S. Akar, E. Cogneras, S. Monteil, S. Ordonez-Soto*
B2KShh' \(\mu\)-group Meeting
April 14th, 2025
Time-integrated Amplitude Analysis of the decay \(B_{s}\rightarrow K_{S}^{0}\pi^{+}\pi^{-}\) with Run I and Run II data
Outline
Sebastian Ordoñez-Soto
April 14th, 2025
- Introduction
- Analysis strategy
-
Towards the nominal DP model
- Mass fit
- Efficiency maps
- Background model
- Preliminary Dalitz plot fit
- Conclusion and outlook
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Introduction
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Sebastian Ordoñez-Soto
April 14th, 2025
Introduction
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
April 14th, 2025
- The Amplitude Analysis of the \(B_{s}^{0}\rightarrow K_{S}^{0}\pi^{+}\pi^{-}\) provides access to the following observables:
- The direct \(CP\) asymmetries of the quasi-two-body decays with an untagged time-integrated (TI) Dalitz analysis:
- Flavour specific: \(\bar{B}_{s}^{0}\rightarrow K^{*+}_{0}(1430)\pi^{-}\), \(\bar{B}_{s}^{0}\rightarrow K^{*+}(892)\pi^{-}\)
- \(CP\)-eigenstates: \(B_{s}^{0}\rightarrow \rho^{0}K_{S}^{0}\)
- Fit fractions of the different amplitudes contributing to the decay.
- The direct \(CP\) asymmetries of the quasi-two-body decays with an untagged time-integrated (TI) Dalitz analysis:
Physics motivation
Data sample
- The data used in this analysis corresponds to: B2pipiKS Secondary Optimization
-
The cut
ProbNNp < 0.9has been included. - Let's recall the charm and charmonia vetoes applied:
- Charm meson vetoes (30 MeV): \(D^{+}_{(s)}\rightarrow K_{S}^{0}\pi^{+}\), \(D^{0}\rightarrow \pi^{+}\pi^{-}\)
- Charmonia vetoes (48 MeV): \(J/\psi\rightarrow \pi^{+}\pi^{-}\), \(\chi_{c0}\rightarrow \pi^{+}\pi^{-}\)
-
The cut
Introduction
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
April 14th, 2025
The general PDf describing the dynamics of the decay \(B_{s}^{0}\rightarrow K_{S}^{0}\pi^{+}\pi^{-}\) reads:
Dalitz signal PDF
\mathcal{S}(s_{+},s_{-},t,r_{\text{tag}}) = \frac{\text{d} \Gamma_{B^0_{S},\bar{B}^{0}_{S}}(t)}{\text{d}t} = \frac{ 1}{2}e^{-\Gamma t} \left( |\mathcal{A}(s_{+},s_{-})|^2 + |\bar{\mathcal{A}}(s_{+},s_{-})|^2 \right)\left[ \cosh(\Gamma yt) - K \sinh(\Gamma yt) + r_{\text{tag}}\left(C\cos(\Gamma x t) - S \sin(\Gamma x t)\right)\right]
- \(\mathcal{A}_{f} = \langle f|H_{\Delta F=1}|B_{s}^{0}\rangle\) and \(\bar{\mathcal{A}}_{f} = \langle f|H_{\Delta F=1}|\bar{B}_{s}^{0}\rangle\)
- \(S\), \(C\) and \(K\) are the time-dependent \(CP\) asymmetries
- \(r_{t}\) tagging parameter
- \(\Gamma\) and \(\Delta m\) are the decay rate and mass difference, respectively.
- After integration and with \(r_{\text{tag}} = 0\) simplifies as:
\mathcal{S}(s_{+},s_{-}) \propto |\mathcal{A}(s_{+},s_{-})|^2 + |\bar{\mathcal{A}}(s_{+},s_{-})|^2
- \(\mathcal{A}\) is parametereized by the isobar model:
|\mathcal{A}(s_+, s_-) |^2 = \left| \sum_j a_j e^{i\phi_j} F_j(s_+, s_-) \right|^2
- \(a_{j}\) and \(\phi_{j}\) describe the relative magnitude and phase.
Analysis Strategy
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Sebastian Ordoñez-Soto
April 14th, 2025
Analysis Strategy
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
April 14th, 2025
This analysis follows a similar strategy to that of the DP analysis of the decay \(B_{d}^{0}\rightarrow K_{S}^{0}\pi^{+}\pi^{-}\) with Run I data.
- The results were obtained with CRAFT (Clermont Roofit-based Amplitude Fitter Tool).
- Analysis note: ANAnote Run I B02KSpipi
- WG database: Analysis Run I B02KSpipi TI Dalitz Analysis
- Selection of \(B_{s}^{0}\rightarrow K_{S}^{0}\pi^{+}\pi^{-}\) signal candidates
- Fit the mass spectrum \(K_{S}^{0}\pi^{+}\pi^{-}\) and define a signal window around \(B_{s}^{0}\) signal peak.
- Determine the fraction of signal and bkg. (Combinatorial and \(B_{d}^{0}\rightarrow K_{S}^{0}\pi^{+}\pi^{-}\))
- Obtain the spline histogram of the efficiency variation across the DP from MC.
- Determine a model for the different background components.
- Fit simultaneously the different samples an educate the final model.
Precedents
Stages
Analysis Strategy
Sebastian Ordoñez-Soto
| Selection of the signal |
| Efficiency evaluation over the DP |
| Background model |
| Simultaneous Dalitz plot Fit |
| Mass fit on data |
Schematic of the analysis workflow
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
April 14th, 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Analysis Strategy
Done!
Inherited from the BF Analysis
April 14th, 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Analysis Strategy
Done?
Pending latest version from the simultaneous fit.
April 14th, 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Analysis Strategy
Efficiency maps available, also inherited from BF analysis.
Done!
March 24th, 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Analysis Strategy
Work in progress!
First fit with a simple model.
April 14th, 2025
Towards the nominal DP model
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Sebastian Ordoñez-Soto
April 14th, 2025
\(K_{S}^{0}\pi^{+}\pi^{-}\) Invariant Mass fit
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
A preliminary fit to the invariant mass, not simultaneous, has been done to determine in the signal mass window (\([\mu_{B_{s}^{0}}-1.4\cdot\sigma_{B_{s}^{0}}, \mu_{B_{s}^{0}}+3.0\cdot\sigma_{B_{s}^{0}}]\)):
- \(f_{\text{sig}}\): Fraction of \(B_{s}^{0}\rightarrow K_{S}^{0}\pi^{+}\pi^{-}\) signal
- \(f_{\text{comb bkg.}}\): Fraction of combinatorial bkg.
- \(f_{B_{d}^{0} \text{ bkg.}}\): Fraction of \(B_{d}^{0}\rightarrow K_{S}^{0}\pi^{+}\pi^{-}\) bkg.
This preliminary fit follows the same procedure than the one of the BF:
- The signal MC, \(B_{s}^{0}\) and \(B_{d}^{0}\), is fitted using a Symmetric Crystal Ball PDF.
- The partial bkg. MC is fitted using: Argus \(\circledast\) Symmetric Crystal Ball PDF.
- The combinatorial bkg. is fitted using a first order polynomial, with the slope floated.
- The shape parameters (\(\alpha_{R,L},n_{R,L}\), etc) are fixed in the data fit.
April 14th, 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
\(K_{S}^{0}\pi^{+}\pi^{-}\) Invariant Mass fit
April 14th, 2025
Summary of fractions for each component which are inputs for the Dalitz plot fit.
In the signal window:
- Run 2 DD: \(N_{\text{Sig}}^{B_{s}^{0}} \approx 775 \)
- Run 2 LL: \(N_{\text{Sig}}^{B_{s}^{0}} \approx 345\)
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Efficiency across DP
2018-DD
2018-LL
April 14th, 2025
- The efficiency maps in the square Dalitz plot (sDP) have been obtained in the BF analysis.
- For this analysis the spline technique will be the baseline for the efficiency modeling.
- The maps are smoothed out by a 2D cubic spline and are symmetrized.
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Background model
- The combinatorial background under the signal is modeled using candidates from the right-hand sideband
- \([5450,5750] \text{MeV}\)
- Due to the limited statistics, a combined sample including all Run 2 data (DD + LL) is used.
- The resulting background sDP distribution is smoothed and used as input for the combinatorial background model.
April 14th, 2025
Combinatorial background
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Background model
\(B_{d}^{0}\rightarrow K_{S}^{0}\pi^{+}\pi^{-}\) background
- The \(B_{d}^{0}\rightarrow K_{S}^{0}\pi^{+}\pi^{-}\) background is estimated using the model for this decay from Run I:
- Paper: Amplitude analysis of the decay \(B_{d}^{0}\rightarrow K_{S}^{0}\pi^{+}\pi^{-}\) and first observation of the CP asymmetry in \(B_{d}^{0}\rightarrow K^{*}(892)\pi^{+}\).
- Large toy MC generated using CRAFT.
- The toy MC is weighted by the corresponding efficiency map.
2018-DD
April 14th, 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Preliminary signal model
April 14th, 2025
- A preliminary signal model is proposed based on Standard Model expectations.
- \(\overline{B}_s \to \rho^0 K^0_S\)
- \(\overline{B}_s \to K_0^{*+}(1430)\pi^{-}\)
- \(\overline{B}_s \to K^0_S \pi^+ \pi^- \text{ (NR)}\)
- \(\overline{B}_s \to K^{*+}(892) \pi^-\)
- The model parameterizes the signal amplitude as the isobar sum of three resonances (and conjugates) plus a non-resonant (NR) contribution.
*Chosen as reference \(\Rightarrow\) \(x=2\), \(y=0\) and \(\bar{y} = 0\)
*
Dalitz Plot fitting
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Sebastian Ordoñez-Soto
April 14th, 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dalitz plot Fit
- A simultaneous fit to DD+LL 2018 data has been done using the simple signal model.
April 14th, 2025
2018-LL \(\Rightarrow\)
2018-DD \(\Rightarrow\)
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dalitz plot Fit
April 14th, 2025
2018-LL \(\Rightarrow\)
2018-DD \(\Rightarrow\)
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dalitz plot Fit
April 14th, 2025
Fit results
- The simple model presents a reasonable description of the Dalitz plot data.
Amplitudes
Phases
Dalitz plot PDF
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dalitz plot Fit
- A simultaneous fit to DD+LL 2018 data has been done using the simple model + \(f_{2}(1270)\).
April 14th, 2025
2018-LL \(\Rightarrow\)
2018-DD \(\Rightarrow\)
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dalitz plot Fit
April 14th, 2025
2018-LL \(\Rightarrow\)
2018-DD \(\Rightarrow\)
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dalitz plot Fit
April 14th, 2025
Amplitudes
Phases
Dalitz plot PDF
Fit results
- A simultaneous fit to DD+LL 2018 data has been done using the simple model + \(f_{2}(1270)\).
Conclusion and Outlook
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Sebastian Ordoñez-Soto
April 14th, 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Conclusion and outlook
April 14th, 2025
- Most elements for the time integrated Dalitz plot are in place.
- Preliminary simultaneous (only 2018) fit with a simple model gives a reasonable description of the Dalitz for both DD and LL.
- There are indications of the potential contribution of \(f_{2}(1270)\) and \(f_{0}(1500)\).
- Include, when available, the new inputs (\(f_{\text{sig}}, f_{\text{comb. bkg}}, f_{B_{d}^{0} \text{ bkg}}\)) from the BF analysis.
- Run simultaneous fits including all Run 1+2 samples (DD and LL).
- Incorporate the goodness-of-fit to quantitatively estimate the performance of the fits
- The point-to-point dissimilarity test will be employed for this purpose:
- Educate the final model by adding new resonances and define the nominal model.
Conclusion
Outlook
Thank you!
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Sebastian Ordoñez-Soto
April 14th, 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model
May 2025
\boxed{p_{\text{global}} = 0.38}
Fisher's method
P-values per sub-sample baseline
Global p-value (Fisher) baseline: 0.38
Global p-value (Stouffer) baseline: 0.16
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model
May 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model
May 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model
May 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model
May 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model
May 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model
May 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model
May 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model+f2
May 2025
\boxed{p_{\text{global}} = 0.5}
Fisher's method
P-values per sub-sample baseline+f2
Global p-value (Fisher) baseline+f2: 0.5
Global p-value (Stouffer) baseline+f2: 0.21
P-values per sub-sample
baseline
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model+f2
May 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model+f2
May 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model+f2
May 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model+f2
May 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model+f2
May 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model+f2
May 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
Baseline model+f2
May 2025
Sebastian Ordoñez-Soto
AmAn of the \(B_{s}^{0}\rightarrow K_{S}^{0} \pi^{+}\pi^{-}\) decay
Dissimilarity test results
May 2025
p-values per sub-sample baseline+f2
Global p-value (Fisher) baseline+f2: 0.12
Global p-value (Stouffer) baseline+f2: 0.1
P-values per sub-sample
baseline
Comparison using gaussian correlation function
Global p-value (Fisher) baseline: 0.12
Global p-value (Stouffer) baseline: 0.11
p-value full Run 2
baseline+f2
[Bs2KSpipi AmAn/Anatomy+Preliminary results] B2KShh' mu-Group meeting-14/04/25
By Sebastian Ordoñez
