Implications of perturbative unitarity for scalar di-boson resonance searches at LHC
Eur. Phys. J. C
Implications of perturbative unitarity for scalar di-boson resonance searches at LHC
Luca Di Luzio 1 2
Jernej F. Kamenik 0 5
Marco Nardecchia 3 4
0 Jožef Stefan Institute , Jamova 39, 1000 Ljubljana , Slovenia
1 Institute for Particle Physics Phenomenology, Department of Physics, Durham University , Durham DH1 3LE , UK
2 Dipartimento di Fisica, Università di Genova and INFN, Sezione di Genova , via Dodecaneso 33, 16159 Genova , Italy
3 Theoretical Physics Department, CERN , Geneva , Switzerland
4 DAMTP, University of Cambridge , Wilberforce Road, Cambridge CB3 0WA , UK
5 Faculty of Mathematics and Physics, University of Ljubljana , Jadranska 19, 1000 Ljubljana , Slovenia
We study the constraints implied by partial wave unitarity on new physics in the form of spin-zero di-boson resonances at LHC. We derive the scale where the effective description in terms of the SM supplemented by a single resonance is expected to break down depending on the resonance mass and signal cross section. Likewise, we use unitarity arguments in order to set perturbativity bounds on renormalizable UV completions of the effective description. We finally discuss under which conditions scalar di-boson resonance signals can be accommodated within weakly coupled models. 1 Introduction . . . . . . . . . . . . . . . . . . . . . 1 2 Brief review on partial wave unitarity . . . . . . . . 2 3 Effective field theory of a scalar resonance . . . . . 3 3.1 Scalar mediated boson scattering . . . . . . . . 4 3.2 Fermion-scalar contact interactions . . . . . . 5 3.3 Unitarity bounds . . . . . . . . . . . . . . . . 5 4 Weakly coupled models . . . . . . . . . . . . . . . 7 4.1 Single fermion case . . . . . . . . . . . . . . . 9 4.2 Single scalar case . . . . . . . . . . . . . . . . 11 4.3 Generalization in flavor space . . . . . . . . . . 12 4.4 Application to mediator models . . . . . . . . . 14 5 Conclusions . . . . . . . . . . . . . . . . . . . . . 15 Appendix A: Amplitudes . . . . . . . . . . . . . . . . 16 A. 1 γ γ → γ γ scattering . . . . . . . . . . . . . . 16 A.2 ψ ψ → ψ ψ scattering . . . . . . . . . . . . . . 17 References . . . . . . . . . . . . . . . . . . . . . . . . 18
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Contents
1 Introduction
Unitarity of the time evolution of an isolated quantum system
and in particular of the associated S-matrix is one of the
cornerstones of quantum field theory. In practical perturbative
calculations however, S-matrix unitarity is always
approximate and asymptotic. Nonetheless, significant violations of
unitarity at low orders in perturbation theory are heralds of
a strongly coupled system and can be used to constrain the
range of validity of a given (effective) quantum field theory
description.
Perhaps most famously, constraints imposed by
perturbative unitarity in W W scattering have been used in the
past to infer an upper bound on the Higgs boson mass or,
alternatively, on the scale where the standard model (SM)
description of weak interactions would need to be completed
in the ultraviolet (UV) in terms of some new strongly
coupled dynamics [1, 2]. Correspondingly it allowed one to
narrow down the relevant mass search window and motivate the
construction of the LHC with capabilities that ensured the
eventual Higgs boson discovery (cf. [3] for a review).
More generally, perturbative unitarity constraints on the
validity of a certain theoretical description are applicable
both in non-renormalizable as well as renormalizable
models. In both cases they allow one to assess the limitations of
a perturbative expansion. In the non-renormalizable
effective field theory (EFT) approach this amounts to a truncated
power expansion in (E / ), where E is a typical energy in a
process and is the EFT cut-off scale. Violations of
perturbative unitarity signal the breakdown of such an expansion,
when the leading powers do not represent a good
approximation to the physical result. A notable standard example is the
pion scattering in chiral perturbation theory, where the loop
and power expansion are adequate at low enough scattering
energies but violate perturbative unitarity at higher energies
and eventually need to be UV completed with the inclusion
of dynamical vector resonances. On the other hand within
renormalizable models, the expansion proceeds in terms of
positive powers of the renormalizable couplings. Sizable
violations of unitarity at leading (tree) order signal the
breakdown of such an expansion and the onset of strongly coupled
dynamics. Here the most renown case is that of the
aforementioned W W boson scattering in the presence of a heavy
SM Higgs boson.
The recently rekindled interest in new physics (NP) in the
form of (possibly broad) di-photon resonances [4–8] at the
LHC prompt us to reconsider the implications of perturbative
unitarity for EFT interpretations of resonances decaying to
di-boson final states. In particular, focusing on promptly
produced scalar SM singlets decaying to two SM gauge bosons
we aim to addres (...truncated)