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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Neubert, Heavy quark symmetry, Phys. Rept. 245 (1994) 259 [hep-ph/9306320] [INSPIRE].
L.N. Lipatov, Asymptotic behavior of multicolor QCD at high energies in connection with exactly solvable spin models, JETP Lett. 59 (1994) 596 [hep-th/9311037] [INSPIRE].
L.D. Faddeev and G.P. Korchemsky, High-energy QCD as a completely integrable model, Phys. Lett. B 342 (1995) 311 [hep-th/9404173] [INSPIRE].
V.M. Braun, S.E. Derkachov and A.N. Manashov, Integrability of three particle evolution equations in QCD, Phys. Rev. Lett. 81 (1998) 2020 [hep-ph/9805225] [INSPIRE].
V.M. Braun, S.E. Derkachov, G.P. Korchemsky and A.N. Manashov, Baryon distribution amplitudes in QCD, Nucl. Phys. B 553 (1999) 355 [hep-ph/9902375] [INSPIRE].
A.V. Belitsky, Renormalization of twist-three operators and integrable lattice models, Nucl. Phys. B 574 (2000) 407 [hep-ph/9907420] [INSPIRE].
L.D. Faddeev, E.K. Sklyanin and L.A. Takhtajan, The Quantum Inverse Problem Method. 1, Theor. Math. Phys. 40 (1980) 688 [INSPIRE].
L.A. Takhtajan and L.D. Faddeev, The quantum method of the inverse problem and the Heisenberg XYZ model, Russ. Math. Surveys 34 (1979) 11 [INSPIRE].
P.P. Kulish, N. Yu. Reshetikhin and E.K. Sklyanin, Yang-Baxter Equation and Representation Theory. 1., Lett. Math. Phys. 5 (1981) 393 [INSPIRE].
E.K. Sklyanin, Separation of variables: new trends, Prog. Theor. Phys. Suppl. 118 (1995) 35 [solv-int/9504001] [INSPIRE].
V.M. Braun, G.P. Korchemsky and A.N. Manashov, Evolution of twist-three parton distributions in QCD beyond the large N c limit, Phys. Lett. B 476 (2000) 455 [hep-ph/0001130] [INSPIRE].
H.J. De Vega and L.N. Lipatov, Interaction of reggeized gluons in the Baxter-Sklyanin representation, Phys. Rev. D 64 (2001) 114019 [hep-ph/0107225] [INSPIRE].
S.E. Derkachov, G.P. Korchemsky and A.N. Manashov, Noncompact Heisenberg spin magnets from high-energy QCD: 1. Baxter Q operator and separation of variables, Nucl. Phys. B 617 (2001) 375 [hep-th/0107193] [INSPIRE].
V.M. Braun, A.N. Manashov and J. Rohrwild, Renormalization of Twist-Four Operators in QCD, Nucl. Phys. B 826 (2010) 235 [arXiv:0908.1684] [INSPIRE].
J.A. Minahan and K. Zarembo, The Bethe ansatz for N = 4 superYang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
V.M. Braun, S.E. Derkachov and A.N. Manashov, Integrability of the evolution equations for heavy-light baryon distribution amplitudes, Phys. Lett. B 738 (2014) 334 [arXiv:1406.0664] [INSPIRE].
V.M. Braun, A.N. Manashov and N. Offen, Evolution equation for the higher-twist B-meson distribution amplitude, Phys. Rev. D 92 (2015) 074044 [arXiv:1507.03445] [INSPIRE].
V.M. Braun, Y. Ji and A.N. Manashov, Higher-twist B-meson Distribution Amplitudes in HQET, JHEP 05 (2017) 022 [arXiv:1703.02446] [INSPIRE].
L.N. Lipatov, Integrability of scattering amplitudes in N = 4 SUSY, J. Phys. A 42 (2009) 304020 [arXiv:0902.1444] [INSPIRE].
B. Basso, Exciting the GKP string at any coupling, Nucl. Phys. B 857 (2012) 254 [arXiv:1010.5237] [INSPIRE].
J. Bartels, L.N. Lipatov and A. Prygarin, Integrable spin chains and scattering amplitudes, J. Phys. A 44 (2011) 454013 [arXiv:1104.0816] [INSPIRE].
A.V. Belitsky, OPE for null Wilson loops and open spin chains, Phys. Lett. B 709 (2012) 280 [arXiv:1110.1063] [INSPIRE].
G.P. Korchemsky and A.V. Radyushkin, Infrared factorization, Wilson lines and the heavy quark limit, Phys. Lett. B 279 (1992) 359 [hep-ph/9203222] [INSPIRE].
B.O. Lange and M. Neubert, Renormalization group evolution of the B meson light cone distribution amplitude, Phys. Rev. Lett. 91 (2003) 102001 [hep-ph/0303082] [INSPIRE].
V.M. Braun, D. Yu. Ivanov and G.P. Korchemsky, The B meson distribution amplitude in QCD, Phys. Rev. D 69 (2004) 034014 [hep-ph/0309330] [INSPIRE].
M. Knodlseder and N. Offen, Renormalisation of heavy-light light ray operators, JHEP 10 (2011) 069 [arXiv:1105.4569] [INSPIRE].
V.M. Braun and A.N. Manashov, Conformal symmetry of the Lange-Neubert evolution equation, Phys. Lett. B 731 (2014) 316 [arXiv:1402.5822] [INSPIRE].
A.P. Bukhvostov, G.V. Frolov, L.N. Lipatov and E.A. Kuraev, Evolution Equations for Quasi-Partonic Operators, Nucl. Phys. B 258 (1985) 601 [INSPIRE].
I.M. Gelfand, M.I. Graev and N.Y. Vilenkin, Generalized functions, Vol. 5, AMS Chelsea Publishing, Providence, RI, U.S.A., (2016).
P. Ball, V.M. Braun and E. Gardi, Distribution Amplitudes of the Λ b Baryon in QCD, Phys. Lett. B 665 (2008) 197 [arXiv:0804.2424] [INSPIRE].
W. Wang, Factorization of Heavy-to-Light Baryonic Transitions in SCET, Phys. Lett. B 708 (2012) 119 [arXiv:1112.0237] [INSPIRE].
A. Ali, C. Hambrock, A. Ya. Parkhomenko and W. Wang, Light-Cone Distribution Amplitudes of the Ground State Bottom Baryons in HQET, Eur. Phys. J. C 73 (2013) 2302 [arXiv:1212.3280] [INSPIRE].
E.K. Sklyanin, Quantum inverse scattering method. Selected topics, hep-th/9211111 [INSPIRE].
S.E. Derkachov, G.P. Korchemsky and A.N. Manashov, Separation of variables for the quantum SL(2, ℝ) spin chain, JHEP 07 (2003) 047 [hep-th/0210216] [INSPIRE].
S.E. Derkachov and A.N. Manashov, Spin chains and Gustafson’s integrals, J. Phys. A 50 (2017) 294006 [arXiv:1611.09593] [INSPIRE].
S.E. Derkachov, Baxter’s Q-operator for the homogeneous XXX spin chain, J. Phys. A 32 (1999) 5299 [solv-int/9902015] [INSPIRE].
A.V. Belitsky, S.E. Derkachov and A.N. Manashov, Quantum mechanics of null polygonal Wilson loops, Nucl. Phys. B 882 (2014) 303 [arXiv:1401.7307] [INSPIRE].
S.E. Derkachov, Factorization of the R-matrix. I., math/0503396 [INSPIRE].
S.E. Derkachov, Factorization of R-matrix and Baxter’s Q-operator, J. Math. Sci. 151 (2008) 2848 [math/0507252] [INSPIRE].
E.K. Sklyanin, Boundary Conditions for Integrable Quantum Systems, J. Phys. A 21 (1988) 2375 [INSPIRE].
S.E. Derkachov, G.P. Korchemsky and A.N. Manashov, Baxter Q operator and separation of variables for the open SL(2, ℝ) spin chain, JHEP 10 (2003) 053 [hep-th/0309144] [INSPIRE].
S.E. Derkachov, G.P. Korchemsky and A.N. Manashov, Evolution equations for quark gluon distributions in multicolor QCD and open spin chains, Nucl. Phys. B 566 (2000) 203 [hep-ph/9909539] [INSPIRE].
V.M. Braun, G.P. Korchemsky and D. Mueller, The uses of conformal symmetry in QCD, Prog. Part. Nucl. Phys. 51 (2003) 311 [hep-ph/0306057] [INSPIRE].
A.V. Belitsky, A.S. Gorsky and G.P. Korchemsky, Logarithmic scaling in gauge/string correspondence, Nucl. Phys. B 748 (2006) 24 [hep-th/0601112] [INSPIRE].
M. Beccaria and F. Catino, Large spin expansion of the long-range Baxter equation in the sl(2) sector of N = 4 SYM, JHEP 01 (2008) 067 [arXiv:0710.1991] [INSPIRE].
A.V. Belitsky, Integrability and WKB solution of twist-three evolution equations, Nucl. Phys. B 558 (1999) 259 [hep-ph/9903512] [INSPIRE].
V.M. Braun, A.N. Manashov and B. Pirnay, Scale dependence of twist-three contributions to single spin asymmetries, Phys. Rev. D 80 (2009) 114002 [Erratum ibid. D 86 (2012) 119902] [arXiv:0909.3410] [INSPIRE].
Y. Ji and A.V. Belitsky, Renormalization of twist-four operators in light-cone gauge, Nucl. Phys. B 894 (2015) 161 [arXiv:1405.2828] [INSPIRE].
V.M. Braun, A.N. Manashov and J. Rohrwild, Baryon Operators of Higher Twist in QCD and Nucleon Distribution Amplitudes, Nucl. Phys. B 807 (2009) 89 [arXiv:0806.2531] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1804.06289
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Braun, V.M., Ji, Y. & Manashov, A.N. Integrability in heavy quark effective theory. J. High Energ. Phys. 2018, 17 (2018). https://doi.org/10.1007/JHEP06(2018)017
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2018)017