Abstract
We study the axion field range and low energy couplings in models with Stückelberg mixing between axions and U(1) gauge bosons. It is noted that the gauge- invariant axion combination ξ in the model is periodic modulo an appropriate shift of gauge-variant axions eaten by the massive U(1) gauge bosons, which in some cases makes the connection between the field range and the low energy couplings less transparent. We derive the field range of ξ for generic forms of the axion kinetic metric and U(1) charges, and identify the field basis for which all non-derivative couplings of ξ are quantized in a manner manifestly consistent with the periodicity of ξ. Generically Stückelberg mixing reduces the axion field range. In particular, the mixings between N axions and (N − 1) U(1) gauge bosons typically result in an exponentially reduced field range \( {M}_{\xi }=\mathcal{O}\left({k}^{-\left(N-1\right)}f/\sqrt{N!}\right) \) for the residual gauge-invariant axion ξ in the limit N ≫ 1, where f and k denote the typical decay constant and the root mean square of the U(1) gauge charges of the original N axions. Using simple examples, we study also the reparameterization-invariant physical quantities such as the axion effective potential and 1PI couplings to gauge bosons, which are determined by the reparameterization-dependent axion couplings in the model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.E. Kim and G. Carosi, Axions and the strong CP problem, Rev. Mod. Phys.82 (2010) 557 [arXiv:0807.3125] [INSPIRE].
M. Kawasaki and K. Nakayama, Axions: theory and cosmological role, Ann. Rev. Nucl. Part. Sci.63 (2013) 69 [arXiv:1301.1123] [INSPIRE].
D.J.E. Marsh, Axion cosmology, Phys. Rept.643 (2016) 1 [arXiv:1510.07633] [INSPIRE].
K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation with pseudo-Nambu-Goldstone bosons, Phys. Rev. Lett.65 (1990) 3233 [INSPIRE].
K. Choi, String or M-theory axion as a quintessence, Phys. Rev.D 62 (2000) 043509 [hep-ph/9902292] [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].
E. Witten, Some properties of O(32) superstrings, Phys. Lett.B 149 (1984) 351 [INSPIRE].
K. Choi and J.E. Kim, Harmful axions in superstring models, Phys. Lett.B 154 (1985) 393 [Erratum ibid.B 156 (1985) 452] [INSPIRE].
K. Choi and J.E. Kim, Compactification and axions in E 8× \( {E}_8^{\prime } \)superstring models, Phys. Lett.B 165 (1985) 71 [INSPIRE].
P. Svrček and E. Witten, Axions in string theory, JHEP06 (2006) 051 [hep-th/0605206] [INSPIRE].
A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, String axiverse, Phys. Rev.D 81 (2010) 123530 [arXiv:0905.4720] [INSPIRE].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The string landscape, black holes and gravity as the weakest force, JHEP06 (2007) 060 [hep-th/0601001] [INSPIRE].
N. Arkani-Hamed, H.-C. Cheng, P. Creminelli and L. Randall, Extra natural inflation, Phys. Rev. Lett.90 (2003) 221302 [hep-th/0301218] [INSPIRE].
J.E. Kim, H.P. Nilles and M. Peloso, Completing natural inflation, JCAP01 (2005) 005 [hep-ph/0409138] [INSPIRE].
S. Dimopoulos, S. Kachru, J. McGreevy and J.G. Wacker, N -flation, JCAP08 (2008) 003 [hep-th/0507205] [INSPIRE].
E. Silverstein and A. Westphal, Monodromy in the CMB: gravity waves and string inflation, Phys. Rev.D 78 (2008) 106003 [arXiv:0803.3085] [INSPIRE].
N. Kaloper and L. Sorbo, A natural framework for chaotic inflation, Phys. Rev. Lett.102 (2009) 121301 [arXiv:0811.1989] [INSPIRE].
F. Marchesano, G. Shiu and A.M. Uranga, F-term axion monodromy inflation, JHEP09 (2014) 184 [arXiv:1404.3040] [INSPIRE].
K. Choi, H. Kim and S. Yun, Natural inflation with multiple sub-Planckian axions, Phys. Rev.D 90 (2014) 023545 [arXiv:1404.6209] [INSPIRE].
T. Higaki and F. Takahashi, Natural and multi-natural inflation in axion landscape, JHEP07 (2014) 074 [arXiv:1404.6923] [INSPIRE].
T.C. Bachlechner, M. Dias, J. Frazer and L. McAllister, Chaotic inflation with kinetic alignment of axion fields, Phys. Rev.D 91 (2015) 023520 [arXiv:1404.7496] [INSPIRE].
I. Ben-Dayan, F.G. Pedro and A. Westphal, Hierarchical axion inflation, Phys. Rev. Lett.113 (2014) 261301 [arXiv:1404.7773] [INSPIRE].
T. Rudelius, On the possibility of large axion moduli spaces, JCAP04 (2015) 049 [arXiv:1409.5793] [INSPIRE].
T.C. Bachlechner, C. Long and L. McAllister, Planckian axions in string theory, JHEP12 (2015) 042 [arXiv:1412.1093] [INSPIRE].
A. de la Fuente, P. Saraswat and R. Sundrum, Natural inflation and quantum gravity, Phys. Rev. Lett.114 (2015) 151303 [arXiv:1412.3457] [INSPIRE].
G. Shiu, W. Staessens and F. Ye, Widening the axion window via kinetic and Stückelberg mixings, Phys. Rev. Lett.115 (2015) 181601 [arXiv:1503.01015] [INSPIRE].
G. Shiu, W. Staessens and F. Ye, Large field inflation from axion mixing, JHEP06 (2015) 026 [arXiv:1503.02965] [INSPIRE].
M. Montero, A.M. Uranga and I. Valenzuela, Transplanckian axions!?, JHEP08 (2015) 032 [arXiv:1503.03886] [INSPIRE].
J. Brown, W. Cottrell, G. Shiu and P. Soler, Fencing in the swampland: quantum gravity constraints on large field inflation, JHEP10 (2015) 023 [arXiv:1503.04783] [INSPIRE].
A. Hebecker, P. Mangat, F. Rompineve and L.T. Witkowski, Winding out of the swamp: evading the weak gravity conjecture with F-term winding inflation?, Phys. Lett.B 748 (2015) 455 [arXiv:1503.07912] [INSPIRE].
D. Junghans, Large-field inflation with multiple axions and the weak gravity conjecture, JHEP02 (2016) 128 [arXiv:1504.03566] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Weak gravity strongly constrains large-field axion inflation, JHEP12 (2015) 108 [arXiv:1506.03447] [INSPIRE].
K. Choi and S.H. Im, Realizing the relaxion from multiple axions and its UV completion with high scale supersymmetry, JHEP01 (2016) 149 [arXiv:1511.00132] [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, JHEP02 (2017) 036 [arXiv:1610.07962] [INSPIRE].
T.C. Bachlechner, K. Eckerle, O. Janssen and M. Kleban, Multiple-axion framework, Phys. Rev.D 98 (2018) 061301 [arXiv:1703.00453] [INSPIRE].
T.C. Bachlechner, K. Eckerle, O. Janssen and M. Kleban, Systematics of aligned axions, JHEP11 (2017) 036 [arXiv:1709.01080] [INSPIRE].
G. Shiu and W. Staessens, Phases of inflation, JHEP10 (2018) 085 [arXiv:1807.00888] [INSPIRE].
N. Fonseca, B. von Harling, L. de Lima and C.S. Machado, Super-Planckian axions from near-conformality, Phys. Rev.D 100 (2019) 105019 [arXiv:1906.10193] [INSPIRE].
Q. Bonnefoy, E. Dudas and S. Pokorski, Axions in a highly protected gauge symmetry model, Eur. Phys. J.C 79 (2019) 31 [arXiv:1804.01112] [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: 1909.11685
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Choi, K., Shin, C.S. & Yun, S. Axion scales and couplings with Stückelberg mixing. J. High Energ. Phys. 2019, 33 (2019). https://doi.org/10.1007/JHEP12(2019)033
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2019)033