Catalog · Charm · C007

C007 $\mathcal{B}(D^+\to\pi^+\mu^+\mu^-)$

Rare semileptonic decay $D+ \to \pi^+ \mu^+ \mu^-$

Status REVIEWED VERIFIED High Code: NO Priority Medium

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
BR(D+ $ \to \pi^+ \mu^+ \mu^-$)	6.7e-8 branching fraction	2026	PDG Live/API S031.42	source ↑
BR(D+ $ \to \pi^+ \mu^+ \mu^-$)	6.7e-8 branching fraction	2021	LHCb JHEP 06 (2021) 044 / arXiv:2011.00217	source ↑
Number of rare or forbidden $D+$ and $Ds+$ decay modes investigated	25 decay modes	2021	LHCb JHEP 06 (2021) 044 / arXiv:2011.00217	source ↑
Short-distance Standard Model branching-fraction scale for FCNC $D+$ and $Ds+$ modes	1e-12 branching fraction, order of magnitude	2021	LHCb JHEP 06 (2021) 044 / arXiv:2011.00217	source ↑
BR(D+ $ \to \pi^+ \mu^+ \mu^-$), nonresonant	7.3e-8 branching fraction	2013	LHCb Phys. Lett. B 724 (2013) 203 / arXiv:1304.6365	source ↑
$D_(s$) $ \to $ P l+ l- rare-charm EFT context	?	2015	de Boer and Hiller 2015	source ↑

Why this constrains the RS scan

Anarchic warped models can induce up-sector flavor-changing neutral currents through nonuniversal KK gauge couplings, $Z$-like flavor violation, Higgs or radion scalar effects, and lepton-current extensions. This process is the charged semileptonic $\Delta C=1$ analogue of the implemented neutral $D^0$-mixing lane: it probes $c\to u$ vector, axial-vector, and possible scalar semileptonic operators rather than four-quark $\Delta F=2$ operators. It is therefore a roadmap constraint for a broader flavor backend, not a constraint currently applied by the quark scan.

What's changed since the original paper

The arXiv:0804.1954 RS-flavor baseline predates the modern LHCb rare-charm program. Since then, LHCb first set nonresonant $D^+\to\pi^+\mu^+\mu^-$ limits at the $10^{-8}$ level in 2013 and then folded the channel into a 2021 search for 25 rare or forbidden $D^+$ and $D_s^+$ decays. The 2021 analysis found no evidence in any of the investigated modes and tightened the PDG-listed C007 limit to $6.7\times10^{-8}$ at 90\% C.L. On the theory side, post-2008 rare-charm EFT work, especially de Boer and Hiller 2015, clarified that $D_{(s)}\to P\ell^+\ell^-$ branching-ratio recasts must separate short-distance Wilson coefficients from resonance-dominated long-distance physics; the LHCb 2021 introduction quotes short-distance SM branching fractions of order $10^{-12}$, with dilepton resonances dominating the physical spectrum.

Validity and model dependence

The experimental upper limit is robust as a counting result, but its use as an RS short-distance bound is model dependent. Long-distance hadronic resonances, weak-annihilation effects, and the exact phase-space definition of the ``nonresonant'' signal matter. A conservative catalog use is an upper bound on additional short-distance $c\to u\mu^+\mu^-$ contributions in the same experimental region, with an explicit recast needed before treating it as a hard scan veto.

Code coverage in this repo

NO. The required catalog greps and a focused search for D+.*pi+.*mu, c.?->.?u, rare.?charm, semileptonic.*charm, C9, and C10 found no $D^+\to\pi^+\mu^+\mu^-$ implementation in quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, or tests/. 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 $\mu\to e\gamma$ is separate at flavorConstraints/muToEGamma.py:75.

Linked evidence (opens GitHub blob at flavor-catalog-website/2026q2):

Implementation difficulty

HIGH. A production implementation needs a new $\Delta C=1$ semileptonic operator basis and matching for $C_{9,10}^{(\prime)}$ and possible scalar/tensor terms, plus a $D\to\pi\mu^+\mu^-$ mode calculation with form factors, phase-space cuts, and a documented treatment of resonant long-distance contributions.

Reason: Needs a new $\Delta C = 1$ semileptonic operator/matching layer plus a $D \to \pi$ mu+ mu- branching-fraction calculation with form factors, phase-space/resonance treatment, and recast conventions.

Key references

Process-local keys before bibliography consolidation: PDG2026:DPlusPiMuMu, LHCb2021:DPlusPiMuMu, LHCb2013:DPlusPiMuMu, DeBoerHiller2015:RareCharmLeptons, and CsakiFalkowskiWeiler2008:CompositeFlavor.

value 6.7e-08

AMBIGUOUS

Match 1 of 3 snapshot line 28

L25:   confidence_level: 90.0
L26:   measurement:
L27:     column_name: VALUE
L28:     value: 6.7E-8
L29:     value_text: <6.7 E-8
L30:     limit_type: U
L31:     used_in_average: true

Match 2 of 3 snapshot line 29

L26:   measurement:
L27:     column_name: VALUE
L28:     value: 6.7E-8
L29:     value_text: <6.7 E-8
L30:     limit_type: U
L31:     used_in_average: true
L32:     used_in_fit: true

Match 3 of 3 snapshot line 33

L30:     limit_type: U
L31:     used_in_average: true
L32:     used_in_fit: true
L33:     display_value_text: <6.7 E-8
L34: 
L35: AAIJ 2013AF
L36:   publication: PL B724 203

value 6.7e-08

RESOLVED

Match snapshot line 44

L41: D+ -> pi+ mu+ mu-    0.6        67          74          2.4        180          210
L42: 
L43: Interpretation for C007:
L44:   B(D+ -> pi+ mu+ mu-) < 67 x 10^-9 = 6.7 x 10^-8 at 90% CL.
L45:   Companion 95% CL limit: <74 x 10^-9 = 7.4 x 10^-8.

value 25

RESOLVED

Match snapshot line 9

L6: DOI: 10.1007/JHEP06(2021)044
L7: Journal: JHEP 06 (2021) 044
L8: Report number: LHCb-PAPER-2020-007; CERN-EP-2020-140
L9: Title: Searches for 25 rare and forbidden decays of D+ and Ds+ mesons
L10: Authors: LHCb Collaboration
L11: 
L12: Abstract-page metadata extract:

value 1e-12

RESOLVED

Match snapshot line 29

L26: transitions. These processes are rare in the Standard Model because only
L27: weak-annihilation processes can occur at tree level. At the loop level,
L28: FCNC transitions are GIM suppressed. The source states that short-distance
L29: SM branching fractions are of order 10^-12, while significant long-distance
L30: contributions from dilepton resonances are expected to dominate across the
L31: dilepton invariant-mass-squared distribution. The analysis uses 1.6 fb^-1
L32: of 2016 LHCb data. Four resonant D_(s)+ -> pi+ phi(->ll) decays are used