Abstract
We investigate the ground state energies of vector ρ ± and K ±∗ mesons depending on the magnetic field value in the SU(3) lattice gauge theory. It has been shown that the energy of a vector particle depends on its spin projection on the field axis. The magnetic dipole polarizability and hyperpolarizabilities give significant contributions to the energy value which prevents the formation of the charged vector meson condensate at high magnetic fields. We calculate the g-factor of ρ ± and K ±∗ mesons and the dipole magnetic polarizability of ρ ± mesons.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. Skokov, A. Yu. Illarionov and V. Toneev, Estimate of the magnetic field strength in heavy-ion collisions, Int. J. Mod. Phys. A 24 (2009) 5925 [arXiv:0907.1396] [INSPIRE].
G. Martinelli, G. Parisi, R. Petronzio and F. Rapuano, The Proton and Neutron Magnetic Moments in Lattice QCD, Phys. Lett. B 116 (1982) 434 [INSPIRE].
M. D’Elia, S. Mukherjee and F. Sanfilippo, QCD Phase Transition in a Strong Magnetic Background, Phys. Rev. D 82 (2010) 051501 [arXiv:1005.5365] [INSPIRE].
M. D’Elia, Lattice QCD with purely imaginary sources at zero and non-zero temperature, PoS(LATTICE2014)020 [arXiv:1502.06047] [INSPIRE].
B.B. Brandt, G. Bali, G. Endrödi and B. Glässle, QCD spectroscopy and quark mass renormalisation in external magnetic fields with Wilson fermions, PoS(LATTICE 2015)265 [arXiv:1510.03899] [INSPIRE].
E.V. Luschevskaya, O.E. Solovjeva, O.A. Kochetkov and O.V. Teryaev, Magnetic polarizabilities of light mesons in SU(3) lattice gauge theory, Nucl. Phys. B 898 (2015) 627 [arXiv:1411.4284] [INSPIRE].
E.V. Luschevskaya, O.A. Kochetkov, O.V. Teryaev and O.E. Solovjeva, π ± and ρ 0,± mesons in a strong magnetic field on the lattice, JETP Lett. 101 (2015) 674 [INSPIRE].
NPLQCD collaboration, S.R. Beane et al., Ab initio Calculation of the np → dγ Radiative Capture Process, Phys. Rev. Lett. 115 (2015) 132001 [arXiv:1505.02422] [INSPIRE].
M.A. Andreichikov, B.O. Kerbikov, V.D. Orlovsky and Yu. A. Simonov, Meson Spectrum in Strong Magnetic Fields, Phys. Rev. D 87 (2013) 094029 [arXiv:1304.2533] [INSPIRE].
H. Liu, L. Yu and M. Huang, Charged and neutral vector ρ mesons in a magnetic field, Phys. Rev. D 91 (2015) 014017 [arXiv:1408.1318] [INSPIRE].
H. Taya, Hadron Masses in Strong Magnetic Fields, Phys. Rev. D 92 (2015) 014038 [arXiv:1412.6877] [INSPIRE].
M. Kawaguchi and S. Matsuzaki, Vector meson masses from a hidden local symmetry in a constant magnetic field, Phys. Rev. D 93 (2016) 125027 [arXiv:1511.06990] [INSPIRE].
K. Hattori, T. Kojo and N. Su, Mesons in strong magnetic fields: (I) General analyses, Nucl. Phys. A 951 (2016) 1 [arXiv:1512.07361] [INSPIRE].
S. Cho, K. Hattori, S.H. Lee, K. Morita and S. Ozaki, Charmonium Spectroscopy in Strong Magnetic Fields by QCD Sum Rules: S-Wave Ground States, Phys. Rev. D 91 (2015) 045025 [arXiv:1411.7675] [INSPIRE].
P. Gubler, K. Hattori, S.H. Lee, M. Oka, S. Ozaki and K. Suzuki, D mesons in a magnetic field, Phys. Rev. D 93 (2016) 054026 [arXiv:1512.08864] [INSPIRE].
A. Klein, Low-Energy Theorems for Renormalizable Field Theories, Phys. Rev. 99 (1955) 998 [INSPIRE].
A.M. Baldin, Polarizability of nucleons, Nucl. Phys. 18 (1960) 310.
Yu. M. Antipov et al., Measurement of π − -xMeson Polarizability in Pion Compton Effect, Phys. Lett. B 121 (1983) 445 [INSPIRE].
L.V. Fil’kov and V.L. Kashevarov, Determination of pi+- meson polarizabilities from the γγ → π + π − process, Phys. Rev. C 73 (2006) 035210 [nucl-th/0512047] [INSPIRE].
COMPASS collaboration, C. Adolph et al., Measurement of the charged-pion polarizability, Phys. Rev. Lett. 114 (2015) 062002 [arXiv:1405.6377] [INSPIRE].
J. Gasser, M.A. Ivanov and M.E. Sainio, Low-energy photon-photon collisions to two loops revisited, Nucl. Phys. B 728 (2005) 31 [hep-ph/0506265] [INSPIRE].
A. Aleksejevs and S. Barkanova, Hadron Structure in Chiral Perturbation Theory, Nucl. Phys. Proc. Suppl. 245 (2013) 17 [arXiv:1309.3313] [INSPIRE].
E.V. Luschevskaya, O.E. Solovjeva and O.V. Teryaev, Magnetic polarizability of pion, Phys. Lett. B 761 (2016) 393 [arXiv:1511.09316] [INSPIRE].
W. Andersen and W. Wilcox, Lattice charge overlap. 1. Elastic limit of pi and rho mesons, Annals Phys. 255 (1997) 34 [hep-lat/9502015] [INSPIRE].
A. Samsonov, Magnetic moment of the rho meson in QCD sum rules: α s corrections, JHEP 12 (2003) 061 [hep-ph/0308065] [INSPIRE].
V.V. Braguta and A.I. Onishchenko, rho meson form-factors and QCD sum rules, Phys. Rev. D 70 (2004) 033001 [hep-ph/0403258] [INSPIRE].
J.N. Hedditch, W. Kamleh, B.G. Lasscock, D.B. Leinweber, A.G. Williams and J.M. Zanotti, Pseudoscalar and vector meson form-factors from lattice QCD, Phys. Rev. D 75 (2007) 094504 [hep-lat/0703014] [INSPIRE].
V.D. Orlovsky and Yu. A. Simonov, Nambu-Goldstone mesons in strong magnetic field, JHEP 09 (2013) 136 [arXiv:1306.2232] [INSPIRE].
D. Djukanovic, E. Epelbaum, J. Gegelia and U.G. Meissner, The magnetic moment of the ρ-meson, Phys. Lett. B 730 (2014) 115 [arXiv:1309.3991] [INSPIRE].
B. Owen, W. Kamleh, D. Leinweber, B. Menadue and S. Mahbub, Light Meson Form Factors at near Physical Masses, Phys. Rev. D 91 (2015) 074503 [arXiv:1501.02561] [INSPIRE].
H. Neuberger, Exactly massless quarks on the lattice, Phys. Lett. B 417 (1998) 141 [hep-lat/9707022] [INSPIRE].
L. Giusti, C. Hölbling, M. Lüscher and H. Wittig, Numerical techniques for lattice QCD in the ϵ-regime, Comput. Phys. Commun. 153 (2003) 31 [hep-lat/0212012] [INSPIRE].
H. Neff, N. Eicker, T. Lippert, J.W. Negele and K. Schilling, On the low fermionic eigenmode dominance in QCD on the lattice, Phys. Rev. D 64 (2001) 114509 [hep-lat/0106016] [INSPIRE].
M. Lüscher and P. Weisz, On-Shell Improved Lattice Gauge Theories, Commun. Math. Phys. 97 (1985) 59 [Erratum ibid. 98 (1985) 433] [INSPIRE].
V.G. Bornyakov, E.M. Ilgenfritz and M. Müller-Preussker, Universality check of Abelian monopoles, Phys. Rev. D 72 (2005) 054511 [hep-lat/0507021] [INSPIRE].
M.H. Al-Hashimi and U.J. Wiese, Discrete Accidental Symmetry for a Particle in a Constant Magnetic Field on a Torus, Annals Phys. 324 (2009) 343 [arXiv:0807.0630] [INSPIRE].
G. ’t Hooft, A Property of Electric and Magnetic Flux in Nonabelian Gauge Theories, Nucl. Phys. B 153 (1979) 141 [INSPIRE].
H. Zainuddin, Group theoretic quantization of a particle on a torus in a constant magnetic field, Phys. Rev. D 40 (1989) 636 [INSPIRE].
G.-H. Chen et al., Degeneracy of Landau levels and quantum qroup sl q (2), Phys. Rev. B 53 (1996) 9540.
C. Gattringer and C.B. Lang, Quantum Chromodynamics on the Lattice, Lect. Notes Phys. 788, Springer-Verlag Berlin Heidelberg (2010).
F.X. Lee, S. Moerschbacher and W. Wilcox, Magnetic moments of vector, axial and tensor mesons in lattice QCD, Phys. Rev. D 78 (2008) 094502 [arXiv:0807.4150] [INSPIRE].
D. García Gudiño and G. Toledo Sánchez, Determination of the magnetic dipole moment of the rho meson using 4 pion electroproduction data, Int. J. Mod. Phys. Conf. Ser. 35 (2014) 1460463 [arXiv:1305.6345] [INSPIRE].
T.M. Aliev, A. Özpineci and M. Savci, Magnetic and quadrupole moments of light spin-1 mesons in light cone QCD sum rules, Phys. Lett. B 678 (2009) 470 [arXiv:0902.4627] [INSPIRE].
J.P. B.C. de Melo and T. Frederico, Covariant and light front approaches to the rho meson electromagnetic form-factors, Phys. Rev. C 55 (1997) 2043 [nucl-th/9706032] [INSPIRE].
O.V. Teryaev, Gravitational form factors and nucleon spin structure, Front. Phys. (Beijing) 11 (2016) 111207 [INSPIRE].
H.R. Grigoryan and A.V. Radyushkin, Form Factors and Wave Functions of Vector Mesons in Holographic QCD, Phys. Lett. B 650 (2007) 421 [hep-ph/0703069] [INSPIRE].
V.V. Skalozub, Abrikosov’s lattice in the theory of electroweak interactions (in Russian), Yad. Fiz. 43 (1986) 1045 [INSPIRE].
M.N. Chernodub, Superconductivity of QCD vacuum in strong magnetic field, Phys. Rev. D 82 (2010) 085011 [arXiv:1008.1055] [INSPIRE].
P.V. Buividovich, M.I. Polikarpov and O.V. Teryaev, Lattice studies of magnetic phenomena in heavy-ion collisions, Lect. Notes Phys. 871 (2013) 377 [arXiv:1211.3014] [INSPIRE].
Y. Hidaka and A. Yamamoto, Charged vector mesons in a strong magnetic field, Phys. Rev. D 87 (2013) 094502 [arXiv:1209.0007] [INSPIRE].
G.S. Bali, B.B. Brandt, G. Endrödi and B. Glässle, Meson masses in electromagnetic fields with Wilson fermions, arXiv:1707.05600 [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: 1608.03472
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Luschevskaya, E., Solovjeva, O. & Teryaev, O. Determination of the properties of vector mesons in external magnetic field by quenched SU(3) lattice QCD. J. High Energ. Phys. 2017, 142 (2017). https://doi.org/10.1007/JHEP09(2017)142
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2017)142