Catalog · Beauty · B003

B003 $\Delta m_s$

$B_s^0-B_{sbar}^0$ oscillation frequency / mass splitting

Status REVIEWED VERIFIED Low Code: YES Priority High

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
$\Delta m_s$	17.766 ps^-1	2024	HFLAV Fall 2024 recommended b-hadron lifetime and oscillation averages	source ↑
$x_s$	26.94 dimensionless	2024	HFLAV Fall 2024 recommended b-hadron lifetime and oscillation averages	source ↑
$\chi_s$	0.499314 dimensionless	2024	HFLAV Fall 2024 recommended b-hadron lifetime and oscillation averages	source ↑
$1/\Gamma_s$	1.516 ps	2024	HFLAV Fall 2024 recommended b-hadron lifetime and oscillation averages	source ↑
$DeltaGamma_s$	0.0781 ps^-1	2024	HFLAV Fall 2024 recommended b-hadron lifetime and oscillation averages	source ↑
$\Delta m_s$	17.765 ps^-1	2025	HFLAV averages prepared for PDG 2025	source ↑
$\Delta m_s$ from Bs $ \to $ Ds $\pi$, Run 2	17.7683 ps^-1	2022	LHCb Collaboration, Nature Physics 18 (2022) 1-5	source ↑

Why this constrains the RS scan

In anarchic Randall--Sundrum flavor, tree-level KK-gluon and electroweak exchange generate $\Delta B=2$ four-quark operators. $B_s$ mixing is the down-sector $s-b$ analogue of $B_d$ mixing and complements the stronger kaon constraints by testing a different localization and CKM structure. The existing code treats $\Delta m_s$ as a direct bound on the new-physics contribution to $M_{12}^s$, with separate weights for current-current and left-right operators.

What's changed since the original paper

The 2008 RS-flavor baseline in cfw\_2008\_rs\_flavor predates the precision LHCb $B_s$ oscillation program. The key post-2008 experimental step for this catalog is the LHCb measurement in lhcb\_2021\_deltams\_arxiv: using $6~{\rm fb}^{-1}$ of Run-2 $B_s\to D_s\pi$ data, LHCb finds \[ \Delta m_s=17.7683\pm0.0051_{\rm stat}\pm0.0032_{\rm syst}~{\rm ps}^{-1}, \] and a LHCb-only combination \[ \Delta m_s=17.7656\pm0.0057~{\rm ps}^{-1}. \] On the theory side, flag\_2024\_bmixing records the FLAG Review 2024 $N_f=2+1+1$ auxiliary inputs \[ f_{B_s}\sqrt{\hat B_{B_s}}=256.1\pm5.7~{\rm MeV},\qquad \xi=1.216\pm0.016, \] with a warning that correlated decay-constant and mixing inputs should not be reconstructed from separate averages.

Validity and model dependence

The experimental oscillation frequency is very clean. The model-dependent step is translating it into a new-physics allowance: a conservative catalog can bound $|M_{12}^{s,{\rm NP}}|$ directly from the measured splitting, while a sharper SM-subtracted interpretation depends on CKM inputs and FLAG lattice matrix elements. The constraint is therefore a robust $\Delta F=2$ magnitude test, but cancellations between SM and new physics or correlated CKM-fit choices should be made explicit in any live likelihood.

Code coverage in this repo

YES-D2-BS. The v1 $\Delta F=2$ input bundle defines the $B_s$ system at quarkConstraints/deltaf2.py:238 with key b\_s at quarkConstraints/deltaf2.py:239 and down-sector generations (1, 2) at quarkConstraints/deltaf2.py:244. The hadronic constants include the $B_s$ decay constant at quarkConstraints/deltaf2.py:645 and $\Delta m_s$ input at quarkConstraints/deltaf2.py:651. The budget helper is at quarkConstraints/deltaf2.py:893; the evaluator is evaluate\_bs\_mixing at quarkConstraints/deltaf2.py:922, with the QCD-running wrapper at quarkConstraints/deltaf2.py:969. The modern policy also carries $B_s$ in quarkConstraints/modern/phenomenology.py:23, defines the policy entry at quarkConstraints/modern/phenomenology.py:135, and routes it through the bridge evaluator at quarkConstraints/modern/phenomenology.py:657 and quarkConstraints/modern/phenomenology.py:1346. The shared $\Delta F=2$ operator basis is documented at quarkConstraints/qcd\_running.py:7.

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

Implementation difficulty

LOW. The existing $\Delta F=2$ basis and RG path already cover the needed VLL, VRR, scalar, and left-right structures for $B_s$ mixing. Future production work is mostly input hygiene: decide the HFLAV/PDG value policy, refresh FLAG normalization constants, and document whether the live constraint uses a conservative absolute $M_{12}^{\rm NP}$ budget or an SM-subtracted one.

Key references

Process-local reference keys before bibliography consolidation: hflav\_2024\_dms, hflav\_pdg2025\_dms, lhcb\_2021\_deltams\_arxiv, flag\_2024\_bmixing, and cfw\_2008\_rs\_flavor.

fallback_value_uncertainty Delta m_s = 17.766 +- 0.006 ps^-1

RESOLVED

Match snapshot line 21

L18: on B_s^0 mixing is obtained from time-dependent measurements of the oscillation
L19: frequency Delta m_s at high-energy hadron colliders:
L20: 
L21:   Delta m_s = 17.766 +/- 0.006 ps^-1  CDF, LHCb, CMS
L22: 
L23: The same section states that, with 1/Gamma_s = 1.516 +/- 0.006 ps,
L24: DeltaGamma_s = +0.0781 +/- 0.0035 ps^-1, and the assumption of no CP violation

fallback_value_uncertainty x_s = 26.94 +- 0.1

RESOLVED

Match snapshot line 27

L24: DeltaGamma_s = +0.0781 +/- 0.0035 ps^-1, and the assumption of no CP violation
L25: in B_s^0 mixing, this leads to:
L26: 
L27:   x_s = 26.94 +/- 0.10
L28:   chi_s = 0.499314 +/- 0.000005
L29: 
L30: Notes for catalog use:

fallback_value_uncertainty chi_s = 0.499314 +- 5e-06

RESOLVED

Match snapshot line 28

L25: in B_s^0 mixing, this leads to:
L26: 
L27:   x_s = 26.94 +/- 0.10
L28:   chi_s = 0.499314 +/- 0.000005
L29: 
L30: Notes for catalog use:
L31: - The measured observable for pdg_or_equivalent is Delta m_s.

fallback_value_uncertainty 1/Gamma_s = 1.516 +- 0.006 ps

RESOLVED

Match snapshot line 23

L20: 
L21:   Delta m_s = 17.766 +/- 0.006 ps^-1  CDF, LHCb, CMS
L22: 
L23: The same section states that, with 1/Gamma_s = 1.516 +/- 0.006 ps,
L24: DeltaGamma_s = +0.0781 +/- 0.0035 ps^-1, and the assumption of no CP violation
L25: in B_s^0 mixing, this leads to:
L26:

fallback_value_uncertainty DeltaGamma_s = 0.0781 +- 0.0035 ps^-1

RESOLVED

Match snapshot line 24

L21:   Delta m_s = 17.766 +/- 0.006 ps^-1  CDF, LHCb, CMS
L22: 
L23: The same section states that, with 1/Gamma_s = 1.516 +/- 0.006 ps,
L24: DeltaGamma_s = +0.0781 +/- 0.0035 ps^-1, and the assumption of no CP violation
L25: in B_s^0 mixing, this leads to:
L26: 
L27:   x_s = 26.94 +/- 0.10

fallback_value_uncertainty Delta m_s = 17.765 +- 0.006 ps^-1

RESOLVED

Match snapshot line 20

L17: on B_s^0 mixing is obtained from time-dependent measurements of the oscillation
L18: frequency Delta m_s at high-energy hadron colliders:
L19: 
L20:   Delta m_s = 17.765 +/- 0.006 ps^-1  CDF, LHCb, CMS
L21: 
L22: The same section states that, with 1/Gamma_s = 1.516 +/- 0.006 ps,
L23: DeltaGamma_s = +0.082 +/- 0.005 ps^-1, and the assumption of no CP violation

fallback_value_uncertainty Delta m_s from Bs -> Ds pi, Run 2 = 17.7683 +- +/- 0.0051(stat) +/- 0.0032(syst) ps^-1

AMBIGUOUS

Match 1 of 2 snapshot line 17

L14: Extracted result definitions from the arXiv source:
L15:   combinationAll = 17.7656 +/- 0.0057
L16:   combinationHadronic = 17.7666 +/- 0.0057
L17:   resultstat = 17.7683 +/- 0.0051
L18:   resultsyst = 0.0032
L19: 
L20: Abstract/result excerpt, paraphrased from the arXiv source:

Match 2 of 2 snapshot line 26

L23: corresponds to 6 fb^-1 collected in 2015-2018. The oscillation frequency is
L24: found to be
L25: 
L26:   Delta m_s = 17.7683 +/- 0.0051(stat) +/- 0.0032(syst) ps^-1.
L27: 
L28: Combining this result with previous LHCb measurements gives
L29:

fallback_value_uncertainty = 6 fb^-1

AMBIGUOUS

Match 1 of 3 snapshot line 17

L14: Extracted result definitions from the arXiv source:
L15:   combinationAll = 17.7656 +/- 0.0057
L16:   combinationHadronic = 17.7666 +/- 0.0057
L17:   resultstat = 17.7683 +/- 0.0051
L18:   resultsyst = 0.0032
L19: 
L20: Abstract/result excerpt, paraphrased from the arXiv source:

Match 2 of 3 snapshot line 23

L20: Abstract/result excerpt, paraphrased from the arXiv source:
L21: The paper presents a measurement of Delta m_s using B_s -> D_s^- pi^+
L22: decays in pp collisions collected with the LHCb detector. The Run-2 data set
L23: corresponds to 6 fb^-1 collected in 2015-2018. The oscillation frequency is
L24: found to be
L25: 
L26:   Delta m_s = 17.7683 +/- 0.0051(stat) +/- 0.0032(syst) ps^-1.

Match 3 of 3 snapshot line 26

L23: corresponds to 6 fb^-1 collected in 2015-2018. The oscillation frequency is
L24: found to be
L25: 
L26:   Delta m_s = 17.7683 +/- 0.0051(stat) +/- 0.0032(syst) ps^-1.
L27: 
L28: Combining this result with previous LHCb measurements gives
L29:

fallback_value_uncertainty = 17.7656 +- 0.0057 ps^-1

AMBIGUOUS

Match 1 of 2 snapshot line 15

L12: Submitted 9 Apr 2021; last revised 20 Feb 2022.
L13: 
L14: Extracted result definitions from the arXiv source:
L15:   combinationAll = 17.7656 +/- 0.0057
L16:   combinationHadronic = 17.7666 +/- 0.0057
L17:   resultstat = 17.7683 +/- 0.0051
L18:   resultsyst = 0.0032

Match 2 of 2 snapshot line 30

L27: 
L28: Combining this result with previous LHCb measurements gives
L29: 
L30:   Delta m_s = 17.7656 +/- 0.0057 ps^-1,
L31: 
L32: described by the paper as the legacy measurement of the original LHCb detector.
L33: