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Bottomonium Mesons and Strategies for Their Observation  [PDF]
Stephen Godfrey,Kenneth Moats
Physics , 2015, DOI: 10.1103/PhysRevD.92.054034
Abstract: The $B$-factories and Large Hadron Collider experiments have demonstrated the ability to observe and measure the properties of bottomonium mesons. In order to discover missing states it is useful to know their properties to develop a successful search strategy. To this end we calculate the masses and decay properties of excited bottomonium states. We use the relativized quark model to calculate the masses and wavefunctions and the $^3P_0$ quark-pair creation model to calculate decay widths to open bottom. We also summarize results for radiative transitions, annihilation decays, hadronic transitions and production cross sections which are used to develop strategies to find these states. We find that the $b\bar{b}$ system has a rich spectroscopy that we expect to be substantially extended by the LHC and $e^+e^-$ experiments in the near future. Some of the most promising possibilities at the LHC are observing the $\chi_{b(1,2)}(3P)$, $\chi_{b(1,2)}(4P)$ and $\eta_b(3S)$ states in $\gamma \mu^+\mu^-$ final states that proceed via radiative transitions through $\Upsilon(nS)$ intermediate states and $1^3D_J$ and $2^3D_J$ into $\gamma\gamma \mu^+\mu^-$ final states proceeding via $1^3P_J\to 1^3S_1$ and $2^3P_J\to 2^3S_1$ intermediate states respectively. Some of the most interesting possibilities in $e^+e^-$ collisions are studying the $1^3D_J$ states via $4\gamma$ cascades starting with the $\Upsilon (3S)$ and the $3^3P_J$ states in $\gamma\gamma\mu^+ \mu^-$ final states starting with the $\Upsilon (4S)$ and proceeding via $\Upsilon (nS)$ intermediate states. Completing the bottomonium spectrum is an important validation of lattice QCD calculations and a test of our understanding of bottomonium states in the context of the quark model.
A relativistic treatment of pion wave functions in the annihilation antiproton-proton -> pi^-pi^+  [PDF]
B. El-Bennich,W. M. Kloet
Physics , 2004, DOI: 10.1103/PhysRevC.70.034001
Abstract: Quark model intrinsic wave functions of highly energetic pions in the reaction \bar pp->\pi^-\pi^+ are subjected to a relativistic treatment. The annihilation is described in a constituent quark model with A2 and R2 flavor-flux topology and the annihilated quark-antiquark pairs are in 3P_0 and 3S_1 states. We study the effects of pure Lorentz transformations on the antiquark and quark spatial wave functions and their respective spinors in the pion. The modified quark geometry of the pion has considerable impact on the angular dependence of the annihilation mechanisms.
$D^\star_{s1}(2700)^\pm$ and $D^\star_{sJ}(2860)^\pm$ revisited within the $^3P_0$ model  [PDF]
Ling Yuan,Bing Chen,Ailin Zhang
Physics , 2012,
Abstract: The strong decays of $D^\star_{s1}(2700)^\pm$ and $D^\star_{sJ}(2860)^\pm$ are investigated within the $^3P_0$ model. It is found that the interpretation of these two states depends on the mixing schemes and the ways of choices of the harmonic oscillator parameter $\beta$. If $D^\star_{s1}(2700)^\pm$ and $D^\star_{sJ}(2860)^\pm$ are two pure states, $D^\star_{s1}(2700)^\pm$ seems impossibly the $2^3S_1$ $D_s$, but may be the $1^3D_1$ $D_s$. $D^\star_{sJ}(2860)^\pm$ may be the $1^3D_3$. If there is mixing between the $2^3S_1$ and $1^3D_1$, $D^\star_{s1}(2700)^\pm$ may be the mixed $1^-$ state with a small mixing angle in the case of a special $\beta$ for each meson, and $D^\star_{sJ}(2860)^\pm$ is the orthogonal partner of $D^\star_{s1}(2700)^\pm$; $D^\star_{s1}(2700)^\pm$ may also be the mixed $1^-$ state with a large mixing angle based on a universal $\beta$ for all mesons, and $D^\star_{sJ}(2860)^\pm$ seems impossibly the orthogonal partner of $D^\star_{s1}(2700)^\pm$. Other uncertainties related to the choices of constituent quark masses and phase spaces are also explored.
A Study of \bar{p}p -> Two Neutral Pseudoscalar Mesons at the chi_c0(1^3P_0) Formation Energy  [PDF]
M. Andreotti
Physics , 2005, DOI: 10.1103/PhysRevD.72.112002
Abstract: Fermilab experiment E835 has studied reactions \bar{p}p -> pi0 pi0, pi0 eta, eta eta, pi0 eta' and eta eta' in the energy region of the chi_c0(1^3P_0) from 3340 MeV to 3470 MeV. Interference between resonant and continuum production is observed in the pi0 pi0 and eta eta channels, and the product of the input and output branching fractions is measured. Limits on resonant production are set for the pi0 eta and pi0 eta' channels. An indication of interference is observed in the eta eta' channel. The technique for extracting resonance parameters in an environment dominated by continuum production is described.
Annihilation range and final-state interaction in the antiproton-proton annihilation into pi-pi+  [PDF]
Bruno El-Bennich,W. M Kloet,B. Loiseau
Physics , 2003, DOI: 10.1103/PhysRevC.68.014003
Abstract: The large set of accurate data on differential cross section and analyzing power from the CERN LEAR experiment on $\bar pp \to \pi^+\pi^-$ in the range from 360 to 1550 MeV/c is well reproduced within a distorted wave approximation approach. The initial $\bar pp$ scattering wave functions originate from a recent $\bar N N$ model. The transition operator is obtained from a combination of the $^3P_0$ and $^3S_1$ quark-antiquark annihilation mechanisms. A good fit to the data, in particular the reproduction of the double dip structure observed in the analyzing powers, requires quark wave functions for proton, antiproton, and pions with radii slightly larger than the respective measured charge radii. This corresponds to an increase in range of the annihilation mechanisms and consequently the amplitudes for total angular momentum J=2 and higher are much larger than in previous approaches. The final state $\pi\pi$ wave functions, parameterized in terms of $\pi\pi$ phase shifts and inelasticities, are also a very important ingredient for the fine tuning of the fit to the observables.
Properties of Excited Charm and Charm-Strange Mesons  [PDF]
Stephen Godfrey,Kenneth Moats
Physics , 2015,
Abstract: We calculate the properties of excited charm and charm-strange mesons. We use the relativized quark model to calculate their masses and wavefunctions that are used to calculate radiative transition partial widths and the $^3P_0$ quark-pair-creation model to calculate their strong decay widths. We use these results to make quark model spectroscopic assignments for recently observed charm and charm-strange mesons. In particular we find that the properties of the $D_J(2550)^0$ and $D_J^*(2600)^0$ are consistent with those of the $2^1S_0(c\bar{u})$ and the $2^3S_1(c\bar{u})$ states respectively, the $D_1^*(2760)^0$, $D_3^*(2760)^-$, and $D_J(2750)^0$ with those of the $1^3D_1(c\bar{u})$, $1^3D_3(d\bar{c})$, and $1D_2(c\bar{u})$ states respectively. We tentatively identify the $D^*_J(3000)^0$ as the $1^3F_4(c\bar{u})$ and favour the $D_J(3000)^0$ to be the $3^1S_0(c\bar{u})$ although we do not rule out the $1F_3$ and $1F_3'$ assignment. For the recently observed charm-strange mesons we identify the $D_{s1}^*(2709)^\pm$, $D_{s1}^*(2860)^-$, and $D_{s3}^*(2860)^-$ as the $2^3S_1(c\bar{s})$, $1^3D_1(s\bar{c})$, and $1^3D_3(s\bar{c})$ states respectively and suggest that the $D_{sJ}(3044)^\pm$ is most likely the $D_{s1}(2P_1')$ or $D_{s1}(2P_1)$ states although it might be the $D_{s2}^*(2^3P_2)$ with the $DK$ final state too small to be observed with current statistics. Based on the predicted properties of excited states, that they not have too large a total width and they have a reasonable branching ratio to simple final states, we suggest states that should be able to be found in the near future. We expect that the tables of properties summarizing our results will be useful for interpreting future observations of charm and charm-strange mesons.
Newly observed $D_J(3000)^{+,0}$ and $D_J^*(3000)^0$ as $2P$ states in $D$ meson family  [PDF]
Yuan Sun,Xiang Liu,Takayuki Matsuki
Physics , 2013, DOI: 10.1103/PhysRevD.88.094020
Abstract: In this work, we study the newly observed $D_J(3000)$ and $D_J^*(3000)$ through the analysis of mass spectrum and calculation of the corresponding two-body strong decay behaviors. Our results show that $D_J(3000)$ and $D_J^*(3000)$ are explained as the $2P(1^+)$ and $2^3P_0$ states in the $D$ meson family, respectively, which is supported by the calculated masses of these two states and their decay behaviors. As a byproduct, the decay behaviors of $3^1S_0$, $3^3S_1$, $2D(2^-)$, $2^3D_1$, $2D^\prime(2^-)$, $2^3D_3$, $2P^\prime(1^+)$, $2^3P_2$, $1F(3^+)$, $1^3F_2$, $1F^\prime(3^+)$, and $1^3F_4$ states are also given, which will be helpful to further experimentally study mixings of these $D$ mesons, too.
Is $Y(4008)$ possibly a $1^{--}$ $ψ(3^3S_1)$ state?  [PDF]
Li-Jin Chen,Dan-Dan Ye,Ailin Zhang
Physics , 2014, DOI: 10.1140/epjc/s10052-014-3031-z
Abstract: The strong decays of the radially excited $\psi(3^3S_1)$ state are studied within the $^3P_0$ model. As a believed $\psi(3^3S_1)$, some strong decay widths and relevant ratios of $\psi(4040)$ are calculated in the model. The theoretical results are consistent with experiments. In a similar way, as a possible $\psi(3^3S_1)$, the same strong decay widths and relevant ratios of $Y(4008)$ are presented. Our study indicates that $Y(4008)$ is hard to be identified with a $\psi(3^3S_1)$ charmonium once it is confirmed under the $D^*\bar{D}^*$ threshold, but it is very possibly a $\psi(3^3S_1)$ charmonium once it is confirmed above the $D^*\bar{D}^*$ threshold by experiment.
Decay constants of $P$-wave mesons
Wang, Guo-Li
High Energy Physics - Phenomenology , 2007, DOI: 10.1016/j.physletb.2007.05.001
Abstract: Decay constants of $P$-wave mesons are computed in the framework of instantaneous Bethe-Salpeter method (Salpeter method). By analyzing the parity and possible charge conjugation parity, we give the relativistic configurations of wave functions with definite parity and possible charge conjugation parity. With these wave functions as input, the full Salpeter equations for different $P$-wave states are solved, and the mass spectra as well as the numerical values of wave functions are obtained. Finally we compute the leptonic decay constants of heavy-heavy and heavy-light $^3P_0$, $^3P_1$ and $^1P_1$ states.
Measurements of the reaction $\bar{p}p \to φη$ of antiproton annihilation at rest at three hydrogen target densities  [PDF]
OBELIX Collaboration,V. Alberico,A. Bertin
Physics , 1998, DOI: 10.1016/S0370-2693(98)00633-9
Abstract: The proton-antiproton annihilation at rest into the $\phi\eta$ final state was measured for three different target densities: liquid hydrogen, gaseous hydrogen at NTP and at a low pressure of 5 mbar. The yield of this reaction in the liquid hydrogen target is smaller than in the low-pressure gas target. The branching ratios of the $\phi\eta$ channel were calculated on the basis of simultaneous analysis of the three data samples. The branching ratio for annihilation into $\phi\eta$ from the $^3S_1$ protonium state turns out to be about ten times smaller as compared to the one from the $^1P_1$ state.
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