Flavour changing charged current decays at LHCb

This paper presents LHCb measurements of the branching fraction for the $\Lambda_b \to p \mu^{-} \bar{\nu}_{\mu}$ decay and form factor parameters for the $B^0 \to D^{*+} \mu^{-} \nu_{\mu}$ decay, which serve as powerful probes for testing the Standard Model and searching for New Physics.

The Gist

Imagine the universe as a giant, high-speed race track where tiny particles called quarks zoom around. Sometimes, these particles change their "identity" (flavor) and decay into other particles. Physicists at the LHCb experiment (a giant particle detector at CERN) are like race officials trying to understand the rules of this race. They are specifically looking at "b-hadrons," which are heavy particles that eventually break apart.

This paper presents two major discoveries made by the LHCb team, led by Biljana Mitreska. Here is the breakdown in simple terms:

1. The "Ghost" Problem

In these particle races, one of the particles produced is a neutrino. Think of a neutrino as a ghost. It passes through everything without leaving a trace. The detectors at LHCb can see the other particles (like protons and muons), but they cannot see the ghost.

This makes it very hard to figure out exactly what happened in the crash. It's like trying to figure out the speed of a car that hit a wall, but you can only see the debris and not the car itself. The scientists had to develop clever math tricks to "guess" where the ghost went based on the debris they could see.

2. Discovery #1: The "Lambda" Particle's Secret Life

The first part of the paper looks at a specific particle called the Lambda b-hadron ($\Lambda_b$).

• The Event: This particle decays into a proton, a muon (a heavy cousin of an electron), and our invisible ghost (the neutrino).
• The Goal: The team wanted to measure exactly how often this happens (the "branching fraction").
• The Analogy: Imagine you are counting how many times a specific type of coin lands on "heads" out of a million tosses. But you can't see the coin directly; you have to infer it from the sound it makes when it hits the table.
• The Result: They found the answer with twice the precision of the previous best measurement.
• Why it matters: This helps check a fundamental rule of the universe called Lepton Flavor Universality. The Standard Model (our current rulebook) says that electrons and muons should behave exactly the same way, just with different weights. The team compared the "muon version" of this decay to the "electron version." Their results matched the rulebook perfectly, confirming that, so far, the universe is playing fair.

3. Discovery #2: The "Dance" of the B-Meson

The second part looks at a different particle, the $B^0$ meson, decaying into a $D^*$ particle, a muon, and a neutrino.

• The Event: This isn't just about how often it happens, but how it happens.
• The Analogy: Imagine a dancer spinning on a stage. You can't just count how many times they spin; you need to know the angle of their arms, the direction of their spin, and how fast they are moving at every moment.
• The Method: The scientists performed a 5-dimensional analysis. They looked at the angles of the particles, the energy they carried, and the "missing" energy from the ghost neutrino. They treated the data like a complex 3D puzzle, trying to fit it into three different theoretical "molds" (called CLN, BGL, and BLPR).
• The Result: This was the first time LHCb measured these specific "dance moves" (form factors) for this particle.
• Why it matters: These "dance moves" tell us about the internal structure of the particles. The results matched predictions from supercomputers (Lattice QCD) and other experiments (like Belle). This is good news because it means our current rulebook (the Standard Model) is still holding up. If the dance had looked weird, it would have been a sign of "New Physics"—a brand new rule we didn't know about.

The Big Picture: Why Should We Care?

Think of the Standard Model as a massive, complex instruction manual for how the universe works.

• The Tension: Recently, other experiments found some "typos" in this manual (discrepancies in how heavy particles decay). Physicists are worried these typos might mean the manual is incomplete.
• The LHCb Role: This paper is like a rigorous proofreading session. By measuring these decays with extreme precision, LHCb is checking if those "typos" are real or just calculation errors.
• The Verdict: So far, the LHCb measurements say, "The manual looks correct here." The particles are behaving exactly as predicted.

What's Next?

The LHCb detector is getting an upgrade. Imagine giving the race officials better cameras and faster computers. In the future, they will collect even more data, allowing them to measure these "dance moves" with even greater precision (aiming for 3% accuracy).

In summary: This paper is a victory for precision. It confirms that our current understanding of particle physics is solid, even as we keep looking for cracks in the foundation that might lead to a whole new understanding of the universe.

Technical Summary

1. Problem Statement and Motivation

Semileptonic $b$-hadron decays are critical probes for testing the Standard Model (SM) and searching for Beyond the Standard Model (BSM) physics. Two primary tensions exist in current flavor physics:

• Lepton Flavour Universality (LFU) Violation: Measurements of the ratios $R(D)$ and $R(D^*)$ (comparing decays to $\tau$ vs. $\mu$ leptons) show a $3.8\sigma$ tension with SM predictions.
• CKM Matrix Discrepancies: There is a persistent $2\text{--}3\sigma$ discrepancy between inclusive and exclusive determinations of the CKM matrix elements $|V_{ub}|$ and $|V_{cb}|$.

Specific Challenges:

• Neutrino Detection: In $pp$ collisions at the LHC, neutrinos escape detection, making kinematic reconstruction difficult.
• Backgrounds: Semileptonic decays suffer from significant combinatorial and physics backgrounds that require precise modeling.

This paper addresses these challenges by presenting two recent LHCb measurements:

1. The branching fraction of the hyperon decay $\Lambda \to p\mu^-\bar{\nu}_\mu$.
2. The first LHCb angular analysis of $B^0 \to D^{*-}\mu^+\nu_\mu$ to extract hadronic form factor parameters.

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2. Methodology

A. $\Lambda \to p\mu^-\bar{\nu}_\mu$ Branching Fraction Measurement

• Dataset: LHCb data collected between 2016–2018 ($5.4 \text{ fb}^{-1}$).
• Normalization: The measurement is relative to the well-known decay $\Lambda \to p\pi^-$ ($\mathcal{B} \approx 0.641$).
• Kinematic Reconstruction: Since the neutrino is invisible, the analysis utilizes the transverse momentum of the missing neutrino, $p_T(\nu_\mu)$, derived from the visible proton and muon momenta.
  • A physical constraint is applied: $p_T(\nu_\mu) < \frac{m_\Lambda^2 - m_{p\mu}^2}{2m_\Lambda}$. This creates a boundary in the $p_T(\nu_\mu)$ vs. $m(p\mu)$ plane that signal events satisfy but combinatorial backgrounds typically do not.
  • An additional selection is applied in the Armenteros–Podolanski plane to further suppress background.
• Yield Extraction:
  • Normalization: Fitted from the $m(p\pi)$ distribution of selected candidates.
  • Signal: Extracted via a binned maximum-likelihood fit in the $m_{corr}(p\pi)$ vs. $m(p\pi)$ plane. Templates for signal, normalization, and background (combinatorial and misidentified $\Lambda \to p\pi^-$) are derived from simulation and control samples.

B. $B^0 \to D^{*-}\mu^+\nu_\mu$ Angular Analysis

• Dataset: LHCb data from 2011–2012 ($3.0 \text{ fb}^{-1}$ at $\sqrt{s} = 7, 8 \text{ TeV}$).
• Kinematic Ambiguity: Due to the missing neutrino, the $B^0$ momentum is determined up to a quadratic ambiguity; one solution is selected randomly, resulting in $8\text{--}12\%$ resolution on decay angles and $q^2$.
• Observable: A five-dimensional fit is performed on:
  1. Three decay angles ($\theta_\ell, \theta_d, \chi$).
  2. Squared momentum transfer ($q^2$).
  3. Squared missing mass ($m^2_{miss}$), calculated using a rest-frame approximation.
• Form Factor Parametrizations: The analysis tests three theoretical frameworks:
  • CLN (Caprini–Lellouch–Neubert)
  • BGL (Boyd–Grinstein–Lebed)
  • BLPR (Bernlochner–Ligeti–Papucci–Robinson)
• Fit Strategy:
  • Templates are constructed using simulation and control samples.
  • The HAMMER tool is used to vary form factor parameters within the RooFit framework.
  • The Bayesian Information Criterion (BIC) is used to determine the optimal order of the BGL coefficient series.
  • Backgrounds, primarily from $B \to D^{**}\mu\nu$ (including $D_1(2420)$, $D^*_2(2460)$), are modeled explicitly.

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3. Key Contributions and Results

1. $\Lambda \to p\mu^-\bar{\nu}_\mu$ Branching Fraction

• Result: $\mathcal{B}(\Lambda \to p\mu^-\bar{\nu}_\mu) = (1.46 \pm 0.10) \times 10^{-4}$.
  • Total uncertainty: 6.9% (a factor of two improvement over previous BESIII results).
• CKM Extraction: Using Lattice QCD predictions, $|V_{us}|$ is extracted as:
  • $0.235 \pm 0.016$ (conservative input).
  • $0.2459 \pm 0.0085$ (alternative, less conservative input).
• LFU Test: The ratio $R_{\mu e} = \frac{\Gamma(\Lambda \to p\mu\bar{\nu})}{\Gamma(\Lambda \to pe\bar{\nu})}$ is measured as $0.175 \pm 0.012$.
  • This is consistent with the main Lattice QCD prediction ($0.1735 \pm 0.0098$) at the $0.1\sigma$ level.

2. $B^0 \to D^{*-}\mu^+\nu_\mu$ Form Factors

• Firsts: This is the first measurement of hadronic form factor parameters for this channel at LHCb using CLN, BGL, and BLPR formalisms.
• Parameters:
  • BGL: Measured coefficients $a_0, a_1, b_1, c_1, c_2$ satisfy unitarity constraints.
  • CLN & BLPR: Parameters $R_1, R_2, \rho^2$ (CLN) and $\bar{\rho}^*_2, \chi_2, \eta$ (BLPR) were determined.
• Consistency:
  • Results from the three parametrizations are mutually consistent.
  • The $F_1$ form factor results (BGL) show better agreement with Fermilab-MILC and JLQCD lattice calculations than HPQCD.
  • The forward-backward asymmetry ($A_{FB}$) derived from these parameters shows excellent agreement with Belle measurements.

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4. Significance and Outlook

• Precision Improvement: The $\Lambda \to p\mu^-\bar{\nu}_\mu$ measurement significantly reduces the uncertainty on $|V_{us}|$ and provides a clean test of LFU in the strange sector, currently showing no deviation from the SM.
• Theoretical Input: The $B^0 \to D^{*-}\mu^+\nu_\mu$ analysis provides crucial data-driven inputs for hadronic form factors. This helps mitigate the large systematic uncertainties associated with theoretical modeling in exclusive $B$ decays, which are central to the $|V_{cb}|$ tension.
• Future Prospects: With planned LHCb upgrades increasing instantaneous luminosity, statistical precision on semileptonic ratios is expected to reach $\sim 3\%$. This will allow for more stringent tests of LFU and the resolution of current tensions in CKM unitarity.
• Broader Impact: These measurements offer complementary information to $B$-factory experiments (Belle, BaBar), reinforcing the LHCb program's role in probing deviations from Standard Model expectations in $b \to c \ell \nu$ transitions.