Catalog · Charm · C002

C002 $|q/p|, \phi_D \,\text{in}\, D^0-\bar{D}^0 \,\text{mixing}\,$

CP violation in neutral-charm mixing

Status SUBTLETY-ADDED VERIFIED Low Code: PARTIAL Priority High

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
\|q/p\| in D0-D0bar mixing	0.983 dimensionless	2025	HFLAV CKM25 global fit, all-CPV fit	source ↑
$\phi_D$ = Arg(q/p) in D0-D0bar mixing	-1.51 degrees	2025	HFLAV CKM25 global fit, all-CPV fit	source ↑
No indirect CP violation point (\|q/p\|, $\phi$) = (1,0)	?	2025	HFLAV CKM25 global fit, all-CPV fit	source ↑
PDG cross-check of HFLAV \|q/p\| and $\phi_D$	?	2025	PDG 2025 D0-D0bar Mixing review, Table 70.7 excerpt	source ↑
Contextual RS-flavor baseline for post-2008 comparison	?	2008	Csaki, Falkowski, and Weiler, arXiv:0804.1954	source ↑

Why this constrains the RS scan

Anarchic warped models generate short-distance $\Delta C=2$ amplitudes through flavor-changing neutral-current exchange. C002 is the CP-odd counterpart of the D-mixing magnitude bound: it tests whether the complex phase of a new $c-u$ mixing amplitude is aligned well enough to avoid visible indirect CP violation. It is especially useful because the repo's current D0 lane constrains $|M_{12}^{D,{\rm NP}}|$, while C002 asks about the phase-sensitive part of the same amplitude.

What's changed since the original paper

The baseline RS-flavor paper arXiv:0804.1954 predates the modern high-statistics neutral-charm mixing program. Since then, LHCb added CPV-sensitive model-independent $D^0\to K_S^0\pi^+\pi^-$ inputs, including the post-Run-2 result summarized in lhcb2023\_arxiv2208\_06512.txt. Belle and Belle II have also supplied new large-sample model-independent mixing information (belle\_belleii2025\_arxiv2410\_22961.txt). HFLAV now combines these inputs in a global fit with explicit $|q/p|$ and $\phi_D$ parameters, and the current result remains compatible with no indirect CP violation.

Validity and model dependence

This is a short-distance-sensitive but global-fit-dependent constraint. The experimental fit is precise enough to bound new CP phases, but the Standard Model charm-mixing amplitude is long-distance dominated and difficult to calculate. A safe RS interpretation should therefore constrain the allowed new-physics phase conservatively, without subtracting a precise SM prediction. In down-aligned or kaon-protected RS variants, up-sector observables become leading rather than secondary diagnostics.

Code coverage in this repo

PARTIAL. The legacy scan defines a D-mixing input at quarkConstraints/deltaf2.py:252 and evaluates D0 mixing through evaluate\_d0\_mixing at quarkConstraints/deltaf2.py:941, but that result uses $|M_{12}^{\rm NP}|$ and returns only a magnitude ratio. The scan exports d\_mix\_ratio at quarkConstraints/scan.py:103 and quarkConstraints/scan.py:439. The modern policy labels D0 as conservative\_non\_cp\_mixing\_amplitude\_hadronic at quarkConstraints/modern/phenomenology.py:46. A paper-mode helper does retain complex $M_{12}^{D0}$ and exposes im\_M12\_D0\_NP\_GeV at quarkConstraints/paper\_0710\_1869/eft\_deltaf2/observables.py:1403, but there is no exported $|q/p|$ or $\phi_D$ evaluator.

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

Implementation difficulty

LOW. The existing $\Delta F=2$ operator and RG machinery is the right basis for C002, so no new operator class is required. The missing step is a CPV observable wrapper or likelihood policy that maps the complex D0 mixing amplitude onto a conservative HFLAV $|q/p|,\phi_D$ constraint.

Reason: The existing $\Delta F = 2$ operator basis and D0 M12 machinery cover the relevant short-distance amplitude; implementation would need a CPV observable wrapper or conservative HFLAV likelihood policy, not a new operator or RG calculation.

Key references

Process-local source keys before bibliography consolidation: hflav\_ckm25\_dmixing\_cpv\_fit, pdg2025\_dmixing\_review\_cpv, lhcb2023\_arxiv2208\_06512, belle\_belleii2025\_arxiv2410\_22961, and cfw2008\_arxiv0804\_1954.

value 0.983

RESOLVED

Match snapshot line 23

L20: Selected table_results.pdf text, extracted only for the C002 observables:
L21: 
L22: Parameter                           No indirect CPV     No subleading amplitudes     All CPV       95% C.L. interval in All CPV
L23: |q/p|                               1                   1.002 +/- 0.005              0.983 +0.015/-0.014 [0.955, 1.012]
L24: phi (degrees)                       0                   -0.08 +/- 0.19               -1.51 +1.03/-1.06 [-3.63, 0.51]
L25: phiM (degrees)                      0                   -0.78 +1.60/-1.63            -0.03 +0.70/-0.71 [-1.48, 1.35]
L26: phiGamma (degrees)                  0                   0                            2.03 +1.54/-1.52 [-0.94, 5.08]

value -1.51

RESOLVED

Match snapshot line 24

L21: 
L22: Parameter                           No indirect CPV     No subleading amplitudes     All CPV       95% C.L. interval in All CPV
L23: |q/p|                               1                   1.002 +/- 0.005              0.983 +0.015/-0.014 [0.955, 1.012]
L24: phi (degrees)                       0                   -0.08 +/- 0.19               -1.51 +1.03/-1.06 [-3.63, 0.51]
L25: phiM (degrees)                      0                   -0.78 +1.60/-1.63            -0.03 +0.70/-0.71 [-1.48, 1.35]
L26: phiGamma (degrees)                  0                   0                            2.03 +1.54/-1.52 [-0.94, 5.08]
L27: chi2/d.o.f.                         72.817/(63-7)       72.797/(63-8)                70.711/(63-10)