C008 $\mathcal{B}(D^+\to\pi^+e^\pm\mu^\mp)$
LFV semileptonic charm decay $D+ \to \pi^+$ e $\mu$ Status REVIEWED VERIFIED High Code: NO Priority Low
PDG / equivalent values
Why this constrains the RS scan
This process tests a product of up-sector flavor violation and charged-lepton
flavor violation: schematically, short-distance operators such as
\((\bar u\,\Gamma c)(\bar e\,\Gamma'\mu)\). Minimal quark-only RS scans do
not generate a live constraint for this mode, but lepton-sector extensions
with nonuniversal KK gauge couplings, scalar exchange, or flavor-violating
brane terms can generate it. It is therefore a useful catalog marker for a
future combined quark-plus-lepton flavor backend rather than a current veto.
What's changed since the original paper
The arXiv:0804.1954 RS-flavor baseline
CsakiFalkowskiWeiler2008:CompositeFlavor predates the modern
rare/forbidden semileptonic charm searches. BaBar
BaBar2011:RareForbiddenCharm subsequently set or improved limits for
charged-charm LFV modes in \(384\,{\rm fb}^{-1}\). LHCb
LHCb2021:DPlusPiEMu searched for 25 rare and forbidden \(D^+\) and
\(D_s^+\) modes in 2016 data, found no significant deviation from background,
and tightened the two C008 charge channels to the present
\(2\times10^{-7}\)-level limits.Validity and model dependence
The experimental limits are robust upper bounds on the listed exclusive
branching fractions. Their interpretation as RS constraints is model
dependent because the mapping requires a \(\Delta C=1\), LFV semileptonic
operator basis, \(D\to\pi\) form factors, lepton-chirality assumptions, and a
phase-space treatment matching the LHCb analysis. The Standard Model
background for charged-LFV final states is negligible for catalog purposes.
Code coverage in this repo
NO. The sidecar
code\_coverage block records the required
coverage greps over quarkConstraints/,
qcd/, flavorConstraints/, neutrinos/,
yukawa/, warpConfig/, solvers/,
scanParams/, and tests/, plus a focused search for
D+.*pi+.*e.*mu, pi+.*e.*mu, rare-charm, and
$c \to u$ LFV patterns, found no \(D^+\to\pi^+e^\pm\mu^\mp\)
implementation. Nearby hits are unrelated: \(D^0\) mixing appears at
quarkConstraints/deltaf2.py:252 and
quarkConstraints/deltaf2.py:941, the modern policy lists only
\(D^0\) mixing at quarkConstraints/modern/phenomenology.py:23 and
quarkConstraints/modern/phenomenology.py:668, and the implemented
LFV observable is \(\mu\to e\gamma\) at
flavorConstraints/muToEGamma.py:75.
Linked evidence (opens GitHub blob at flavor-catalog-website/2026q2):
- Focused implementation-dir search for D+ -> pi+ e mu and rare semileptonic charm patterns returned no matches.
- quarkConstraints/deltaf2.py:252 and quarkConstraints/deltaf2.py:941 are D0 mixing hits, not D+ -> pi+ e mu.
- quarkConstraints/modern/phenomenology.py:23 and quarkConstraints/modern/phenomenology.py:668 are D0 mixing policy/evaluator hits, not rare semileptonic charm.
- flavorConstraints/muToEGamma.py:75 is the separate mu -> e gamma LFV dipole check.
Implementation difficulty
HIGH. A production implementation needs a new \(\Delta C=1\)
LFV semileptonic operator basis and a \(D^+\to\pi^+e\mu\) branching-fraction
calculation with form factors, phase-space acceptance, and chirality
conventions. This is beyond adding an input to the existing \(\Delta F=2\)
or \(\mu\to e\gamma\) paths.
Reason: Needs a new $\Delta C = 1$ charged-LFV semileptonic operator basis plus a $D+ \to \pi^+$ e mu mode calculation with form factors, phase-space acceptance, and chirality conventions.
Key references
Process-local keys before bibliography consolidation:
PDG2026:DPlusPiEMuPlus, PDG2026:DPlusPiEMuMinus,
LHCb2021:DPlusPiEMu, BaBar2011:RareForbiddenCharm, and
CsakiFalkowskiWeiler2008:CompositeFlavor.