arXiv subjects

Stephan Narison

Publications and source records attributed to Stephan Narison.

At least 19 recordsLinked to original sources

arXiv2026

$2^{++}$ Light Tensor Hybrid Meson from QCD Laplace Sum Rules

We present an analysis of the light tensor ($J^{PC}=2^{++}$) hybrid meson mass and coupling from QCD Laplace Sum Rules where the next-to-leading order (NLO) perturbative (PT) corrections and the contributions of the non-perturbative (NP) condensates up to dimension-six ($D=6$) are included. NLO leading-logarithms corrections due to the condensates which contribute in the chiral limit are considered. We obtain the mass $M_{2^+}= (2038\pm 190)$ MeV and a relatively small coupling $f_{2^+}=(10.5\pm 2.9)$ MeV normalized as $f_\pi=93$ MeV. Our results suggest that the $f_2(1950)$ or/and the $f'_2(2010)$ may have a sizeable $\bar qqg$ hybrid component. We also compute the tensor hybrid topological charge (value of the two-point function at zero momentum) and find (for the first time) at NLO: $\Pi_{qg}(0)=(2.41\pm 0.43) \times 10^{-4}{\rm GeV}^6$ which could be checked from some lattice QCD or/and low energy theorems (LET).

hep-ph↗

arXiv2025

QCD condensates and $\alpha_s$ from $e^+e^-$ and $\tau$-decays

In this talk, I review the determinations of the QCD condensates and $\alpha_s$ within the SVZ expansion using the ratio of Laplace sum rule (LSR) and $\tau$-like moments in $e^+e^-\to I=1$ Hadrons and in $\tau\to \nu_\tau+$Hadrons Axial-vector (A) and V-A channels. Some misprints in the original papers [1-3] have been corrected. We found that the value of the gluon condensate agrees with the one $\langle \alpha_s G^2\rangle=(6.35\pm 0.35)\times 10^{-2}$ GeV$^4$ from quarkonia and some other sum rules but less accurate, while the factorization of the four-quark condensate is violated by a factor about 6: $\rho\langle\bar\psi\psi\rangle^2=(5.98\pm 0.64)\times 10^{-4}$ GeV$^6$ which confirms previous findings. Extracting the QCD condensates up to dimension D=20 from $e^+e^-$ and the axial-vector channel of $\tau$-decay, we do not find any exponential growth of their values in the Euclidian region, thus excluding (by duality) any significant effect of the so-called Duality Violation (DV) in the Time-like one. The optimal values of $\alpha_s(M_\tau)$ from $e^+e^-\to$ Hadrons and $\tau$-decays agree each others and lead to the average: $\alpha_s(M_\tau)=0.3128(51)$ [resp.0.3330(57)] $ \longrightarrow \alpha_s(M_Z) = 0.1176$ [resp. 0.1201] $(7)_{fit}(3)_{evol.}$ for Fixed Order (FO) [resp. Contour improved (CI)] PT series to be compared with the PDG24 average (without Lattice calculations): $ \alpha_s(M_Z) = 0.1175(10)$.

hep-ph↗

arXiv2025

Revisiting the Muon Anomaly from $e^+ e^-\to$ Hadrons

In this talk, I revisit and present a more comprehensive estimate of the lowest order Hadronic Vacuum Polarization (HVP) contribution $a_\mu\vert_{hvp}^{lo}$ to the muon anomalous magnetic moment (muon anomaly) from $e^+e^-\to$ Hadrons obtained recently in Ref.[1]. New CMD-3 data on $e^+e^-\to 2\pi$ [2] and precise BABAR [3] and recent BELLE2 [4] $e^+e^-\to 3\pi$ data are usedto update the estimate of the $I=0$ isoscalar channel below the $\phi$-meson mass. Adding the data compiled by PDG22 [5] above 1 GeV and the QCD improved continuum used in Ref. [1], one deduces: $a_\mu\vert^{hvp}_{lo}=(7043\pm 37)\times 10^{-11} $.A comparison with previous data driven ($e^+e^-$ and $\tau$-decays) estimates is done.Including the Higher Order $a_\mu\vert_{hvp}^{ho}$ corrections, the phenomenological estimate of the Hadronic Light by Light scattering up to NLO and the QED and Electroweak (EW) contributions, one obtains: $\Delta a_\mu^{pheno}\equiv a_\mu^{exp}-a_{\mu}^{pheno}= (81\pm 41)\times 10^{-11}$ where the recent experimental value $a_\mu^{exp}$ [6] has been used. This result consolidates the previous one in Ref.[1], after adding the $\pi^0\gamma,\eta\gamma$ contributions, and can be compared with the one from the most precise Lattice result $\Delta a_\mu^{lattice}= (90\pm 56)\times 10^{-11}$. Then, we deduce the (tentative) SM prediction average : $\Delta a_\mu^{SM} = (87\pm 33)\times 10^{-11}$. We complete the paper by revising our predictions on the LO HVP contributions in adding the $\pi^0\gamma,\eta\gamma$ contributions to the ones in Ref.[1]. Then, we obtain: $a_\tau\vert^{hvp}_{lo}=(3516\pm 25)\times 10^{-11} $ and $\Delta \alpha^{(5)}_{had}(M_Z^2)=(2770.7\pm 4.5)\times 10^{-5}$ for 5 flavours.

hep-ph↗

arXiv2024

$2^{++}$ Di-gluonium from LSR at higher order

We improve the determination of the mass and coupling of the $2^{++}$ tensor di-gluonium by using relativistic QCD Laplace sum rules (LSR). In so doing, we evaluate the next-to-leading order (NLO) corrections to the perturbative (PT) and $\langle \alpha_s G^2 \rangle$ condensate and the lowest order (LO) $\langle G^3 \rangle$ contributions to the $2^{++}$ di-gluonium two-point correlator. Within a vacuum saturation estimate ($k_G=1$) of the dimension-eight gluon condensates, we obtain: $M_{T}=3028(287)\mbox{MeV}$ and the renormalization group invariant (RGI) coupling $\hat{f}_T=224(33)\mbox{MeV}$. Assuming that the factorization hypothesis can be violated, we study the effect of the violation factor $k_G$ on the results and obtain: $M_T=3188(337)\mbox{MeV}$ and $\hat{f}_T=245(32)\mbox{MeV}$ for $k_G=(3\pm 2)$. Our estimation does not favour the interpretation of the observed $f_2(2010)$, $f_2(2300)$ and $f_2(2340)$ as pure glueball state.

hep-ph↗

arXiv2024

QCD parameters and SM-high precision from $e^+e^-$ to Hadrons: Updated

1. I update my previous comparison of the theoretical value of the muon anomaly with the new measurement and found $\Delta a_\mu\equiv a_\mu^{exp}-a_\mu^{th} = (143\pm 42_{th}\pm 22_{exp})\times 10^{-11}$ which is about 3$\sigma$ discrepancy between the SM predictions and experiment. 2. I improve the estimate of QCD power corrections up to dimension D=12 and provide a new estimate of the ones up to D=20 within the SVZ expansion by combining the ratio of the Laplace sum rules (LSR) with the BNP $\tau$-like decay moments for the I=1 vector current. The results in Table 1 confirm a violation of the factorization of the four-quark condensates and the value of the gluon one $ <\alpha_s G^2>$ from some other sources. Up to D=20, I there is not any factorial nor exponential growth of the size of these power corrections. 3. I use these new values of power corrections to extract $\alpha_s$ from the BNP lowest moment. To order $\alpha_s^4$, I find within the SVZ expansion: $\alpha_s(M_\tau)= 0.3081(50)_{fit}(71)_{\alpha_s^5}$ [resp. $0.3260 (47)_{fit}(62)_{\alpha_s^5}]$ implying $\alpha_s(M_Z)= 0.1170(6)(3)_{evol}$ [resp. $0.1192(6)(3)_{evol}$] for Fixed Order (FO) [resp. Contour Improved (CI)] PT series. They lead to the mean: $ \alpha_s(M_\tau)\vert_{SVZ}=0.3179(58)_{fit}(81)_{syst}$ and $ \alpha_s(M_Z)\vert_{SVZ}= 0.1182(12)(3)_{evol}$ where the systematic error(syst) takes into account the discrepancy between FO and CI. Using the lowest BNP moment, we also obtain from the vector (V) component of $\tau$-decay the mean: $ \alpha_s(M_\tau)\vert_{\tau,V}=0.3219(52)(91)_{syst}$ giving: $\alpha_s(M_Z)\vert_{\tau,V}=0.1187(13)(3)_{evol}$. The average of the two determinations leads to: $ \alpha_s(M_\tau)=0.3198(72)$ and $\alpha_s(M_Z)= 0.1185(9)(3)_{evol}$. 4. Some contributions beyond the SVZ expansion ($1/Q^2$, instantons and duality violation) expected to be small are discussed in Sections 10,11.

hep-ph↗

arXiv2023

QCD parameters and SM-high precisions from $e^+e^-\to$ Hadrons : Summary

In this talk, I summarize the results obtained recently in Ref.\,\cite{SNe} using the PDG 22 compilation of the $e^+e^-\to$ Hadrons $\oplus$ the recent CMD3 data for the pion form factor. Using the gluon condensate $\langle \alpha_s G^2\rangle=(6.49\pm 0.35)\times 10^{-2}$ GeV$^4$ from heavy quark sum rules, the extracted QCD four-quark and dimension eight condensate condensates values are: $\rho\alpha_s\langle\bar\psi\psi\rangle^2= (5.98\pm 0.64)\times 10^{-4}$ GeV$^6$ and $d_8= (4.3\pm 3.0)\times 10^{-2}$ GeV$^8$ from the ratio ${\cal R}_{10}$ of Laplace sum rules to order $\alpha_s^4$. Inversely using these estimated values of the condensates, we obtain from ${\cal R}_{10}$: $\langle \alpha_s G^2\rangle=(6.12\pm 0.61)\times 10^{-2}$ GeV$^4$ which leads to the average $(6.40\pm 0.30)\times 10^{-2}$ GeV$^4$. %from light and heavy quark systems. Using the lowest $\tau$-like decay moment, the mean result of Fixed Order (FO) and Contour Improved (CI) PT series within the standard OPE is : $\alpha_s(M_\tau)=0.3385(50)(136)_{syst}$ [resp. $0.3262(37)(78)_{syst}$] to order $\alpha_s^4$ [resp. $\alpha_s^5$] leading to $\alpha_s(M_Z)$=0.1207(17)(3) [resp. 0.1193(11)(3)], while the sum of the non-perturbative contribution at $M_\tau$ is\,: $\delta^V_{NP}(M_\tau)=(2.3\pm 0.2)\times 10^{-2}$. Using the same data, one also obtains the LO hadronic vacuum polarization to the muon and $\tau$ anomalous magnetic moments: $a_\mu\vert^{hvp}_{l.o}= (7036.5\pm 38.9)\times10^{-11}, \, a_\tau\vert^{hvp}_{l.o}= (3494.8\pm 24.7)\times10^{-9} $ which leads to : $\Delta a_\mu\equiv a_\mu^{exp}-a_\mu^{th} = (143\pm 42_{th}\pm 22_{exp})\times 10^{-11}$ indicating about 3$\sigma$ discrepancy between the SM predictions and experiment. One also finds: $\alpha^{(5)}(M_Z)\vert_{had}=(2766.3\pm 4.5)\times 10^{-5}$.

hep-ph↗

arXiv2023

Laplace Sum Rules in Quantum ChromoDynamics

We shortly review some applications of the (inverse) Laplace (LSR) transform sum rules in Quantum ChromoDynamics (QCD) for extracting the fundamental QCD parameters (coupling constant $\alpha_s$, quark and gluon condensates) and the hadron properties (masses and decay constants). Links of LSR to some other forms of QCD spectral sum rules are also discussed. As prototype examples, we discuss in detail the $\rho$ and $\pi$ meson sum rules.

hep-ph↗

arXiv2023

QCD parameters and SM-high precisions from e+e- to Hadrons

Using the PDG 22 compilation of the $e^+e^-\to$ Hadrons $\oplus$ the recent CMD3 data for the pion form factor and the value of gluon condensate $<\alpha_s G^2>$ from heavy quarkonia, we extract the value of the four-quark condensate : $\rho\alpha_s<\bar\psi\psi>^2= (5.98\pm 0.64)\times 10^{-4}$ GeV$^6$ and the dimension eight condensate: $d_8= (4.3\pm 3.0)\times 10^{-2}$ GeV$^8$from the ratio ${\cal R}_{10}$ of Laplace sum rules to order $\alpha_s^4$. We show the inconsistency in using at the same time the standard SVZ value of the gluon and the vacuum saturation of the four-quark condensates. Using the previous values of the four-quark and $d_8$ condensates, we re-extract $<\alpha_s G^2>$ from ${\cal R}_{10}$ to be: $(6.12\pm 0.61)\times 10^{-2}$ GeV$^4$ in perfect agreement with the one from heavy quarkonia. We also use the lowest $\tau$-like decay moment ${\cal R}_\tau^{ee}$ to extract the value of the QCD coupling $\alpha_s(M^2_\tau)$=0.3385(145)[resp. 0.3262(86)] (mean of fixed order (FO) and Contour Improved (CI) PT series) to order $\alpha_s^4$ [resp. $\alpha_s^5$] and the standard OPE. The corresponding value of the sum of the non-perturbative contribution is: $\delta_{NP}(M_\tau)=(3.74\pm 0.40)\times 10^{-2}$. Reciprocally, using $\alpha_s(M_\tau)$, $<\alpha_s G^2>$ and $d_8$ as inputs, we test the stability of the value of the four-quark condensate obtained from the lowest $\tau$-like moment. We complete our analysis by updating our previous determinations of the lowest order hadronic vacuum polarization contributions to the lepton anomalies and to $\alpha(M^2_Z)$. We obtain in Table 2 : $a_\mu\vert^{hvp}_{l.o}= (7036.5\pm 38.9)\times10^{-11}, a_\tau\vert^{hvp}_{l.o}= (3494.8\pm 24.7)\times10^{-9} $ and $\alpha(M^2_Z)=(2766.3\pm 4.5)\times 10^{-5}$. This new value of $a_\mu$ leads to: $\Delta a_\mu\equiv a_\mu^{exp}-a_\mu^{th} = (142\pm 42_{th}\pm 41_{exp})\times 10^{-11}$.

hep-ph↗

arXiv2022

QCD spectral sum rules 2022

We present a compact review of the status of QCD spectral sum rules until 2022. We emphasize the recent progresses for determining the QCD input parameters ($\alpha_s$, running quark masses, quark and gluon condensates) where their correlations have been taken into account. Some selected phenomenological uses of the sum rules in different channels (light and heavy quarks, gluonia/glueballs, hybrids and four-quark states) are briefly reviewed and commented. The estimate of the $1^{-+}$ light hybrid mass is revised which confirms the hybrid nature of the $\pi_1(1600)$ but not the $\pi_1(2050)$.

hep-ph↗

arXiv2021

Slope of the topological charge, proton spin and $0^{-+}$ pseudoscalar di-gluonia spectra

We discuss the topics mentioned in the title by scrutinizing and improving the $0^{-+}$ di-gluonia sum rules within the standard SVZ-expansion at N2LO without instantons. First, we reconsider the estimate of the slope of the topological charge $\chi'(0)=24.3(3.4)$ MeV which imply $0.144(5) [\rm data: 0.145(13)]$ for the first moment of the polarized proton structure function (proton spin) and $G_A^{(0)} = 0.337(50) [\rm data=0.330(39)]$ for the singlet form factor of the axial current. Second, we work with high degree moments and parametrize the spectral function beyond the minimal duality ansatz: "One resonance plus QCD continuum" to get the $0^{-+}$ di-gluonia spectra. Then, we obtain three groups of gluonia: The familiar light $\eta_1$ [singlet gluon component of the $\eta'(958)$] with $[M_{\eta_1},f_{\eta_1}]= [825 , 905(72)]$; The two new medium gluonia with $M_{P_{1a}}=1338(112)$ MeV and $[M_{P_{1b}}=1462(117) $ MeV or their mean $[M_{P_1},f_{P_1}]=[1397(81),594(144)]$ MeV which support the gluonium nature of the candidate $\eta(1405)$ and may bring a small gluon piece to the $\eta(1295)$; Their 1st radial excitations: $M_{P'_{1a}}=1508(226)$ MeV and $M_{P'_{1b}}=1553(139)$ MeV with their mean: $[M_{P'_1},f_{P'_1}]=[1541(118),205(282)]$ MeV which may be identified (up to some eventual mixings with $\bar qq$ states) with the $\eta(1475,1700)$ states; The heavy gluonium with : $[M_{P_2}, f_{P_2}]=[2751(140),500(43)]$ MeV comparable with the lattice results. One can remark the (natural) one to one correspondence between the pseudoscalar gluonia and their chiral scalar analogue from Ref.1: $\sigma(1)\to \eta_1;~G_1(1.55)\to P_{1}; [\sigma'(1.1),G'(1.56)]\to P'_{1a,1b};~G_2(3)\to P_2$ which is mainly due to the importance of QCD PT in the sum rule analysis that are almost equal in these two channels. Results for the spectra are in Table 2.

hep-ph↗

arXiv2021

Di-Gluonium Sum Rules, I = 0 Scalar Mesons and Conformal Anomaly

We revisit, scrutinize, improve, confirm and complete our previous results [1-3] from the scalar di-gluonium sum rules within the standard SVZ-expansion at N2LO without instantons and beyond the minimal duality ansatz : "one resonance + QCD continuum" parametrization of the spectral function which is necessary for a better understanding of the complex spectra of the $I=0$ scalar mesons. We select different (un)subtracted sum rules (USR) moments of degree $\leq$ 4 for extracting the two lowest gluonia masses and couplings. We obtain: $[M_{\sigma_B},f_{\sigma_B}]=[1.07(13),0.46(16)],~[M_{G_1},f_{G_1}][1.55(12),0.37(11)]$ GeV and the corresponding masses of the radial excitations : $M_{\sigma'_B}$= 1.11(12) and $M_{G'_1}=1.56(14)$ GeV which are (unexpectedly) almost degenerated with the ground states. The 2nd radial excitation is found to have a much heavier mass: $M_{G_2}\simeq$ 2.99(22) GeV. Combining these results with some Low-Energy Vertex Sum Rules (LEV-SR), we predict some hadronic widths and classify them into two groups : -- The $\sigma$-like ($\sigma_B,\sigma'_B$) which decay copiously to $\pi\pi$ from OZI-violating process and the $\sigma'_B$ to $2(\pi\pi)S$ through $\sigma\sigma$. -- The $G$-like $(G_1,~G'_1$ and eventually $G_2$) which decay into $\eta'\eta, ~\eta\eta$ through the $U(1)_A$ gluonic vertex. Besides some eventual mixings with quarkonia states, we may expect that the observed $\sigma/f_0(500)$ and $f_0(137)$ are $\sigma$-like while the $f_0(1.5)$ and $f_0(1.7)$ are $G$-like gluonia. The high mass $G_2(2.99)$ can also mix with the $G_1,~G'_1$ to bring the gluon component of the gluonia candidates above 2 GeV. We also estimate the conformal charge $\psi_G(0)=2.09(29)$ GeV$^4$ and its slope $10^2\psi'_G(0)=-22(29)$ GeV$^2$. Our results are summarized in Table 1.

hep-ph↗

arXiv2021

Modern status of heavy quark sum rules in QCD

We briefly report the modern status of heavy quark sum rules (HQSR) based on stability criteria by emphasizing the recent progresses for determining the QCD parameters (alpha_s, m_{c,b} and gluon condensates)where their correlations have been taken into account. The results: alpha_s(M_Z)=0.1181(16)(3), m_c(m_c)=1286(16) MeV, m_b(m_b)=4202(7) MeV, = (6.49+-0.35)10^-2 GeV^4, < g^3 G^3 >= (8.2+-1.0) GeV^2 and the ones from recent light quark sum rules are summarized in Table 2. One can notice that the SVZ value of has been underestimated by a factor 1.6, is much bigger than the instanton model estimate, while the four-quark condensate which mixes under renormalization is incompatible with the vacuum saturation which is phenomenologically violated by a factor (2~4). The uses of HQSR for molecules and tetraquarks states are commented.

hep-ph↗

arXiv2020

The First Months of COVID-19 in Madagascar

Using the official data and aware of the uncertain source and insufficient number of samples, we present a first and (for the moment) unique attempt to study the first two months spread of COVID-19 in Madagascar. The approach has been tested by predicting the number of contaminated persons for the next week after fitting the inputs data collected within 7 or 15 days using standard least $\chi^2$-fit method. Encouraged by this first test, we study systematically during 67 days , 1-2 weeks new data and predict the contaminated persons for the coming week. We find that the first month data are well described by a linear or quadratic polynomial with an increase of about (4-5) infected persons per day. Pursuing the analysis, one note that data until 46 days favour a cubic polynomial behaviour which signals an eventual near future stronger growth as confirmed by the new data on the 48th day. We complete the analysis until 67 days and find that the data until 77 days confirm the cubic polynomial behaviour which is a remarkable feature of the pandemic spread in Madagascar. We expect that these results will be useful for some new model buildings. A comparison with some other SI-like models predictions is done.These results may also be interpreted as the lowest values of the real case due to the insufficient number of samples (12907 for 27 million habitants on 05/06/20). The data analysis of the absolute number of cured persons until 67 days shows an approximate linear behaviour with about 3 cured persons per day. However, the number of percentage number of cured persons decreases above 42-46 days indicating the limits of the hospital equipment and care to face the 2nd phase of the pandemic for the 67th first days. Some comments on the social, economical and political impacts of COVID-19 and confinement for Madagascar and, in general, for Worldwide are shortly discussed.

physics.soc-ph↗

arXiv2020

Spectra and Decay Constants of $B_c$-like and $B^*_0$ Mesons in QCD

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.

hep-ph↗

arXiv2020

QCD parameters and $f_{B_c}$ from heavy quark sum rules

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=(6.35\pm 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.

hep-ph↗

arXiv2019

m_c and m_b from M_B_c and improved estimate of f_B_c and f_B_c (2S)

We extract (for the first time) the correlated values of the running masses m_c and m_b from M_Bc using QCD Laplace sum rules (LSR) within stability criteria where pertubative (PT) expressions at N2LO and non-perturbative (NP) gluon condensates at LO are included. Allowing the values of m_{c,b}(m_{c,b}) to move inside the enlarged range of recent estimates from charmonium and bottomium sum rules (Table 1) obtained using similar stability criteria, wee deduce : m_c(m_c) = 1286(16) MeV and m_b(m_b) = 4208(8) MeV. Combined with previous estimates (Table 2), we deduce a tentative QCD Spectral Sum Rules (QSSR) average m_c(m_c) = 1266(6) MeV and m_b(m_b) = 4197(8) MeV, where the errors come from the precise determinations from J/psi and Upsilon sum rules. As a result, we present an improved prediction of f_B_c =371(17)MeV and the tentative upper bound f_B_c(2S)<139(6) MeV, which are useful for a further analysis of B_c-decays.

hep-ph↗

arXiv2018

$\alpha_s(\mu)$ from $M_{\chi_{0c(0b)}}-M_{\eta_{c(b)}}$@N2LO

This note complements and clarifies the results obtained in the original paper {\it QCD Parameters Correlations from Heavy Quarkonia} [1] where, here, we present a more detailed discussion of the \alpha_s-results obtained @ N2LO at two different subtraction scales \mu=2.85 and 9.50 GeV from the (pseudo)scalar heavy quarkonia mass-spliitings M_{\chi_{0c(0b)}}-M_{\eta_{c(b)}}. We obtain from the M_{\chi_{0c}}-M_{\eta_{c}} sum rule: \alpha_s(2.85)=0.262(9) --> \alpha_s(M_\tau)=0.318(15) --> \alpha_s(M_Z)=0.1183(19)(3) and from the M_{\chi_{0b}}-M_{\eta_{b}} one: \alpha_s(9.50)=0.180(8) --> \alpha_s(M_\tau)=0.312(27) --> \alpha_s(M_Z)=0.1175(32)(3), in complete agreement with the world average: \alpha_s(M_Z)=0.1181(11).

hep-ph↗

arXiv2018

Updating m_c,b(m_c,b) from SVZ-Moments and their Ratios

Using recent values of \alpha_s, the gluon condensates <\alpha_s G^2> and and the new data on the \psi/\Upsilon-families, we update our determinations of the MS-bar running quark masses m_c,b(m_c,b) from the SVZ-Moments M_n(Q^2) and their ratios by including higher order perturbative (PT) corrections, non-perturbative (NPT) terms up to dimension d=8 and using the degree n-stability criteria of the (ratios of) moments. Optimal results from different (ratios of) moments converge to the accurate mean values: m_c(m_c)=1264(6) MeV} and m_b(m_b)=4188(8) MeV in Table 4, which improve and confirm our previous findings [1,2] and the recent ones from Laplace sum rules [3]. Comments on some other determinations of m_c(m_c) and <\alpha_s G^2> from the SVZ-(ratios of) moments in the vector channel are given in Section 5.

hep-ph↗