Constraints on Higgs Light Yukawa Couplings with the CMS Detector

This paper presents the latest direct and indirect measurements from the CMS experiment regarding the challenging task of constraining light Higgs Yukawa couplings, such as the Higgs-charm coupling, and discusses future prospects for improvement.

The Gist

The Cosmic "Missing Link": Hunting for the Higgs Boson’s Secret Handshake

Imagine you are hosting a massive, high-society gala (this is the Large Hadron Collider). At this gala, the most important guest is the Higgs Boson. The Higgs is essentially the "social glue" of the universe; it’s the reason particles have mass and why the universe isn't just a collection of weightless, flying ghosts.

We already know the Higgs is very good at dancing with the "VIPs"—the heavy, third-generation particles like the Top Quark and the Bottom Quark. They have a strong, obvious connection. But scientists have a suspicion: the Higgs also has a "secret handshake" with the much lighter, more elusive members of the party, like the Charm Quark.

The problem? The Charm Quark is incredibly shy and moves so fast that it’s almost impossible to spot. This paper, written by Alberto Zucchetta and the CMS team, is a report on their latest attempt to catch the Higgs and the Charm Quark in the act of interacting.

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The Three Ways to Catch a Ghost

Since the Charm Quark is so hard to see, the scientists used three different "detective strategies" to find them:

1. The "Crowded Room" Strategy (Direct Searches)

Imagine trying to see if two specific people are shaking hands in a room filled with a thousand people dancing wildly. That is what searching for $H \to c\bar{c}$ (the Higgs decaying into charm quarks) is like. The "noise" from other particles is deafening.

To solve this, the scientists used Super-Powered Digital Eyes (advanced AI called ParticleNet). Instead of just looking at the whole crowd, this AI looks at the tiny, microscopic movements of individual dancers to figure out, "Wait, that person over there is definitely a Charm Quark!"

They looked at two specific scenarios:

• The $t\bar{t}H$ method: Looking for the Higgs when it's hanging out with heavy Top Quarks.
• The $VH$ method: Looking for the Higgs when it's accompanied by a "bodyguard" (a W or Z boson).

The Result: They haven't "caught" the Higgs-Charm handshake yet, but they have narrowed down the search area significantly. They’ve basically said, "We haven't seen them dancing, but we know they aren't doing anything crazy outside of the expected rules."

2. The "Sidekick" Strategy (Associated Production)

Instead of waiting for the Higgs to decay, scientists looked for a different setup: a single Charm Quark appearing alongside a Higgs boson (the $cH$ process).

Think of this like looking for a specific duo walking into a club together. If you see a Charm Quark and a Higgs walking in tandem, it’s a huge clue. They checked this using two different "filters": one looking for flashes of light (photons) and one looking for a pair of W bosons.

3. The "Echo" Strategy (Indirect Probes)

Sometimes, you can't see the person, but you can see the ripple they leave in a pond. This is called an indirect measurement.

The scientists looked at rare decays, like the Higgs turning into a $J/\Psi$ meson (a tiny particle) and a photon. Because the Charm Quark is involved in the "inner machinery" of this transformation, the way the decay happens tells us if the Charm Quark is playing its part correctly. It’s like hearing the sound of a specific instrument in an orchestra; even if you can't see the musician, the sound tells you they are there.

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The Bottom Line: Why Does This Matter?

Right now, everything we see matches the Standard Model—the current "rulebook" of physics. The rulebook says the Higgs should interact with the Charm Quark in a very specific, very weak way.

The CMS team’s work is like checking the rulebook against reality. If they eventually find that the Higgs is shaking hands with the Charm Quark more strongly than expected, it would be like discovering a new law of gravity. It would mean our "rulebook" is incomplete and that there is New Physics—new forces or particles—waiting to be discovered.

In short: We haven't found the "secret handshake" yet, but thanks to incredible AI and massive amounts of data, we are getting closer to seeing if the universe follows the rules we think it does.

Technical Summary

Technical Summary: Constraints on Higgs Light Yukawa Couplings with the CMS Detector

1. Problem Statement

While the Higgs boson's couplings to third-generation fermions (top, bottom, and tau) and gauge bosons have been firmly established, the Yukawa couplings to the second generation (specifically the charm quark, $y_c$) remain largely unconstrained. In the Standard Model (SM), these couplings are proportional to the fermion mass ($y_f = \sqrt{2}m_f/v$), making the charm coupling significantly weaker and harder to detect. Measuring these couplings is essential to verify the SM mechanism of electroweak symmetry breaking and to search for New Physics, which often predicts deviations in the relationship between mass and coupling.

2. Methodology

The CMS Collaboration employs a multi-pronged approach to probe the charm-Higgs coupling ($\kappa_c$), utilizing direct, associated, and indirect measurement techniques:

• Direct Searches ($H \to c\bar{c}$):
  • $t\bar{t}H$ Production: Targets the Higgs produced with top quarks. This is a high-complexity final state (up to 8 jets, leptons, and neutrinos). CMS uses the ParticleNet algorithm (a Dynamic Graph Convolutional Neural Network) for advanced jet flavor tagging and a transformer-based neural network to classify events into 9 distinct categories (signals and backgrounds).
  • Associated Production ($VH$): Targets Higgs production with a $W$ or $Z$ boson. This method uses "boosted" categories where the Higgs decay products are captured in a single large-radius jet to improve signal-to-background ratios.
• Associated Production with a Charm Quark ($cH$): Searches for the Higgs produced in association with a single charm jet. This is analyzed through two decay channels:
  • Diphoton ($H \to \gamma\gamma$): Uses Boosted Decision Trees (BDTs) to separate signal from QCD and gluon-fusion backgrounds.
  • Diboson ($H \to WW^*$): Focuses on the $e\nu\mu\nu$ final state, utilizing the DeepJet algorithm for charm-tagging.
• Indirect Probes:
  • Radiative Decays ($H \to J/\Psi \gamma$): Probes the charm coupling through quantum loops. The analysis uses angular correlations and a three-body invariant mass spectrum fit.
  • Global Fits: Constraints are derived from the precision measurement of $H \to ZZ^* \to 4\ell$ and $\gamma H$ production, assuming other couplings follow SM predictions.

3. Key Contributions

• Advanced Machine Learning Integration: The paper highlights the transition from older taggers (DeepJet) to state-of-the-art architectures like ParticleNet and Transformer-based networks, which have improved the separation between $b$, $c$, and light-flavor jets by up to a factor of 2.
• First Observation of $VZ, Z \to c\bar{c}$: A significant milestone where CMS observed the $Z$ boson decaying to charm quarks at a hadronic collider with $>5\sigma$ significance.
• Statistical Combination: The integration of $VH$ and $t\bar{t}H$ datasets to provide a unified and more stringent constraint on the charm Yukawa modifier.

4. Key Results

• Direct $H \to c\bar{c}$ Constraints: The combination of $VH$ and $t\bar{t}H$ analyses yielded the most stringent limit to date, constraining the charm coupling modifier to $|\kappa_c| < 3.5$ (observed) and $< 2.7$ (expected) at 95% CL.
• $t\bar{t}H$ Specifics: While $H \to c\bar{c}$ is too small to be measured directly in this channel, the $H \to b\bar{b}$ process was measured with a signal strength of $\mu = 0.91$ and a significance of $4.4\sigma$.
• $cH$ Production: The diphoton channel provided an upper limit of $|\kappa_c| < 38.1$ (observed).
• Indirect Limits: The $H \to J/\Psi \gamma$ search set branching fraction limits ($B < 2.6 \times 10^{-4}$), while global fits of $H \to ZZ^*$ constrained $\kappa_c$ to the range $-4.0 < \kappa_c < 3.5$.

5. Significance

The results are entirely consistent with the Standard Model, meaning no immediate evidence of New Physics was found in the charm sector. However, the work represents a massive leap in experimental capability. The progress in jet flavor tagging and complex event classification via deep learning has opened "previously inaccessible" channels. These methodologies lay the groundwork for the High-Luminosity LHC (HL-LHC) era, where the increased statistical precision is expected to move from setting upper limits to the actual observation of the charm-Higgs coupling.