And From And Improved Estimates of And

Stephan Narison (Laboratoire Particules et Univers de Montpellier, CNRS-IN2P3, Case 070, Place Eugène Bataillon, 34095, Montpellier, France)

We extract (for the first time) the correlated values of the running masses mc and mb from MBc using QCD Laplace sum rules (LSR) within stability criteria where perturbative (PT) expressions at N2LO and non-perturbative (NP) gluon condensates at LO are included. Allowing the values of mc,b(mc,b) to move inside the enlarged range of recent estimates from charmonium and bottomium sum rules (Table 1) obtained using similar stability criteria, we deduce: mc(mc)=1286(16) MeV and mb(mb)=4202(8) MeV. Combined with previous estimates (Table 2), we deduce a tentative QCD Spectral Sum Rules (QSSR) average: mc(mc)=1266(6) MeV and mb(mb)=4197(8) MeV where the errors come from the precise determinations from J/ψ and ϒ sum rules. As a result, we present an improved prediction of fBc=371(17) MeV and the tentative upper bound fBc(2S)139(6) MeV, which are useful for a further analysis of Bc-decays.

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      "value": "We extract (for the first time) the correlated values of the running masses <math><msub><mrow><mover><mrow><mi>m</mi></mrow><mo>\u203e</mo></mover></mrow><mrow><mi>c</mi></mrow></msub></math> and <math><msub><mrow><mover><mrow><mi>m</mi></mrow><mo>\u203e</mo></mover></mrow><mrow><mi>b</mi></mrow></msub></math> from <math><msub><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></msub></math> using QCD Laplace sum rules (LSR) within stability criteria where perturbative (PT) expressions at N2LO and non-perturbative (NP) gluon condensates at LO are included. Allowing the values of <math><msub><mrow><mover><mrow><mi>m</mi></mrow><mo>\u203e</mo></mover></mrow><mrow><mi>c</mi><mo>,</mo><mi>b</mi></mrow></msub><mo>(</mo><msub><mrow><mover><mrow><mi>m</mi></mrow><mo>\u203e</mo></mover></mrow><mrow><mi>c</mi><mo>,</mo><mi>b</mi></mrow></msub><mo>)</mo></math> to move inside the enlarged range of recent estimates from charmonium and bottomium sum rules (Table 1) obtained using similar stability criteria, we deduce: <math><msub><mrow><mover><mrow><mi>m</mi></mrow><mo>\u203e</mo></mover></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><msub><mrow><mover><mrow><mi>m</mi></mrow><mo>\u203e</mo></mover></mrow><mrow><mi>c</mi></mrow></msub><mo>)</mo><mo>=</mo><mn>1286</mn><mo>(</mo><mn>16</mn><mo>)</mo></math> MeV and <math><msub><mrow><mover><mrow><mi>m</mi></mrow><mo>\u203e</mo></mover></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><msub><mrow><mover><mrow><mi>m</mi></mrow><mo>\u203e</mo></mover></mrow><mrow><mi>b</mi></mrow></msub><mo>)</mo><mo>=</mo><mn>4202</mn><mo>(</mo><mn>8</mn><mo>)</mo></math> MeV. Combined with previous estimates (Table 2), we deduce a tentative QCD Spectral Sum Rules (QSSR) average: <math><msub><mrow><mover><mrow><mi>m</mi></mrow><mo>\u203e</mo></mover></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><msub><mrow><mover><mrow><mi>m</mi></mrow><mo>\u203e</mo></mover></mrow><mrow><mi>c</mi></mrow></msub><mo>)</mo><mo>=</mo><mn>1266</mn><mo>(</mo><mn>6</mn><mo>)</mo></math> MeV and <math><msub><mrow><mover><mrow><mi>m</mi></mrow><mo>\u203e</mo></mover></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><msub><mrow><mover><mrow><mi>m</mi></mrow><mo>\u203e</mo></mover></mrow><mrow><mi>b</mi></mrow></msub><mo>)</mo><mo>=</mo><mn>4197</mn><mo>(</mo><mn>8</mn><mo>)</mo></math> MeV where the errors come from the precise determinations from <math><mi>J</mi><mo>/</mo><mi>\u03c8</mi></math> and \u03d2 sum rules. As a result, we present an improved prediction of <math><msub><mrow><mi>f</mi></mrow><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></msub><mo>=</mo><mn>371</mn><mo>(</mo><mn>17</mn><mo>)</mo></math> MeV and the tentative upper bound <math><msub><mrow><mi>f</mi></mrow><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></mrow></msub><mo>\u2264</mo><mn>139</mn><mo>(</mo><mn>6</mn><mo>)</mo></math> MeV, which are useful for a further analysis of <math><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></math>-decays."
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Published on:
15 January 2020
Publisher:
Elsevier
Published in:
Physics Letters B , Volume 802 C (2020)

Article ID: 135221
DOI:
https://doi.org/10.1016/j.physletb.2020.135221
Copyrights:
The Author
Licence:
CC-BY-3.0

Fulltext files: