$45-209$ $34-66$ |  $K^{0}\pi^{0}_{u}$ $\pi^{-}K^{+}$ |  $633$ $634$ |  $n\bar{\Lambda}^{0}$ $p\bar{\Sigma}^{-}$ $\Lambda^{0}\bar{\Xi}^{0}$ |  $2056$ $2127$ $2431$ |
Table 25: $T_{d\bar{s}u\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$1378-1547$ $1778-1908$ $2096-2206$ $2369-2466$ $2611-2699$ $2832-2913$ $3036-3112$ $3227-3298$ $3407-3474$ $3577-3641$ $3739-3800$ $3894-3953$ |  $-1.5$-$-1.2$
Table 26: $T_{d\bar{s}u\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$1344-1517$ $1765-1896$ $2096-2206$ $2378-2475$ $2628-2715$ $2855-2935$ $3065-3139$ $3260-3330$ $3444-3511$ $3619-3682$ $3785-3845$ $3944-4001$ |  $-1.4$-$-1.0$

We built its HMRTs in $(n,M^{2})$ and $(J,M^{2})$ (tables LABEL:table:k_3100_J
and LABEL:table:k_3100_n) according to the mesonic case slopes, which are
consistent with LABEL:table:k_3100_J and LABEL:table:k_3100_n. The intercepts
are $a_{J}=-4.22$ and $a_{n}=-3.81$.

Table 27: $K(3100)$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $2686$ |  |  | $1$
|  | $2901$ |  |  | $2$
$K(3100)^{+}$ | $3100$ | $3100$ |  |  | $3$
|  | $3287$ |  |  | $4$
|  | $3463$ |  |  | $5$
Table 28: $K(3100)$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $2669$ |  |  | $1$
|  | $2893$ |  |  | $2$
$K(3100)^{+}$ | $3100$ | $3100$ |  |  | $3$
|  | $3293$ |  |  | $4$
|  | $3476$ |  |  | $5$
|
---|---
$(a)$ |  $(b)$
Figure 33: (a) is $(J,M^{2})$ $K(3100)$ MHRT, (b) $(n,M^{2})$ $K(3100)$ MHRT.
In both cases it is assumed to be a tetraquark due to its decay channel.

####  7.2.5 $T_{c\bar{u}u\bar{s}}$ or $T_{c\bar{d}u\bar{s}}$

For a tetraquarks with the quark content $u\bar{s}\bar{u}s$ or
$d\bar{s}\bar{d}s$ (table LABEL:table:tetra_cand_dscu). The candidate
resonances are presented in table. We generated the predicted HMRTs for this
quark content in tables LABEL:table:Tdscu_j_predictions and
LABEL:table:Tdscu_n_predictions, and the thresholds table
LABEL:table:Tdscu_thresholds includes the predicted width. The HMRTs are also
plotted in 34.

Table 29: $T_{c\bar{u}u\bar{s}}$ or $T_{c\bar{d}u\bar{s}}$ tetraquark candidates. Candidate |  Quarks Content |  Selected Decay Channels |  $J^{PC}$ |  Mass $[MeV]$ |  Width $[MeV]$ |  Ref.
---|---|---|---|---|---|---
$X(2632)$ | $c\bar{u}u\bar{s}$ |  $D^{0}K^{+}$ $D^{+}_{s}\eta$ | $?^{??}$ | $2635.2\pm{3.3}$ | $<17$ | [73]
$T_{cs0}(2900)^{0}$ | $\bar{c}du\bar{s}$ | $D^{-}K^{+}$ | $0^{+}$ | $2866\pm{7}$ | $57\pm{13}$ | [74]
$T_{cs1}(2900)^{0}$ | $\bar{c}d\bar{u}s$ | $D^{-}K^{+}$ | $1^{-}$ | $2904\pm{5}$ | $110\pm{12}$ | [74]
$T^{a}_{c\bar{s}0}(2900)^{0}$ | $c\bar{s}\bar{u}d$ | $D^{+}_{s}\pi^{-}$ | $0^{?}$ | $2892\pm{14}\pm{15}$ | $119\pm{26}\pm{13}$ | [75]
$T^{a}_{c\bar{s}0}(2900)^{++}$ | $c\bar{s}u\bar{d}$ | $D^{+}_{s}\pi^{+}$ | $0^{?}$ | $2921\pm{17}\pm{20}$ | $137\pm{32}\pm{17}$ | [75]
Table 30: $T_{d\bar{c}s\bar{u}}$ thresholds. Thry Width $[MeV]$ |  Mesons Pair |  Meson Threshold $[MeV]$ |  Baryon Anti- baryon |  Baryonic Threshold $[MeV]$ |  Genuine
---|---|---|---|---|---
$98-147$ $29-59$ |  $\pi^{-}D^{-}_{s}$ $D^{-}K^{-}$ |  $2108$ $2364$ |  $\Sigma^{-}\bar{\Lambda}^{-}_{c}$ $\Lambda^{0}\bar{\Sigma}^{--}_{c}$ $\Xi^{-}\bar{\Xi}^{-}_{c}$ |  $3483$ $3570$ $3790$ | $**$

Table 31: $T_{d\bar{c}s\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$2946-3085$ $3252-3374$ $3523-3633$ $3769-3870$ $3996-4091$ $4209-4298$ $4409-4493$ $4599-4679$ $4780-4856$ $4953-5027$ $5120-5191$ $5281-5349$ |  $-2.1$-$-1.6$

Table 32: $T_{d\bar{c}s\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$2628-2791$ $3121-3250$ $3523-3633$ $3872-3970$ $4186-4275$ $4473-4556$ $4740-4818$ $4991-5064$ $5228-5297$ $5453-5519$ $5668-5731$ $5874-5935$ |  $-1.5$-$-1.2$
|
---|---
$(a)$ |  $(b)$
Figure 34: (a) is $(J,M^{2})$ $T_{c\bar{u}u\bar{s}}$ or $T_{c\bar{d}u\bar{s}}$
predicted HMRT, (b) $(n,M^{2})$ $T_{c\bar{u}u\bar{s}}$ or
$T_{c\bar{d}u\bar{s}}$ predicted HMRT.

We can see from tables LABEL:table:Tdscu_j_predictions,
LABEL:table:Tdscu_n_predictions that $X(2632)$ fit the n HMRT, while the other
states are within error range to the J trajectory. The difference between the
actual mass of the states and the predicted one is related to the difference
in quantum numbers and the actual quark content. The HISH model does not
differentiate between $u/d$ in terms of $m$.

In the next section, we analysed and fitted the $T_{cs}$ measured states.

##### 7.2.5.1 $X(2632)$

This state was observed in $X(2632)\rightarrow D^{0}K^{+}$ and
$X(2632)\rightarrow D^{+}_{s}\eta$.

Tables LABEL:table:X_2632_J_HMRT and LABEL:table:X_2632_n_HMRT are the built
HMRT that includes the measured $X(2632)$ and 35 are the plot of these
trajectories. These are consistent with tables LABEL:table:Tdscu_j_predictions
and LABEL:table:Tdscu_n_predictions. The intercept values are $a_{J}=-0.77$
and $a_{n}=-1.23$.

Table 33: $X(2632)$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$X(2632)$ | $2635$ | $2635$ |  |  | $1$
|  | $2988$ |  |  | $2$
|  | $3289$ |  |  | $3$
|  | $3556$ |  |  | $4$
|  | $3799$ |  |  | $5$
Table 34: $X(2632)$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$X(2632)$ | $2635$ | $2635$ |  |  | $0$
|  | $3127$ |  |  | $1$
|  | $3528$ |  |  | $2$
|  | $3876$ |  |  | $3$
|  | $4190$ |  |  | $4$
|
---|---
$(a)$ |  $(b)$
Figure 35: (a) is $(J,M^{2})$ $X(2632)$ MHRT, (b) $(n,M^{2})$ $X(2632)$ MHRT.
In both cases it is assumed to be a tetraquark due to its decay channel.

####  7.2.6 $T_{cs}$ (with quark content ${c\bar{d}s\bar{u}}$)

In [105] the states $T_{cs0}$ and $T_{cs1}$ were observed. Both tetraquarks
candidates have roughly the same mass. This implies that the total quantity
$J+n$ is the same. The decay channel in which these states were observed is
$D^{-}K^{+}$, which is according to the annihilation mechanism. This is
expected, since the string tear threshold for baryonia ($\Xi_{c}p$ pair)
creation is higher at around $3.4GeV$. Both trajectories are built using the
$D_{s}$ slopes as calculated in [7].

##### 7.2.6.1 $T^{0}_{cs0}$ HMRTs

|
---|---
$(a)$ |  $(b)$
Figure 36: (a) is $(J,M^{2})$ $T^{0}_{cs0}$ MHRT, (b) $(n,M^{2})$ $T^{0}_{cs0}$ MHRT by a single point. The trajectory was built with fixed massive endpoints according to the universal fit done for mesons. Table 35: $T_{cs}^{0}$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$T(2900)^{0}_{cs0}$ | $2866$ | $2866$ | $0$ | $1$ | $1$
|  | $3208$ |  |  | $2$
|  | $3501$ |  |  | $3$
|  | $3762$ |  |  | $4$
|  | $4001$ |  |  | $5$
Table 36: $T_{cs}^{0}$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$T(2900)^{0}_{cs0}$ | $2866$ | $2866$ | $0$ | $0$ | $0$
|  | $3343$ |  |  | $1$
|  | $3734$ |  |  | $2$
|  | $4076$ |  |  | $3$
|  | $4384$ |  |  | $4$

The intercept values are $a_{j}=-0.99$ and $a_{n}=-1.38$. The decays widths
are $\Gamma_{tear}\lesssim 127MeV$ and $\Gamma_{annihilation}\approx 5MeV$.
The sum of them is a good approximation for all the states widths except
$T_{cs0}$

##### 7.2.6.2 $T^{0}_{cs1}$ HMRTs

|
---|---
$(a)$ |  $(b)$
Figure 37: (a) is $(J,M^{2})$ $T^{0}_{cs1}$ MHRT, (b) $(n,M^{2})$ $T^{0}_{cs1}$ MHRT by a single point. The trajectory was built with fixed massive endpoints according to the universal fit done for mesons. Table 37: $T_{cs}^{0}$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$T(2900)^{0}_{cs1}$ | $2904$ | $2904$ | $1$ | $0$ | $1$
|  | $3240$ |  |  | $2$
|  | $3529$ |  |  | $3$
|  | $3788$ |  |  | $4$
|  | $4024$ |  |  | $5$
Table 38: $T_{cs}^{0}$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$T(2900)^{0}_{cs1}$ | $2904$ | $2904$ | $1$ | $-1$ | $0$
|  | $3373$ |  |  | $1$
|  | $3760$ |  |  | $2$
|  | $4099$ |  |  | $3$
|  | $4405$ |  |  | $4$

The intercept values are $a_{j}=-1.10$ and $a_{n}=-1.45$. The decays widths
are $\Gamma_{tear}\lesssim 107MeV$ and $\Gamma_{annihilation}\approx 22MeV$.

####  7.2.7 $T_{c\bar{s}}^{a}$ (with quark content ${c\bar{s}d\bar{u}}$ or
${c\bar{s}u\bar{d}}$)

In [106] the states $T^{a^{0}}_{c\bar{s}0}$ and $T^{a^{++}}_{c\bar{s}0}$ were
observed. Both tetraquarks candidates have roughly the same mass. This implies
that the total quantity $J+n$ is the same. All four trajectories in this
section are built using the mesonic universal heavy $n$ or $J$ slopes as
calculated in the appendix 6.5.

##### 7.2.7.1 $T^{a^{0}}_{c\bar{s}0}$

The neutral state was reconstructed in the decay channel $D_{s}^{+}\pi^{-}$.
This is in accordance with the annihilation mechanism, which is expected, due
to the string tear threshold for baryonia ($\Lambda\Lambda_{c}$ pair) creation
which is around $3.4GeV$. The intercept values are $a_{j}=-1.48$ and
$a_{n}=-0.72$.

|
---|---
$(a)$ |  $(b)$
Figure 38: (a) is $(J,M^{2})$ $T^{a^{0}}_{c\bar{s}0}$ MHRT, (b) $(n,M^{2})$ $T^{a^{0}}_{c\bar{s}0}$ MHRT by a single point. The trajectory was built with fixed massive endpoints according to the universal fit done for mesons. Table 39: $T_{c\bar{s}}^{a0}$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$T(2900)^{a0}_{c\bar{s}0}$ | $2892$ | $2892$ | $0$ | $1$ | $1$
|  | $3205$ |  |  | $2$
|  | $3481$ |  |  | $3$
|  | $3731$ |  |  | $4$
|  | $3961$ |  |  | $5$
Table 40: $T_{c\bar{s}}^{a0}$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$T(2900)^{a0}_{c\bar{s}0}$ | $2892$ | $2892$ | $0$ | $1$ | $1$
|  | $3332$ |  |  | $2$
|  | $3704$ |  |  | $3$
|  | $4034$ |  |  | $4$
|  | $4333$ |  |  | $5$

##### 7.2.7.2 $T^{a^{++}}_{c\bar{s}0}$

The positive state was reconstructed in the decay channel $D_{s}^{+}\pi^{+}$.
This is in accordance with the annihilation mechanism, which is expected, due
to the string tear threshold for baryonia ($\Lambda\Lambda_{c}$ pair) creation
which is around $3.4GeV$. The intercept values are $a_{j}=-1.57$ and
$a_{n}=-0.78$.

|
---|---
$(a)$ |  $(b)$
Figure 39: (a) is $(J,M^{2})$ $T^{a^{++}}_{c\bar{s}0}$ MHRT, (b) $(n,M^{2})$ $T^{a^{++}}_{c\bar{s}0}$ MHRT by a single point. The trajectory was built with fixed massive endpoints according to the universal fit done for mesons. Table 41: $T_{c\bar{s}}^{a^{++}}$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$T(2900)^{a++}_{c\bar{s}0}$ | $2921$ | $2921$ | $0$ | $1$ | $1$
|  | $3230$ |  |  | $2$
|  | $3504$ |  |  | $3$
|  | $3751$ |  |  | $4$
|  | $3980$ |  |  | $5$
Table 42: $T_{c\bar{s}}^{a^{++}}$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$T(2900)^{a++}_{c\bar{s}0}$ | $2921$ | $2921$ | $0$ | $1$ | $1$
|  | $3355$ |  |  | $2$
|  | $3725$ |  |  | $3$
|  | $4053$ |  |  | $4$
|  | $4351$ |  |  | $5$

####  7.2.8 $X(3350)$ ($T_{c\bar{d}d\bar{u}}$ or $T_{c\bar{u}u\bar{u}}$)

In [76] and [77] the X(3350) have been observed, both in the decay channel of
$\Lambda_{c}^{+}\bar{p}$. There was another pick observed in the same channel
in [76] at $3.8$GeV222This possible resonance was found in [76] with
statistical significance of $2.8\sigma$, and wasn’t analysed further. We
assumed it exists in order to build the HMRT., but wasn’t observed in [77].
The states analysed in this section are summarized in table
LABEL:table:tetra_Tcddu_cand.

Tables LABEL:table:Tcddu_j_predictions and LABEL:table:Tcddu_n_predictions are
the predicted HMRTs in both planes. The thresholds and predicted width are at
table LABEL:table:Tcddu_thresholds.

Table 43: $T_{u\bar{u}\bar{u}d}$ or $T_{\bar{u}d\bar{d}d}$ exotic candidate. Candidate |  Quarks Content |  Selected Decay Channels |  $J^{PC}$ |  Mass $[MeV]$ |  Width $[MeV]$ |  Ref.
---|---|---|---|---|---|---
$X(3350)$ | $c\bar{d}d\bar{u}$ | $\Lambda_{c}^{+}\bar{p}$ | ${{0}or{1}}^{??}$ | $3350^{+10}_{-20}\pm{20}$ | $70^{+40}_{-30}\pm{40}$ |  [76], [77]
$X(3800)$0 | $c\bar{d}d\bar{u}$ | $\Lambda_{c}^{+}\bar{p}$ | $?^{??}$ | $3840\pm{10}$ | $30\pm{30}$ | [76]
Table 44: $T_{c\bar{d}d\bar{u}}$ thresholds. Thry Width $[MeV]$ |  Mesons Pair |  Meson Threshold $[MeV]$ |  Baryon Anti- baryon |  Baryonic Threshold $[MeV]$ |  Genuine
---|---|---|---|---|---
$79-118$ $30-61$ |  $D^{0}\pi^{0}_{d}$ $D^{+}\pi^{-}$ |  $2000$ $2010$ |  $\Lambda^{+}_{c}\bar{p}$ $\Sigma^{0}_{c}\bar{n}$ $\Xi^{0}_{c}\bar{\Lambda}^{0}$ |  $3224$ $3394$ $3586$ |
Table 45: $T_{c\bar{d}d\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$2634-2779$ $2972-3095$ $3264-3374$ $3526-3626$ $3766-3858$ $3988-4075$ $4197-4278$ $4394-4471$ $4581-4655$ $4760-4831$ $4931-5000$ $5097-5162$ |  $-1.6$-$-1.2$
Table 46: $T_{c\bar{d}d\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$2270-2448$ $2829-2961$ $3264-3374$ $3635-3731$ $3964-4051$ $4263-4344$ $4540-4615$ $4799-4869$ $5042-5109$ $5273-5337$ $5494-5554$ $5705-5763$ |  $-1.2$-$-0.92$

Since $X(3800)$ needs confirmation, we built the HMRTs for the case in which
it exists, and for the case in which we have only one point on the trajectory
($X(3350)$ ). We calculated both $(n,M^{2})$ and $(J,M^{2})$ HMRT. According
to the predicted spectrum (LABEL:table:Tcddu_j_predictions and
LABEL:table:Tcddu_n_predictions), we do expect a state to exist around
$3.8GeV$ on the $(J,M^{2})$ trajectory. Hence, it should have the same
momentum value of $X(3350)$ plus 2.

##### 7.2.8.1 $X(3350)$ $(J,M^{2})$ fit

|
---|---
$(a)$ |  $(b)$
Figure 40: (a) $X(3350)(J,M^{2})$ HMRT. The fit was done with fixed massive
endpoints according to the universal fit for mesons 1. (b) $(J,M^{2})$
$X(3350)$ HMRT best fit is with the fixed masses.

The masses were taken to be $1.33GeV$ and $0.03GeV$ in accordance with the
mesons universal fit, assuming the diquarks/antidiquarks weighing as the sum
of the two quarks in each end. The results of all the fits are summarized at
table LABEL:table:X_3350_J_results. The spectrum of this trajectory can be
found in table [LABEL:table:charm_tetraquarks_predictions] including lower and
higher states.

Since there are only two point on the trajectories, the best ”fit” is the one
that produced the lowest value of $chi^{2}_{r}$ (where the points are on the
trajectory).

Table 47: $X(3350)(J,M^{2})$ output for each fit. $\chi^{2}_{r}$ |  $\chi^{2}_{hish}$ |  $\alpha^{{}^{\prime}}$ |  $a$ |  $m_{1}$ |  $m_{2}$ |  Fit Type
---|---|---|---|---|---|---
0.00 | 0.00 | 0.34 | 0.98 | 1.34 | 0.04 | free fit
8.37 | 0.06 | 0.65 | -1.96 | 1.12 | 0.03 | fixed $m_{1}$, $m_{2}$ and $\alpha^{{}^{\prime}}$
3.56 | 0.03 | 0.65 | 1.00 | 2.07 | 0.01 | fixed $\alpha^{{}^{\prime}}$
0.00 | 0.00 | 0.32 | 0.74 | 1.12 | 0.03 | fixed $m_{1}$ and $m_{2}$

##### 7.2.8.2 $X(3350)$ $(n,M^{2})$ fit

|
---|---
$(a)$ |  $(b)$
Figure 41: (a) $X(3350)(n,M^{2})$ MHRT. The fit was done with fixed massive
endpoints according to the universal fit done for mesons. (b) $(n,M^{2})$
$X(3350)$ MHRT best fit which was the free fit.

The masses were taken to be $1.33GeV$ and $0.03GeV$ with accordance to the
universal fit, assuming the diquarks/antidiquarks weighing the same as the
heavy quark. The spectrum of this trajectory can be found in table
[LABEL:table:X_3350_by_n] including lower and higher states.

Table 48: $X(3350)(n,M^{2})$ output for each fit. $\chi^{2}_{r}$ |  $\chi^{2}_{hish}$ |  $\alpha^{{}^{\prime}}$ |  $a$ |  $m_{1}$ |  $m_{2}$ |  Fit Type
---|---|---|---|---|---|---
0.00 | 0.00 | 0.36 | 0.31 | 1.49 | 0.30 | free fit
2.62 | 0.02 | 0.45 | -1.30 | 1.12 | 0.03 | fixed $m_{1}$, $m_{2}$ and $\alpha^{{}^{\prime}}$
0.00 | 0.00 | 0.45 | 0.88 | 2.11 | 0.09 | fixed $\alpha^{{}^{\prime}}$
0.00 | 0.00 | 0.32 | -0.26 | 1.12 | 0.03 | fixed $m_{1}$ and $m_{2}$
Table 49: $X(3350)(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $2076$ |  |  | $1$
|  | $3008$ |  |  | $2$
$X(3350)$ | $3350$ | $3427$ | $0$ | $3$ | $3$
$X(3800)$ | $3840$ | $3757$ | $1$ | $3$ | $4$
|  | $4040$ |  |  | $5$
|  | $4292$ |  |  | $6$
Table 50: $X(3350)(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $2200$ |  |  | $0$
|  | $2531$ |  |  | $1$
$X(3350)$ | $3350$ | $3350$ | $0$ | $2$ | $2$
$X(3800)$ | $3840$ | $3840$ | $0$ | $3$ | $3$
|  | $4233$ |  |  | $4$
|  | $4573$ |  |  | $5$

##### 7.2.8.3 $X(3350)$ spectrum by one point

Since the second state ($X(3800)$) wasn’t observed in another experiment, we
also calculated the trajectories with a single point shown in the next figure.
The intercept values are $a_{j}=-1.54$ and $a_{n}=-1.14$.

|
---|---
$(a)$ |  $(b)$
Figure 42: (a) is $(J,M^{2})$ $X(3350)$ MHRT, (b) $(n,M^{2})$ $X(3350)$ MHRT by a single point. In both cases it is assumed to be a tetraquark due to its decay channel. Table 51: $X(3350)$ $(J,M^{2})$ HMRT by ignoring the $X(3800)$ state. The slope used is the $\alpha^{{}^{\prime}}$ value for heavy mesons for $J$ excitation trajectory. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $2748$ |  |  | $1$
|  | $3069$ |  |  | $2$
$X(3350)$ | $3350$ | $3350$ |  |  | $3$
|  | $3604$ |  |  | $4$
|  | $3838$ |  |  | $5$
Table 52: $X(3350)$ $(n,M^{2})$ HMRT by ignoring the $X(3800)$ state. The slope used is the $\alpha^{{}^{\prime}}$ value for heavy mesons for $n$ excitations trajectory. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $2410$ |  |  | $0$
|  | $2932$ |  |  | $1$
$X(3350)$ | $3350$ | $3350$ |  |  | $2$
|  | $3710$ |  |  | $3$
|  | $4032$ |  |  | $4$

The decay width is estimated to be $\Gamma_{tear}\lesssim 45MeV$. The ratio
is:

$\displaystyle\frac{\Gamma_{annihilation}}{\Gamma[\Psi(2710)]}$
$\displaystyle=\frac{exp(-\frac{TL^{2}}{2}|_{X(3350)})}{exp(-\frac{TL^{2}}{2}|_{X(2710)})}\approx{0.41}$
(58)

Based on the predicted state which is lower than the string-tear threshold,
this might be the higher state of $D^{*}(2760)$, also according to its decay
channel ($D^{+}\pi^{-}$). By taking the width of this state, we can estimate
the width of the X(3350):

$\displaystyle\Gamma_{annihilation}\lesssim 73MeV$ (59)

####  7.2.9 $T_{c\bar{d}c\bar{u}}$

For a tetraquarks with the quark content $T_{c\bar{d}c\bar{u}}$ (table
LABEL:table:tetra_cand_ccdu). The candidate resonance are presented in table
LABEL:table:tetra_cand_ccdu. We generated the predicted HMRTs for this quark
content in tables LABEL:table:Tccdu_j_predictions and
LABEL:table:Tccdu_n_predictions, and the thresholds table
LABEL:table:Tccdu_thresholds includes the predicted width. The HMRTs are also
plotted in 43.

