Abstract
We compute the renormalization group equations (RGEs) of the Standard Model effective field theory (EFT) extended with a real scalar singlet, up to dimension-five and one-loop accuracy. We compare our renormalization results with those found in the shift-symmetry preserving limit, which characterizes axion-like particles (ALPs). The matching and running equations below the electroweak scale are also obtained, including the mixing effects in the scalar sector. Such mixing leads to interesting phenomenological consequences that are absent in the EFT at the renormalizable level, namely new correlations among the triplet and quartic Higgs couplings are predicted. All RGEs obtained in this work are implemented in a new Mathematica package — ALPRunner, together with functions to solve the running numerically for an arbitrary set of UV parameters. As an application, we obtain electric dipole moment constraints on particular regions of the singlet parameter space, and quantify the level of shift-breaking in these regions.
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M. Bauer, M. Neubert and A. Thamm, Collider probes of axion-like particles, JHEP 12 (2017) 044 [arXiv:1708.00443] [INSPIRE].
D.B. Kaplan and H. Georgi, SU(2) × U(1) breaking by vacuum misalignment, Phys. Lett. B 136 (1984) 183 [INSPIRE].
D.B. Kaplan, H. Georgi and S. Dimopoulos, Composite Higgs scalars, Phys. Lett. B 136 (1984) 187 [INSPIRE].
B. Gripaios, A. Pomarol, F. Riva and J. Serra, Beyond the minimal composite Higgs model, JHEP 04 (2009) 070 [arXiv:0902.1483] [INSPIRE].
M. Chala, h → γγ excess and dark matter from composite Higgs models, JHEP 01 (2013) 122 [arXiv:1210.6208] [INSPIRE].
L. Vecchi, The natural composite Higgs, arXiv:1304.4579 [INSPIRE].
B. Bellazzini, C. Csáki and J. Serra, Composite Higgses, Eur. Phys. J. C 74 (2014) 2766 [arXiv:1401.2457] [INSPIRE].
G. Cacciapaglia, G. Ferretti, T. Flacke and H. Serôdio, Light scalars in composite Higgs models, Front. in Phys. 7 (2019) 22 [arXiv:1902.06890] [INSPIRE].
J. McDonald, Gauge singlet scalars as cold dark matter, Phys. Rev. D 50 (1994) 3637 [hep-ph/0702143] [INSPIRE].
C.P. Burgess, M. Pospelov and T. ter Veldhuis, The minimal model of nonbaryonic dark matter: a singlet scalar, Nucl. Phys. B 619 (2001) 709 [hep-ph/0011335] [INSPIRE].
G. Arcadi, A. Djouadi and M. Raidal, Dark matter through the Higgs portal, Phys. Rept. 842 (2020) 1 [arXiv:1903.03616] [INSPIRE].
S. Profumo, M.J. Ramsey-Musolf and G. Shaughnessy, Singlet Higgs phenomenology and the electroweak phase transition, JHEP 08 (2007) 010 [arXiv:0705.2425] [INSPIRE].
J.R. Espinosa, B. Gripaios, T. Konstandin and F. Riva, Electroweak baryogenesis in non-minimal composite Higgs models, JCAP 01 (2012) 012 [arXiv:1110.2876] [INSPIRE].
M. Chala, G. Nardini and I. Sobolev, Unified explanation for dark matter and electroweak baryogenesis with direct detection and gravitational wave signatures, Phys. Rev. D 94 (2016) 055006 [arXiv:1605.08663] [INSPIRE].
J. Ellis et al., The scalar singlet extension of the standard model: gravitational waves versus baryogenesis, JHEP 01 (2023) 093 [arXiv:2210.16305] [INSPIRE].
E. Witten, Some properties of O(32) superstrings, Phys. Lett. B 149 (1984) 351 [INSPIRE].
T. Banks and M. Dine, Couplings and scales in strongly coupled heterotic string theory, Nucl. Phys. B 479 (1996) 173 [hep-th/9605136] [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].
R.D. Peccei and H.R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38 (1977) 1440 [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].
M. Chala, G. Guedes, M. Ramos and J. Santiago, Running in the ALPs, Eur. Phys. J. C 81 (2021) 181 [arXiv:2012.09017] [INSPIRE].
M. Bauer et al., The low-energy effective theory of axions and ALPs, JHEP 04 (2021) 063 [arXiv:2012.12272] [INSPIRE].
J. Bonilla, I. Brivio, M.B. Gavela and V. Sanz, One-loop corrections to ALP couplings, JHEP 11 (2021) 168 [arXiv:2107.11392] [INSPIRE].
Q. Bonnefoy, C. Grojean and J. Kley, Shift-invariant orders of an axionlike particle, Phys. Rev. Lett. 130 (2023) 111803 [arXiv:2206.04182] [INSPIRE].
S. Das Bakshi, J. Machado and M. Ramos., ALPRunner GitHub repository, https://github.com/sdbakshi13/ALPRunner.
D. O’Connell, M.J. Ramsey-Musolf and M.B. Wise, Minimal extension of the standard model scalar sector, Phys. Rev. D 75 (2007) 037701 [hep-ph/0611014] [INSPIRE].
V. Barger et al., LHC phenomenology of an extended standard model with a real scalar singlet, Phys. Rev. D 77 (2008) 035005 [arXiv:0706.4311] [INSPIRE].
B. Gripaios and D. Sutherland, An operator basis for the standard model with an added scalar singlet, JHEP 08 (2016) 103 [arXiv:1604.07365] [INSPIRE].
H. Georgi, D.B. Kaplan and L. Randall, Manifesting the invisible axion at low-energies, Phys. Lett. B 169 (1986) 73 [INSPIRE].
P. Agrawal et al., Some open questions in axion theory, in the proceedings of the Snowmass 2021, (2022) [arXiv:2203.08026] [INSPIRE].
K. Fraser and M. Reece, Axion periodicity and coupling quantization in the presence of mixing, JHEP 05 (2020) 066 [arXiv:1910.11349] [INSPIRE].
I. Brivio et al., ALPs effective field theory and collider signatures, Eur. Phys. J. C 77 (2017) 572 [arXiv:1701.05379] [INSPIRE].
A. Alloul et al., FeynRules 2.0 — a complete toolbox for tree-level phenomenology, Comput. Phys. Commun. 185 (2014) 2250 [arXiv:1310.1921] [INSPIRE].
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
T. Hahn, S. Paßehr and C. Schappacher, FormCalc 9 and extensions, PoS LL2016 (2016) 068 [arXiv:1604.04611] [INSPIRE].
A. Carmona, A. Lazopoulos, P. Olgoso and J. Santiago, Matchmakereft: automated tree-level and one-loop matching, SciPost Phys. 12 (2022) 198 [arXiv:2112.10787] [INSPIRE].
L.F. Abbott, Introduction to the background field method, Acta Phys. Polon. B 13 (1982) 33 [INSPIRE].
B.M. Gavela, E.E. Jenkins, A.V. Manohar and L. Merlo, Analysis of general power counting rules in effective field theory, Eur. Phys. J. C 76 (2016) 485 [arXiv:1601.07551] [INSPIRE].
C. Grojean, E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group scaling of Higgs operators and Γ(h → γγ), JHEP 04 (2013) 016 [arXiv:1301.2588] [INSPIRE].
A. Beniwal, M. Lewicki, M. White and A.G. Williams, Gravitational waves and electroweak baryogenesis in a global study of the extended scalar singlet model, JHEP 02 (2019) 183 [arXiv:1810.02380] [INSPIRE].
M. Aiko and M. Endo, Electroweak precision test of axion-like particles, JHEP 05 (2023) 147 [arXiv:2302.11377] [INSPIRE].
J. Bonilla et al., The cost of an ALP solution to the neutral B-anomalies, JHEP 02 (2023) 138 [arXiv:2209.11247] [INSPIRE].
P. Langacker, Grand unified theories and proton decay, Phys. Rept. 72 (1981) 185 [INSPIRE].
L. Di Luzio, R. Gröber and P. Paradisi, Hunting for CP-violating axionlike particle interactions, Phys. Rev. D 104 (2021) 095027 [arXiv:2010.13760] [INSPIRE].
W. Dekens et al., Unraveling models of CP violation through electric dipole moments of light nuclei, JHEP 07 (2014) 069 [arXiv:1404.6082] [INSPIRE].
Particle Data Group collaboration, Review of particle physics, PTEP 2022 (2022) 083C01 [INSPIRE].
ACME collaboration, Improved limit on the electric dipole moment of the electron, Nature 562 (2018) 355 [INSPIRE].
B. Graner, Y. Chen, E.G. Lindahl and B.R. Heckel, Reduced limit on the permanent electric dipole moment of 199Hg, Phys. Rev. Lett. 116 (2016) 161601 [Erratum ibid. 119 (2017) 119901] [arXiv:1601.04339] [INSPIRE].
Q. Bonnefoy, E. Gendy, C. Grojean and J.T. Ruderman, Opportunistic CP violation, JHEP 06 (2023) 141 [arXiv:2302.07288] [INSPIRE].
R.K. Ellis et al., Physics briefing book: input for the European strategy for particle physics update 2020, arXiv:1910.11775 [INSPIRE].
S. Das Bakshi, J. Chakrabortty and S.K. Patra, CoDEx: Wilson coefficient calculator connecting SMEFT to UV theory, Eur. Phys. J. C 79 (2019) 21 [arXiv:1808.04403] [INSPIRE].
Acknowledgments
We are grateful to Quentin Bonnefoy, Mikael Chala, Víctor Enguita, Renato Fonseca, Belén Gavela, Jonathan Kley, Javier Fuentes-Martín, Luca Merlo and Jorge Fernández de Trocóniz for illuminating discussions, and José Santiago and Pablo Olgoso for helping with matchmakereft [37]. We thank Luca Di Luzio and Paride Paradisi for pointing out a misunderstanding in the computation of the EDM contributions. We thank Anisha and Guilherme Guedes for comments on the manuscript, and Sunando Patra for suggestions on Mathematica utilities, and functions imported (and modified) from CoDEx [52]. The work of M. R. is supported by the Marie Sklodowska-Curie grant agreement No 860881-HIDDeN. The work of J.M.R. is supported by the Spanish MICIU through the National Program FPI-Severo Ochoa (grant number PRE2019-089233). S.D.B. acknowledges financial support from the Spanish Research Agency (Agencia Estatal de Investigación) under the grants No. PID2019-106087GB-C21/10.13039/501100011033 and PID2021-128396NB-100/AEI/10.13039/501100011-033; by the Junta de Andalucía (Spain) under the grants No FQM- 101, A-FQM-467-UGR18 and P18-FR-4314 (FEDER). J.M.R. acknowledges partial financial support from the Spanish Research Agency through the grants IFT Centro de excelencia Severo Ochoa Program No CEX2020-001007-S and PID2019-108892RB-I00, funded by MCIN/AEI/10.13039/50110001103. The logo of ALPRunner was inspired by output from DALL.E 2 of OpenAI.
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Bakshi, S.D., Machado-Rodríguez, J. & Ramos, M. Running beyond ALPs: shift-breaking and CP-violating effects. J. High Energ. Phys. 2023, 133 (2023). https://doi.org/10.1007/JHEP11(2023)133
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DOI: https://doi.org/10.1007/JHEP11(2023)133