scholarly journals QCD CORRECTIONS IN Γsl(B)

2002 ◽  
Vol 17 (35) ◽  
pp. 2317-2325 ◽  
Author(s):  
NIKOLAI URALTSEV

Short-distance expansion of the total semileptonic B widths is reviewed for the OPE-conformable scheme employing low-scale running quark masses. The third- and fourth-order BLM corrections are given and the complete resummation of the BLM series presented. The effect of higher perturbative orders with running quark masses is found to be very small. Numerical consequences for |Vcb| are addressed.

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Johan Bijnens ◽  
Nils Hermansson-Truedsson ◽  
Laetitia Laub ◽  
Antonio Rodríguez-Sánchez

Abstract The hadronic light-by-light contribution to the muon anomalous magnetic moment depends on an integration over three off-shell momenta squared ($$ {Q}_i^2 $$ Q i 2 ) of the correlator of four electromagnetic currents and the fourth leg at zero momentum. We derive the short-distance expansion of this correlator in the limit where all three $$ {Q}_i^2 $$ Q i 2 are large and in the Euclidean domain in QCD. This is done via a systematic operator product expansion (OPE) in a background field which we construct. The leading order term in the expansion is the massless quark loop. We also compute the non-perturbative part of the next-to-leading contribution, which is suppressed by quark masses, and the chiral limit part of the next-to-next-to leading contributions to the OPE. We build a renormalisation program for the OPE. The numerical role of the higher-order contributions is estimated and found to be small.


1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.


1979 ◽  
Vol 44 (12) ◽  
pp. 3501-3508 ◽  
Author(s):  
Jan Linek

Isobaric vapour-liquid equilibria in the isobutyl formate-isobutyl alcohol and n-butyl formate-isobutyl alcohol systems have been measured at atmospheric pressure. A modified circulation still of the Gillespie type has been used for the measurements. The experimental data have been correlated by means of the third- and fourth-order Margules equations.


2012 ◽  
Vol 25 (2) ◽  
pp. 161-170 ◽  
Author(s):  
Aleksandar Atanaskovic ◽  
Natasa Males-Ilic ◽  
Bratislav Milovanovic

The linearization effects on two-way Doherty amplifiers are presented in this paper. Symmetrical Doherty amplifier with the additional circuit for linearization has been realized and measurements of the linearization influence on the third- and fifth-order intermodulation products have been carried out. Asymmetrical Doherty amplifier has been designed and effects of the applied linearization technique have been considered through the simulation process. The linearization approach uses the fundamental signals? second harmonics and fourth-order nonlinear signals that are extracted at the output of the peaking cell, adjusted in amplitude and phase and injected at the input and output of the carrier cell in Doherty amplifier.


Author(s):  
Peter Mitchell

Over 50,000 years ago a Neanderthal hunter approached a wild ass on the plains of northeastern Syria. Taking aim from the right as the animal nervously assessed the threat, he launched his stone-tipped spear into its neck, penetrating the third cervical vertebra and paralyzing it immediately. Butchered at the kill site, this bone and most of the rest of the animal were taken back to the hunter’s camp at Umm el Tlel, a short distance away. Closely modelled on archaeological observations of that vertebra and the Levallois stone point still embedded within it, this incident helps define the framework for this chapter. At the start of the period it covers, human interactions with the donkey’s ancestors were purely a matter of hunting wild prey, but by its end the donkey had been transformed into a domesticated animal. Chapter 2 thus looks at how this process came about, where it did so, and what the evolutionary history of the donkey’s forebears had been until that point. Donkeys and the wild asses that are their closest relatives form part of the equid family to which zebras and horses also belong. Collectively, equids, like rhinoceroses and tapirs, fall within the Perissodactyla, the odd-toed division of hoofed mammals or ungulates. Though this might suggest a close connection with the much larger order known as the Artiodactyla, the even-toed antelopes (including deer, cattle, sheep, and goats), their superficial resemblances may actually reflect evolutionary convergence; some genetic studies hint that perissodactyls are more closely related to carnivores. Like tapirs and rhinoceroses, the earliest equids had three toes, not the one that has characterized them for the past 40 million years. That single toe, the third, now bears all their weight in the form of a single, enlarged hoof with the adjacent toes reduced to mere splints. This switch, and the associated elongation of the third (or central) metapodial linking the toe to the wrist or ankle, is one of the key evolutionary transformations through which equids have passed. A second involves diet since the earliest perissodactyls were all browsers, not grazers like the equids of today.


1972 ◽  
Vol 13 (2) ◽  
pp. 147-152 ◽  
Author(s):  
Don B. Hinton

Numerous formulae have been given which exhibit the asymptotic behaviour as t → ∞solutions ofwhere F(t) is essentially positive and Several of these results have been unified by a theorem of F. V. Atkinson [1]. It is the purpose of this paper to establish results, analogous to the theorem of Atkinson, for the third order equationand for the fourth order equation


2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
S. Z. Ahmad ◽  
F. Ismail ◽  
N. Senu ◽  
M. Suleiman

We constructed three two-step semi-implicit hybrid methods (SIHMs) for solving oscillatory second order ordinary differential equations (ODEs). The first two methods are three-stage fourth-order and three-stage fifth-order with dispersion order six and zero dissipation. The third is a four-stage fifth-order method with dispersion order eight and dissipation order five. Numerical results show that SIHMs are more accurate as compared to the existing hybrid methods, Runge-Kutta Nyström (RKN) and Runge-Kutta (RK) methods of the same order and Diagonally Implicit Runge-Kutta Nyström (DIRKN) method of the same stage. The intervals of absolute stability or periodicity of SIHM for ODE are also presented.


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