Catalog · Beauty · B034

B034 $\phi_s^{s\bar{s}s}, |\lambda|(B_s^0\to\phi\phi)$

$B_s \to \phi \phi b \to s \bar{s}$ s penguin

Status REVIEWED VERIFIED High Code: NO Priority Low

Why this constrains the RS scan

In warped anarchic flavour models, flavour-changing KK gluon, electroweak-KK, or misaligned $Z/H$-like effects can induce new $\Delta B=1$ penguin operators with phases not fixed by the Standard Model CKM fit. $B_s^0\to \phi\phi$ is therefore a useful null test for new weak phases in $b\to s\bar{s}s$ amplitudes. It is complementary to the existing repo's $B_s$-mixing magnitude lane: a new phase could appear in the decay amplitude or in mixing-decay interference even when a simple $\Delta m_s$ bound is satisfied.

What's changed since the original paper

The process matured after the arXiv:0804.1954 era. LHCb's 2014 analysis used $3.0\,{\rm fb}^{-1}$, about 4000 signal decays, and found $\phi_s=-0.17\pm0.15\pm0.03\ {\rm rad}$ (lhcb2014\_bs\_phiphi\_cp\_arxiv). The 2019 update used $5.0\,{\rm fb}^{-1}$, about 9000 signal decays, and reported $\phi_s^{s\bar{s}s}=-0.073\pm0.115\pm0.027\ {\rm rad}$ with $|\lambda|=0.99\pm0.05\pm0.01$ (lhcb2019\_bs\_phiphi\_cp\_cds). The 2023 precision measurement used $6\,{\rm fb}^{-1}$ at $13\,{\rm TeV}$, giving $\phi_s^{s\bar{s}s}=-0.042\pm0.075\pm0.009\ {\rm rad}$ and $|\lambda|=1.004\pm0.030\pm0.009$ before combination (lhcb2023\_bs\_phiphi\_cp\_cds). The combined LHCb result remains consistent with CP conservation and Standard Model expectations.

Validity and model dependence

This is a strong experimental null test but a model-dependent hard constraint. The Standard Model expectation for the penguin phase is close to zero, while $|\lambda|=1$ corresponds to no direct CP violation, but a production bound requires a $\Delta B=1$ operator normalization, QCD running, polarization treatment, hadronic amplitudes, and strong-phase assumptions. It should be cataloged as a high-value contextual penguin-phase observable until a specific nonleptonic framework is chosen.

Code coverage in this repo

NO. Required greps over quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ found no $B_s^0\to\phi\phi$, $b\to s\bar{s}s$ penguin, time-dependent charmless CP, or angular-likelihood implementation. Adjacent code only covers neutral $B_s$ mixing: quarkConstraints/deltaf2.py:239 defines the $B_s$ input, quarkConstraints/deltaf2.py:922 evaluates $B_s$ mixing, and quarkConstraints/modern/phenomenology.py:657 bridges the modern $B_s$-mixing evaluator.

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

Implementation difficulty

HIGH. The existing $\Delta F=2$ basis does not compute $\Delta B=1$ penguin amplitudes. A live constraint needs new nonleptonic operators, matching, running, angular/polarization likelihood handling, and a hadronic-amplitude prescription.

Reason: Requires a new $\Delta B = 1$ nonleptonic $b \to s$ sbar s operator and amplitude/likelihood treatment. Existing $\Delta F = 2$ SLL/SLR/VLL/VRR/LR1/LR2 neutral-meson machinery covers B_s mixing magnitudes but not $B_s \to \phi \phi$ decay amplitudes, polarization-dependent angular observables, or strong-phase model dependence.

Key references

pdg2025\_bs\_phiphi\_cp, lhcb2023\_bs\_phiphi\_cp\_cds, lhcb2019\_bs\_phiphi\_cp\_cds, lhcb2014\_bs\_phiphi\_cp\_arxiv, hflav2024\_bs\_phiphi\_branching, and cfw2008\_arxiv0804\_1954.

observables[0].fallback_value_uncertainty beta_s(b -> s sbar s) = 3.7 +- 3.5 10^-2 rad

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Match snapshot line 10

L7: 
L8: Relevant extracted values:
L9: - PDG table "CP Violation phase beta_s (b -> s sbar s)" reports
L10:   beta_s = (3.7 +/- 3.5) x 10^-2 rad, document AAIJ 23AT, LHCb,
L11:   pp at 7, 8, 13 TeV.
L12: - PDG note for AAIJ 23AT reports phi_s^{s sbar s} = -0.074 +/- 0.069 rad
L13:   and |lambda| = 1.009 +/- 0.030.

