Catalog · Charm · C003

C003 $\Delta A_{CP}(D^0\to K^+K^-,\pi^+\pi^-)$

Direct CP violation in D0 $ \to $ K+K- and D0 $ \to \pi^+\pi^-$

Status SUBTLETY-ADDED VERIFIED High Code: NO Priority Medium

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
$\Delta a_{CP}^{dir}$	-0.159 percent	2025	HFLAV Combination of Direct and Indirect CP Violation	source ↑
$a_{CP}^{ind}$	-0.01 percent	2025	HFLAV Combination of Direct and Indirect CP Violation	source ↑
No-CPV point in the $\Delta a_{CP}^{dir}$ vs $a_{CP}^{ind}$ fit	?	2025	HFLAV Combination of Direct and Indirect CP Violation	source ↑
$\Delta A_{CP}$ = $A_{CP}(D0 \to $ K-K+) - $A_{CP}(D0 \to \pi^-\pi^+$)	-15.4 dimensionless asymmetry	2019	LHCb Collaboration, arXiv:1903.08726 / Phys. Rev. Lett. 122, 211803	source ↑
$A_{CP}^K$ - $A_{CP}^\pi$	-0.154 percent	2025	HFLAV CKM25 D Mixing Results allowing for CPV	source ↑
$A_\pi$ in all-CPV-allowed fit #3	0.225 percent	2025	HFLAV CKM25 table_results.pdf text extraction	source ↑
$A_K$ in all-CPV-allowed fit #3	0.068 percent	2025	HFLAV CKM25 table_results.pdf text extraction	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 flavor generically carries new CP phases in both up- and down-sector flavor transitions. Unlike neutral-charm mixing, this is not a $\Delta C=2$ mixing constraint: it probes $\Delta C=1$ nonleptonic amplitudes, including possible chromomagnetic dipoles and four-quark penguin structures. It is therefore a diagnostic for BSM CP phases in $c\to u$ transitions that can be hidden by a neutral-meson-mixing-only scan.

What's changed since the original paper

The CFW 2008 RS-flavor baseline predates the charm direct-CP observation. The important post-2008 change is experimental: LHCb reported the first observation of CP violation in charm decays in 2019, and HFLAV now provides a compact direct-vs-indirect CPV combination with percent-level fit parameters. The 2025 CKM25 charm fit additionally folds the $\Delta A_{CP}$ input into a global all-CPV fit together with $A_K$ and $A_{\pi}$.

Validity and model dependence

The experimental observable is robust because the difference cancels many production and detection asymmetries. Interpreting it as a bound on a specific new-physics Wilson coefficient is much less clean: Standard Model long-distance charm amplitudes are difficult to compute, and the HFLAV extraction separates direct and indirect CPV using small mixing corrections. Treat this as a model-dependent $\Delta C=1$ CP-phase constraint, not as a clean short-distance subtraction. In down-aligned or kaon-protected RS variants, up-sector observables become leading rather than secondary diagnostics.

Code coverage in this repo

NO. The required grep finds neutral $D^0$-mixing support but no direct charm CP-asymmetry implementation. The current implemented charm surface is evaluate\_d0\_mixing at quarkConstraints/deltaf2.py:941; the modern policy labels $D^0$ as conservative non-CP mixing at quarkConstraints/modern/phenomenology.py:46. Focused searches for DeltaA\_CP, A\_CP, direct CP, and $D^0\to K^+K^-,\pi^+\pi^-$ across the required implementation directories found no C003 observable.

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

Implementation difficulty

HIGH. Production integration would require a new $\Delta C=1$ operator/matching layer, RG treatment for the relevant four-quark and dipole operators, and a hadronic-amplitude or likelihood prescription for the nonleptonic charm modes. The existing $\Delta F=2$ basis does not cover it.

Reason: A production constraint would need new $\Delta C = 1$ operator matching, RG treatment for four-quark and chromomagnetic operators, and a nonleptonic charm hadronic-amplitude or likelihood prescription; the current $\Delta F = 2$ machinery does not cover this observable.

Key references

Process-local source keys before bibliography consolidation: hflav2025\_direct\_indirect\_cpv, hflav\_ckm25\_dcpv\_inputs, lhcb2019\_arxiv1903\_08726, and cfw2008\_arxiv0804\_1954.

value_uncertainty -0.159 +/- 0.029

RESOLVED

Match snapshot line 36

L33: 
L34: Central values and one-standard-deviation errors:
L35: a_CP^ind = (-0.010 +/- 0.012)%
L36: Delta a_CP^dir = (-0.159 +/- 0.029)%

value -0.01

RESOLVED

Match snapshot line 35

L32: or 5.3 standard deviations.
L33: 
L34: Central values and one-standard-deviation errors:
L35: a_CP^ind = (-0.010 +/- 0.012)%
L36: Delta a_CP^dir = (-0.159 +/- 0.029)%

value_uncertainty -15.4 +/- 2.9

RESOLVED

Match snapshot line 26

L23: for muon-tagged D0 mesons.
L24: 
L25: Combining these with previous LHCb results leads to
L26: Delta A_CP = (-15.4 +/- 2.9) x 10^-4,
L27: where the uncertainty includes both statistical and systematic contributions.
L28: The measured value differs from zero by more than five standard deviations.
L29: This is the first observation of CP violation in the decay of charm hadrons.

value_uncertainty -0.154 +/- 0.029

RESOLVED

Match snapshot line 18

L15: Selected measured-observable input:
L16: Index 60:
L17: Observable: A_CP^K - A_CP^pi
L18: Value: (-0.154 +/- 0.029)%
L19: Source: LHCb, 8.9 fb^-1 pp collisions at sqrt(s) = 7, 8, 13 TeV.
L20: Flavor tags: D*+ -> D0 pi+ and B -> D0 mu- X.
L21: Mean time inputs: (<t>_K - <t>_pi) / tau_D = 0.115 +/- 0.002;

value_uncertainty 0.225 +/- 0.057

RESOLVED

Match snapshot line 35

L32: Final HFLAV CKM25 table_results.pdf extract from pdftotext:
L33: All-CPV-allowed fit #3:
L34: A_D (%) = -0.81 +/- 0.88, 95% C.L. interval [-2.54, 0.92].
L35: A_pi (%) = 0.225 +/- 0.057, 95% C.L. interval [0.11, 0.34].
L36: A_K (%) = 0.068 +/- 0.051, 95% C.L. interval [-0.03, 0.17].
L37: chi^2/d.o.f. = 70.711/(63 - 10) = 1.33.

value_uncertainty 0.068 +/- 0.051

RESOLVED

Match snapshot line 36

L33: All-CPV-allowed fit #3:
L34: A_D (%) = -0.81 +/- 0.88, 95% C.L. interval [-2.54, 0.92].
L35: A_pi (%) = 0.225 +/- 0.057, 95% C.L. interval [0.11, 0.34].
L36: A_K (%) = 0.068 +/- 0.051, 95% C.L. interval [-0.03, 0.17].
L37: chi^2/d.o.f. = 70.711/(63 - 10) = 1.33.