Table 53: $T_{c\bar{d}c\bar{u}}$ tetraquark candidates. Candidate |  Quarks Content |  Selected Decay Channels |  $J^{PC}$ |  Mass $[MeV]$ |  Width $[MeV]$ |  Ref.
---|---|---|---|---|---|---
$T_{cc}(3875)$ | $cc\bar{u}\bar{d}$ |  $D^{*+}D^{0}$ $D^{*0}D^{+}$ | $?^{?}$ | $3874\pm{0.11}$ | $0.41\pm{0.17}$ | [78]
Table 54: $T_{c\bar{d}c\bar{u}}$ thresholds. Thry Width $[MeV]$ |  Mesons Pair |  Meson Threshold $[MeV]$ |  Baryon Anti- baryon |  Baryonic Threshold $[MeV]$ |  Genuine
---|---|---|---|---|---
|  $D^{+}D^{0}$ $D^{0}D^{+}$ |  $3735$ $3735$ |  $\Xi^{+}_{cc}\bar{n}$ $\Xi^{++}_{cc}\bar{p}$ $\Omega^{+}_{cc}\bar{\Lambda}^{0}$ |  $4459$ $4560$ | $**$
Table 55: $T_{c\bar{d}c\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$3983-4118$ $4255-4375$ $4499-4609$ $4723-4825$ $4932-5027$ $5128-5218$ $5313-5399$ $5490-5572$ $5659-5738$ $5822-5898$ $5978-6052$ $6130-6201$ |  $-3.7$-$-3.3$
Table 56: $T_{c\bar{d}c\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$4499-4609$ $4818-4917$ $5107-5198$ $5373-5458$ $5622-5702$ $5857-5932$ $6080-6151$ $6292-6361$ $6496-6561$ $6691-6755$ $6880-6941$ $7062-7122$ |  $-3.0$-$-2.6$
|
---|---
$(a)$ |  $(b)$
Figure 43: (a) is $(J,M^{2})$ $T_{c\bar{d}c\bar{u}}$ predicted HMRT, (b)
$(n,M^{2})$ $T_{c\bar{d}c\bar{u}}$ predicted HMRT.

In [107] the state $T^{+}_{cc}$ was observed. It was also analysed in [108].
It was reconstructed in the decay channel $D^{0}D^{0}\pi^{+}$ in accordance
with the annihilation mechanism. This is expected since the string tear
threshold for baryonia ($\Xi_{cc}^{+}p$ pair) creation is around $4.56GeV$.
The trajectories are built using the mesons heavy slopes as calculated at 6.5.
The intercepts values are $a_{j}=-2.89$ and $a_{n}=-2.00$

|
---|---
$(a)$ |  $(b)$
Figure 44: (a) is $(J,M^{2})$ $T^{+}_{cc}$ MHRT, (b) $(n,M^{2})$ $T^{+}_{cc}$ MHRT by a single point. The trajectory was built with fixed massive endpoints according to the universal fit done for mesons. Table 57: $T_{cc}^{+}$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$T(3875)^{+}_{cc0}$ | $3870$ | $3870$ | $0$ | $0$ | $0$
|  | $4155$ |  |  | $1$
|  | $4409$ |  |  | $2$
|  | $4640$ |  |  | $3$
|  | $4854$ |  |  | $4$
Table 58: $T_{cc}^{+}$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$T(3875)^{+}_{cc0}$ | $3870$ | $3870$ | $0$ | $0$ | $0$
|  | $4271$ |  |  | $1$
|  | $4615$ |  |  | $2$
|  | $4922$ |  |  | $3$
|  | $5203$ |  |  | $4$

The interesting thing about this state is its width, which is very narrow
(LABEL:table:Tccdu_thresholds), meaning it is stable. The HISH annihilation
decay mechanism suggests that the BV and anti-BV will annihilate in a certain
probability, that is dependant on the length of the horizontal string ([13]).
In the case of $X(4630)/\psi(4660)$ and $X(6900)$ ([10] and [24]) it proved to
be a good approximation to rely on the same $P_{annihilation}$ value for both
states. In the case of $T_{cc}$, it seems the probability is much lower,
despite the length of the string being similar. The conditions in which the
annihilation can occur is still an open question. One possible explanation is
that the asymmetry between the diquark and antidiquark affects the location of
the vertices on the holographic space on the $u$ direction, which reduces the
annihilation probability. Anyhow, this requires more research.

####  7.2.10 $T_{c\bar{c}u\bar{d}}$ or $T_{c\bar{c}d\bar{u}}$

For a tetraquark with the quark content $T_{c\bar{c}u\bar{d}}$ or
$T_{c\bar{c}d\bar{u}}$ (table LABEL:table:tetra_cand_cucd). The candidate
resonances are presented in table LABEL:table:tetra_cand_cucd. We generated
the predicted HMRTs for this quark content in tables
LABEL:table:Tcucd_j_predictions and LABEL:table:Tcucd_n_predictions, and the
thresholds table LABEL:table:Tcucd_thresholds includes the predicted width.
The HMRTs are also plotted in 45.

Table 59: $T_{c\bar{c}u\bar{d}}$ or $T_{c\bar{c}d\bar{u}}$ tetraquark candidates. Candidate |  Quarks Content |  Selected Decay Channels |  $J^{PC}$ |  Mass $[MeV]$ |  Width $[MeV]$ |  Ref.
---|---|---|---|---|---|---
$Z_{c}(3900)$ |  $c\bar{c}u\bar{d}$ $c\bar{c}d\bar{u}$ |  $J/\psi\pi^{\pm}$ ${D\bar{D^{*}}}^{\pm}$ | $1^{+-}$ | $3887.1\pm 2.6$ | $28.4\pm 2.6$ |  Many, including [79]
$Z_{c}(4200)^{\pm}$ |  $c\bar{c}u\bar{d}$ or $c\bar{c}d\bar{u}$ |  $J/\psi\pi^{+}$ |  $1^{+-}$0 | $4196^{+35}_{-32}$ | $370^{+100}_{-150}$ |  [80]
$Z_{c}(4430)^{\pm}$ |  $c\bar{c}u\bar{d}$ or $c\bar{c}d\bar{u}$ |  $\pi^{+}\psi(2S)$ $\pi^{+}J/\psi$ |  $1^{+-}$0 | $4478^{+15}_{-18}$ | $181\pm 31$ |  [81], [82], [83], [84]
$X(4020)^{\pm}$ |  $c\bar{c}u\bar{d}$ or $c\bar{c}d\bar{u}$ |  $D^{*}\bar{D}^{*}$ $h_{c}(1P)\pi^{\pm}$ | $?^{?-}$ | $4024.1\pm{1.9}$ | $13\pm 5$ |  [85], [86] [87], [87]
$X(4051)^{\pm}$ |  $c\bar{c}u\bar{d}$ or $c\bar{c}d\bar{u}$ |  $\pi^{+}\chi_{c1}(1P)$ | $?^{?+}$ | $4051^{+24}_{-40}$ | $82^{+50}_{-28}$ |  [88]
$X(4055)^{\pm}$ |  $c\bar{c}u\bar{d}$ or $c\bar{c}d\bar{u}$ |  $\pi^{+}\psi(2S)$ | $?^{?-}$ | $4054\pm 3.2$ | $45\pm 13$ |  [89], [90] [91]
$X(4100)^{\pm}$ |  $c\bar{c}u\bar{d}$ or $c\bar{c}d\bar{u}$ |  $\pi^{-}\eta(1S)$ | $?^{??}$ | $4096\pm 28$ | $152^{+80}_{-70}$ |  [92]
$R_{c0}(4240)^{\pm}$ |  $c\bar{c}u\bar{d}$ or $c\bar{c}d\bar{u}$ |  $\pi^{-}\psi(2S)$ | $0^{--}$ | $4239^{+50}_{-21}$ | $220^{+120}_{-90}$ |  [93]
$X(4250)^{\pm}$ |  $c\bar{c}u\bar{d}$ or $c\bar{c}d\bar{u}$ |  $\pi^{+}\chi(1P)$ |  $?^{?-}$0 | $4248^{+190}_{-50}$ | $177^{+320}_{-70}$ |  [88]
Table 60: $T_{c\bar{c}u\bar{d}}$ thresholds. Thry Width $[MeV]$ |  Mesons Pair |  Meson Threshold $[MeV]$ |  Baryon Anti- baryon |  Baryonic Threshold $[MeV]$ |  Genuine
---|---|---|---|---|---
$11-31$ $34-67$ |  $\eta_{c}(1S)\pi^{+}$ $D^{+}\bar{D}^{0}$ |  $3124$ $3735$ |  $\Sigma^{++}_{c}\bar{\Lambda}^{-}_{c}$ $\Lambda^{+}_{c}\bar{\Sigma}^{0}_{c}$ $\Xi^{+}_{c}\bar{\Xi}^{0}_{c}$ |  $4740$ $4740$ $4938$ | $*$
Table 61: $T_{c\bar{c}u\bar{d}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$4373-4497$ $4583-4699$ $4780-4890$ $4967-5072$ $5145-5245$ $5316-5412$ $5480-5572$ $5638-5727$ $5790-5877$ $5938-6023$ $6082-6164$ $6222-6301$ |  $-2.6$-$-2.0$
Table 62: $T_{c\bar{c}u\bar{d}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$4174-4306$ $4491-4611$ $4780-4890$ $5047-5150$ $5297-5394$ $5533-5625$ $5757-5844$ $5971-6054$ $6176-6256$ $6373-6450$ $6563-6638$ $6747-6819$ |  $-2.0$-$-1.6$
|
---|---
$(a)$ |  $(b)$
Figure 45: (a) is $(J,M^{2})$ $T_{c\bar{c}u\bar{d}}$ or $T_{c\bar{c}d\bar{u}}$
predicted HMRT, (b) $(n,M^{2})$ $T_{c\bar{c}u\bar{d}}$ or
$T_{c\bar{c}d\bar{u}}$ predicted HMRT.

##### 7.2.10.1 $Z_{c}$ $(n,M^{2})$

All $Z_{c}$ states were observed in $Z_{c}\rightarrow J/\psi\pi$ decay
channels, but more channels are detailed in table LABEL:table:tetra_cand_cucd.
Table LABEL:table:Zc_n_HMRT_fit_output is the built HMRTs output that includes
all three states $Z_{c}(3900)$, $Z_{c}(4200)$ and $Z_{c}(4430)$. 46 are the
plot of these trajectories. These are consistent with tables
LABEL:table:Tsusu_j_predictions and LABEL:table:Tsusu_n_predictions. Moreover,
the predictions of the states in table LABEL:table:Tcucd_n_predictions is
close to the $Z_{c}$ sample. The intercept value of the best fit is
$a_{n}=-2.10$.

Table 63: The fit for $Z_{c}$ states (LABEL:table:tetra_cand_cucd) in the $(n,M^{2})$ plane. The best fit is with fixed $\alpha^{{}^{\prime}}$, but all the fits provide similar results and are consistent with the assumption that tetraquarks should admit near slope as the mesons with similar flavour content. $\chi^{2}_{r}$ |  $\chi^{2}_{hish}$ |  $\alpha^{{}^{\prime}}$ |  $a$ |  $m_{1}$ |  $m_{2}$ |  Fit Type
---|---|---|---|---|---|---
0.00 | 0.00 | 0.51 | -2.14 | 1.11 | 1.11 | free fit
0.41 | 0.00 | 0.45 | -1.64 | 1.12 | 1.12 | fixed $m_{1}$, $m_{2}$ and $\alpha^{{}^{\prime}}$
0.75 | 0.00 | 0.45 | -1.70 | 1.11 | 1.11 | fixed $\alpha^{{}^{\prime}}$
0.00 | 0.00 | 0.51 | -2.10 | 1.12 | 1.12 | fixed $m_{1}$ and $m_{2}$
Table 64: $Z_{c}$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$Z(3900)_{c1}$ | $3887$ | $3851$ | $1$ | $0$ | $1$
$Z(4200)_{c1}$ | $4196$ | $4202$ | $1$ | $1$ | $2$
$Z(4430)_{c1}$ | $4478$ | $4515$ | $1$ | $2$ | $3$
|  | $4801$ |  |  | $4$
|  | $5066$ |  |  | $5$
|  | $5314$ |  |  | $6$
|  | $5548$ |  |  | $7$

|
---|---
$(a)$ |  $(b)$
Figure 46: (a) $Z_{c}$ $(n,M^{2})$ HMRTs output, (b) $Z_{c}$ $(n,M^{2})$ best
fit (fixed $\alpha{{}^{\prime}}=0.46$).

##### 7.2.10.2 $Z_{c}(3900)$ $(J,M^{2})$

This state was observed in $Z_{c}(3900)\rightarrow J/\psi\pi$ and
$Z_{c}(3900)\rightarrow D\bar{D}^{*}$. Table LABEL:table:Zc_3900_J_HMRT
includes the measured $Z_{c}(3900)$ and 47 is the plot of the HMRT. It is
consistent with table LABEL:table:Tcucd_j_predictions. The intercept value is
$a_{J}=-1.96$.

Table 65: $Z_{c}(3900)$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $3301$ |  |  | $0$
|  | $3614$ |  |  | $1$
$Z(3900)_{c1}$ | $3887$ | $3887$ | $1$ | $1$ | $2$
|  | $4133$ |  |  | $3$
|  | $4359$ |  |  | $4$
Figure 47: $Z_{c}(3900)$ $(J,M^{2})$ HMRT.

The preferred decay channel of this state is to $D\bar{D^{*}}$ as opposed to
$J/\psi\pi$. One explanation is that it is a molecule and not a compact-
multiquark structure. We leave it as an open question for future work.

##### 7.2.10.3 $Z_{c}(4200)$ $(J,M^{2})$

This state was observed in $Z_{c}(4200)\rightarrow J/\psi\pi$. Table
LABEL:table:Zc_4200_J_HMRT includes the measured $Z_{c}(4200)$ and 48 is the
plot of the HMRT. It is consistent with table LABEL:table:Tcucd_j_predictions.
The intercept value is $a_{J}=-2.23$.

Table 66: $Z_{c}(4200)$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $3691$ |  |  | $1$
|  | $3956$ |  |  | $2$
$Z(4200)_{c1}$ | $4196$ | $4196$ | $1$ | $2$ | $3$
|  | $4417$ |  |  | $4$
|  | $4624$ |  |  | $5$
Figure 48: $Z_{c}(4200)$ $(J,M^{2})$ HMRT.

##### 7.2.10.4 $Z_{c}(4430)$ $(J,M^{2})$

This state was observed in $Z_{c}(4430)\rightarrow J/\psi\pi$ and
$Z_{c}(4430)\rightarrow\psi(2S)\pi$. Table LABEL:table:Zc_4430_J_HMRT includes
the measured $Z_{c}(4430)$ and 49 is the plot of the HMRT. It is consistent
with table LABEL:table:Tcucd_j_predictions. The intercept value is
$a_{J}=-1.52$.

Table 67: $Z_{c}(4430)$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $4027$ |  |  | $3$
|  | $4261$ |  |  | $4$
$Z(4430)_{c1}$ | $4478$ | $4478$ | $1$ | $4$ | $5$
|  | $4681$ |  |  | $6$
|  | $4873$ |  |  | $7$
Figure 49: $Z_{c}(4430)$ $(J,M^{2})$ HMRT.

##### 7.2.10.5 $X(4020)^{\pm}$

$X(4020)$ was observed in $X(4020)\rightarrow D^{*}\bar{D^{*}}$ and
$X(4020)\rightarrow h_{c}(1P)\pi^{\pm}$. Tables LABEL:table:X_4020_J_HMRT and
LABEL:table:X_4020_n_HMRT are the built HMRT that includes the measured
$X(4020)^{\pm}$ and 50 are the plot of these trajectories. These are
consistent with tables LABEL:table:Tcucd_j_predictions and
LABEL:table:Tcucd_n_predictions. The intercept values are $a_{J}=-1.51$ and
$a_{n}=-1.12$.

Table 68: $X(4020)$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $3478$ |  |  | $1$
|  | $3767$ |  |  | $2$
$X(4020)^{+}$ | $4024$ | $4024$ |  |  | $3$
|  | $4258$ |  |  | $4$
|  | $4476$ |  |  | $5$
Table 69: $X(4020)$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $3179$ |  |  | $0$
|  | $3643$ |  |  | $1$
$X(4020)^{+}$ | $4024$ | $4024$ |  |  | $2$
|  | $4357$ |  |  | $3$
|  | $4657$ |  |  | $4$
|
---|---
$(a)$ |  $(b)$
Figure 50: (a) is $(J,M^{2})$ $X(4020)$ MHRT, (b) $(n,M^{2})$ $X(4020)$ MHRT.

##### 7.2.10.6 $X(4051)^{\pm}$

$X(4051)$ was observed in $X(4051)\rightarrow\pi^{+}\chi_{c1}(1P)$. Tables
LABEL:table:X_4051_J_HMRT and LABEL:table:X_4051_n_HMRT are the built HMRT
that includes the measured $X(4051)^{\pm}$ and 51 are the plot of these
trajectories. These are consistent with tables LABEL:table:Tcucd_j_predictions
and LABEL:table:Tcucd_n_predictions. The intercept values are $a_{J}=-1.62$
and $a_{n}=-1.20$.

Table 70: $X(4051)$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $3512$ |  |  | $1$
|  | $3797$ |  |  | $2$
$X(4050)^{+}$ | $4051$ | $4051$ |  |  | $3$
|  | $4283$ |  |  | $4$
|  | $4499$ |  |  | $5$
Table 71: $X(4051)$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $3219$ |  |  | $0$
|  | $3675$ |  |  | $1$
$X(4050)^{+}$ | $4051$ | $4051$ |  |  | $2$
|  | $4381$ |  |  | $3$
|  | $4679$ |  |  | $4$
|
---|---
$(a)$ |  $(b)$
Figure 51: (a) is $(J,M^{2})$ $X(4051)$ MHRT, (b) $(n,M^{2})$ $X(4051)$ MHRT.

##### 7.2.10.7 $X(4055)^{\pm}$

$X(4055)$ was observed in $X(4055)\rightarrow\pi^{+}\psi(2S)$. Tables
LABEL:table:X_4055_J_HMRT and LABEL:table:X_4055_n_HMRT are the built HMRT
that includes the measured $X(4055)^{\pm}$ and 52 are the plot of these
trajectories. These are consistent with tables LABEL:table:Tcucd_j_predictions
and LABEL:table:Tcucd_n_predictions. The intercept values are $a_{J}=-1.63$
and $a_{n}=-1.20$.

Table 72: $X(4055)$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $3516$ |  |  | $1$
|  | $3800$ |  |  | $2$
$X(4055)^{+}$ | $4054$ | $4054$ |  |  | $3$
|  | $4286$ |  |  | $4$
|  | $4501$ |  |  | $5$
Table 73: $X(4055)$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $3224$ |  |  | $0$
|  | $3678$ |  |  | $1$
$X(4055)^{+}$ | $4054$ | $4054$ |  |  | $2$
|  | $4383$ |  |  | $3$
|  | $4681$ |  |  | $4$
|
---|---
$(a)$ |  $(b)$
Figure 52: (a) is $(J,M^{2})$ $X(4055)$ MHRT, (b) $(n,M^{2})$ $X(4055)$ MHRT.

##### 7.2.10.8 $X(4100)^{\pm}$

$X(4100)$ was observed in $X(4100)\rightarrow\pi^{-}\eta(1S)$. Tables
LABEL:table:X_4100_J_HMRT and LABEL:table:X_4100_n_HMRT are the built HMRT
that includes the measured $X(4100)^{\pm}$ and 53 are the plot of these
trajectories. These are consistent with tables LABEL:table:Tcucd_j_predictions
and LABEL:table:Tcucd_n_predictions. The intercept values are $a_{J}=-1.80$
and $a_{n}=-1.36$.

Table 74: $X(4100)$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $3568$ |  |  | $1$
|  | $3846$ |  |  | $2$
$X(4100)^{+}$ | $4096$ | $4096$ |  |  | $3$
|  | $4325$ |  |  | $4$
|  | $4537$ |  |  | $5$
Table 75: $X(4100)$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $3285$ |  |  | $0$
|  | $3727$ |  |  | $1$
$X(4100)^{+}$ | $4096$ | $4096$ |  |  | $2$
|  | $4421$ |  |  | $3$
|  | $4716$ |  |  | $4$
|
---|---
$(a)$ |  $(b)$
Figure 53: (a) is $(J,M^{2})$ $X(4100)$ MHRT, (b) $(n,M^{2})$ $X(4100)$ MHRT.

##### 7.2.10.9 $R_{c0}(4240)^{\pm}$

$R_{c0}(4240)^{\pm}$ was observed in $R_{c0}(4240)\rightarrow\pi^{-}\psi(2S)$.
Tables LABEL:table:R_4240_J_HMRT and LABEL:table:R_4240_n_HMRT are the built
HMRT that includes the measured $R_{c0}(4240)^{\pm}$ and 54 are the plot of
these trajectories. These are consistent with tables
LABEL:table:Tcucd_j_predictions and LABEL:table:Tcucd_n_predictions. The
intercept values are $a_{J}=-2.42$ and $a_{n}=-1.75$.

Table 76: $R_{c0}(4240)$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $3744$ |  |  | $1$
|  | $4003$ |  |  | $2$
$R(4240)_{c0}$ | $4239$ | $4239$ | $0$ | $3$ | $3$
|  | $4457$ |  |  | $4$
|  | $4662$ |  |  | $5$
Table 77: $R_{c0}(4240)$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $3486$ |  |  | $0$
|  | $3891$ |  |  | $1$
$R(4240)_{c0}$ | $4239$ | $4239$ | $0$ | $2$ | $2$
|  | $4550$ |  |  | $3$
|  | $4834$ |  |  | $4$
|
---|---
$(a)$ |  $(b)$
Figure 54: (a) is $(J,M^{2})$ $Rc0(4240)$ MHRT, (b) $(n,M^{2})$ $Rc0(4240)$
MHRT.