observables[1].fallback_value_uncertainty phi_s^{s sbar s}, LHCb combined note = -0.074 +- 0.069 rad

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Match snapshot line 12

L9: - PDG table "CP Violation phase beta_s (b -> s sbar s)" reports
L10:   beta_s = (3.7 +/- 3.5) x 10^-2 rad, document AAIJ 23AT, LHCb,
L11:   pp at 7, 8, 13 TeV.
L12: - PDG note for AAIJ 23AT reports phi_s^{s sbar s} = -0.074 +/- 0.069 rad
L13:   and |lambda| = 1.009 +/- 0.030.
L14: - Measurement note: time-dependent fit to B_s^0 -> phi phi decays, assuming
L15:   independence of the helicity of the phi phi decay.

observables[2].fallback_value_uncertainty |lambda|, LHCb combined note = 1.009 +- 0.03

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Match snapshot line 13

L10:   beta_s = (3.7 +/- 3.5) x 10^-2 rad, document AAIJ 23AT, LHCb,
L11:   pp at 7, 8, 13 TeV.
L12: - PDG note for AAIJ 23AT reports phi_s^{s sbar s} = -0.074 +/- 0.069 rad
L13:   and |lambda| = 1.009 +/- 0.030.
L14: - Measurement note: time-dependent fit to B_s^0 -> phi phi decays, assuming
L15:   independence of the helicity of the phi phi decay.
L16:

observables[0].fallback_value_uncertainty phi_s^{s sbar s}, helicity-independent 2023 fit = -0.042 +- 0.075 rad

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Match snapshot line 19

L16: - Flavor-tagged time-dependent angular analysis of B_s^0 -> phi phi using
L17:   pp collision data at sqrt(s) = 13 TeV, integrated luminosity 6 fb^-1.
L18: - Helicity-independent fit:
L19:   phi_s^{s sbar s} = -0.042 +/- 0.075(stat) +/- 0.009(syst) rad.
L20:   |lambda| = 1.004 +/- 0.030(stat) +/- 0.009(syst).
L21: - Polarization-dependent determinations showed no evidence for polarization
L22:   dependence.

observables[1].fallback_value_uncertainty |lambda|, helicity-independent 2023 fit = 1.004 +- 0.03

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Match snapshot line 20

L17:   pp collision data at sqrt(s) = 13 TeV, integrated luminosity 6 fb^-1.
L18: - Helicity-independent fit:
L19:   phi_s^{s sbar s} = -0.042 +/- 0.075(stat) +/- 0.009(syst) rad.
L20:   |lambda| = 1.004 +/- 0.030(stat) +/- 0.009(syst).
L21: - Polarization-dependent determinations showed no evidence for polarization
L22:   dependence.
L23: - Combination with previous LHCb 7 and 8 TeV measurements:

observables[2].fallback_value_uncertainty phi_s^{s sbar s}, LHCb Run 1 + Run 2 combination = -0.074 +- 0.069 rad

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Match snapshot line 24

L21: - Polarization-dependent determinations showed no evidence for polarization
L22:   dependence.
L23: - Combination with previous LHCb 7 and 8 TeV measurements:
L24:   phi_s^{s sbar s} = -0.074 +/- 0.069 rad.
L25:   |lambda| = 1.009 +/- 0.030.
L26: - CDS records this as the most precise study of time-dependent CP violation
L27:   in a penguin-dominated B meson decay, consistent with CP symmetry and SM

observables[3].fallback_value_uncertainty |lambda|, LHCb Run 1 + Run 2 combination = 1.009 +- 0.03

RESOLVED

Match snapshot line 25

L22:   dependence.
L23: - Combination with previous LHCb 7 and 8 TeV measurements:
L24:   phi_s^{s sbar s} = -0.074 +/- 0.069 rad.
L25:   |lambda| = 1.009 +/- 0.030.
L26: - CDS records this as the most precise study of time-dependent CP violation
L27:   in a penguin-dominated B meson decay, consistent with CP symmetry and SM
L28:   predictions.

observables[0].fallback_value_uncertainty B(B_s^0 -> phi(1020) phi(1020)) = 1.85 +- 0.14 10^-5

AMBIGUOUS

Match 1 of 4 snapshot line 9

L6: Snapshot type: Minimal HFLAV HTML table extract.
L7: 
L8: Relevant extracted values:
L9: - Average B(B_s^0 -> phi(1020) phi(1020)) = (1.85 +/- 0.14) x 10^-5.
L10: - HFLAV page gives Delta chi^2 = 8.10 and p = 0.52 with ndf = 9.
L11: - PDG row on the same HFLAV page: (1.85 +/- 0.14) x 10^-5.
L12: - LHCb input: (1.85 +/- 0.05 +/- 0.16) x 10^-5 using

