Abstract
The interpretation of Higgs data is typically based on different assumptions about whether there can be additional decay modes of the Higgs or if any couplings can be bounded by theoretical arguments. Going beyond these assumptions requires either a precision measurement of the Higgs width or an absolute measurement of a coupling to eliminate a flat direction in precision fits that occurs when \( \left|{g}_{hVV}/{g}_{hVV}^{SM}\right| \) > 1, where V = W±, Z. In this paper we explore how well a high energy muon collider can test Higgs physics without having to make assumptions on the total width of the Higgs. In particular, we investigate off-shell methods for Higgs production used at the LHC and searches for invisible decays of the Higgs to see how powerful they are at a muon collider. We then investigate the theoretical requirements on a model which can exist in such a flat direction. Combining expected Higgs precision with other constraints, the most dangerous flat direction is described by generalized Georgi-Machacek models. We find that by combining direct searches with Higgs precision, a high energy muon collider can robustly test single Higgs precision down to the \( \mathcal{O}\left(.1\%\right) \) level without having to assume SM Higgs decays. Furthermore, it allows one to bound new contributions to the width at the sub-percent level as well. Finally, we comment on how even in this difficult flat direction for Higgs precision, a muon collider can robustly test or discover new physics in multiple ways. Expanding beyond simple coupling modifiers/EFTs, there is a large region of parameter space that muon colliders can explore for EWSB that is not probed with only standard Higgs precision observables.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
H. Al Ali et al., The muon Smasher’s guide, Rept. Prog. Phys. 85 (2022) 084201 [arXiv:2103.14043] [INSPIRE].
C. Aime et al., Muon Collider Physics Summary, arXiv:2203.07256 [INSPIRE].
K.M. Black et al., Muon Collider Forum Report, arXiv:2209.01318 [INSPIRE].
D. Buttazzo, R. Franceschini and A. Wulzer, Two Paths Towards Precision at a Very High Energy Lepton Collider, JHEP 05 (2021) 219 [arXiv:2012.11555] [INSPIRE].
ILC International Development Team collaboration, The International Linear Collider: Report to Snowmass 2021, arXiv:2203.07622 [INSPIRE].
CEPC Physics Study Group collaboration, The physics potential of the CEPC. Prepared for the US Snowmass Community Planning Exercise (Snowmass 2021), in the proceedings of the Snowmass 2021, Seattle, U.S.A., July 17–26 (2022) [arXiv:2205.08553] [INSPIRE].
G. Bernardi et al., The Future Circular Collider: a Summary for the US 2021 Snowmass Process, arXiv:2203.06520 [INSPIRE].
M. Bai et al., C3: A “Cool” Route to the Higgs Boson and Beyond, in the proceedings of the Snowmass 2021, Seattle, U.S.A., July 17–26 (2022) [arXiv:2110.15800] [INSPIRE].
O. Brunner et al., The CLIC project, arXiv:2203.09186 [INSPIRE].
M. Benedikt et al., Future Circular Hadron Collider FCC-hh: Overview and Status, arXiv:2203.07804 [INSPIRE].
D. Buttazzo, D. Redigolo, F. Sala and A. Tesi, Fusing Vectors into Scalars at High Energy Lepton Colliders, JHEP 11 (2018) 144 [arXiv:1807.04743] [INSPIRE].
T. Han, Y. Ma and K. Xie, High energy leptonic collisions and electroweak parton distribution functions, Phys. Rev. D 103 (2021) L031301 [arXiv:2007.14300] [INSPIRE].
T. Han, Y. Ma and K. Xie, Quark and gluon contents of a lepton at high energies, JHEP 02 (2022) 154 [arXiv:2103.09844] [INSPIRE].
M. Forslund and P. Meade, High precision higgs from high energy muon colliders, JHEP 08 (2022) 185 [arXiv:2203.09425] [INSPIRE].
T. Han, D. Liu, I. Low and X. Wang, Electroweak couplings of the Higgs boson at a multi-TeV muon collider, Phys. Rev. D 103 (2021) 013002 [arXiv:2008.12204] [INSPIRE].
