Catalog · Beauty · B001

B001 $\Delta m_d$

Neutral $B_d$ mixing mass difference

Status REVIEWED VERIFIED Low Code: YES Priority High

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
$\Delta m_d$ in B0-B0bar mixing	0.5069 ps^-1	2025	HFLAV PDG 2025 averages	source ↑
$x_d$	0.7697 dimensionless	2025	HFLAV PDG 2025 averages	source ↑
$\chi_d$	0.186 dimensionless	2025	HFLAV PDG 2025 averages	source ↑

Why this constrains the RS scan

Anarchic warped models generate tree-level flavor-changing neutral currents from KK gluon and electroweak exchange after rotating to the quark-mass basis. $B_d$ mixing probes the $b\leftrightarrow d$ down-sector alignment and is a direct test of the same Wilson-coefficient pipeline used for kaon and $B_s$ mixing. Compared with $\varepsilon_K$, it is less chirally enhanced but constrains a different row-column structure of the anarchic profiles.

What's changed since the original paper

The arXiv:0804.1954 RS-flavor baseline, source key cfw\_2008\_rs\_flavor, highlighted KK-gluon flavor bounds near $21\,{\rm TeV}$ in standard RS scenarios and $33\,{\rm TeV}$ in the pseudo-Goldstone setup, with boundary kinetic terms and flavor assumptions as caveats. Since then, $\Delta m_d$ has become a precision-average observable. Belle II has repeated the benchmark measurement with early SuperKEKB data, reporting \[ \Delta m_d = 0.516 \pm 0.008_{\rm stat}\pm0.005_{\rm syst}\ {\rm ps}^{-1} \] from $190\,{\rm fb}^{-1}$, with both numbers recorded under source key belleii\_2023\_bd\_mixing. On the theory side, source key flag2024\_b\_mixing documents the FLAG Review 2024 heavy-quark inputs relevant for $B$-mixing matrix elements and global unitarity-triangle fits; those inputs are theory normalization data, not the measured observable.

Validity and model dependence

This is a robust neutral-meson-mixing magnitude constraint. The experimental average is precise, but turning it into a new-physics exclusion requires a policy for the SM contribution and CKM inputs. The current code uses an allowed NP budget rather than a full correlated CKM fit, so catalog users should treat it as a conservative magnitude screen, not as a global-fit replacement.

Code coverage in this repo

YES-D2-BD. The legacy $\Delta F=2$ backend defines the $B_d$ input at quarkConstraints/deltaf2.py:225 and notes the hadronic matrix-element treatment at quarkConstraints/deltaf2.py:236. The in-code $B_d$ hadronic and experimental constants are at quarkConstraints/deltaf2.py:631--638. The scan dispatches b\_d through evaluate\_bd\_mixing at quarkConstraints/deltaf2.py:383--391; the evaluator itself is quarkConstraints/deltaf2.py:903--915, with the running wrapper at quarkConstraints/deltaf2.py:960--966. The modern metadata layer also carries $B_d$ as a policy system at quarkConstraints/modern/phenomenology.py:23 and mirrors the input at quarkConstraints/modern/inputs.py:967--976.

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

Implementation difficulty

LOW. The existing $\Delta F=2$ SLL/SLR/VLL/VRR/LR machinery and BMU-style running cover the $B_d$ mixing magnitude observable. A future production refresh would mainly improve provenance, unit conversion, and likelihood policy rather than adding new operators or RG evolution.

Key references

Process-local reference keys before bibliography consolidation: hflav\_pdg2025\_bd\_mixing, belleii\_2023\_bd\_mixing, flag2024\_b\_mixing, and cfw\_2008\_rs\_flavor.

fallback_value_uncertainty Delta m_d in B0-B0bar mixing = 0.5069 +- 0.0019 ps^-1

AMBIGUOUS

Match 1 of 3 snapshot line 13

L10: 
L11: Extracted value block: B0 mixing: oscillations and mass difference.
L12: - Combined time-dependent oscillation-frequency result:
L13:   Delta m_d = 0.5069 +- 0.0019 ps^-1
L14:   Inputs listed by HFLAV: ALEPH, DELPHI, L3, OPAL, CDF, D0, BABAR, BELLE, LHCb.
L15: - Time-integrated mixing probability input:
L16:   chi_d = 0.182 +- 0.015

Match 2 of 3 snapshot line 19

L16:   chi_d = 0.182 +- 0.015
L17:   Inputs listed by HFLAV: ARGUS and CLEO.
L18: - World averages after assuming no CP violation in mixing, no width difference in the B0 system, and using tau(B0) = 1.517 +- 0.004 ps:
L19:   Delta m_d = 0.5069 +- 0.0019 ps^-1
L20:   x_d = 0.7697 +- 0.0035
L21:   chi_d = 0.1860 +- 0.0011
L22:   Inputs listed by HFLAV for chi_d world average: ALEPH, DELPHI, L3, OPAL, CDF, D0, BABAR, BELLE, LHCb, ARGUS, CLEO.

Match 3 of 3 snapshot line 25

L22:   Inputs listed by HFLAV for chi_d world average: ALEPH, DELPHI, L3, OPAL, CDF, D0, BABAR, BELLE, LHCb, ARGUS, CLEO.
L23: 
L24: Use in B001:
L25: - Canonical measured experimental observable for B001 is Delta m_d = 0.5069 +- 0.0019 ps^-1.
L26: - x_d and chi_d are companion quantities, not separate B001 headline observables.

fallback_value_uncertainty x_d = 0.7697 +- 0.0035

RESOLVED

Match snapshot line 20

L17:   Inputs listed by HFLAV: ARGUS and CLEO.
L18: - World averages after assuming no CP violation in mixing, no width difference in the B0 system, and using tau(B0) = 1.517 +- 0.004 ps:
L19:   Delta m_d = 0.5069 +- 0.0019 ps^-1
L20:   x_d = 0.7697 +- 0.0035
L21:   chi_d = 0.1860 +- 0.0011
L22:   Inputs listed by HFLAV for chi_d world average: ALEPH, DELPHI, L3, OPAL, CDF, D0, BABAR, BELLE, LHCb, ARGUS, CLEO.
L23:

fallback_value_uncertainty chi_d = 0.186 +- 0.0011

RESOLVED

Match snapshot line 21

L18: - World averages after assuming no CP violation in mixing, no width difference in the B0 system, and using tau(B0) = 1.517 +- 0.004 ps:
L19:   Delta m_d = 0.5069 +- 0.0019 ps^-1
L20:   x_d = 0.7697 +- 0.0035
L21:   chi_d = 0.1860 +- 0.0011
L22:   Inputs listed by HFLAV for chi_d world average: ALEPH, DELPHI, L3, OPAL, CDF, D0, BABAR, BELLE, LHCb, ARGUS, CLEO.
L23: 
L24: Use in B001: