Ref Arxiv: 1004.5333
DOI: 10.1016/j.physletb.2010.09.007
Ref. & Cit.: NASA ADS
56 citations
Abstract:

We extract (for the first time) the ratio of the gluon condensate < g^3f_{abc}G^3 >/< alpha_s G^2 > expressed in terms of the liquid instanton radius rho_c from charmonium moments sum rules by examining the effects of < alpha_s G^2 > in the determinations of both rho_c and the running MS mass m_c(m_c). Using a global analysis of selected ratios of moments at different Q^2=0, 4m_c^2 and 8m_c^2 and taking < alpha_s G^2 > from 0.06 GeV^4, where the estimate of rho_c is almost independent of < alpha_s G^2 >, we deduce: rho_c=0.98(21) GeV^{-1} which corresponds to < g^3f_{abc}G^3 > = (31+- 13) GeV^2 < alpha_s G^2 >. The value of m_c(m_c) is less affected (within the errors) by the variation of < alpha_s G^2 >, where a common solution from different moments are reached for < alpha_s G^2 > greater than 0.02 GeV^4. Using the values of < alpha_s G^2 >=0.06(2) GeV^4 from some other channels and the previous value of < g^3f_{abc}G^3 >, we deduce: m_c(m_c)=1260(18) MeV and m_b(m_b)=4173(10) MeV, where an estimate of the 4-loops contribution has been included. Our analysis indicates that the errors in the determinations of the charm quark mass without taking into account the ones of the gluon condensates have been underestimated. To that accuracy, one can deduce the running light and heavy quark masses and their ratios evaluated at M_Z, where it is remarkable to notice the approximate equalities: m_s/m_u= m_b/m_s= m_t/m_b= 51(4), which might reveal some eventual underlying novel symmetry of the quark mass matrix in some Grand Unified Theories.

Comments: 8 pages, 2 figures, 5 tables. Due to a bug in the program, values of m_b(m_b) in Table 5 have been changed and are in excellent agreement with the ones from Q^2-moments (arXiv:1105.2922[hep-ph]) and exponential sum rules (arXiv:1105.5070[hep-ph]) within stability criteria. These changes will be published as an erratum in PLB Journal: Phys.Lett.B693:559-566,2010

Ref Arxiv: 1105.2922
Ref. & Cit.: NASA ADS
Abstract:

We reconsider the extraction of the gluon condensates , and the MS running quark masses m_{c,b} from different M_n(Q^2) Moments and their Ratios by including PT corrections to order alpha_s^3, NPT terms up to and using stability criteria of the results versus the degree n (number of Q^2-derivative). We explicitly show that the spectral part of the lowest moment M_1(0) depends strongly (as expected) on its high-energy (continuum) contribution, which is minimized for M_{n> 3-4}(0). Using higher moments and the correlations of with and < G^4>, we obtain =(7.0+- 1.3)10^{-2} GeV^4 and =(8.8+- 5.5) GeV^2 , while our analysis favours a modified factorisation for . Using the previous results, we re-determine m_c(m_c) and find that the commonly used M_1(0) lowest moment tends to overestimate its value compared to the ones from higher moments where stable values of m_c(m_c) versus the variations of n and the continuum models are reached. These features can indicate that the quoted errors of m_{c,b} from M_1(0) may have been underestimated. Optimal results from different high-n moments converge to the accurate (artithmetic) mean values: m_c(m_c)=1261(16) MeV and m_b(m_b)=4171(14) MeV, in excellent agreement with results obtained in [1] using some judicious choices of ratios of moments.

Comments: 11 pages, 9 figures, 5 tables. Improved version to appear in Phys. Lett. B including a reevaluation of the different sources of the errors

Ref Arxiv: 1105.5070
Ref. & Cit.: NASA ADS
Abstract:

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 <\alpha_s G^2> and < g^3f_{abc} G^3>. From charmonium systems and using the charm quark mass as input, we deduce:< g^3f_{abc} G^3> =(8.2+-1.0)GeV^2 <\alpha_s G^2> corresponding to < \alpha_s G^2>=(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.

Comments: 5 pages, 4 figures, 2 references added on the proofs (Phys. Lett. B in press)

Ref Arxiv: 1105.5630
Ref. & Cit.: NASA ADS
Abstract:

We have studied, using double ratio of QCD (spectral) sum rules, the ratio between the masses of $T_{cc}$ and X(3872) assuming that they are respectively described by the $D-{D}^*$ and $D-\bar{D}^*$ molecular currents. We found (within our approximation) that the masses of these two states are almost degenerate. Since the pion exchange interaction between these mesons is exactly the same, we conclude that if the observed X(3872) meson is a $D\bar{D}^*+c.c.$ molecule, then the $DD^*$ molecule should also exist with approximately the same mass. An extension of the analysis to the $b$-quark case leads to the same conclusion. We also study the SU(3) breakings for the $T^s_{QQ}/T_{QQ}$ mass ratios. Motivated by the recent Belle observation of two $Z_b$ states, we revise our determination of $X_b$ by combining results from exponential and FESR sum rules.

Comments: revised version to appear on Phys. Lett. B

Ref Arxiv: 1006.2091
Ref. & Cit.: NASA ADS
Abstract:

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.

Comments: 8 pages, 12 figures, 2 tables, improved version including radiative corrections, some additional references and a new summary table

Ref Arxiv: 1006.4802
DOI: 10.1103/PhysRevD.83.016004
Ref. & Cit.: NASA ADS
31 citations
Abstract:

We have studied some possible four-quark and molecule contents of the X(3872) using double ratios of sum rules, which are more accurate than the usual simple ratios often used in the literature for getting the hadron masses. We found that the different structures (\bar 3-3 and \bar 6-6 tetraquarks and D-D^{(*)} molecule) lead to the same prediction for the mass (within the accuracy of the method), indicating that the alone prediction of the X mass may not be sufficient to reveal its nature. In doing these analyses, we also find that (within our approximation) the use of the \bar{MS} running {\bar m}_c(m_c^2), rather than the on-shell mass, is more appropriate to obtain the J/\psi and X meson masses. Using vertex sum rules to roughly estimate the X(3872) hadronic and radiative widths, we found that the available experimental data does not exclude a \lambda-J/\psi-like molecule current.

Comments: Latex sources, 9 pages, 5 figures, 1 table. Improved version to be published in Phys. Rev. D with the inclusion of the estimate of the X radiative width. More references added Journal: Phys.Rev.D83:016004,2011

Ref Arxiv: 1007.4575
DOI: 10.1016/j.nuclphysbps.2010.10.064
Ref. & Cit.: NASA ADS
3 citations
Abstract:

Using the QCD spectral sum rule approach we investigate different currents with $J^{PC}=1^{++}$, which could be associated with the $X(3872)$ meson. Our results indicate that, with a four-quark or molecular structure, it is very difficult to explain the narrow width of the state unless the quarks have a special color configuration.

Comments: 4 pages. Contribution to the proceedings of the 15th International QCD Conference (QCD10) Journal: Nucl.Phys.Proc.Suppl.207-208:249-252,2010