Home Unitarity Triangle Angles

Results on time-dependent CP violation and measurements related to the angles of the Unitarity Triangle
Prepared for the CKM 2025 conference

Overview
\( \beta = (22.6^{+0.5}_{-0.4})^\circ \)
beta
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\( \alpha = (84.1^{+4.5}_{-3.8})^\circ \)
alpha
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\( \gamma = (66.4^{+2.8}_{-3.0})^\circ \)
gamma
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\( \bar{\rho} = 0.141 \pm 0.015 \) \( \bar{\eta} = 0.359 \pm 0.009 \)
rhoeta
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Measurements related to CKM angle \( \beta \equiv \phi_1 \)
Studies of \( b \to c \mkern2mu \bar{\phantom{c}}\mkern-8mu c \mkern2mu s \) transitions
Studies of colour suppressed \( b \to c \mkern2mu \bar{\phantom{u}}\mkern-10mu u \mkern2mu d \) transitions
Studies of \( b \to c \mkern2mu \bar{\phantom{c}}\mkern-8mu c \mkern2mu d \) transitions
Studies of \( b \to q \mkern2mu \bar{\phantom{q}}\mkern-8mu q \mkern2mu s \) (penguin) transitions
Studies of \( b \to q \mkern2mu \bar{\phantom{q}}\mkern-8mu q \mkern2mu d \) (penguin) transitions
Studies of \( b \to s \mkern2mu \gamma \) transitions
Studies of \( b \to d \mkern2mu \gamma \) transitions
Measurements related to CKM angle \( \alpha \equiv \phi_2 \)
Studies of \( b \to u \mkern2mu \bar{\phantom{u}}\mkern-10mu u \mkern2mu d \) transitions

Time-dependent \(CP\) asymmetries in \(B^0 \to \pi^+ \pi^-\)

Experiment \(\boldsymbol{C_{CP}(\pi^+ \pi^-)}\) \(\boldsymbol{S_{CP}(\pi^+ \pi^-)}\) Correlation Reference
BaBar
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 467\,\mathrm{M}\) 		\( -0.25 \pm 0.08 \pm 0.02 \) \( -0.68 \pm 0.10 \pm 0.03 \) \( -0.06 \) (stat) PRD 87 (2013) 052009
Belle
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 772\,\mathrm{M}\) 		\( -0.33 \pm 0.06 \pm 0.03 \) \( -0.64 \pm 0.08 \pm 0.03 \) \( -0.10 \) (stat) PRD 88 (2013) 092003
LHCb
\(\mathcal{L} = 4.9\,\mathrm{fb}^{-1}\) 		\( -0.32 \pm 0.04 \) \( -0.672 \pm 0.034 \) \( 0.41 \) (stat) JHEP 2103 (2021) 075
Average \( -0.311 \pm 0.030 \) \( -0.666 \pm 0.029 \) \( 0.29 \) (stat) HFLAV correlated average
\( \chi^2 / \mathrm{dof} = 0.78 / 4 \)
\( p = 0.94 \Rightarrow 0.1\sigma \)
Figures fig here fig here Av fig

Time-dependent Dalitz plot analysis of \(B^0 \to \pi^+ \pi^-\pi^0\)

Experiment \(\boldsymbol{\Delta C(\rho^\pm \pi^\mp)}\) \(\boldsymbol{S(\rho^\pm \pi^\mp)}\) \(\boldsymbol{\Delta S(\rho^\pm \pi^\mp)}\) \(\boldsymbol{C(\rho^\pm \pi^\mp)}\) \(\boldsymbol{A_{CP}(\rho^\pm \pi^\mp)}\) Correlation Reference
BaBar
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 471\,\mathrm{M}\) 		\( 0.23 \pm 0.06 \pm 0.05 \) \( 0.053 \pm 0.081 \pm 0.034 \) \( 0.05 \pm 0.08 \pm 0.04 \) \( 0.02 \pm 0.06 \pm 0.04 \) \( -0.100 \pm 0.029 \pm 0.021 \) \( \) (stat) PRD 88 (2013) 012003
Belle
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 449\,\mathrm{M}\) 		\( 0.36 \pm 0.10 \pm 0.05 \) \( 0.06 \pm 0.13 \pm 0.05 \) \( -0.08 \pm 0.13 \pm 0.05 \) \( -0.13 \pm 0.09 \pm 0.05 \) \( -0.12 \pm 0.05 \pm 0.04 \) \( \) (stat) PRL 98 (2007) 221602
Average \( 0.27 \pm 0.06 \) \( 0.06 \pm 0.07 \) \( 0.01 \pm 0.08 \) \( -0.03 \pm 0.06 \) \( -0.107 \pm 0.031 \) \( \) (stat) HFLAV correlated average
\( \chi^2 / \mathrm{dof} = 3.76 / 5 \)
\( p = 0.58 \Rightarrow 0.5\sigma \)
Figures fig here fig here fig here fig here fig here Av fig
Experiment \(\boldsymbol{A_{\pm}(\rho^\pm \pi^\mp)}\) \(\boldsymbol{A_{\mp}(\rho^\mp \pi^\pm)}\) Correlation Reference
BaBar
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 471\,\mathrm{M}\) 		\( 0.09 \pm 0.06 \pm 0.04 \) \( -0.12 \pm 0.08 \pm 0.04 \) \( 0.55 \) (stat) PRD 88 (2013) 012003
Belle
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 449\,\mathrm{M}\) 		\( 0.21 \pm 0.08 \pm 0.04 \) \( 0.08 \pm 0.16 \pm 0.11 \) \( 0.47 \) (stat) PRL 98 (2007) 221602
Average \( 0.13 \pm 0.05 \) \( -0.07 \pm 0.08 \) \( 0.52 \) (stat) HFLAV correlated average
\( \chi^2 / \mathrm{dof} = 1.37 / 2 \)
\( p = 0.50 \Rightarrow 0.7\sigma \)
Figures fig here fig here Av fig
Experiment \(\boldsymbol{S(\rho^0 \pi^0)}\) \(\boldsymbol{C(\rho^0 \pi^0)}\) Correlation Reference
BaBar
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 471\,\mathrm{M}\) 		\( -0.37 \pm 0.34 \pm 0.20 \) \( 0.19 \pm 0.23 \pm 0.15 \) \( 0.00 \) (stat) PRD 88 (2013) 012003
Belle
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 449\,\mathrm{M}\) 		\( 0.17 \pm 0.57 \pm 0.35 \) \( 0.49 \pm 0.36 \pm 0.28 \) \( 0.08 \) (stat) PRL 98 (2007) 221602
Average \( -0.24 \pm 0.34 \) \( 0.26 \pm 0.23 \) \( 0.02 \) (stat) HFLAV correlated average
\( \chi^2 / \mathrm{dof} = 0.76 / 2 \)
\( p = 0.68 \Rightarrow 0.4\sigma \)
Figures fig here fig here Av fig

Time-dependent \(CP\) asymmetries in \(B^0 \to \rho^+ \rho^-\)

Experiment \(\boldsymbol{C_{CP}(\rho^+ \rho^-)}\) \(\boldsymbol{S_{CP}(\rho^+ \rho^-)}\) Correlation Reference
BaBar
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 387\,\mathrm{M}\) 		\( 0.01 \pm 0.15 \pm 0.06 \) \( -0.17 \pm 0.20 \pm 0.05 \) \( -0.04 \) (stat) PRD 76 (2007) 052007
Belle
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 772\,\mathrm{M}\) 		\( 0.00 \pm 0.10 \pm 0.06 \) \( -0.13 \pm 0.15 \pm 0.05 \) \( -0.02 \) (stat) PRD 93 (2016) 032010
Average \( 0.00 \pm 0.09 \) \( -0.15 \pm 0.12 \) \( -0.02 \) (stat) HFLAV correlated average
\( \chi^2 / \mathrm{dof} = 0.03 / 2 \)
\( p = 0.99 \Rightarrow 0.0\sigma \)
Figures fig here fig here Av fig

Time-dependent \(CP\) asymmetries in \(B^0 \to \rho^0 \rho^0\)

Experiment \(\boldsymbol{C_CP}\) \(\boldsymbol{S_CP}\) Correlation Reference
BaBar
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 465\,\mathrm{M}\) 		\( 0.2 \pm 0.8 \pm 0.3 \) \( 0.3 \pm 0.7 \pm 0.2 \) \( -0.04 \) (stat) PRD 78 (2008) 071104(R)

