Open Charm and Beauty Chiral Multiplets in QCD

We study the dynamics of the the spin zero open charm and beauty mesons using QCD spectral sum rules (QSSR), where we observe the important r\^ole of the chiral condensate in the mass-splittings between the scalar-pseudoscalar mesons. Fixing the sum rule parameters for reproducing the well-known D(0-) and Ds(0-) masses, we re-obtain the running charm quark mass: mc(mc)=1.13^{+0.08}_{-0.04} GeV, which confirms our recent estimate from this channel [1]. Therefore, using sum rules, with no-free parameters, we deduce M_{Ds(0+)}= (2297+- 113) MeV, which is consistent with the observed Ds(2317) meson, while a small SU(3) breaking of about 25 MeV for the Ds(0+)-D(0+) mass-difference has been obtained. We extend our analysis to the B-system and find M{B(0+)}- M{B(0-)}= (422+- 196) MeV confirming our old result from moment sum rules [2]. Assuming an approximate (heavy and light) flavour and spin symmetries of the mass-splittings as indicated by our results, we also deduce M_{D*s(1+)}= (2440+-113) MeV in agreement with the observed D{sJ}(2457). We also get: f{D(0+)}= (217+- 25) MeV much bigger than fpi=130.6 MeV, while the size of the SU(3) breaking ratio f{Ds(0+)}/f{D(0+)}= 0.93+- 0.02 is opposite to the one of the 0- channel of about 1.14.Comment: Comments adde

B^0_{d,s} - \bar{B}^0_{d,s} mass-differences from QCD spectral sum rules

We present the first QCD spectral sum rules analysis of the SU(3) breaking parameter \xi and an improved estimate of the renormalization group invariant (RGI) bag constant \hat{B}_{B_q} both entering into the B^0_{d,s} - \bar{B}^0_{d,s} mass-differences. The averages of the results from the Laplace and moment sum rules to order \alpha_s are f_B\sqrt{\hat B_B} \simeq (247 \pm 59) MeV and \xi \equiv f_{B_s} \sqrt{\hat B_{B_s}} / f_{B} \sqrt{\hat B_{B}} \simeq (1.18\pm 0.03), in units where f_\pi=130.7 MeV. Combined with the experimental data on the mass-differences \Delta M_{d,s}, one obtains the constraint on the CKM weak mixing angle |V_{ts}/V_{td}|^2 > 20.0 (1.1). Alternatively, using the weak mixing angle from the analysis of the unitarity triangle and the data on \Delta M_d, one predicts \Delta M_s=18.6 (2.2) ps^{-1} in agreement with the present experimental lower bound and within the reach of Tevatron 2.Comment: 7 pages with 2 figures, uses espcrc2.sty. Version to appear in Phys. Lett.

Gluon Condensates and m_b(m_b) from QCD-Exponential Moments at Higher Orders

We test the convergence of the QCD exponential moments by including PT corrections to order \alpha_s^3 and the NP contributions up to D=8 condensates. Then, using the ratio of exponential sum rules where the QCD PT series is more convergent, we study the correlation between the gluon condensates and . From charmonium systems and using the charm quark mass as input, we deduce: =(8.2+-1.0)GeV^2 corresponding to =(7.5+- 2.0) 10^{-2} GeV^4. Using these results for the bottomium systems, we obtain: m_b(m_b)= 4212(32) MeV, which is slightly higher but consistent within the errrors with the ones from Q^2-moments and their ratios: m_b(m_b)= 4172(12) MeV. We are tempted to consider as a final result from the sum rules approaches, the average m_b(m_b)= 4177(11) MeV of the two previous determinations.Comment: 5 pages, 4 figures, 2 references added on the proofs (Phys. Lett. B in press

1-- and 0++ heavy four-quark and molecule states in QCD

We estimate the masses of the 1^{--} heavy four-quark and molecule states by combining exponential Laplace (LSR) and finite energy (FESR) sum rules known perturbatively to lowest order (LO) in alpha_s but including non-perturbative terms up to the complete dimension-six condensate contributions. This approach allows to fix more precisely the value of the QCD continuum threshold (often taken ad hoc) at which the optimal result is extracted. We use double ratio of sum rules (DRSR) for determining the SU(3) breakings terms. We also study the effects of the heavy quark mass definitions on these LO results. The SU(3) mass-splittings of about (50 - 110) MeV and the ones of about (250 - 300) MeV between the lowest ground states and their 1st radial excitations are (almost) heavy-flavour independent. The mass predictions summarized in Table 4 are compared with the ones in the literature (when available) and with the three Y_c(4260,~4360,~4660) and Y_b(10890) 1^{--} experimental candidates. We conclude (to this order approximation) that the lowest observed state cannot be a pure 1^{--} four-quark nor a pure molecule but may result from their mixings. We extend the above analyzes to the 0^{++} four-quark and molecule states which are about (0.5-1) GeV heavier than the corresponding 1^{--} states, while the splittings between the 0^{++} lowest ground state and the 1st radial excitation is about (300-500) MeV. We complete the analysis by estimating the decay constants of the 1^{--} and 0^{++} four-quark states which are tiny and which exhibit a 1/M_Q behaviour. Our predictions can be further tested using some alternative non-perturbative approaches or/and at LHCb and some other hadron factories.Comment: 13 pages, 15 figures, 4 tables, version to appear in PLB (more general choice of the interpolating currents, estimate of the four-quark meson decay constants, new references added, slight numerical changes for the 0++ mass predictions

Mass-splittings of doubly heavy baryons in QCD

We consider (for the first time) the ratios of doubly heavy baryon masses (spin 3/2 over spin 1/2 and SU(3) mass-splittings) using double ratios of sum rules (DRSR), which are more accurate than the usual simple ratios often used in the literature for getting the hadron masses. In general, our results agree and compete in precision with potential model predictions. In our approach, the alpha_s corrections induced by the anomalous dimensions of the correlators are the main sources of the Xi^*_{QQ}- Xi_{QQ} mass-splittings, which seem to indicate a 1/M_Q behaviour and can only allow the electromagnetic decay Xi^*_{QQ} to Xi_{QQ}+ gamma but not to Xi_{QQ}+ pi. Our results also show that the SU(3) mass-splittings are (almost) independent of the spin of the baryons and behave approximately like 1/M_Q, which could be understood from the QCD expressions of the corresponding two-point correlator. Our results can improved by including radiative corrections to the SU(3) breaking terms and can be tested, in the near future, at Tevatron and LHCb.Comment: 8 pages, 12 figures, 2 tables, improved version including radiative corrections, some additional references and a new summary tabl

B∗Bπ(γ)B^*B\pi(\gamma) couplings and D^*\rar D\pi(\gamma) -decays within a 1/M1/M-expansion in fullfull QCD

To leading order in $\alpha_s$, we evaluate the leading and non-leading $1/M_b$ corrections to the $B^*B\pi$ and $B^*B\gamma$ couplings using QCD spectral moment sum rules in the full theory. We find that, for large $M_b$ and contrary to the heavy-to-light B\rar \pi(\rho) l\bar \nu form factors, which are dominated by the $soft$ light quark vacuum condensate, these couplings are governed by the $hard$ perturbative graph, like other heavy-to-heavy transitions. We also find that for the B^{*}\rar B\gamma, the $1/M_b$ correction is mainly due to the perturbative and light quark condensate contributions originating from the graphs involving the heavy quark part of the electromagnetic current, which are essential for explaining the large charge dependence in the observed D^{*-}\rar D^-\gamma and D^{*0}\rar D^0\gamma decays. Our $best$ numerical predictions {\it without any free parameters} for the $B^*$-meson are: $g_{B^{*-}B^0\pi^-}\simeq 14\pm 4$, \Gamma_{B^{*-}\rar B^-\gamma}\simeq (0.10\pm 0.03) keV and the large charge dependence of the ratio: {\Gamma_{B^{*-}\rar B^- \gamma}}/ {\Gamma_{B^{*0}\rar B^0 \gamma}}\simeq 2.5~. For the $D^*$-meson, we find: \Gamma_{D^{*-}\rar D^0\pi^-}\simeq 1.54\Gamma_{D^{*0}\rar D^0\pi^0} \simeq (8\pm 5) keV, \Gamma_{D^{*-}\rar D^-\gamma}\simeq (0.09^{+0.40}_{-0.07} ) keV and \Gamma_{D^{*0}\rar D^0\gamma}\simeq (3.7\pm 1.2) keV, where the branching ratios agree within the errors with the present data, while the total widths \Gamma_{D^{*0}\rar all} \simeq (11\pm 4) keV and \Gamma_{D^{*-}\rar all}\simeq (12\pm 7) keV are much smaller than the present experimental upper limits.Comment: published version to appear in Phys. Lett. B (minor modifications compared with the previous version

A fresh look into m_{c,b} and precise f_{D_(s),B_(s)} from heavy-light QCD spectral sum rules

Using recent values of the QCD (non-) perturbative parameters given in Table 1 and an estimate of the N3LO QCD perturbative contributions based on the geometric growth of the PT series, we re-use QCD spectral sum rules (QSSR) known to N2LO PT series and including all dimension-six NP condensate contributions in the full QCD theory, for improving the existing estimates of {m}_{c,b} and f_{D_(s)}, f_{B_(s)} from the open charm and beauty systems. We especially study the effects of the subtraction point on "different QSSR data" and use (for the first time) the Renormalization Group Invariant (RGI) scale independent quark masses in the analysis. The estimates [rigourous model-independent upper bounds within the SVZ framework] reported in Table 8: f_D/f_\pi=1.56(5)[< 1.68(1)], f_B/f_\pi=1.58(5)[< 1.80(3)] and f_{D_s}/f_K= 1.58(4) [< 1.63(1)], f_{B_s}/f_K=1.50(3)[< 1.61(3.5)], which improve previous QSSR estimates, are in perfect agreement (in values and precisions) with some of the experimental data on f_{D,D_s} and on recent lattice simulations within dynamical quarks. These remarkable agreements confirm both the success of the QSSR semi-approximate approach based on the OPE in terms of the quark and gluon condensates and of the Minimal Duality Ansatz (MDA) for parametrizing the hadronic spectral function which we have tested from the complete data of the J/\psi and \Upsilon systems. The values of the running quark masses m_c(m_c)=1286(66) MeV and m_b(m_b)= 4236(69) MeV from M_{D,B} are in good agreement though less accurate than the ones from recent J/\psi and \Upsilon sum rules.Comment: 14 pages, 20 figures, 8 tables: partly presented at the 16th QCD international conference (QCD 12), Montpellier, 2-6th july 2012; version which matches with the one to appear in PL

How reliable are the HQET-sum rule predictions?

We test the internal consistencies and the reliability of the existing estimates of the decay constant $f_B$ in the static limit, the meson-quark mass gap $\bar \Lambda$ and the kinetic energy $K$ of a heavy quark obtained from the heavy quark effective theory (HQET)-sum rules. Finite energy local duality sum rules (FESR) have also been used to fix $approximatively$ the value of the continuum energy and to study the correlations among these different parameters. Then, we deduce to two-loop accuracy: \bl=(0.65\pm 0.05) GeV, $K=-(0.5 \pm 0.2)$GeV^2$, implying the value of the pole mass in HQET:$M_b= (4.61 \pm 0.05)$GeV. By combining the results from the sum rules in HQET and in the full theory, we obtain$f_B^\infty=(1.98 \pm 0.31)f_\pi$and the quadratic mass dependence of the pseudoscalar decay constant:$f_P\sqrt{M_P}=(0.33 \pm 0.06)$GeV$^{3/2}\als^{1/\beta_1}2}\als^{1/\beta_1 1-2\als/3\pi-1.1/M_Q +0.7/M_Q^2 .$Comment: PS file, figures available by reques

Tests of the nature and of the gluon content of the \sigma(0.6) from D and D_{s} semileptonic decays

We summarize the different features which show that QCD spectral sum rule analyses of the scalar two- and three-point functions do not favour the $\bar uu+\bar dd$ interpretation of the broad and low mass $\sigma (0.6)$ and emphasize that a measurement of the $D_s$ semileptonic decays into $\pi\pi$ can reveal in a model-independent way its eventual gluon component $\sigma_B$. The analysis also implies that one expects an observation of the $K\bar K$ final states from the $\sigma_B$ which may compete (if phase space allowed) with the one from a low mass $\bar ss$ state assumed in the literature to be the SU(3) partner of the observed $\sigma (0.6)$ if the latter is a $\bar uu+\bar dd$ stateComment: 6 pages latex file. 4 fig.ep

Strange quark mass from e+e- revisited and present status of light quark masses

We reconsider the determinations of the strange quark mass m_s from e+e- into hadrons data using a new combination of FESR and revisiting the existing tau-like sum rules by including non-resonant contributions to the spectral functions. To order alpha_s^3 and including the tachyonic gluon mass lambda^2 contribution, which phenomenologically parametrizes the UV renormalon effect into the PT series, we obtain the invariant mass m_s=(119 +- 17)MeV leading to: m_s(2 GeV)=(104+- 15)MeV. Combining this value with the recent and independent phenomenological determinations from some other channels, to order alpha_s^3 and including lambda^2, we deduce the weighted average: m_s (2 GeV)=(96.1 +- 4.8)MeV . The positivity of the spectral functions in the (pseudo)scalar [resp. vector] channels leads to the lower [resp. upper] bounds of m_s(2 GeV): (71 +- 4) MeV < m_s(2 GeV) < (151 +- 14) MeV, to order alpha_s^3. Using the ChPT mass ratio r_3 = 2m_s/(m_u+m_d)=24.2 +- 1.5, and the average value of m_s, we deduce: (m_u+m_d)(2 GeV)=(7.9 +- 0.6) MeV, consistent with the pion sum rule result, which, combined with the ChPT value for m_u/m_d, gives: m_d(2 GeV)=(5.1 +- 0.4)MeV and m_u(2 GeV)=(2.8 +- 0.2)MeV. Finally, using (m_u+m_d) from the pion sum rule and the average value of m_s (without the pion sum rule), the method gives: r_3= 23.5 +- 5.8 in perfect agreement with the ChPT ratio, indicating the self-consistency of the sum rule results. Using the value: m_b(m_b)=(4.23 +- 0.06) GeV, we also obtain the model-building useful scale-independent mass ratio: m_b/m_s=50 +- 3.Comment: Updated and improved average values. Version to appear in Phys. Rev.