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Register a new userSpectra and Decay Constants of $B_c$-like and $B^*_0$ Mesons in QCD
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Stephan Narison
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Using the existing state of art of the QCD expressions of the two-point correlators into the Inverse Laplace sum rules (LSR) within stability criteria, we present a first analysis of the spectra and decay constants of B_c-like scalar (0^{++}) and axial-vector (1^{++}) mesons and revisit the ones of the B^*_c(1^{--}) vector meson. Improved predictions are obtained by combining these LSR results with the some mass-splittings from Heavy Quark Symmetry (HQS). We complete the analysis by revisiting the B^*_{0}(0^{++}) mass which might be likely identified with the B^*_J(5732) experimental candidate. The results for the spectra collected in Table 2 are compared with some recent lattice and potential models ones. New estimates of the decay constants are given in Table 3.
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We summarize recently improved results for the pseudoscalar [1,2] and vector [3] meson decay constants and their ratios from QCD spectral sum rules where N2LO + estimate of the N3LO PT and power corrections up to d< 6 dimensions have been included in the SVZ expansion. The optimal results based on stability criteria with respect to the variations of the Laplace/Moments sum rule variables, QCD continuum threshold and subtraction constant mu are compared with recent sum rules and lattice calculations. To understand the apparent tension between some recent results for f_B*/f_B, we present in Section 8 a novel extraction of this ratio from heavy quark effective theory (HQET) sum rules by including the normalization factor (M_b/M_B)^2 relating the pseudoscalar to the universal HQET correlators for finite b-quark and B-meson masses. We obtain f_B*/f_B=1.025(16) in good agreement with the one 1.016(16) from (pseudo)scalar sum rules in full QCD [3]. We complete the paper by including new improved estimates of the scalar, axial-vector and B^*_c meson decays constants (Sections 11-13). For further phenomenological uses, we attempt to extract a Global Average of different sum rules and lattice determinations of the decay constants which are summarized in Tables 2-6. We do not found any deviation of these SM results from the present data.
Finite energy QCD sum rules with Legendre polynomial integration kernels are used to determine the heavy meson decay constant $f_{B_c}$, and revisit $f_B$ and $f_{B_s}$. Results exhibit excellent stability in a wide range of values of the integration radius in the complex squared energy plane, and of the order of the Legendre polynomial. Results are $f_{B_c} = 528 pm 19$ MeV, $f_B = 186 pm 14$ MeV, and $f_{B_s} = 222 pm 12$ MeV.
We determine the masses and decay constants of pseudoscalar mesons $ D $, $ D_s $, and $ K $ in quenched lattice QCD with exact chiral symmetry. For 100 gauge configurations generated with single-plaquette action at $ beta = 6.1 $ on the $ 20^3 times 40 $ lattice, we compute point-to-point quark propagators for 30 quark masses in the range $ 0.03 le m_q a le 0.80 $, and measure the time-correlation functions of pseudoscalar and vector mesons. The inverse lattice spacing $ a^{-1} $ is determined with the experimental input of $ f_pi $, while the strange quark bare mass $ m_s a = 0.08 $, and the charm quark bare mass $ m_c a = 0.80 $ are fixed such that the masses of the corresponding vector mesons are in good agreement with $ phi(1020) $ and $ J/psi(3097) $ respectively. Our results of pseudoscalar-meson decay constants are $ f_K = 152(6)(10) $ MeV, $ f_D = 235(8)(14)$ MeV, and $ f_{D_s} = 266(10)(18) $ MeV.
We report results of our recent works [1,2] where we where the correlations between the c,b-quark running masses{m}_{c,b}, the gluon condensate<alpha_s G^2> and the QCD coupling alpha_s in the MS-scheme from an analysis of the charmonium and bottomium spectra and the B_c-meson mass. We use optimized ratios of relativistic Laplace sum rules (LSR) evaluated at the mu-subtraction stability point where higher orders PT and D< 6-8-dimensions non-perturbative condensates corrections are included. We obtain [1] alpha_s(2.85)=0.262(9) and alpha_s(9.50)=0.180(8) from the (pseudo)scalar M_{chi_{0c(0b)}}-M_{eta_{c(b)}} mass-splittings at mu=2.85(9.50) GeV. The most precise result from the charm channel leads to alpha_s(M_tau)=0.318(15) and alpha_s(M_Z)=0.1183(19)(3) in excellent agreement with the world average: alpha_s(M_Z)=0.1181(11)[3,4]. Updated results from a global fit of the (axial-)vector and (pseudo)scalar channels using Laplace and Moments sum rules @ N2LO [1] combined with the one from M_{B_c} [2] lead to the new tentative QCD spectral sum rules (QSSR) average : m_c(m_c)|_average= 1266(6) MeV and m_b(m_b)|_average=4196(8) MeV. The values of the gluon condensate <alpha_s G^2> from the (axial)-vector charmonium channels combined with previous determinations in Table 1, leads to the new QSSR average [1]: <alpha_s G^2>_average=(6.35pm 0.35)x 10^{-2} GeV^4. 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. As a biproduct, we deduce the B_c-decay constants f_{B_c}=371(17) MeV and f_{B_c}(2S)< 139(6) MeV.
We present a global analysis of the observed Z_c, Z_cs and future Z_css-like spectra using the inverse Laplace transform (LSR) version of QCD spectral sum rules (QSSR) within stability criteria. Integrated compact QCD expressions of the LO spectral functions up to dimension-six condensates are given. Next-to-Leading Order (NLO) factorized perturbative contributions are included. We re-emphasize the importance to include PT radiative corrections (though numerically small) for heavy quark sum rules in order to justify the (ad hoc) definition and value of the heavy quark mass used frequently at LO in the literature. We also demonstrate that, contrary to a naive qualitative 1/N_c counting, the two-meson scattering contributions to the four-quark spectral functions are numerically negligible confirming the reliability of the LSR predictions. Our results are summarized in Tables III to VI. The Z_c(3900) and Z_cs(3983) spectra are well reproduced by the T_c(3900) and T_cs(3973) tetramoles (superposition of quasi-degenerated molecules and tetraquark states having the same quantum numbers and with almost equal couplings to the currents). The Z_c(4025) or Z_c(4040) state can be fitted with the D*_0D_1 molecule having a mass 4023(130) MeV while the Z_cs bump around 4.1 GeV can be likely due to the (D^*_s0D_1+ D^*_0D_s1) molecules. The Z_c(4430) can be a radial excitation of the Z_c(3900) weakly coupled to the current, while all strongly coupled ones are in the region (5634-6527) MeV. The double strange tetramole state T_css which one may identify with the future Z_css is predicted to be at 4064(46) MeV. It is remarkable to notice the regular mass-spliitings of the tetramoles due to SU(3) breakings M_{T_cs}-M_{T_c}= M_{T_css}-M_{T_cs= (73- 91) MeV.
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