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Register a new userAnnihilation Rates of $^3D_2(2^{--})$ and $^3D_3(3^{--})$ Heavy Quarkonia
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We calculate the annihilation decay rates of the $^3D_2(2^{--})$ and $^3D_3(3^{--})$ charmonia and bottomonia by using the instantaneous Bethe-Salpeter method. The wave functions of states with quantum numbers $J^{PC}=2^{--}$ and $3^{--}$ are constructed. By solving the corresponding instantaneous Bethe-Salpeter equations, we obtain the mass spectra and wave functions of the quarkonia. The annihilation amplitude is written within Mandelstam formalism and the relativistic corrections are taken into account properly. This is important, especially for high excited states, since their relativistic corrections are large. The results for the $3g$ channel are as follows: $Gamma_{^3D_2(cbar c)rightarrow ggg} = 9.24$ keV, $Gamma_{^3D_3(cbar c)rightarrow ggg}=25.0$ keV, $Gamma_{^3D_2(bbar b)rightarrow ggg}= 1.87$ keV, and $Gamma_{^3D_3(bbar b)rightarrow ggg}= 0.815$ keV.
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Within the framework of nonrelativistic quark-antiquark Cornell potential model formalism, we study the annihilation of heavy quarkonia. We determine their annihilation widths resulting into $gammagamma$, $gg$, $3gamma$, $3g$ and $gamma gg$ and compare our findings with the available theoretical results and experimental data. We also provide the charge radii and absolute square of radial Schrodinger wave function at zero quark-antiquark separation.
We develop a formalism for computing inclusive production cross sections of heavy quarkonia based on the nonrelativistic QCD and the potential nonrelativistic QCD effective field theories. Our formalism applies to strongly coupled quarkonia, which include excited charmonium and bottomonium states. Analogously to heavy quarkonium decay processes, we express nonrelativistic QCD long-distance matrix elements in terms of quarkonium wavefunctions at the origin and universal gluonic correlators. Our expressions for the long-distance matrix elements are valid up to corrections of order $1/N_c^2$. These expressions enhance the predictive power of the nonrelativistic effective field theory approach to inclusive production processes by reducing the number of nonperturbative unknowns, and make possible first-principle determinations of long-distance matrix elements once the gluonic correlators are known. Based on this formalism, we compute the production cross sections of $P$-wave charmonia and bottomonia at the LHC, and find good agreement with measurements.
Correlations between the QCD coupling alpha_s, the gluon condensate < alpha_s G^2 >, and the c,b-quark running masses m_c,b in the MS-scheme are explicitly studied (for the first time) from the (axial-)vector and (pseudo)scalar charmonium and bottomium ratios of Laplace sum rules (LSR) evaluated at the mu-subtraction stability point where PT @N2LO, N3LO and < alpha_s G^2> @NLO corrections are included. Our results clarify the (apparent) discrepancies between different estimates of < alpha_s G^2> from J/psi sum rule but also shows the sensitivity of the sum rules on the choice of the mu-subtraction scale which does not permit a high-precision estimate of m_c,b. We obtain from the (axial-)vector [resp. (pseudo)scalar] channels <alpha_s G^2>=(8.5+- 3.0)> [resp. (6.34+-.39)] 10^-2 GeV^4, m_c(m_c)= 1256(30) [resp. 1266(16)] MeV and m_b(m_b)=4192(15) MeV. Combined with our recent determinations from vector channel, one obtains the average: m_c(m_c)= 1263(14) MeV and m_b(m_b) 4184(11) MeV. Adding our value of the gluon condensate with different previous estimates, we obtain the new sum rule average: <alpha_s G^2>=(6.35+- 0.35) 10^-2 GeV^4. The mass-splittings M_chi_0c(0b)-M_eta_c(b) give @N2LO: alpha_s(M_Z)=0.1183(19)(3) in good agreement with the world average (see more detailed discussions in the section: addendum). .
The ladder kernel of the Bethe-Salpeter equation is amended by introducing a different flavor dependence of the dressing functions in the heavy-quark sector. Compared with earlier work this allows for the simultaneous calculation of the mass spectrum and leptonic decay constants of light pseudoscalar mesons, the $D_u$, $D_s$, $B_u$, $B_s$ and $B_c$ mesons and the heavy quarkonia $eta_c$ and $eta_b$ within the same framework at a physical pion mass. The corresponding Bethe-Salpeter amplitudes are projected onto the light front and we reconstruct the distribution amplitudes of the mesons in the full theory. A comparison with the first inverse moment of the heavy meson distribution amplitude in heavy quark effective theory is made.
We compute the color-singlet and color-octet nonrelativistic QCD (NRQCD) long-distance matrix elements for inclusive production of $P$-wave quarkonia in the framework of potential NRQCD. In this way, the color-octet NRQCD long-distance matrix element can be determined without relying on measured cross section data, which has not been possible so far. We obtain inclusive cross sections of $chi_{cJ}$ and $chi_{bJ}$ at the LHC, which are in good agreement with data. In principle, the formalism developed in this Letter can be applied to all inclusive production processes of heavy quarkonia.
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