Observation of a $B_c^{*+}$ meson with the ATLAS detector

Using 13 TeV proton-proton collision data from the ATLAS detector, physicists have achieved the first observation of the $B_c^{*+}$ meson, a new vector state decaying into a $B_c^+$ meson and a photon, with a statistical significance exceeding 8 standard deviations.

The Gist

Imagine the universe as a giant, cosmic construction site where particles are the building blocks. Most of the time, these blocks come in matching pairs: a heavy "beauty" quark and a heavy "charm" quark usually stick together to form a specific type of particle called a $B_c$ meson. Think of this particle as a stable, ground-floor apartment in a high-rise building.

For a long time, physicists knew that if you added energy to this apartment, it could move up to a "higher floor" (an excited state). They had already found a few of these higher floors, but there was one specific, very low floor that had remained elusive: the $B_c^*$ meson.

The Challenge: The "Whisper" of a Photon

The problem with finding this specific excited state is how it falls back down to the ground floor. When it drops, it doesn't crash or explode; it simply releases a tiny, almost invisible packet of energy called a photon (a particle of light).

Because the energy difference between the "excited" state and the "ground" state is so small, the photon released is extremely weak—like a whisper in a hurricane. In the noisy, chaotic environment of the Large Hadron Collider (LHC), where billions of collisions happen every second, detecting such a faint whisper is incredibly difficult. Most detectors are tuned to hear the "shouts" (high-energy particles), not the whispers.

The Detective Work: ATLAS Steps In

The ATLAS experiment at CERN acted like a team of super-sleuths. They didn't just look for the whisper; they looked for the footprints left behind.

1. The Trail: They knew the $B_c$ meson decays into a specific set of three muons (heavy cousins of electrons) and a neutrino (a ghost particle that is hard to catch).
2. The Trick: To find the faint photon, they didn't look for the light itself directly. Instead, they looked for the "shadow" the photon cast. When a photon hits the detector's material, it can split into an electron and a positron (a pair of charged particles). The team built a special tool to catch these pairs, even when they were moving very slowly.
3. The Filter: They had to filter out millions of "fake" signals. It's like trying to find a specific person in a crowded stadium by looking for someone wearing a very specific, rare hat, while ignoring everyone else who might be wearing a similar hat by mistake.

The Discovery: A New Floor Found

After sifting through data from 140 trillion collisions (an enormous amount of information), the team found a distinct pattern. They saw a cluster of events where the mass of the $B_c$ meson plus the faint photon was exactly 64.5 MeV heavier than the ground-state $B_c$ meson.

To put that in perspective: If the ground-state $B_c$ meson weighed as much as a large apple, this new excited state would weigh just a tiny fraction of a grain of sand more.

The Verdict

The team calculated that the chance of this pattern appearing just by random luck is less than one in a billion (specifically, it exceeds 8 standard deviations, which is the gold standard for a "discovery" in physics).

What does this mean?

• Confirmation: They have officially observed the $B_c^*$ meson, the lowest excited state of the beauty-charm system.
• Theory Check: The mass they measured matches what theoretical models predicted for this specific "floor" in the particle building.
• The Mystery: Interestingly, the measured mass difference is slightly higher than the most precise recent computer simulations (Lattice QCD) predicted. This suggests that while our theories are very good, there might be a tiny piece of the puzzle regarding how these heavy quarks interact that we still need to refine.

In short, the ATLAS team successfully heard the "whisper" of a new particle that had been hiding in plain sight, confirming a key piece of the map of how matter is built at the most fundamental level.

Technical Summary

Technical Summary: Observation of a $B^*_c$ Meson with the ATLAS Detector

Problem and Motivation
The $B_c$ meson, composed of a $b$-antiquark and a $c$-quark, represents a unique system for studying heavy-quark bound-state dynamics due to the mass asymmetry of its constituents. While extensive theoretical predictions exist for the $\bar{b}c$ excitation spectrum, experimental knowledge has been limited by suppressed production rates requiring simultaneous generation of two heavy quark–antiquark pairs. Previous observations by ATLAS, CMS, and LHCb have identified excited states such as the $2S$ radial excitation and $1P$ orbital excitations, which exhibit mass differences relative to the ground state ($B_c^+$) in the range of 400–600 MeV.

However, theoretical models, including Lattice QCD and QCD potential models, predict the existence of a lowest vector excited state, the $B_c^*$ meson, with a significantly smaller mass splitting relative to the ground state, estimated between 50 and 70 MeV. This state is expected to decay almost exclusively into $B_c^+ \gamma$. The small mass difference results in a very soft photon spectrum (typically below 1–2 GeV), making experimental detection at the LHC challenging as such photons are difficult to reconstruct using standard calorimeter-based approaches.

Methodology
This analysis utilizes proton-proton collision data collected by the ATLAS detector at $\sqrt{s} = 13$ TeV during LHC Run 2 (2015–2018), corresponding to an integrated luminosity of 140 fb$^{-1}$.

• Signal Reconstruction: The $B_c^+$ mesons are reconstructed via the decay chain $B_c^+ \to J/\psi(\to \mu^+\mu^-)\mu^+\nu_\mu X$. This channel was selected over the $B_c^+ \to J/\psi\pi^+$ mode due to an approximately 20 times larger branching fraction, which compensates for the complexities introduced by the undetected neutrino and the resulting partially reconstructed final state. The $B_c^+$ candidates are identified by a displaced vertex formed by three muons.
• Photon Reconstruction: To detect the soft photons from the $B_c^* \to B_c^+ \gamma$ decay, the analysis exploits photon conversions in the detector material. Pairs of oppositely charged tracks ($e^+e^-$) are reconstructed as conversion vertices within the silicon pixel detector volume. A dedicated track reconstruction setup was employed to lower the transverse momentum ($p_T$) threshold for electrons to 100 MeV, significantly below the typical 400–500 MeV used in standard ATLAS analyses.
• Event Selection and Background Suppression:
  • Candidates are required to have a $B_c^+$ transverse momentum $p_T > 25$ GeV.
  • To isolate the signal from background, the analysis defines two regions based on the vertex fit quality ($\chi^2$) of a modified fit where the third muon is assigned a kaon mass hypothesis. Region 1 ($\chi^2/N_{dof} \le 2.5$) contains significant contributions from $B^+ \to J/\psi K^+$ decays and combinatorial background. Region 2 ($\chi^2/N_{dof} > 2.5$) is designed to be practically free of the $B^+ \to J/\psi K^+$ contribution.
  • The signal is identified using the mass difference distribution $\Delta m = m(J/\psi \mu^+ e^+ e^-) - m(J/\psi \mu^+)$.
• Statistical Analysis: An extended unbinned maximum-likelihood fit is performed simultaneously on the $\Delta m$ distributions of both regions. Signal templates for $B_c^* \to B_c^+ \gamma$ are derived from Monte Carlo simulations using adaptive Gaussian kernel density estimation (KDE). Background contributions are modeled using a data-driven event mixing technique, corrected for biases in the photon $p_T$ spectrum.

Key Contributions and Results
The analysis reports the first observation of a meson state consistent with the theoretical expectations for the $B_c^*$ meson.

• Significance: The new state is observed with a statistical significance exceeding 8 standard deviations (local and global significance both exceed 10$\sigma$ under the nominal model).
• Mass Measurement: The mass difference between the observed state and the ground-state $B_c^+$ meson is measured to be:
  $$\Delta m = 64.5 \pm 1.4 \text{ (stat.) } ^{+1.0}_{-1.4} \text{ (syst.) MeV}$$
  This corresponds to a mass for the observed state of $6339.0 \pm 1.4 \text{ (stat.) } ^{+1.0}_{-1.4} \text{ (syst.) } \pm 0.3 (m_{B_c^+}) \text{ MeV}$.
• Systematic Uncertainties: The dominant systematic uncertainties arise from the modeling of the inner detector material and the photon momentum scale/resolution. Other contributions include $B_c^+$ production modeling, decay modeling, and background shape parametrization.
• Yield: The total fitted signal yield is $N_{B_c^*} = 163 \pm 19$ (statistical uncertainty only).

Significance of the Work
The paper claims that the measured mass difference of 64.5 MeV aligns with general theoretical expectations for the lowest vector state of the $\bar{b}c$ quarkonium system, which predict a splitting in the 50–70 MeV range. The observation confirms the existence of the $B_c^*$ meson, a state previously elusive due to the experimental challenges posed by its soft decay photon. While the measured value is consistent with broad theoretical predictions, the authors note it is larger than the most recent precise Lattice QCD calculations, which predict values below 60 MeV. This result provides a new data point for refining theoretical models of heavy-quark bound-state dynamics.