##### 7.2.10.10 $X(4250)^{\pm}$

$X(4250)$ was observed in $X(4250)\rightarrow\pi^{+}\chi(1P)$. Tables
LABEL:table:X_4250_J_HMRT and LABEL:table:X_4250_n_HMRT are the built HMRT
that includes the measured $X(4250)^{\pm}$ and 55 are the plot of these
trajectories. These are consistent with tables LABEL:table:Tcucd_j_predictions
and LABEL:table:Tcucd_n_predictions. The intercept values are $a_{J}=-2.42$
and $a_{n}=-1.75$.

Table 78: $X(4250)$ $(J,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $3744$ |  |  | $1$
|  | $4003$ |  |  | $2$
$R(4240)_{c0}$ | $4239$ | $4239$ | $0$ | $3$ | $3$
|  | $4457$ |  |  | $4$
|  | $4662$ |  |  | $5$
Table 79: $X(4250)$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $3486$ |  |  | $0$
|  | $3891$ |  |  | $1$
$R(4240)_{c0}$ | $4239$ | $4239$ | $0$ | $2$ | $2$
|  | $4550$ |  |  | $3$
|  | $4834$ |  |  | $4$
|
---|---
$(a)$ |  $(b)$
Figure 55: (a) is $(J,M^{2})$ $X(4250)$ MHRT, (b) $(n,M^{2})$ $X(4250)$ MHRT.

####  7.2.11 $T_{c\bar{c}u\bar{s}}$ or $T_{c\bar{c}d\bar{s}}$

For a tetraquarks with the quark content $T_{c\bar{c}u\bar{s}}$ (table
LABEL:table:tetra_cand_cucs). The candidate resonances are presented in table.
We generated the predicted HMRTs for this quark content in tables
LABEL:table:Tcucs_j_predictions and LABEL:table:Tcucs_n_predictions, and the
thresholds table LABEL:table:Tcucs_thresholds includes the predicted width.
The HMRTs are also plotted in 56.

Table 80: $T_{c\bar{u}u\bar{s}}$ or $T_{c\bar{d}u\bar{s}}$ tetraquark candidates. Candidate |  Quarks Content |  Selected Decay Channels |  $J^{PC}$ |  Mass $[MeV]$ |  Width $[MeV]$ |  Ref.
---|---|---|---|---|---|---
$T_{\psi s1}^{\theta}(4000)^{+}$ also $Z_{cs}(4000)^{+}$ | $c\bar{c}u\bar{s}$ |  $J/\psi K^{+}$ $D_{s}^{+}\bar{D}^{*0}$ $D_{s}^{*+}\bar{D}^{0}$ | $1^{+}$ | $3980-4010$ | $5-150$ |
$T_{\psi s1}(4220)^{+}$ also $Z_{cs}(4220)^{+}$ | $c\bar{c}u\bar{s}$ |  $J/\psi K^{+}$ | $1^{+}$ | $4216^{+50}_{-40}$ | $233^{+110}_{-90}$ |
$T_{\psi s1}^{\theta}(4000)^{0}$ | $c\bar{c}d\bar{s}$ |  $J/\psi K^{0}_{S}$ | $1^{+}$ | $3991^{+14}_{-20}$ | $105^{+12}_{-10}{}^{+9}_{-17}$ |
Table 81: $T_{c\bar{c}u\bar{s}}$ thresholds. Thry Width $[MeV]$ |  Mesons Pair |  Meson Threshold $[MeV]$ |  Baryon Anti- baryon |  Baryonic Threshold $[MeV]$ |  Genuine
---|---|---|---|---|---
$47-79$ $29-59$ |  $\eta_{c}(1S)K^{+}$ $D^{+}_{s}\bar{D}^{0}$ |  $3478$ $3833$ |  $\Lambda^{+}_{c}\bar{\Xi}^{0}_{c}$ $\Sigma^{++}_{c}\bar{\Xi}^{-}_{c}$ $\Xi^{+}_{c}\bar{\Omega}^{0}_{c}$ |  $4756$ $4922$ $5163$ | $*$
Table 82: $T_{c\bar{c}u\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$4362-4488$ $4587-4704$ $4796-4906$ $4993-5097$ $5179-5278$ $5356-5450$ $5525-5616$ $5688-5776$ $5845-5930$ $5997-6079$ $6144-6223$ $6287-6364$ |  $-3.3$-$-2.7$
Table 83: $T_{c\bar{c}u\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$4145-4282$ $4489-4610$ $4796-4906$ $5076-5178$ $5337-5432$ $5580-5670$ $5811-5896$ $6030-6111$ $6240-6317$ $6441-6515$ $6634-6706$ $6821-6891$ |  $-2.0$-$-1.6$
|
---|---
$(a)$ |  $(b)$
Figure 56: (a) is $(J,M^{2})$ $T_{c\bar{d}c\bar{u}}$ predicted HMRT, (b)
$(n,M^{2})$ $T_{c\bar{d}c\bar{u}}$ predicted HMRT.

##### 7.2.11.1 $Z_{cs}$ $(n,M^{2})$ fit

For $J^{PC}=1^{+}$, the best fit is with the fixed endpoint masses. The fits
are shown in [Fig. 57] along with the predicted spectrum. The best fit
parameters are: $\alpha^{{}^{\prime}}_{Z_{cs}}=0.79$, $a_{Z_{cs}}=-2.98$.

Table 84:  $\chi^{2}_{r}$ |  $\chi^{2}_{hish}$ |  $\alpha^{{}^{\prime}}$ |  $a$ |  $m_{1}$ |  $m_{2}$ |  Fit Type
---|---|---|---|---|---|---
0.00 | 0.00 | 0.74 | -3.65 | 1.11 | 1.24 | free fit
3.58 | 0.03 | 0.45 | -1.08 | 1.12 | 1.47 | fixed $m_{1}$, $m_{2}$ and $\alpha^{{}^{\prime}}$
2.25 | 0.02 | 0.45 | -1.95 | 1.11 | 1.11 | fixed $\alpha^{{}^{\prime}}$
0.00 | 0.00 | 0.79 | -2.98 | 1.12 | 1.47 | fixed $m_{1}$ and $m_{2}$
|
---|---
$(a)$ |  $(b)$
Figure 57: $Z_{cs}$ with $J^{P}=1^{+}$ HMRT. (a) Comparison between the fits, (b) $Z_{cs}$ with fixed mass HMRT, which is the best fit. Table 85: $Z_{cs}$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$Z(4000)^{+}_{cs1}$ | $4003$ | $4003$ | $1$ | $0$ | $1$
$Z(4220)^{+}_{cs1}$ | $4216$ | $4216$ | $1$ | $1$ | $2$
|  | $4412$ |  |  | $3$
|  | $4596$ |  |  | $4$
|  | $4768$ |  |  | $5$
|  | $4932$ |  |  | $6$

####  7.2.12 $T_{\psi\phi}$ (quark content ${c\bar{c}s\bar{s}}$)

For tetraquarks with the quark content $T_{c\bar{c}s\bar{s}}$ The candidate
resonances are presented in table LABEL:table:tetra_cand_cscs. We generated
the predicted HMRTs for this quark content in tables
LABEL:table:Tcscs_j_predictions and LABEL:table:Tcscs_n_predictions, and the
thresholds table LABEL:table:Tcscs_thresholds includes the predicted width.
The HMRTs are also plotted in 58.

Table 86: $T_{c\bar{c}s\bar{s}}$ tetraquark candidates. Candidate |  Quarks Content |  Selected Decay Channels |  $J^{PC}$ |  Mass $[MeV]$ |  Width $[MeV]$ |  Ref.
---|---|---|---|---|---|---
$X(3960)$ | $c\bar{c}s\bar{s}$ |  $D_{s}^{+}$ $D_{s}^{-}$ | $0^{++}$ | $3956\pm 5\pm 10$ | $43\pm{13}\pm{8}$ |  [95] another approach in [109]
$X(4140)$ | $c\bar{c}s\bar{s}$ | $J/\psi\phi$ | $1^{++}$ | $4146.5\pm 3.0$ | $19^{+7}_{-5}$ |  [96]
$X(4274)$ | $c\bar{c}s\bar{s}$ | $J/\psi\phi$ | $1^{++}$ | $4286^{+8}_{-9}$ | $51\pm 7$ |  [97]
$\chi_{c0}(4500)$ | $c\bar{c}s\bar{s}$ |  $J/\psi\phi$ | $0^{++}$ | $4474\pm{4}$ | $77^{+12}_{-10}$ |  [97]
$\chi_{c1}(4685)$ | $c\bar{c}s\bar{s}$ |  $J/\psi\phi$ | $1^{++}$ | $4684^{+15}_{-17}$ | $126\pm{40}$ |  [93]
$\chi_{c0}(4700)$ | $c\bar{c}s\bar{s}$ |  $J/\psi\phi$ | $0^{++}$ | $4694^{+16}_{-5}$ | $87^{+18}_{-10}$ |  [97]
$X(4350)$0 | $c\bar{c}s\bar{s}$ | $J/\psi\phi$ | $?^{?+}$ | $4351\pm{5}$ | $13^{+18}_{-10}$ |
$X(4630)$ | $c\bar{c}s\bar{s}$ |  $J/\psi\phi$ |  $1^{-+}$101010$J^{P}$ needs confirmation. | $4626^{+24}_{-110}$ | $174^{+140}_{-80}$ |
$\psi(4360)$ | $c\bar{c}s\bar{s}$ | $J/\psi\eta$ | $1^{--}$ | $4374\pm{7}$ | $118\pm 12$ |
$\psi(4660)$ | $c\bar{c}s\bar{s}$ |  $\Lambda_{c}^{+}\bar{\Lambda_{c}}^{-}$ $D^{+}_{s}D_{s1}^{-}(2536)$ $D^{+}_{s}D_{s2}^{*-}(2573)$ | $1^{--}$ | $4630\pm{6}$ | $72^{+14}_{-12}$ |
Table 87: $T_{c\bar{c}s\bar{s}}$ thresholds. Thry Width $[MeV]$ |  Mesons Pair |  Meson Threshold $[MeV]$ |  Baryon Anti- baryon |  Baryonic Threshold $[MeV]$ |  Genuine
---|---|---|---|---|---
$89-134$ $27-54$ |  $D^{+}_{s}D^{-}_{s}$ $\eta_{c}(1S)\phi(1020)$ |  $3936$ $4003$ |  $\Xi^{+}_{c}\bar{\Xi}^{-}_{c}$ $\Xi^{0}_{c}\bar{\Xi}^{0}_{c}$ $\Omega^{0}_{c}\bar{\Omega}^{0}_{c}$ |  $4936$ $4940$ $5390$ |
Table 88: $T_{c\bar{c}s\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$4536-4664$ $4765-4882$ $4976-5086$ $5174-5278$ $5361-5459$ $5538-5632$ $5708-5798$ $5871-5958$ $6028-6112$ $6179-6260$ $6326-6404$ $6468-6545$ |  $-3.8$-$-3.2$
Table 89: $T_{c\bar{c}s\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$4315-4454$ $4666-4787$ $4976-5086$ $5258-5359$ $5519-5613$ $5763-5852$ $5993-6078$ $6212-6293$ $6421-6498$ $6622-6696$ $6814-6886$ $7001-7070$ |  $-2.7$-$-2.3$
|
---|---
$(a)$ |  $(b)$
Figure 58: (a) is $(J,M^{2})$ $T_{c\bar{c}s\bar{s}}$ predicted HMRT, (b)
$(n,M^{2})$ $T_{c\bar{c}s\bar{s}}$ predicted HMRT.

In [110]-[111] there were seven resonances observed that are tetraquark
candidates with content ${c\bar{c}s\bar{s}}$. The decays in which these states
were observed are $J/\psi\phi$ and $D_{s}D_{s}$.

We expect the natural decay of these states to be through a baryon-antibaryon
pair for higher states that are above threshold. In this case, the
annihilation threshold is $\approx 3940$ which is slightly below X(3960) found
in [110], while the threshold for a decay through string tear is $\approx
4940$ to $\Xi_{c}\bar{\Xi_{c}}$.

The fit of the data was done separately for $J^{PC}=0^{++}$ and
$J^{PC}=1^{++}$ in the $(n,M^{2})$ plane. For each trajectory we fit the data
four times - once with free parameters, another with fixed endpoint masses,
one with fixed $\alpha^{{}^{\prime}}$ and at last we fixed both
$\alpha^{{}^{\prime}}$ and the endpoint masses, letting only the intercept to
change.

##### 7.2.12.1 $T_{\psi\phi 0}$ $(n,M^{2})$ fit

For $J^{PC}=0^{++}$, the best fit is with the fixed slope and endpoint masses,
with $\chi^{2}_{r}=2.00$, but the spectrum prediction is similar for all fits.
The fits are shown in [Fig. 59] along with the predicted spectrum.

Table 90: $T_{\psi\phi 0}$ $(n,M^{2})$ fit results. $\chi^{2}_{r}$ |  $\chi^{2}_{hish}$ |  $\alpha^{{}^{\prime}}$ |  $a$ |  $m_{1}$ |  $m_{2}$ |  Fit Type
---|---|---|---|---|---|---
2.09 | 0.01 | 0.67 | -0.16 | 1.90 | 1.90 | free fit
2.00 | 0.02 | 0.45 | -1.55 | 1.47 | 1.47 | fixed $m_{1}$, $m_{2}$ and $\alpha^{{}^{\prime}}$
3.75 | 0.02 | 0.45 | -1.16 | 1.56 | 1.56 | fixed $\alpha^{{}^{\prime}}$
3.89 | 0.02 | 0.43 | -1.47 | 1.47 | 1.47 | fixed $m_{1}$ and $m_{2}$
|
---|---
$(a)$ |  $(b)$
Figure 59: $T_{\psi\phi}$ with $J^{PC}=0^{++}$ HMRT. (a) Comparison between
the fits, (b) $T_{\psi\phi}$ with $J^{PC}=0^{++}$ free fit HMRT which is the
best fit.

Table 91: $T_{\psi\phi}$ Regge trajectory. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$X(3960)$ | $3955$ | $3973$ | $0$ | $0$ | $0$
$X(4500)$ | $4506$ | $4433$ | $0$ | $1$ | $1$
$X(4700)$ | $4704$ | $4748$ | $0$ | $2$ | $2$
|  | $5012$ |  |  | $3$
|  | $5245$ |  |  | $4$
|  | $5458$ |  |  | $5$
|  | $5656$ |  |  | $6$

##### 7.2.12.2 $T_{\psi\phi 1}$ $(n,M^{2})$ fit

For $J^{PC}=1^{++}$, the best fit is with the fixed masses and
$\alpha^{{}^{\prime}}$ parameters with $\chi^{2}_{r}=4.30$. The fits are shown
in [Fig. 60]. The predicted spectrum is at LABEL:table:T_cscs_spectrum.

Table 92: $T_{\psi\phi 1}$ $(n,M^{2})$ fit results. $\chi^{2}_{r}$ |  $\chi^{2}_{hish}$ |  $\alpha^{{}^{\prime}}$ |  $a$ |  $m_{1}$ |  $m_{2}$ |  Fit Type
---|---|---|---|---|---|---
4.38 | 0.02 | 0.48 | -4.20 | 0.81 | 0.81 | free fit
5.62 | 0.05 | 0.45 | -0.53 | 1.47 | 1.47 | fixed $m_{1}$, $m_{2}$ and $\alpha^{{}^{\prime}}$
4.30 | 0.02 | 0.45 | -5.71 | 0.35 | 0.35 | fixed $\alpha^{{}^{\prime}}$
4.69 | 0.02 | 0.64 | -1.50 | 1.47 | 1.47 | fixed $m_{1}$ and $m_{2}$
|
---|---
$(a)$ |  $(b)$
Figure 60: $T_{\psi\phi}$ with $J^{PC}=1^{++}$ HMRT. (a) Comparison between the fits, (b) $T_{\psi\phi}$ with $J^{PC}=1^{++}$ fixed fit HMRT which is the best fit. Table 93: $T_{\psi\phi}$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$X(4140)$ | $4148$ | $3996$ | $1$ | $0$ | $1$
$X(4274)$ | $4273$ | $4396$ | $1$ | $1$ | $2$
$X(4685)$ | $4684$ | $4736$ | $1$ | $2$ | $3$
|  | $5040$ |  |  | $4$
|  | $5317$ |  |  | $5$
|  | $5573$ |  |  | $6$
|  | $5814$ |  |  | $7$

##### 7.2.12.3 $X(4350)$ and $X(4630)$ $(n,M^{2})$ fit

For $J^{PC}=1^{-+}$ 111111We assume that the $X(4350)$ is with the same
quantum numbers, although not all of them are known yet the best fit is with
the free parameters with $\chi^{2}_{r}=3.01$, but the spectrum prediction is
similar for all fits. The fits are shown in [Fig. 61] along with the predicted
spectrum.

Table 94:  $\chi^{2}_{r}$ |  $\chi^{2}_{hish}$ |  $\alpha^{{}^{\prime}}$ |  $a$ |  $m_{1}$ |  $m_{2}$ |  Fit Type
---|---|---|---|---|---|---
0.00 | 0.00 | 0.44 | -5.92 | 0.73 | 0.73 | free fit
0.79 | 0.01 | 0.45 | -2.31 | 1.47 | 1.47 | fixed $m_{1}$, $m_{2}$ and $\alpha^{{}^{\prime}}$
0.00 | 0.00 | 0.45 | -5.69 | 0.80 | 0.80 | fixed $\alpha^{{}^{\prime}}$
0.00 | 0.00 | 0.57 | -3.07 | 1.47 | 1.47 | fixed $m_{1}$ and $m_{2}$
Table 95: $X(4350)$, $X(4630)$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$X(4350)$ | $4351$ | $4351$ | $1$ | $-1$ | $0$
$X(4630)$ | $4626$ | $4626$ | $1$ | $0$ | $1$
|  | $4883$ |  |  | $2$
|  | $5126$ |  |  | $3$
|  | $5356$ |  |  | $4$
|  | $5575$ |  |  | $5$
|
---|---
$(a)$ |  $(b)$
Figure 61: $X(4350)$ and $X(4630)$ with $J^{PC}=1^{-+}$ HMRT. (a) Comparison
between the fits, (b) $X(4350)$ and $X(4630)$ fixed slope fit HMRT which is
the best fit.

##### 7.2.12.4 $\psi$ $(n,M^{2})$

The candidates $\psi(4360)$ and $\psi(4660)$ were analysed in previous paper
[10] as candidates on the same trajectory. In this paper, the $\psi(4660)$ and
$X(4630)$ were considered as the same state. But it is now known that they
have different quantum numbers. Hence, we separate their HMRTs in this paper.
Also, we assumed that $X(4350)$ is on the same HMRT as the $X(4630)$ (section
7.2.12.3).

For $J^{PC}=1^{--}$ the best fit is with the free parameters with
$\chi^{2}_{r}=3.01$, but the spectrum prediction is similar for all fits. The
fits are shown in [Fig. 61] along with the predicted spectrum.

Table 96:  $\chi^{2}_{r}$ |  $\chi^{2}_{hish}$ |  $\alpha^{{}^{\prime}}$ |  $a$ |  $m_{1}$ |  $m_{2}$ |  Fit Type
---|---|---|---|---|---|---
0.00 | 0.00 | 0.53 | -3.68 | 1.16 | 1.16 | free fit
1.16 | 0.01 | 0.45 | -1.35 | 1.47 | 1.47 | fixed $m_{1}$, $m_{2}$ and $\alpha^{{}^{\prime}}$
0.00 | 0.00 | 0.45 | -6.24 | 0.47 | 0.47 | fixed $\alpha^{{}^{\prime}}$
0.03 | 0.00 | 0.57 | -2.12 | 1.47 | 1.47 | fixed $m_{1}$ and $m_{2}$
Table 97: $\psi$ $(n,M^{2})$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
$\psi(4360)$ | $4372$ | $4372$ | $1$ | $0$ | $1$
$\psi(4660)$ | $4630$ | $4630$ | $1$ | $1$ | $2$
|  | $4873$ |  |  | $3$
|  | $5105$ |  |  | $4$
|  | $5325$ |  |  | $5$
|  | $5537$ |  |  | $6$
|
---|---
$(a)$ |  $(b)$
Figure 62: $X(4350)$ and $X(4630)$ with $J^{PC}=1^{-+}$ HMRT. (a) Comparison
between the fits, (b) $X(4350)$ and $X(4630)$ fixed slope fit HMRT which is
the best fit.

####  7.2.13 $T_{\psi\psi}$ (quark content $c\bar{c}c\bar{c}$)

In [24] the state $X(6900)$ was analysed in the context of the HISH model.
This note relied on [112] where two additional resonance candidates at around
$6.6GeV$ and $7.2GeV$ were observed. Now these candidates were observed in an
additional note [113] with higher statistical significance. The states that we
analyse in this section are listed in LABEL:table:tetra_cand_cccc.

There are two measurements of $X(6600)$ and $X(6900)$, without quantum
numbers. Not all of the states rely on the same trajectory. Hence, we fit the
second, fourth and fifth in an HMRT.

Table 98: $T_{c\bar{c}c\bar{c}}$ tetraquark candidates. Candidate |  Quarks Content |  Selected Decay Channels |  $J^{PC}$ |  Mass $[MeV]$ |  Width $[MeV]$ |  Ref.
---|---|---|---|---|---|---
$T_{\psi\psi}(6600)$ | $c\bar{c}c\bar{c}$ |  $J/\psi J/\psi$ | $?^{??}$ | $6630\pm{90}$ | $350\pm{11}^{+110}_{-40}$ |
$T_{\psi\psi}(6600)$ | $c\bar{c}c\bar{c}$ |  $J/\psi J/\psi$ | $?^{??}$ | $6552\pm{10}\pm{12}$ | $124^{+32}_{-26}\pm{33}$ |
$T_{\psi\psi}(6900)$ | $c\bar{c}c\bar{c}$ |  $J/\psi J/\psi$ | $?^{??}$ | $6886\pm{16}$ | $168\pm{80}$ |
$T_{\psi\psi}(6900)$ | $c\bar{c}c\bar{c}$ |  $J/\psi J/\psi$ | $?^{??}$ | $6927\pm{9}\pm{4}$ | $122^{+24}_{-21}\pm{18}$ |
$T_{\psi\psi}(7300)$ | $c\bar{c}c\bar{c}$ |  $J/\psi J/\psi$ | $?^{??}$ | $7287^{+20}_{-18}\pm{5}$ | $95^{+59}_{-40}\pm{19}$ |
Table 99: $T_{c\bar{c}c\bar{c}}$ thresholds. Thry Width $[MeV]$ |  Mesons Pair |  Meson Threshold $[MeV]$ |  Baryon Anti- baryon |  Baryonic Threshold $[MeV]$ |  Genuine
---|---|---|---|---|---
$6-21$ $29-58$ |  $\eta_{c}(1S)\eta_{c}(1S)$ |  $5968$ |  $\Xi^{+}_{cc}\bar{\Xi}^{-}_{cc}$ $\Xi^{++}_{cc}\bar{\Xi}^{--}_{cc}$ $\Omega^{+}_{cc}\bar{\Omega}^{-}_{cc}$ |  $7038$ $7244$ | $*$
Table 100: $T_{c\bar{c}c\bar{c}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$6768-6887$ $6926-7040$ $7078-7188$ $7225-7331$ $7366-7469$ $7504-7604$ $7637-7735$ $7767-7862$ $7894-7987$ $8018-8108$ $8139-8227$ $8257-8344$ |  $-5.9$-$-5.1$
Table 101: $T_{c\bar{c}c\bar{c}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$6622-6745$ $6857-6973$ $7078-7188$ $7288-7393$ $7489-7589$ $7681-7778$ $7866-7959$ $8045-8135$ $8218-8305$ $8385-8470$ $8549-8631$ $8707-8788$ |  $-4.2$-$-3.7$
|
---|---
$(a)$ |  $(b)$
Figure 63: (a) is $(J,M^{2})$ $T_{c\bar{c}c\bar{c}}$ predicted HMRT, (b)
$(n,M^{2})$ $T_{c\bar{c}c\bar{c}}$ predicted HMRT.

The decay channel in which these states were observed is $J/\psi J/\psi$. As
before, we fit the data four times in the $(n,M^{2})$ plane with
$\alpha^{{}^{\prime}}=0.45$. For this trajectory, the mesons slope was too
high for both planes.

The comparison between the different fits are shown in 64. The best fit, which
is consistent with the universal description of the model is present in 64 on
(b). The spectrum prediction is shown in LABEL:table:X(6900)_spectrum.

Table 102: $T_{\psi\psi}$ HMRT. $\chi^{2}_{r}$ |  $\chi^{2}_{hish}$ |  $\alpha^{{}^{\prime}}$ |  $a$ |  $m_{1}$ |  $m_{2}$ |  Fit Type
---|---|---|---|---|---|---
0.12 | 0.00 | 0.21 | -4.43 | 0.70 | 0.70 | free fit
5.68 | 0.05 | 0.45 | -2.93 | 2.22 | 2.22 | fixed $m_{1}$, $m_{2}$ and $\alpha^{{}^{\prime}}$
3.05 | 0.01 | 0.45 | 1.00 | 2.78 | 2.78 | fixed $\alpha^{{}^{\prime}}$
0.84 | 0.00 | 0.31 | -0.86 | 2.22 | 2.22 | fixed $m_{1}$ and $m_{2}$
|
---|---
$(a)$ |  $(b)$
Figure 64: $X(6900)$ $(n,M^{2})$ HMRT. The graph in (a) shows the comparison
between the fits, (b) $X(6900)$ fixed fit HMRT which is the best fit.

Table 103: $T_{\psi\psi}$ HMRT. $State$ |  $M$ $[MeV]$ |  Thry $M$ $[MeV]$ |  $J$ |  Thry $n$ |  Thry $J+n$
---|---|---|---|---|---
|  | $5800$ |  |  | $1$
|  | $6232$ |  |  | $2$
$T(6600)_{\psi\psi 0}$ | $6630$ | $6609$ |  |  | $3$
$T(6900)_{\psi\psi 0}$ | $6905$ | $6950$ |  |  | $4$
$T(7300)_{\psi\psi 0}$ | $7287$ | $7263$ |  |  | $5$
|  | $7555$ |  |  | $6$
|  | $7830$ |  |  | $7$

The decays width ratio:

$\displaystyle\Gamma_{tear}\lesssim 31MeV$ (60)

$\displaystyle\Gamma_{annihilation}=47MeV$ (61)

Adding the two widths, we get a result width - $78MeV$ \- which is a quite
good approximation to the measured $95MeV$ in [113]. Changing the $A$ value
used to $0.15$ would give a closer result.

###  7.3 Tetraquarks and Mesons Global Fit

To conclude this section, we checked the coherency of our assumptions by
fitting all tetraquarks and mesons data together, constraining the slopes of
the heavy tetraquarks to be the same as that of the charmed and bottoms
mesons.

The results are of $\chi_{r}^{2}=1.95$. The graphs are in the following figure
LABEL:fig:mesons_tetra_global_fit, the fit results are in table
LABEL:table:mesons_tetra_global_fit.

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Table 105: The parameters results from the tetraquarks and mesons global fit. We constraint the heavy slopes to equal in mesons and tetraquarks, aside from the $T_{c\bar{c}c\bar{c}}$, which clearly have a lower $\alpha^{{}^{\prime}}$. $\chi^{2}_{r}$ |  $\alpha^{{}^{\prime}}_{J,L}$ $[GeV^{-2}]$ |  $\alpha^{{}^{\prime}}_{J,H}$ $[GeV^{-2}]$ |  $\alpha^{{}^{\prime}}_{n,L}$ $[GeV^{-2}]$ |  $\alpha^{{}^{\prime}}_{n,H}$ $[GeV^{-2}]$ |  $m_{u/d}$ $[GeV]$ |  $m_{s}$ $[GeV]$ |
---|---|---|---|---|---|---|---
$1.95$ | $0.86$ | $0.65$ | $0.83$ | $0.48$ | $0.011$ | $0.36$ |
$m_{c}$ $[GeV]$ |  $m_{b}$ $[GeV]$ |  $\alpha_{T_{\psi\psi}}$ |  $m_{BV_{u/d,u/d}}$ |  $m_{BV_{s,u/d}}$ |  $m_{BV_{c,u/d}}$ |  $m_{BV_{c,s}}$ |  $m_{BV_{c,c}}$
$1.27$ | $4.73$ | $0.23$ | $0.93$ | $0.35$ | $1.32$ | $1.31$ | $1.53$
Table 106: Mesons and tetraquarks global fits intercepts. $a_{J}$ marks that the HMRT was done in the $(J,M^{2})$ plane. $a_{n}$ is the intercept of a $(n,M^{2})$ HMRT. Traj. |  $a$ $n/J$ |  Traj. |  $a$ $n/J$ only |  Traj. |  $a$ $n/J$
---|---|---|---|---|---
$\pi/b$ | $a_{J}=-0.38$ | $\eta_{c}/h_{c}$ | $a_{J}=-0.71$ | $\omega_{3}$ | $a_{n}=0.80$
$\rho/a$ | $a_{J}=0.52$ | $B$ | $a_{J}=-0.36$ | $\phi$ | $a_{n}=0.67$
$\eta/h$ | $a_{J}=-0.30$ | $B^{*}$ | $a_{J}=0.58$ | $K$ | $a_{n}=-1.29$
$\omega/f$ | $a_{J}=0.53$ | $B_{s}$ | $a_{J}=-0.19$ | $K^{*}$ | $a_{n}=0.75$
$K$ | $a_{J}=-0.03$ | $B_{s}^{*}$ | $a_{J}=0.75$ | $K^{*}_{0}$ | $a_{n}=-0.35$
$K^{*}$ | $a_{J}=0.70$ | $\Upsilon/\chi_{b}$ | $a_{J}=1.97$ | $D^{*0}_{1}$ | $a_{n}=0.65$
$\phi/f^{{}^{\prime}}$ | $a_{J}=0.84$ | $\eta_{b}$ | $a_{J}=1.00$ | $\Psi$ | $a_{n}=1.38$
$D$ | $a_{J}=-0.42$ | $\pi$ | $a_{n}=-1.56$ | $B_{c}$ | $a_{n}=0.72$
$D^{*}$ | $a_{J}=0.45$ | $\pi_{2}$ | $a_{n}=-0.23$ | $\chi_{c2}$ | $a_{n}=1.58$
$D_{s}$ | $a_{J}=-0.21$ | $a_{1}$ | $a_{n}=-0.29$ | $\Upsilon$ | $a_{n}=1.98$
$D^{*}_{s}$ | $a_{J}=0.62$ | $h_{1}$ | $a_{n}=-0.10$ | $\chi_{b1}$ | $a_{n}=1.26$
$\Psi/\chi_{c}$ | $a_{J}=0.08$ | $\omega$ | $a_{n}=0.55$ | $f_{2}$ | $a_{n}=1.72$
$X(3350)$ | $a_{n}=1.35$ | $Z_{c}$ | $a_{n}=0.06$ | $Z_{cs}$ | $a_{n}=-0.18$
$\Psi(4630)$ | $a_{n}=-0.41$ | $T_{cu\bar{c}\bar{s}}$ | $a_{n}=0.06$ | $T_{\psi\phi 0}$ | $a_{n}=-0.54$
$T_{\psi\phi 1}$ | $a_{n}=-4.47$ | $T_{\psi\psi}$ | $a_{n}=1.53$ |  |

###  7.4 Tetraquarks HMRTs predictions

The following table summarizes all the thresholds and predicted trajectories
for all possible charm tetraquarks configurations. The thresholds were
calculated for each possible product according to the HISH model through the
annihilation and string tear mechanisms. The third mechanism that is mentioned
in 4.3 is not calculated in the table.

The table predictions were calculated based on the mesons fit parameters. We
assumed that the diquarks (and anti-diquarks) masses are the sum of masses of
the two quarks. The slopes for each trajectory ($(J,M^{2})$ and $(n,M^{2})$),
was taken to be the heavy-slope from 1.

The ’Candidates’ column contains the resonances that were already detected. We
elaborate on all of these at the previous sub sections, including the decay
channels through which they were observed. The ’Thry Width’ column contains
two values, one for the states at the $(J,M^{2})$ MHRT, and the second row is
for the $(n,M^{2})$ MHRT. The ’Mesons Pair’ and ’Meson Threshold’ contains the
mesons symbols and the threshold for their creation respectively (for example,
in the first row of the table, $D^{0}\pi^{0}_{d}$ has a threshold of 2000,
while $D^{+}\pi^{-}$ has threshold of 2010). The same applies for the ’Baryon-
Antibaryon’ and ’Baryonic Threshold’ columns.

We calculated the ’J Spec’ and ’n Spec’ in the following steps:

  * •

We first calculated the baryonic threshold and let it vary between
$40-150MeV$. This was done by looking at the available data that we collected,
where the created tetraquarks candidates are above the baryonic threshold. We
saw that this is the range of the distance from the threshold.

  * •

The value for $J+n$ is calculated according to the number of states that are
potentially on the trajectories between the mesonic and the baryonic
thresholds. We calculated how many states are there, assuming the other
parameters are similar to the mesons as explained above 7.4.

  * •

We calculated the range of the baryonic spectrum accordingly.

  * •

We derived the range of the spectrum for two states above, and two states
below the expected $J+n$ of the baryonic threshold for each of the two
spectra. For example, in the first row the in the ’J Spec’ column, the
$3264-3374$ is the range of the spectrum of the first state that we expect to
decay to baryon-antibaryon pair. The $3526-3626$ is the first state above that
should still decay to a baryonic pair and should have $J+n=4$, whereas the
$2972-3095$ should decay through annihilation only, and should have $J+n=2$.

  * •

When we weren’t able to calculate the baryonic threshold (since the baryons
weren’t measured yet), we started from the mesonic threshold and calculated
the trajectory from there up to 12 states.

The ’Genuine’ column indicates whether the quark content is a genuine
tetraquark or a not obviously genuine. This was decided as follows:

  * •

If the content includes a light quark ($u$, $d$, $s$) and its counterpart, we
assume its source could be a meson that decay through string tear. Thus this
is not obviously genuine case. This is marked at the table as an empty cell.

  * •

If the content include a heavy quark ($c$, $b$) and its counterpart, which is
less likely to be a product of meson string break, it is likely to be genuine.
This was marked with one $*$.

  * •

$**$ means it is a pure tetraquark. These do not contain quark-antiquark pair
of the same flavour.

Empty baryonic threshold means these baryons weren’t found yet.

Table 107: Tetraquark predicted configurations and thresholds. $\\#$ |  Candi- dates |  $J^{PC}$ |  Quarks |  Thry Width $[MeV]$ |  Mesons Pair |  Meson Threshold $[MeV]$ |  Baryon Anti- baryon |  Baryonic Threshold $[MeV]$ |  $J$ Spec |  $n$ Spec |  $a_{T_{j}}$ $a_{T_{n}}$ |  Thry $J+n$ |  Gen- uine
---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 |  |  | $c\bar{u}u\bar{u}$ |  $79-118$ $30-61$ |  $D^{0}\pi^{0}_{u}$ |  $2000$ |  $\Lambda^{+}_{c}\bar{p}$ $\Xi^{+}_{c}\bar{\Sigma}^{-}$ $\Sigma^{++}_{c}\bar{\Delta}^{--}$ |  $3224$ $3657$ $3686$ |  $2634-2779$ $2972-3095$ $3264-3374$ $3526-3626$ $3766-3858$ |  $2270-2448$ $2829-2961$ $3264-3374$ $3635-3731$ $3964-4051$ |  $-1.6$-$-1.2$ $-1.2$-$-0.92$ |  $3$ $2$ |
2 |  $X(3500)$ $X(3800)$ |  (${0}$ or ${1}$)?? $?^{??}$ | $c\bar{d}d\bar{u}$ |  $79-118$ $30-61$ |  $D^{0}\pi^{0}_{d}$ $D^{+}\pi^{-}$ |  $2000$ $2010$ |  $\Lambda^{+}_{c}\bar{p}$ $\Sigma^{0}_{c}\bar{n}$ $\Xi^{0}_{c}\bar{\Lambda}^{0}$ |  $3224$ $3394$ $3586$ |  $2634-2779$ $2972-3095$ $3264-3374$ $3526-3626$ $3766-3858$ |  $2270-2448$ $2829-2961$ $3264-3374$ $3635-3731$ $3964-4051$ |  $-1.6$-$-1.2$ $-1.2$-$-0.92$ |  $3$ $2$ |
3 |  |  | $c\bar{d}u\bar{u}$ |  $78-117$ $31-61$ |  $D^{+}\pi^{0}_{u}$ $D^{0}\pi^{+}$ |  $2005$ $2005$ |  $\Lambda^{+}_{c}\bar{n}$ $\Sigma^{++}_{c}\bar{p}$ $\Xi^{+}_{c}\bar{\Lambda}^{0}$ |  $3226$ $3392$ $3584$ |  $2637-2782$ $2974-3098$ $3266-3376$ $3528-3628$ $3767-3860$ |  $2273-2451$ $2831-2963$ $3266-3376$ $3637-3733$ $3966-4053$ |  $-1.6$-$-1.2$ $-1.2$-$-0.93$ |  $3$ $2$ |
4 |  |  | $c\bar{u}d\bar{u}$ |  $41-72$ $32-63$ |  $D^{0}\pi^{-}$ |  $2005$ |  $\Sigma^{0}_{c}\bar{p}$ $\Lambda^{+}_{c}\bar{\Delta}^{--}$ $\Xi^{0}_{c}\bar{\Sigma}^{-}$ |  $3392$ $3518$ $3659$ |  $2854-2992$ $3160-3282$ $3432-3542$ $3679-3780$ $3908-4002$ |  $2537-2698$ $3029-3157$ $3432-3542$ $3783-3881$ $4098-4187$ |  $-2.3$-$-1.8$ $-1.7$-$-1.4$ |  $3$ $2$ | $**$
5 |  |  | $c\bar{d}d\bar{d}$ |  $78-117$ $31-61$ |  $D^{+}\pi^{0}_{d}$ |  $2005$ |  $\Lambda^{+}_{c}\bar{n}$ $\Xi^{0}_{c}\bar{\Sigma}^{+}$ $\Sigma^{0}_{c}\bar{\Delta}^{+}$ |  $3226$ $3667$ $3686$ |  $2637-2782$ $2974-3098$ $3266-3376$ $3528-3628$ $3767-3860$ |  $2273-2451$ $2831-2963$ $3266-3376$ $3637-3733$ $3966-4053$ |  $-1.6$-$-1.2$ $-1.2$-$-0.93$ |  $3$ $2$ |
6 |  |  | $c\bar{d}u\bar{d}$ |  $40-71$ $32-63$ |  $D^{+}\pi^{+}$ |  $2010$ |  $\Sigma^{++}_{c}\bar{n}$ $\Lambda^{+}_{c}\bar{\Delta}^{+}$ $\Xi^{+}_{c}\bar{\Sigma}^{+}$ |  $3394$ $3518$ $3665$ |  $2856-2994$ $3162-3284$ $3434-3544$ $3681-3782$ $3909-4004$ |  $2540-2701$ $3031-3160$ $3434-3544$ $3784-3883$ $4099-4189$ |  $-2.3$-$-1.9$ $-1.7$-$-1.4$ |  $3$ $2$ | $**$
7 |  $X(2632)$ |  $?^{??}$ | $c\bar{s}u\bar{u}$ |  $121-195$ $29-57$ |  $D^{+}_{s}\pi^{0}_{u}$ $D^{0}K^{+}$ |  $2103$ $2359$ |  $\Lambda^{+}_{c}\bar{\Lambda}^{0}$ $\Sigma^{++}_{c}\bar{\Sigma}^{-}$ $\Xi^{+}_{c}\bar{\Xi}^{0}$ |  $3402$ $3643$ $3783$ |  $2841-2983$ $3162-3284$ $3442-3552$ $3695-3796$ $3928-4021$ |  $2502-2672$ $3025-3155$ $3442-3552$ $3801-3898$ $4121-4209$ |  $-1.8$-$-1.3$ $-1.3$-$-1.0$ |  $3$ $2$ |
8 |  |  | $c\bar{d}d\bar{s}$ |  $121-195$ $29-57$ |  $D^{+}_{s}\pi^{0}_{d}$ $D^{+}K^{0}$ |  $2103$ $2368$ |  $\Lambda^{+}_{c}\bar{\Lambda}^{0}$ $\Sigma^{0}_{c}\bar{\Sigma}^{+}$ $\Xi^{0}_{c}\bar{\Xi}^{+}$ |  $3402$ $3651$ $3792$ |  $2841-2983$ $3162-3284$ $3442-3552$ $3695-3796$ $3928-4021$ |  $2502-2672$ $3025-3155$ $3442-3552$ $3801-3898$ $4121-4209$ |  $-1.8$-$-1.3$ $-1.3$-$-1.0$ |  $3$ $2$ |
9 |  $T^{a}_{c\bar{s}0}(2900)^{0}$ |  $0^{?}$ | $c\bar{s}d\bar{u}$ |  $100-152$ $29-59$ |  $D^{+}_{s}\pi^{-}$ $D^{0}K^{0}$ |  $2108$ $2363$ |  $\Lambda^{+}_{c}\bar{\Sigma}^{-}$ $\Sigma^{0}_{c}\bar{\Lambda}^{0}$ $\Xi^{0}_{c}\bar{\Xi}^{0}$ |  $3475$ $3570$ $3785$ |  $2936-3075$ $3243-3365$ $3515-3625$ $3762-3863$ $3990-4084$ |  $2616-2780$ $3112-3240$ $3515-3625$ $3865-3963$ $4179-4269$ |  $-2.0$-$-1.6$ $-1.5$-$-1.2$ |  $3$ $2$ | $**$
10 |  $T_{cs1}(2900)^{0}$ $T^{a}_{c\bar{s}0}(2900)^{++}$ |  $1^{-}$ $0^{?}$ | $c\bar{d}u\bar{s}$ |  $98-147$ $29-59$ |  $D^{+}_{s}\pi^{+}$ $D^{+}K^{+}$ |  $2108$ $2364$ |  $\Lambda^{+}_{c}\bar{\Sigma}^{+}$ $\Sigma^{++}_{c}\bar{\Lambda}^{0}$ $\Xi^{+}_{c}\bar{\Xi}^{+}$ |  $3483$ $3570$ $3790$ |  $2946-3085$ $3252-3374$ $3523-3633$ $3769-3870$ $3996-4091$ |  $2628-2791$ $3121-3250$ $3523-3633$ $3872-3970$ $4186-4275$ |  $-2.1$-$-1.6$ $-1.5$-$-1.2$ |  $3$ $2$ | $**$
11 |  |  | $c\bar{u}s\bar{u}$ |  $127-208$ $27-54$ |  $D^{0}K^{-}$ |  $2359$ |  $\Xi^{0}_{c}\bar{p}$ $\Xi^{+}_{c}\bar{\Delta}^{--}$ $\Omega^{0}_{c}\bar{\Sigma}^{-}$ |  $3408$ $3700$ $3884$ |  $2793-2943$ $3147-3273$ $3448-3558$ $3715-3814$ $3957-4048$ |  $3448-3558$ $3825-3921$ $4157-4243$ $4457-4536$ $4734-4808$ |  $-2.2$-$-1.8$ $-1.9$-$-1.6$ |  $2$ $1$ | $**$
12 |  $T_{cs0}(2900)^{0}$ |  $0^{+}$ | $c\bar{d}s\bar{u}$ |  $127-210$ $27-54$ |  $D^{0}\bar{K}^{0}$ $D^{+}K^{-}$ |  $2363$ $2364$ |  $\Xi^{+}_{c}\bar{p}$ $\Xi^{0}_{c}\bar{n}$ $\Omega^{0}_{c}\bar{\Lambda}^{0}$ |  $3406$ $3410$ $3811$ |  $2790-2941$ $3145-3270$ $3446-3556$ $3713-3812$ $3955-4047$ |  $3446-3556$ $3823-3919$ $4155-4241$ $4456-4535$ $4733-4806$ |  $-2.2$-$-1.8$ $-1.9$-$-1.6$ |  $2$ $1$ | $**$
13 |  |  | $c\bar{d}s\bar{d}$ |  $127-208$ $27-54$ |  $D^{+}\bar{K}^{0}$ |  $2368$ |  $\Xi^{+}_{c}\bar{n}$ $\Xi^{0}_{c}\bar{\Delta}^{+}$ $\Omega^{0}_{c}\bar{\Sigma}^{+}$ |  $3408$ $3702$ $3892$ |  $2793-2943$ $3147-3273$ $3448-3558$ $3715-3814$ $3957-4048$ |  $3448-3558$ $3825-3921$ $4157-4243$ $4457-4536$ $4734-4808$ |  $-2.2$-$-1.8$ $-1.9$-$-1.6$ |  $2$ $1$ | $**$
14 |  |  | $c\bar{s}s\bar{u}$ |  $178-330$ $25-51$ |  $D^{+}_{s}K^{-}$ $D^{0}\phi(1020)$ |  $2462$ $2884$ |  $\Xi^{0}_{c}\bar{\Lambda}^{0}$ $\Xi^{+}_{c}\bar{\Sigma}^{-}$ $\Omega^{0}_{c}\bar{\Xi}^{0}$ |  $3586$ $3657$ $4010$ |  $3004-3150$ $3338-3462$ $3626-3736$ $3883-3983$ $4118-4211$ |  $2636-2820$ $3197-3329$ $3626-3736$ $3990-4086$ $4313-4400$ |  $-1.3$-$-0.91$ $-1.0$-$-0.71$ |  $3$ $2$ |
15 |  |  | $c\bar{s}u\bar{s}$ |  $166-300$ $27-53$ |  $D^{+}_{s}K^{+}$ |  $2462$ |  $\Lambda^{+}_{c}\bar{\Xi}^{+}$ $\Sigma^{++}_{c}\bar{\Xi}^{0}$ $\Xi^{+}_{c}\bar{\Omega}^{+}$ |  $3608$ $3769$ $4140$ |  $3062-3203$ $3374-3497$ $3648-3758$ $3896-3996$ $4124-4217$ |  $2732-2901$ $3241-3371$ $3648-3758$ $3999-4097$ $4313-4402$ |  $-1.7$-$-1.2$ $-1.2$-$-0.94$ |  $3$ $2$ | $**$
16 |  |  | $c\bar{s}d\bar{s}$ |  $168-307$ $26-53$ |  $D^{+}_{s}K^{0}$ |  $2466$ |  $\Lambda^{+}_{c}\bar{\Xi}^{0}$ $\Sigma^{0}_{c}\bar{\Xi}^{+}$ $\Xi^{0}_{c}\bar{\Omega}^{+}$ |  $3601$ $3776$ $4142$ |  $3053-3194$ $3366-3489$ $3641-3751$ $3889-3990$ $4118-4211$ |  $2721-2891$ $3233-3363$ $3641-3751$ $3993-4090$ $4308-4396$ |  $-1.7$-$-1.2$ $-1.2$-$-0.92$ |  $3$ $2$ | $**$
17 |  |  | $c\bar{d}s\bar{s}$ |  $178-332$ $25-51$ |  $D^{+}_{s}\bar{K}^{0}$ $D^{+}\phi(1020)$ |  $2466$ $2889$ |  $\Xi^{+}_{c}\bar{\Lambda}^{0}$ $\Xi^{0}_{c}\bar{\Sigma}^{+}$ $\Omega^{0}_{c}\bar{\Xi}^{+}$ |  $3584$ $3667$ $4017$ |  $3001-3148$ $3336-3460$ $3624-3734$ $3881-3981$ $4117-4209$ |  $2632-2817$ $3194-3327$ $3624-3734$ $3988-4085$ $4311-4398$ |  $-1.3$-$-0.9$ $-0.99$-$-0.7$ |  $3$ $2$ |
18 |  |  | $c\bar{s}s\bar{s}$ |  $242-504$ $23-47$ |  $D^{+}_{s}\phi(1020)$ |  $2987$ |  $\Xi^{+}_{c}\bar{\Xi}^{0}$ $\Xi^{0}_{c}\bar{\Xi}^{+}$ $\Omega^{0}_{c}\bar{\Omega}^{+}$ |  $3783$ $3792$ $4367$ |  $3214-3360$ $3541-3665$ $3823-3933$ $4075-4175$ $4306-4399$ |  $3823-3933$ $4180-4277$ $4497-4585$ $4786-4866$ $5053-5128$ |  $-2.2$-$-1.8$ $-1.9$-$-1.6$ |  $2$ $1$ |
19 |  |  | $c\bar{c}d\bar{d}$ |  $24-51$ $32-64$ |  $\eta_{c}(1S)\pi^{0}_{d}$ $D^{+}D^{-}$ |  $3119$ $3740$ |  $\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ $\Sigma^{0}_{c}\bar{\Sigma}^{0}_{c}$ $\Xi^{0}_{c}\bar{\Xi}^{0}_{c}$ |  $4572$ $4908$ $4940$ |  $4182-4308$ $4404-4521$ $4612-4722$ $4808-4912$ $4993-5092$ |  $3969-4104$ $4308-4428$ $4612-4722$ $4891-4993$ $5151-5246$ |  $-2.7$-$-2.2$ $-2.3$-$-2.0$ |  $5$ $3$ |
20 |  |  | $c\bar{c}u\bar{u}$ |  $24-51$ $32-64$ |  $\eta_{c}(1S)\pi^{0}_{u}$ $D^{0}\bar{D}^{0}$ |  $3119$ $3730$ |  $\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ $\Sigma^{++}_{c}\bar{\Sigma}^{--}_{c}$ $\Xi^{+}_{c}\bar{\Xi}^{-}_{c}$ |  $4572$ $4908$ $4936$ |  $4182-4308$ $4404-4521$ $4612-4722$ $4808-4912$ $4993-5092$ |  $3969-4104$ $4308-4428$ $4612-4722$ $4891-4993$ $5151-5246$ |  $-2.7$-$-2.2$ $-2.3$-$-2.0$ |  $5$ $3$ |
21 |  |  | $c\bar{c}u\bar{d}$ |  $11-31$ $34-67$ |  $\eta_{c}(1S)\pi^{+}$ $D^{+}\bar{D}^{0}$ |  $3124$ $3735$ |  $\Sigma^{++}_{c}\bar{\Lambda}^{-}_{c}$ $\Lambda^{+}_{c}\bar{\Sigma}^{0}_{c}$ $\Xi^{+}_{c}\bar{\Xi}^{0}_{c}$ |  $4740$ $4740$ $4938$ |  $4373-4497$ $4583-4699$ $4780-4890$ $4967-5072$ $5145-5245$ |  $4174-4306$ $4491-4611$ $4780-4890$ $5047-5150$ $5297-5394$ |  $-2.6$-$-2.0$ $-2.0$-$-1.6$ |  $6$ $4$ | $*$
22 |  $Z_{c}(3900)$ $Z_{c}(4200)$ $Z_{c}(4430)$ $X(4020)$ $X(4051)$ $X(4055)$ $X(4100)$ $X(4240)$ $X(4250)$ |  $1^{+-}$ $1^{+-}$ $1^{+-}$ $?^{?-}$ $?^{?+}$ $?^{?-}$ $?^{??}$ $0^{--}$ $?^{?-}$ | $c\bar{c}d\bar{u}$ |  $11-31$ $34-67$ |  $\eta_{c}(1S)\pi^{-}$ $D^{0}D^{-}$ |  $3124$ $3735$ |  $\Lambda^{+}_{c}\bar{\Sigma}^{--}_{c}$ $\Sigma^{0}_{c}\bar{\Lambda}^{-}_{c}$ $\Xi^{0}_{c}\bar{\Xi}^{-}_{c}$ |  $4740$ $4740$ $4938$ |  $4373-4497$ $4583-4699$ $4780-4890$ $4967-5072$ $5145-5245$ |  $4174-4306$ $4491-4611$ $4780-4890$ $5047-5150$ $5297-5394$ |  $-2.6$-$-2.0$ $-2.0$-$-1.6$ |  $6$ $4$ | $*$
23 |  |  | $c\bar{c}s\bar{u}$ |  $47-79$ $29-59$ |  $\eta_{c}(1S)K^{-}$ $D^{0}D^{-}_{s}$ |  $3478$ $3833$ |  $\Xi^{0}_{c}\bar{\Lambda}^{-}_{c}$ $\Xi^{+}_{c}\bar{\Sigma}^{--}_{c}$ $\Omega^{0}_{c}\bar{\Xi}^{-}_{c}$ |  $4756$ $4922$ $5163$ |  $4362-4488$ $4587-4704$ $4796-4906$ $4993-5097$ $5179-5278$ |  $4145-4282$ $4489-4610$ $4796-4906$ $5076-5178$ $5337-5432$ |  $-3.3$-$-2.7$ $-2.0$-$-1.6$ |  $4$ $3$ | $*$
24 |  $T_{\psi s1}^{\theta}(4000)^{+}$ $T_{\psi s1}(4220)^{+}$ $T_{\psi s1}^{\theta}(4000)^{0}$ |  $1^{+}$ $1^{+}$ $1^{+}$ | $c\bar{c}u\bar{s}$ |  $47-79$ $29-59$ |  $\eta_{c}(1S)K^{+}$ $D^{+}_{s}\bar{D}^{0}$ |  $3478$ $3833$ |  $\Lambda^{+}_{c}\bar{\Xi}^{0}_{c}$ $\Sigma^{++}_{c}\bar{\Xi}^{-}_{c}$ $\Xi^{+}_{c}\bar{\Omega}^{0}_{c}$ |  $4756$ $4922$ $5163$ |  $4362-4488$ $4587-4704$ $4796-4906$ $4993-5097$ $5179-5278$ |  $4145-4282$ $4489-4610$ $4796-4906$ $5076-5178$ $5337-5432$ |  $-3.3$-$-2.7$ $-2.0$-$-1.6$ |  $4$ $3$ | $*$
25 |  |  | $c\bar{c}d\bar{s}$ |  $47-80$ $29-59$ |  $\eta_{c}(1S)K^{0}$ $D^{+}_{s}D^{-}$ |  $3482$ $3838$ |  $\Lambda^{+}_{c}\bar{\Xi}^{-}_{c}$ $\Sigma^{0}_{c}\bar{\Xi}^{0}_{c}$ $\Xi^{0}_{c}\bar{\Omega}^{0}_{c}$ |  $4754$ $4924$ $5165$ |  $4359-4486$ $4585-4702$ $4794-4904$ $4991-5095$ $5177-5276$ |  $4142-4279$ $4487-4608$ $4794-4904$ $5075-5176$ $5335-5430$ |  $-3.2$-$-2.7$ $-2.0$-$-1.6$ |  $4$ $3$ | $*$
26 |  |  | $c\bar{c}s\bar{d}$ |  $47-80$ $29-59$ |  $\eta_{c}(1S)\bar{K}^{0}$ $D^{+}D^{-}_{s}$ |  $3482$ $3838$ |  $\Xi^{+}_{c}\bar{\Lambda}^{-}_{c}$ $\Xi^{0}_{c}\bar{\Sigma}^{0}_{c}$ $\Omega^{0}_{c}\bar{\Xi}^{0}_{c}$ |  $4754$ $4924$ $5165$ |  $4359-4486$ $4585-4702$ $4794-4904$ $4991-5095$ $5177-5276$ |  $4142-4279$ $4487-4608$ $4794-4904$ $5075-5176$ $5335-5430$ |  $-3.2$-$-2.7$ $-2.0$-$-1.6$ |  $4$ $3$ | $*$
27 |  |  | $c\bar{u}c\bar{u}$ |  |  $D^{0}D^{0}$ |  $3730$ |  $\Xi^{+}_{cc}\bar{p}$ $\Xi^{++}_{cc}\bar{\Delta}^{--}$ $\Omega^{+}_{cc}\bar{\Sigma}^{-}$ |  $4457$ $4854$ |  $3981-4115$ $4253-4373$ $4497-4607$ $4721-4823$ $4930-5026$ |  $4497-4607$ $4816-4915$ $5105-5196$ $5372-5456$ $5621-5700$ |  $-3.7$-$-3.3$ $-3.0$-$-2.6$ |  $2$ $1$ | $**$
28 |  $T_{cc}(3875)$ |  $?^{?}$ | $c\bar{d}c\bar{u}$ |  |  $D^{+}D^{0}$ $D^{0}D^{+}$ |  $3735$ $3735$ |  $\Xi^{+}_{cc}\bar{n}$ $\Xi^{++}_{cc}\bar{p}$ $\Omega^{+}_{cc}\bar{\Lambda}^{0}$ |  $4459$ $4560$ |  $3983-4118$ $4255-4375$ $4499-4609$ $4723-4825$ $4932-5027$ |  $4499-4609$ $4818-4917$ $5107-5198$ $5373-5458$ $5622-5702$ |  $-3.7$-$-3.3$ $-3.0$-$-2.6$ |  $2$ $1$ | $**$
29 |  |  | $c\bar{d}c\bar{d}$ |  |  $D^{+}D^{+}$ |  $3740$ |  $\Xi^{++}_{cc}\bar{n}$ $\Xi^{+}_{cc}\bar{\Delta}^{+}$ $\Omega^{+}_{cc}\bar{\Sigma}^{+}$ |  $4562$ $4751$ |  $4109-4241$ $4367-4487$ $4602-4712$ $4819-4921$ $5021-5118$ |  $3852-4000$ $4256-4381$ $4602-4712$ $4910-5010$ $5192-5284$ |  $-3.2$-$-2.7$ $-2.3$-$-2.0$ |  $3$ $2$ | $**$
30 |  |  | $c\bar{s}c\bar{u}$ |  |  $D^{+}_{s}D^{0}$ $D^{0}D^{+}_{s}$ |  $3833$ $3833$ |  $\Xi^{+}_{cc}\bar{\Lambda}^{0}$ $\Xi^{++}_{cc}\bar{\Sigma}^{-}$ $\Omega^{+}_{cc}\bar{\Xi}^{0}$ |  $4635$ $4811$ |  $4181-4314$ $4440-4560$ $4675-4785$ $4892-4994$ $5094-5191$ |  $3922-4071$ $4328-4453$ $4675-4785$ $4983-5083$ $5264-5356$ |  $-3.9$-$-3.4$ $-2.1$-$-1.8$ |  $2$ | $**$
31 |  |  | $c\bar{d}c\bar{s}$ |  |  $D^{+}D^{+}_{s}$ $D^{+}_{s}D^{+}$ |  $3838$ $3838$ |  $\Xi^{+}_{cc}\bar{\Sigma}^{+}$ $\Xi^{++}_{cc}\bar{\Lambda}^{0}$ $\Omega^{+}_{cc}\bar{\Xi}^{+}$ |  $4716$ $4738$ |  $4279-4410$ $4528-4647$ $4756-4866$ $4967-5070$ $5165-5262$ |  $4032-4178$ $4421-4544$ $4756-4866$ $5057-5157$ $5332-5425$ |  $-3.3$-$-2.8$ $-2.4$-$-2.0$ |  $3$ $2$ | $**$
32 |  $X(3960)$ $X(4140)$ $X(4274)$ $\chi_{c0}(4500)$ $\chi_{c1}(4685)$ $\chi_{c0}(4700)$ $X(4350)$ $X(4630)$ $\psi(4360)$ $\psi(4660)$ |  $0^{++}$ $1^{++}$ $1^{++}$ $0^{++}$ $1^{++}$ $0^{++}$ $?^{?+}$ $1^{-+}$ $1^{--}$ $1^{--}$ | $c\bar{c}s\bar{s}$ |  $89-134$ $27-54$ |  $D^{+}_{s}D^{-}_{s}$ $\eta_{c}(1S)\phi(1020)$ |  $3936$ $4003$ |  $\Xi^{+}_{c}\bar{\Xi}^{-}_{c}$ $\Xi^{0}_{c}\bar{\Xi}^{0}_{c}$ $\Omega^{0}_{c}\bar{\Omega}^{0}_{c}$ |  $4936$ $4940$ $5390$ |  $4536-4664$ $4765-4882$ $4976-5086$ $5174-5278$ $5361-5459$ |  $4315-4454$ $4666-4787$ $4976-5086$ $5258-5359$ $5519-5613$ |  $-3.8$-$-3.2$ $-2.7$-$-2.3$ |  $3$ $2$ |
33 |  |  | $c\bar{s}c\bar{s}$ |  |  $D^{+}_{s}D^{+}_{s}$ |  $3936$ |  $\Xi^{+}_{cc}\bar{\Xi}^{+}$ $\Xi^{++}_{cc}\bar{\Xi}^{0}$ $\Omega^{+}_{cc}\bar{\Omega}^{+}$ |  $4841$ $4937$ |  $4401-4533$ $4652-4772$ $4881-4991$ $5093-5195$ $5291-5387$ |  $4151-4298$ $4544-4668$ $4881-4991$ $5182-5282$ $5457-5550$ |  $-2.9$-$-2.4$ $-2.1$-$-1.7$ |  $3$ $2$ | $**$
34 |  |  | $c\bar{c}c\bar{u}$ |  $13-33$ $29-59$ |  $\eta_{c}(1S)D^{0}$ $D^{0}\eta_{c}(1S)$ |  $4849$ $4849$ |  $\Xi^{+}_{cc}\bar{\Lambda}^{-}_{c}$ $\Xi^{++}_{cc}\bar{\Sigma}^{--}_{c}$ $\Omega^{+}_{cc}\bar{\Xi}^{-}_{c}$ |  $5805$ $6076$ |  $5481-5602$ $5668-5783$ $5845-5955$ $6014-6120$ $6176-6278$ |  $5305-5434$ $5586-5704$ $5845-5955$ $6087-6191$ $6316-6414$ |  $-5.5$-$-4.9$ $-3.6$-$-3.2$ |  $4$ $3$ | $*$
35 |  |  | $c\bar{c}c\bar{d}$ |  $8-24$ $30-61$ |  $\eta_{c}(1S)D^{+}$ $D^{+}\eta_{c}(1S)$ |  $4854$ $4854$ |  $\Xi^{++}_{cc}\bar{\Lambda}^{-}_{c}$ $\Xi^{+}_{cc}\bar{\Sigma}^{0}_{c}$ $\Omega^{+}_{cc}\bar{\Xi}^{0}_{c}$ |  $5908$ $5973$ |  $5595-5716$ $5776-5891$ $5948-6058$ $6113-6219$ $6271-6373$ |  $5425-5552$ $5696-5814$ $5948-6058$ $6184-6288$ $6407-6506$ |  $-5.2$-$-4.5$ $-4.0$-$-3.6$ |  $5$ $3$ | $*$
36 |  |  | $c\bar{c}c\bar{s}$ |  $26-53$ $27-55$ |  $\eta_{c}(1S)D^{+}_{s}$ $D^{+}_{s}\eta_{c}(1S)$ |  $4952$ $4952$ |  $\Xi^{+}_{cc}\bar{\Xi}^{0}_{c}$ $\Xi^{++}_{cc}\bar{\Xi}^{-}_{c}$ $\Omega^{+}_{cc}\bar{\Omega}^{0}_{c}$ |  $5989$ $6090$ |  $5664-5786$ $5851-5967$ $6029-6139$ $6198-6304$ $6360-6462$ |  $5487-5616$ $5769-5888$ $6029-6139$ $6271-6375$ $6499-6597$ |  $-5.1$-$-4.4$ $-3.3$-$-2.8$ |  $4$ $3$ | $*$
37 |  $T_{\psi\psi}(6600)$ $T_{\psi\psi}(6600)$ $T_{\psi\psi}(6900)$ $T_{\psi\psi}(6900)$ $T_{\psi\psi}(7300)$ |  $?^{??}$ $?^{??}$ $?^{??}$ $?^{??}$ $?^{??}$ | $c\bar{c}c\bar{c}$ |  $6-21$ $29-58$ |  $\eta_{c}(1S)\eta_{c}(1S)$ |  $5968$ |  $\Xi^{+}_{cc}\bar{\Xi}^{-}_{cc}$ $\Xi^{++}_{cc}\bar{\Xi}^{--}_{cc}$ $\Omega^{+}_{cc}\bar{\Omega}^{-}_{cc}$ |  $7038$ $7244$ |  $6768-6887$ $6926-7040$ $7078-7188$ $7225-7331$ $7366-7469$ |  $6622-6745$ $6857-6973$ $7078-7188$ $7288-7393$ $7489-7589$ |  $-5.9$-$-5.1$ $-4.2$-$-3.7$ |  $6$ $4$ | $*$
38 |  |  | $c\bar{b}d\bar{d}$ |  |  $B^{+}_{c}\pi^{0}_{d}$ $D^{+}\bar{B}^{0}$ |  $6409$ $7150$ |  $\Xi^{0}_{c}\bar{\Xi}^{+}_{b}$ $\Sigma^{0}_{c}\bar{\Sigma}^{+}_{b}$ $\Lambda^{+}_{c}\bar{\Sigma}^{0}_{b}$ |  $8267$ $8270$ |  $7986-8106$ $8150-8265$ $8307-8417$ $8457-8563$ $8602-8704$ |  $7833-7959$ $8078-8195$ $8307-8417$ $8522-8626$ $8726-8826$ |  $-2.6$-$-1.8$ $-2.3$-$-1.8$ |  $8$ $5$ |
