Interference effects in BSM processes with a generalised narrow-width approximation.
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It is demonstrated that interference effects of this kind arising in BSM models can be very large, leading to drastic modifications of predictions based on the standard NWA.The generalised NWA, based on on-shell matrix elements or their approximations leading to simple weight factors, is shown to produce UV- and IR-finite results which are numerically close to the result of the full process at tree level and at one-loop order, where an agreement of better than [Formula: see text] is found for the considered process.The most accurate prediction for this process based on the generalised NWA, taking into account also corrections that are formally of higher orders, is briefly discussed.
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Affiliation: DESY, Deutsches Elektronen-Synchrotron, Notkestr. 85, 22607 Hamburg, Germany.
ABSTRACT
A generalisation of the narrow-width approximation (NWA) is formulated which allows for a consistent treatment of interference effects between nearly mass-degenerate particles in the factorisation of a more complicated process into production and decay parts. It is demonstrated that interference effects of this kind arising in BSM models can be very large, leading to drastic modifications of predictions based on the standard NWA. The application of the generalised NWA is demonstrated both at tree level and at one-loop order for an example process where the neutral Higgs bosons h and H of the MSSM are produced in the decay of a heavy neutralino and subsequently decay into a fermion pair. The generalised NWA, based on on-shell matrix elements or their approximations leading to simple weight factors, is shown to produce UV- and IR-finite results which are numerically close to the result of the full process at tree level and at one-loop order, where an agreement of better than [Formula: see text] is found for the considered process. The most accurate prediction for this process based on the generalised NWA, taking into account also corrections that are formally of higher orders, is briefly discussed. No MeSH data available. Related in: MedlinePlus |
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Mentions: First of all, we verify that the other conditions from Sect. 2.2 for the NWA are met. The widths of the involved Higgs bosons do not exceed of their masses, hence they can be considered narrow (see Fig. 3). At tree level, there are no unfactorisable contributions so that the scalar propagator is separable from the matrix elements. Besides, our scenario is far away from the production and decay thresholds since holds independently of the parameters, and with neutralino masses of GeV and GeV, also GeV does not violate the threshold condition. The neutralino masses are independent of . Thus, the NWA is applicable for the individual contributions of h and H, so the factorised versions99\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \Gamma ^{i}_\mathrm{{NWA}}:= \Gamma _{P_i}(\tilde{\chi }_4^0\rightarrow \tilde{\chi }_{1}^{0}h_i)\,\text {BR}_i(h_i\rightarrow \tau ^{+}\tau ^{-}) \end{aligned}$$\end{document}ΓNWAi:=ΓPi(χ~40→χ~10hi)BRi(hi→τ+τ-)should agree with the separate terms of the 3-body decays via the exchange of only one of the Higgs bosons, ,100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \Gamma ^{i}_{1\rightarrow 3}:=\Gamma (\tilde{\chi }_4^0\mathop {\rightarrow }\limits ^{h_i}\tilde{\chi }_{1}^{0}\tau ^{+}\tau ^{-}) \end{aligned}$$\end{document}Γ1→3i:=Γ(χ~40→hiχ~10τ+τ-)within the uncertainty of . This is tested in Fig. 4. The blue lines compare (solid) with the factorised process (dotted), the green lines represent the corresponding expressions for H. The standard narrow-width approximation is composed of the incoherent sum of both factorised processes, i.e.,101\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \Gamma _\mathrm{{sNWA}}= \Gamma _{P_h}\,\text {BR}_h + \Gamma _{P_H}\,\text {BR}_H. \end{aligned}$$\end{document}ΓsNWA=ΓPhBRh+ΓPHBRH.This is confronted with the incoherent sum of the 3-body decays which are only h-mediated or H-mediated. For a direct comparison with the sNWA, the interference term is not included,102\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \Gamma ^\mathrm{{incoh}}_{1\rightarrow 3} = \Gamma ^{h}_{1\rightarrow 3}+\Gamma ^{H}_{1\rightarrow 3}. \end{aligned}$$\end{document}Γ1→3incoh=Γ1→3h+Γ1→3H.The sNWA (dotted) and the incoherent sum of the 3-body decay widths are both shown in grey. Their relative deviation of 0.8–3.3 % is of the order of the ratio from Fig. 3d. Consequently, the NWA is applicable to the terms of the separate h / H-exchange within the expected uncertainty.Fig. 4 |
View Article: PubMed Central - PubMed
Affiliation: DESY, Deutsches Elektronen-Synchrotron, Notkestr. 85, 22607 Hamburg, Germany.
A generalisation of the narrow-width approximation (NWA) is formulated which allows for a consistent treatment of interference effects between nearly mass-degenerate particles in the factorisation of a more complicated process into production and decay parts. It is demonstrated that interference effects of this kind arising in BSM models can be very large, leading to drastic modifications of predictions based on the standard NWA. The application of the generalised NWA is demonstrated both at tree level and at one-loop order for an example process where the neutral Higgs bosons h and H of the MSSM are produced in the decay of a heavy neutralino and subsequently decay into a fermion pair. The generalised NWA, based on on-shell matrix elements or their approximations leading to simple weight factors, is shown to produce UV- and IR-finite results which are numerically close to the result of the full process at tree level and at one-loop order, where an agreement of better than [Formula: see text] is found for the considered process. The most accurate prediction for this process based on the generalised NWA, taking into account also corrections that are formally of higher orders, is briefly discussed.
No MeSH data available.