Abstract
The flavour problem of the Standard Model can be addressed through the Froggatt-Nielsen (FN) mechanism. In this work, we develop an approach to the study of FN textures building a direct link between FN-charge assignments and the measured masses and mixing angles via unitary transformations in flavour space. We specifically focus on the quark sector to identify the most economic FN models able to provide a dynamical and natural understanding of the flavour puzzle. Remarkably, we find viable FN textures, involving charges under the horizontal symmetry that do not exceed one in absolute value (in units of the flavon charge). Within our approach, we also explore the degree of tuning of FN models in solving the flavour problem via a measure analogous to the Barbieri-Giudice one. We find that most of the solutions do not involve peculiar cancellations in flavour space.
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References
J.L. Feng, Naturalness and the Status of Supersymmetry, Ann. Rev. Nucl. Part. Sci. 63 (2013) 351 [arXiv:1302.6587] [INSPIRE].
N. Craig, The State of Supersymmetry after Run I of the LHC, in Beyond the Standard Model after the first run of the LHC, Florence Italy (2013) [arXiv:1309.0528] [INSPIRE].
G. Panico and A. Wulzer, The Composite Nambu-Goldstone Higgs, Lecture Notes Phys. 913 (2016) 1.
M. Farina, D. Pappadopulo and A. Strumia, A modified naturalness principle and its experimental tests, JHEP 08 (2013) 022 [arXiv:1303.7244] [INSPIRE].
A. de Gouvêa, D. Hernandez and T.M.P. Tait, Criteria for Natural Hierarchies, Phys. Rev. D 89 (2014) 115005 [arXiv:1402.2658] [INSPIRE].
M. Dine, Naturalness Under Stress, Ann. Rev. Nucl. Part. Sci. 65 (2015) 43 [arXiv:1501.01035] [INSPIRE].
P.W. Graham, D.E. Kaplan and S. Rajendran, Cosmological Relaxation of the Electroweak Scale, Phys. Rev. Lett. 115 (2015) 221801 [arXiv:1504.07551] [INSPIRE].
G.F. Giudice, The Dawn of the Post-Naturalness Era, in From My Vast Repertoire ...: Guido Altarelli’s Legacy, A. Levy, S. Forte and G. Ridolfi eds., World Scientific, New York U.S.A. (2019), pg. 267 [arXiv:1710.07663] [INSPIRE].
S. Weinberg, The Problem of Mass, Trans. New York Acad. Sci. 38 (1977) 185.
H. Fritzsch and Z.-z. Xing, Mass and flavor mixing schemes of quarks and leptons, Prog. Part. Nucl. Phys. 45 (2000) 1 [hep-ph/9912358] [INSPIRE].
S. Raby, Introduction to theories of fermion masses, Trieste HEP Cosmology, Trieste Italy (1994), pg. 0126 [hep-ph/9501349] [INSPIRE].
G. Ross, Models of fermion masses, in Flavor Physics for the Millennium, World Scientific, New York U.S.A. (2001), pg. 775.
N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett. 10 (1963) 531 [INSPIRE].
M. Kobayashi and T. Maskawa, CP Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49 (1973) 652 [INSPIRE].
B. Pontecorvo, Inverse beta processes and nonconservation of lepton charge, Sov. Phys. JETP 7 (1958) 172 [INSPIRE].
Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870 [INSPIRE].
K.S. Babu, TASI Lectures on Flavor Physics, in Theoretical Advanced Study Institute in Elementary Particle Physics: The Dawn of the LHC Era, Boulder U.S.A. (2008), pg. 49 [arXiv:0910.2948] [INSPIRE].
F. Feruglio, Pieces of the Flavour Puzzle, Eur. Phys. J. C 75 (2015) 373 [arXiv:1503.04071] [INSPIRE].
F. Feruglio and A. Romanino, Neutrino Flavour Symmetries, arXiv:1912.06028 [INSPIRE].
R. Barbieri, G.R. Dvali, A. Strumia, Z. Berezhiani and L.J. Hall, Flavor in supersymmetric grand unification: A Democratic approach, Nucl. Phys. B 432 (1994) 49 [hep-ph/9405428] [INSPIRE].
R. Barbieri, L.J. Hall, S. Raby and A. Romanino, Unified theories with U(2) flavor symmetry, Nucl. Phys. B 493 (1997) 3 [hep-ph/9610449] [INSPIRE].
S.F. King and G.G. Ross, Fermion masses and mixing angles from SU(3) family symmetry and unification, Phys. Lett. B 574 (2003) 239 [hep-ph/0307190] [INSPIRE].
S.F. King, Predicting neutrino parameters from SO(3) family symmetry and quark-lepton unification, JHEP 08 (2005) 105 [hep-ph/0506297] [INSPIRE].