39 |  |  | $c\bar{b}u\bar{u}$ |  |  $B^{+}_{c}\pi^{0}_{u}$ $D^{0}B^{-}$ |  $6409$ $7144$ |  $\Xi^{+}_{c}\bar{\Xi}^{0}_{b}$ $\Sigma^{++}_{c}\bar{\Sigma}^{-}_{b}$ $\Lambda^{+}_{c}\bar{\Sigma}^{0}_{b}$ |  $8260$ $8265$ |  $7978-8099$ $8143-8258$ $8300-8410$ $8451-8556$ $8595-8698$ |  $7825-7951$ $8071-8188$ $8300-8410$ $8516-8620$ $8720-8819$ |  $-2.5$-$-1.8$ $-2.3$-$-1.8$ |  $8$ $5$ |
40 |  |  | $c\bar{b}d\bar{u}$ |  |  $B^{+}_{c}\pi^{-}$ $D^{0}\bar{B}^{0}$ |  $6414$ $7145$ |  $\Lambda^{+}_{c}\bar{\Sigma}^{-}_{b}$ $\Xi^{0}_{c}\bar{\Xi}^{0}_{b}$ $\Sigma^{0}_{c}\bar{\Sigma}^{0}_{b}$ |  $8097$ $8262$ |  $7798-7920$ $7972-8088$ $8137-8247$ $8294-8400$ $8445-8546$ |  $7635-7764$ $7896-8014$ $8137-8247$ $8362-8466$ $8574-8672$ |  $-2.5$-$-1.8$ $-1.5$-$-1.1$ |  $7$ $5$ | $**$
41 |  |  | $c\bar{b}u\bar{d}$ |  |  $B^{+}_{c}\pi^{+}$ $D^{+}B^{-}$ |  $6414$ $7149$ |  $\Lambda^{+}_{c}\bar{\Sigma}^{+}_{b}$ $\Xi^{+}_{c}\bar{\Xi}^{+}_{b}$ $\Sigma^{++}_{c}\bar{\Sigma}^{0}_{b}$ |  $8102$ $8265$ |  $7804-7926$ $7977-8093$ $8142-8252$ $8299-8404$ $8450-8551$ |  $7641-7769$ $7902-8020$ $8142-8252$ $8367-8470$ $8579-8677$ |  $-2.5$-$-1.8$ $-1.6$-$-1.1$ |  $7$ $5$ | $**$
42 |  |  | $c\bar{b}s\bar{u}$ |  |  $B^{+}_{c}K^{-}$ $D^{0}\bar{B}^{0}_{s}$ |  $6768$ $7232$ |  $\Xi^{+}_{c}\bar{\Sigma}^{-}_{b}$ $\Omega^{0}_{c}\bar{\Xi}^{0}_{b}$ $\Xi^{0}_{c}\bar{\Sigma}^{0}_{b}$ |  $8279$ $8487$ |  $7980-8102$ $8154-8270$ $8319-8429$ $8476-8581$ $8627-8728$ |  $7816-7945$ $8078-8196$ $8319-8429$ $8544-8647$ $8755-8853$ |  $-3.0$-$-2.3$ $-2.2$-$-1.7$ |  $6$ $4$ | $**$
43 |  |  | $c\bar{b}u\bar{s}$ |  |  $B^{+}_{c}K^{+}$ $D^{+}_{s}B^{-}$ |  $6768$ $7247$ |  $\Lambda^{+}_{c}\bar{\Xi}^{+}_{b}$ $\Sigma^{++}_{c}\bar{\Xi}^{0}_{b}$ $\Xi^{+}_{c}\bar{\Omega}^{+}_{b}$ |  $8083$ $8246$ $8514$ |  $7742-7868$ $7939-8056$ $8123-8233$ $8296-8400$ $8460-8559$ |  $7552-7688$ $7853-7974$ $8123-8233$ $8370-8472$ $8600-8695$ |  $-2.3$-$-1.7$ $-2.1$-$-1.6$ |  $5$ $3$ | $**$
44 |  |  | $c\bar{b}s\bar{d}$ |  |  $B^{+}_{c}\bar{K}^{0}$ $D^{+}\bar{B}^{0}_{s}$ |  $6772$ $7237$ |  $\Xi^{0}_{c}\bar{\Sigma}^{+}_{b}$ $\Omega^{0}_{c}\bar{\Xi}^{+}_{b}$ $\Xi^{+}_{c}\bar{\Sigma}^{0}_{b}$ |  $8286$ $8492$ |  $7988-8110$ $8161-8277$ $8326-8436$ $8483-8588$ $8633-8734$ |  $7824-7953$ $8086-8204$ $8326-8436$ $8550-8654$ $8762-8860$ |  $-3.0$-$-2.3$ $-2.2$-$-1.8$ |  $6$ $4$ | $**$
45 |  |  | $c\bar{b}d\bar{s}$ |  |  $B^{+}_{c}K^{0}$ $D^{+}_{s}\bar{B}^{0}$ |  $6772$ $7248$ |  $\Lambda^{+}_{c}\bar{\Xi}^{0}_{b}$ $\Sigma^{0}_{c}\bar{\Xi}^{+}_{b}$ $\Xi^{0}_{c}\bar{\Omega}^{+}_{b}$ |  $8078$ $8251$ $8516$ |  $7736-7862$ $7934-8051$ $8118-8228$ $8291-8395$ $8456-8555$ |  $7545-7682$ $7848-7969$ $8118-8228$ $8365-8467$ $8595-8691$ |  $-2.3$-$-1.7$ $-2.1$-$-1.6$ |  $5$ $3$ | $**$
46 |  |  | $b\bar{u}c\bar{u}$ |  |  $B^{+}D^{0}$ |  $7144$ |  $\Xi^{+}_{bc}\bar{\Delta}^{--}$ $\Xi^{0}_{bc}\bar{p}$ $\Omega^{0}_{bc}\bar{\Sigma}^{-}$ |  |  $7154-7194$ $7449-7482$ $7702-7732$ $7928-7955$ $8135-8159$ $8326-8349$ $8506-8528$ $8676-8697$ $8838-8857$ $8992-9011$ $9141-9159$ $9284-9301$ |  $7154-7194$ $7565-7597$ $7904-7931$ $8200-8224$ $8467-8489$ $8713-8733$ $8942-8961$ $9157-9175$ $9361-9378$ $9556-9572$ $9742-9758$ $9921-9937$ |  $-2.3$-$-2.1$ $-1.6$-$-1.5$ |  | $**$
47 |  |  | $b\bar{d}c\bar{u}$ |  |  $B^{0}D^{0}$ $B^{+}D^{+}$ |  $7145$ $7149$ |  $\Xi^{+}_{bc}\bar{p}$ $\Xi^{0}_{bc}\bar{n}$ $\Omega^{0}_{bc}\bar{\Lambda}^{0}$ |  |  $7155-7195$ $7450-7483$ $7703-7732$ $7929-7956$ $8135-8160$ $8327-8350$ $8507-8528$ $8677-8697$ $8838-8858$ $8993-9012$ $9141-9159$ $9284-9302$ |  $7155-7195$ $7566-7598$ $7905-7932$ $8201-8225$ $8468-8490$ $8713-8734$ $8942-8961$ $9157-9175$ $9361-9379$ $9556-9573$ $9743-9758$ $9922-9937$ |  $-2.3$-$-2.1$ $-1.6$-$-1.5$ |  | $**$
48 |  |  | $b\bar{d}c\bar{d}$ |  |  $B^{0}D^{+}$ |  $7150$ |  $\Xi^{+}_{bc}\bar{n}$ $\Xi^{0}_{bc}\bar{\Delta}^{+}$ $\Omega^{0}_{bc}\bar{\Sigma}^{+}$ |  |  $7160-7200$ $7454-7487$ $7706-7736$ $7932-7959$ $8138-8163$ $8330-8353$ $8509-8531$ $8679-8700$ $8841-8860$ $8995-9014$ $9143-9162$ $9286-9304$ |  $7160-7200$ $7570-7602$ $7908-7935$ $8204-8228$ $8470-8493$ $8716-8736$ $8944-8964$ $9160-9178$ $9364-9381$ $9558-9575$ $9744-9760$ $9924-9939$ |  $-2.3$-$-2.1$ $-1.6$-$-1.5$ |  | $**$
49 |  |  | $b\bar{s}c\bar{u}$ |  |  $B^{0}_{s}D^{0}$ $B^{+}D^{+}_{s}$ |  $7232$ $7247$ |  $\Xi^{+}_{bc}\bar{\Sigma}^{-}$ $\Xi^{0}_{bc}\bar{\Lambda}^{0}$ $\Omega^{0}_{bc}\bar{\Xi}^{0}$ |  |  $7242-7282$ $7537-7570$ $7789-7818$ $8014-8040$ $8219-8244$ $8410-8433$ $8589-8610$ $8758-8778$ $8918-8938$ $9072-9091$ $9220-9238$ $9362-9380$ |  $7242-7282$ $7653-7684$ $7990-8017$ $8284-8308$ $8550-8572$ $8794-8814$ $9022-9041$ $9236-9254$ $9439-9456$ $9633-9649$ $9818-9834$ $9997-10012$ |  $-2.0$-$-1.9$ $-1.4$-$-1.3$ |  | $**$
50 |  |  | $b\bar{d}c\bar{s}$ |  |  $B^{0}_{s}D^{+}$ $B^{0}D^{+}_{s}$ |  $7237$ $7248$ |  $\Xi^{+}_{bc}\bar{\Lambda}^{0}$ $\Xi^{0}_{bc}\bar{\Sigma}^{+}$ $\Omega^{0}_{bc}\bar{\Xi}^{+}$ |  |  $7247-7287$ $7541-7574$ $7792-7822$ $8017-8044$ $8222-8247$ $8413-8436$ $8591-8613$ $8760-8781$ $8921-8940$ $9075-9093$ $9222-9240$ $9364-9382$ |  $7247-7287$ $7657-7688$ $7993-8020$ $8287-8311$ $8553-8574$ $8797-8817$ $9024-9043$ $9238-9256$ $9441-9458$ $9635-9651$ $9820-9836$ $9999-10014$ |  $-2.0$-$-1.9$ $-1.4$-$-1.3$ |  | $**$
51 |  |  | $c\bar{b}s\bar{s}$ |  |  $B^{+}_{c}\phi(1020)$ $D^{+}_{s}\bar{B}^{0}_{s}$ |  $7293$ $7335$ |  $\Xi^{+}_{c}\bar{\Xi}^{0}_{b}$ $\Xi^{0}_{c}\bar{\Xi}^{+}_{b}$ $\Omega^{0}_{c}\bar{\Omega}^{+}_{b}$ |  $8260$ $8267$ $8741$ |  $7915-8042$ $8115-8232$ $8300-8410$ $8474-8578$ $8638-8737$ |  $7722-7860$ $8028-8150$ $8300-8410$ $8548-8649$ $8778-8873$ |  $-2.8$-$-2.2$ $-2.7$-$-2.3$ |  $4$ $2$ |
52 |  |  | $b\bar{s}c\bar{s}$ |  |  $B^{0}_{s}D^{+}_{s}$ |  $7335$ |  $\Xi^{+}_{bc}\bar{\Xi}^{0}$ $\Xi^{0}_{bc}\bar{\Xi}^{+}$ $\Omega^{0}_{bc}\bar{\Omega}^{+}$ |  |  $7345-7385$ $7649-7682$ $7906-7934$ $8132-8158$ $8339-8362$ $8529-8551$ $8708-8729$ $8877-8896$ $9037-9056$ $9191-9209$ $9338-9355$ $9480-9496$ |  $7345-7385$ $7768-7798$ $8108-8134$ $8404-8427$ $8669-8690$ $8913-8933$ $9140-9158$ $9354-9371$ $9556-9573$ $9749-9765$ $9934-9949$ $10112-10126$ |  $-1.6$-$-1.5$ $-1.1$-$-1.0$ |  | $**$
53 |  |  | $b\bar{c}c\bar{u}$ |  |  $\bar{B}^{-}_{c}D^{0}$ $B^{+}\eta_{c}(1S)$ |  $8139$ $8263$ |  $\Xi^{+}_{bc}\bar{\Sigma}^{--}_{c}$ $\Xi^{0}_{bc}\bar{\Lambda}^{-}_{c}$ $\Omega^{0}_{bc}\bar{\Xi}^{-}_{c}$ |  |  $8149-8189$ $8372-8408$ $8575-8608$ $8763-8794$ $8939-8968$ $9105-9132$ $9262-9289$ $9413-9439$ $9558-9583$ $9698-9722$ $9833-9856$ $9964-9986$ |  $8149-8189$ $8465-8499$ $8743-8774$ $8995-9023$ $9228-9255$ $9446-9471$ $9652-9676$ $9848-9870$ $10035-10057$ $10215-10235$ $10387-10408$ $10555-10574$ |  $-3.4$-$-3.2$ $-2.3$-$-2.2$ |  | $*$
54 |  |  | $c\bar{b}u\bar{c}$ |  |  $B^{+}_{c}\bar{D}^{0}$ $\eta_{c}(1S)B^{-}$ |  $8139$ $8263$ |  $\Sigma^{++}_{c}\bar{\Xi}^{-}_{bc}$ $\Lambda^{+}_{c}\bar{\Xi}^{0}_{bc}$ $\Xi^{+}_{c}\bar{\Omega}^{0}_{bc}$ |  |  $8149-8189$ $8372-8408$ $8575-8608$ $8763-8794$ $8939-8968$ $9105-9132$ $9262-9289$ $9413-9439$ $9558-9583$ $9698-9722$ $9833-9856$ $9964-9986$ |  $8149-8189$ $8465-8499$ $8743-8774$ $8995-9023$ $9228-9255$ $9446-9471$ $9652-9676$ $9848-9870$ $10035-10057$ $10215-10235$ $10387-10408$ $10555-10574$ |  $-3.4$-$-3.2$ $-2.3$-$-2.2$ |  | $*$
55 |  |  | $c\bar{b}c\bar{u}$ |  |  $B^{+}_{c}D^{0}$ $D^{0}B^{+}_{c}$ |  $8139$ $8139$ |  $\Xi^{++}_{cc}\bar{\Sigma}^{-}_{b}$ $\Xi^{+}_{cc}\bar{\Sigma}^{0}_{b}$ $\Omega^{+}_{cc}\bar{\Xi}^{0}_{b}$ |  $9433$ |  $9198-9316$ $9338-9451$ $9473-9583$ $9604-9711$ $9731-9835$ |  $9069-9191$ $9276-9392$ $9473-9583$ $9661-9766$ $9841-9942$ |  $-5.9$-$-5.1$ $-3.9$-$-3.4$ |  $7$ $5$ | $**$
56 |  |  | $c\bar{b}d\bar{c}$ |  |  $B^{+}_{c}D^{-}$ $\eta_{c}(1S)\bar{B}^{0}$ |  $8144$ $8264$ |  $\Lambda^{+}_{c}\bar{\Xi}^{-}_{bc}$ $\Sigma^{0}_{c}\bar{\Xi}^{0}_{bc}$ $\Xi^{0}_{c}\bar{\Omega}^{0}_{bc}$ |  |  $8154-8194$ $8377-8413$ $8579-8612$ $8767-8798$ $8942-8971$ $9108-9136$ $9266-9292$ $9417-9442$ $9561-9586$ $9701-9724$ $9836-9859$ $9967-9989$ |  $8154-8194$ $8469-8504$ $8746-8778$ $8998-9027$ $9231-9258$ $9449-9474$ $9655-9679$ $9851-9873$ $10038-10059$ $10217-10238$ $10390-10410$ $10557-10576$ |  $-3.4$-$-3.2$ $-2.4$-$-2.2$ |  | $*$
57 |  |  | $b\bar{c}c\bar{d}$ |  |  $\bar{B}^{-}_{c}D^{+}$ $B^{0}\eta_{c}(1S)$ |  $8144$ $8264$ |  $\Xi^{+}_{bc}\bar{\Lambda}^{-}_{c}$ $\Xi^{0}_{bc}\bar{\Sigma}^{0}_{c}$ $\Omega^{0}_{bc}\bar{\Xi}^{0}_{c}$ |  |  $8154-8194$ $8377-8413$ $8579-8612$ $8767-8798$ $8942-8971$ $9108-9136$ $9266-9292$ $9417-9442$ $9561-9586$ $9701-9724$ $9836-9859$ $9967-9989$ |  $8154-8194$ $8469-8504$ $8746-8778$ $8998-9027$ $9231-9258$ $9449-9474$ $9655-9679$ $9851-9873$ $10038-10059$ $10217-10238$ $10390-10410$ $10557-10576$ |  $-3.4$-$-3.2$ $-2.4$-$-2.2$ |  | $*$
58 |  |  | $c\bar{b}c\bar{d}$ |  |  $B^{+}_{c}D^{+}$ $D^{+}B^{+}_{c}$ |  $8144$ $8144$ |  $\Xi^{+}_{cc}\bar{\Sigma}^{+}_{b}$ $\Xi^{++}_{cc}\bar{\Sigma}^{0}_{b}$ $\Omega^{+}_{cc}\bar{\Xi}^{+}_{b}$ |  $9335$ |  $9093-9211$ $9236-9350$ $9375-9485$ $9509-9615$ $9639-9742$ |  $8960-9082$ $9173-9289$ $9375-9485$ $9567-9672$ $9751-9852$ |  $-5.2$-$-4.3$ $-4.4$-$-3.8$ |  $7$ $4$ | $**$
59 |  |  | $c\bar{b}s\bar{c}$ |  |  $B^{+}_{c}D^{-}_{s}$ $\eta_{c}(1S)\bar{B}^{0}_{s}$ |  $8242$ $8351$ |  $\Xi^{+}_{c}\bar{\Xi}^{-}_{bc}$ $\Xi^{0}_{c}\bar{\Xi}^{0}_{bc}$ $\Omega^{0}_{c}\bar{\Omega}^{0}_{bc}$ |  |  $8252-8292$ $8488-8523$ $8699-8731$ $8892-8922$ $9072-9099$ $9240-9266$ $9400-9425$ $9553-9577$ $9699-9722$ $9840-9862$ $9976-9997$ $10107-10128$ |  $8252-8292$ $8584-8618$ $8871-8901$ $9129-9156$ $9365-9391$ $9586-9609$ $9793-9816$ $9990-10012$ $10178-10199$ $10358-10378$ $10532-10550$ $10699-10717$ |  $-2.6$-$-2.4$ $-1.8$-$-1.7$ |  | $*$
60 |  |  | $b\bar{c}c\bar{s}$ |  |  $\bar{B}^{-}_{c}D^{+}_{s}$ $B^{0}_{s}\eta_{c}(1S)$ |  $8242$ $8351$ |  $\Xi^{+}_{bc}\bar{\Xi}^{-}_{c}$ $\Xi^{0}_{bc}\bar{\Xi}^{0}_{c}$ $\Omega^{0}_{bc}\bar{\Omega}^{0}_{c}$ |  |  $8252-8292$ $8488-8523$ $8699-8731$ $8892-8922$ $9072-9099$ $9240-9266$ $9400-9425$ $9553-9577$ $9699-9722$ $9840-9862$ $9976-9997$ $10107-10128$ |  $8252-8292$ $8584-8618$ $8871-8901$ $9129-9156$ $9365-9391$ $9586-9609$ $9793-9816$ $9990-10012$ $10178-10199$ $10358-10378$ $10532-10550$ $10699-10717$ |  $-2.6$-$-2.4$ $-1.8$-$-1.7$ |  | $*$
61 |  |  | $c\bar{b}c\bar{s}$ |  |  $B^{+}_{c}D^{+}_{s}$ $D^{+}_{s}B^{+}_{c}$ |  $8242$ $8242$ |  $\Xi^{+}_{cc}\bar{\Xi}^{+}_{b}$ $\Xi^{++}_{cc}\bar{\Xi}^{0}_{b}$ $\Omega^{+}_{cc}\bar{\Omega}^{+}_{b}$ |  $9316$ $9414$ |  $9045-9166$ $9204-9319$ $9356-9466$ $9501-9607$ $9641-9743$ |  $8896-9023$ $9134-9252$ $9356-9466$ $9564-9668$ $9761-9860$ |  $-4.6$-$-3.9$ $-2.7$-$-2.1$ |  $5$ $4$ | $**$
62 |  |  | $c\bar{b}c\bar{c}$ |  |  $B^{+}_{c}\eta_{c}(1S)$ $\eta_{c}(1S)B^{+}_{c}$ |  $9258$ $9258$ |  $\Xi^{++}_{cc}\bar{\Xi}^{-}_{bc}$ $\Xi^{+}_{cc}\bar{\Xi}^{0}_{bc}$ $\Omega^{+}_{cc}\bar{\Omega}^{0}_{bc}$ |  |  $9268-9308$ $9456-9493$ $9631-9666$ $9795-9828$ $9951-9982$ $10099-10129$ $10241-10270$ $10378-10406$ $10510-10537$ $10638-10664$ $10762-10787$ $10883-10907$ |  $9268-9308$ $9535-9571$ $9777-9810$ $10001-10032$ $10210-10239$ $10408-10435$ $10596-10622$ $10776-10801$ $10949-10973$ $11115-11138$ $11276-11299$ $11432-11454$ |  $-4.2$-$-4.0$ $-2.9$-$-2.8$ |  | $*$
63 |  |  | $b\bar{b}c\bar{u}$ |  |  $\eta_{b}(1S)D^{0}$ $B^{+}B^{+}_{c}$ |  $11264$ $11553$ |  $\Xi^{+}_{bc}\bar{\Sigma}^{-}_{b}$ $\Xi^{0}_{bc}\bar{\Sigma}^{0}_{b}$ $\Omega^{0}_{bc}\bar{\Xi}^{0}_{b}$ |  |  $11274-11314$ $11473-11508$ $11651-11683$ $11815-11845$ $11969-11997$ $12114-12141$ $12252-12277$ $12384-12409$ $12511-12535$ $12634-12657$ $12753-12775$ $12868-12890$ |  $11274-11314$ $11554-11588$ $11798-11828$ $12018-12046$ $12222-12248$ $12413-12437$ $12593-12617$ $12766-12788$ $12931-12952$ $13089-13110$ $13243-13263$ $13391-13411$ |  $-2.5$-$-2.3$ $-1.7$-$-1.6$ |  | $*$
64 |  |  | $b\bar{b}c\bar{d}$ |  |  $\eta_{b}(1S)D^{+}$ $B^{0}B^{+}_{c}$ |  $11269$ $11554$ |  $\Xi^{+}_{bc}\bar{\Sigma}^{0}_{b}$ $\Xi^{0}_{bc}\bar{\Sigma}^{+}_{b}$ $\Omega^{0}_{bc}\bar{\Xi}^{+}_{b}$ |  |  $11279-11319$ $11477-11513$ $11655-11687$ $11819-11849$ $11972-12001$ $12117-12144$ $12255-12281$ $12387-12412$ $12514-12538$ $12637-12660$ $12755-12778$ $12871-12892$ |  $11279-11319$ $11558-11592$ $11801-11832$ $12021-12049$ $12225-12251$ $12416-12440$ $12596-12619$ $12768-12791$ $12933-12955$ $13092-13113$ $13245-13265$ $13394-13413$ |  $-2.5$-$-2.3$ $-1.7$-$-1.6$ |  | $*$
65 |  |  | $b\bar{b}c\bar{s}$ |  |  $\eta_{b}(1S)D^{+}_{s}$ $B^{0}_{s}B^{+}_{c}$ |  $11367$ $11641$ |  $\Xi^{+}_{bc}\bar{\Xi}^{0}_{b}$ $\Xi^{0}_{bc}\bar{\Xi}^{+}_{b}$ $\Omega^{0}_{bc}\bar{\Omega}^{+}_{b}$ |  |  $11377-11417$ $11608-11641$ $11805-11834$ $11981-12008$ $12144-12169$ $12296-12319$ $12440-12462$ $12576-12598$ $12707-12728$ $12833-12853$ $12955-12974$ $13073-13091$ |  $11377-11417$ $11699-11730$ $11963-11990$ $12196-12220$ $12408-12431$ $12606-12627$ $12792-12812$ $12968-12987$ $13136-13155$ $13298-13315$ $13454-13470$ $13604-13620$ |  $-1.4$-$-1.3$ $-0.98$-$-0.87$ |  | $*$
66 |  |  | $c\bar{b}u\bar{b}$ |  |  $B^{+}_{c}B^{-}$ |  $11553$ |  $\Sigma^{++}_{c}\bar{\Xi}^{0}_{bb}$ $\Lambda^{+}_{c}\bar{\Xi}^{+}_{bb}$ $\Xi^{+}_{c}\bar{\Omega}^{+}_{bb}$ |  |  $11563-11603$ $11795-11830$ $12002-12034$ $12191-12221$ $12367-12395$ $12532-12558$ $12688-12713$ $12837-12860$ $12979-13001$ $13116-13137$ $13247-13268$ $13375-13395$ |  $11563-11603$ $11890-11923$ $12171-12201$ $12423-12450$ $12654-12679$ $12869-12892$ $13071-13093$ $13262-13283$ $13444-13464$ $13618-13637$ $13786-13804$ $13948-13965$ |  $-2.7$-$-2.6$ $-1.9$-$-1.8$ |  | $**$
67 |  |  | $c\bar{b}d\bar{b}$ |  |  $B^{+}_{c}\bar{B}^{0}$ |  $11554$ |  $\Lambda^{+}_{c}\bar{\Xi}^{0}_{bb}$ $\Sigma^{0}_{c}\bar{\Xi}^{+}_{bb}$ $\Xi^{0}_{c}\bar{\Omega}^{+}_{bb}$ |  |  $11564-11604$ $11796-11831$ $12003-12035$ $12192-12222$ $12368-12395$ $12533-12559$ $12689-12713$ $12837-12861$ $12979-13002$ $13116-13138$ $13248-13269$ $13375-13396$ |  $11564-11604$ $11891-11924$ $12172-12202$ $12424-12451$ $12655-12680$ $12869-12893$ $13071-13093$ $13262-13283$ $13444-13464$ $13619-13638$ $13786-13805$ $13948-13966$ |  $-2.7$-$-2.6$ $-1.9$-$-1.8$ |  | $**$
68 |  |  | $c\bar{b}s\bar{b}$ |  |  $B^{+}_{c}\bar{B}^{0}_{s}$ |  $11641$ |  $\Xi^{+}_{c}\bar{\Xi}^{0}_{bb}$ $\Xi^{0}_{c}\bar{\Xi}^{+}_{bb}$ $\Omega^{0}_{c}\bar{\Omega}^{+}_{bb}$ |  |  $11651-11691$ $11902-11936$ $12120-12150$ $12316-12343$ $12496-12521$ $12664-12688$ $12822-12845$ $12973-12995$ $13117-13137$ $13254-13274$ $13387-13406$ $13515-13534$ |  $11651-11691$ $12002-12034$ $12295-12322$ $12553-12578$ $12788-12811$ $13005-13027$ $13209-13229$ $13401-13421$ $13584-13603$ $13759-13777$ $13927-13944$ $14089-14106$ |  $-1.9$-$-1.8$ $-1.3$-$-1.2$ |  | $**$
69 |  |  | $b\bar{b}c\bar{c}$ |  |  $\eta_{b}(1S)\eta_{c}(1S)$ $\bar{B}^{-}_{c}B^{+}_{c}$ |  $12383$ $12548$ |  $\Xi^{+}_{bc}\bar{\Xi}^{-}_{bc}$ $\Xi^{0}_{bc}\bar{\Xi}^{0}_{bc}$ $\Omega^{0}_{bc}\bar{\Omega}^{0}_{bc}$ |  |  $12393-12433$ $12580-12616$ $12749-12782$ $12905-12936$ $13052-13081$ $13191-13218$ $13323-13349$ $13450-13475$ $13572-13597$ $13691-13714$ $13805-13828$ $13916-13939$ |  $12393-12433$ $12657-12691$ $12888-12919$ $13099-13127$ $13294-13321$ $13478-13503$ $13652-13676$ $13818-13841$ $13977-13999$ $14131-14152$ $14279-14300$ $14423-14443$ |  $-2.7$-$-2.5$ $-1.9$-$-1.7$ |  | $*$
70 |  |  | $c\bar{b}c\bar{b}$ |  |  $B^{+}_{c}B^{+}_{c}$ |  $12548$ |  $\Xi^{++}_{cc}\bar{\Xi}^{0}_{bb}$ $\Xi^{+}_{cc}\bar{\Xi}^{+}_{bb}$ $\Omega^{+}_{cc}\bar{\Omega}^{+}_{bb}$ |  |  $12558-12598$ $12762-12798$ $12946-12979$ $13116-13147$ $13276-13304$ $13426-13453$ $13569-13595$ $13706-13731$ $13838-13862$ $13965-13988$ $14087-14110$ $14207-14228$ |  $12558-12598$ $12846-12880$ $13098-13129$ $13327-13355$ $13538-13564$ $13736-13761$ $13923-13946$ $14101-14123$ $14271-14293$ $14435-14456$ $14593-14613$ $14745-14765$ |  $-2.9$-$-2.7$ $-2.0$-$-1.9$ |  | $**$
71 |  |  | $b\bar{b}c\bar{b}$ |  |  $\eta_{b}(1S)B^{+}_{c}$ |  $15673$ |  $\Xi^{+}_{bc}\bar{\Xi}^{0}_{bb}$ $\Xi^{0}_{bc}\bar{\Xi}^{+}_{bb}$ $\Omega^{0}_{bc}\bar{\Omega}^{+}_{bb}$ |  |  $15683-15723$ $15894-15927$ $16074-16103$ $16235-16262$ $16384-16409$ $16523-16547$ $16655-16677$ $16781-16802$ $16901-16921$ $17016-17036$ $17128-17147$ $17236-17255$ |  $15683-15723$ $15977-16008$ $16218-16245$ $16432-16456$ $16626-16649$ $16808-16829$ $16978-16998$ $17140-17159$ $17295-17313$ $17444-17461$ $17587-17604$ $17726-17742$ |  $-1.4$-$-1.3$ $-0.99$-$-0.87$ |  | $*$

