$ GeV$^2$. The complete results for the different scalar states are given in Tables 1 to 3. We conclude from the complete analysis that the assignement of the nature of the scalar mesons is not crystal clear and needs further studies.

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arXiv2025

QCD condensates and $\alpha_s$ from $\tau$-decay: Summary

In this talk, I summarize the recent determinations in Ref.[1] of the QCD condensates and $\alpha_s$ within the SVZ expansion using the ratio of Laplace sum rule (LSR) ${\cal R}_{10}^A(\tau)$ and $\tau$-like moments ${\cal R}_{n,A},\, {\cal R}_{n,V-A}$within stability criteria in the axial-vector (A) and V-A channels of the $\tau$- semi-hadronic decays. The factorization of the four-quark condensate is violated by a factor 6 like in the case of the $e^+e^-\to$ Hadrons data. There is no exponential growth of the size of higher dimension condensates which does not favour (by duality) a significant effect of the so-called Duality Violation (DV). The extracted value of $\alpha_s$ is in good agreement with the one from $e^+e^-$ and indicates that the determination at the observed $\tau$-mass is not the optimal one and leads to an overestimate of its actual value.

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arXiv2024

Light scalar quarkonia from Laplace sum rule at NLO

We review our results on light scalar quarkonia ($\bar{q}q$ and four-quark states) from (inverse) QCD Laplace sum rules (LSR) and their ratios ${\cal R}$ within stability criteria and including higher order perturbative (PT) corrections up to the (estimated) ${\mathcal O}(\alpha_{s}^{5})$. As the Operator Product Expansion (OPE) usually converges for $D\leqslant 6-8$, we evaluated the QCD spectral functions at Lowest Order (LO) of PT QCD and up to the $D=6$ dimension vaccum condensates. We request that the optimal results obey the constraint: Pole (Resonance) contribution to the spectral integral is larger than the QCD continuum one which excludes an on-shell mass around $(500-600)$MeV obtained for values of the QCD continuum threshold $t_c\leqslant(1\sim 1.5)$ GeV$^2$. Our results for the different assignments of the scalar mesons are compiled in Tables 1 to 3

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arXiv2024

QCD condensates and $\alpha_s$ from $\tau$-decay

We improve the determinations of the QCD condensates within the SVZ expansion in the axial-vector (A) channel using the ratio of Laplace sum rule (LSR) ${\cal R}_{10}^A(\tau)$ within stability criteria and $\tau$-like higher moments ${R}_{n,A}$ within stability for arbitrary $\tau$-mass squared $s_0$. We find the same violation of the factorization by a factor 6 of the four-quark condensate as from $e^+e^- \to$ Hadrons data. One can notice a systematic alternate sign and no exponential growth of the size of these condensates. Then, we extract $\alpha_s$ from the lowest $\tau$-decay like moment and find: $\alpha_s(M_\tau)\vert_{V-A}=0.3135(83)$ (FO) and 0.3322 (81) (CI) leading to: $\alpha_s(M_Z)\vert_{V-A}=0.1177(10)_{fit}(3)_{evol.}$ (FO) and $0.1200(9)_{fit}(3)_{evol.}$\,(CI). We extend the analysis to the V--A channel and find: $ \alpha_s(M_\tau)\vert_{V-A}=0.3135(83)$ (FO) and 0.3322 (81) (CI) leading to: $\alpha_s(M_Z)\vert_{V-A}=0.1177(10)_{fit}(3)_{evol.}$ (FO) and $0.1200(9)_{fit}(3)_{evol.}$\,(CI). We observe that in different channels ($e^+e^-\to$ Hadrons, \, A,\,V-A), the extraction of $\alpha_s(M_\tau)$ at the observed $\tau$-mass leads to an overestimate of its value. Our determinations from these different channels lead to the mean: $ \alpha_s(M_\tau)=0.3140(44)$ (FO) and 0.3346 (35) (CI) leading to: $\alpha_s(M_Z)=0.1178(6)_{fit}(3)_{evol.}$ (FO) and $0.1202(4)_{fit}(3)_{evol.}$(CI). Comparisons with some other results are done.

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arXiv2023

Fully and Doubly-heavy four-quarks within QCD Laplace sum rule

We present a review of our results for the masses and couplings of the scalar fully heavy four-quarks and $T_{QQ\bar{q}\bar{q}'}\, (J^P=0^\pm , 1^\pm)$ tetraquarks states from QCD Laplace sum rule (LSR), their ratios ${\cal R}$ and double ratio of sum rules (DRSR) within stability criteria and including Factorized Next-to-Leading Order (FNLO) Perturbative (PT) corrections. As the Operator Product Expansion (OPE) usually converges for $d\leqslant 6-8$, we evaluated the QCD spectral functions at Lowest Order of PT QCD and up to $\langle G^3 \rangle$. Our results for the $0^{++}$ fully heavy four-quark states may explain the LHCb broad structure around (6.2-6.7)GeV which can be due to $\overline{\eta_c} \eta_c,~~ \overline{\chi_{c1}}\chi_{c1}$ and $\overline{J/\psi}J/\psi$ molecules or/and their analogue $S_c S_c,~~ A_cA_c$ and $V_cV_c$ tetraquarks. The peak at (6.8-6.9)GeV can be identified to the $\overline{\chi_{c0}}\chi_{c0}$ molecule or/and the $P_c P_c$ tetraquark state. Then, combining ${\cal R}$ and DRSR we focus on the analysis of the four-quark nature of $T_{cc\bar{q}\bar{q}'}$ $1^{\pm}$ and $0^{\pm}$ states. We show that combining ${\cal R}$ and DRSR can provide more precise results: $M_{T^{1^+}_{cc}}=3886(6)$MeV and $M_{T^{0^+}_{cc}}=3883(3)$MeV. From our estimates of the masses of the Pseudoscalar and Vector $T_{cc\bar{q}\bar{q}'}$ states, we observe that the interpolating currents lead to two classes: Class H (Heavy) states with masses around 6GeV and Class L (Light) states around (3.8-4.4)GeV where the pseudoscalar (resp. all vector states) are below the $\overline{D}D_0,~~ overline{D}_s D_{s0}$ (resp. $\overline{D}D_1,~~ \overline{D}_s D_{s1}$) open charm thresholds. Finally, we extend the whole study to the bottom sector and confront our results with the ones from different LSR predictions and some other approaches in the literature.

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arXiv2023

$2^{++}$ Tensor Di-Gluonium from Laplace Sum Rules at NLO

We evaluate the next-to-leading (NLO) corrections to the perturbative (PT) and $< \alpha_s G^2>$ condensate and the LO constant term of the $< G^3 > $ contributions to the $2^{++}$ tensor di-gluonium two-point correlator. Using these results into the inverse Laplace transform sum rules (LSR) moments and their ratio, we estimate the mass and coupling of the lowest ground state. We obtain\,: $M_T=3028(287)$ MeV and the renormalization group invariant (RGI) coupling $\hat f_T=224(33)$ MeV within a vacuum saturation estimate of the $D=8$ dimension gluon condensates ($k_G=1$). We study the effect of $k_G$ on the result and find: $M_T=3188(337)$ MeV and $\hat f_T$=245(32) MeV for $k_G=(3\pm 2)$. Our result does not favour the pure gluonia/glueball nature of the observed $f_2(2010,2300,2340)$ states.

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arXiv2023

Scrutinizing the Light Scalar Quarkonia from LSR at Higher Orders

We scrutinize, improve some determinations of the masses and couplings of light scalar quarkonia ($\bar qq$ and four-quark states) and present new results for the $\pi^+\pi^-,K^+K^-,\dots$ molecules using QCD Laplace Sum Rule (LSR) truncated at the $D=6$ dimension vacuum condensates. We pay a special attention on the higher order perturbative (PT) corrections up to the (estimated) ${\cal O}(\alpha_s^5)$ which improve the quality of the analysis. We request that the optimal results obey the rigorous constraint: {\it Resonance $\geq$ QCD continuum contributions ($R_{P/C}\geq 1$)} in the LSR which excludes a Breit-Wigner / on-shell (not to be confused with a complex pole) scalar meson mass around (500-600) MeV obtained for values [$t_c\leq (1\sim 1.5)$ GeV$^2$] of the QCD continuum threshold. Mass-splittings due to $SU3$ breakings are small. We discuss the different assignements of the observed scalar mesons below 2 GeV in the Conclusions where the $I=0$ states are compared with the scalar gluonia. The results are compiled in Table 3 to 6.

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arXiv2023

Pseudoscalar and Vector $T_{QQ\bar q\bar q'}$ Spectra and Couplings from LSR at NLO

We present systematic and improved estimates of the masses and couplings of the $(0^-)$ and $(1^-)$ $T_{QQ\bar q\bar q'}$ states ($Q= c,b;q,q'= u,d,s$) using QCD Laplace sum rules (LSR) and their ratios R within $\tau$ and $t_c$-stabilities criteria complemented by the (rigorous) condition: $R_{P/C} \equiv$ { Pole (Resonance) over the QCD continuum contributions} $ \geq 1$. NLO factorized perturbative (PT) QCD corrections are included for giving a meaning on the choice of the used running MS heavy quark mass, while the OPE is truncated at the under-controlled $d=6$ dimension condensates. Our results are compiled in Tables 4,7,10,12 and compared with some LO existing ones. We observe that the icurrents lead to two classes : Class H (Heavy) states with masses around 6 (resp. 13) GeV for charm (resp. bottom) channels. Class L (Light) states $T_{cc\bar q\bar q'}(3.8\sim 4.4)$ where the pseudoscalar (resp. all vector states) are below the open charm thresholds and $T_{bb\bar q\bar q'}(\simeq 10.4)$ where all of them are below the open beauty thresholds. Mass-splittings due to SU3 breakings are tiny (< 50 MeV). Though more accessible experimentally, Class L states have weaker couplings to the currents than the Class H ones and may be difficult to observe. The mass-splittings between the 1st radial excitation and the ground state are about 2 GeV which are (almost) heavy flavour and current-type independent while their couplings are large signaling new dynamics of these exotic states. Quark masses behaviours of the masses and couplings based on empirical observation are discussed. The eventual findings of the $T_{cc\bar u\bar d}$(6.3) $0^-$ ground state which may not be obscured by the Class L 1st radial excitations can be an alternative way to test the vacuum saturation violation of the four-quark $d=6$ condensates.

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arXiv2022

1+ XTZ States within QCD Sum Rules

We present improved estimates of the couplings, masses and mass ratios of the $X_Q, Z_Q$ and $T_{QQ\bar q\bar q'}$ states using (inverse) QCD Laplace sum rules (LSR), their ratios ${\cal R}$ and double ratios (DRSR), within stability criteria. We conclude that the observed $X_c(3872)$ and $Z_c(3900)$ are tetramoles states (superposition of quasi-degenerated molecule and tetraquark states having similar couplings to the currents) with the predicted masses: $M_{{\cal T}_{X_c}}=3876(44)$ MeV and $M_{{\cal T}_{Z_c}}=3900(42)$ MeV. We also do an extensive analysis of the four-quark nature of different $T_{QQ\bar q\bar q'}$ axial-vector states. Then, combining ${\cal R}$ and DRSR, we reanalyze the observed state $X_c(3872)$ and we obtain a precise prediction of $M_{T_{cc}^{1^+}}$=3886(6) MeV. Extending to the beauty sector, we find the results: $M_{{\cal T}_{Z_b}}=10579(99)$ MeV and $M_{X_b}=10545(131)$ MeV. Finally, we confront our combined LSR $\oplus$ DRSR results with the ones from some other approaches (lattices and quark models).

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arXiv2022

$0^+$ XTZ states from QCD spectral sum rules

We review our results in\,\cite{ANR22} for the masses and couplings of $T_{ccqq'}\, (J^P=0^+)$ states from (inverse) QCD Laplace sum rule (LSR), their ratios ${\cal R}$ and double ratio of sum rules (DRSR) within stability criteria and including Factorized Next-to-Leading Order (FNLO) Perturbative (PT) corrections and Lowest Order (LO) QCD condensates up to $\langle G^3 \rangle$. We show that combining ${\cal R}$ and DRSR can provide more precise results. Calibrated to the observed $X_c(3872)$ and $T^{1^+}_{cc}(3875)$, ${\cal R}$ combined with DRSR lead to a more precise prediction of $M_{T^{0^+}_{cc}}=3883(3)~\rm{MeV}$. In a similar way, calibrated to the new prediction of $T^{0^+}_{cc}$ ${\cal R} \oplus$DRSR lead to the improved mass predictions: $M_{T^{0^+}_{cc\bar{s}\bar{u}}}=3927(6)~\rm{MeV}$ and $M_{T^{0^+}_{cc\bar{s}\bar{s}}}=3993(11)~\rm{MeV}$. We extend our analysis to the bottom sector and compare our results with the ones from different LSR predictions and some other determinations (lattice, quark and potential models,...) in the literature.

