Catalog · Beauty · B032

B032 $\bar{B}\to \pi\bar{K}$

$\bar{B} \to \pi \bar{K}$ nonleptonic charmless

Status REVIEWED VERIFIED High Code: NO Priority Low

Why this constrains the RS scan

$\bar B\to\pi\bar K$ is a $b\to s$ charmless penguin system with tree, QCD-penguin, and electroweak-penguin amplitudes. Anarchic RS models can induce nonstandard $b\to s$ flavor-changing $Z$, dipole, or four-quark operators after KK matching. This process is therefore a diagnostic of penguin flavor structure that is complementary to the existing neutral-meson $\Delta F=2$ constraints, but it is not a clean tree-level bound by itself.

What's changed since the original paper

Since the arXiv:0804.1954 RS-flavor benchmark era, the main changes are experimental. Belle and BaBar final samples were folded into HFLAV, LHCb measured $A_{CP}(B^+\to K^+\pi^0)=0.025\pm0.015\pm0.006\pm0.003$ and explicitly sharpened the charged--neutral $K\pi$ direct-asymmetry puzzle, under source key lhcb2021\_bplus\_kplus\_pi0\_acp, and Belle II added 2024 measurements of all four $K\pi$ branching fractions and direct asymmetries under belleii2024\_btokpi. Belle II also measured $B^0\to K_S^0\pi^0$ time-dependent CP in 2023, providing the largest modern input to the PDG/HFLAV $S_{K^0\pi^0}$ average. The Belle II $K\pi$ sum-rule test, $-0.03\pm0.13\pm0.04$, is currently consistent with the SM expectation (belleii2024\_btokpi).

Validity and model dependence

This is an experimentally mature but SM-theory-limited nonleptonic constraint. Branching fractions and CP asymmetries are easy to catalog, while interpreting them as RS exclusions requires a hadronic amplitude framework, electroweak penguin conventions, strong phases, and correlated treatment of the four isospin-related modes. It should be treated as a model-dependent penguin diagnostic until a dedicated likelihood or conservative amplitude scan exists.

Code coverage in this repo

NO. A focused grep for $B\to K\pi$, charmless, nonleptonic, and electroweak-penguin strings across quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ found no implementation. The modern policy surface lists only $\epsilon_K$, $K$, $B_d$, $B_s$, and $D^0$ at quarkConstraints/modern/phenomenology.py:23; its notes say this is a policy-only fence with no numeric EFT backend at quarkConstraints/modern/phenomenology.py:165. The implemented default inputs in quarkConstraints/deltaf2.py:209 are neutral-meson $\Delta F=2$ systems only, and the dipole code found at flavorConstraints/muToEGamma.py:75 is the lepton $\mu\to e\gamma$ constraint.

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

Implementation difficulty

HIGH. A production constraint would need a new nonleptonic $b\to s\bar q q$ operator/amplitude layer, electroweak-penguin matching, hadronic strong-phase treatment, and a correlated four-mode likelihood or conservative theory envelope. The existing $\Delta F=2$ SLL/SLR/VLL/VRR basis does not cover this calculation.

Reason: Requires a new nonleptonic $b \to s$ qbar q amplitude/likelihood layer with electroweak-penguin matching, hadronic strong phases, and correlated four-mode treatment; the existing $\Delta F = 2$ basis does not cover $B \to \pi$ K.

Key references

Process-local raw reference keys before bibliography consolidation: hflav\_dec2025\_btopik, pdg2025\_k0pi0\_time\_dependent\_cp\_api, belleii2024\_btokpi, lhcb2021\_bplus\_kplus\_pi0\_acp, belleii2023\_b0\_ks\_pi0\_cp, and cfw2008\_rs\_flavor.

fallback_value_uncertainty BR(B+ -> K0 pi+) = (2.392 +- 0.062)e-5

RESOLVED

Match snapshot line 23

L20: 
L21: Branching-fraction averages from the individual HFLAV HTML pages.
L22: Units are 10^-5:
L23: - B(B+ -> K0 pi+) = 2.392 +/- 0.062. HFLAV table p=0.70, ndf=5.
L24:   The same row lists the PDG value 2.389 +/- 0.063.
L25: - B(B+ -> K+ pi0) = 1.322 +/- 0.043. HFLAV table p=0.62, ndf=3.
L26:   The same row lists the PDG value 1.323 +/- 0.043.

fallback_value_uncertainty BR(B+ -> K+ pi0) = (1.322 +- 0.043)e-5

RESOLVED

Match snapshot line 25

L22: Units are 10^-5:
L23: - B(B+ -> K0 pi+) = 2.392 +/- 0.062. HFLAV table p=0.70, ndf=5.
L24:   The same row lists the PDG value 2.389 +/- 0.063.
L25: - B(B+ -> K+ pi0) = 1.322 +/- 0.043. HFLAV table p=0.62, ndf=3.
L26:   The same row lists the PDG value 1.323 +/- 0.043.
L27: - B(B0 -> K+ pi-) = 2.007 +/- 0.040. HFLAV table p=0.80, ndf=17.
L28:   The same row lists the PDG value 2.003 +/- 0.041.

fallback_value_uncertainty BR(B0 -> K+ pi-) = (2.007 +- 0.04)e-5

RESOLVED

Match snapshot line 27

L24:   The same row lists the PDG value 2.389 +/- 0.063.
L25: - B(B+ -> K+ pi0) = 1.322 +/- 0.043. HFLAV table p=0.62, ndf=3.
L26:   The same row lists the PDG value 1.323 +/- 0.043.
L27: - B(B0 -> K+ pi-) = 2.007 +/- 0.040. HFLAV table p=0.80, ndf=17.
L28:   The same row lists the PDG value 2.003 +/- 0.041.
L29: - B(B0 -> K0 pi0) = 1.012 +/- 0.043. HFLAV table p=0.70, ndf=3.
L30:   The same row lists the PDG value 1.012 +/- 0.043.

fallback_value_uncertainty BR(B0 -> K0 pi0) = (1.012 +- 0.043)e-5

AMBIGUOUS

Match 1 of 2 snapshot line 29

L26:   The same row lists the PDG value 1.323 +/- 0.043.
L27: - B(B0 -> K+ pi-) = 2.007 +/- 0.040. HFLAV table p=0.80, ndf=17.
L28:   The same row lists the PDG value 2.003 +/- 0.041.
L29: - B(B0 -> K0 pi0) = 1.012 +/- 0.043. HFLAV table p=0.70, ndf=3.
L30:   The same row lists the PDG value 1.012 +/- 0.043.
L31: 
L32: Direct CP-asymmetry averages from the individual HFLAV HTML pages.

Match 2 of 2 snapshot line 30

L27: - B(B0 -> K+ pi-) = 2.007 +/- 0.040. HFLAV table p=0.80, ndf=17.
L28:   The same row lists the PDG value 2.003 +/- 0.041.
L29: - B(B0 -> K0 pi0) = 1.012 +/- 0.043. HFLAV table p=0.70, ndf=3.
L30:   The same row lists the PDG value 1.012 +/- 0.043.
L31: 
L32: Direct CP-asymmetry averages from the individual HFLAV HTML pages.
L33: Units are 10^-2:

fallback_value_uncertainty A_CP(B+ -> K0_S pi+) = -2.67 +- 0.87 percent

RESOLVED

Match snapshot line 34

L31: 
L32: Direct CP-asymmetry averages from the individual HFLAV HTML pages.
L33: Units are 10^-2:
L34: - A_CP(B+ -> K0_S pi+) = -2.67 +/- 0.87. HFLAV table p=0.77, ndf=4.
L35:   The update includes an unpublished LHCb input shown in blue: -2.8 +/- 0.5 +/- 0.9.
L36: - A_CP(B+ -> K+ pi0) = +2.7 +/- 1.2. HFLAV table p=0.62, ndf=4.
L37:   The LHCb input is +2.5 +/- 1.5 +/- 0.7.

fallback_value_uncertainty A_CP(B+ -> K+ pi0) = 2.7 +- 1.2 percent

RESOLVED

Match snapshot line 36

L33: Units are 10^-2:
L34: - A_CP(B+ -> K0_S pi+) = -2.67 +/- 0.87. HFLAV table p=0.77, ndf=4.
L35:   The update includes an unpublished LHCb input shown in blue: -2.8 +/- 0.5 +/- 0.9.
L36: - A_CP(B+ -> K+ pi0) = +2.7 +/- 1.2. HFLAV table p=0.62, ndf=4.
L37:   The LHCb input is +2.5 +/- 1.5 +/- 0.7.
L38: - A_CP(B0 -> K+ pi-) = -8.31 +/- 0.31. HFLAV table p=0.54, ndf=4.
L39:   The LHCb input is -8.31 +/- 0.34 and combines Run 2 with Run 1.

fallback_value_uncertainty A_CP(B0 -> K+ pi-) = -8.31 +- 0.31 percent

AMBIGUOUS

Match 1 of 2 snapshot line 38

L35:   The update includes an unpublished LHCb input shown in blue: -2.8 +/- 0.5 +/- 0.9.
L36: - A_CP(B+ -> K+ pi0) = +2.7 +/- 1.2. HFLAV table p=0.62, ndf=4.
L37:   The LHCb input is +2.5 +/- 1.5 +/- 0.7.
L38: - A_CP(B0 -> K+ pi-) = -8.31 +/- 0.31. HFLAV table p=0.54, ndf=4.
L39:   The LHCb input is -8.31 +/- 0.34 and combines Run 2 with Run 1.
L40: - A_CP(B0 -> K0 pi0) = -1 +/- 13. HFLAV table includes the Belle II input
L41:   -1 +/- 12 +/- 4, described as a combination of time-integrated and

Match 2 of 2 snapshot line 39

L36: - A_CP(B+ -> K+ pi0) = +2.7 +/- 1.2. HFLAV table p=0.62, ndf=4.
L37:   The LHCb input is +2.5 +/- 1.5 +/- 0.7.
L38: - A_CP(B0 -> K+ pi-) = -8.31 +/- 0.31. HFLAV table p=0.54, ndf=4.
L39:   The LHCb input is -8.31 +/- 0.34 and combines Run 2 with Run 1.
L40: - A_CP(B0 -> K0 pi0) = -1 +/- 13. HFLAV table includes the Belle II input
L41:   -1 +/- 12 +/- 4, described as a combination of time-integrated and
L42:   time-dependent analyses using BLUE.

fallback_value_uncertainty A_CP(B0 -> K0 pi0) = -1.0 +- 13.0 percent

AMBIGUOUS

Match 1 of 2 snapshot line 40

L37:   The LHCb input is +2.5 +/- 1.5 +/- 0.7.
L38: - A_CP(B0 -> K+ pi-) = -8.31 +/- 0.31. HFLAV table p=0.54, ndf=4.
L39:   The LHCb input is -8.31 +/- 0.34 and combines Run 2 with Run 1.
L40: - A_CP(B0 -> K0 pi0) = -1 +/- 13. HFLAV table includes the Belle II input
L41:   -1 +/- 12 +/- 4, described as a combination of time-integrated and
L42:   time-dependent analyses using BLUE.

Match 2 of 2 snapshot line 41

L38: - A_CP(B0 -> K+ pi-) = -8.31 +/- 0.31. HFLAV table p=0.54, ndf=4.
L39:   The LHCb input is -8.31 +/- 0.34 and combines Run 2 with Run 1.
L40: - A_CP(B0 -> K0 pi0) = -1 +/- 13. HFLAV table includes the Belle II input
L41:   -1 +/- 12 +/- 4, described as a combination of time-integrated and
L42:   time-dependent analyses using BLUE.

fallback_value_uncertainty C(K0 pi0) in B0 -> K0 pi0 = 0.0 +- 0.08

AMBIGUOUS

Match 1 of 21 snapshot line 8

L5: - https://pdgapi.lbl.gov/summaries/S042CKP
L6: - https://pdgapi.lbl.gov/listings/S042CKP
L7: - https://pdgapi.lbl.gov/summaries/S042SKP
L8: - https://pdgapi.lbl.gov/listings/S042SKP
L9: 
L10: Summary excerpt:
L11: - edition: 2025

Match 2 of 21 snapshot line 11

L8: - https://pdgapi.lbl.gov/listings/S042SKP
L9: 
L10: Summary excerpt:
L11: - edition: 2025
L12: - pdgid: S042CKP
L13: - description: C(K0 pi0) (B0 --> K0 pi0)
L14: - pdg_values: OUR AVERAGE value_text "0.00+-0.08";

Match 3 of 21 snapshot line 12

L9: 
L10: Summary excerpt:
L11: - edition: 2025
L12: - pdgid: S042CKP
L13: - description: C(K0 pi0) (B0 --> K0 pi0)
L14: - pdg_values: OUR AVERAGE value_text "0.00+-0.08";
L15:   numeric value -9.010944052367896E-4; symmetric error 0.07727590775925162.

Match 4 of 21 snapshot line 13

L10: Summary excerpt:
L11: - edition: 2025
L12: - pdgid: S042CKP
L13: - description: C(K0 pi0) (B0 --> K0 pi0)
L14: - pdg_values: OUR AVERAGE value_text "0.00+-0.08";
L15:   numeric value -9.010944052367896E-4; symmetric error 0.07727590775925162.
L16:

Match 5 of 21 snapshot line 14

L11: - edition: 2025
L12: - pdgid: S042CKP
L13: - description: C(K0 pi0) (B0 --> K0 pi0)
L14: - pdg_values: OUR AVERAGE value_text "0.00+-0.08";
L15:   numeric value -9.010944052367896E-4; symmetric error 0.07727590775925162.
L16: 
L17: - edition: 2025

Match 6 of 21 snapshot line 15

L12: - pdgid: S042CKP
L13: - description: C(K0 pi0) (B0 --> K0 pi0)
L14: - pdg_values: OUR AVERAGE value_text "0.00+-0.08";
L15:   numeric value -9.010944052367896E-4; symmetric error 0.07727590775925162.
L16: 
L17: - edition: 2025
L18: - pdgid: S042SKP

Match 7 of 21 snapshot line 17

L14: - pdg_values: OUR AVERAGE value_text "0.00+-0.08";
L15:   numeric value -9.010944052367896E-4; symmetric error 0.07727590775925162.
L16: 
L17: - edition: 2025
L18: - pdgid: S042SKP
L19: - description: S(K0 pi0) (B0 --> K0 pi0)
L20: - pdg_values: OUR AVERAGE value_text "0.64+-0.13";

Match 8 of 21 snapshot line 18

L15:   numeric value -9.010944052367896E-4; symmetric error 0.07727590775925162.
L16: 
L17: - edition: 2025
L18: - pdgid: S042SKP
L19: - description: S(K0 pi0) (B0 --> K0 pi0)
L20: - pdg_values: OUR AVERAGE value_text "0.64+-0.13";
L21:   numeric value 0.6449839379030179; error +0.1310306135865286 -0.1379414020760354.

Match 9 of 21 snapshot line 19

L16: 
L17: - edition: 2025
L18: - pdgid: S042SKP
L19: - description: S(K0 pi0) (B0 --> K0 pi0)
L20: - pdg_values: OUR AVERAGE value_text "0.64+-0.13";
L21:   numeric value 0.6449839379030179; error +0.1310306135865286 -0.1379414020760354.
L22:

Match 10 of 21 snapshot line 20

L17: - edition: 2025
L18: - pdgid: S042SKP
L19: - description: S(K0 pi0) (B0 --> K0 pi0)
L20: - pdg_values: OUR AVERAGE value_text "0.64+-0.13";
L21:   numeric value 0.6449839379030179; error +0.1310306135865286 -0.1379414020760354.
L22: 
L23: Listing excerpt for S(K0 pi0), inputs marked used in the average:

Match 11 of 21 snapshot line 21

L18: - pdgid: S042SKP
L19: - description: S(K0 pi0) (B0 --> K0 pi0)
L20: - pdg_values: OUR AVERAGE value_text "0.64+-0.13";
L21:   numeric value 0.6449839379030179; error +0.1310306135865286 -0.1379414020760354.
L22: 
L23: Listing excerpt for S(K0 pi0), inputs marked used in the average:
L24: - ADACHI 2023E, PRL 131 111803, DOI 10.1103/PhysRevLett.131.111803:

Match 12 of 21 snapshot line 23

L20: - pdg_values: OUR AVERAGE value_text "0.64+-0.13";
L21:   numeric value 0.6449839379030179; error +0.1310306135865286 -0.1379414020760354.
L22: 
L23: Listing excerpt for S(K0 pi0), inputs marked used in the average:
L24: - ADACHI 2023E, PRL 131 111803, DOI 10.1103/PhysRevLett.131.111803:
L25:   S = 0.75 +0.20 -0.23 +/- 0.04, used_in_average true.
L26: - FUJIKAWA 2010A, PR D81 011101, DOI 10.1103/PhysRevD.81.011101:

Match 13 of 21 snapshot line 24

L21:   numeric value 0.6449839379030179; error +0.1310306135865286 -0.1379414020760354.
L22: 
L23: Listing excerpt for S(K0 pi0), inputs marked used in the average:
L24: - ADACHI 2023E, PRL 131 111803, DOI 10.1103/PhysRevLett.131.111803:
L25:   S = 0.75 +0.20 -0.23 +/- 0.04, used_in_average true.
L26: - FUJIKAWA 2010A, PR D81 011101, DOI 10.1103/PhysRevD.81.011101:
L27:   S = 0.67 +/- 0.31 +/- 0.08, used_in_average true.

Match 14 of 21 snapshot line 25

L22: 
L23: Listing excerpt for S(K0 pi0), inputs marked used in the average:
L24: - ADACHI 2023E, PRL 131 111803, DOI 10.1103/PhysRevLett.131.111803:
L25:   S = 0.75 +0.20 -0.23 +/- 0.04, used_in_average true.
L26: - FUJIKAWA 2010A, PR D81 011101, DOI 10.1103/PhysRevD.81.011101:
L27:   S = 0.67 +/- 0.31 +/- 0.08, used_in_average true.
L28: - AUBERT 2009I, PR D79 052003, DOI 10.1103/PhysRevD.79.052003:

Match 15 of 21 snapshot line 26

L23: Listing excerpt for S(K0 pi0), inputs marked used in the average:
L24: - ADACHI 2023E, PRL 131 111803, DOI 10.1103/PhysRevLett.131.111803:
L25:   S = 0.75 +0.20 -0.23 +/- 0.04, used_in_average true.
L26: - FUJIKAWA 2010A, PR D81 011101, DOI 10.1103/PhysRevD.81.011101:
L27:   S = 0.67 +/- 0.31 +/- 0.08, used_in_average true.
L28: - AUBERT 2009I, PR D79 052003, DOI 10.1103/PhysRevD.79.052003:
L29:   S = 0.55 +/- 0.20 +/- 0.03, used_in_average true.

Match 16 of 21 snapshot line 27

L24: - ADACHI 2023E, PRL 131 111803, DOI 10.1103/PhysRevLett.131.111803:
L25:   S = 0.75 +0.20 -0.23 +/- 0.04, used_in_average true.
L26: - FUJIKAWA 2010A, PR D81 011101, DOI 10.1103/PhysRevD.81.011101:
L27:   S = 0.67 +/- 0.31 +/- 0.08, used_in_average true.
L28: - AUBERT 2009I, PR D79 052003, DOI 10.1103/PhysRevD.79.052003:
L29:   S = 0.55 +/- 0.20 +/- 0.03, used_in_average true.
L30:

Match 17 of 21 snapshot line 28

L25:   S = 0.75 +0.20 -0.23 +/- 0.04, used_in_average true.
L26: - FUJIKAWA 2010A, PR D81 011101, DOI 10.1103/PhysRevD.81.011101:
L27:   S = 0.67 +/- 0.31 +/- 0.08, used_in_average true.
L28: - AUBERT 2009I, PR D79 052003, DOI 10.1103/PhysRevD.79.052003:
L29:   S = 0.55 +/- 0.20 +/- 0.03, used_in_average true.
L30: 
L31: Listing excerpt for C(K0 pi0), representative inputs marked used in the fit:

Match 18 of 21 snapshot line 29

L26: - FUJIKAWA 2010A, PR D81 011101, DOI 10.1103/PhysRevD.81.011101:
L27:   S = 0.67 +/- 0.31 +/- 0.08, used_in_average true.
L28: - AUBERT 2009I, PR D79 052003, DOI 10.1103/PhysRevD.79.052003:
L29:   S = 0.55 +/- 0.20 +/- 0.03, used_in_average true.
L30: 
L31: Listing excerpt for C(K0 pi0), representative inputs marked used in the fit:
L32: - ADACHI 2024, PR D109 012001, DOI 10.1103/PhysRevD.109.012001:

Match 19 of 21 snapshot line 31

L28: - AUBERT 2009I, PR D79 052003, DOI 10.1103/PhysRevD.79.052003:
L29:   S = 0.55 +/- 0.20 +/- 0.03, used_in_average true.
L30: 
L31: Listing excerpt for C(K0 pi0), representative inputs marked used in the fit:
L32: - ADACHI 2024, PR D109 012001, DOI 10.1103/PhysRevD.109.012001:
L33:   C = -0.01 +/- 0.12 +/- 0.04, used_in_average true.
L34: - FUJIKAWA 2010A, PR D81 011101: C = -0.14 +/- 0.13 +/- 0.06,

Match 20 of 21 snapshot line 32

L29:   S = 0.55 +/- 0.20 +/- 0.03, used_in_average true.
L30: 
L31: Listing excerpt for C(K0 pi0), representative inputs marked used in the fit:
L32: - ADACHI 2024, PR D109 012001, DOI 10.1103/PhysRevD.109.012001:
L33:   C = -0.01 +/- 0.12 +/- 0.04, used_in_average true.
L34: - FUJIKAWA 2010A, PR D81 011101: C = -0.14 +/- 0.13 +/- 0.06,
L35:   with footnote that the paper reports A = -C.

Match 21 of 21 snapshot line 33

L30: 
L31: Listing excerpt for C(K0 pi0), representative inputs marked used in the fit:
L32: - ADACHI 2024, PR D109 012001, DOI 10.1103/PhysRevD.109.012001:
L33:   C = -0.01 +/- 0.12 +/- 0.04, used_in_average true.
L34: - FUJIKAWA 2010A, PR D81 011101: C = -0.14 +/- 0.13 +/- 0.06,
L35:   with footnote that the paper reports A = -C.
L36: - AUBERT 2009I, PR D79 052003: C = 0.13 +/- 0.13 +/- 0.03.

fallback_value_uncertainty S(K0 pi0) in B0 -> K0 pi0 = 0.64 +- 0.13

AMBIGUOUS

Match 1 of 2 snapshot line 20

L17: - edition: 2025
L18: - pdgid: S042SKP
L19: - description: S(K0 pi0) (B0 --> K0 pi0)
L20: - pdg_values: OUR AVERAGE value_text "0.64+-0.13";
L21:   numeric value 0.6449839379030179; error +0.1310306135865286 -0.1379414020760354.
L22: 
L23: Listing excerpt for S(K0 pi0), inputs marked used in the average:

Match 2 of 2 snapshot line 21

L18: - pdgid: S042SKP
L19: - description: S(K0 pi0) (B0 --> K0 pi0)
L20: - pdg_values: OUR AVERAGE value_text "0.64+-0.13";
L21:   numeric value 0.6449839379030179; error +0.1310306135865286 -0.1379414020760354.
L22: 
L23: Listing excerpt for S(K0 pi0), inputs marked used in the average:
L24: - ADACHI 2023E, PRL 131 111803, DOI 10.1103/PhysRevLett.131.111803:

fallback_value_uncertainty A_CP(B+ -> K+ pi0) = 0.025 +- +/- 0.015 stat +/- 0.006 syst +/- 0.003 external

RESOLVED

Match snapshot line 13

L10: Relevant arXiv abstract excerpt:
L11: LHCb reports direct CP violation in B+ -> K+ pi0 using 5.4 fb^-1 at
L12: sqrt(s) = 13 TeV.  The measured CP asymmetry is
L13: 0.025 +/- 0.015 +/- 0.006 +/- 0.003.  The abstract identifies this observable
L14: as a key input to the long-standing K pi puzzle and states that it enhances
L15: the anomalous difference between the direct CP asymmetries of B0 -> K+ pi-
L16: and B+ -> K+ pi0.

fallback_value_uncertainty Belle II Kpi sum-rule test = -0.03 +- +/- 0.13 stat +/- 0.04 syst

RESOLVED

Match snapshot line 15

L12: B0 -> K+ pi-, B+ -> K+ pi0, B+ -> K0 pi+, and B0 -> K0 pi0, using
L13: 387 x 10^6 bottom-antibottom meson pairs at the Upsilon(4S).  The analysis
L14: also tests the Standard Model isospin-based sum rule and obtains
L15: -0.03 +/- 0.13 +/- 0.04 for that sum-rule quantity.
L16: 
L17: Catalog use:
L18: Post-2008 Belle II input to HFLAV B -> K pi branching fractions and direct