Catalog · Beauty · B004

B004 $\phi_s^{c\bar c s}$

CP phase $\phi_s$ in Bs0 $ \to J/\psi \phi$

Status REVIEWED VERIFIED Low Code: PARTIAL Priority High

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
$\phi_s^{ccs}$, all combined b $ \to $ c $\bar{c}$ s Bs0 decays	-0.041 rad	2025	HFLAV PDG 2025 phi_s inputs	source ↑
$\phi_s^{ccs}$, Bs0 $ \to J/\psi K+ K-$ combined	-0.05 rad	2025	HFLAV PDG 2025 phi_s inputs	source ↑
$\phi_s$ in Bs0 $ \to J/\psi(\mu^+\mu^-$) $K+ K-$ near $\phi(1020$)	-0.039 rad	2024	LHCb Collaboration, Phys. Rev. Lett. 132 (2024) 051802	source ↑
-2 $\beta_s$	-0.0368 rad	-	LHCb Collaboration, quoting global CKM fits	source ↑

Why this constrains the RS scan

In anarchic warped models, tree-level KK-gluon and electroweak exchange can generate a complex new contribution to $B_s-\bar B_s$ mixing. $\phi_s$ is therefore the phase complement to the $\Delta m_s$ magnitude constraint: a point can satisfy the mass splitting while still shifting $\arg M_{12}^s$. The process is especially clean for RS quark scans because the dominant decay amplitude is the CKM-favored $b\to c\bar c s$ transition, while new physics mainly enters through $\Delta B=2$ mixing.

What's changed since the original paper

The 2008 RS-flavor baseline in cfw\_2008\_rs\_flavor predates the LHCb era and treats neutral-meson mixing as a generic $\Delta F=2$ stress test rather than as a precision $\phi_s$ input. Since then, Tevatron, ATLAS, CMS, and especially LHCb measurements have turned $\phi_s$ into a precision phase test. The 2024 LHCb Run-2 analysis superseded the earlier Run-2 result in the same channel, added improved flavor tagging and decay-time calibration, and found no evidence for polarization dependence (lhcb\_2024\_jpsikk\_phis\_arxiv). HFLAV's PDG 2025 combination now reaches $0.016~{\rm rad}$ precision and is consistent with the small SM phase (hflav\_pdg2025\_phis\_inputs).

Validity and model dependence

This is a robust neutral-meson-mixing phase constraint, but it is not identical to a pure $\arg M_{12}^s$ observable without assumptions. The interpretation uses a CKM phase convention, assumes no large new physics in the tree-dominated decay amplitude, and must budget subleading penguin effects. The vector--vector final state also requires an angular analysis and experimental correlations with $\Delta\Gamma_s$. For the present catalog, it should be classified as a robust $\Delta F=2$ phase observable with small decay-amplitude systematics.

Code coverage in this repo

PARTIAL. A focused grep for phi\_s, phis, J/psi, Jpsi, psi.*phi, B\_s.*phi, and beta\_s found no direct observable implementation in the required implementation and test directories. The underlying $B_s$ mixing lane exists: quarkConstraints/deltaf2.py:239 defines the b\_s input, quarkConstraints/deltaf2.py:651 stores $\Delta m_s$, and quarkConstraints/deltaf2.py:922 evaluates the $B_s$ mixing contribution. However, quarkConstraints/deltaf2.py:929 reduces the computed complex amplitude to $\lvert M_{12}^{s,\rm NP}\rvert$, so the phase needed for $\phi_s$ is not exposed. The modern bridge also evaluates only the magnitude-style $B_s$ mixing contribution at quarkConstraints/modern/phenomenology.py:657; 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. No new operator basis is required: the existing SLL/SLR/VLL/VRR/LR $\Delta F=2$ machinery covers the $B_s$ mixing amplitude. The missing work is to retain the complex $M_{12}^s$, combine it with the SM $-2\beta_s$ convention, and add a likelihood or tolerance policy including the HFLAV uncertainty and small penguin-systematic allowance.

Key references

Process-local reference keys before bibliography consolidation: hflav\_pdg2025\_phis\_inputs, lhcb\_2024\_jpsikk\_phis\_arxiv, and cfw\_2008\_rs\_flavor.

fallback_value_uncertainty phi_s^ccs, all combined b -> c cbar s Bs0 decays = -0.041 +- 0.016 rad

RESOLVED

Match snapshot line 26

L23:   phi_s^ccs = -0.050 +/- 0.017 rad;
L24:   DeltaGamma_s = +0.077 +/- 0.006 ps^-1.
L25: - All combined:
L26:   phi_s^ccs = -0.041 +/- 0.016 rad;
L27:   DeltaGamma_s = +0.079 +/- 0.006 ps^-1.
L28: 
L29: Reference identities in the HFLAV table for the key post-2008 inputs:

fallback_value_uncertainty phi_s^ccs, Bs0 -> J/psi K+ K- combined = -0.05 +- 0.017 rad

RESOLVED

Match snapshot line 23

L20:   phi_s^ccs = -0.033 +/- 0.018 rad;
L21:   DeltaGamma_s = +0.085 +/- 0.004 ps^-1.
L22: - Bs0 -> J/psi K+K- combined:
L23:   phi_s^ccs = -0.050 +/- 0.017 rad;
L24:   DeltaGamma_s = +0.077 +/- 0.006 ps^-1.
L25: - All combined:
L26:   phi_s^ccs = -0.041 +/- 0.016 rad;

fallback_value_uncertainty phi_s in Bs0 -> J/psi(mu+mu-) K+ K- near phi(1020) = -0.039 +- 0.022 rad

RESOLVED

Match snapshot line 22

L19: the phi(1020) resonance.
L20: 
L21: The values obtained are:
L22:   phi_s = -0.039 +/- 0.022 +/- 0.006 rad,
L23:   DeltaGamma_s = 0.0845 +/- 0.0044 +/- 0.0024 ps^-1,
L24:   Gamma_s - Gamma_d = -0.0056^{+0.0013}_{-0.0015} +/- 0.0014 ps^-1,
L25: where the first uncertainty is statistical and the second systematic.

fallback_value_uncertainty -2 beta_s = -0.0368 +- 0.0009 rad

RESOLVED

Match snapshot line 33

L30: Neglecting subleading loop contributions in b -> c cbar s transitions,
L31: phi_s is predicted in the Standard Model to equal -2 beta_s. Global CKM fits
L32: quoted by the paper give
L33:   -2 beta_s = -0.0368^{+0.0009}_{-0.0006} rad.
L34: At the time of the paper, the world average quoted in the introduction was
L35:   phi_s^ccs = -0.049 +/- 0.019 rad.
L36: