Nonstandard heavy mesons and baryons: Experimental evidence

Quantum chromodynamics (QCD), the generally accepted theory for strong interactions, describes the interactions between quarks and gluons. The strongly interacting particles that are seen in nature are hadrons, which are composites of quarks and gluons. Since QCD is a strongly coupled theory at distance scales that are characteristic of observable hadrons, there are no rigorous, first-principle methods to derive the spectrum and properties of the hadrons from the QCD Lagrangian, except for lattice QCD simulations that are not yet able to cope with all aspects of complex and short-lived states. Instead, a variety of “QCD inspired” phenomenological models have been proposed. Common features of these models are predictions for the existence of hadrons with substructures that are more complex than the standard quark-antiquark mesons and the three-quark baryons of the original quark model that provides a concise description of most of the low-mass hadrons. Recently, an assortment of candidates for nonstandard multiquark mesons, meson-gluon hybrids, and pentaquark baryons that contain heavy (charm or bottom) quarks has been discovered. Here the experimental evidence for these states is reviewed and some general comparisons of their measured properties with standard quark model expectations and predictions of various models for nonstandard hadrons are made. The conclusion is that the spectroscopy of all but the simplest hadrons is not yet understood.

Figure 1

(a) The color makeup of baryons, antibaryons, and a meson. (b) Single gluon exchange between two quarks. Gluons have two color indices that can be viewed as two color charges that propagate in opposite directions.

Figure 2

(a) The lowest-order QED vacuum polarization diagram for electron-electron scattering. (b) The lowest-order QCD vacuum polarization diagrams for quark-quark scattering.

Figure 3

The behavior of the QCD coupling strength ${\alpha }_s$ as a function of the inverse momentum transfer $1/Q$ or, equivalently, the quark separation distance $r$. Descriptions of the data points and the associated references are provided in [337].

Figure 4

The current status of the charmonium spectrum. The dashed (red) lines indicate the expected states and their masses based on recent calculations ([108]) based on the Godfrey-Isgur relativized potential model ([220]). The solid (black) lines indicate the experimentally established charmonium states with masses and spin-parity ($J^{PC}$) quantum number assignments taken from [337], and labeled by their spectroscopic designations. The open-flavor threshold is also indicated (blue line).

Figure 5

The current status of the bottomonium spectrum. The dashed lines indicate the expected states and their masses based on recent calculations ([221]) based on the Godfrey-Isgur relativized potential model ([220]). The solid lines indicate the experimentally established bottomonium states, with masses and spin-parity ($J^{PC}$) quantum number assignments from [337] and labeled by their spectroscopic designations. The open-flavor threshold is also indicated (blue line).

Figure 6

(a) Combining a red and a blue quark triplet produces a magenta (antigreen) antitriplet and sextet. The antitriplet is antisymmetric in color and flavor while the sextet is color antisymmetric and flavor symmetric. (b) The three anticolored diquark antitriplets. (c) Some of the multiquark, color-singlet states that can be formed from quarks, antiquarks, diquarks, and diantiquarks.

Figure 7

(a) A meson-meson and (b) a meson-baryon molecularlike structure bound by Yukawa-type meson-exchange forces. (c) A sketch of the hadrocharmonium configuration of multiquark states. Here a color-singlet $Q\overline{Q}$ core state interacts with a surrounding “blob” of gluons and light quarks via QCD versions of van der Waals-type forces. (d) In adjoint charmonium states, a color-octet $Q\overline{Q}$ pair interacts with surrounding gluons and light quarks via color forces.

Figure 8

(a) Low order diagrams that describe a three-body decay process $Y\to \pi D{\overline{D}}^{*}$ scattering near the $\sqrt{s}=m_D+m_{D^{*}}$ threshold. From [231]. (b) The scattering amplitude near threshold. The dotted curve is $\mathrm{I}\mathrm{m}T$, the dashed curve is $\mathrm{R}\mathrm{e}T$, and the solid curve is $|T|$. Adapted from [362]. (c) A three-body decay with an internal triangle. This diagram is singular when the three virtual particles that form the triangle are all simultaneously on the mass shell.

Figure 9

The LQCD hadron spectrum from MILC ([94]; [111]), PACS-CS ([73]), BMW ([197]), QCDSF ([122]), RBC and UKQCD ([176]), Hadron Spectrum ([196]), UKQCD ([225]), Fermilab-MILC ([116]), HPQCD ([226]), and [318]. The $b$-flavored meson masses are offset by $-4000\mathrm{MeV}$. Horizontal bars (gray boxes) denote experimentally measured masses (widths). From [268].

Figure 10

Results of the lattice computations of $\mathrm{\Delta }N=m_n-m_p$, $\mathrm{\Delta }\mathrm{\Sigma }=m_{{\mathrm{\Sigma }}^{-}}-m_{{\mathrm{\Sigma }}^{+}}$, $\mathrm{\Delta }\mathrm{\Xi }=m_{{\mathrm{\Xi }}^{-}}-m_{{\mathrm{\Xi }}^0}$, $\mathrm{\Delta }D=m_{D^{+}}-m_{D^0}$, and $\mathrm{\Delta }{\mathrm{\Xi }}_{cc}=m_{{\mathrm{\Xi }}_{cc}^{++}}-m_{{\mathrm{\Xi }}_{cc}^{+}}$ isospin mass splittings, and a test of the Coleman-Glashow relation ([184]) ${\mathrm{\Delta }}_{\mathrm{CG}}\equiv \mathrm{\Delta }{M}_{\mathrm{N}}-\mathrm{\Delta }{M}_{\mathrm{\Sigma }}-\mathrm{\Delta }{M}_{\mathrm{\Xi }}=0$. The horizontal lines are the experimental values and the gray shaded regions represent the experimental error. The computed precision for the quantities with labels in blue shaded boxes is better than that of current measurements. From [132].

Figure 11

(a) Total cross-section measurements for $e^{+}{e}^{-}$ annihilation into hadronic final states in units of the QED cross section ${\sigma }_{\mathrm{QED}}(e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-})=86.8\mathrm{nb}/s({\mathrm{GeV}}^2)$ ([96]; [100]; [185]; [101], [102]). The inset shows the results of a fit to the measurements in the 3.6 to 4.6 GeV energy interval that identifies the $1^{--}$ charmonium states in this region ([37]). (b) Measurements of $\sigma (e^{+}{e}^{-}\to \text{hadrons})$ in the 9.45 to 10.62 GeV energy region from CUSP ([345]). The inset shows measurements between 10.55 and 11.5 GeV from CLEO ([117]).

Figure 12

Processes that produce $c\overline{c}$ pairs in $e^{+}{e}^{-}$ collisions near $E_{\mathrm{c.m.}}=10.6\mathrm{GeV}$: (a) $B\to K(c\overline{c})$ decays, (b) two-photon fusion processes, (c) $e^{+}{e}^{-}$ annihilation into $c\overline{c}c\overline{c}$, and (d) initial state radiation.

Figure 13

(a) $M_{\mathrm{bc}}$, (b) $\mathrm{\Delta }{E}_{\mathrm{c.m.}}$, and (c) $M({\pi }^{+}{\pi }^{-}J/\psi )$ distributions for $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}J/\psi$ decays. The narrow ${\pi }^{+}{\pi }^{-}J/\psi$ mass peak in (c) is the $X(3872)$ signal. From [174].

Figure 14

(a) The distribution of masses recoiling from the $J/\psi$ in inclusive $e^{+}{e}^{-}\to J/\psi X$ events. From [35]. (b) The ${\pi }^{+}{\pi }^{-}J/\psi$ invariant mass distribution for $e^{+}{e}^{-}\to {\gamma }_{\mathrm{isr}}{\pi }^{+}{\pi }^{-}J/\psi$ events. From [77].

Figure 15

The projection of events with $\gamma {\pi }^{+}{\pi }^{-}$ recoil mass near the ${\eta }_c$ mass onto $\gamma {\eta }_c$ mass for $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma {\eta }_c$ candidate events in BESIII. From [41].

Figure 16

The $\mathrm{\Delta }M=M({\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-})-M({\mu }^{+}{\mu }^{-})$ distributions for central events (solid points) and end-cap events (open circles). The similarity between the relative signal yields in the $X(3872)$ and ${\psi }^{\prime }$ peaks indicates that the production mechanism for the two states has similar dependence on pseudorapidity ($|y|$). From [29].

Figure 17

The data points in the upper panel show the invariant mass distribution for $X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi$ candidates in the CDF detector. The solid curve shows the result of an unbinned likelihood fit and the dashed curve shows the background component. The lower panel shows the fit residuals. From [26].

