“…[34], but, to our knowledge, has never been discussed for three-particle distributions. Mathematically, the first task consists of defining anomalous dimensions as analytic functions of N such that their values at positive integer N are given by the eigenvalues of the evolution kernel H 3/2 and the asymptotics at infinity is such that γ N ∼ exp(−δ|N|) with δ < π [35]. The anomalous dimensions of the different components of the distribution amplitude do not necessary coincide and it is known from the studies of the deep inelastic scattering that one may need to consider analytic continuation from odd and even N separately, which in general correspond to contributions of operators with different parity.…”
Section: Analytical Continuation and The Parton Modelmentioning
We develop a new theoretical framework for the description of leading twist light-cone baryon distribution amplitudes which is based on integrability of the helicity λ = 3/2 evolution equation to leading logarithmic accuracy. A physical interpretation is that one can identify a new 'hidden' quantum number which distinguishes components in the λ = 3/2 distribution amplitudes with different scale dependence. The solution of the corresponding evolution equation is reduced to a simple three-term recurrence relation. The exact analytic solution is found for the component with the lowest anomalous dimension for all moments N, and the WKB-type expansion is constructed for other levels, which becomes asymptotically exact at large N. Evolution equations for the λ = 1/2 distribution amplitudes (e.g. for the nucleon) are studied as well. We find that the two lowest anomalous dimensions for the λ = 1/2 operators (one for each parity) are separated from the rest of the spectrum by a finite 'mass gap'. These special states can be interpreted as scalar diquarks.
“…[34], but, to our knowledge, has never been discussed for three-particle distributions. Mathematically, the first task consists of defining anomalous dimensions as analytic functions of N such that their values at positive integer N are given by the eigenvalues of the evolution kernel H 3/2 and the asymptotics at infinity is such that γ N ∼ exp(−δ|N|) with δ < π [35]. The anomalous dimensions of the different components of the distribution amplitude do not necessary coincide and it is known from the studies of the deep inelastic scattering that one may need to consider analytic continuation from odd and even N separately, which in general correspond to contributions of operators with different parity.…”
Section: Analytical Continuation and The Parton Modelmentioning
We develop a new theoretical framework for the description of leading twist light-cone baryon distribution amplitudes which is based on integrability of the helicity λ = 3/2 evolution equation to leading logarithmic accuracy. A physical interpretation is that one can identify a new 'hidden' quantum number which distinguishes components in the λ = 3/2 distribution amplitudes with different scale dependence. The solution of the corresponding evolution equation is reduced to a simple three-term recurrence relation. The exact analytic solution is found for the component with the lowest anomalous dimension for all moments N, and the WKB-type expansion is constructed for other levels, which becomes asymptotically exact at large N. Evolution equations for the λ = 1/2 distribution amplitudes (e.g. for the nucleon) are studied as well. We find that the two lowest anomalous dimensions for the λ = 1/2 operators (one for each parity) are separated from the rest of the spectrum by a finite 'mass gap'. These special states can be interpreted as scalar diquarks.
“…The 25-fold genetic variation in "isocoumarin" levels also suggests a potential for genetic improvement of bitterness (5,6). Dominance for mild flavor over harsh flavor in an F-hybrid grown in nine environments (21) and in a range of F-hybrids grown in two different environments (Table II) suggest excellent prospects for improving the flavor of hybrid carrots by including at least one mild flavored parent in the hybrid.…”
Section: Current Status and Future Prospects For Improvement Of Carromentioning
“…Based on the kinetic theory of gases, (15,26,39,40) the relationship between the forces Fj and F2 and the pressure p is given by the equations -AiP and F7 . A2E (12) when the orifices are infinitesimal in length and when the gas effuses into a vacuum.…”
Section: Figure 7 a Horizontal Full Section Of An Effusion Cellmentioning
confidence: 99%
“…The quantities AS-g and AHg can then be calculated from equations similar to Equations (33) and (34). In like manner, AFg^ and A^^^ may be calculated from equations similar to Equations (38) and (40).…”
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