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Isgur‐Wise functions and the Lorentz group
Author(s) -
Le Yaouanc A.,
Oliver L.,
Raynal J.C.
Publication year - 2010
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.201000060
Subject(s) - lorentz transformation , scalar (mathematics) , group (periodic table) , lorentz group , lorentz space , function (biology) , sum rule in quantum mechanics , hilbert space , physics , theoretical physics , mathematics , pure mathematics , mathematical physics , particle physics , classical mechanics , quantum mechanics , geometry , evolutionary biology , biology , quantum chromodynamics
Bjorken‐like sum rules have proven to be very powerful in constraining the derivatives of the Isgur‐Wise (IW) function. We expose here, adapted to the simpler case of the baryon transition Λ b → Λ c ℓ ν (j = 0 for the light could), that the reason behind these strong constraints is the general idea that the IW function is expressed in terms of scalar products of states of the light cloud in a Hilbert space, related by Lorentz transformations. This fact leads to strong constraints on their possible shape. Both Lorentz group and the sum rule approaches are equivalent.