Abstract
I discuss the implementation of the Peccei-Quinn mechanism in a minimal realization of the Pati-Salam partial unification scheme. The axion mass is shown to be related to the Pati-Salam breaking scale and it is predicted via a two-loop renormalization group analysis to be in the window ma ∈ [10−11, 3 × 10−7] eV, as a function of a sliding Left-Right symmetry breaking scale. This parameter space will be fully covered by the late phases of the axion Dark Matter experiments ABRACADABRA and CASPEr-Electric. A Left-Right symmetry breaking scenario as low as 20 TeV is obtained for a Pati-Salam breaking of the order of the reduced Planck mass.
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References
J.C. Pati and A. Salam, Lepton number as the fourth color, Phys. Rev. D 10 (1974) 275 [Erratum ibid. 11 (1975) 703] [INSPIRE].
R.N. Mohapatra and J.C. Pati, A natural Left-Right symmetry, Phys. Rev. D 11 (1975) 2558 [INSPIRE].
G. Senjanović and R.N. Mohapatra, Exact Left-Right symmetry and spontaneous violation of parity, Phys. Rev. D 12 (1975) 1502 [INSPIRE].
R.N. Mohapatra and G. Senjanović, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].
H. Fritzsch and P. Minkowski, Unified interactions of leptons and hadrons, Annals Phys. 93 (1975) 193 [INSPIRE].
H. Georgi, The state of the art — Gauge theories, AIP Conf. Proc. 23 (1975) 575 [INSPIRE].
A. Melfo and G. Senjanović, Minimal supersymmetric Pati-Salam theory: determination of physical scales, Phys. Rev. D 68 (2003) 035013 [hep-ph/0302216] [INSPIRE].
D. Chang et al., Experimental Tests of new SO(10) grand unification, Phys. Rev. D 31 (1985) 1718 [INSPIRE].
N.G. Deshpande, E. Keith and P.B. Pal, Implications of LEP results for SO(10) grand unification with two intermediate stages, Phys. Rev. D 47 (1993) 2892 [hep-ph/9211232] [INSPIRE].
S. Bertolini, L. Di Luzio and M. Malinsky, Intermediate mass scales in the non-supersymmetric SO(10) grand unification: A Reappraisal, Phys. Rev. D 80 (2009) 015013 [arXiv:0903.4049] [INSPIRE].
M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].
S. Davidson, E. Nardi and Y. Nir, Leptogenesis, Phys. Rept. 466 (2008) 105 [arXiv:0802.2962] [INSPIRE].
M. Nemevšek, G. Senjanović and Y. Zhang, Warm dark matter in low scale left-right theory, JCAP 07 (2012) 006 [arXiv:1205.0844] [INSPIRE].
R.D. Peccei and H.R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
R.D. Peccei and H.R. Quinn, Constraints imposed by CP conservation in the presence of instantons, Phys. Rev. D 16 (1977) 1791 [INSPIRE].
S. Weinberg, A new light boson?, Phys. Rev. Lett. 40 (1978) 223 [INSPIRE].
F. Wilczek, Problem of strong P and T invariance in the presence of instantons, Phys. Rev. Lett. 40 (1978) 279 [INSPIRE].
J. Preskill, M.B. Wise and F. Wilczek, Cosmology of the invisible axion, Phys. Lett. B 120 (1983) 127 [INSPIRE].
L.F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. B 120 (1983) 133 [INSPIRE].
M. Dine and W. Fischler, The not so harmless axion, Phys. Lett. B 120 (1983) 137 [INSPIRE].
K.S. Babu and R.N. Mohapatra, Predictive neutrino spectrum in minimal SO(10) grand unification, Phys. Rev. Lett. 70 (1993) 2845 [hep-ph/9209215] [INSPIRE].
L. Di Luzio, M. Giannotti, E. Nardi and L. Visinelli, The landscape of QCD axion models, arXiv:2003.01100 [INSPIRE].
R.N. Mohapatra and G. Senjanović, The superlight axion and neutrino masses, Z. Phys. C 17 (1983) 53 [INSPIRE].
A. Davidson and K.C. Wali, Minimal flavor unification via multigenerational Peccei-Quinn symmetry, Phys. Rev. Lett. 48 (1982) 11 [INSPIRE].
D.B. Reiss, Invisible axion at an intermediate symmetry breaking scale, Phys. Lett. B 109 (1982) 365 [INSPIRE].
G. Lazarides, SO(10) and the invisible axion, Phys. Rev. D 25 (1982) 2425 [INSPIRE].
R. Holman, G. Lazarides and Q. Shafi, Axions and the dark matter of the universe, Phys. Rev. D 27 (1983) 995 [INSPIRE].
S. Kalara and R.N. Mohapatra, Geometric gauge hierarchy in a supersymmetric SO(10) × U(1)-pq model, Phys. Rev. D 28 (1983) 2241 [INSPIRE].
A. Davidson, V.P. Nair and K.C. Wali, Peccei-Quinn symmetry as flavor symmetry and grand unification, Phys. Rev. D 29 (1984) 1504 [INSPIRE].
A. Davidson, V.P. Nair and K.C. Wali, Mixing angles and CP Violation in the SO(10) × U(1)-(pq) model, Phys. Rev. D 29 (1984) 1513 [INSPIRE].
D. Chang and G. Senjanović, On axion and familons, Phys. Lett. B 188 (1987) 231 [INSPIRE].
T. Fukuyama and T. Kikuchi, Axion and right-handed neutrino in the minimal SUSY SO(10) model, JHEP 05 (2005) 017 [hep-ph/0412373] [INSPIRE].
B. Bajc, A. Melfo, G. Senjanović and F. Vissani, Yukawa sector in non-supersymmetric renormalizable SO(10), Phys. Rev. D 73 (2006) 055001 [hep-ph/0510139] [INSPIRE].
G. Altarelli and D. Meloni, A non supersymmetric SO(10) grand unified model for all the physics below MGUT , JHEP 08 (2013) 021 [arXiv:1305.1001] [INSPIRE].
K.S. Babu and S. Khan, Minimal nonsupersymmetric SO(10) model: gauge coupling unification, proton decay and fermion masses, Phys. Rev. D 92 (2015) 075018 [arXiv:1507.06712] [INSPIRE].
S. Saad, Fermion masses and mixings, leptogenesis and baryon number violation in Pati-Salam model, Nucl. Phys. B 943 (2019) 114630 [arXiv:1712.04880] [INSPIRE].
A. Ernst, A. Ringwald and C. Tamarit, Axion Predictions in SO(10) × U(1)PQ models, JHEP 02 (2018) 103 [arXiv:1801.04906] [INSPIRE].
A. Ernst, L. Di Luzio, A. Ringwald and C. Tamarit, Axion properties in GUTs, PoS(CORFU2018)054 [arXiv:1811.11860] [INSPIRE].
S.M. Boucenna, T. Ohlsson and M. Pernow, A minimal non-supersymmetric SO(10) model with Peccei–Quinn symmetry, Phys. Lett. B 792 (2019) 251 [Erratum ibid. 797 (2019) 134902] [arXiv:1812.10548] [INSPIRE].
K.S. Babu, T. Fukuyama, S. Khan and S. Saad, Peccei-Quinn symmetry and nucleon decay in renormalizable SUSY SO(10), JHEP 06 (2019) 045 [arXiv:1812.11695] [INSPIRE].
Y. Hamada, M. Ibe, Y. Muramatsu, K.-y. Oda and N. Yokozaki, Proton decay and axion dark matter in SO(10) grand unification via minimal Left-Right symmetry, Eur. Phys. J. C 80 (2020) 482 [arXiv:2001.05235] [INSPIRE].
G. Lazarides and Q. Shafi, Axion model with intermediate scale fermionic dark matter, arXiv:2004.11560 [INSPIRE].
P. Sikivie, Invisible axion search methods, arXiv:2003.02206 [INSPIRE].
I.G. Irastorza and J. Redondo, New experimental approaches in the search for axion-like particles, Prog. Part. Nucl. Phys. 102 (2018) 89 [arXiv:1801.08127] [INSPIRE].
D. Budker et al., Proposal for a Cosmic Axion Spin Precession Experiment (CASPEr), Phys. Rev. X 4 (2014) 021030 [arXiv:1306.6089] [INSPIRE].
D.F. Jackson Kimball et al., Overview of the Cosmic Axion Spin Precession Experiment (CASPEr), arXiv:1711.08999 [INSPIRE].
Y. Kahn, B.R. Safdi and J. Thaler, Broadband and resonant approaches to axion dark matter detection, Phys. Rev. Lett. 117 (2016) 141801 [arXiv:1602.01086] [INSPIRE].
L. Di Luzio, A. Ringwald and C. Tamarit, Axion mass prediction from minimal grand unification, Phys. Rev. D 98 (2018) 095011 [arXiv:1807.09769] [INSPIRE].
B. Bajc and G. Senjanović, Seesaw at LHC, JHEP 08 (2007) 014 [hep-ph/0612029] [INSPIRE].
B. Bajc, M. Nemevšek and G. Senjanović, Probing seesaw at LHC, Phys. Rev. D 76 (2007) 055011 [hep-ph/0703080] [INSPIRE].
L. Di Luzio and L. Mihaila, Unification scale vs. electroweak-triplet mass in the SU(5) + 24F model at three loops, Phys. Rev. D 87 (2013) 115025 [arXiv:1305.2850] [INSPIRE].
P. Fileviez Pérez, C. Murgui and A.D. Plascencia, The QCD axion and unification, JHEP 11 (2019) 093 [arXiv:1908.01772] [INSPIRE].
P. Fileviez Pérez, C. Murgui and A.D. Plascencia, Axion dark matter, proton decay and unification, JHEP 01 (2020) 091 [arXiv:1911.05738] [INSPIRE].
R.T. Co, F. D’Eramo and L.J. Hall, Supersymmetric axion grand unified theories and their predictions, Phys. Rev. D 94 (2016) 075001 [arXiv:1603.04439] [INSPIRE].
T.W.B. Kibble, G. Lazarides and Q. Shafi, Strings in SO(10), Phys. Lett. B 113 (1982) 237 [INSPIRE].
T.W.B. Kibble, G. Lazarides and Q. Shafi, Walls bounded by strings, Phys. Rev. D 26 (1982) 435 [INSPIRE].
D. Chang, R.N. Mohapatra and M.K. Parida, Decoupling parity and SU(2)-R breaking scales: a new approach to Left-Right symmetric models, Phys. Rev. Lett. 52 (1984) 1072 [INSPIRE].
D. Chang, R.N. Mohapatra and M.K. Parida, A new approach to Left-Right symmetry breaking in unified gauge theories, Phys. Rev. D 30 (1984) 1052 [INSPIRE].
A. Maiezza and M. Nemevšek, Strong P invariance, neutron electric dipole moment and minimal left-right parity at LHC, Phys. Rev. D 90 (2014) 095002 [arXiv:1407.3678] [INSPIRE].
S. Bertolini, A. Maiezza and F. Nesti, Kaon CP-violation and neutron EDM in the minimal left-right symmetric model, Phys. Rev. D 101 (2020) 035036 [arXiv:1911.09472] [INSPIRE].
G. Senjanović and V. Tello, Strong CP-violation: problem or blessing?, arXiv:2004.04036 [INSPIRE].
J.C. Pati, A. Salam and U. Sarkar, ∆B = −∆L, neutron → e− π+ , e− K + , μ− π+ and μ− K + DECAY modes in SU(2)L × SU(2)R × SU(4)C or SO(10), Phys. Lett. B 133 (1983) 330 [INSPIRE].
A.S. Joshipura and K.M. Patel, Fermion masses in SO(10) models, Phys. Rev. D 83 (2011) 095002 [arXiv:1102.5148] [INSPIRE].
S. Bertolini, L. Di Luzio and F. Nesti, Axion properties in Left-Right symmetric models, in preparation.
M. Srednicki, Axion couplings to matter. 1. CP conserving parts, Nucl. Phys. B 260 (1985) 689 [INSPIRE].
G. Grilli di Cortona, E. Hardy, J. Pardo Vega and G. Villadoro, The QCD axion, precisely, JHEP 01 (2016) 034 [arXiv:1511.02867] [INSPIRE].
M. Pospelov and A. Ritz, Theta induced electric dipole moment of the neutron via QCD sum rules, Phys. Rev. Lett. 83 (1999) 2526 [hep-ph/9904483] [INSPIRE].
D. Buttazzo et al., Scalar gauge dynamics and dark matter, JHEP 01 (2020) 130 [arXiv:1911.04502] [INSPIRE].
L. Di Luzio et al., Maximal flavour violation: a Cabibbo mechanism for leptoquarks, JHEP 11 (2018) 081 [arXiv:1808.00942] [INSPIRE].
M. Gorghetto and G. Villadoro, Topological susceptibility and QCD axion mass: QED and NNLO corrections, JHEP 03 (2019) 033 [arXiv:1812.01008] [INSPIRE].
F. del Aguila and L.E. Ibanez, Higgs bosons in SO(10) and partial unification, Nucl. Phys. B 177 (1981) 60.
R.N. Mohapatra and G. Senjanović, Higgs boson effects in grand unified theories, Phys. Rev. D 27 (1983) 1601 [INSPIRE].
L.N. Mihaila, J. Salomon and M. Steinhauser, Renormalization constants and β-functions for the gauge couplings of the Standard Model to three-loop order, Phys. Rev. D 86 (2012) 096008 [arXiv:1208.3357] [INSPIRE].
S. Borsányi et al., Calculation of the axion mass based on high-temperature lattice quantum chromodynamics, Nature 539 (2016) 69 [arXiv:1606.07494] [INSPIRE].
A. Vilenkin, Cosmic strings and domain walls, Phys. Rept. 121 (1985) 263 [INSPIRE].
G. Lazarides and Q. Shafi, The fate of primordial magnetic monopoles, Phys. Lett. B 94 (1980) 149 [INSPIRE].
G. Lazarides, M. Magg and Q. Shafi, Phase transitions and magnetic monopoles in SO(10), Phys. Lett. B 97 (1980) 87 [INSPIRE].
S. Dawson and A.N. Schellekens, Monopole catalysis of proton decay in SO(10) grand unified models, Phys. Rev. D 27 (1983) 2119 [INSPIRE].
A. Sen, Baryon number violation induced by the monopoles of the Pati-Salam model, Phys. Lett. B 153 (1985) 55 [INSPIRE].
A. Sen, Monopole induced baryon number violation due to weak anomaly, Nucl. Phys. B 250 (1985) 1 [INSPIRE].
T.W.B. Kibble, Topology of cosmic domains and strings, J. Phys. A 9 (1976) 1387 [INSPIRE].
W.H. Zurek, Cosmological experiments in superfluid helium?, Nature 317 (1985) 505 [INSPIRE].
H. Murayama and J. Shu, Topological dark matter, Phys. Lett. B 686 (2010) 162 [arXiv:0905.1720] [INSPIRE].
V.V. Khoze and G. Ro, Dark matter monopoles, vectors and photons, JHEP 10 (2014) 061 [arXiv:1406.2291] [INSPIRE].
E.N. Parker, The origin of magnetic fields, Astrophys. J. 160 (1970) 383 [INSPIRE].
M.S. Turner, E.N. Parker and T.J. Bogdan, Magnetic monopoles and the survival of galactic magnetic fields, Phys. Rev. D 26 (1982) 1296 [INSPIRE].
MACRO collaboration, Final results of magnetic monopole searches with the MACRO experiment, Eur. Phys. J. C 25 (2002) 511 [hep-ex/0207020] [INSPIRE].
Super-Kamiokande collaboration, Search for GUT monopoles at Super–Kamiokande, Astropart. Phys. 36 (2012) 131 [arXiv:1203.0940] [INSPIRE].
C.G. Callan Jr., Dyon-fermion dynamics, Phys. Rev. D 26 (1982) 2058 [INSPIRE].
V.A. Rubakov, Adler-Bell-Jackiw anomaly and fermion number breaking in the presence of a magnetic monopole, Nucl. Phys. B 203 (1982) 311 [INSPIRE].
G. Ballesteros, J. Redondo, A. Ringwald and C. Tamarit, Standard Model-axion-seesaw-Higgs portal inflation. Five problems of particle physics and cosmology solved in one stroke, JCAP 08 (2017) 001 [arXiv:1610.01639] [INSPIRE].
A.D. Linde, Generation of isothermal density perturbations in the inflationary universe, Phys. Lett. B 158 (1985) 375 [INSPIRE].
D. Seckel and M.S. Turner, Isothermal density perturbations in an axion dominated inflationary universe, Phys. Rev. D 32 (1985) 3178 [INSPIRE].
M. Beltrán, J. García-Bellido and J. Lesgourgues, Isocurvature bounds on axions revisited, Phys. Rev. D 75 (2007) 103507 [hep-ph/0606107] [INSPIRE].
M.P. Hertzberg, M. Tegmark and F. Wilczek, Axion cosmology and the energy scale of inflation, Phys. Rev. D 78 (2008) 083507 [arXiv:0807.1726] [INSPIRE].
J. Hamann, S. Hannestad, G.G. Raffelt and Y.Y.Y. Wong, Isocurvature forecast in the anthropic axion window, JCAP 06 (2009) 022 [arXiv:0904.0647] [INSPIRE].
R. Penrose, Gravitational collapse: The role of general relativity, Riv. Nuovo Cim. 1 (1969) 252. [Gen. Rel. Grav. 34 (2002) 1141].
A. Arvanitaki and S. Dubovsky, Exploring the string axiverse with precision black hole physics, Phys. Rev. D 83 (2011) 044026 [arXiv:1004.3558] [INSPIRE].
A. Arvanitaki, M. Baryakhtar and X. Huang, Discovering the QCD axion with black holes and gravitational waves, Phys. Rev. D 91 (2015) 084011 [arXiv:1411.2263] [INSPIRE].
V. Cardoso et al., Constraining the mass of dark photons and axion-like particles through black-hole superradiance, JCAP 03 (2018) 043 [arXiv:1801.01420] [INSPIRE].
J.L. Ouellet et al., First results from ABRACADABRA-10 cm: a search for sub-μeV axion dark matter, Phys. Rev. Lett. 122 (2019) 121802 [arXiv:1810.12257] [INSPIRE].
P.W. Graham and S. Rajendran, New observables for direct detection of axion dark matter, Phys. Rev. D 88 (2013) 035023 [arXiv:1306.6088] [INSPIRE].
M. Pospelov and A. Ritz, Theta vacua, QCD sum rules and the neutron electric dipole moment, Nucl. Phys. B 573 (2000) 177 [hep-ph/9908508] [INSPIRE].
M. Abramczyk et al., Lattice calculation of electric dipole moments and form factors of the nucleon, Phys. Rev. D 96 (2017) 014501 [arXiv:1701.07792] [INSPIRE].
J. Dragos et al., Confirming the existence of the strong CP problem in lattice QCD with the gradient flow, arXiv:1902.03254 [INSPIRE].
G. Valencia and S. Willenbrock, Quark-lepton unification and rare meson decays, Phys. Rev. D 50 (1994) 6843 [hep-ph/9409201] [INSPIRE].
A.V. Kuznetsov and N.V. Mikheev, Vector leptoquarks could be rather light?, Phys. Lett. B 329 (1994) 295 [hep-ph/9406347] [INSPIRE].
A.D. Smirnov, Vector leptoquark mass limits and branching ratios of \( {K}_L^0,{B}^0,{B}_s\to {l}_i^{+}{l}_j^{-} \) decays with account of fermion mixing in leptoquark currents, Mod. Phys. Lett. A 33 (2018) 1850019 [arXiv:1801.02895] [INSPIRE].
R.N. Mohapatra and R.E. Marshak, Local B-L symmetry of electroweak interactions, Majorana neutrinos and neutron Oscillations, Phys. Rev. Lett. 44 (1980) 1316 [Erratum ibid. 44 (1980) 1643] [INSPIRE].
R.N. Mohapatra, Neutron-anti-neutron oscillation: theory and phenomenology, J. Phys. G 36 (2009) 104006 [arXiv:0902.0834] [INSPIRE].
J.C. Pati, Nucleon decays into lepton + lepton + anti-lepton + mesons within SU(4) of color, Phys. Rev. D 29 (1984) 1549 [INSPIRE].
P.J. O’Donnell and U. Sarkar, Three lepton decay mode of the proton, Phys. Lett. B 316 (1993) 121 [hep-ph/9307254] [INSPIRE].
