[Paper Review] TASI 2013 lectures on Higgs physics within and beyond the Standard Model

Heather E. Logan|arXiv (Cornell University)|Jun 6, 2014

Particle physics theoretical and experimental studies22 references16 citations

TL;DR

This paper provides a pedagogical introduction to the Higgs mechanism in the Standard Model (SM), detailing Higgs boson interactions, decays, and production at hadron and $e^+e^-$ colliders. It extends to beyond-SM physics via two case studies: two-Higgs-doublet models illustrating minimal flavor violation and triplet scalar models demonstrating custodial symmetry, offering key insights into Higgs phenomenology and model-building constraints.

ABSTRACT

These lectures start with a detailed pedagogical introduction to electroweak symmetry breaking in the Standard Model, including gauge boson and fermion mass generation and the resulting predictions for Higgs boson interactions. I then survey Higgs boson decays and production mechanisms at hadron and $e^+e^-$ colliders. I finish with two case studies of Higgs physics beyond the Standard Model: two-Higgs-doublet models, which I use to illustrate the concept of minimal flavor violation, and models with isospin-triplet scalar(s), which I use to illustrate the concept of custodial symmetry.

Motivation & Objective

• To provide a comprehensive, pedagogical introduction to electroweak symmetry breaking and Higgs boson interactions in the Standard Model.
• To survey SM Higgs boson decay and production mechanisms at hadron and $e^+e^-$ colliders, including branching ratios and coupling extraction at the LHC.
• To explore beyond-SM Higgs physics through two case studies: flavor-conserving two-Higgs-doublet models and custodial-symmetry-preserving scalar triplets.
• To illustrate foundational concepts such as minimal flavor violation and custodial symmetry using explicit model constructions.
• To equip graduate students and researchers with the theoretical tools to analyze LHC Higgs data and interpret deviations from SM predictions.

Proposed method

• Derives the Higgs mechanism in the SM using the Higgs doublet field with spontaneous symmetry breaking, leading to massive $W^\pm$, $Z$ bosons, and fermion masses.
• Computes Higgs couplings to gauge bosons and fermions via the Yukawa interaction, with the Higgs vacuum expectation value $v = 246$ GeV as a key parameter.
• Analyzes Higgs decays into fermions, $W^+W^-$, $ZZ$, and loop-induced modes ($gg$, $\gamma\gamma$, $Z\gamma$) using perturbative field theory and the unitarity gauge.
• Evaluates Higgs production cross sections at hadron colliders (via gluon fusion, vector boson fusion, etc.) and $e^+e^-$ colliders (via $W^+W^-$ fusion and $Z$-boson fusion).
• Introduces two-Higgs-doublet models (2HDM) to study flavor-conserving dynamics and the concept of Yukawa alignment, ensuring natural flavor conservation.
• Examines scalar triplet models to explore custodial symmetry violation and restoration, using the $\rho$ parameter as a diagnostic tool for electroweak precision constraints.

Experimental results

Research questions

• RQ1 How does the Higgs mechanism generate masses for the $W^\pm$, $Z$ bosons, and fermions in the Standard Model?
• RQ2 What are the dominant decay modes and production mechanisms of the Higgs boson at the LHC and future $e^+e^-$ colliders?
• RQ3 How do two-Higgs-doublet models realize minimal flavor violation, and what constraints arise from Yukawa alignment?
• RQ4 In what way do scalar triplets break or preserve custodial symmetry, and how does this affect the $\rho$ parameter?
• RQ5 Can deviations in Higgs signal rates at the LHC be explained by invisible or unobserved decay modes without altering observable rates?

Key findings

• The Higgs boson decay width into bottom quarks is given by $\Gamma(h\to b\bar{b}) = \frac{3}{8\pi} \frac{m_b^2}{v^2} m_h \left(1 - \frac{4m_b^2}{m_h^2}\right)^{3/2}$, with $v = 246$ GeV.
• The SM Higgs self-coupling is $-3i m_h^2 / v$, and the $hhh$ vertex is $-3i m_h^2 / v$ at tree level, with corrections from higher-dimensional operators.
• In models with a $\phi^6$ term in the potential, the Higgs mass and self-couplings receive corrections proportional to $1/\Lambda^2$, altering the $m_h$–$hhh$ relation from the SM.
• A flat direction exists in Higgs coupling fits: increasing all couplings by a factor $\kappa$ while introducing an unobserved decay mode with BR$_{\text{new}} = \kappa^2 - 1$ preserves all observable signal rates.
• A septet of SU(2)$_L$ with hypercharge $Y=2$ can reproduce the correct $W$ and $Z$ boson mass ratio, requiring $v_7 = v_{\text{SM}} \approx 246$ GeV if it were the sole source of mass generation.
• All SM mass generation cannot be achieved via a septet alone, as it fails to generate fermion masses without additional Yukawa couplings, and would break custodial symmetry unless carefully tuned.