Abstract
We present the result of our computation of the lowest lying meson masses for SU(N) gauge theory in the large N limit (with Nf /N → 0). The final values are given in units of the square root of the string tension, and with errors which account for both statistical and systematic errors. By using 4 different values of the lattice spacing we have seen that our results scale properly. We have studied various values of N (169, 289 and 361) to monitor the N-dependence of the most sensitive quantities. Our methodology is based upon a first principles approach (lattice gauge theory) combined with large N volume independence. We employed both Wilson fermions and twisted mass fermions with maximal twist. In addition to masses in the pseudoscalar, vector, scalar and axial vector channels, we also give results on the pseudoscalar decay constant and various remormalization factors.
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References
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
K. G. Wilson, Confinement of Quarks, Phys. Rev. D 10 (1974) 2445 [INSPIRE].
B. Lucini and M. Teper, SU(N) gauge theories in four-dimensions: Exploring the approach to N = infinity, JHEP 06 (2001) 050 [hep-lat/0103027] [INSPIRE].
B. Lucini, M. Teper and U. Wenger, The deconfinement transition in SU(N) gauge theories, Phys. Lett. B 545 (2002) 197 [hep-lat/0206029] [INSPIRE].
B. Lucini and M. Panero, SU(N) gauge theories at large N, Phys. Rept. 526 (2013) 93 [ar**v:1210.4997] [INSPIRE].
R. Kaiser and H. Leutwyler, Large Nc in chiral perturbation theory, Eur. Phys. J. C 17 (2000) 623 [hep-ph/0007101] [INSPIRE].
R. Kaiser and H. Leutwyler, Pseudoscalar decay constants at large Nc, in Workshop on Methods of Nonperturbative Quantum Field Theory, (1998) [hep-ph/9806336] [INSPIRE].
T. Eguchi and H. Kawai, Reduction of Dynamical Degrees of Freedom in the Large N Gauge Theory, Phys. Rev. Lett. 48 (1982) 1063 [INSPIRE].
G. Bhanot, U. M. Heller and H. Neuberger, The Quenched Eguchi-Kawai Model, Phys. Lett. B 113 (1982) 47 [INSPIRE].
R. Narayanan and H. Neuberger, Large N reduction in continuum, Phys. Rev. Lett. 91 (2003) 081601 [hep-lat/0303023] [INSPIRE].
P. Kovtun, M. Ünsal and L. G. Yaffe, Volume independence in large Nc QCD-like gauge theories, JHEP 06 (2007) 019 [hep-th/0702021] [INSPIRE].
M. Ünsal and L. G. Yaffe, Center-stabilized Yang-Mills theory: Confinement and large N volume independence, Phys. Rev. D 78 (2008) 065035 [ar**v:0803.0344] [INSPIRE].
A. González-Arroyo and M. Okawa, A Twisted Model for Large N Lattice Gauge Theory, Phys. Lett. B 120 (1983) 174 [INSPIRE].
A. González-Arroyo and M. Okawa, The Twisted Eguchi-Kawai Model: A Reduced Model for Large N Lattice Gauge Theory, Phys. Rev. D 27 (1983) 2397 [INSPIRE].
G. ’t Hooft, A Property of Electric and Magnetic Flux in Nonabelian Gauge Theories, Nucl. Phys. B 153 (1979) 141 [INSPIRE].
G. ’t Hooft, Confinement and Topology in Nonabelian Gauge Theories, Acta Phys. Austriaca Suppl. 22 (1980) 531 [INSPIRE].
G. ’t Hooft, Aspects of Quark Confinement, Phys. Scripta 24 (1981) 841 [INSPIRE].
A. González-Arroyo and C. P. Korthals Altes, Reduced Model for Large N Continuum Field Theories, Phys. Lett. B 131 (1983) 396 [INSPIRE].
A. Connes and M. A. Rieffel, Yang-Mills for noncommutative two-tori, Contemp. Math. 62 (1987) 237.
M. R. Douglas and N. A. Nekrasov, Noncommutative field theory, Rev. Mod. Phys. 73 (2001) 977 [hep-th/0106048] [INSPIRE].
A. González-Arroyo and M. Okawa, Large N reduction with the Twisted Eguchi-Kawai model, JHEP 07 (2010) 043 [ar**v:1005.1981] [INSPIRE].
A. González-Arroyo and M. Okawa, Testing volume independence of SU(N) pure gauge theories at large N , JHEP 12 (2014) 106 [ar**v:1410.6405] [INSPIRE].
A. González-Arroyo and M. Okawa, String Tension for Large N Gauge Theory, Phys. Lett. B 133 (1983) 415 [INSPIRE].
K. Fabricius and O. Haan, Numerical Analysis of the Twisted Eguchi-Kawai Model in Four-dimensions, Phys. Lett. B 139 (1984) 293 [INSPIRE].
A. González-Arroyo and M. Okawa, The string tension from smeared Wilson loops at large N , Phys. Lett. B 718 (2013) 1524 [ar**v:1206.0049] [INSPIRE].
R. Lohmayer and H. Neuberger, Rectangular Wilson Loops at Large N , JHEP 08 (2012) 102 [ar**v:1206.4015] [INSPIRE].
A. Athenodorou, B. Bringoltz and M. Teper, Closed flux tubes and their string description in D = 3 + 1 SU(N) gauge theories, JHEP 02 (2011) 030 [ar**v:1007.4720] [INSPIRE].
A. González-Arroyo and M. Okawa, Large N meson masses from a matrix model, Phys. Lett. B 755 (2016) 132 [ar**v:1510.05428] [INSPIRE].
A. González-Arroyo and M. Okawa, Large N meson propagators from twisted space-time reduced model, PoS LATTICE2015 (2016) 291 [ar**v:1511.00477] [INSPIRE].
M. García Pérez, A. González-Arroyo and M. Okawa, Meson masses and decay constants at large N, PoS LATTICE2016 (2016) 319 [ar**v:1611.04128] [INSPIRE].
M. García Pérez, A. González-Arroyo and M. Okawa, The meson spectrum of large N gauge theories, PoS LATTICE2019 (2019) 113 [ar**v:2001.00172] [INSPIRE].
L. Del Debbio, B. Lucini, A. Patella and C. Pica, Quenched mesonic spectrum at large N , JHEP 03 (2008) 062 [ar**v:0712.3036] [INSPIRE].
G. S. Bali and F. Bursa, Mesons at large Nc from lattice QCD, JHEP 09 (2008) 110 [ar**v:0806.2278] [INSPIRE].
A. Hietanen, R. Narayanan, R. Patel and C. Prays, The vector meson mass in the large N limit of QCD, Phys. Lett. B 674 (2009) 80 [ar**v:0901.3752] [INSPIRE].
G. S. Bali et al., Mesons in large-N QCD, JHEP 06 (2013) 071 [ar**v:1304.4437] [INSPIRE].
T. DeGrand and Y. Liu, Lattice study of large Nc QCD, Phys. Rev. D 94 (2016) 034506 [Erratum ibid. 95 (2017) 019902] [ar**v:1606.01277] [INSPIRE].
P. Hernández, C. Pena and F. Romero-López, Large Nc scaling of meson masses and decay constants, Eur. Phys. J. C 79 (2019) 865 [ar**v:1907.11511] [INSPIRE].
G. Aldazabal, N. Parga, M. Okawa and A. González-Arroyo, Large N Reduced Models and Stochastic Quantization, Phys. Lett. B 129 (1983) 90 [INSPIRE].
T. Ishikawa and M. Okawa, ZN symmetry breaking on the numerical simulation of twisted Eguchi-Kawai model, talk given at the Annual Meeting of the Physical Society of Japan, March 28–31, Sendai, Japan (2003).
W. Bietenholz, J. Nishimura, Y. Susaki and J. Volkholz, A non-perturbative study of 4-D U(1) non-commutative gauge theory: The fate of one-loop instability, JHEP 10 (2006) 042 [hep-th/0608072] [INSPIRE].
M. Teper and H. Vairinhos, Symmetry breaking in twisted Eguchi-Kawai models, Phys. Lett. B 652 (2007) 359 [hep-th/0612097] [INSPIRE].
M. García Pérez, A. González-Arroyo, L. Keegan and M. Okawa, The SU(∞) twisted gradient flow running coupling, JHEP 01 (2015) 038 [ar**v:1412.0941] [INSPIRE].
Alpha collaboration, Lattice QCD with a chirally twisted mass term, JHEP 08 (2001) 058 [hep-lat/0101001] [INSPIRE].
R. Frezzotti and G. C. Rossi, Chirally improving Wilson fermions. 1. O(a) improvement, JHEP 08 (2004) 007 [hep-lat/0306014] [INSPIRE].
A. Shindler, Twisted mass lattice QCD, Phys. Rept. 461 (2008) 37 [ar**v:0707.4093] [INSPIRE].
M. García Pérez, A. González-Arroyo, L. Keegan, M. Okawa and A. Ramos, A comparison of updating algorithms for large N reduced models, JHEP 06 (2015) 193 [ar**v:1505.05784] [INSPIRE].
K. Fabricius and O. Haan, Heat Bath Method for the Twisted Eguchi-Kawai Model, Phys. Lett. B 143 (1984) 459 [INSPIRE].
R. Sommer, A new way to set the energy scale in lattice gauge theories and its applications to the static force and αs in SU(2) Yang-Mills theory, Nucl. Phys. B 411 (1994) 839 [hep-lat/9310022] [INSPIRE].
M. Lüscher, Properties and uses of the Wilson flow in lattice QCD, JHEP 08 (2010) 071 [Erratum ibid. 03 (2014) 092] [ar**v:1006.4518] [INSPIRE].
TXL collaboration, Evaluating sea quark contributions to flavor singlet operators in lattice QCD, Phys. Lett. B 389 (1996) 720 [hep-lat/9608040] [INSPIRE].
TXL collaboration, The pion nucleon sigma term with dynamical Wilson fermions, Phys. Rev. D 59 (1999) 054504 [hep-lat/9809066] [INSPIRE].
M. Della Morte, R. Frezzotti and J. Heitger, Quenched twisted mass QCD at small quark masses and in large volume, Nucl. Phys. B Proc. Suppl. 106 (2002) 260 [hep-lat/0110166] [INSPIRE].
C. Michael, Adjoint Sources in Lattice Gauge Theory, Nucl. Phys. B 259 (1985) 58 [INSPIRE].
M. Lüscher and U. Wolff, How to Calculate the Elastic Scattering Matrix in Two-dimensional Quantum Field Theories by Numerical Simulation, Nucl. Phys. B 339 (1990) 222 [INSPIRE].
A. Skouroupathis and H. Panagopoulos, Two-loop renormalization of vector, axial-vector and tensor fermion bilinears on the lattice, Phys. Rev. D 79 (2009) 094508 [ar**v:0811.4264] [INSPIRE].
M. Booth, G. Chiladze and A. F. Falk, Quenched chiral perturbation theory for vector mesons, Phys. Rev. D 55 (1997) 3092 [hep-ph/9610532] [INSPIRE].
T. DeGrand, Lattice baryons in the 1/N expansion, Phys. Rev. D 86 (2012) 034508 [ar**v:1205.0235] [INSPIRE].
R. Narayanan and H. Neuberger, The quark mass dependence of the pion mass at infinite N, Phys. Lett. B 616 (2005) 76 [hep-lat/0503033] [INSPIRE].
G. S. Bali, L. Castagnini, B. Lucini and M. Panero, Large-N mesons, PoS LATTICE2013 (2014) 100 [ar**v:1311.7559] [INSPIRE].
L. Castagnini, Meson spectroscopy in Large-N QCD, Ph.D. Thesis, Regensburg University, Germany (2015).
J. R. Pelaez, From controversy to precision on the sigma meson: a review on the status of the non-ordinary f0 (500) resonance, Phys. Rept. 658 (2016) 1 [ar**v:1510.00653] [INSPIRE].
J. R. Pelaez and G. Rios, Nature of the f0 (600) from its Nc dependence at two loops in unitarized Chiral Perturbation Theory, Phys. Rev. Lett. 97 (2006) 242002 [hep-ph/0610397] [INSPIRE].
J. Nieves and E. Ruiz Arriola, Properties of the ρ and σ Mesons from Unitary Chiral Dynamics, Phys. Rev. D 80 (2009) 045023 [ar**v:0904.4344] [INSPIRE].
J. Nieves, A. Pich and E. Ruiz Arriola, Large-Nc Properties of the ρ and f0 (600) Mesons from Unitary Resonance Chiral Dynamics, Phys. Rev. D 84 (2011) 096002 [ar**v:1107.3247] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
M. Kruczenski, D. Mateos, R. C. Myers and D. J. Winters, Meson spectroscopy in AdS/CFT with flavor, JHEP 07 (2003) 049 [hep-th/0304032] [INSPIRE].
J. Babington, J. Erdmenger, N. J. Evans, Z. Guralnik and I. Kirsch, Chiral symmetry breaking and pions in nonsupersymmetric gauge/gravity duals, Phys. Rev. D 69 (2004) 066007 [hep-th/0306018] [INSPIRE].
M. Kruczenski, D. Mateos, R. C. Myers and D. J. Winters, Towards a holographic dual of large Nc QCD, JHEP 05 (2004) 041 [hep-th/0311270] [INSPIRE].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].
J. Erdmenger, N. Evans, I. Kirsch and E. Threlfall, Mesons in Gauge/Gravity Duals — A Review, Eur. Phys. J. A 35 (2008) 81 [ar**v:0711.4467] [INSPIRE].
J. Erlich, E. Katz, D. T. Son and M. A. Stephanov, QCD and a holographic model of hadrons, Phys. Rev. Lett. 95 (2005) 261602 [hep-ph/0501128] [INSPIRE].
L. Da Rold and A. Pomarol, The scalar and pseudoscalar sector in a five-dimensional approach to chiral symmetry breaking, JHEP 01 (2006) 157 [hep-ph/0510268] [INSPIRE].
J. Hirn and V. Sanz, Interpolating between low and high energy QCD via a 5-D Yang-Mills model, JHEP 12 (2005) 030 [hep-ph/0507049] [INSPIRE].
M. Bochicchio, Glueball and Meson Spectrum in Large-N QCD, Few Body Syst. 57 (2016) 455.
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Pérez, M.G., González-Arroyo, A. & Okawa, M. Meson spectrum in the large N limit. J. High Energ. Phys. 2021, 230 (2021). https://doi.org/10.1007/JHEP04(2021)230
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DOI: https://doi.org/10.1007/JHEP04(2021)230