First exclusive reconstruction of the B$^{*+}$, B$^{*0}$, and B$^{*0}_\text{s}$ mesons and precise measurement of their masses

Using 140 fb$^{-1}$ of proton-proton collision data at 13 TeV, the CMS experiment achieved the first full exclusive reconstruction of the B$^{*+}$, B$^{*0}$, and B$^{*0}_\text{s}$ mesons, measuring their mass differences with a precision improved by an order of magnitude compared to previous results.

The Gist

Imagine the universe is a giant, high-speed racetrack where tiny particles zoom around at nearly the speed of light. In this race, scientists at CERN's CMS experiment are trying to catch a glimpse of some very specific, fleeting racers: beauty mesons.

Think of these beauty mesons as "parent" particles. Usually, when we study them, we only see the calm, stable "ground state" versions (like a parent sitting quietly on a couch). But sometimes, these parents get excited and jump up, becoming "excited" or "vector" states. In the world of physics, these excited versions are called $B^*$ mesons.

The problem is, these excited parents are very shy and unstable. They almost instantly calm down back to their ground state by spitting out a tiny, low-energy photon (a particle of light). This photon is like a whisper—so quiet and low-energy that most detectors in the world are too deaf to hear it. For decades, scientists could only guess at the properties of these excited mesons because they couldn't "see" the whisper that proved they existed.

The Big Breakthrough
This paper announces the first time scientists have successfully "heard" that whisper and fully reconstructed the three types of excited beauty mesons ($B^{*+}$, $B^{*0}$, and $B^{*0}_s$).

Here is how they did it, using a few creative analogies:

1. The "Conversion" Trick: Since the whispering photon is too weak to be caught directly, the scientists used a clever trick. They waited for the photon to crash into the metal walls of the detector (specifically the beam pipe). When a photon hits metal, it can turn into a pair of electrons and positrons (like a photon splitting into two twins). The CMS detector is very good at spotting these twins. By finding the twins, they could work backward to figure out exactly where the whispering photon came from and how much energy it had.
2. The "Family Portrait": To identify the excited meson, they didn't just look at the photon. They looked at the whole family. They found the "parent" beauty meson (which had already settled down) and paired it with the "twins" (the electron-positron pair from the photon). By measuring the total weight (mass) of this family unit, they could calculate the exact weight of the excited parent before it calmed down.
3. The "Scale Calibration": One of the biggest challenges was that the detector's "ruler" for measuring energy wasn't perfectly straight. To fix this, the scientists used a known standard: the $\pi^0$ meson. Think of the $\pi^0$ as a "gold standard" weight in a physics lab. They measured how the detector weighed this known particle and adjusted their ruler accordingly. This calibration was crucial to get the numbers right.

What They Found
Using data from 13 trillion electron-volt collisions (a massive amount of energy) collected over three years, the team measured the "mass difference" between the excited mesons and their calm ground-state siblings.

Think of it like measuring the difference in weight between a person standing on tiptoes (excited) versus standing flat-footed (ground state). The paper reports these differences with incredible precision:

• $B^{*+}$ difference: 45.277 MeV
• $B^{*0}$ difference: 45.471 MeV
• $B^{*0}_s$ difference: 49.407 MeV

The most important part is the precision. The paper claims these measurements are ten times more precise than any previous attempts. It's like going from measuring a person's height with a tape measure that has gaps in the inches, to using a laser scanner that measures down to the width of a human hair.

Why It Matters (According to the Paper)
The paper states that these precise numbers are a vital new input for our understanding of Quantum Chromodynamics (QCD). You can think of QCD as the rulebook for how the "glue" (strong force) holds quarks together to form particles like protons and mesons.

By knowing the exact "energy cost" to make these mesons excited, scientists can test their theoretical models of how this glue works. The paper notes that while current computer simulations (Lattice QCD) predict these values, their predictions are still a bit fuzzy (10 to 100 times less precise than this new measurement). This new data acts as a strict referee, telling theorists, "Your rulebook needs to be sharper to match what we actually see in the real world."

In Summary
This paper is a triumph of detective work. The CMS team managed to catch a ghost (the excited meson) by listening for its faint whisper (the low-energy photon) using a special trick (conversion to electron pairs) and calibrating their instruments with a known standard. They have now provided the most accurate "weight" measurements of these excited particles ever recorded, giving physicists a much clearer picture of the fundamental forces that build our universe.

Technical Summary

Technical Summary: First Exclusive Reconstruction of $B^*$ Mesons and Precise Mass Measurements

Problem and Motivation
While the ground states of beauty mesons ($B^+$, $B^0$, and $B^0_s$) have been extensively characterized, their corresponding excited vector meson states ($B^{*+}$, $B^{*0}$, and $B^{*0}_s$) remain significantly less explored. The primary experimental challenge in reconstructing these excited states is the low energy of the photons emitted in the radiative decay $B^* \to B\gamma$. In the $B^*$ rest frame, these photons possess energies between 40 and 50 MeV, which typically fall below the detection thresholds of most particle physics experiments. Previous measurements relied on indirect methods, such as combining $b$-jets with converted photons at LEP or analyzing $P$-wave decays without reconstructing the low-energy photon. Consequently, existing measurements of the hyperfine splitting (the mass difference between the excited and ground states) lacked precision or, in the case of the $B^{*0}_s$, showed tension between different experimental results (CLEO vs. Belle). Precise measurements of these splittings are critical for testing Quantum Chromodynamics (QCD) mechanisms, quark models of hadrons, and lattice QCD predictions.

Methodology
This analysis utilizes proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13$ TeV during LHC Run 2 (2016–2018), corresponding to an integrated luminosity of 140 fb$^{-1}$. The study achieves the first exclusive reconstruction of the three vector $B$ meson states by detecting the low-energy photons via their conversion into $e^+e^-$ pairs within the beam pipe and detector material.

The reconstruction strategy involves:

1. Ground State Reconstruction: $B$ mesons are reconstructed via specific decay chains: $B^+ \to J/\psi(\to \mu^+\mu^-)K^+$, $B^0 \to J/\psi(\to \mu^+\mu^-)K^{*0}(\to K^+\pi^-)$, and $B^0_s \to J/\psi(\to \mu^+\mu^-)\phi(\to K^+K^-)$. The analysis also includes $\psi(2S)$ decays.
2. Photon Conversion: Photon candidates are identified as pairs of opposite-sign tracks forming a vertex with a small distance of closest approach, located at least 1.5 cm from the beam axis. Only conversions with $p_T > 300$ MeV and $|\eta| < 1.5$ are retained to ensure adequate resolution.
3. Kinematic Fitting and Calibration: To improve mass resolution, the $B\gamma$ invariant mass is calculated using a kinematic vertex fit that constrains the $B$ meson, the photon candidate, and the primary vertex tracks to a common origin. A crucial component of the analysis is a new Photon Energy Scale (PES) correction derived from $\pi^0 \to \gamma\gamma$ decays where both photons convert. This correction accounts for energy losses of electrons and positrons traversing the tracker, adjusting the measured photon energy to match the true value.
4. Statistical Analysis: A simultaneous extended unbinned maximum likelihood fit is performed on the $B\gamma$ invariant mass distributions across multiple categories defined by the photon pseudorapidity ($|\eta(\gamma)|$). Signal shapes are modeled using a sum of two Crystal Ball functions, while backgrounds are described by threshold functions. The fit accounts for cross-feed contributions (e.g., $B^{*0}_s \to B^0_s\gamma$ mimicking $B^0$ signals) and Cabibbo-suppressed decays.

Key Contributions

• First Exclusive Reconstruction: This work presents the first full, exclusive reconstruction of the $B^{*+}$, $B^{*0}$, and $B^{*0}_s$ mesons in a single analysis, directly observing the $B^* \to B\gamma$ transition.
• Novel Calibration: The implementation of a photon energy scale correction based on converted $\pi^0$ decays significantly reduces systematic uncertainties associated with low-energy photon reconstruction.
• Comprehensive Mass Measurements: The analysis provides precise measurements of the mass differences between the excited vector states and their ground states, as well as the masses of the vector states themselves.

Results
The measured mass differences (hyperfine splittings) are:

• $m(B^{*+}) - m(B^+) = 45.277 \pm 0.039 \text{ (stat)} \pm 0.027 \text{ (syst)} \text{ MeV}$
• $m(B^{*0}) - m(B^0) = 45.471 \pm 0.056 \text{ (stat)} \pm 0.028 \text{ (syst)} \text{ MeV}$
• $m(B^{*0}_s) - m(B^0_s) = 49.407 \pm 0.132 \text{ (stat)} \pm 0.041 \text{ (syst)} \text{ MeV}$

These results improve the precision of previous measurements by approximately an order of magnitude. The analysis also reports:

• The absolute masses of the vector states: $m(B^{*+}) = 5324.69 \pm 0.04 \pm 0.03 \pm 0.07$ MeV, $m(B^{*0}) = 5325.19 \pm 0.06 \pm 0.03 \pm 0.08$ MeV, and $m(B^{*0}_s) = 5416.34 \pm 0.13 \pm 0.04 \pm 0.10$ MeV.
• Mass differences between the vector states (e.g., $m(B^{*0}) - m(B^{*+}) = 0.50 \pm 0.07 \pm 0.01 \pm 0.05$ MeV), which are consistent with previous indirect measurements but significantly more precise.
• Ratios of the mass differences, which benefit from the cancellation of experimental systematic uncertainties. For instance, $\Delta m(B^{*0}_s)/\Delta m(B^{*+}) = 1.0912 \pm 0.0031 \pm 0.0007$.

Significance
The paper claims that these measurements provide a stringent test for theoretical models of heavy-quark systems. The results are consistent with predictions from lattice QCD, although the experimental uncertainties are now an order of magnitude smaller than the theoretical uncertainties. The measured hyperfine splittings and their ratios offer new, high-precision inputs for quark models and phenomenological descriptions of hadron formation. Specifically, the measurement of the $B^{*0}_s$ mass difference resolves previous tensions, agreeing with the Belle result while differing by approximately two standard deviations from the CLEO result. The precision achieved in this analysis surpasses current theoretical predictions, highlighting the need for improved lattice QCD calculations to fully exploit the experimental data.