M. Linster and R. Ziegler, A Realistic U(2) Model of Flavor, JHEP 08 (2018) 058 [arXiv:1805.07341] [INSPIRE].
F. Arias-Aragón, C. Bouthelier-Madre, J.M. Cano and L. Merlo, Data Driven Flavour Model, Eur. Phys. J. C 80 (2020) 854 [arXiv:2003.05941] [INSPIRE].
L.E. Ibáñez and G.G. Ross, Fermion masses and mixing angles from gauge symmetries, Phys. Lett. B 332 (1994) 100 [hep-ph/9403338] [INSPIRE].
T. Kobayashi, H.P. Nilles, F. Ploger, S. Raby and M. Ratz, Stringy origin of non-Abelian discrete flavor symmetries, Nucl. Phys. B 768 (2007) 135 [hep-ph/0611020] [INSPIRE].
M. Berasaluce-Gonzalez, P.G. Cámara, F. Marchesano, D. Regalado and A.M. Uranga, Non-Abelian discrete gauge symmetries in 4d string models, JHEP 09 (2012) 059 [arXiv:1206.2383] [INSPIRE].
S.F. King and C. Luhn, Neutrino Mass and Mixing with Discrete Symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].
M.-C. Chen, M. Fallbacher, K.T. Mahanthappa, M. Ratz and A. Trautner, CP Violation from Finite Groups, Nucl. Phys. B 883 (2014) 267 [arXiv:1402.0507] [INSPIRE].
P. Binetruy and P. Ramond, Yukawa textures and anomalies, Phys. Lett. B 350 (1995) 49 [hep-ph/9412385] [INSPIRE].
P. Binetruy, S. Lavignac and P. Ramond, Yukawa textures with an anomalous horizontal Abelian symmetry, Nucl. Phys. B 477 (1996) 353 [hep-ph/9601243] [INSPIRE].
S. Weinberg, Electromagnetic and weak masses, Phys. Rev. Lett. 29 (1972) 388 [INSPIRE].
H. Georgi and S.L. Glashow, Attempts to calculate the electron mass, Phys. Rev. D 7 (1973) 2457 [INSPIRE].
S.M. Barr and A. Zee, A New Approach to the electron-Muon Mass Ratio, Phys. Rev. D 15 (1977) 2652 [INSPIRE].
B.S. Balakrishna, A.L. Kagan and R.N. Mohapatra, Quark Mixings and Mass Hierarchy From Radiative Corrections, Phys. Lett. B 205 (1988) 345 [INSPIRE].
A. Crivellin, L. Hofer, U. Nierste and D. Scherer, Phenomenological consequences of radiative flavor violation in the MSSM, Phys. Rev. D 84 (2011) 035030 [arXiv:1105.2818] [INSPIRE].
W. Altmannshofer, C. Frugiuele and R. Harnik, Fermion Hierarchy from Sfermion Anarchy, JHEP 12 (2014) 180 [arXiv:1409.2522] [INSPIRE].
D.B. Kaplan, Flavor at SSC energies: A New mechanism for dynamically generated fermion masses, Nucl. Phys. B 365 (1991) 259 [INSPIRE].
A.J. Buras, C. Grojean, S. Pokorski and R. Ziegler, FCNC Effects in a Minimal Theory of Fermion Masses, JHEP 08 (2011) 028 [arXiv:1105.3725] [INSPIRE].
G. Panico and A. Pomarol, Flavor hierarchies from dynamical scales, JHEP 07 (2016) 097 [arXiv:1603.06609] [INSPIRE].
N. Arkani-Hamed and M. Schmaltz, Hierarchies without symmetries from extra dimensions, Phys. Rev. D 61 (2000) 033005 [hep-ph/9903417] [INSPIRE].
T. Gherghetta and A. Pomarol, Bulk fields and supersymmetry in a slice of AdS, Nucl. Phys. B 586 (2000) 141 [hep-ph/0003129] [INSPIRE].
S.J. Huber and Q. Shafi, Fermion masses, mixings and proton decay in a Randall-Sundrum model, Phys. Lett. B 498 (2001) 256 [hep-ph/0010195] [INSPIRE].
D.E. Kaplan and T.M.P. Tait, New tools for fermion masses from extra dimensions, JHEP 11 (2001) 051 [hep-ph/0110126] [INSPIRE].
A. Ahmed, A. Carmona, J. Castellano Ruiz, Y. Chung and M. Neubert, Dynamical origin of fermion bulk masses in a warped extra dimension, JHEP 08 (2019) 045 [arXiv:1905.09833] [INSPIRE].
C.D. Froggatt and H.B. Nielsen, Hierarchy of Quark Masses, Cabibbo Angles and CP-violation, Nucl. Phys. B 147 (1979) 277 [INSPIRE].
M. Leurer, Y. Nir and N. Seiberg, Mass matrix models, Nucl. Phys. B 398 (1993) 319 [hep-ph/9212278] [INSPIRE].
M. Leurer, Y. Nir and N. Seiberg, Mass matrix models: The Sequel, Nucl. Phys. B 420 (1994) 468 [hep-ph/9310320] [INSPIRE].
L. Calibbi, Z. Lalak, S. Pokorski and R. Ziegler, The Messenger Sector of SUSY Flavour Models and Radiative Breaking of Flavour Universality, JHEP 06 (2012) 018 [arXiv:1203.1489] [INSPIRE].
Y. Ema, K. Hamaguchi, T. Moroi and K. Nakayama, Flaxion: a minimal extension to solve puzzles in the standard model, JHEP 01 (2017) 096 [arXiv:1612.05492] [INSPIRE].
L. Calibbi, F. Goertz, D. Redigolo, R. Ziegler and J. Zupan, Minimal axion model from flavor, Phys. Rev. D 95 (2017) 095009 [arXiv:1612.08040] [INSPIRE].
T. Alanne, S. Blasi and F. Goertz, Common source for scalars: Flavored axion-Higgs unification, Phys. Rev. D 99 (2019) 015028 [arXiv:1807.10156] [INSPIRE].
Q. Bonnefoy, E. Dudas and S. Pokorski, Chiral Froggatt-Nielsen models, gauge anomalies and flavourful axions, JHEP 01 (2020) 191 [arXiv:1909.05336] [INSPIRE].
J. Martin Camalich, M. Pospelov, P.N.H. Vuong, R. Ziegler and J. Zupan, Quark Flavor Phenomenology of the QCD Axion, Phys. Rev. D 102 (2020) 015023 [arXiv:2002.04623] [INSPIRE].
M. Bauer, T. Schell and T. Plehn, Hunting the Flavon, Phys. Rev. D 94 (2016) 056003 [arXiv:1603.06950] [INSPIRE].
F. Giese and T. Konstandin, Vacuum stability of Froggatt-Nielsen models, JHEP 12 (2019) 091 [arXiv:1909.04067] [INSPIRE].
A. Falkowski, M. Nardecchia and R. Ziegler, Lepton Flavor Non-Universality in B-meson Decays from a U(2) Flavor Model, JHEP 11 (2015) 173 [arXiv:1509.01249] [INSPIRE].
R. Barbieri and R. Ziegler, Quark masses, CKM angles and Lepton Flavour Universality violation, JHEP 07 (2019) 023 [arXiv:1904.04121] [INSPIRE].
M. Bordone, O. Catà and T. Feldmann, Effective Theory Approach to New Physics with Flavour: General Framework and a Leptoquark Example, JHEP 01 (2020) 067 [arXiv:1910.02641] [INSPIRE].
D.E. Kaplan and R. Rattazzi, Large field excursions and approximate discrete symmetries from a clockwork axion, Phys. Rev. D 93 (2016) 085007 [arXiv:1511.01827] [INSPIRE].
G.F. Giudice and M. McCullough, A Clockwork Theory, JHEP 02 (2017) 036 [arXiv:1610.07962] [INSPIRE].
R. Alonso, A. Carmona, B.M. Dillon, J.F. Kamenik, J. Martin Camalich and J. Zupan, A clockwork solution to the flavor puzzle, JHEP 10 (2018) 099 [arXiv:1807.09792] [INSPIRE].
F. Sannino, J. Smirnov and Z.-W. Wang, Asymptotically safe clockwork mechanism, Phys. Rev. D 100 (2019) 075009 [arXiv:1902.05958] [INSPIRE].
A. Smolkovič, M. Tammaro and J. Zupan, Anomaly free Froggatt-Nielsen models of flavor, JHEP 10 (2019) 188 [arXiv:1907.10063] [INSPIRE].
M. Berkooz, Y. Nir and T. Volansky, Baryogenesis from the Kobayashi-Maskawa phase, Phys. Rev. Lett. 93 (2004) 051301 [hep-ph/0401012] [INSPIRE].
L. Calibbi, A. Crivellin and B. Zaldívar, Flavor portal to dark matter, Phys. Rev. D 92 (2015) 016004 [arXiv:1501.07268] [INSPIRE].
I. Baldes, T. Konstandin and G. Servant, A first-order electroweak phase transition from varying Yukawas, Phys. Lett. B 786 (2018) 373 [arXiv:1604.04526] [INSPIRE].
I. Baldes, T. Konstandin and G. Servant, Flavor Cosmology: Dynamical Yukawas in the Froggatt-Nielsen Mechanism, JHEP 12 (2016) 073 [arXiv:1608.03254] [INSPIRE].
B. Lillard, M. Ratz, T. Tait, M.P. and S. Trojanowski, The Flavor of Cosmology, JCAP 07 (2018) 056 [arXiv:1804.03662] [INSPIRE].
M.-C. Chen, S. Ipek and M. Ratz, Baryogenesis from Flavon Decays, Phys. Rev. D 100 (2019) 035011 [arXiv:1903.06211] [INSPIRE].
F. Elahi and S.R. Zadeh, Flavon magnetobaryogenesis, Phys. Rev. D 102 (2020) 096018 [arXiv:2008.04434] [INSPIRE].
J. Preskill, Gauge anomalies in an effective field theory, Annals Phys. 210 (1991) 323 [INSPIRE].
G. ’t Hooft, Symmetry Breaking Through Bell-Jackiw Anomalies, Phys. Rev. Lett. 37 (1976) 8 [INSPIRE].
E. Dudas, S. Pokorski and C.A. Savoy, Yukawa matrices from a spontaneously broken Abelian symmetry, Phys. Lett. B 356 (1995) 45 [hep-ph/9504292] [INSPIRE].
E. Dudas, C. Grojean, S. Pokorski and C.A. Savoy, Abelian flavor symmetries in supersymmetric models, Nucl. Phys. B 481 (1996) 85 [hep-ph/9606383] [INSPIRE].
A. Dery and Y. Nir, FN-2HDM: Two Higgs Doublet Models with Froggatt-Nielsen Symmetry, JHEP 04 (2017) 003 [arXiv:1612.05219] [INSPIRE].
L.J. Hall and A. Rasin, On the generality of certain predictions for quark mixing, Phys. Lett. B 315 (1993) 164 [hep-ph/9303303] [INSPIRE].
Y. Grossman and J.T. Ruderman, CKM substructure, JHEP 01 (2021) 143 [arXiv:2007.12695] [INSPIRE].
J. Charles et al., Current status of the Standard Model CKM fit and constraints on ∆F = 2 New Physics, Phys. Rev. D 91 (2015) 073007 [arXiv:1501.05013] [INSPIRE].
Utfit collaboration, Unitarity Triangle Analysis and D meson mixing in the Standard Model and Beyond, PoS(EPS-HEP2017)205.
Utfit collaboration, Fit results: Summer 2018, http://www.utfit.org/UTfit/ResultsSummer2018.
Particle Data Group collaboration, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
A. Rasin, Diagonalization of quark mass matrices and the Cabibbo-Kobayashi-Maskawa matrix, hep-ph/9708216 [INSPIRE].
H. Fritzsch and Z.-z. Xing, On the parametrization of flavor mixing in the standard model, Phys. Rev. D 57 (1998) 594 [hep-ph/9708366] [INSPIRE].
J.R. Ellis, K. Enqvist, D.V. Nanopoulos and F. Zwirner, Observables in Low-Energy Superstring Models, Mod. Phys. Lett. A 1 (1986) 57 [INSPIRE].
R. Barbieri and G.F. Giudice, Upper Bounds on Supersymmetric Particle Masses, Nucl. Phys. B 306 (1988) 63 [INSPIRE].
Z.-z. Xing, H. Zhang and S. Zhou, Impacts of the Higgs mass on vacuum stability, running fermion masses and two-body Higgs decays, Phys. Rev. D 86 (2012) 013013 [arXiv:1112.3112] [INSPIRE].
L.-L. Chau and W.-Y. Keung, Comments on the Parametrization of the Kobayashi-Maskawa Matrix, Phys. Rev. Lett. 53 (1984) 1802 [INSPIRE].
UTfit collaboration, Model-independent constraints on ∆F = 2 operators and the scale of new physics, JHEP 03 (2008) 049 [arXiv:0707.0636] [INSPIRE].
S. Antusch and V. Maurer, Running quark and lepton parameters at various scales, JHEP 11 (2013) 115 [arXiv:1306.6879] [INSPIRE].
G.-y. Huang and S. Zhou, Precise Values of Running Quark and Lepton Masses in the Standard Model, Phys. Rev. D 103 (2021) 016010 [arXiv:2009.04851] [INSPIRE].
D. Wales and J. Doye, Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms, J. Phys. Chem. A 101 (1997) 5111 [cond-mat/9803344].
F. James and M. Roos, Minuit: A System for Function Minimization and Analysis of the Parameter Errors and Correlations, Comput. Phys. Commun. 10 (1975) 343 [INSPIRE].
iminuit team, iminuit — a python interface to minuit, https://github.com/scikit-hep/iminuit.
A. Hocker and Z. Ligeti, CP violation and the CKM matrix, Ann. Rev. Nucl. Part. Sci. 56 (2006) 501 [hep-ph/0605217] [INSPIRE].
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Fedele, M., Mastroddi, A. & Valli, M. Minimal Froggatt-Nielsen textures. J. High Energ. Phys. 2021, 135 (2021). https://doi.org/10.1007/JHEP03(2021)135
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DOI: https://doi.org/10.1007/JHEP03(2021)135