Abstract
We calculate the coupling between a vector resonance and two Goldstone bosons in SU(2) gauge theory with Nf = 2 Dirac fermions in the fundamental representation. The considered theory can be used to construct a minimal Composite Higgs models. The coupling is related to the width of the vector resonance and we determine it by simulating the scattering of two Goldstone bosons where the resonance is produced. The resulting coupling is gVPP = 7.8 ± 0.6, not far from gρππ ≃ 6 in QCD. This is the first lattice calculation of the resonance properties for a minimal UV completion. This coupling controls the production cross section of the lightest expected resonance at the LHC and enters into other tests of the Standard Model, from Vector Boson Fusion to electroweak precision tests. Our prediction is crucial to constrain the model using lattice input and for understanding the behavior of the vector meson production cross section as a function of the underlying gauge theory. We also extract the coupling \( {g}_{\mathrm{VPP}}^{\mathrm{KSRF}} \) = 9.4 ± 0.6 assuming the vector-dominance and find that this phenomenological estimate slightly overestimates the value of the coupling.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
M. J. Dugan, H. Georgi and D. B. Kaplan, Anatomy of a composite Higgs model, Nucl. Phys. B 254 (1985) 299 [INSPIRE].
R. Contino and M. Salvarezza, One-loop effects from spin-1 resonances in composite Higgs models, JHEP 07 (2015) 065 [arXiv:1504.02750] [INSPIRE].
R. Contino, D. Marzocca, D. Pappadopulo and R. Rattazzi, On the effect of resonances in composite Higgs phenomenology, JHEP 10 (2011) 081 [arXiv:1109.1570] [INSPIRE].
M. Gallinaro et al., Beyond the Standard Model in vector boson scattering signatures, in International workshop on BSM models in vector boson scattering processes, (2020) [arXiv:2005.09889] [INSPIRE].
D. Liu, L.-T. Wang and K.-P. Xie, Broad composite resonances and their signals at the LHC, Phys. Rev. D 100 (2019) 075021 [arXiv:1901.01674] [INSPIRE].
C. Helsens, D. Jamin, M. L. Mangano, T. G. Rizzo and M. Selvaggi, Heavy resonances at energy-frontier hadron colliders, Eur. Phys. J. C 79 (2019) 569 [arXiv:1902.11217] [INSPIRE].
D. Buarque Franzosi, G. Cacciapaglia and A. Deandrea, Sigma-assisted low scale composite Goldstone-Higgs, Eur. Phys. J. C 80 (2020) 28 [arXiv:1809.09146] [INSPIRE].
D. Liu, L.-T. Wang and K.-P. Xie, Prospects of searching for composite resonances at the LHC and beyond, JHEP 01 (2019) 157 [arXiv:1810.08954] [INSPIRE].
D. Buarque Franzosi, Implications of vector boson scattering unitarity in composite Higgs models, PoS(EPS-HEP2017)264 (2017).
D. Greco and D. Liu, Hunting composite vector resonances at the LHC: naturalness facing data, JHEP 12 (2014) 126 [arXiv:1410.2883] [INSPIRE].
G. Cacciapaglia and F. Sannino, Fundamental composite (Goldstone) Higgs dynamics, JHEP 04 (2014) 111 [arXiv:1402.0233] [INSPIRE].
G. Cacciapaglia, C. Pica and F. Sannino, Fundamental composite dynamics: a review, Phys. Rept. 877 (2020) 1 [arXiv:2002.04914] [INSPIRE].
A. Arbey, G. Cacciapaglia, H. Cai, A. Deandrea, S. Le Corre and F. Sannino, Fundamental composite electroweak dynamics: status at the LHC, Phys. Rev. D 95 (2017) 015028 [arXiv:1502.04718] [INSPIRE].
D. Buarque Franzosi, G. Cacciapaglia, H. Cai, A. Deandrea and M. Frandsen, Vector and axial-vector resonances in composite models of the Higgs boson, JHEP 11 (2016) 076 [arXiv:1605.01363] [INSPIRE].
M. Lüscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B 354 (1991) 531 [INSPIRE].
K. Rummukainen and S. A. Gottlieb, Resonance scattering phase shifts on a nonrest frame lattice, Nucl. Phys. B 450 (1995) 397 [hep-lat/9503028] [INSPIRE].
CP-PACS collaboration, Lattice QCD calculation of the ρ meson decay width, Phys. Rev. D 76 (2007) 094506 [arXiv:0708.3705] [INSPIRE].
CS collaboration, ρ meson decay in 2 + 1 flavor lattice QCD, Phys. Rev. D 84 (2011) 094505 [arXiv:1106.5365] [INSPIRE].
X. Feng, K. Jansen and D. B. Renner, Resonance parameters of the ρ-meson from lattice QCD, Phys. Rev. D 83 (2011) 094505 [arXiv:1011.5288] [INSPIRE].
C. B. Lang, D. Mohler, S. Prelovsek and M. Vidmar, Coupled channel analysis of the ρ meson decay in lattice QCD, Phys. Rev. D 84 (2011) 054503 [Erratum ibid. 89 (2014) 059903] [arXiv:1105.5636] [INSPIRE].
Hadron Spectrum collaboration, Energy dependence of the ρ resonance in ππ elastic scattering from lattice QCD, Phys. Rev. D 87 (2013) 034505 [Erratum ibid. 90 (2014) 099902] [arXiv:1212.0830] [INSPIRE].
F. Erben, J. R. Green, D. Mohler and H. Wittig, Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarization, Phys. Rev. D 101 (2020) 054504 [arXiv:1910.01083] [INSPIRE].
C. Alexandrou et al., P -wave ππ scattering and the ρ resonance from lattice QCD, Phys. Rev. D 96 (2017) 034525 [arXiv:1704.05439] [INSPIRE].
R. Arthur, V. Drach, M. Hansen, A. Hietanen, C. Pica and F. Sannino, SU(2) gauge theory with two fundamental flavors: a minimal template for model building, Phys. Rev. D 94 (2016) 094507 [arXiv:1602.06559] [INSPIRE].
R. Arthur, V. Drach, A. Hietanen, C. Pica and F. Sannino, SU(2) gauge theory with two fundamental flavours: scalar and pseudoscalar spectrum, arXiv:1607.06654 [INSPIRE].
R. Arthur, V. Drach, M. Hansen, A. Hietanen, C. Pica and F. Sannino, Scattering lengths in SU(2) gauge theory with two fundamental fermions, PoS(LATTICE2014)271 (2014) [arXiv:1412.4771] [INSPIRE].
V. Drach, A. Hietanen, C. Pica, J. Rantaharju and F. Sannino, Template composite dark matter: SU(2) gauge theory with 2 fundamental flavours, PoS(LATTICE2015)234 (2016) [arXiv:1511.04370] [INSPIRE].
A. Hietanen, R. Lewis, C. Pica and F. Sannino, Fundamental composite Higgs dynamics on the lattice: SU(2) with two flavors, JHEP 07 (2014) 116 [arXiv:1404.2794] [INSPIRE].
A. Hietanen, R. Lewis, C. Pica and F. Sannino, Composite Goldstone dark matter: experimental predictions from the lattice, JHEP 12 (2014) 130 [arXiv:1308.4130] [INSPIRE].
K. Kawarabayashi and M. Suzuki, Partially conserved axial vector current and the decays of vector mesons, Phys. Rev. Lett. 16 (1966) 255 [INSPIRE].
Riazuddin and Fayyazuddin, Algebra of current components and decay widths of ρ and K∗ mesons, Phys. Rev. 147 (1966) 1071 [INSPIRE].
D. Nogradi and L. Szikszai, The model dependence of mϱ/fπ, PoS(LATTICE2019)237 (2019) [arXiv:1912.04114] [INSPIRE].
D. Nogradi and L. Szikszai, The flavor dependence of mϱ/fπ, JHEP 05 (2019) 197 [arXiv:1905.01909] [INSPIRE].
E. Bennett et al., Sp(4) gauge theories on the lattice: quenched fundamental and antisymmetric fermions, Phys. Rev. D 101 (2020) 074516 [arXiv:1912.06505] [INSPIRE].
E. Bennett et al., Sp(4) gauge theories on the lattice: Nf = 2 dynamical fundamental fermions, JHEP 12 (2019) 053 [arXiv:1909.12662] [INSPIRE].
V. Ayyar et al., Spectroscopy of SU(4) composite Higgs theory with two distinct fermion representations, Phys. Rev. D 97 (2018) 074505 [arXiv:1710.00806] [INSPIRE].
Lattice Strong Dynamics collaboration, Nonperturbative investigations of SU(3) gauge theory with eight dynamical flavors, Phys. Rev. D 99 (2019) 014509 [arXiv:1807.08411] [INSPIRE].
K. G. Wilson, Confinement of quarks, Phys. Rev. D 10 (1974) 2445 [INSPIRE].
B. Sheikholeslami and R. Wohlert, Improved continuum limit lattice action for QCD with Wilson fermions, Nucl. Phys. B 259 (1985) 572 [INSPIRE].
M. Lüscher and P. Weisz, On-shell improved lattice gauge theories, Commun. Math. Phys. 97 (1985) 59 [Erratum ibid. 98 (1985) 433] [INSPIRE].
S. Borsányi et al., High-precision scale setting in lattice QCD, JHEP 09 (2012) 010 [arXiv:1203.4469] [INSPIRE].
O. Bär and M. Golterman, Chiral perturbation theory for gradient flow observables, Phys. Rev. D 89 (2014) 034505 [Erratum ibid. 89 (2014) 099905] [arXiv:1312.4999] [INSPIRE].
G. Martinelli, C. Pittori, C. T. Sachrajda, M. Testa and A. Vladikas, A general method for nonperturbative renormalization of lattice operators, Nucl. Phys. B 445 (1995) 81 [hep-lat/9411010] [INSPIRE].
M. Gockeler et al., Nonperturbative renormalization of composite operators in lattice QCD, Nucl. Phys. B 544 (1999) 699 [hep-lat/9807044] [INSPIRE].
P. F. Bedaque, Aharonov-Bohm effect and nucleon nucleon phase shifts on the lattice, Phys. Lett. B 593 (2004) 82 [nucl-th/0402051] [INSPIRE].
C. T. Sachrajda and G. Villadoro, Twisted boundary conditions in lattice simulations, Phys. Lett. B 609 (2005) 73 [hep-lat/0411033] [INSPIRE].
L. Del Debbio, M. T. Frandsen, H. Panagopoulos and F. Sannino, Higher representations on the lattice: perturbative studies, JHEP 06 (2008) 007 [arXiv:0802.0891] [INSPIRE].
M. Lüscher, Signatures of unstable particles in finite volume, Nucl. Phys. B 364 (1991) 237 [INSPIRE].
T. A. Ryttov and F. Sannino, Ultra minimal technicolor and its dark matter TIMP, Phys. Rev. D 78 (2008) 115010 [arXiv:0809.0713] [INSPIRE].
C. Michael, Adjoint sources in lattice gauge theory, Nucl. Phys. B 259 (1985) 58 [INSPIRE].
M. Lüscher and U. Wolff, How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation, Nucl. Phys. B 339 (1990) 222 [INSPIRE].
B. Blossier, M. Della Morte, G. von Hippel, T. Mendes and R. Sommer, On the generalized eigenvalue method for energies and matrix elements in lattice field theory, JHEP 04 (2009) 094 [arXiv:0902.1265] [INSPIRE].
V. Drach, T. Janowski and C. Pica, Update on SU(2) gauge theory with NF = 2 fundamental flavours, EPJ Web Conf. 175 (2018) 08020 [arXiv:1710.07218] [INSPIRE].
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: 2012.09761
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
Drach, V., Janowski, T., Pica, C. et al. Scattering of Goldstone bosons and resonance production in a composite Higgs model on the lattice. J. High Energ. Phys. 2021, 117 (2021). https://doi.org/10.1007/JHEP04(2021)117
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2021)117