“…Recent measurements (see eg. [30,28] and references therein) of the differential rate dΓ/ds where s denotes the mass of the hadronic system have led to a large number of consistency tests, strengthening the confidence in this precision measurement of α s . Moments R kl τ are defined by introducing additional weight functions (1 − s/m 2 τ ) k (s/m τ ) l which can be measured [28,30] and at the same time calculated in pQCD [31].…”
Section: Inclusive Decays and The Strong Coupling Constantmentioning
confidence: 97%
“…Their absorptive parts are available up to order α 3 s . As a consequence of the present ignorance of c 4 , the coefficient of the α 4 s term, and the large value of α s at the scale m τ differentat present equivalent -prescriptions for the evaluation lead to significantly different results for α s at m τ and correspondingly at M z [28]. Once "educated guesses" for c 4 , based on dominant terms in the perturbative series are implemented, the spread in α s decreases significantly [29].…”
Section: Inclusive Decays and The Strong Coupling Constantmentioning
confidence: 99%
“…The analysis of moments of R V τ (s) and R A τ (s) separately leads to an improved determination of the vacuum condensates [30,28], the weighted integrals of the difference…”
Section: Inclusive Decays and The Strong Coupling Constantmentioning
confidence: 99%
“…. (From[28], see also [dependence of α(5) s (M z ) calculated from α(4) s (m τ ) = 0.36 and m b = 4.7 GeV using decoupling relations at one (dotted), two (dashed), three (dot-dashed) and four (solid) loop (from [37]).…”
“…Recent measurements (see eg. [30,28] and references therein) of the differential rate dΓ/ds where s denotes the mass of the hadronic system have led to a large number of consistency tests, strengthening the confidence in this precision measurement of α s . Moments R kl τ are defined by introducing additional weight functions (1 − s/m 2 τ ) k (s/m τ ) l which can be measured [28,30] and at the same time calculated in pQCD [31].…”
Section: Inclusive Decays and The Strong Coupling Constantmentioning
confidence: 97%
“…Their absorptive parts are available up to order α 3 s . As a consequence of the present ignorance of c 4 , the coefficient of the α 4 s term, and the large value of α s at the scale m τ differentat present equivalent -prescriptions for the evaluation lead to significantly different results for α s at m τ and correspondingly at M z [28]. Once "educated guesses" for c 4 , based on dominant terms in the perturbative series are implemented, the spread in α s decreases significantly [29].…”
Section: Inclusive Decays and The Strong Coupling Constantmentioning
confidence: 99%
“…The analysis of moments of R V τ (s) and R A τ (s) separately leads to an improved determination of the vacuum condensates [30,28], the weighted integrals of the difference…”
Section: Inclusive Decays and The Strong Coupling Constantmentioning
confidence: 99%
“…. (From[28], see also [dependence of α(5) s (M z ) calculated from α(4) s (m τ ) = 0.36 and m b = 4.7 GeV using decoupling relations at one (dotted), two (dashed), three (dot-dashed) and four (solid) loop (from [37]).…”
“…The metallic tube is thus traveling on an equipotential line and not distorting the field. It is also presumed that the plastic tube is small enough and not distorting The propagation constant and therefore the dielectric constant can be derived from the second derivative of E [41]:…”
Section: Antenna Sensor For One-sided Accessmentioning
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