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arXiv2022

Tests of the Z_c-like Laplace Sum Rule (LSR) results using FESR at NLO

In this note, we use local duality Finite Energy Sum Rule (FESR) to test the validity of the Laplace sum rules (LSR) results truncated at the dimension-six condensates for the estimates of the masses and couplings of the Z_c-like ground states in Ref.1 by taking the example of the D^*D molecule configuration. We confirm the existence of an eventual (D^*D)_1 radial excitation with a mass around 5700 MeV and coupling of 197(25) keV to the current which may mask the eventual Z_c(4430) radial excitation candidate (named (D^*D)_0 in Ref.1) having a relatively small coupling f_{(D^*D)_0}=46(56) keV. We add more explanations on the estimates in Ref.1 from LSR and comment the results in Ref.2.

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arXiv2022

Improved XTZ masses and mass ratios from Laplace Sum Rules at NLO

We present improved estimates of the couplings, masses and mass ratios of the Z_Q,X_Q and T_{QQqq} states using QCD Laplace sum rules (LSR), their ratios R and double ratios DRSR within stability criteria, where the NLO factorized PT QCD corrections are included which is important for giving a meaning on the running MS heavy quark mass used in the analysis. We show that combined R and DRSR can provide more precise results. First, we conclude that the observed X_c(3872) and Z_c(3900) are tetramoles states (superposition of quasi-degenerated molecule and a tetraquark states having (almost) the same coupling to the currents) with the predicted masses: M_{T_{X_c}}=3876(44) MeV and M_{ T_{Z_c}}=3900(42) MeV. In the 2nd part, we focus on the analysis of the four-quark nature of different T_{QQqq'} 1^+ and 0^+ states within the 3_c3_c interpolating currents. The final results are summarized in Table 7. Combined R and DRSR calibrated to the observed X_c(3872) lead to a precise prediction of e.g. M_{T_{cc}^{1^+}}=3886(6) MeV. In a similar way, the DRSR for M_{T_{cc}^{0^+}}/M_{T_{cc}^{1^+}} calibrated to M_{T_{cc}^{1^+}} gives M_{T_{cc}^{0^+}}= 3883(3) MeV. The SU3 breaking ratios M_{T_{ccss}^{0^+}}/ M_{T_{cc}^{0^+}} lead to the improved mass predictions: M_{T_{ccss}^{0^+}}=3988(12) MeV. In the 3rd part, the analysis is extended to the beauty mesons, where we find the tetramole masses : M_{ T_{Z_b}}=10579(99) MeV and M_{X_b}=10545(131) MeV. We also observe that the T^{1^+,0^+}_{bbqq'} states are (almost) stable (within the errors) against strong interactions. In the 4th part, we (critically) review and correct some recent LSR estimates of the T^{1^+,0^+}_{QQqq'} masses. Our results from LSR+DRSR are confronted with the ones from some other approaches (lattices and quark models) in Fig. 25.

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arXiv2021

$DK$ and $BK$-like spectra from Laplace sum rule at NLO

Encouraged by the agreement, with the recent LHCb data on the $D^-K^+$ invariant mass from $B \rightarrow D^+D^-K^+$ decay, of our results for the masses of the $0^+$ and $1^-$ open charm $(\bar c\bar d)(u s)$ tetraquarks and molecules states from QCD spectral sum rules within stability criteria, which we review here, we extend our analysis to the $b$-quark channel. We find, in the $0^+$ case the lowest mass $M_{BK}=5195(15)~{\rm MeV}$ with $f_{BK}=8.3(2.4)~{\rm keV}$ and three (almost) degenerate states having respectively the masses $M_{SS}=5702(60)~{\rm MeV}$, $M_{AA}=5661(75)~{\rm MeV}$ and $M_{B^*K^*}=5720(71)~{\rm MeV}$ and couplings $f_{SS}=22.2(2.3)~{\rm keV}$, $f_{AA}=30.1(3.1)~{\rm keV}$ and $f_{B^*K^*}=26.5(2.8)~{\rm keV}$, from which we can associate a scalar tetramole with $M_{\mathcal T_{\mathcal M_0}}=5694(69)~{\rm MeV}~\text{and} ~ f_{\mathcal T_{\mathcal M_0}}=26.5(2.7)~{\rm keV}$. In the spin 1 case, we find four (almost) degenerate states associated with a tetramole having $M_{\mathcal T_{\mathcal M_1}}=5700(81)~{\rm MeV}~\text{and} ~ f_{\mathcal T_{\mathcal M_1}}=16.2(2.6)~{\rm keV}$. For the first radial excitation of the $BK$ molecule, we have $M_{(BK)_1} = 6265(146) ~{\rm MeV}$ and $f_{(BK)_1} = 22.8(3.2) ~{\rm keV}$ . For the remaining states, we associate a scalar and vector tetramoles having respectively $M_{\mathcal (T_{\mathcal M_0})_1}=7439(314)~{\rm MeV}, ~ f_{\mathcal (T_{\mathcal M_0})_1}=74.7(8.4)~{\rm keV}$ and $M_{\mathcal (T_{\mathcal M_1})_1}=7544(345)~{\rm MeV}, ~ f_{\mathcal (T_{\mathcal M_1})_1}=33.0(6.7)~{\rm keV}$.

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arXiv2021

Z_{c,b}-like states from QCD Laplace sum rules at NLO

We review our results on $Z_{c}$-like states[1] which we complete with the ones on $Z_{b}$-like states by using relativistic QCD Laplace Sum Rules (LSR) within stability criteria and including Factorized Next-to-Leading Order (FNLO) Perturbative (PT) corrections and Lowest Order (LO) QCD condensates up to $\langle G^3 \rangle$. We emphasize the importance of PT radiative corrections for heavy quark sum rules in order to justify the use of the running heavy quark mass in the analysis. Our estimates are compiled in Tables 3 and 4. From our results, the observed $Z_{cs}(3983)$ state are good candidate for being ${\mathcal T}_{cs}$ tetramole (superposition of nearly degenerated molecules and tetraquark states having the same quatum numbers $J^{PC}$ and with almost the same couplings to the currents). The $Z_{cs}$ bump around 4100 MeV can be interpreted as a combination of $D^{*}_{0}D_{s1}$ and $D^{*}_{s0}D_{1}$ molecules. The physical states $Z_{cs}(4000)$ and $Z_{cs}(4220)$ found by LHCb are too low to be considered as the first radial excitations of $Z_{cs}(3983)$. For the future $Z_{b}$, $Z_{bs}$ and $Z_{bss}$, we suggest to scan the region around $(10.3 \sim 10.9)$ GeV while the 1st radial excitations are about 2.4 GeV above the ground states.

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arXiv2021

The New Charm-Strange Resonances in the D^- K^+ Channel

We evaluate the masses and decay constants of the $0^+$ and $1^-$ open-charm $(\bar{c}\bar{d})(us)$ tetraquarks and molecular states from QCD spectral sum rules (QSSR) by using QCD Laplace sum rule (LSR). This method takes into account the stability criteria where the factorized perturbative NLO corrections and the contributions of quark and gluon condensates up to dimension-6 in the OPE are included. We confront our results with the $D^- K^+$ invariant mass recently reported by LHCb from $B^+ \to D^+(D^- K^+)$ decays. We expect that the resonance near the $D^- K^+$ threshold can be originated from the $0^{+}(D^-K^+)$ molecule and/or $D^- K^+$ scattering. The $X_0(2900)$ scalar state and the resonance $X_J(3150)$ (if $J = 0$) can emerge from a minimal mixing model, with a tiny mixing angle $θ_0 \simeq (5.2 \pm 1.9)^0$, between a scalar Tetramole $({\cal T}_{\!\!{\cal M}0})$ (superposition of nearly degenerated hypothetical molecules and compact tetraquarks states with the same quantum numbers), having a mass $M_{{\cal T}_{\!\!{\cal M}0}} = 2743(18)$ MeV, and the first radial excitation of the $D^- K^+$ molecule with mass $M_{(DK)_1} = 3678(310)$ MeV. In an analogous way, the $X_1(2900)$ and the $X_J(3350)$ (if $J = 1$) could be a mixture between the vector Tetramole $({\cal T}_{\!\!{\cal M}1})$, with a mass $M_{{\cal T}_{\!\!{\cal M}1}} = 2656(20)$ MeV, and its first radial excitation having a mass $M_{{\cal T}_{\!\!{\cal M}1}} = 4592(141)$ MeV with an angle $θ_0 \simeq (9.1 \pm 0.6)^0$. A (non)-confirmation of these statements requires experimental findings of the quantum numbers of the resonances at $3150$ and $3350$ MeV.

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arXiv2021

Doubly hidden $0^{++}$ molecules and tetraquarks states from QCD at NLO

Motivated by the LHCb-group discovery of exotic hadrons in the range (6.2 $\sim$ 6.9) GeV, we present new results for the masses and couplings of $0^{++}$ fully heavy $(\bar{Q}Q)(Q\bar{Q})$ molecules and $(QQ)(\overline{QQ})$ tetraquaks states from relativistic QCD Laplace Sum Rule (LSR) within stability criteria where Next-to-Leading Order (NLO) Factorized (F) Perturbative (PT) corrections is included. As the Operator Product Expansion (OPE) usually converges for $d\leqslant 6-8$, we evaluated the QCD spectral functions at Lowest Order (LO) of PT QCD and up to $\langle G^3 \rangle$. We also emphasize the importance of PT radiative corrections for heavy quark sum rules in order to justify the use of the running heavy quark mass value in the analysis. We compare our predictions in Table 3 with the ones from ratio of Moments (MOM). The broad structure arround (6.2 $\sim$ 6.9) GeV can be described by the $\overlineη_cη_c$, $\overline{J/ψ}J/ψ$ and $\overlineχ_{c1}χ_{c1}$ molecules or/and $\overline{S}_c S_c$, $\overline{A}_c A_c$ and $\overline{V}_c V_c$ tetraquarks lowest mass ground states. The narrow structure at (6.8 $\sim$ 6.9) GeV if it is a $0^{++}$ state can be a $\overlineχ_{c0}χ_{c0}$ molecules or/and its analogue $\overline{P}_c P_c$ tetraquark. The $\overlineχ_{c1}χ_{c1}$ predicted mass is found to be below the $χ_{c1}χ_{c1}$ threshold while for the beauty states, all of the estimated masses are above the $η_b η_b$ and $Υ(1S)Υ(1S)$ threshold.

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arXiv2021

Z_c -like spectra from QCD Laplace sum rules at NLO

We present a global analysis of the observed Z_c, Z_cs and future Z_css-like spectra using the inverse Laplace transform (LSR) version of QCD spectral sum rules (QSSR) within stability criteria. Integrated compact QCD expressions of the LO spectral functions up to dimension-six condensates are given. Next-to-Leading Order (NLO) factorized perturbative contributions are included. We re-emphasize the importance to include PT radiative corrections (though numerically small) for heavy quark sum rules in order to justify the (ad hoc) definition and value of the heavy quark mass used frequently at LO in the literature. We also demonstrate that, contrary to a na\"ive qualitative 1/N_c counting, the two-meson scattering contributions to the four-quark spectral functions are numerically negligible confirming the reliability of the LSR predictions. Our results are summarized in Tables III to VI. The Z_c(3900) and Z_cs(3983) spectra are well reproduced by the T_c(3900) and T_cs(3973) tetramoles (superposition of quasi-degenerated molecules and tetraquark states having the same quantum numbers and with almost equal couplings to the currents). The Z_c(4025) or Z_c(4040) state can be fitted with the D*_0D_1 molecule having a mass 4023(130) MeV while the Z_cs bump around 4.1 GeV can be likely due to the (D^*_s0D_1+ D^*_0D_s1) molecules. The Z_c(4430) can be a radial excitation of the Z_c(3900) weakly coupled to the current, while all strongly coupled ones are in the region (5634-6527) MeV. The double strange tetramole state T_css which one may identify with the future Z_css is predicted to be at 4064(46) MeV. It is remarkable to notice the regular mass-spliitings of the tetramoles due to SU(3) breakings M_{T_cs}-M_{T_c}= M_{T_css}-M_{T_cs= (73- 91) MeV.

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