Flavour Changing Neutral Current decays at LHCb

Imagine the Standard Model of particle physics as a very strict rulebook for how the universe's smallest building blocks behave. In this rulebook, there is a specific rule: a heavy particle called a "bottom quark" is generally forbidden from turning into a lighter "strange quark" while simultaneously creating a pair of electrons or muons (heavy cousins of electrons) without changing its electric charge. This is called a Flavour Changing Neutral Current (FCNC) decay.

Think of it like a bank vault that is supposed to be impenetrable. According to the rulebook, you can't just walk in and swap the gold for silver. However, the rulebook allows for a tiny, sneaky loophole: if you borrow a particle for a split second from the "quantum vacuum" (a virtual particle), you might be able to sneak the swap through. Because this requires a "loan" from the quantum world, it happens very rarely and very slowly.

Why is this exciting?
If "New Physics" (mysterious, undiscovered particles or forces) exists, it could act like a master thief with a master key. It could make these forbidden swaps happen much more often than the rulebook predicts, or change how they happen. The LHCb experiment at CERN is like a high-speed security camera system designed to catch these rare, sneaky swaps.

Here is a breakdown of what the paper found, using simple analogies:

1. The Detective Work: Counting the Rare Swaps

The scientists looked at billions of collisions to find specific decays where a bottom quark turns into a strange quark and a pair of muons ( $b \to s\mu^+\mu^-$ ).

The Result: They found that these decays happen slightly less often than the Standard Model predicts. Imagine if the rulebook said a specific rare event should happen 100 times a year, but the camera only caught it 80 times.
The Catch: The rulebook's prediction isn't perfect because it has to guess how messy "hadronic" (strong force) interactions work. It's like trying to predict the exact path of a leaf in a hurricane; the wind (hadronic uncertainty) makes it hard to be 100% sure of the baseline.

2. The "Twist" in the Story: Angular Analysis

It's not just about how many times the swap happens, but how the particles fly out. Imagine a spinning top. If you know the rules, you can predict exactly which way the top will wobble.

The Finding: In the decay of a specific particle called $B^0$ into a $K^{*0}$ and two muons, the "wobble" (angular distribution) didn't match the prediction. In the middle range of energies, the data was off by about 2.6 to 2.7 "standard deviations" (a statistical way of saying "this is weird").
The "Magic Number": When they tried to fix the math by adjusting one specific "knob" in the theory (called $C_9$ ), they found they needed to turn it quite a bit to match the data. This adjustment had a significance of about 4 sigma. In the world of particle physics, 3 sigma is a "hint," and 5 sigma is a "discovery." They are sitting right on the edge of a discovery, but not quite there yet.

3. The "Charm Loop" Problem

Why aren't they declaring a discovery yet?
The paper explains that the "rulebook" (Standard Model) has a fuzzy area called the "charm loop." Imagine trying to calculate the speed of a car, but you don't know exactly how much friction the tires have on the road. The "charm loop" is a complex quantum effect involving charm quarks that is very hard to calculate precisely.

The Conclusion: The tension between the data and the theory might be because the "friction" (hadronic uncertainty) is different than we thought, not because there is a new thief (New Physics). Until we understand the friction better, we can't be sure if the car is speeding because of a new engine or just bad tires.

4. Other Findings

Radiative Decays (Light and Magic): They also looked at decays where a photon (light) is emitted. They found these happen exactly as the rulebook predicts, which is good news—it means the rulebook works well in some areas.
Lepton Universality (The Equal Opportunity Rule): The Standard Model says electrons and muons should be treated exactly the same (except for their weight). The scientists checked this by comparing how often the swap happens with muons versus electrons. In the high-energy range, the ratio was 1.08, which is very close to the expected 1.0. This suggests that, in this specific high-energy zone, the "Equal Opportunity" rule still holds true.
New Data (Run 3): The experiment has started collecting a massive new batch of data (Run 3). They tested their new camera system with a "control" decay (a known event) and found it works perfectly. This gives them confidence that their future measurements will be even more precise.

The Bottom Line

The LHCb team has found some very intriguing "glitches" in the universe's rulebook. The data suggests that heavy particles are behaving slightly differently than expected, particularly in how they spin and how often they decay.

However, the paper is cautious. It says, "We see a tension, but it might just be because our understanding of the messy background (hadronic uncertainties) isn't perfect yet." It's like hearing a strange noise in your house; it could be a ghost (New Physics), or it could just be the pipes settling (theoretical uncertainty).

To solve the mystery, the scientists need two things:

Better Theory: Mathematicians need to calculate the "friction" (hadronic effects) more precisely.
More Data: The new, massive dataset from Run 3 will allow them to measure these rare events with such precision that the answer will eventually become clear.

For now, the universe is still holding its secrets, but the clues are getting clearer.

Technical Summary: Flavour Changing Neutral Current decays at LHCb

Problem and Motivation
Flavour Changing Neutral Current (FCNC) decays are forbidden at the lowest perturbative order in the Standard Model (SM) and proceed only via quantum loops. Consequently, these transitions are heavily suppressed within the SM, making them highly sensitive probes for New Physics (NP). Heavy new particles can contribute significantly to these processes through virtual corrections, potentially allowing sensitivity to mass scales of $\mathcal{O}(100 \text{ TeV})$ , far beyond the reach of direct searches. Of particular interest are semileptonic $b \to s(d)\ell^+\ell^-$ and radiative $b \to s(d)\gamma$ decays. These channels allow for model-agnostic NP searches and the probing of operator structures through various observables, including branching fractions, angular distributions, CP-asymmetries, and tests of lepton flavour universality (LFU). However, SM predictions for these processes are complicated by significant hadronic uncertainties arising from non-perturbative form factors and non-local charm-loop contributions.

Methodology
The LHCb experiment utilizes its high efficiency for reconstructing secondary vertices from $b$ -hadron decays, enabled by the Vertex Locator (VeLo) with an impact parameter resolution of $\sim 20 \, \mu\text{m}$ , and its excellent tracking and particle identification systems. The analysis presented covers data from LHC Run 1 and Run 2 (totaling $8.4 \, \text{fb}^{-1}$ ) and preliminary results from Run 3 ( $>22 \, \text{fb}^{-1}$ collected, with specific analyses using $1 \, \text{fb}^{-1}$ ).

Key methodological approaches include:

Branching Fraction Measurements: Rare $b \to s\mu^+\mu^-$ processes are measured relative to corresponding tree-level $b \to c\bar{c}s$ decays (via $J/\psi \to \mu^+\mu^-$ ) to minimize systematic uncertainties. Measurements are binned in $q^2 = m^2(\mu^+\mu^-)$ .
Angular Analyses: The flagship decay $B^0 \to K^{*0}(\to K^+\pi^-)\mu^+\mu^-$ is analyzed using a model-independent approach. The decay is described by five degrees of freedom: three angles ( $\vec{\Omega} = \{\cos \theta_l, \cos \theta_K, \phi\}$ ), $q^2$ , and the $K^+\pi^-$ mass. Fits are performed for CP-asymmetries ( $S_i, A_i$ ) and in the $P_i^{(')}$ basis, where form-factor uncertainties cancel to leading order.
Radiative Decays: Radiative $b \to d\gamma$ decays ( $B^0 \to \rho^0\gamma$ and $B^0_s \to K^-\pi^+\gamma$ ) are reconstructed, with the latter utilizing photon conversions ( $\gamma \to e^+e^-$ ) to improve mass resolution and separate the $B^0_s$ signal from the $B^0$ peak.
LFU Tests: Ratios of branching fractions $R_{K^{(*)}} = \mathcal{B}(b \to s\mu^+\mu^-)/\mathcal{B}(b \to se^+e^-)$ are measured in high- $q^2$ regions. These ratios are theoretically clean as hadronic uncertainties largely cancel.

Key Contributions and Results

Branching Fractions and Tensions:
- Measurements of $B^0_s \to \phi\mu^+\mu^-$ , $B^+ \to K^+\mu^+\mu^-$ , $B^0 \to K^0\mu^+\mu^-$ , and $\Lambda_b^0 \to \Lambda^0\mu^+\mu^-$ show consistent tensions with SM predictions, particularly at intermediate $q^2$ values. For instance, the $B^0_s \to \phi\mu^+\mu^-$ measurement lies approximately $3\sigma$ below SM predictions.
- A significant update to the normalization mode $\Lambda_b^0 \to J/\psi\Lambda^0$ led to a revised, lower branching fraction for the rare $\Lambda_b^0 \to \Lambda^0\mu^+\mu^-$ decay, which remains $\sim 2\sigma$ below SM predictions.
- First evidence ( $3.5\sigma$ ) is reported for the baryonic decay $B^+ \to \bar{\Lambda}^0 p \mu^+\mu^-$ .
- World's most precise measurements are presented for radiative $B^0 \to \rho^0\gamma$ , consistent with the world average. First evidence ( $3.5\sigma$ ) is found for the rare $B^0_s \to K^-\pi^+\gamma$ decay.
Angular Analysis of $B^0 \to K^{*0}\mu^+\mu^-$ :
- Using $8.4 \, \text{fb}^{-1}$ of data, a comprehensive angular analysis was performed. The results confirm tensions with SM predictions at intermediate $q^2$ for the angular observable $P'_5$ and the forward-backward asymmetry $A_{FB}$ .
- In the $q^2$ bins $[4, 6]$ and $[6, 8] \, \text{GeV}^2/c^4$ , local significances of $2.6\text{--}2.7\sigma$ are observed relative to specific SM predictions.
- A fit to the effective vector coupling $ReC_9$ yields a shift of $\Delta ReC_9 \approx -0.93$ with a significance of $4.0\text{--}4.1\sigma$ .
- Despite the high statistical significance of the deviation in $ReC_9$ , the authors note that angular observables remain susceptible to pollution from charm-loop contributions. Therefore, no definitive evidence for NP is claimed.
CP-Asymmetries and LFU:
- Time-dependent CP-asymmetry measurements in $B^0 \to K_S^0\mu^+\mu^-$ yield parameters $S = 0.82 \pm 0.29$ and $C = -0.13 \pm 0.32$ , consistent with SM expectations ( $S = \sin 2\beta_d, C=0$ ).
- The LFU ratio $R_{K^*}$ in the high- $q^2$ region ( $>14 \, \text{GeV}^2/c^4$ ) is measured to be $1.08^{+0.14}_{-0.12} \pm 0.07$ , showing good agreement with the SM prediction of unity.
Run 3 Data Quality:
- Preliminary angular analyses of $B^+ \to J/\psi K^+$ using $1 \, \text{fb}^{-1}$ of 2024 Run 3 data show no significant deviations from zero for the forward-backward asymmetry and flat parameter, validating the quality of the new data sample.

Significance and Claims
The paper summarizes the "legacy" results of the LHCb collaboration on FCNC decays from Run 1 and 2. The primary significance lies in the confirmation of persistent, consistent tensions between experimental data and SM predictions in branching fractions and angular analyses of $b \to s\mu^+\mu^-$ transitions. Specifically, the $4\sigma$ tension in the $ReC_9$ coupling derived from the $B^0 \to K^{*0}\mu^+\mu^-$ angular analysis is a notable result.

However, the authors maintain a modest stance regarding the interpretation of these tensions. They explicitly state that the significance of these deviations depends heavily on assumptions regarding hadronic uncertainties, particularly the non-local charm-loop contributions, which are currently under discussion in the theoretical community. Consequently, while the data shows intriguing deviations, the paper concludes that these tensions do not yet constitute evidence for New Physics. The clarification of these issues requires further theoretical work on hadronic uncertainties and experimental precision measurements with the large Run 3 dataset.