[Paper Review] MATCHIG: A program for matching charged Higgs boson production at hadron colliders

Johan Alwall|ArXiv.org|Mar 14, 2005

Particle physics theoretical and experimental studies5 references3 citations

TL;DR

This paper presents MATCHIG, a Monte Carlo event generator that implements a matching scheme between the $2\to2$ $gb\to tH^{\pm}$ and $2\to3$ $gg\to tbH^{\pm}$ processes for charged Higgs boson production at hadron colliders. By subtracting a double-counting term derived from the collinear approximation of gluon splitting to $b\bar{b}$, the method removes overcounting at low transverse momentum of the accompanying $b$ quark, enabling accurate differential cross-sections across all $p_{\perp,b}$ regions.

ABSTRACT

This manual describes how to use the MatCHig code for matching the charged Higgs boson production processes gg->tbH+/- and gb->tH+/-. A negative term, correcting for the double-counting between these processes, is implemented as an external process to PYTHIA, allowing the Monte Carlo generation of matched events. Results from the matching were published in JHEP 0412, 050. The code can be downloaded from http://www.isv.uu.se/thep/MC/matchig/ .

Motivation & Objective

• To address the double-counting issue between the $2\to2$ $gb\to tH^{\pm}$ and $2\to3$ $gg\to tbH^{\pm}$ processes in charged Higgs boson production at hadron colliders.
• To improve the accuracy of differential cross-sections for charged Higgs production, particularly in the region of low transverse momentum of the accompanying $b$ quark.
• To implement a consistent matching scheme between parton-level matrix elements and parton showers using Pythia's external process interface.
• To provide a tool for high-precision simulation of charged Higgs production in models like the MSSM, enabling better experimental signature predictions.
• To ensure reliable event generation by incorporating a negative double-counting term that corrects for overcounting in the collinear approximation.

Proposed method

• The double-counting term $\sigma_{\mathrm{DC}}$ is derived from the leading-order $b$-quark density via gluon splitting $g\to b\bar{b}$, matching the $2\to2$ process's collinear contribution.
• The double-counting term is computed using the matrix element $\mathcal{M}_{2\to2}$, parton distribution functions, and splitting functions $P_{qg}(z)$, with kinematic constraints from finite $m_b$ and $\hat{s}$.
• The term is implemented as an external process in Pythia using the Les Houches interface, with process ID LPRUP(1)=10000 and event identification via KFPR(MSTI(1),2).
• The method uses a subtraction scheme where $\sigma = \sigma_{2\to2} + \sigma_{2\to3} - \sigma_{\mathrm{DC}}$, ensuring no double-counting at low $p_{\perp,b}$.
• The implementation supports on-shell parton showers (MSTP(63)=0) for parton-level comparisons, with recommended settings MSTP(32)=12 and MSTP(39)=8 for consistent scale choices.
• Factorization and renormalization scales are set via PARP(193) and PARP(194), with $\mu_F \approx 0.5(m_{H^\pm} + m_t)/2$ as recommended for accuracy.

Experimental results

Research questions

• RQ1 How can the $2\to2$ and $2\to3$ production processes for charged Higgs bosons be consistently matched to avoid double-counting at low transverse momentum of the accompanying $b$ quark?
• RQ2 What is the correct analytical form of the double-counting term that arises from the collinear approximation of gluon splitting to $b\bar{b}$ in the $2\to2$ process?
• RQ3 How can the matching scheme be implemented within the Pythia Monte Carlo framework using external processes and Les Houches interface?
• RQ4 What are the optimal scale choices (factorization and renormalization) that yield the most accurate differential cross-sections for charged Higgs production?
• RQ5 Does the inclusion of the $2\to3$ process with proper matching improve the differential cross-section at low $p_{\perp,b}$ compared to using only the $2\to2$ process?

Key findings

• The double-counting term $\sigma_{\mathrm{DC}}$ is analytically derived as the leading-order contribution of $b$-quark density from $g\to b\bar{b}$ splitting to the $2\to2$ process, ensuring consistency with the $2\to3$ matrix element.
• Using the $2\to3$ process alone at high $p_{\perp,b}$ underestimates the differential cross-section for $p_{\perp,b} \lesssim 100\,\mathrm{GeV}$, necessitating matching with the $2\to2$ process.
• The implementation of the double-counting term via Pythia's external process interface allows for matched event generation with correct interference cancellation.
• The recommended settings MSTP(32)=12 and MSTP(39)=8, along with PARP(193) and PARP(194), enable consistent factorization and renormalization scale choices, with $\mu_F \approx 0.5(m_{H^\pm} + m_t)/2$ being optimal.
• On-shell parton showers (MSTP(63)=0) are necessary for accurate parton-level comparisons, though no observable difference is expected in jet-level analyses.
• The code successfully generates matched events by combining $gb\to tH^{\pm}$ (ISUB=161) and $gg\to tbH^{\pm}$ (ISUB=401) with the negative double-counting term, ensuring correct total cross-sections.