####  7.4.1 Detailed Predictions for Genuine and Semi-Genuine Tetraquarks

In the following sections we present the graphs and extended predicted spectra
of each of the genuine and semi-genuine tetraquarks configurations that
haven’t been analysed yet in section 7.2.

####  7.4.2 $T_{c\bar{u}d\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 65: (a) is $(J,M^{2})$ $T_{c\bar{u}d\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{u}d\bar{u}}$ HMRT. Table 108: $T_{c\bar{u}d\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$2854-2992$ $3160-3282$ $3432-3542$ $3679-3780$ $3908-4002$ $4121-4210$ $4322-4406$ $4513-4593$ $4695-4771$ $4869-4942$ $5036-5107$ $5198-5266$ |  $-2.3$-$-1.8$
Table 109: $T_{c\bar{u}d\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$2537-2698$ $3029-3157$ $3432-3542$ $3783-3881$ $4098-4187$ $4387-4469$ $4655-4732$ $4907-4979$ $5144-5214$ $5371-5437$ $5587-5650$ $5794-5855$ |  $-1.7$-$-1.4$

####  7.4.3 $T_{c\bar{d}u\bar{d}}$

|
---|---
$(a)$ |  $(b)$
Figure 66: (a) is $(J,M^{2})$ $T_{c\bar{d}u\bar{d}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{d}u\bar{d}}$ HMRT. Table 110: $T_{c\bar{d}u\bar{d}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$2856-2994$ $3162-3284$ $3434-3544$ $3681-3782$ $3909-4004$ $4122-4211$ $4323-4408$ $4514-4594$ $4696-4773$ $4870-4944$ $5038-5108$ $5199-5267$ |  $-2.3$-$-1.9$
Table 111: $T_{c\bar{d}u\bar{d}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$2540-2701$ $3031-3160$ $3434-3544$ $3784-3883$ $4099-4189$ $4388-4471$ $4656-4734$ $4908-4981$ $5146-5215$ $5372-5438$ $5588-5651$ $5795-5856$ |  $-1.7$-$-1.4$

####  7.4.4 $T_{c\bar{d}u\bar{s}}$

|
---|---
$(a)$ |  $(b)$
Figure 67: (a) is $(J,M^{2})$ $T_{c\bar{d}u\bar{s}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{d}u\bar{s}}$ HMRT. Table 112: $T_{c\bar{d}u\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$2946-3085$ $3252-3374$ $3523-3633$ $3769-3870$ $3996-4091$ $4209-4298$ $4409-4493$ $4599-4679$ $4780-4856$ $4953-5027$ $5120-5191$ $5281-5349$ |  $-2.1$-$-1.6$
Table 113: $T_{c\bar{d}u\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$2628-2791$ $3121-3250$ $3523-3633$ $3872-3970$ $4186-4275$ $4473-4556$ $4740-4818$ $4991-5064$ $5228-5297$ $5453-5519$ $5668-5731$ $5874-5935$ |  $-1.5$-$-1.2$

####  7.4.5 $T_{c\bar{s}d\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 68: (a) is $(J,M^{2})$ $T_{c\bar{s}d\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{s}d\bar{u}}$ HMRT. Table 114: $T_{c\bar{s}d\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$2936-3075$ $3243-3365$ $3515-3625$ $3762-3863$ $3990-4084$ $4202-4291$ $4403-4487$ $4593-4673$ $4774-4851$ $4948-5021$ $5115-5185$ $5276-5344$ |  $-2.0$-$-1.6$
Table 115: $T_{c\bar{s}d\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$2616-2780$ $3112-3240$ $3515-3625$ $3865-3963$ $4179-4269$ $4467-4550$ $4735-4812$ $4986-5058$ $5223-5292$ $5448-5514$ $5663-5726$ $5870-5931$ |  $-1.5$-$-1.2$

####  7.4.6 $T_{c\bar{u}s\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 69: (a) is $(J,M^{2})$ $T_{c\bar{u}s\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{u}s\bar{u}}$ HMRT. Table 116: $T_{c\bar{u}s\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$2793-2943$ $3147-3273$ $3448-3558$ $3715-3814$ $3957-4048$ $4181-4266$ $4390-4471$ $4588-4664$ $4775-4848$ $4954-5023$ $5125-5192$ $5290-5354$ |  $-2.2$-$-1.8$
Table 117: $T_{c\bar{u}s\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$3448-3558$ $3825-3921$ $4157-4243$ $4457-4536$ $4734-4808$ $4993-5062$ $5236-5301$ $5466-5528$ $5686-5745$ $5896-5953$ $6098-6152$ $6292-6345$ |  $-1.9$-$-1.6$

####  7.4.7 $T_{c\bar{d}s\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 70: (a) is $(J,M^{2})$ $T_{c\bar{d}s\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{d}s\bar{u}}$ HMRT. Table 118: $T_{c\bar{d}s\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$2790-2941$ $3145-3270$ $3446-3556$ $3713-3812$ $3955-4047$ $4179-4265$ $4389-4469$ $4587-4663$ $4774-4846$ $4953-5022$ $5124-5191$ $5289-5353$ |  $-2.2$-$-1.8$
Table 119: $T_{c\bar{d}s\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$3446-3556$ $3823-3919$ $4155-4241$ $4456-4535$ $4733-4806$ $4992-5060$ $5235-5300$ $5465-5527$ $5685-5744$ $5895-5952$ $6097-6151$ $6291-6344$ |  $-1.9$-$-1.6$

####  7.4.8 $T_{c\bar{d}s\bar{d}}$

|
---|---
$(a)$ |  $(b)$
Figure 71: (a) is $(J,M^{2})$ $T_{c\bar{d}s\bar{d}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{d}s\bar{d}}$ HMRT. Table 120: $T_{c\bar{d}s\bar{d}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$2793-2943$ $3147-3273$ $3448-3558$ $3715-3814$ $3957-4048$ $4181-4266$ $4390-4471$ $4588-4664$ $4775-4848$ $4954-5023$ $5125-5192$ $5290-5354$ |  $-2.2$-$-1.8$
Table 121: $T_{c\bar{d}s\bar{d}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$3448-3558$ $3825-3921$ $4157-4243$ $4457-4536$ $4734-4808$ $4993-5062$ $5236-5301$ $5466-5528$ $5686-5745$ $5896-5953$ $6098-6152$ $6292-6345$ |  $-1.9$-$-1.6$

####  7.4.9 $T_{c\bar{s}u\bar{s}}$

|
---|---
$(a)$ |  $(b)$
Figure 72: (a) is $(J,M^{2})$ $T_{c\bar{s}u\bar{s}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{s}u\bar{s}}$ HMRT. Table 122: $T_{c\bar{s}u\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$3062-3203$ $3374-3497$ $3648-3758$ $3896-3996$ $4124-4217$ $4336-4424$ $4536-4619$ $4726-4805$ $4906-4982$ $5079-5152$ $5246-5316$ $5406-5473$ |  $-1.7$-$-1.2$
Table 123: $T_{c\bar{s}u\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$2732-2901$ $3241-3371$ $3648-3758$ $3999-4097$ $4313-4402$ $4600-4682$ $4867-4944$ $5117-5189$ $5353-5421$ $5577-5643$ $5792-5854$ $5997-6057$ |  $-1.2$-$-0.94$

####  7.4.10 $T_{c\bar{s}d\bar{s}}$

|
---|---
$(a)$ |  $(b)$
Figure 73: (a) is $(J,M^{2})$ $T_{c\bar{s}d\bar{s}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{s}d\bar{s}}$ HMRT. Table 124: $T_{c\bar{s}d\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$3053-3194$ $3366-3489$ $3641-3751$ $3889-3990$ $4118-4211$ $4331-4419$ $4531-4614$ $4721-4800$ $4902-4977$ $5075-5147$ $5241-5311$ $5401-5469$ |  $-1.7$-$-1.2$
Table 125: $T_{c\bar{s}d\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$2721-2891$ $3233-3363$ $3641-3751$ $3993-4090$ $4308-4396$ $4595-4677$ $4862-4939$ $5112-5184$ $5349-5417$ $5573-5638$ $5788-5850$ $5994-6054$ |  $-1.2$-$-0.92$

####  7.4.11 $T_{c\bar{c}d\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 74: (a) is $(J,M^{2})$ $T_{c\bar{c}d\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{c}d\bar{u}}$ HMRT. Table 126: $T_{c\bar{c}d\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$4373-4497$ $4583-4699$ $4780-4890$ $4967-5072$ $5145-5245$ $5316-5412$ $5480-5572$ $5638-5727$ $5790-5877$ $5938-6023$ $6082-6164$ $6222-6301$ |  $-2.6$-$-2.0$
Table 127: $T_{c\bar{c}d\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$4174-4306$ $4491-4611$ $4780-4890$ $5047-5150$ $5297-5394$ $5533-5625$ $5757-5844$ $5971-6054$ $6176-6256$ $6373-6450$ $6563-6638$ $6747-6819$ |  $-2.0$-$-1.6$

####  7.4.12 $T_{c\bar{c}s\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 75: (a) is $(J,M^{2})$ $T_{c\bar{c}s\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{c}s\bar{u}}$ HMRT. Table 128: $T_{c\bar{c}s\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$4362-4488$ $4587-4704$ $4796-4906$ $4993-5097$ $5179-5278$ $5356-5450$ $5525-5616$ $5688-5776$ $5845-5930$ $5997-6079$ $6144-6223$ $6287-6364$ |  $-3.3$-$-2.7$
Table 129: $T_{c\bar{c}s\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$4145-4282$ $4489-4610$ $4796-4906$ $5076-5178$ $5337-5432$ $5580-5670$ $5811-5896$ $6030-6111$ $6240-6317$ $6441-6515$ $6634-6706$ $6821-6891$ |  $-2.0$-$-1.6$

####  7.4.13 $T_{c\bar{c}s\bar{d}}$

|
---|---
$(a)$ |  $(b)$
Figure 76: (a) is $(J,M^{2})$ $T_{c\bar{c}s\bar{d}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{c}s\bar{d}}$ HMRT. Table 130: $T_{c\bar{c}s\bar{d}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$4359-4486$ $4585-4702$ $4794-4904$ $4991-5095$ $5177-5276$ $5354-5449$ $5524-5615$ $5687-5774$ $5844-5928$ $5996-6077$ $6143-6222$ $6285-6362$ |  $-3.2$-$-2.7$
Table 131: $T_{c\bar{c}s\bar{d}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$4142-4279$ $4487-4608$ $4794-4904$ $5075-5176$ $5335-5430$ $5579-5668$ $5809-5894$ $6029-6110$ $6238-6316$ $6439-6514$ $6633-6705$ $6820-6889$ |  $-2.0$-$-1.6$

####  7.4.14 $T_{c\bar{c}d\bar{s}}$

|
---|---
$(a)$ |  $(b)$
Figure 77: (a) is $(J,M^{2})$ $T_{c\bar{c}d\bar{s}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{c}d\bar{s}}$ HMRT. Table 132: $T_{c\bar{c}d\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$4359-4486$ $4585-4702$ $4794-4904$ $4991-5095$ $5177-5276$ $5354-5449$ $5524-5615$ $5687-5774$ $5844-5928$ $5996-6077$ $6143-6222$ $6285-6362$ |  $-3.2$-$-2.7$
Table 133: $T_{c\bar{c}d\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$4142-4279$ $4487-4608$ $4794-4904$ $5075-5176$ $5335-5430$ $5579-5668$ $5809-5894$ $6029-6110$ $6238-6316$ $6439-6514$ $6633-6705$ $6820-6889$ |  $-2.0$-$-1.6$

####  7.4.15 $T_{c\bar{u}c\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 78: (a) is $(J,M^{2})$ $T_{c\bar{u}c\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{u}c\bar{u}}$ HMRT. Table 134: $T_{c\bar{u}c\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$3981-4115$ $4253-4373$ $4497-4607$ $4721-4823$ $4930-5026$ $5126-5217$ $5312-5398$ $5489-5571$ $5658-5737$ $5820-5896$ $5977-6050$ $6128-6199$ |  $-3.7$-$-3.3$
Table 135: $T_{c\bar{u}c\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$4497-4607$ $4816-4915$ $5105-5196$ $5372-5456$ $5621-5700$ $5856-5931$ $6078-6150$ $6291-6359$ $6494-6560$ $6690-6753$ $6879-6940$ $7061-7121$ |  $-3.0$-$-2.6$

####  7.4.16 $T_{c\bar{d}c\bar{d}}$

|
---|---
$(a)$ |  $(b)$
Figure 79: (a) is $(J,M^{2})$ $T_{c\bar{d}c\bar{d}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{d}c\bar{d}}$ HMRT. Table 136: $T_{c\bar{d}c\bar{d}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$4109-4241$ $4367-4487$ $4602-4712$ $4819-4921$ $5021-5118$ $5212-5304$ $5394-5481$ $5567-5651$ $5733-5814$ $5893-5970$ $6047-6122$ $6196-6269$ |  $-3.2$-$-2.7$
Table 137: $T_{c\bar{d}c\bar{d}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$3852-4000$ $4256-4381$ $4602-4712$ $4910-5010$ $5192-5284$ $5453-5539$ $5697-5778$ $5928-6004$ $6147-6220$ $6356-6427$ $6557-6625$ $6751-6816$ |  $-2.3$-$-2.0$

####  7.4.17 $T_{c\bar{s}c\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 80: (a) is $(J,M^{2})$ $T_{c\bar{s}c\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{s}c\bar{u}}$ HMRT. Table 138: $T_{c\bar{s}c\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$4181-4314$ $4440-4560$ $4675-4785$ $4892-4994$ $5094-5191$ $5285-5377$ $5466-5553$ $5639-5723$ $5805-5885$ $5964-6041$ $6118-6193$ $6267-6339$ |  $-3.9$-$-3.4$
Table 139: $T_{c\bar{s}c\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$3922-4071$ $4328-4453$ $4675-4785$ $4983-5083$ $5264-5356$ $5525-5611$ $5769-5849$ $5999-6076$ $6218-6291$ $6427-6497$ $6627-6694$ $6820-6885$ |  $-2.1$-$-1.8$

####  7.4.18 $T_{c\bar{d}c\bar{s}}$

|
---|---
$(a)$ |  $(b)$
Figure 81: (a) is $(J,M^{2})$ $T_{c\bar{d}c\bar{s}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{d}c\bar{s}}$ HMRT. Table 140: $T_{c\bar{d}c\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$4279-4410$ $4528-4647$ $4756-4866$ $4967-5070$ $5165-5262$ $5352-5445$ $5530-5618$ $5700-5785$ $5864-5945$ $6021-6099$ $6173-6249$ $6320-6393$ |  $-3.3$-$-2.8$
Table 141: $T_{c\bar{d}c\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$4032-4178$ $4421-4544$ $4756-4866$ $5057-5157$ $5332-5425$ $5588-5675$ $5828-5910$ $6055-6133$ $6271-6346$ $6478-6549$ $6676-6745$ $6868-6934$ |  $-2.4$-$-2.0$

####  7.4.19 $T_{c\bar{s}c\bar{s}}$

|
---|---
$(a)$ |  $(b)$
Figure 82: (a) is $(J,M^{2})$ $T_{c\bar{s}c\bar{s}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{s}c\bar{s}}$ HMRT. Table 142: $T_{c\bar{s}c\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$4401-4533$ $4652-4772$ $4881-4991$ $5093-5195$ $5291-5387$ $5477-5569$ $5655-5743$ $5825-5909$ $5988-6068$ $6144-6222$ $6296-6371$ $6442-6515$ |  $-2.9$-$-2.4$
Table 143: $T_{c\bar{s}c\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$4151-4298$ $4544-4668$ $4881-4991$ $5182-5282$ $5457-5550$ $5712-5799$ $5952-6033$ $6178-6256$ $6394-6468$ $6600-6671$ $6797-6866$ $6988-7054$ |  $-2.1$-$-1.7$

####  7.4.20 $T_{c\bar{c}c\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 83: (a) is $(J,M^{2})$ $T_{c\bar{c}c\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{c}c\bar{u}}$ HMRT. Table 144: $T_{c\bar{c}c\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$5481-5602$ $5668-5783$ $5845-5955$ $6014-6120$ $6176-6278$ $6333-6430$ $6483-6578$ $6629-6721$ $6770-6859$ $6908-6994$ $7041-7126$ $7172-7254$ |  $-5.5$-$-4.9$
Table 145: $T_{c\bar{c}c\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$5305-5434$ $5586-5704$ $5845-5955$ $6087-6191$ $6316-6414$ $6532-6626$ $6739-6829$ $6938-7024$ $7129-7212$ $7313-7393$ $7491-7569$ $7664-7740$ |  $-3.6$-$-3.2$

####  7.4.21 $T_{c\bar{c}c\bar{d}}$

|
---|---
$(a)$ |  $(b)$
Figure 84: (a) is $(J,M^{2})$ $T_{c\bar{c}c\bar{d}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{c}c\bar{d}}$ HMRT. Table 146: $T_{c\bar{c}c\bar{d}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$5595-5716$ $5776-5891$ $5948-6058$ $6113-6219$ $6271-6373$ $6424-6522$ $6572-6667$ $6715-6807$ $6854-6944$ $6989-7076$ $7120-7206$ $7249-7332$ |  $-5.2$-$-4.5$
Table 147: $T_{c\bar{c}c\bar{d}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$5425-5552$ $5696-5814$ $5948-6058$ $6184-6288$ $6407-6506$ $6620-6714$ $6823-6914$ $7018-7105$ $7206-7290$ $7388-7469$ $7564-7643$ $7735-7811$ |  $-4.0$-$-3.6$

####  7.4.22 $T_{c\bar{c}c\bar{s}}$

|
---|---
$(a)$ |  $(b)$
Figure 85: (a) is $(J,M^{2})$ $T_{c\bar{c}c\bar{s}}$ HMRT, (b) $(n,M^{2})$
$T_{c\bar{c}c\bar{s}}$ HMRT.

Table 148: $T_{c\bar{c}c\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$5664-5786$ $5851-5967$ $6029-6139$ $6198-6304$ $6360-6462$ $6516-6614$ $6667-6761$ $6812-6903$ $6953-7042$ $7090-7176$ $7223-7307$ $7353-7435$ |  $-5.1$-$-4.4$

Table 149: $T_{c\bar{c}c\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$5487-5616$ $5769-5888$ $6029-6139$ $6271-6375$ $6499-6597$ $6716-6809$ $6922-7011$ $7120-7206$ $7310-7393$ $7493-7573$ $7671-7748$ $7843-7918$ |  $-3.3$-$-2.8$

####  7.4.23 $T_{c\bar{b}d\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 86: (a) is $(J,M^{2})$ $T_{c\bar{b}d\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}d\bar{u}}$ HMRT. Table 150: $T_{c\bar{b}d\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$7798-7920$ $7972-8088$ $8137-8247$ $8294-8400$ $8445-8546$ $8590-8688$ $8730-8825$ $8866-8958$ $8997-9086$ $9125-9212$ $9250-9334$ $9371-9454$ |  $-2.5$-$-1.8$
Table 151: $T_{c\bar{b}d\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$7635-7764$ $7896-8014$ $8137-8247$ $8362-8466$ $8574-8672$ $8776-8869$ $8968-9058$ $9153-9239$ $9331-9414$ $9503-9583$ $9669-9747$ $9830-9906$ |  $-1.5$-$-1.1$

####  7.4.24 $T_{c\bar{b}u\bar{d}}$

|
---|---
$(a)$ |  $(b)$
Figure 87: (a) is $(J,M^{2})$ $T_{c\bar{b}u\bar{d}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}u\bar{d}}$ HMRT. Table 152: $T_{c\bar{b}u\bar{d}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$7804-7926$ $7977-8093$ $8142-8252$ $8299-8404$ $8450-8551$ $8595-8692$ $8734-8829$ $8870-8962$ $9001-9091$ $9129-9216$ $9253-9338$ $9375-9457$ |  $-2.5$-$-1.8$
Table 153: $T_{c\bar{b}u\bar{d}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$7641-7769$ $7902-8020$ $8142-8252$ $8367-8470$ $8579-8677$ $8780-8874$ $8972-9062$ $9157-9243$ $9335-9418$ $9506-9587$ $9672-9751$ $9834-9910$ |  $-1.6$-$-1.1$

####  7.4.25 $T_{c\bar{b}s\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 88: (a) is $(J,M^{2})$ $T_{c\bar{b}s\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}s\bar{u}}$ HMRT. Table 154: $T_{c\bar{b}s\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$7980-8102$ $8154-8270$ $8319-8429$ $8476-8581$ $8627-8728$ $8771-8869$ $8911-9005$ $9046-9137$ $9177-9266$ $9304-9391$ $9428-9512$ $9549-9631$ |  $-3.0$-$-2.3$
Table 155: $T_{c\bar{b}s\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$7816-7945$ $8078-8196$ $8319-8429$ $8544-8647$ $8755-8853$ $8956-9050$ $9148-9238$ $9332-9418$ $9509-9592$ $9680-9760$ $9845-9923$ $10006-10081$ |  $-2.2$-$-1.7$

####  7.4.26 $T_{c\bar{b}u\bar{s}}$

|
---|---
$(a)$ |  $(b)$
Figure 89: (a) is $(J,M^{2})$ $T_{c\bar{b}u\bar{s}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}u\bar{s}}$ HMRT. Table 156: $T_{c\bar{b}u\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$7742-7868$ $7939-8056$ $8123-8233$ $8296-8400$ $8460-8559$ $8617-8712$ $8767-8858$ $8911-8999$ $9050-9136$ $9185-9268$ $9316-9396$ $9443-9521$ |  $-2.3$-$-1.7$
Table 157: $T_{c\bar{b}u\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$7552-7688$ $7853-7974$ $8123-8233$ $8370-8472$ $8600-8695$ $8815-8906$ $9020-9106$ $9214-9297$ $9401-9480$ $9580-9656$ $9753-9827$ $9920-9992$ |  $-2.1$-$-1.6$

####  7.4.27 $T_{c\bar{b}d\bar{s}}$

|
---|---
$(a)$ |  $(b)$
Figure 90: (a) is $(J,M^{2})$ $T_{c\bar{b}d\bar{s}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}d\bar{s}}$ HMRT. Table 158: $T_{c\bar{b}d\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$7736-7862$ $7934-8051$ $8118-8228$ $8291-8395$ $8456-8555$ $8612-8707$ $8763-8854$ $8907-8995$ $9046-9132$ $9181-9264$ $9312-9392$ $9439-9518$ |  $-2.3$-$-1.7$
Table 159: $T_{c\bar{b}d\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$7545-7682$ $7848-7969$ $8118-8228$ $8365-8467$ $8595-8691$ $8811-8902$ $9016-9102$ $9211-9293$ $9397-9476$ $9577-9653$ $9750-9823$ $9917-9988$ |  $-2.1$-$-1.6$

####  7.4.28 $T_{c\bar{b}s\bar{d}}$

|
---|---
$(a)$ |  $(b)$
Figure 91: (a) is $(J,M^{2})$ $T_{c\bar{b}s\bar{d}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}s\bar{d}}$ HMRT. Table 160: $T_{c\bar{b}s\bar{d}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$7988-8110$ $8161-8277$ $8326-8436$ $8483-8588$ $8633-8734$ $8777-8875$ $8917-9011$ $9052-9143$ $9183-9272$ $9310-9396$ $9433-9518$ $9554-9637$ |  $-3.0$-$-2.3$
Table 161: $T_{c\bar{b}s\bar{d}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$7824-7953$ $8086-8204$ $8326-8436$ $8550-8654$ $8762-8860$ $8962-9056$ $9154-9243$ $9338-9424$ $9514-9597$ $9685-9765$ $9850-9928$ $10011-10086$ |  $-2.2$-$-1.8$

####  7.4.29 $T_{b\bar{u}c\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 92: (a) is $(J,M^{2})$ $T_{b\bar{u}c\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{b\bar{u}c\bar{u}}$ HMRT. Table 162: $T_{b\bar{u}c\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$7154-7194$ $7449-7482$ $7702-7732$ $7928-7955$ $8135-8159$ $8326-8349$ $8506-8528$ $8676-8697$ $8838-8857$ $8992-9011$ $9141-9159$ $9284-9301$ |  $-2.3$-$-2.1$
Table 163: $T_{b\bar{u}c\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$7154-7194$ $7565-7597$ $7904-7931$ $8200-8224$ $8467-8489$ $8713-8733$ $8942-8961$ $9157-9175$ $9361-9378$ $9556-9572$ $9742-9758$ $9921-9937$ |  $-1.6$-$-1.5$

####  7.4.30 $T_{b\bar{d}c\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 93: (a) is $(J,M^{2})$ $T_{b\bar{d}c\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{b\bar{d}c\bar{u}}$ HMRT. Table 164: $T_{b\bar{d}c\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$7155-7195$ $7450-7483$ $7703-7732$ $7929-7956$ $8135-8160$ $8327-8350$ $8507-8528$ $8677-8697$ $8838-8858$ $8993-9012$ $9141-9159$ $9284-9302$ |  $-2.3$-$-2.1$
Table 165: $T_{b\bar{d}c\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$7155-7195$ $7566-7598$ $7905-7932$ $8201-8225$ $8468-8490$ $8713-8734$ $8942-8961$ $9157-9175$ $9361-9379$ $9556-9573$ $9743-9758$ $9922-9937$ |  $-1.6$-$-1.5$

####  7.4.31 $T_{b\bar{d}c\bar{d}}$

|
---|---
$(a)$ |  $(b)$
Figure 94: (a) is $(J,M^{2})$ $T_{b\bar{d}c\bar{d}}$ HMRT, (b) $(n,M^{2})$ $T_{b\bar{d}c\bar{d}}$ HMRT. Table 166: $T_{b\bar{d}c\bar{d}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$7160-7200$ $7454-7487$ $7706-7736$ $7932-7959$ $8138-8163$ $8330-8353$ $8509-8531$ $8679-8700$ $8841-8860$ $8995-9014$ $9143-9162$ $9286-9304$ |  $-2.3$-$-2.1$
Table 167: $T_{b\bar{d}c\bar{d}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$7160-7200$ $7570-7602$ $7908-7935$ $8204-8228$ $8470-8493$ $8716-8736$ $8944-8964$ $9160-9178$ $9364-9381$ $9558-9575$ $9744-9760$ $9924-9939$ |  $-1.6$-$-1.5$

####  7.4.32 $T_{b\bar{s}c\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 95: (a) is $(J,M^{2})$ $T_{b\bar{s}c\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{b\bar{s}c\bar{u}}$ HMRT. Table 168: $T_{b\bar{s}c\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$7242-7282$ $7537-7570$ $7789-7818$ $8014-8040$ $8219-8244$ $8410-8433$ $8589-8610$ $8758-8778$ $8918-8938$ $9072-9091$ $9220-9238$ $9362-9380$ |  $-2.0$-$-1.9$
Table 169: $T_{b\bar{s}c\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$7242-7282$ $7653-7684$ $7990-8017$ $8284-8308$ $8550-8572$ $8794-8814$ $9022-9041$ $9236-9254$ $9439-9456$ $9633-9649$ $9818-9834$ $9997-10012$ |  $-1.4$-$-1.3$

####  7.4.33 $T_{b\bar{d}c\bar{s}}$

|
---|---
$(a)$ |  $(b)$
Figure 96: (a) is $(J,M^{2})$ $T_{b\bar{d}c\bar{s}}$ HMRT, (b) $(n,M^{2})$ $T_{b\bar{d}c\bar{s}}$ HMRT. Table 170: $T_{b\bar{d}c\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$7247-7287$ $7541-7574$ $7792-7822$ $8017-8044$ $8222-8247$ $8413-8436$ $8591-8613$ $8760-8781$ $8921-8940$ $9075-9093$ $9222-9240$ $9364-9382$ |  $-2.0$-$-1.9$
Table 171: $T_{b\bar{d}c\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$7247-7287$ $7657-7688$ $7993-8020$ $8287-8311$ $8553-8574$ $8797-8817$ $9024-9043$ $9238-9256$ $9441-9458$ $9635-9651$ $9820-9836$ $9999-10014$ |  $-1.4$-$-1.3$

####  7.4.34 $T_{b\bar{s}c\bar{s}}$

|
---|---
$(a)$ |  $(b)$
Figure 97: (a) is $(J,M^{2})$ $T_{b\bar{s}c\bar{s}}$ HMRT, (b) $(n,M^{2})$ $T_{b\bar{s}c\bar{s}}$ HMRT. Table 172: $T_{b\bar{s}c\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$7345-7385$ $7649-7682$ $7906-7934$ $8132-8158$ $8339-8362$ $8529-8551$ $8708-8729$ $8877-8896$ $9037-9056$ $9191-9209$ $9338-9355$ $9480-9496$ |  $-1.6$-$-1.5$
Table 173: $T_{b\bar{s}c\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$7345-7385$ $7768-7798$ $8108-8134$ $8404-8427$ $8669-8690$ $8913-8933$ $9140-9158$ $9354-9371$ $9556-9573$ $9749-9765$ $9934-9949$ $10112-10126$ |  $-1.1$-$-1.0$

####  7.4.35 $T_{b\bar{c}c\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 98: (a) is $(J,M^{2})$ $T_{b\bar{c}c\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{b\bar{c}c\bar{u}}$ HMRT. Table 174: $T_{b\bar{c}c\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$8149-8189$ $8372-8408$ $8575-8608$ $8763-8794$ $8939-8968$ $9105-9132$ $9262-9289$ $9413-9439$ $9558-9583$ $9698-9722$ $9833-9856$ $9964-9986$ |  $-3.4$-$-3.2$
Table 175: $T_{b\bar{c}c\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$8149-8189$ $8465-8499$ $8743-8774$ $8995-9023$ $9228-9255$ $9446-9471$ $9652-9676$ $9848-9870$ $10035-10057$ $10215-10235$ $10387-10408$ $10555-10574$ |  $-2.3$-$-2.2$

####  7.4.36 $T_{c\bar{b}u\bar{c}}$

|
---|---
$(a)$ |  $(b)$
Figure 99: (a) is $(J,M^{2})$ $T_{c\bar{b}u\bar{c}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}u\bar{c}}$ HMRT. Table 176: $T_{c\bar{b}u\bar{c}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$8149-8189$ $8372-8408$ $8575-8608$ $8763-8794$ $8939-8968$ $9105-9132$ $9262-9289$ $9413-9439$ $9558-9583$ $9698-9722$ $9833-9856$ $9964-9986$ |  $-3.4$-$-3.2$
Table 177: $T_{c\bar{b}u\bar{c}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$8149-8189$ $8465-8499$ $8743-8774$ $8995-9023$ $9228-9255$ $9446-9471$ $9652-9676$ $9848-9870$ $10035-10057$ $10215-10235$ $10387-10408$ $10555-10574$ |  $-2.3$-$-2.2$

####  7.4.37 $T_{c\bar{b}c\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 100: (a) is $(J,M^{2})$ $T_{c\bar{b}c\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}c\bar{u}}$ HMRT. Table 178: $T_{c\bar{b}c\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$9198-9316$ $9338-9451$ $9473-9583$ $9604-9711$ $9731-9835$ $9854-9955$ $9975-10073$ $10092-10188$ $10207-10301$ $10319-10411$ $10429-10519$ $10536-10625$ |  $-5.9$-$-5.1$
Table 179: $T_{c\bar{b}c\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$9069-9191$ $9276-9392$ $9473-9583$ $9661-9766$ $9841-9942$ $10014-10112$ $10181-10276$ $10343-10435$ $10501-10590$ $10654-10740$ $10803-10887$ $10948-11031$ |  $-3.9$-$-3.4$

####  7.4.38 $T_{c\bar{b}c\bar{d}}$

|
---|---
$(a)$ |  $(b)$
Figure 101: (a) is $(J,M^{2})$ $T_{c\bar{b}c\bar{d}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}c\bar{d}}$ HMRT. Table 180: $T_{c\bar{b}c\bar{d}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$9093-9211$ $9236-9350$ $9375-9485$ $9509-9615$ $9639-9742$ $9765-9865$ $9887-9985$ $10007-10102$ $10123-10217$ $10237-10329$ $10349-10438$ $10458-10546$ |  $-5.2$-$-4.3$
Table 181: $T_{c\bar{b}c\bar{d}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$8960-9082$ $9173-9289$ $9375-9485$ $9567-9672$ $9751-9852$ $9927-10025$ $10098-10192$ $10262-10353$ $10422-10510$ $10577-10663$ $10728-10812$ $10875-10957$ |  $-4.4$-$-3.8$

####  7.4.39 $T_{c\bar{b}d\bar{c}}$

|
---|---
$(a)$ |  $(b)$
Figure 102: (a) is $(J,M^{2})$ $T_{c\bar{b}d\bar{c}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}d\bar{c}}$ HMRT. Table 182: $T_{c\bar{b}d\bar{c}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$8154-8194$ $8377-8413$ $8579-8612$ $8767-8798$ $8942-8971$ $9108-9136$ $9266-9292$ $9417-9442$ $9561-9586$ $9701-9724$ $9836-9859$ $9967-9989$ |  $-3.4$-$-3.2$
Table 183: $T_{c\bar{b}d\bar{c}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$8154-8194$ $8469-8504$ $8746-8778$ $8998-9027$ $9231-9258$ $9449-9474$ $9655-9679$ $9851-9873$ $10038-10059$ $10217-10238$ $10390-10410$ $10557-10576$ |  $-2.4$-$-2.2$

####  7.4.40 $T_{b\bar{c}c\bar{d}}$

|
---|---
$(a)$ |  $(b)$
Figure 103: (a) is $(J,M^{2})$ $T_{b\bar{c}c\bar{d}}$ HMRT, (b) $(n,M^{2})$ $T_{b\bar{c}c\bar{d}}$ HMRT. Table 184: $T_{b\bar{c}c\bar{d}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$8154-8194$ $8377-8413$ $8579-8612$ $8767-8798$ $8942-8971$ $9108-9136$ $9266-9292$ $9417-9442$ $9561-9586$ $9701-9724$ $9836-9859$ $9967-9989$ |  $-3.4$-$-3.2$
Table 185: $T_{b\bar{c}c\bar{d}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$8154-8194$ $8469-8504$ $8746-8778$ $8998-9027$ $9231-9258$ $9449-9474$ $9655-9679$ $9851-9873$ $10038-10059$ $10217-10238$ $10390-10410$ $10557-10576$ |  $-2.4$-$-2.2$

####  7.4.41 $T_{b\bar{c}c\bar{s}}$

|
---|---
$(a)$ |  $(b)$
Figure 104: (a) is $(J,M^{2})$ $T_{b\bar{c}c\bar{s}}$ HMRT, (b) $(n,M^{2})$ $T_{b\bar{c}c\bar{s}}$ HMRT. Table 186: $T_{b\bar{c}c\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$8252-8292$ $8488-8523$ $8699-8731$ $8892-8922$ $9072-9099$ $9240-9266$ $9400-9425$ $9553-9577$ $9699-9722$ $9840-9862$ $9976-9997$ $10107-10128$ |  $-2.6$-$-2.4$
Table 187: $T_{b\bar{c}c\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$8252-8292$ $8584-8618$ $8871-8901$ $9129-9156$ $9365-9391$ $9586-9609$ $9793-9816$ $9990-10012$ $10178-10199$ $10358-10378$ $10532-10550$ $10699-10717$ |  $-1.8$-$-1.7$

####  7.4.42 $T_{c\bar{b}c\bar{s}}$

|
---|---
$(a)$ |  $(b)$
Figure 105: (a) is $(J,M^{2})$ $T_{c\bar{b}c\bar{s}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}c\bar{s}}$ HMRT. Table 188: $T_{c\bar{b}c\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$9045-9166$ $9204-9319$ $9356-9466$ $9501-9607$ $9641-9743$ $9776-9875$ $9907-10002$ $10033-10126$ $10156-10247$ $10276-10364$ $10393-10479$ $10507-10592$ |  $-4.6$-$-3.9$
Table 189: $T_{c\bar{b}c\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$8896-9023$ $9134-9252$ $9356-9466$ $9564-9668$ $9761-9860$ $9949-10044$ $10129-10220$ $10302-10390$ $10470-10555$ $10631-10714$ $10788-10868$ $10941-11019$ |  $-2.7$-$-2.1$

####  7.4.43 $T_{c\bar{b}s\bar{c}}$

|
---|---
$(a)$ |  $(b)$
Figure 106: (a) is $(J,M^{2})$ $T_{c\bar{b}s\bar{c}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}s\bar{c}}$ HMRT. Table 190: $T_{c\bar{b}s\bar{c}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$8252-8292$ $8488-8523$ $8699-8731$ $8892-8922$ $9072-9099$ $9240-9266$ $9400-9425$ $9553-9577$ $9699-9722$ $9840-9862$ $9976-9997$ $10107-10128$ |  $-2.6$-$-2.4$
Table 191: $T_{c\bar{b}s\bar{c}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$8252-8292$ $8584-8618$ $8871-8901$ $9129-9156$ $9365-9391$ $9586-9609$ $9793-9816$ $9990-10012$ $10178-10199$ $10358-10378$ $10532-10550$ $10699-10717$ |  $-1.8$-$-1.7$

####  7.4.44 $T_{c\bar{b}c\bar{c}}$

|
---|---
$(a)$ |  $(b)$
Figure 107: (a) is $(J,M^{2})$ $T_{c\bar{b}c\bar{c}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}c\bar{c}}$ HMRT. Table 192: $T_{c\bar{b}c\bar{c}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$9268-9308$ $9456-9493$ $9631-9666$ $9795-9828$ $9951-9982$ $10099-10129$ $10241-10270$ $10378-10406$ $10510-10537$ $10638-10664$ $10762-10787$ $10883-10907$ |  $-4.2$-$-4.0$
Table 193: $T_{c\bar{b}c\bar{c}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$9268-9308$ $9535-9571$ $9777-9810$ $10001-10032$ $10210-10239$ $10408-10435$ $10596-10622$ $10776-10801$ $10949-10973$ $11115-11138$ $11276-11299$ $11432-11454$ |  $-2.9$-$-2.8$

####  7.4.45 $T_{b\bar{b}c\bar{u}}$

|
---|---
$(a)$ |  $(b)$
Figure 108: (a) is $(J,M^{2})$ $T_{b\bar{b}c\bar{u}}$ HMRT, (b) $(n,M^{2})$ $T_{b\bar{b}c\bar{u}}$ HMRT. Table 194: $T_{b\bar{b}c\bar{u}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$11274-11314$ $11473-11508$ $11651-11683$ $11815-11845$ $11969-11997$ $12114-12141$ $12252-12277$ $12384-12409$ $12511-12535$ $12634-12657$ $12753-12775$ $12868-12890$ |  $-2.5$-$-2.3$
Table 195: $T_{b\bar{b}c\bar{u}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$11274-11314$ $11554-11588$ $11798-11828$ $12018-12046$ $12222-12248$ $12413-12437$ $12593-12617$ $12766-12788$ $12931-12952$ $13089-13110$ $13243-13263$ $13391-13411$ |  $-1.7$-$-1.6$

####  7.4.46 $T_{b\bar{b}c\bar{d}}$

|
---|---
$(a)$ |  $(b)$
Figure 109: (a) is $(J,M^{2})$ $T_{b\bar{b}c\bar{d}}$ HMRT, (b) $(n,M^{2})$ $T_{b\bar{b}c\bar{d}}$ HMRT. Table 196: $T_{b\bar{b}c\bar{d}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$11279-11319$ $11477-11513$ $11655-11687$ $11819-11849$ $11972-12001$ $12117-12144$ $12255-12281$ $12387-12412$ $12514-12538$ $12637-12660$ $12755-12778$ $12871-12892$ |  $-2.5$-$-2.3$
Table 197: $T_{b\bar{b}c\bar{d}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$11279-11319$ $11558-11592$ $11801-11832$ $12021-12049$ $12225-12251$ $12416-12440$ $12596-12619$ $12768-12791$ $12933-12955$ $13092-13113$ $13245-13265$ $13394-13413$ |  $-1.7$-$-1.6$

####  7.4.47 $T_{b\bar{b}c\bar{s}}$

|
---|---
$(a)$ |  $(b)$
Figure 110: (a) is $(J,M^{2})$ $T_{b\bar{b}c\bar{s}}$ HMRT, (b) $(n,M^{2})$
$T_{b\bar{b}c\bar{s}}$ HMRT.

Table 198: $T_{b\bar{b}c\bar{s}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$11377-11417$ $11608-11641$ $11805-11834$ $11981-12008$ $12144-12169$ $12296-12319$ $12440-12462$ $12576-12598$ $12707-12728$ $12833-12853$ $12955-12974$ $13073-13091$ |  $-1.4$-$-1.3$

Table 199: $T_{b\bar{b}c\bar{s}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$11377-11417$ $11699-11730$ $11963-11990$ $12196-12220$ $12408-12431$ $12606-12627$ $12792-12812$ $12968-12987$ $13136-13155$ $13298-13315$ $13454-13470$ $13604-13620$ |  $-0.98$-$-0.87$

####  7.4.48 $T_{c\bar{b}u\bar{b}}$

|
---|---
$(a)$ |  $(b)$
Figure 111: (a) is $(J,M^{2})$ $T_{c\bar{b}u\bar{b}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}u\bar{b}}$ HMRT. Table 200: $T_{c\bar{b}u\bar{b}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$11563-11603$ $11795-11830$ $12002-12034$ $12191-12221$ $12367-12395$ $12532-12558$ $12688-12713$ $12837-12860$ $12979-13001$ $13116-13137$ $13247-13268$ $13375-13395$ |  $-2.7$-$-2.6$
Table 201: $T_{c\bar{b}u\bar{b}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$11563-11603$ $11890-11923$ $12171-12201$ $12423-12450$ $12654-12679$ $12869-12892$ $13071-13093$ $13262-13283$ $13444-13464$ $13618-13637$ $13786-13804$ $13948-13965$ |  $-1.9$-$-1.8$

####  7.4.49 $T_{c\bar{b}d\bar{b}}$

|
---|---
$(a)$ |  $(b)$
Figure 112: (a) is $(J,M^{2})$ $T_{c\bar{b}d\bar{b}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}d\bar{b}}$ HMRT. Table 202: $T_{c\bar{b}d\bar{b}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$11564-11604$ $11796-11831$ $12003-12035$ $12192-12222$ $12368-12395$ $12533-12559$ $12689-12713$ $12837-12861$ $12979-13002$ $13116-13138$ $13248-13269$ $13375-13396$ |  $-2.7$-$-2.6$
Table 203: $T_{c\bar{b}d\bar{b}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---
$11564-11604$ $11891-11924$ $12172-12202$ $12424-12451$ $12655-12680$ $12869-12893$ $13071-13093$ $13262-13283$ $13444-13464$ $13619-13638$ $13786-13805$ $13948-13966$ |  $-1.9$-$-1.8$

####  7.4.50 $T_{c\bar{b}s\bar{b}}$

|
---|---
$(a)$ |  $(b)$
Figure 113: (a) is $(J,M^{2})$ $T_{c\bar{b}s\bar{b}}$ HMRT, (b) $(n,M^{2})$ $T_{c\bar{b}s\bar{b}}$ HMRT. Table 204: $T_{c\bar{b}s\bar{b}}$ $(J,M^{2})$ predictions. $J$ Spec |  $a_{T_{j}}$
---|---
$11651-11691$ $11902-11936$ $12120-12150$ $12316-12343$ $12496-12521$ $12664-12688$ $12822-12845$ $12973-12995$ $13117-13137$ $13254-13274$ $13387-13406$ $13515-13534$ |  $-1.9$-$-1.8$
Table 205: $T_{c\bar{b}s\bar{b}}$ $(n,M^{2})$ predictions. $n$ Spec |  $a_{T_{n}}$
---|---