Abstract
It was found that renormalization group equations in the heavy-quark effective theory (HQET) for the operators involving one effective heavy quark and light degrees of freedom are completely integrable in some cases and are related to spin chain models with the Hamiltonian commuting with the nondiagonal entry C(u) of the monodromy matrix. In this work we provide a more complete mathematical treatment of such spin chains in the QISM framework. We also discuss the relation of integrable models that appear in the HQET context with the large-spin limit of integrable models in QCD with light quarks. We find that the conserved charges and the “ground state” wave functions in HQET models can be obtained from the light-quark counterparts in a certain scaling limit.
Highlights
Their solutions in great detail, see e.g. [5, 11,12,13,14] for several concrete applications
It was found that renormalization group equations in the heavy-quark effective theory (HQET) for the operators involving one effective heavy quark and light degrees of freedom are completely integrable in some cases and are related to spin chain models with the Hamiltonian commuting with the nondiagonal entry C(u) of the monodromy matrix
It is natural to expect that an EFT describing a certain sector of the underlying theory retains some of the symmetries. It was found [17,18,19] that RGEs in HQET for the operators involving one effective heavy quark and light degrees of freedom are integrable under similar conditions as in QCD with light quarks and are related to unconventional integrable models with the Hamiltonian commuting with the nondiagonal entry C(u) of the monodromy matrix
Summary
For our discussion the two-component spinor formalism is the most convenient. We write the Dirac spinor as q=. The effective heavy quark field of HQET hv can be represented by a Wilson line in a timelike direction v = (1/2)(n + n), v2 = 1 with an attached free Dirac spinor so that [24]: 0|hv(0)|h, v = [0, −v∞] = Pexp ig dα vμAμ(αv). In what follows we imply using dimensional regularization with minimal subtraction (MS-scheme) It was noticed [28] that this operator can be written in a simpler form in terms of the generator of special conformal transformations. The “Hamiltonians” appearing in the RGEs for such operators to one loop accuracy have a pairwise structure, e.g. where the “heavy-light” two-particle evolution kernels have the form similar to (2.11) with the generators in the appropriate representation, and the “light-light” ones can be written in terms of the corresponding quadratic Casimir operators [29]. In this work we construct and discuss the corresponding spin chain models which differ somewhat from the standard ones and may be interesting in other applications
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