M. Chiesa et al., Measuring the quartic Higgs self-coupling at a multi-TeV muon collider, JHEP 09 (2020) 098 [arXiv:2003.13628] [INSPIRE].
LHC Higgs Cross Section Working Group collaboration, LHC HXSWG interim recommendations to explore the coupling structure of a Higgs-like particle, arXiv:1209.0040 [INSPIRE].
LHC Higgs Cross Section Working Group collaboration, Handbook of LHC Higgs Cross Sections: 3. Higgs Properties, arXiv:1307.1347 [https://doi.org/10.5170/CERN-2013-004] [INSPIRE].
J. de Blas et al., Higgs Boson Studies at Future Particle Colliders, JHEP 01 (2020) 139 [arXiv:1905.03764] [INSPIRE].
A. Azatov et al., Off-shell Higgs Interpretations Task Force: Models and Effective Field Theories Subgroup Report, arXiv:2203.02418 [https://doi.org/10.17181/LHCHWG-2022-001] [INSPIRE].
F. Caola and K. Melnikov, Constraining the Higgs boson width with ZZ production at the LHC, Phys. Rev. D 88 (2013) 054024 [arXiv:1307.4935] [INSPIRE].
J.M. Campbell, R.K. Ellis and C. Williams, Bounding the Higgs Width at the LHC Using Full Analytic Results for gg → e−e+μ−μ+, JHEP 04 (2014) 060 [arXiv:1311.3589] [INSPIRE].
ATLAS collaboration, Evidence of off-shell Higgs boson production from ZZ leptonic decay channels and constraints on its total width with the ATLAS detector, Phys. Lett. B 846 (2023) 138223 [arXiv:2304.01532] [INSPIRE].
CMS collaboration, Measurement of the Higgs boson width and evidence of its off-shell contributions to ZZ production, Nature Phys. 18 (2022) 1329 [arXiv:2202.06923] [INSPIRE].
S. Dawson et al., Report of the Topical Group on Higgs Physics for Snowmass 2021: The Case for Precision Higgs Physics, in the proceedings of the Snowmass 2021, Seattle, U.S.A., July 17–26 (2022) [arXiv:2209.07510] [INSPIRE].
J. Campbell, M. Carena, R. Harnik and Z. Liu, Interference in the gg → h → γγ On-Shell Rate and the Higgs Boson Total Width, Phys. Rev. Lett. 119 (2017) 181801 [Addendum ibid. 119 (2017) 199901] [arXiv:1704.08259] [INSPIRE].
F. An et al., Precision Higgs physics at the CEPC, Chin. Phys. C 43 (2019) 043002 [arXiv:1810.09037] [INSPIRE].
V.D. Barger, M.S. Berger, J.F. Gunion and T. Han, s channel Higgs boson production at a muon muon collider, Phys. Rev. Lett. 75 (1995) 1462 [hep-ph/9504330] [INSPIRE].
V.D. Barger, M.S. Berger, J.F. Gunion and T. Han, Higgs Boson physics in the s channel at μ+μ− colliders, Phys. Rept. 286 (1997) 1 [hep-ph/9602415] [INSPIRE].
T. Han and Z. Liu, Potential precision of a direct measurement of the Higgs boson total width at a muon collider, Phys. Rev. D 87 (2013) 033007 [arXiv:1210.7803] [INSPIRE].
J. de Blas, J. Gu and Z. Liu, Higgs boson precision measurements at a 125 GeV muon collider, Phys. Rev. D 106 (2022) 073007 [arXiv:2203.04324] [INSPIRE].
M. Chen and D. Liu, Top Yukawa Coupling at the Muon Collider, arXiv:2212.11067 [INSPIRE].
Z. Liu, K.-F. Lyu, I. Mahbub and L.-T. Wang, Top Yukawa Coupling Determination at High Energy Muon Collider, arXiv:2308.06323 [INSPIRE].
H.E. Logan, Hiding a Higgs width enhancement from off-shell gg(→ h*) → ZZ measurements, Phys. Rev. D 92 (2015) 075038 [arXiv:1412.7577] [INSPIRE].
H. Georgi and M. Machacek, Doubly charged Higgs bosons, Nucl. Phys. B 262 (1985) 463 [INSPIRE].
M.S. Chanowitz and M. Golden, Higgs Boson Triplets With MW = MZ cos θw, Phys. Lett. B 165 (1985) 105 [INSPIRE].
P. Galison, Large Weak Isospin and the W Mass, Nucl. Phys. B 232 (1984) 26 [INSPIRE].
R.W. Robinett, Extended strongly interacting Higgs theories, Phys. Rev. D 32 (1985) 1780 [INSPIRE].
H.E. Haber and H.E. Logan, Radiative corrections to the Z b anti-b vertex and constraints on extended Higgs sectors, Phys. Rev. D 62 (2000) 015011 [hep-ph/9909335] [INSPIRE].
S. Chang, C.A. Newby, N. Raj and C. Wanotayaroj, Revisiting Theories with Enhanced Higgs Couplings to Weak Gauge Bosons, Phys. Rev. D 86 (2012) 095015 [arXiv:1207.0493] [INSPIRE].
H.E. Logan and V. Rentala, All the generalized Georgi-Machacek models, Phys. Rev. D 92 (2015) 075011 [arXiv:1502.01275] [INSPIRE].
C.-W. Chiang and K. Yagyu, Models with higher weak-isospin Higgs multiplets, Phys. Lett. B 786 (2018) 268 [arXiv:1808.10152] [INSPIRE].
A. Kundu, P. Mondal and P.B. Pal, Custodial symmetry, the Georgi-Machacek model, and other scalar extensions, Phys. Rev. D 105 (2022) 115026 [arXiv:2111.14195] [INSPIRE].
J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].
R. Alonso, E.E. Jenkins and A.V. Manohar, Sigma Models with Negative Curvature, Phys. Lett. B 756 (2016) 358 [arXiv:1602.00706] [INSPIRE].
D. Liu, A. Pomarol, R. Rattazzi and F. Riva, Patterns of Strong Coupling for LHC Searches, JHEP 11 (2016) 141 [arXiv:1603.03064] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2022 (2022) 083C01 [INSPIRE].
J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson, The Higgs Hunter’s Guide, Front. Phys. 80 (2000) 1 [INSPIRE].
J. Hisano and K. Tsumura, Higgs boson mixes with an SU (2) septet representation, Phys. Rev. D 87 (2013) 053004 [arXiv:1301.6455] [INSPIRE].
S. Kanemura, M. Kikuchi and K. Yagyu, Probing exotic Higgs sectors from the precise measurement of Higgs boson couplings, Phys. Rev. D 88 (2013) 015020 [arXiv:1301.7303] [INSPIRE].
C. Alvarado, L. Lehman and B. Ostdiek, Surveying the Scope of the SU(2)L Scalar Septet Sector, JHEP 05 (2014) 150 [arXiv:1404.3208] [INSPIRE].
K. Hally, H.E. Logan and T. Pilkington, Constraints on large scalar multiplets from perturbative unitarity, Phys. Rev. D 85 (2012) 095017 [arXiv:1202.5073] [INSPIRE].
J.F. Gunion, R. Vega and J. Wudka, Naturalness problems for ρ = 1 and other large one loop effects for a standard model Higgs sector containing triplet fields, Phys. Rev. D 43 (1991) 2322 [INSPIRE].
S. Blasi, S. De Curtis and K. Yagyu, Effects of custodial symmetry breaking in the Georgi-Machacek model at high energies, Phys. Rev. D 96 (2017) 015001 [arXiv:1704.08512] [INSPIRE].
B. Keeshan, H.E. Logan and T. Pilkington, Custodial symmetry violation in the Georgi-Machacek model, Phys. Rev. D 102 (2020) 015001 [arXiv:1807.11511] [INSPIRE].
J.F. Gunion, R. Vega and J. Wudka, Higgs triplets in the standard model, Phys. Rev. D 42 (1990) 1673 [INSPIRE].
M. Aoki and S. Kanemura, Unitarity bounds in the Higgs model including triplet fields with custodial symmetry, Phys. Rev. D 77 (2008) 095009 [Erratum ibid. 89 (2014) 059902] [arXiv:0712.4053] [INSPIRE].
S. Godfrey and K. Moats, Exploring Higgs Triplet Models via Vector Boson Scattering at the LHC, Phys. Rev. D 81 (2010) 075026 [arXiv:1003.3033] [INSPIRE].
H.E. Logan and M.-A. Roy, Higgs couplings in a model with triplets, Phys. Rev. D 82 (2010) 115011 [arXiv:1008.4869] [INSPIRE].
I. Low and J. Lykken, Revealing the Electroweak Properties of a New Scalar Resonance, JHEP 10 (2010) 053 [arXiv:1005.0872] [INSPIRE].
I. Low, J. Lykken and G. Shaughnessy, Have We Observed the Higgs (Imposter)?, Phys. Rev. D 86 (2012) 093012 [arXiv:1207.1093] [INSPIRE].
C.-W. Chiang and K. Yagyu, Testing the custodial symmetry in the Higgs sector of the Georgi-Machacek model, JHEP 01 (2013) 026 [arXiv:1211.2658] [INSPIRE].
A. Falkowski, S. Rychkov and A. Urbano, What if the Higgs couplings to W and Z bosons are larger than in the Standard Model?, JHEP 04 (2012) 073 [arXiv:1202.1532] [INSPIRE].
R. Killick, K. Kumar and H.E. Logan, Learning what the Higgs boson is mixed with, Phys. Rev. D 88 (2013) 033015 [arXiv:1305.7236] [INSPIRE].
C. Englert, E. Re and M. Spannowsky, Triplet Higgs boson collider phenomenology after the LHC, Phys. Rev. D 87 (2013) 095014 [arXiv:1302.6505] [INSPIRE].
C. Englert, E. Re and M. Spannowsky, Pinning down Higgs triplets at the LHC, Phys. Rev. D 88 (2013) 035024 [arXiv:1306.6228] [INSPIRE].
K. Hartling, K. Kumar and H.E. Logan, The decoupling limit in the Georgi-Machacek model, Phys. Rev. D 90 (2014) 015007 [arXiv:1404.2640] [INSPIRE].
C.-W. Chiang and T. Yamada, Electroweak phase transition in Georgi-Machacek model, Phys. Lett. B 735 (2014) 295 [arXiv:1404.5182] [INSPIRE].
C.-W. Chiang, S. Kanemura and K. Yagyu, Novel constraint on the parameter space of the Georgi-Machacek model with current LHC data, Phys. Rev. D 90 (2014) 115025 [arXiv:1407.5053] [INSPIRE].
S.I. Godunov, M.I. Vysotsky and E.V. Zhemchugov, Double Higgs production at LHC, see-saw type II and Georgi-Machacek model, J. Exp. Theor. Phys. 120 (2015) 369 [arXiv:1408.0184] [INSPIRE].
K. Hartling, K. Kumar and H.E. Logan, Indirect constraints on the Georgi-Machacek model and implications for Higgs boson couplings, Phys. Rev. D 91 (2015) 015013 [arXiv:1410.5538] [INSPIRE].
K. Hartling, K. Kumar and H.E. Logan, GMCALC: a calculator for the Georgi-Machacek model, arXiv:1412.7387 [INSPIRE].
C.-W. Chiang and K. Tsumura, Properties and searches of the exotic neutral Higgs bosons in the Georgi-Machacek model, JHEP 04 (2015) 113 [arXiv:1501.04257] [INSPIRE].
C.-W. Chiang, S. Kanemura and K. Yagyu, Phenomenology of the Georgi-Machacek model at future electron-positron colliders, Phys. Rev. D 93 (2016) 055002 [arXiv:1510.06297] [INSPIRE].
C.-W. Chiang, A.-L. Kuo and T. Yamada, Searches of exotic Higgs bosons in general mass spectra of the Georgi-Machacek model at the LHC, JHEP 01 (2016) 120 [arXiv:1511.00865] [INSPIRE].
C. Degrande, K. Hartling and H.E. Logan, Scalar decays to γγ, Zγ, and Wγ in the Georgi-Machacek model, Phys. Rev. D 96 (2017) 075013 [Erratum ibid. 98 (2018) 019901] [arXiv:1708.08753] [INSPIRE].
D. Das and I. Saha, Cornering variants of the Georgi-Machacek model using Higgs precision data, Phys. Rev. D 98 (2018) 095010 [arXiv:1811.00979] [INSPIRE].
N. Ghosh, S. Ghosh and I. Saha, Charged Higgs boson searches in the Georgi-Machacek model at the LHC, Phys. Rev. D 101 (2020) 015029 [arXiv:1908.00396] [INSPIRE].
A. Ismail, H.E. Logan and Y. Wu, Updated constraints on the Georgi-Machacek model from LHC Run 2, arXiv:2003.02272 [INSPIRE].
C. Wang et al., Search for a lighter neutral custodial fiveplet scalar in the Georgi-Machacek model, Chin. Phys. C 46 (2022) 083107 [arXiv:2204.09198] [INSPIRE].
Z. Bairi and A. Ahriche, More constraints on the Georgi-Machacek model, Phys. Rev. D 108 (2023) 055028 [arXiv:2207.00142] [INSPIRE].
C.H. de Lima and H.E. Logan, Unavoidable Higgs coupling deviations in the Z2-symmetric Georgi-Machacek model, Phys. Rev. D 106 (2022) 115020 [arXiv:2209.08393] [INSPIRE].
M. Chakraborti et al., New physics implications of vector boson fusion searches exemplified through the Georgi-Machacek model, Phys. Rev. D 109 (2024) 015016 [arXiv:2308.02384] [INSPIRE].
T. Corbett, A. Joglekar, H.-L. Li and J.-H. Yu, Exploring Extended Scalar Sectors with Di-Higgs Signals: A Higgs EFT Perspective, JHEP 05 (2018) 061 [arXiv:1705.02551] [INSPIRE].
Anisha et al., Effective limits on single scalar extensions in the light of recent LHC data, Phys. Rev. D 107 (2023) 055028 [arXiv:2111.05876] [INSPIRE].
A. Ismail, B. Keeshan, H.E. Logan and Y. Wu, Benchmark for LHC searches for low-mass custodial fiveplet scalars in the Georgi-Machacek model, Phys. Rev. D 103 (2021) 095010 [arXiv:2003.05536] [INSPIRE].
ATLAS collaboration, Search for doubly and singly charged Higgs bosons decaying into vector bosons in multi-lepton final states with the ATLAS detector using proton-proton collisions at \( \sqrt{s} \) = 13 TeV, JHEP 06 (2021) 146 [arXiv:2101.11961] [INSPIRE].
ATLAS collaboration, Search for supersymmetry in events with four or more charged leptons in 139 fb−1 of \( \sqrt{s} \) = 13 TeV pp collisions with the ATLAS detector, JHEP 07 (2021) 167 [arXiv:2103.11684] [INSPIRE].
NNPDF collaboration, Parton distributions with QED corrections, Nucl. Phys. B 877 (2013) 290 [arXiv:1308.0598] [INSPIRE].
D. Rainwater and T.M.P. Tait, Testing Grand Unification at the (S)LHC, Phys. Rev. D 75 (2007) 115014 [hep-ph/0701093] [INSPIRE].
D.S.M. Alves, J. Galloway, J.T. Ruderman and J.R. Walsh, Running Electroweak Couplings as a Probe of New Physics, JHEP 02 (2015) 007 [arXiv:1410.6810] [INSPIRE].
C. Gross, O. Lebedev and J.M. No, Drell–Yan constraints on new electroweak states: LHC as a pp → l+l− precision machine, Mod. Phys. Lett. A 32 (2017) 1750094 [arXiv:1602.03877] [INSPIRE].
