On the Validity of the Effective Field Theory Approach to SM Precision Tests

Contino, Roberto; Grojean, Christophe; Falkowski, Adam; Riva, Francesco; Goertz, Florian

doi:10.1007/JHEP07(2016)144

Article
Report number	arXiv:1604.06444 ; DESY-16-067 ; CERN-TH-2016-082 ; LPT-Orsay-16-32 ; CERN-TH-2016-082
Title	On the Validity of the Effective Field Theory Approach to SM Precision Tests
Author(s)	Contino, Roberto (ITPP, Lausanne ; CERN) ; Falkowski, Adam (Orsay, LPT) ; Goertz, Florian (CERN) ; Grojean, Christophe (DESY) ; Riva, Francesco (CERN)
Publication	2016-07-28
Imprint	21 Apr 2016
Number of pages	26
Note	26 pages, 2 figures; v2: Comments and references added, conclusions unchanged
In:	JHEP 07 (2016) 144
DOI	10.1007/JHEP07(2016)144
Subject category	Particle Physics - Phenomenology
Abstract	We discuss the conditions for an effective field theory (EFT) to give an adequate low-energy description of an underlying physics beyond the Standard Model (SM). Starting from the EFT where the SM is extended by dimension-6 operators, experimental data can be used without further assumptions to measure (or set limits on) the EFT parameters. The interpretation of these results requires instead a set of broad assumptions (e.g. power counting rules) on the UV dynamics. This allows one to establish, in a bottom-up approach, the validity range of the EFT description, and to assess the error associated with the truncation of the EFT series. We give a practical prescription on how experimental results could be reported, so that they admit a maximally broad range of theoretical interpretations. Namely, the experimental constraints on dimension-6 operators should be reported as functions of the kinematic variables that set the relevant energy scale of the studied process. This is especially important for hadron collider experiments where collisions probe a wide range of energy scales.
Copyright/License	arXiv nonexclusive-distrib. 1.0 preprint: © 2016-2024 CERN (License: CC-BY-4.0) publication: © 2016-2024 The Author(s) (License: CC-BY-4.0), sponsored by SCOAP³

$\emph{Left: The partonic $u \bar d \to W^+ h$ cross section as a function of the center-of-mass energy of the parton collision. The black lines correspond to the $SU(2)_L$ triplet model with $M_V =1\,$TeV, $g_H=-g_q = 0.25$ (dashed), $M_V = 2\,$TeV, $g_H=-g_q = 0.5$ (dotted), and $M_V = 7\,$TeV, and $g_H=-g_q = 1.75$ (solid). The corresponding EFT predictions are shown in the linear approximation (solid red), and when quadratic terms in $D\!=\!6$ parameters are included in the calculation of the cross section (solid purple). Right: Theory error as a function of $M_V$ (solid line). The error is defined to be the relative difference between the constraints on $g_*^2 \equiv g_H^2 = g_q^2$ obtained by recasting the limits derived in the framework of a $D\!=\!6$ EFT and those derived from the resonance model. The limits come from re-interpreting the hypothetical experimental constraints with $M_{\rm cut} = 3\,$TeV, as described in the text. The dotted line corresponds to the naive estimate $(M_{\rm cut}/M_V)^2$. }$ $\emph{Left: The partonic $u \bar d \to W^+ h$ cross section as a function of the center-of-mass energy of the parton collision. The black lines correspond to the $SU(2)_L$ triplet model with $M_V =1\,$TeV, $g_H=-g_q = 0.25$ (dashed), $M_V = 2\,$TeV, $g_H=-g_q = 0.5$ (dotted), and $M_V = 7\,$TeV, and $g_H=-g_q = 1.75$ (solid). The corresponding EFT predictions are shown in the linear approximation (solid red), and when quadratic terms in $D\!=\!6$ parameters are included in the calculation of the cross section (solid purple). Right: Theory error as a function of $M_V$ (solid line). The error is defined to be the relative difference between the constraints on $g_*^2 \equiv g_H^2 = g_q^2$ obtained by recasting the limits derived in the framework of a $D\!=\!6$ EFT and those derived from the resonance model. The limits come from re-interpreting the hypothetical experimental constraints with $M_{\rm cut} = 3\,$TeV, as described in the text. The dotted line corresponds to the naive estimate $(M_{\rm cut}/M_V)^2$. }$ $\emph{{ Limits on the coupling strength $g_* \equiv - g_H = g_q$ as a function of the resonance mass~$M_V$. The solid and dashed red curves are obtained respectively from the vector resonance model and a naive analysis in terms of a $D$=6 truncated EFT, including data from all energies. The dark (light) blue region corresponds instead to the bound derived from a consistent EFT analysis where only data with $M_{Wh}<M_{\rm cut}=\kappa M_V$ are used with $\kappa$=0.5 (1). } }$ Show more plots

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