Figure 18

The upper (lower) panel shows the $M(J/\psi \gamma )$ [$M({\psi }^{\prime }\gamma )$] distribution for events with $M(J/\psi \gamma K^{+})$ [$M({\psi }^{\prime }\gamma K^{+})$] within $3\sigma$ of $m_{B^{+}}=5.28\mathrm{GeV}$. From [10].

Figure 19

The $M(B_s^0{\pi }^{\pm })$ distribution together with the background distribution (dashed curve) and fit results (solid curve) for events (a) with and (b) without the application of the $B_s^0-{\pi }^{\pm }$ opening angle requirement. From [32].

Figure 20

The invariant mass distribution $M(B_s^0{\pi }^{\pm })$ for the $B_s^0\to D_s\mu X$ event sample with the results of the fit superimposed. From [402].

Figure 21

The $B_s^0{\pi }^{\pm }$ distributions (points with error bars) observed by (left) the LHCb [from 17] and by (right) the CMS [from 355]. The LHCb plot shows the result of a fit of an $X(5568)$ signal (not visible) included on top of the combinatorial background. The continuous blue band in the CMS plot is the distribution observed for the $B_s^0$-mass sideband data. The vertical red band illustrates the $M_X\pm {\mathrm{\Gamma }}_X$ region of the $X(5568)$ state claimed by D0.

Figure 22

(a) The $M({\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-})-M({\ell }^{+}{\ell }^{-})$ distribution for $B\to K{\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$ events with $|M({\ell }^{+}{\ell }^{-})-m_{J/\psi }|<20\mathrm{MeV}$. From [171]. (b) The ${\pi }^{+}{\pi }^{-}$ invariant mass distribution for $X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi$ events in Belle ([171]). The curves show results of fits to a $\rho \to {\pi }^{+}{\pi }^{-}$ line shape including $\rho -\omega$ interference ([174]). The dashed (solid) curve is for even (odd) $X(3872)$ parity

Figure 23

(a) The $M({\pi }^{+}{\pi }^{-}J/\psi )-m_{J/\psi }$ distribution for $B^{+}\to K^{+}{\pi }^{+}{\pi }^{-}J/\psi$ events. (b) Distributions of $t\equiv -2\ln [{\mathcal{L}}^{\mathrm{alt}}/{\mathcal{L}}^{++}]$ for simulated experiments for alternative $J^{PC}$ hypotheses (solid blue histograms) and $1^{--}$ (dashed red histograms). The vertical lines show the values of $t$ determined from the data. Similar results for $J^{PC}=3^{\pm +}$ and $4^{\pm +}$ are not shown. From [15].

Figure 24

$M(D^0{\overline{D}}^{*0})$ distributions from $B\to K{D}^0{\overline{D}}^{*0}$. (a) From Belle. From [99]. (b) From BABAR. From [88]. The peaks near threshold are the signals $X(3872)\to D^0{\overline{D}}^{*0}$ decays.

Figure 25

Differential cross sections for particle production vs $p_T$ at the LHC. The solid red (black) circles are ATLAS measurements of prompt $X(3872)$ (${\psi }^{\prime }$) production in $E_{\mathrm{c.m.}}=8\mathrm{TeV}$ $pp$ collisions ([1]). Results for deuteron (green), ${}^3\mathrm{He}$ (orange), and ${}_{\mathrm{\Lambda }}{}^{3}H$ (blue) are extrapolations of ALICE Pb-Pb measurements at $E_{\mathrm{c.m.}}(NN)=2.76$ to $E_{\mathrm{c.m.}}(pp)=7\mathrm{TeV}$ using a Glauber model. Adapted from [205]. The associated curves are the results of fits of the blast-wave model ([351]) expectations in the absence of any corrections for multinucleon collective effects. The blue dash-dotted curve is the extrapolated result for ${}_{\mathrm{\Lambda }}{}^{3}H$ when collective effects are included.

Figure 26

(a) The data points show the BESIII experiment’s $M({\pi }^{+}{\pi }^{-}J/\psi )$ distribution for $e^{+}{e}^{-}\to \gamma {\pi }^{+}{\pi }^{-}J/\psi$ events at energies near the $Y(4260)$ resonance. The fitted peak has a mass and width of $M=3871.9\pm 0.7\mathrm{MeV}$ and $\mathrm{\Gamma }={0.0}_{-0.0}^{+1.7}\mathrm{MeV}$ ($<2.4\mathrm{MeV}$), which are in good agreement with the PDG world-average values for the $X(3872)$. (b) The energy dependence of the BESIII $\sigma \mathbf{(}{e}^{+}{e}^{-}\to \gamma X(3872)\mathbf{)}\times \mathcal{B}\mathbf{(}X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi \mathbf{)}$ measurement. The solid curve is the $Y(4260)$ line shape fitted to the data; the dashed curves show phase-space and linear production model expectations. From [45].

Figure 27

$X(3915)\to \omega J/\psi$ signals in $B\to K\omega J/\psi$ decays. (a) From Belle. From [172]. (b) From BABAR. From [186]. In the latter, the upper panel shows results for $B^{+}\to K^{+}\omega J/\psi$ and the lower panel shows those for $B^0\to K_S\omega J/\psi$. The inset in the upper panel shows an expanded view of the low end of the $\omega J/\psi$ mass scale, where the smaller, low-mass peak is due to the $X(3872)\to \omega J/\psi$ and the larger, higher-mass peak is the $X(3915)\to \omega J/\psi$ signal.

Figure 28

$X(3915)\to \omega J/\psi$ signals in $\gamma \gamma \to \omega J/\psi$ fusion reactions. (a) From Belle. From [375]. (b) From BABAR. From [279]. The bold solid curves are results of fits with a BW resonance shape to represent the signal and a smooth function of $p^{*}$ to represent the background, where $p^{*}$ is the $J/\psi$ momentum in the $\gamma \gamma$ c.m. system. The dash-dotted curve in (a) is the result of a fit with no BW resonance term; the dashed vertical line in (b) indicates the location of $W=3872\mathrm{MeV}$. The shaded histograms show the non-$J/\psi$ background estimated from events in the $J/\psi$ mass sidebands.

Figure 29

(a) The data points show the Born cross sections for $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$, measured via the initial-state radiation process $e^{+}{e}^{-}\to {\gamma }_{\mathrm{isr}}{\pi }^{+}{\pi }^{-}J/\psi$ by BABAR. The curve shows results of a fit that used a single BW resonance to represent the $Y(4260)$ resonance plus a linear background term. From [278]. (b) Belle measurements of the same cross sections. From [296].

Figure 30

Measurements of the ratio $R={\sigma }_{\mathrm{tot}}(e^{+}{e}^{-}\to \text{hadrons})/{\sigma }_{\mathrm{QED}}(e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-})$, where ${\sigma }_{\mathrm{QED}}(e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-})=86.85\mathrm{nb}/s$ ($s$ in ${\mathrm{GeV}}^2$). The structures above $R\simeq 2$ are attributed to the indicated $1^{--}$ charmonium mesons decaying to $D\overline{D}$, $D{\overline{D}}^{*}$ open-charmed, or $D^{*}{\overline{D}}^{*}$ final states. The expected position for a $Y(4260)$ signal, indicated by an arrow, is located at a local minimum in the measured cross section. From [102].

Figure 31

(a) The data points show the ${\pi }^{+}{\pi }^{-}{\psi }^{\prime }$ invariant mass distribution for $e^{+}{e}^{-}\to {\gamma }_{\mathrm{isr}}{\pi }^{+}{\pi }^{-}{\psi }^{\prime }$ events in BABAR. The solid curve shows results of a fit that used a single-BW resonance to represent the signal plus a linear background term. The dashed curve shows the results of a fit with mass and width constrained to the $Y(4260)$ values. From [85]. (b) The blue histogram shows the corresponding results from Belle. The solid curve shows the results of a fit that uses two interfering BW amplitudes, one with mass near 4360 MeV and the other near 4660 MeV. The dashed curves show the individual resonance contributions from two equally good fits that have different interference phases. From [384].

Figure 32

(a) Cross-section measurements for $e^{+}{e}^{-}\to \eta J/\psi$ from BESIII shown as black points. For comparison, Belle isr measurements of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ cross section over the same energy range are shown as blue crosses ([296]). The red star indicates a previous BESIII $\eta J/\psi$ cross-section measurement near the peak of the $\psi (4040)$ charmonium state ([39]). Adapted from [48]. (b) The data points show BESIII measurements of the cross section for $e^{+}{e}^{-}\to \omega {\chi }_{c0}$. The solid curve shows the result of a fit of a threshold-constrained BW resonance shape to the data. The dash-dotted curve indicates what a phase-space-only distribution would be like. From [52].

Figure 33

BESIII measurements of the cross section for $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ for (a) the “high luminosity” and (b) the “low luminosity” scan data. Dashed arrows in both plots indicate the “$Y(4260)$” mass value from the PDG-2016 average of results based on single-BW resonance fits to pre-2016 measurements given in Eq. (9). Adapted from [55].

Figure 34

The data points show BESIII measurements of the cross section for $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c$, where the $h_c$ was detected via its $h_c\to \gamma {\eta }_c$ decay mode with the ${\eta }_c$ reconstructed in one of 16 exclusive multihadron decay channels. The solid black dots are from the low-luminosity-scan and the solid red squares are from the high-luminosity-scan points. The solid red curve shows the results of a fit to the data with a coherent sum of two interfering BW amplitudes discussed in the text. From [53].

Figure 35

(a) The $\mathrm{\Delta }M=M(J/\psi \varphi )-M(J/\psi )$ distribution for a 58 event sample of candidate $B^{+}\to J/\psi \varphi K^{+}$ decays from the CDF experiment. The histogram shows the data and the red curve shows the result of a fit with a BW signal shape and a three-body phase-space term to represent the nonresonant background. From [25]. (b) The corresponding plot for a 2.5 K event sample of candidate $B^{+}$ decays from the CMS experiment. Here the fit includes two BW signal shapes, one for the $X(4140)$ and the other for the enhancement near $\mathrm{\Delta }M\simeq 1.22\mathrm{GeV}$. From [157].

Figure 36

(a) The $M(J/\psi \varphi )$ distribution for a 215 event sample of candidate $B^{+}\to J/\psi \varphi K^{+}$ decays. The solid blue curve is the result of a fit with two BW signal shapes and a three-body phase-space term to represent the nonresonant background. From [30]. (b) The distribution of invariant masses for prompt $J/\psi \varphi$ combinations produced in inclusive $p\overline{p}\to J/\psi \varphi X$ reactions. From [31].

Figure 37

The solid black squares with error bars show the distribution of $J/\psi \varphi$ invariant masses in the LHCb experiment’s 4.3 K event sample of candidate $B^{+}\to J/\psi \varphi K^{+}$ decays. The non-$B$-decay background estimate is shown by the lower red histogram. Projection of the six-dimensional amplitude fit with the four $X\to J/\psi \varphi$ resonance terms shown as hatched histograms plus contributions from a $X\to J/\psi \varphi$ nonresonant amplitude (open blue circles) and $K^{*+}\to \varphi K^{+}$ excitations is shown by the solid-line red histogram with error bars. From [20], [23].

Figure 38

The efficiency-corrected and background-subtracted $J/\psi \varphi$ invariant mass spectrum for $B^{+}\to J/\psi \varphi K^{+}$ decays (red light points) from LHCb ([20], [23]) and the $J/\psi \omega$ mass spectrum for $B^{+}\to J/\psi \varphi K^{+}$ decays (blue dark points) from BABAR ([281]), where the signal yields (in arbitrary units) have been divided by the $J/\psi$ momentum in the $X$ rest frame to account for phase-space differences. The two distributions are normalized to have equal areas for masses above the $J/\psi \varphi$ threshold.

Figure 39

(a) The distribution of masses recoiling from a reconstructed $J/\psi$ and $D$ meson in $e^{+}{e}^{-}\to J/\psi DX$ annihilation at and near $E_{\mathrm{c.m.}}=10.58\mathrm{GeV}$. The two peaks correspond to exclusive $e^{+}{e}^{-}\to J/\psi D\overline{D}$ and $J/\psi D{\overline{D}}^{*}$ events. The shaded histogram indicates the background level determined from the $J/\psi$ and $D$ mass sidebands. (b) The $D\overline{D}$ invariant mass distribution for the exclusive $e^{+}{e}^{-}\to J/\psi D\overline{D}$ events. The solid blue histogram is the result of a fit with a BW resonant amplitude plus a coherent nonresonant background. The red dashed histogram is the fit result when only a nonresonant amplitude is included. From [169].

Figure 40

(a) The $M(D{\overline{D}}^{*})$ distribution for $e^{+}{e}^{-}\to J/\psi D{\overline{D}}^{*}$ events where the $J/\psi$ and $D$ meson are reconstructed and the four-momentum of the undetected ${\overline{D}}^{*}$ meson is inferred from energy-momentum conservation ([333]). The hatched histogram is the non-$J/\psi$ and/or non-$D$ meson background determined from the $J/\psi$ and $D$-meson mass sidebands. The curve shows the results of the fit to the $X(3940)$ resonance described in the text. (b) The $M(D^{*}{\overline{D}}^{*}$ distribution for exclusive $e^{+}{e}^{-}\to J/\psi D^{*}{\overline{D}}^{*}$ events. The curve is the result of the fit for the $X(4160)$. From [35].

Figure 41

The points with errors show distributions of (upper) $M^2({\psi }^{\prime }{\pi }^{+})$ in ${\overline{B}}^0\to {\psi }^{\prime }{\pi }^{+}{K}^{-}$ decays from LHCb [from 11] and (lower) $M^2(J/\psi {\pi }^{+})$ in ${\overline{B}}^0\to J/\psi {\pi }^{+}{K}^{-}$ from Belle [from 168]. Here only events with $K^{-}{\pi }^{+}$ invariant masses that are between the $K^{*}(892{)}^0$ and $K_2^{*}(1430{)}^0$ resonances are included in order to suppress contributions from the $K\pi$ channel. Projections of four-dimensional amplitude fits that include coherent contributions from kaon excitations and two $Z^{+}$ terms are superimposed as solid line histograms. The individual $Z^{+}$ terms are shown as blue and green points; the dashed red curve in the Belle plot shows the projection of all the $K^{-}{\pi }^{+}$ terms combined.

Figure 42

Fitted values of the real and imaginary parts of the amplitude for (left) $Z(4430{)}^{+}\to {\psi }^{\prime }{\pi }^{+}$ signal [from 11] and (right) $Z(4200{)}^{+}\to J/\psi {\pi }^{+}$ signal [from 168], for six $M^2(\psi ,{\pi }^{+})$ bins of equal width that span the resonance. The solid red curve in the LHCb plot shows the pattern expected for a Breit-Wigner resonance amplitude. Units are arbitrary.

Figure 43

The dots with error bars show background-subtracted and efficiency-corrected $M({\psi }^{\prime }{\pi }^{+})$ distribution for ${\overline{B}}^0\to {\psi }^{\prime }{\pi }^{+}{K}^{-}$ events. The solid (dashed) blue lines correspond to contributions from the $K^{-}{\pi }^{+}$ channel for a maximum-allowed angular momentum of $J_{\max }=2$ ($J_{\max }=3$). Since the lightest known $J=3$ resonance, the $K_3^{*}(1780)$, is already beyond the kinematically allowed $K\pi$ mass limit for $\overline{B}\to {\psi }^{\prime }\pi K$ decay, no plausible contribution from the $K\pi$ channel can account for the shape of the $M({\psi }^{\prime }\pi )$ distribution in the $Z(4430{)}^{+}$ mass region. From [13].

Figure 44

The points with error bars show the $M^2({\chi }_{c1}{\pi }^{+})$ distribution in ${\overline{B}}^0\to {\chi }_{c1}{\pi }^{+}{K}^{-}$ decays. The projection of a two-dimensional amplitude fit that included kaon excitations and two $Z^{+}$ terms are superimposed as a solid line histogram. The dotted line corresponds to all $K^{-}{\pi }^{+}$ terms combined and the non-$B$ and/or non-${\chi }_{c1}$ background contribution is shown by the dashed line. From [316].

Figure 45

The black points show the $M^2({\psi }^{\prime }{\pi }^{+})$ distribution for all of the LHCb ${\overline{B}}^0\to {\psi }^{\prime }{\pi }^{+}{K}^{-}$ events. The solid red histogram is the projection of the four-dimensional fit that includes the $Z(4430{)}^{+}$ amplitude and the dashed brown histogram shows the best fit that was found with no ${\psi }^{\prime }{\pi }^{+}$ resonances. Contributions from individual fit components are shown, with the dominant ones labeled. The upper blue points show the final fit results with the $Z^{+}$ terms removed. The vertical dashed blue line indicates the fitted $Z^{+}$ resonance mass value. Adapted from [11].

Figure 46

Cross sections for $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\mathrm{{\rm Y}}(n_{r}S)$ (upper) ($n_r=1$, 2, 3) and (lower) $e^{+}{e}^{-}\to b\overline{b}$in units of the Born QED cross section for $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ [${\sigma }_{\mathrm{QED}}(e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-})=4\pi {\alpha }^2/3{E_{\mathrm{c.m.}}}^2$] in the vicinity of the $\mathrm{{\rm Y}}(5S)$ resonance. From [348].

Figure 47

(a) Distribution of masses recoiling against ${\pi }^{+}{\pi }^{-}$ pairs at c.m. energies near 10.87 GeV and (b) residuals from piecewise fits to the data with smooth polynomials. The $h_b(1P)$ and $h_b(2P)$ peaks, shaded in yellow (light gray), were the first observations of these two states. From [60].

Figure 48

(a) Invariant mass distributions for (upper) $h_b(1P){\pi }^{+}$ and (lower) $h_b(2P){\pi }^{+}$ from $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_b(n_{r}P)$ events. (b) Invariant mass distributions for (upper) $\mathrm{{\rm Y}}(1S){\pi }^{+}$, (center) $\mathrm{{\rm Y}}(2S){\pi }^{+}$, and (lower) $\mathrm{{\rm Y}}(3S){\pi }^{+}$ in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\mathrm{{\rm Y}}(n_{r}S)$ events. The vertical dashed lines in each panel indicate the mass values given in Eq. (16). From [128].

Figure 49

(a) The $M(B{\overline{B}}^{*})$ distribution for ${\pi }^{+}B{\overline{B}}^{*}$ events and (b) the $M(B^{*}{\overline{B}}^{*})$ distribution for ${\pi }^{+}{B}^{*}{\overline{B}}^{*}$ events. The short dashed curves show results of fits with only a $Z_b(10610)\to B{\overline{B}}^{*}$ contribution to (a) and a $Z_b(10650)\to B^{*}{\overline{B}}^{*}$ contribution to (b). The other curves and the hatched (background) histograms are described in the text. From [218].

Figure 50

Distribution of the larger of the two ${\pi }^{\pm }J/\psi$ masses in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ events collected in the BESIII detector at $E_{\mathrm{c.m.}}=4.260\mathrm{GeV}$. The filled histogram shows the level of the non-$J/\psi$ background, which is determined from $J/\psi$ mass sideband events. From [40].

Figure 51

(a) The $D^0{D}^{*-}$ invariant mass distribution in $e^{+}{e}^{-}\to {\pi }^{+}{D}^0{D}^{*-}$ events collected in the BESIII detector at $E_{\mathrm{c.m.}}=4.260\mathrm{GeV}$. The solid curve shows the result of a fit to the data points with a threshold-modified BW amplitude plus an incoherent phase-space-like background (dashed curve). (b) The efficiency-corrected $Z_c(3885)$ production angle distribution compared to expectations for different $J^P$ quantum number assignments. From [43].

Figure 52

(a) The distribution of the larger of the two ${\pi }^{\pm }{h}_c$ masses in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c$ events collected in the BESIII detector at $E_{\mathrm{c.m.}}=4.260$ and 4.360 GeV. The inset shows a larger $M(\pi h_c)$ that includes the $Z_c(3900)$ mass region. From [41]. (b) The $M_{\max }({\pi }^0{h}_c)$ distribution for $e^{+}{e}^{-}\to {\pi }^0{\pi }^0{h}_c$ events. The filled histograms show the level of the non-$h_c$ background determined from $h_c$ mass sideband events. The curves are described in the text. From [44].

Figure 53

(a) Distribution of masses recoiling against the reconstructed ${\pi }^{-}$ and $D^{+}$ in $e^{+}{e}^{-}\to {\pi }^{-}(D^{*}{\overline{D}}^{*}{)}^{+}$ events collected in the BESIII detector at $E_{\mathrm{c.m.}}=4.260\mathrm{GeV}$. The peak near 2.15 GeV corresponds to $e^{+}{e}^{-}\to {\pi }^{-}(D^{*+}{\overline{D}}^{*0}{)}^{+}$ signal events. (b) The $M(D^{*+}{\overline{D}}^{*0})$ distribution inferred from the ${\pi }^{-}$ momentum for signal events. The filled histograms show the level of the combinatorial background determined from events where the reconstructed pion and $D$ meson have the same electric charge. The curves are described in the text. From [42].

Figure 54

Dalitz plot distribution for ${\mathrm{\Lambda }}_b^0\to J/\psi p{K}^{-}$ decays. From [14].

Figure 55

Projections of the amplitude fit with $P_c(4380{)}^{+}$ and $P_c(4450{)}^{+}$ states included (red histogram) onto the (a) $M(Kp)$ and (b) $M(J/\psi p)$ distributions (black squares with error bars) in ${\mathrm{\Lambda }}_b^0\to J/\psi p{K}^{-}$ event sample. Contributions from individual components of the fit are indicated as different color or line-style histograms as labeled. From [14].

Figure 56

Projections of the amplitude fit with $P_c(4380{)}^{+}$ and $P_c(4450{)}^{+}$ states included (solid red circles) onto the $M(J/\psi p)$ invariant mass distributions from ${\mathrm{\Lambda }}_b^0\to J/\psi p{K}^{-}$ events (black squares with error bars) with (a) $1.55\le M(Kp)\le 1.70\mathrm{GeV}$ and (b) $M(Kp)>2.0\mathrm{GeV}$. The individual fit components are shown with the same color and line-style designations that are used in Fig. 55. Adapted from [14].

Figure 57

Fitted values of the real and imaginary parts of the amplitudes of the (a) $P_c(4450{)}^{+}$ and (b) $P_c(4380{)}^{+}$ states for ${\mathrm{\Lambda }}_b^0\to J/\psi p{K}^{-}$ shown in the Argand diagrams as connected points with the error bars (masses increase counterclockwise). The solid red curves are the predictions from the Breit-Wigner formula, with resonance masses and widths set to the nominal fit results and scaled to the displayed points. From [14].

Figure 58

The efficiency-corrected and background-subtracted distribution of $M(J/\psi p)$ for the LHCb data, shown as black points with error bars, is compared with the best fit obtained using reflections based on the observed $K^{-}p$ mass distribution and moments of the $K^{-}p$ helicity angle patterns, shown as the solid blue curve. The possibility that the $M(J/\psi p)$ distribution can be accommodated by any plausible reflections from the $K^{-}p$ system is ruled out at the $>9\sigma$ level. Adapted from [16].

Figure 59

Comparisons of projections of the amplitude fits (red histogram) onto (a) $M(p\pi )$ and (b) $M(J/\psi p)$ data distributions for ${\mathrm{\Lambda }}_b^0\to J/\psi p{\pi }^{-}$ decays. The dashed green histogram shows the results of a fit with no nonstandard hadrons in the $p\pi$ and $J/\psi p$ channels. The inset in (b) shows the $M(J/\psi p)$ fit-data comparison for events with $M(p\pi )>1.8\mathrm{GeV}$, where there is some hint of a $P_c(4450{)}^{+}$ signal. Adapted from [18].

Figure 60

The current status of the charmoniumlike spectrum. The dashed (red) horizontal lines indicate the expected states and their masses based on recent calculations ([108]) based on the Godfrey-Isgur relativized potential model ([220]), supplemented by the calculations in [298] for high radial excitations of the $P$-wave states. The solid (black) horizontal lines indicate the experimentally established charmonium states, with masses and spin-parity ($J^{PC}$) quantum number assignments from [337] and labeled by their spectroscopic assignment. The open-flavor decay channel thresholds are shown with longer solid (brown) horizontal lines. The candidates for exotic charmoniumlike states are also shown with shorter solid (blue or magenta) horizontal lines with labels reflecting their most commonly used names. All states are organized according to their quantum numbers given on horizontal axes. The last column includes states with unknown quantum numbers, the two pentaquark candidates, and the lightest charmonium $2^{--}$ state. The lines connecting the known states indicate known photon or hadron transitions between them: dashed green are $\gamma$ transitions (thick $E1$, thin $M1$), solid magenta are $\pi$, thin (thick) dashed blue are $\eta$ ($\varphi$), dashed red are $p$, dotted blue are ${\rho }^0$ or $\omega$, and solid blue other $\pi \pi$ transitions, respectively.

Figure 61

The current status of the bottomoniumlike spectrum.The dashed (red) lines indicate the expected states and their masses based on recent calculations ([221]) based on the Godfrey-Isgur relativized potential model ([220]). The solid (black) horizontal lines indicate the experimentally established charmonium states, with masses and spin-parity ($J^{PC}$) quantum number assignments from [337], and labeled by their spectroscopic assignment. The open-flavor decay channel thresholds are shown with longer solid (brown) horizontal lines. The candidates for exotic bottomoniumlike states are also shown with shorter solid (blue or magenta) horizontal lines with labels reflecting their most commonly used names. The known photon and hadron transitions are also indicated (see the caption of Fig. 60).