G. Dvali and A. Vilenkin, Cosmic attractors and gauge hierarchy, Phys. Rev. D 70 (2004) 063501 [hep-th/0304043] [INSPIRE].
G. Dvali, Large hierarchies from attractor vacua, Phys. Rev. D 74 (2006) 025018 [hep-th/0410286] [INSPIRE].
C. Caprini et al., Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions, JCAP 04 (2016) 001 [arXiv:1512.06239] [INSPIRE].
V. Brdar, L. Graf, A.J. Helmboldt and X.-J. Xu, Gravitational waves as a probe of Left-Right symmetry breaking, JCAP 12 (2019) 027 [arXiv:1909.02018] [INSPIRE].
A. Maiezza, M. Nemevšek, F. Nesti and G. Senjanović, Left-Right symmetry at LHC, Phys. Rev. D 82 (2010) 055022 [arXiv:1005.5160] [INSPIRE].
V. Tello et al., Left-Right symmetry: from LHC to neutrinoless double beta decay, Phys. Rev. Lett. 106 (2011) 151801 [arXiv:1011.3522] [INSPIRE].
S. Bertolini, A. Maiezza and F. Nesti, Present and future K and B meson mixing constraints on TeV scale Left-Right symmetry, Phys. Rev. D 89 (2014) 095028 [arXiv:1403.7112] [INSPIRE].
P.S.B. Dev, D. Kim and R.N. Mohapatra, Disambiguating seesaw models using invariant mass variables at hadron colliders, JHEP 01 (2016) 118 [arXiv:1510.04328] [INSPIRE].
R. Ruiz, Lepton number violation at colliders from kinematically inaccessible gauge bosons, Eur. Phys. J. C 77 (2017) 375 [arXiv:1703.04669] [INSPIRE].
M. Nemevšek, F. Nesti and G. Popara, Keung-Senjanović process at the LHC: from lepton number violation to displaced vertices to invisible decays, Phys. Rev. D 97 (2018) 115018 [arXiv:1801.05813] [INSPIRE].
G. Chauhan, P.S.B. Dev, R.N. Mohapatra and Y. Zhang, Perturbativity constraints on U(1)B−L and Left-Right models and implications for heavy gauge boson searches, JHEP 01 (2019) 208 [arXiv:1811.08789] [INSPIRE].
S. Bertolini, L. Di Luzio and M. Malinsky, On the vacuum of the minimal nonsupersymmetric SO(10) unification, Phys. Rev. D 81 (2010) 035015 [arXiv:0912.1796] [INSPIRE].
S. Bertolini, L. Di Luzio and M. Malinsky, Seesaw scale in the minimal renormalizable SO(10) grand unification, Phys. Rev. D 85 (2012) 095014 [arXiv:1202.0807] [INSPIRE].
H.M. Georgi, L.J. Hall and M.B. Wise, Grand unified models with an automatic Peccei-Quinn symmetry, Nucl. Phys. B 192 (1981) 409 [INSPIRE].
M. Kamionkowski and J. March-Russell, Planck scale physics and the Peccei-Quinn mechanism, Phys. Lett. B 282 (1992) 137 [hep-th/9202003] [INSPIRE].
R. Holman et al., Solutions to the strong CP problem in a world with gravity, Phys. Lett. B 282 (1992) 132 [hep-ph/9203206] [INSPIRE].
S.M. Barr and D. Seckel, Planck scale corrections to axion models, Phys. Rev. D 46 (1992) 539 [INSPIRE].
M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 1. Wave function renormalization, Nucl. Phys. B 222 (1983) 83 [INSPIRE].
S. Weinberg, Effective gauge theories, Phys. Lett. B 91 (1980) 51 [INSPIRE].
L.J. Hall, Grand unification of effective gauge theories, Nucl. Phys. B 178 (1981) 75 [INSPIRE].
S. Bertolini, L. Di Luzio and M. Malinsky, Light color octet scalars in the minimal SO(10) grand unification, Phys. Rev. D 87 (2013) 085020 [arXiv:1302.3401] [INSPIRE].
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Di Luzio, L. Pati-Salam axion. J. High Energ. Phys. 2020, 71 (2020). https://doi.org/10.1007/JHEP07(2020)071
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DOI: https://doi.org/10.1007/JHEP07(2020)071