Catalog · Charm · C001

C001 $D^0-\bar{D}^0 \,\text{mixing}\,: x_D, y_D, \Delta m_D$

Neutral charm mixing

Status SUBTLETY-ADDED VERIFIED Low Code: YES Priority Medium

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
$x_D$ = $\Delta m_D$ / $\Gamma_D$	0.405 percent	2025	HFLAV CKM25 global fit, all-CPV fit	source ↑
$y_D$ = $\Delta \Gamma_D$ / (2 $\Gamma_D$)	0.636 percent	2025	HFLAV CKM25 global fit, all-CPV fit	source ↑
$\|m(D1^0$) - $m(D2^0)\|$ = x $\Gamma$	0.997 $10^10 hbar s^-1$	2025	PDG Live S032D, produced by HFLAV	source ↑
$\Delta$ y in the LHCb D0 $ \to K0_S \pi^+ \pi^-$ CPV-allowed input	0.031 percent	2025	HFLAV CKM25 measured-observable input table	source ↑
$\Delta \Gamma_D$ / $\Gamma_D$ = 2 $y_D$	1.272 percent	2025	Derived from HFLAV CKM25 all-CPV y_D	source ↑
contextual generic RS KK-gluon mass scale	generic RS KK-gluon mass bounds around 21 TeV	2008	Csaki-Falkowski-Weiler 2008, arXiv:0804.1954	source ↑
contextual composite pseudo-Goldstone KK-gluon mass scale	stronger composite pseudo-Goldstone bounds around 33 TeV	2008	Csaki-Falkowski-Weiler 2008, arXiv:0804.1954	source ↑

Why this constrains the RS scan

In anarchic warped models, KK-gluon and other heavy neutral exchanges generate $\Delta C=2$ four-quark operators connecting $u$ and $c$. The same operator-basis logic used for $K$, $B_d$, and $B_s$ mixing applies, but the charm system is up-sector and long-distance dominated. It is therefore a useful complementary test of whether the scan's flavor alignment suppresses both down- and up-sector neutral currents.

What's changed since the original paper

The CFW 2008 baseline (cfw2008\_arxiv0804\_1954) already treated warped anarchic flavor as strongly constrained, with generic RS KK-gluon scales around $21$ TeV and composite pseudo-Goldstone scenarios around $33$ TeV. Since then, the charm-mixing experimental picture has become much sharper. LHCb's 2021 $D^0\to K_S^0\pi^+\pi^-$ analysis (lhcb2021\_arxiv2106\_03744) observed a nonzero neutral-charm mass difference, and the current HFLAV/PDG global fits decisively exclude the no-mixing point. The same HFLAV fit remains consistent with no indirect CP violation, so the CP-even magnitudes are the clean C001 inputs.

Validity and model dependence

As a new-physics constraint this is robust in the sense that any short-distance $\Delta C=2$ amplitude contributes to $M_{12}^D$. It is also SM-theory-limited: the observed mixing is believed to be dominated by long-distance Standard Model amplitudes that are hard to compute. The safe catalog interpretation is therefore conservative, bounding the magnitude of a new-physics contribution rather than 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

YES. The legacy lane has a default D-mixing input at quarkConstraints/deltaf2.py:252, with reject reason d\_mix at quarkConstraints/deltaf2.py:256, D0 hadronic inputs starting at quarkConstraints/deltaf2.py:655, and DELTA\_M\_D\_EXP at quarkConstraints/deltaf2.py:665. The numeric evaluator is evaluate\_d0\_mixing at quarkConstraints/deltaf2.py:941. The scan writes d\_mix\_ratio at quarkConstraints/scan.py:103 and quarkConstraints/scan.py:439. The modern policy surface also lists $D^0$ at quarkConstraints/modern/phenomenology.py:23 and evaluates the bridge result at quarkConstraints/modern/phenomenology.py:1356.

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

Implementation difficulty

LOW. The existing $\Delta F=2$ machinery already contains the D0 evaluator and the required VLL/VRR/LR operator structure. A future production update would mainly refresh the experimental value and document the conservative long-distance treatment, not add a new operator basis.

Reason: The existing $\Delta F = 2$ neutral-meson machinery already covers D0 mixing with VLL/VRR/LR operator support and a D0-specific evaluator; catalog updates mainly require source/value refresh and sidecar provenance.

Key references

Process-local source keys before bibliography consolidation: hflav\_ckm25\_dmixing\_global\_fit, pdg2025\_deltam\_d\_pdgLive, pdg2025\_dmixing\_review\_table70\_7, lhcb2021\_arxiv2106\_03744, and cfw2008\_arxiv0804\_1954.

value_uncertainty 0.405 +/- 0.043

RESOLVED

Match snapshot line 16

L13: Selected table_results.pdf text, extracted only for the C001 observables:
L14: 
L15: Parameter                           No indirect CPV     No subleading amplitudes     All CPV       95% C.L. interval in All CPV
L16: x (%)                               0.398 +/- 0.043     0.405 +/- 0.043              0.405 +/- 0.043 [0.320, 0.489]
L17: y (%)                               0.636 +/- 0.023     0.638 +/- 0.023              0.636 +/- 0.024 [0.590, 0.682]
L18: |q/p|                               1                   1.002 +/- 0.005              0.983 +0.015/-0.014 [0.955, 1.012]
L19: phi (degrees)                       0                   -0.08 +/- 0.19               -1.51 +1.03/-1.06 [-3.63, 0.51]

value_uncertainty 0.636 +/- 0.024

RESOLVED

Match snapshot line 17

L14: 
L15: Parameter                           No indirect CPV     No subleading amplitudes     All CPV       95% C.L. interval in All CPV
L16: x (%)                               0.398 +/- 0.043     0.405 +/- 0.043              0.405 +/- 0.043 [0.320, 0.489]
L17: y (%)                               0.636 +/- 0.023     0.638 +/- 0.023              0.636 +/- 0.024 [0.590, 0.682]
L18: |q/p|                               1                   1.002 +/- 0.005              0.983 +0.015/-0.014 [0.955, 1.012]
L19: phi (degrees)                       0                   -0.08 +/- 0.19               -1.51 +1.03/-1.06 [-3.63, 0.51]
L20: x12 (%)                             0.398 +/- 0.043     0.409 +/- 0.044              0.406 +/- 0.043 [0.321, 0.490]

value_uncertainty 0.997 +/- 0.116

RESOLVED

Match snapshot line 16

L13: 
L14: Value table excerpt:
L15: VALUE (10^10 hbar s^-1)
L16: 0.997 +/- 0.116  OUR EVALUATION (Produced by HFLAV)
L17: 0.98 +/- 0.11    OUR AVERAGE
L18: 
L19: Catalog conversion using hbar = 6.582119569e-25 GeV s:

value 0.031

RESOLVED

Match snapshot line 17

L14: x_CP         (0.400 +/- 0.045 +/- 0.020)%
L15: y_CP         (0.551 +/- 0.116 +/- 0.059)%
L16: Delta x      (-0.029 +/- 0.018 +/- 0.001)%
L17: Delta y      (0.031 +/- 0.035 +/- 0.013)%
L18: 
L19: Source line in HFLAV table:
L20: LHCb, D0 -> K0_S pi+ pi- results using 5.4 fb^-1 at sqrt(s)=13 TeV,

value_uncertainty 1.272 +/- 0.048

RESOLVED

Match snapshot line 27

L24: chi2/d.o.f.                         72.817/(63-7)       72.797/(63-8)                70.711/(63-10)
L25: 
L26: Derived for catalog convenience from the all-CPV y value:
L27: DeltaGamma_D/Gamma_D = 2 y = (1.272 +/- 0.048)%.

display_value generic RS KK-gluon mass bounds around 21 TeV

RESOLVED

Match snapshot line 14

L11: - Studies flavor constraints in 5D warped models and composite pseudo-Goldstone
L12:   Higgs scenarios.
L13: - Re-examines flavor constraints in standard Randall-Sundrum-type scenarios.
L14: - Reports generic KK-gluon mass bounds around 21 TeV in standard RS scenarios.
L15: - Reports stronger bounds around 33 TeV in the composite pseudo-Goldstone case.
L16: - Concludes that fully anarchic warped flavor is strongly constrained and may
L17:   require partial flavor symmetries.

display_value stronger composite pseudo-Goldstone bounds around 33 TeV

RESOLVED

Match snapshot line 15

L12:   Higgs scenarios.
L13: - Re-examines flavor constraints in standard Randall-Sundrum-type scenarios.
L14: - Reports generic KK-gluon mass bounds around 21 TeV in standard RS scenarios.
L15: - Reports stronger bounds around 33 TeV in the composite pseudo-Goldstone case.
L16: - Concludes that fully anarchic warped flavor is strongly constrained and may
L17:   require partial flavor symmetries.
L18: