Higgs Boson Production in Association with a Single Top Quark as a Probe of the Top Yukawa Coupling

This paper presents a detailed analysis of Higgs boson production in association with a single top quark at 13 and 14 TeV, utilizing advanced modeling and kinematic optimization to constrain the top quark Yukawa coupling and project future sensitivities for the High-Luminosity LHC.

The Gist

Here is an explanation of the paper, translated into simple language with creative analogies.

The Big Picture: Catching a Ghost with a Heavy Friend

Imagine the Higgs Boson as a shy, invisible ghost that gives mass to other particles. It's very hard to catch on its own because it disappears almost instantly. To study it, physicists at the Large Hadron Collider (LHC) try to "tag" it by creating it alongside a very heavy, famous friend: the Top Quark.

This paper is about a specific way of catching this pair: creating a Higgs boson and a single Top Quark together. The scientists (Tetiana and Ievgenii) are trying to figure out exactly how these two interact. Specifically, they are testing a "secret handshake" between them called the Yukawa coupling.

The Mystery: The "Bad" vs. "Good" Handshake

In the standard rules of physics (the Standard Model), when the Top Quark and the Higgs Boson try to form a pair, they have a "bad handshake."

• The Analogy: Imagine two people trying to push a car. One pushes forward, and the other accidentally pushes backward. They cancel each other out, making it very hard to move the car.
• In Physics: This is called destructive interference. It makes the process of creating this pair very rare and difficult to see.

However, the scientists noticed something strange in recent data from the ATLAS experiment. They saw more of these pairs than the "bad handshake" theory predicted. It was like seeing the car move much faster than expected.

This led to a big question: What if the handshake isn't bad, but actually "good"?

• The Analogy: What if both people are pushing the car in the same direction? They would work together, and the car would zoom forward.
• In Physics: This is called constructive interference (or the "Inverted Top Coupling" scenario). If the Top Quark's "handshake" with the Higgs is flipped, the production rate could jump by 10 times.

What the Scientists Did: The Simulation Lab

Since they can't just flip a switch in the real world to test this, Tetiana and Ievgenii built a virtual laboratory using powerful computer simulations (MadGraph5_aMC@NLO).

Think of their work like a flight simulator:

1. The Flight Plan: They programmed the simulator to run millions of "virtual collisions" at the same energy levels as the real LHC (13 and 14 TeV).
2. Two Different Maps: They had to use two different rulebooks (called "Flavor Schemes") to simulate the collision correctly, depending on which part of the process they were looking at. It's like using a street map for city driving and a highway map for long-distance travel.
3. The "K-Factor" Adjustment: Their initial simulations were a bit rough (like a low-resolution video). They applied a mathematical "zoom lens" (called a K-factor) to sharpen the image and make their rough estimates match the high-precision predictions of the Standard Model.

The Results: The "Zoom" Confirms the Theory

When they ran their simulations with the "Bad Handshake" (Standard Model), the numbers matched what we expect: a rare event.

But when they flipped the switch to the "Good Handshake" (Inverted Coupling):

• The Explosion: The number of virtual Higgs-Top pairs created exploded. It went from a trickle to a flood, increasing by a factor of nearly 10.
• The Shape Shift: It wasn't just about how many were created; it was about how they moved. The particles flew off with more energy (higher "transverse momentum").
  • Analogy: If the Standard Model is a gentle breeze, the Inverted Coupling is a hurricane. The "forward jet" (a spray of particles) shoots out much harder and faster.

Why This Matters: Solving the Puzzle

The paper concludes that the "Good Handshake" theory fits the strange excess of data seen by ATLAS much better than the standard theory.

• The Detective Work: The scientists checked the "footprints" left by these particles (their speed, direction, and energy). The footprints from their "Good Handshake" simulation looked exactly like the footprints ATLAS found in the real world.
• The Future: If this is true, it means our current understanding of the universe is incomplete. It suggests there might be new physics hiding in the way the heaviest particle (Top Quark) talks to the mass-giving particle (Higgs).

Summary in a Nutshell

This paper is a detective story. The scientists used a super-computer to simulate a scenario where the Top Quark and Higgs Boson are best friends (pushing in the same direction) instead of enemies (pushing against each other).

They found that if they are friends, the universe produces 10 times more of them, and they move faster. This perfectly explains a mysterious "glitch" in recent real-world data. If confirmed, it would be a massive discovery, proving that the "rules" of how particles get mass are different than we thought.

Technical Summary

Here is a detailed technical summary of the paper "Higgs Boson Production in Association with a Single Top Quark as a Probe of the Top Yukawa Coupling" by Tetiana Obikhod and Ievgenii Petrenko.

1. Problem Statement

The paper addresses the critical need to precisely measure the top-quark Yukawa coupling ($y_t$), specifically its magnitude and sign. While the Standard Model (SM) predicts a positive coupling ($\kappa_t = +1$), the relative phase between the Higgs-top coupling and the electroweak gauge boson couplings leads to destructive interference in the associated production of a Higgs boson with a single top quark ($tH$). This interference suppresses the production cross-section, making the process rare and difficult to detect.

Recent ATLAS experimental data (Run 2, $\sqrt{s}=13$ TeV) reported a mild excess in $tH$ production ($\mu_{tH} \approx 8.1$, observed significance $2.8\sigma$vs. expected$0.4\sigma$). The authors investigate whether this excess could be explained by an **Inverted Top Coupling (ITC)** scenario where$\kappa_t = -1$. In this scenario, the interference becomes constructive, potentially enhancing the cross-section by an order of magnitude and altering kinematic distributions. The challenge lies in accurately modeling these processes to distinguish between SM fluctuations and new physics.

2. Methodology

The authors employed a hybrid theoretical modeling approach using MadGraph5_aMC@NLO at Leading Order (LO) with MLM matching, scaled to approximate Next-to-Leading Order (NLO) accuracy using K-factors.

• Flavor Schemes: To handle the bottom quark ($b$) correctly in different production modes, the study utilized two distinct schemes:
  • 4-Flavor Scheme (4FS): Used for the $tHq$ (t-channel) process. Here, the $b$-quark is treated as massive and produced perturbatively via gluon splitting ($g \to b\bar{b}$), excluding it from the initial-state Parton Distribution Functions (PDFs). This avoids unphysical enhancements in the t-channel topology.
  • 5-Flavor Scheme (5FS): Used for the $tWH$ (associated) process. Here, the $b$-quark is treated as massless and included in the proton PDFs, resumming large collinear logarithms ($\ln(\mu_F/m_b)$).
• Simulation Setup:
  • PDF Sets: NNPDF3.0nlo (and variants).
  • Scales: Dynamic factorization and renormalization scales ($\mu_F = \mu_R = H_T/2$).
  • K-Factors: Applied to LO+MLM results to match NLO benchmarks:
    • $K_{tHq} \approx 1.5$ (to scale $\sim 47$ fb LO to $\sim 74$ fb NLO).
    • $K_{tWH} \approx 0.7$ (to scale $\sim 22$ fb LO to $\sim 15.2$ fb NLO).
• Analysis Strategy: The study focused on kinematic distributions ($H_T$, $p_T$, $\eta$, $\Delta R$) and compared them against ATLAS expectations. It specifically simulated the Inverted Top Coupling (ITC) scenario ($\kappa_t = -1$) to quantify the enhancement in rates and shape changes.

3. Key Contributions

• Hybrid Modeling Framework: The paper validates a robust simulation chain that combines 4FS for $tHq$ and 5FS for $tWH$, demonstrating consistency with fixed-order NLO calculations and ATLAS modeling choices.
• Quantification of ITC Effects: The authors provide specific cross-section predictions for the inverted coupling scenario, calculating the transition from destructive to constructive interference.
• Kinematic Analysis: Detailed analysis of how the sign flip ($\kappa_t = -1$) alters differential distributions, specifically hardening the transverse momentum ($p_T$) spectra of the Higgs and top quark and modifying angular correlations.
• Validation of ATLAS Excess: The study offers a theoretical interpretation of the ATLAS excess, showing that an ITC scenario naturally accounts for the observed signal strength and provides a mechanism for the enhancement.

4. Key Results

• Standard Model Cross-Sections (at $\sqrt{s}=13$ TeV):
  • $tHq$ (4FS): $\sigma_{NLO} \approx 74.3$ fb.
  • $tWH$ (5FS): $\sigma_{NLO} \approx 15.2$ fb.
  • Total $tH$: $\sigma_{NLO} \approx 89.5$ fb.
  • The authors' scaled LO+MLM result ($\approx 85.9$ fb) agrees well with the SM prediction (within $\sim 4\%$), validating their simulation chain.
• Inverted Top Coupling (ITC, $\kappa_t = -1$) Results:
  • Cross-Section Enhancement: The total cross-section increases dramatically due to constructive interference.
    • $tHq$ increases by a factor of $\sim 4.8$ (LO) to $\sim 10$ (NLO).
    • $tWH$ increases by a factor of $\sim 2.6$ (LO).
    • Total ITC Cross-Section: $\sigma_{NLO, ITC} \approx 380$ fb (authors' scaled result) to $\sim 890$ fb (literature NLO benchmark).
  • Kinematic Shifts:
    • $H_T$ (Scalar sum of $p_T$): The distribution shifts to higher values, with a harder tail compared to the SM.
    • $p_T(H)$ and $p_T(t)$: Both exhibit harder spectra with less suppression at high momentum.
    • Forward Jet ($tHq$): The pseudorapidity distribution ($|\eta_j| \approx 2-4$) remains peaked but with an enhanced event rate.
    • Angular Separation ($\Delta R$): The separation between the forward jet and Higgs peaks at $\Delta R \approx 3-4$, consistent with t-channel topology but with increased rate.
• Uncertainties: Theoretical uncertainties are estimated at $\sim 10-15\%$ (scale variations) and $\sim 3-6\%$ (PDF + $\alpha_s$).

5. Significance

• Probing New Physics: The $tH$ process is uniquely sensitive to the sign of the top Yukawa coupling, unlike loop-induced processes (e.g., $ggF$). This paper confirms that $tH$ is a primary "golden channel" for testing Beyond Standard Model (BSM) physics involving CP-violation or modified Higgs sectors.
• Interpretation of Experimental Data: The results provide a strong theoretical basis for the ATLAS excess, suggesting it could be a signature of an inverted top coupling rather than a statistical fluctuation.
• Future Projections (HL-LHC): The study highlights that with the High-Luminosity LHC (HL-LHC) and integrated luminosities of $3000-4000$fb$^{-1}$at$\sqrt{s}=14$TeV, the top Yukawa coupling can be measured with$5-10%$precision. The kinematic shape differences identified (harder$p_T$tails) will be crucial for multivariate analyses (BDTs) to distinguish the ITC signal from backgrounds like$t\bar{t}+$jets.
• Methodological Benchmark: The paper serves as a technical guide for implementing hybrid flavor schemes and K-factor scaling in Monte Carlo simulations for rare Higgs processes, ensuring reliable comparisons between theory and experiment.