Time-dependent \(CP\) asymmetries in \(B^0 \to a_1^{\pm} \pi^{\mp}\)

Experiment \(\boldsymbol{DeltaC}\) \(\boldsymbol{S}\) \(\boldsymbol{DeltaS}\) \(\boldsymbol{C}\) \(\boldsymbol{A_CP}\) Correlation Reference
BaBar
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 384\,\mathrm{M}\) 		\( 0.26 \pm 0.15 \pm 0.07 \) \( 0.37 \pm 0.21 \pm 0.07 \) \( -0.14 \pm 0.21 \pm 0.06 \) \( -0.10 \pm 0.15 \pm 0.09 \) \( -0.07 \pm 0.07 \pm 0.02 \) \( \) (stat) PRL 98 (2007) 181803
Belle
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 772\,\mathrm{M}\) 		\( 0.54 \pm 0.11 \pm 0.07 \) \( -0.51 \pm 0.14 \pm 0.08 \) \( -0.09 \pm 0.14 \pm 0.06 \) \( -0.01 \pm 0.11 \pm 0.09 \) \( -0.06 \pm 0.05 \pm 0.07 \) \( \) (stat) PRD 86 (2012) 092012
Average \( 0.43 \pm 0.10 \) \( -0.20 \pm 0.13 \) \( -0.10 \pm 0.12 \) \( -0.05 \pm 0.11 \) \( -0.06 \pm 0.06 \) \( \) (stat) HFLAV correlated average
\( \chi^2 / \mathrm{dof} = 12.24 / 5 \)
\( p = 0.03 \Rightarrow 2.1\sigma \)
Figures fig here fig here fig here fig here fig here Av fig
Experiment \(\boldsymbol{A_+-}\) \(\boldsymbol{A_-+}\) Correlation Reference
BaBar
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 384\,\mathrm{M}\) 		\( 0.15 \pm 0.15 \pm 0.07 \) \( 0.07 \pm 0.21 \pm 0.15 \) \( 0.63 \) (stat) PRL 98 (2007) 181803
Belle
\(N(B\smash{\bar{\phantom{B}}}\kern-14mu B) = 772\,\mathrm{M}\) 		\( 0.07 \pm 0.08 \pm 0.10 \) \( -0.04 \pm 0.26 \pm 0.19 \) \( 0.61 \) (stat) PRD 86 (2012) 092012
Average \( 0.1 \pm 0.1 \) \( 0.02 \pm 0.20 \) \( 0.38 \) (stat) HFLAV correlated average
\( \chi^2 / \mathrm{dof} = 0.16 / 2 \)
\( p = 0.92 \Rightarrow 0.1\sigma \)
Figures fig here fig here Av fig
Measurements related to CKM angle \( \gamma \equiv \phi_3 \)
Studies of time-dependent interference between \( b \to c \mkern2mu \bar{\phantom{u}}\mkern-10mu u \mkern2mu d \) and \( \bar{\phantom{b}}\mkern-8mu b \to \bar{\phantom{c}}\mkern-8mu c \mkern2mu u \mkern1mu \bar{\phantom{d}}\mkern-8mu d \) transitions
Studies of time-dependent interference between \( b \to c \mkern2mu \bar{\phantom{u}}\mkern-10mu u \mkern2mu s \) and \( \bar{\phantom{b}}\mkern-8mu b \to \bar{\phantom{c}}\mkern-8mu c \mkern2mu u \mkern1mu \bar{\phantom{s}}\mkern-8mu s \) transitions
Studies of interference between \( b \to c \mkern2mu \bar{\phantom{u}}\mkern-10mu u \mkern2mu s \) and \( b \to u \mkern2mu \bar{\phantom{c}}\mkern-8mu c \mkern2mu s \) transitions (also covering inteference between \( b \to c \mkern2mu \bar{\phantom{u}}\mkern-10mu u \mkern2mu d \) and \( b \to u \mkern2mu \bar{\phantom{c}}\mkern-8mu c \mkern2mu d \) transitions)
Summary of constraints on Unitarity Triangle angles