L. Di Luzio, R. Gröber and G. Panico, Probing new electroweak states via precision measurements at the LHC and future colliders, JHEP 01 (2019) 011 [arXiv:1810.10993] [INSPIRE].
G. Durieux et al., Charting the Higgs self-coupling boundaries, JHEP 12 (2022) 148 [Erratum ibid. 02 (2023) 165] [arXiv:2209.00666] [INSPIRE].
T. Han, Z. Liu, L.-T. Wang and X. Wang, WIMP Dark Matter at High Energy Muon Colliders A White Paper for Snowmass 2021, in the proceedings of the Snowmass 2021, Seattle, U.S.A., July 17–26 (2022) [arXiv:2203.07351] [INSPIRE].
K. Earl, K. Hartling, H.E. Logan and T. Pilkington, Constraining models with a large scalar multiplet, Phys. Rev. D 88 (2013) 015002 [arXiv:1303.1244] [INSPIRE].
M. Cepeda, S. Gori, V.M. Outschoorn and J. Shelton, Exotic Higgs Decays, arXiv:2111.12751 [https://doi.org/10.1146/annurev-nucl-102319-024147] [INSPIRE].
M. Ruhdorfer, E. Salvioni and A. Wulzer, Invisible Higgs boson decay from forward muons at a muon collider, Phys. Rev. D 107 (2023) 095038 [arXiv:2303.14202] [INSPIRE].
M. Cepeda et al., Report from Working Group 2: Higgs Physics at the HL-LHC and HE-LHC, CERN Yellow Rep. Monogr. 7 (2019) 221 [arXiv:1902.00134] [INSPIRE].
M. Narain et al., The Future of US Particle Physics - The Snowmass 2021 Energy Frontier Report, arXiv:2211.11084 [INSPIRE].
T. Sjöstrand et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
F. Garosi, D. Marzocca and S. Trifinopoulos, LePDF: Standard Model PDFs for high-energy lepton colliders, JHEP 09 (2023) 107 [arXiv:2303.16964] [INSPIRE].
DELPHES 3 collaboration, DELPHES 3, A modular framework for fast simulation of a generic collider experiment, JHEP 02 (2014) 057 [arXiv:1307.6346] [INSPIRE].
G.W. Foster and N.V. Mokhov, Backgrounds and detector performance at a 2 × 2 TeV μ+μ− collider, AIP Conf. Proc. 352 (1996) 178 [INSPIRE].
N. Bartosik et al., Preliminary Report on the Study of Beam-Induced Background Effects at a Muon Collider, arXiv:1905.03725 [INSPIRE].
N.V. Mokhov et al., Muon Collider Interaction Region and Machine-Detector Interface Design, Conf. Proc. C 110328 (2011) 82 [arXiv:1202.3979] [INSPIRE].
M. Boronat et al., A robust jet reconstruction algorithm for high-energy lepton colliders, Phys. Lett. B 750 (2015) 95 [arXiv:1404.4294] [INSPIRE].
M. Boronat et al., Jet reconstruction at high-energy electron–positron colliders, Eur. Phys. J. C 78 (2018) 144 [arXiv:1607.05039] [INSPIRE].
J. De Blas et al., HEPfit: a code for the combination of indirect and direct constraints on high energy physics models, Eur. Phys. J. C 80 (2020) 456 [arXiv:1910.14012] [INSPIRE].
Acknowledgments
We would like to thank Dimitrios Athanasakos, Luca Giambastiani, Simone Pagan Griso, Samuel Homiller, Sergo Jindariani, Zhen Liu, Donatella Lucchesi, Federico Meloni, Lorenzo Sestini, and Mauro Valli for useful conversations and details that allowed this study to be completed. This work was supported by the National Science Foundation grant PHY-2210533. PM would also like to acknowledge the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-2210452 where this work was completed.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2308.02633
Rights and permissions
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.
About this article
Cite this article
Forslund, M., Meade, P. Precision Higgs width and couplings with a high energy muon collider. J. High Energ. Phys. 2024, 182 (2024). https://doi.org/10.1007/JHEP01(2024)182
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2024)182