[Paper Review] Top quark rare decays in a two Higgs doublet model for the top

Itzhak Baum|ArXiv.org|Nov 8, 2007

Particle physics theoretical and experimental studies5 references3 citations

TL;DR

This paper investigates top quark rare decays in a Two Higgs Doublet Model for the top (T2HDM), where the top quark couples exclusively to the second Higgs doublet, leading to enhanced flavor-changing interactions. It finds that branching ratios for $ t \to cH^0 $ and $ H^0 \to \bar{t}c $ can be enhanced by many orders of magnitude over the Standard Model and 2HDM-I,II, reaching up to $ \sim 10^{-4} $, potentially detectable at the LHC if above $ 5 \times 10^{-5} $.

ABSTRACT

The two Higgs doublet model for the top (T2HDM) is a 2HDM in which the top quark receives a special status, which endows it with a naturally large mass, and also gives rise to unique FC charged and neutral scalar interactions. We calculate the BR of the t->ch and h->tc rare decays in the T2HDM, at 1-loop and tree level. We find that the FC scalar interactions play a significant role in these decays. We find that the BR of these decays at 1-loop level in the T2HDM can be significantly enhanced over the 2HDM-I,II, reaching up to ~10^-4, and that the BR(t->ch) in the T2HDM can be detected at the LHC.

Motivation & Objective

• To explore the implications of a Two Higgs Doublet Model where the top quark is treated specially by coupling only to the second Higgs doublet.
• To investigate the potential for enhanced flavor-changing (FC) decays involving the top quark and charm quark via new physics beyond the Standard Model.
• To calculate and compare branching ratios for rare decays $ t \to cH^0 $ and $ H^0 \to \bar{t}c $ in the T2HDM against the Standard Model and 2HDM-I,II.
• To determine the detectability of these rare decays at the Large Hadron Collider (LHC), especially in regions of parameter space with large $ \tan\beta $.
• To validate the consistency of the one-loop amplitude calculations through cancellation of ultraviolet divergences.

Proposed method

• Derives the Yukawa and Higgs potential of the T2HDM from first principles, explicitly constructing the scalar-to-quark and triple scalar interaction vertices.
• Computes the one-loop and tree-level amplitudes for $ t \to cH^0 $ and $ H^0 \to \bar{t}c $ using Feynman rules derived for the T2HDM.
• Applies dimensional regularization with $ \varepsilon = 4 - d $ to handle ultraviolet divergences in loop integrals.
• Performs a cancellation check of $ \frac{1}{\varepsilon} $ poles across all one-loop diagrams to ensure renormalization-group invariance and self-consistency.
• Calculates branching ratios using the total width of the Higgs and top quark, comparing results across the T2HDM, SM, and 2HDM-I,II.
• Uses numerical scans over the parameter space of $ m_{H^+}, m_{h^0}, m_{A^0}, \tan\beta $ to explore regions of maximal enhancement.

Experimental results

Research questions

• RQ1 Can the T2HDM significantly enhance the branching ratio of the rare top decay $ t \to cH^0 $ compared to the Standard Model and 2HDM-I,II?
• RQ2 To what extent can the decay $ H^0 \to \bar{t}c $ be enhanced in the T2HDM, and is it accessible at the LHC?
• RQ3 What regions of the T2HDM parameter space lead to the largest enhancements in flavor-changing decays?
• RQ4 How do the one-loop and tree-level contributions to $ t \to cH^0 $ and $ H^0 \to \bar{t}c $ compare in magnitude and structure?
• RQ5 Is the one-loop amplitude calculation self-consistent, as evidenced by cancellation of ultraviolet divergences?

Key findings

• The branching ratio $ \text{BR}(t \to cH^0) $ in the T2HDM can be enhanced by many orders of magnitude compared to the Standard Model and 2HDM-I,II, reaching up to $ \sim 10^{-4} $.
• The branching ratio $ \text{BR}(H^0 \to \bar{t}c) $ in the T2HDM can exceed $ 10^{-4} $, significantly larger than in the SM and 2HDM-I,II.
• The enhancement is most pronounced in regions dominated by the neutral Higgs sector, particularly for large $ \tan\beta $ and specific combinations of $ m_{H^+}, m_{h^0}, m_{A^0} $.
• The LHC can probe $ \text{BR}(t \to cH^0) $ if it exceeds $ \sim 5 \times 10^{-5} $, and the paper finds that this threshold is reached in certain T2HDM parameter regions.
• The cancellation of ultraviolet divergences in the one-loop amplitude is confirmed both analytically and numerically, validating the consistency of the calculation.
• Numerical results show that $ \text{BR}(t \to cH^0) $ increases with $ \tan\beta $ and is sensitive to the charged Higgs mass, with maximal values observed at $ \tan\beta \sim 28 $ and $ m_{H^+} \sim 660 \, \text{GeV} $.