Match 2 of 4 snapshot line 11

L8: Relevant extracted values:
L9: - Average B(B_s^0 -> phi(1020) phi(1020)) = (1.85 +/- 0.14) x 10^-5.
L10: - HFLAV page gives Delta chi^2 = 8.10 and p = 0.52 with ndf = 9.
L11: - PDG row on the same HFLAV page: (1.85 +/- 0.14) x 10^-5.
L12: - LHCb input: (1.85 +/- 0.05 +/- 0.16) x 10^-5 using
L13:   B(B^0 -> phi(1020) K*(892)^0), JHEP 10,053 (2015).
L14: - CDF input: (1.85 +/- 0.15 +/- 0.22) x 10^-5 using

Match 3 of 4 snapshot line 12

L9: - Average B(B_s^0 -> phi(1020) phi(1020)) = (1.85 +/- 0.14) x 10^-5.
L10: - HFLAV page gives Delta chi^2 = 8.10 and p = 0.52 with ndf = 9.
L11: - PDG row on the same HFLAV page: (1.85 +/- 0.14) x 10^-5.
L12: - LHCb input: (1.85 +/- 0.05 +/- 0.16) x 10^-5 using
L13:   B(B^0 -> phi(1020) K*(892)^0), JHEP 10,053 (2015).
L14: - CDF input: (1.85 +/- 0.15 +/- 0.22) x 10^-5 using
L15:   B(B_s^0 -> J/psi phi(1020)), Phys. Rev. Lett. 107,261802 (2011).

Match 4 of 4 snapshot line 14

L11: - PDG row on the same HFLAV page: (1.85 +/- 0.14) x 10^-5.
L12: - LHCb input: (1.85 +/- 0.05 +/- 0.16) x 10^-5 using
L13:   B(B^0 -> phi(1020) K*(892)^0), JHEP 10,053 (2015).
L14: - CDF input: (1.85 +/- 0.15 +/- 0.22) x 10^-5 using
L15:   B(B_s^0 -> J/psi phi(1020)), Phys. Rev. Lett. 107,261802 (2011).
L16: 
L17: Licensing note:

observables[1].fallback_value_uncertainty LHCb input B(B_s^0 -> phi phi) = 1.85 +- 0.05 10^-5

AMBIGUOUS

Match 1 of 4 snapshot line 9

L6: Snapshot type: Minimal HFLAV HTML table extract.
L7: 
L8: Relevant extracted values:
L9: - Average B(B_s^0 -> phi(1020) phi(1020)) = (1.85 +/- 0.14) x 10^-5.
L10: - HFLAV page gives Delta chi^2 = 8.10 and p = 0.52 with ndf = 9.
L11: - PDG row on the same HFLAV page: (1.85 +/- 0.14) x 10^-5.
L12: - LHCb input: (1.85 +/- 0.05 +/- 0.16) x 10^-5 using

Match 2 of 4 snapshot line 11

L8: Relevant extracted values:
L9: - Average B(B_s^0 -> phi(1020) phi(1020)) = (1.85 +/- 0.14) x 10^-5.
L10: - HFLAV page gives Delta chi^2 = 8.10 and p = 0.52 with ndf = 9.
L11: - PDG row on the same HFLAV page: (1.85 +/- 0.14) x 10^-5.
L12: - LHCb input: (1.85 +/- 0.05 +/- 0.16) x 10^-5 using
L13:   B(B^0 -> phi(1020) K*(892)^0), JHEP 10,053 (2015).
L14: - CDF input: (1.85 +/- 0.15 +/- 0.22) x 10^-5 using

Match 3 of 4 snapshot line 12

L9: - Average B(B_s^0 -> phi(1020) phi(1020)) = (1.85 +/- 0.14) x 10^-5.
L10: - HFLAV page gives Delta chi^2 = 8.10 and p = 0.52 with ndf = 9.
L11: - PDG row on the same HFLAV page: (1.85 +/- 0.14) x 10^-5.
L12: - LHCb input: (1.85 +/- 0.05 +/- 0.16) x 10^-5 using
L13:   B(B^0 -> phi(1020) K*(892)^0), JHEP 10,053 (2015).
L14: - CDF input: (1.85 +/- 0.15 +/- 0.22) x 10^-5 using
L15:   B(B_s^0 -> J/psi phi(1020)), Phys. Rev. Lett. 107,261802 (2011).

Match 4 of 4 snapshot line 14

L11: - PDG row on the same HFLAV page: (1.85 +/- 0.14) x 10^-5.
L12: - LHCb input: (1.85 +/- 0.05 +/- 0.16) x 10^-5 using
L13:   B(B^0 -> phi(1020) K*(892)^0), JHEP 10,053 (2015).
L14: - CDF input: (1.85 +/- 0.15 +/- 0.22) x 10^-5 using
L15:   B(B_s^0 -> J/psi phi(1020)), Phys. Rev. Lett. 107,261802 (2011).
L16: 
L17: Licensing note:

observables[2].fallback_value_uncertainty CDF input B(B_s^0 -> phi phi) = 1.85 +- 0.15 10^-5

AMBIGUOUS

Match 1 of 4 snapshot line 9

L6: Snapshot type: Minimal HFLAV HTML table extract.
L7: 
L8: Relevant extracted values:
L9: - Average B(B_s^0 -> phi(1020) phi(1020)) = (1.85 +/- 0.14) x 10^-5.
L10: - HFLAV page gives Delta chi^2 = 8.10 and p = 0.52 with ndf = 9.
L11: - PDG row on the same HFLAV page: (1.85 +/- 0.14) x 10^-5.
L12: - LHCb input: (1.85 +/- 0.05 +/- 0.16) x 10^-5 using

Match 2 of 4 snapshot line 11

L8: Relevant extracted values:
L9: - Average B(B_s^0 -> phi(1020) phi(1020)) = (1.85 +/- 0.14) x 10^-5.
L10: - HFLAV page gives Delta chi^2 = 8.10 and p = 0.52 with ndf = 9.
L11: - PDG row on the same HFLAV page: (1.85 +/- 0.14) x 10^-5.
L12: - LHCb input: (1.85 +/- 0.05 +/- 0.16) x 10^-5 using
L13:   B(B^0 -> phi(1020) K*(892)^0), JHEP 10,053 (2015).
L14: - CDF input: (1.85 +/- 0.15 +/- 0.22) x 10^-5 using

Match 3 of 4 snapshot line 12

L9: - Average B(B_s^0 -> phi(1020) phi(1020)) = (1.85 +/- 0.14) x 10^-5.
L10: - HFLAV page gives Delta chi^2 = 8.10 and p = 0.52 with ndf = 9.
L11: - PDG row on the same HFLAV page: (1.85 +/- 0.14) x 10^-5.
L12: - LHCb input: (1.85 +/- 0.05 +/- 0.16) x 10^-5 using
L13:   B(B^0 -> phi(1020) K*(892)^0), JHEP 10,053 (2015).
L14: - CDF input: (1.85 +/- 0.15 +/- 0.22) x 10^-5 using
L15:   B(B_s^0 -> J/psi phi(1020)), Phys. Rev. Lett. 107,261802 (2011).

Match 4 of 4 snapshot line 14

L11: - PDG row on the same HFLAV page: (1.85 +/- 0.14) x 10^-5.
L12: - LHCb input: (1.85 +/- 0.05 +/- 0.16) x 10^-5 using
L13:   B(B^0 -> phi(1020) K*(892)^0), JHEP 10,053 (2015).
L14: - CDF input: (1.85 +/- 0.15 +/- 0.22) x 10^-5 using
L15:   B(B_s^0 -> J/psi phi(1020)), Phys. Rev. Lett. 107,261802 (2011).
L16: 
L17: Licensing note:

fallback_value_uncertainty = -0.17 +- 0.15 rad

RESOLVED

Match snapshot line 19

L16: - Data sample: 3.0 fb^-1 collected with LHCb.
L17: - Signal yield: approximately 4000 B_s^0 -> phi phi decays.
L18: - CP-violating phase:
L19:   phi_s = -0.17 +/- 0.15(stat) +/- 0.03(syst) rad.
L20: - Triple-product asymmetries:
L21:   A_U = -0.003 +/- 0.017(stat) +/- 0.006(syst).
L22:   A_V = -0.017 +/- 0.017(stat) +/- 0.006(syst).

fallback_value_uncertainty = -0.073 +- 0.115 rad

RESOLVED

Match snapshot line 20

L17:   8 TeV in 2012, and 13 TeV in 2015 and 2016.
L18: - Signal yield: around 9000 B_s^0 -> phi phi decays.
L19: - Helicity-independent phase:
L20:   phi_s^{s sbar s} = -0.073 +/- 0.115(stat) +/- 0.027(syst) rad.
L21: - Helicity-independent direct-CP parameter:
L22:   |lambda| = 0.99 +/- 0.05(stat) +/- 0.01(syst).
L23: - B^0 -> phi phi limit: