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Measurement of the branching fraction, polarization, and time-dependent $CP$ asymmetry in $B^0 \to \rho^+\rho^-$ decays and constraint on the CKM angle $\phi_2$

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Pith's one-line read This paper reports a measurement of the branching fraction, longitudinal polarization fraction, and time-dependent CP-violation parameters of $B^0\to\rho^+\rho^-$ decays, and uses an isospin analysis to extract the CKM angle $\phi_2 =…

desk verdict Solid first Belle II measurement of B0 -> rho+rho- observables that will feed the world averages, with a soft spot in the phi2 extraction where isospin-breaking is assumed rather than quantified. read the letter →

arxiv 2412.19624 v2 pith:7ODJGLA7 submitted 2024-12-27 hep-ex

Belle II Collaboration: I. Adachi , L. Aggarwal , H. Ahmed , N. Akopov , M. Alhakami , A. Aloisio , N. Althubiti , N. Anh Ky
show 371 more authors
D. M. Asner H. Atmacan V. Aushev M. Aversano R. Ayad V. Babu N. K. Baghel P. Bambade Sw. Banerjee M. Barrett M. Bartl J. Baudot A. Baur A. Beaubien J. Becker J. V. Bennett V. Bertacchi M. Bertemes E. Bertholet M. Bessner S. Bettarini B. Bhuyan D. Biswas A. Bobrov D. Bodrov A. Bolz A. Bondar J. Borah A. Boschetti A. Bozek M. Bračko P. Branchini R. A. Briere T. E. Browder A. Budano S. Bussino Q. Campagna M. Campajola G. Casarosa C. Cecchi J. Cerasoli M.-C. Chang P. Chang R. Cheaib P. Cheema B. G. Cheon K. Chilikin K. Chirapatpimol H.-E. Cho K. Cho S.-J. Cho S.-K. Choi S. Choudhury J. Cochran L. Corona J. X. Cui E. De La Cruz-Burelo S. A. De La Motte G. De Nardo G. De Pietro R. de Sangro M. Destefanis S. Dey F. Di Capua J. Dingfelder Z. Doležal I. Domínguez Jiménez T. V. Dong X. Dong M. Dorigo D. Dossett K. Dugic G. Dujany P. Ecker J. Eppelt P. Feichtinger T. Ferber T. Fillinger C. Finck G. Finocchiaro A. Fodor F. Forti B. G. Fulsom A. Gabrielli E. Ganiev M. Garcia-Hernandez R. Garg G. Gaudino V. Gaur A. Gaz A. Gellrich G. Ghevondyan D. Ghosh H. Ghumaryan G. Giakoustidis R. Giordano A. Giri P. Gironella Gironell A. Glazov B. Gobbo R. Godang O. Gogota P. Goldenzweig W. Gradl E. Graziani D. Greenwald Z. Gruberová Y. Guan K. Gudkova I. Haide T. Hara C. Harris K. Hayasaka S. Hazra C. Hearty M. T. Hedges A. Heidelbach I. Heredia de la Cruz M. Hernández Villanueva T. Higuchi M. Hoek M. Hohmann R. Hoppe P. Horak C.-L. Hsu T. Humair T. Iijima K. Inami N. Ipsita A. Ishikawa R. Itoh M. Iwasaki D. Jacobi W. W. Jacobs E.-J. Jang Y. Jin A. Johnson H. Junkerkalefeld M. Kaleta A. B. Kaliyar J. Kandra F. Keil C. Ketter C. Kiesling C.-H. Kim D. Y. Kim J.-Y. Kim K.-H. Kim Y.-K. Kim K. Kinoshita P. Kodyš T. Koga S. Kohani K. Kojima A. Korobov S. Korpar E. Kovalenko R. Kowalewski P. Križan P. Krokovny T. Kuhr Y. Kulii R. Kumar K. Kumara T. Kunigo A. Kuzmin Y.-J. Kwon S. Lacaprara K. Lalwani T. Lam L. Lanceri J. S. Lange T. S. Lau M. Laurenza R. Leboucher F. R. Le Diberder M. J. Lee C. Lemettais P. Leo L. K. Li Q. M. Li W. Z. Li Y. Li Y. B. Li Y. P. Liao J. Libby J. Lin S. Lin M. H. Liu Q. Y. Liu Z. Q. Liu D. Liventsev S. Longo T. Lueck C. Lyu Y. Ma C. Madaan M. Maggiora S. P. Maharana R. Maiti G. Mancinelli R. Manfredi E. Manoni M. Mantovano D. Marcantonio S. Marcello C. Marinas C. Martellini A. Martens A. Martini T. Martinov L. Massaccesi M. Masuda K. Matsuoka D. Matvienko S. K. Maurya M. Maushart J. A. McKenna F. Meier D. Meleshko M. Merola C. Miller M. Mirra S. Mitra K. Miyabayashi H. Miyake G. B. Mohanty S. Mondal S. Moneta H.-G. Moser R. Mussa I. Nakamura M. Nakao Y. Nakazawa M. Naruki Z. Natkaniec A. Natochii M. Nayak G. Nazaryan M. Neu S. Nishida S. Ogawa R. Okubo H. Ono Y. Onuki G. Pakhlova S. Pardi K. Parham H. Park J. Park K. Park S.-H. Park A. Passeri S. Patra T. K. Pedlar I. Peruzzi R. Peschke R. Pestotnik L. E. Piilonen P. L. M. Podesta-Lerma T. Podobnik S. Pokharel C. Praz S. Prell E. Prencipe M. T. Prim H. Purwar S. Raiz K. Ravindran J. U. Rehman M. Reif S. Reiter M. Remnev L. Reuter D. Ricalde Herrmann I. Ripp-Baudot G. Rizzo M. Roehrken J. M. Roney A. Rostomyan N. Rout Y. Sakai D. A. Sanders S. Sandilya L. Santelj V. Savinov B. Scavino C. Schwanda A. J. Schwartz Y. Seino A. Selce K. Senyo J. Serrano M. E. Sevior C. Sfienti W. Shan X. D. Shi T. Shillington J.-G. Shiu D. Shtol B. Shwartz A. Sibidanov F. Simon J. Skorupa R. J. Sobie M. Sobotzik A. Soffer A. Sokolov E. Solovieva S. Spataro B. Spruck W. Song M. Starič P. Stavroulakis S. Stefkova R. Stroili J. Strube M. Sumihama K. Sumisawa N. Suwonjandee H. Svidras M. Takizawa U. Tamponi K. Tanida F. Tenchini A. Thaller O. Tittel R. Tiwary E. Torassa K. Trabelsi I. Tsaklidis I. Ueda T. Uglov K. Unger Y. Unno K. Uno S. Uno P. Urquijo Y. Ushiroda S. E. Vahsen R. van Tonder K. E. Varvell M. Veronesi A. Vinokurova V. S. Vismaya L. Vitale V. Vobbilisetti R. Volpe M. Wakai S. Wallner M.-Z. Wang A. Warburton M. Watanabe S. Watanuki C. Wessel E. Won X. P. Xu B. D. Yabsley S. Yamada W. Yan J. Yelton J. H. Yin K. Yoshihara J. Yuan Y. Yusa L. Zani V. Zhilich J. S. Zhou Q. D. Zhou L. Zhu R. Žlebčík
This is my paper · ORCID
classification hep-ex
keywords B0torho+rho-decaybranchingfractionlongitudinalpolarizationtime-dependentCPasymmetryCKManglephi2isospinanalysisGronau-LondonrelationsUpsilon(4S)
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Using $(387\pm6)\times10^6$ $\Upsilon(4S)$ decays collected at an asymmetric-energy $e^+e^-$ collider, this paper measures the decay $B^0\to\rho^+\rho^-$, which has two neutral pions in the final state. Two unbinned maximum-likelihood fits extract the branching fraction $\mathcal{B} = (2.89^{+0.23}_{-0.22}{}^{+0.29}_{-0.27})\times10^{-5}$, the longitudinal polarization fraction $f_L = 0.921^{+0.024}_{-0.025}{}^{+0.017}_{-0.015}$, and the time-dependent $CP$-violation parameters $S = -0.26\pm0.19\pm0.08$ and $C = -0.02\pm0.12^{+0.06}_{-0.05}$. The results agree with earlier measurements, with $f_L$ somewhat lower than the world average but within $2\sigma$. Combined with world averages for the $\rho\rho$ decay modes in an isospin analysis based on the Gronau-London relations, the paper extracts the CKM angle $\phi_2 = (92.6^{+4.5}_{-4.7})^\circ$, constraining the least well-known angle of the unitarity triangle.

What carries the argument

The argument's engine is the Gronau-London isospin relations, $(1/\sqrt{2})A^{+-}+A^{00}=A^{+0}$ and its charge-conjugate partner, which connect the three $\rho\rho$ decay amplitudes so that the tree-level phase $\phi_2$ can be separated from the loop-induced penguin shift $\Delta\phi_2$. Experimentally, the measurement rests on two unbinned maximum-likelihood fits: the first uses the observables $\Delta E$, $m_{\pi^\pm\pi^0}$, $\cos\theta_{\rho^\pm}$, and a transformed continuum-suppression output $T_C$ to extract $\mathcal{B}$ and $f_L$; the second fits the proper-time difference $\Delta t$ in seven flavor-tag quality bins to extract $S$ and $C$. The signal is split into longitudinal and transverse polarization components and into correctly reconstructed versus self-crossfeed candidates (candidates in which some final-state particles actually come from the other $B$ meson), with a relativistic Breit-Wigner line shape, helicity-angle templates, and control channels calibrating the probability-density functions.

What would settle it

A precise measurement of the direct CP asymmetry in $B^0\to\rho^0\rho^0$ that, through the isospin relations, forces a fitted penguin shift $\Delta\phi_2$ incompatible with $(2.4^{+3.8}_{-3.7})^\circ$, or an independent $\phi_2$ determination from $B\to\pi\pi$ that excludes $92.6^\circ$ at the $95\%$ confidence level, would falsify the isospin-based extraction.

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Extended reading notes

Core claim

The central claim is that $B^0\to\rho^+\rho^-$ decays are governed by a nearly pure longitudinal, $CP$-even configuration with $\mathcal{B} = (2.89^{+0.23}_{-0.22}{}^{+0.29}_{-0.27})\times10^{-5}$, $f_L = 0.921^{+0.024}_{-0.025}{}^{+0.017}_{-0.015}$, $S = -0.26\pm0.19\pm0.08$, and $C = -0.02\pm0.12^{+0.06}_{-0.05}$. Feeding these numbers, together with the world-average branching fractions and $CP$ asymmetries for $B^0\to\rho^0\rho^0$ and $B^+\to\rho^+\rho^0$, into the Gronau-London isospin construction yields two solutions for the CKM angle $\phi_2$; the solution consistent with other unitarity-triangle constraints is $\phi_2 = (92.6^{+4.5}_{-4.7})^\circ$, with a second solution at $177.4^\circ$ excluded by measurements of the angles $\phi_1$ and $\phi_3$ and by unitarity. The uncertainty on $\phi_2$ is dominated by the statistical precision of the mixing-induced $CP$ parameter $S$ in $B^0\to\rho^+\rho^-$ and $B^0\to\rho^0\rho^0$.

Load-bearing premise

The isospin analysis assumes that the strong force treats up and down quarks identically in these decays, so that only the CKM phase distinguishes the amplitudes; if isospin-breaking effects are even a few degrees, the extracted angle would move outside its quoted uncertainty.

Editorial extensions

If this is right

  • The measurement establishes $B^0\to\rho^+\rho^-$ as a nearly pure longitudinal, $CP$-even channel, so the extracted $S$ is an essentially direct probe of $\sin(2\phi_2^{\rm eff})$ with only a small penguin shift $\Delta\phi_2 = (2.4^{+3.8}_{-3.7})^\circ$.
  • Combined with world averages, the isospin analysis yields $\phi_2 = (92.6^{+4.5}_{-4.7})^\circ$, the most stringent constraint on this angle from the $\rho\rho$ family and consistent with the Standard Model.
  • The central value of $f_L$ is lower than the previous world average by about $2\sigma$, implying a slightly larger transverse polarization component than earlier experiments found.
  • The uncertainty on $\phi_2$ is dominated by the $S$ parameters for $B^0\to\rho^+\rho^-$ and $B^0\to\rho^0\rho^0$; therefore further data in these two channels will directly reduce the error on $\phi_2$.
  • The result, together with other unitarity-triangle constraints, can be used to bound possible beyond-Standard-Model contributions to $B^0$-$\bar B^0$ mixing.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If $f_L$ moves lower with more data, the transverse polarization component becomes large enough that its assumed-zero $CP$-violation parameters will need to be measured rather than fixed; otherwise the $S$ extraction could shift by more than the current systematic uncertainty.
  • The same isospin construction applied simultaneously to $B\to\rho\rho$, $B\to\pi\pi$, and $B\to\rho\pi$ would cross-check the size of isospin-breaking corrections, because the three channels share the same SU(2) structure but have independent experimental inputs.
  • A future measurement of the direct $CP$ asymmetry in $B^0\to\rho^0\rho^0$ at the few-percent level would directly probe the penguin shift $\Delta\phi_2$ and test the fitted value of $(2.4^{+3.8}_{-3.7})^\circ$.
  • This analysis uses part of the recorded dataset; if yields scale with luminosity, the $\phi_2$ uncertainty from $\rho\rho$ alone could roughly halve once the full data sample of the experiment is analyzed, making it a leading tree-level determination of the angle.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 4 minor

Summary. This paper presents a Belle II measurement of B^0→ρ^+ρ^- using 365.4 fb^-1 of Υ(4S) data. Two unbinned maximum-likelihood fits are performed: a six-observable extended fit to extract the branching fraction and longitudinal polarization fraction, and a time-dependent CP fit to extract S and C. The results are B(B^0→ρ^+ρ^-) = (2.89+0.23−0.22+0.29−0.27)×10^-5, f_L = 0.921+0.024−0.025+0.017−0.015, S = −0.26 ± 0.19 ± 0.08, and C = −0.02 ± 0.12+0.06−0.05. The Δt PDF is validated with a B^0→D^{*-}π^+ control sample, giving τ_B0 = 1.523 ± 0.033 ps and Δm_d = 0.507 ± 0.017 ps^-1 consistent with world averages. Combining the measured B→ρρ observables with Belle, BaBar, and LHCb results in a Gronau-London isospin analysis yields φ_2 = (92.6+4.5−4.7)°.

Significance. If correct, this is the first Belle II measurement of B^0→ρ^+ρ^- and provides a competitive constraint on the CKM angle φ_2. The experimental analysis is thorough: the signal-extraction and CP fits are cross-checked with control channels, the resolution function is validated on data, null tests with random flavor tags give S and C consistent with zero, and the systematic tables cover efficiency, background, interference, tagging, and resolution effects. The main reservation concerns the isospin-breaking assumption in the φ_2 extraction, which is presented as a quantitative result without an explicit theory-uncertainty term.

major comments (1)
  1. [Sec. VII, Eqs. (16)–(17)] The φ_2 = (92.6+4.5−4.7)° result is derived from the Gronau-London isospin relations under the assumption of strong isospin symmetry, but the paper does not assign a theory uncertainty for isospin breaking (e.g., ρ mass and width differences, π^0–η mixing) or for electroweak-penguin contributions. The quoted uncertainty is dominated by experimental S parameters, yet published estimates of isospin-breaking shifts in B→ρρ are of order a few degrees, comparable to the quoted ±4.5/−4.7°. Because the abstract and title present φ_2 as a headline result, the absence of such a term, or of a demonstration that these shifts are below the quoted uncertainty, makes the precision claim incomplete. Please add a quantitative theory-uncertainty assessment (for example, varying the isospin-breaking inputs within published ranges and quoting the resulting shift in φ_2), or present the φ_2 result as an illustration rather than a precision constraint.
minor comments (4)
  1. [Sec. IV B 3 and Table II] The text says the continuum Δt PDF is a sum of two Gaussians with means set to zero, but the Table II entry 'DG' does not specify whether the two Gaussians share a common mean or whether a resolution function is applied; please clarify.
  2. [Table V] The floated yields for B^0→π^+π^-π^0π^0 and for rare peaking backgrounds are negative (−98.0 ± 62.2 and −31.9 ± 45.3); please comment on whether these values are consistent with zero and whether the fit imposes any positivity constraint on physical yields.
  3. [Sec. VII] The sentence 'The updated values of f_{+-} and f_{00} shift φ_2 by −0.4°' is difficult to reconcile with the two quoted central values 91.5° and 92.6°; please clarify which input is being updated and in which direction.
  4. [Table I] The row labeled 'PDG [12]' is a world average rather than an independent measurement; consider renaming it to avoid implying a separate experimental result.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the measured observables come from unbinned likelihood fits to data, and the phi2 constraint is a standard isospin application using external world averages.

full rationale

The paper's central results (B, fL, S, C) are extracted directly from data via unbinned maximum-likelihood fits (Eqs. 4-7 and 11) with signal yields, helicity-angle templates, and time-dependent CP-asymmetry parameters floated in the fits. No fitted output is renamed as a prediction, and no input is constructed from the target observable. The signal-extraction fit determines B and fL from Eqs. 5-6; the time-dependent fit determines S and C from the Delta-t distributions. Systematic uncertainties are estimated from control samples and ensemble tests, not by imposing the final results. The phi2 extraction in Sec. VII uses the Gronau-London isospin relations (Eqs. 16-17), which are external standard theory cited to Ref. [16], with inputs from PDG world averages and the present measurement. The method is attributed to Belle Ref. [19], but the analysis is not circular: the isospin relations are independent of this paper's measured values, and the phi2 result is consistent with external unitarity-triangle constraints rather than being fed back into the inputs. The absence of a separate isospin-breaking uncertainty is a legitimate physics-assumption concern, but it is a correctness and precision issue, not a circularity in the derivation chain. No step reduces, by construction or self-citation, to its own inputs.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central claim depends on fitted yields in an unbinned maximum-likelihood analysis, on external world-average inputs, and on the theoretical isospin relations. No new particles or forces are introduced. The principal non-empirical input is the Gronau-London isospin structure used to convert CP asymmetries into a phi2 constraint.

free parameters (7)
  • LP signal yield N_LP = 436.3^{+34.2}_{-33.5}
    Fitted in Eq. 4; used in Eqs. 5-6 to determine B and f_L.
  • TP signal yield N_TP = 65.4^{+24.3}_{-22.6}
    Fitted in Eq. 4; the small yield makes f_L statistically limited.
  • Continuum (qq) yield = 1410.2^{+76.5}_{-75.7}
    Floated in the signal-extraction fit; its shape and yield affect the signal yield.
  • Combinatorial BB yield = 849.2^{+73.3}_{-72.3}
    Floated in the fit.
  • SCF yield ratios k_LP_SCFa, k_LP_SCFb, k_TP_SCF = 0.19, 0.16, 0.08
    Fixed to MC expectations; varied by +/-20% as a systematic (Sec. VI A).
  • Signal efficiencies epsilon_LP and epsilon_TP = 4.1% and 7.8%
    Determined from MC with control-sample corrections; enter Eq. 5. The pi0 efficiency uncertainty (+/-7.7%) is the largest systematic for B.
  • Peaking background yields (B0 -> rho±pi∓pi0, B0 -> pi+pi-pi0pi0, B0 -> pi+pi-pi0, B0 -> a1(1260)0 pi0, rare peaking) = 44.9, -98.0, -1.2, 32.0, -31.9 (Table V)
    Partially floated in the signal-extraction fit to account for mis-modeled charmless B decays.
assumptions (6)
  • domain assumption Gronau-London isospin relations (Eqs. 16-17) hold with negligible electroweak penguin and isospin-breaking contributions.
    Used in Sec. VII to extract phi2 from the measured B, f_L, S, C. The paper cites the method of Ref. [19] and does not quote a separate theory uncertainty; if isospin breaking is of order a few degrees, phi2 shifts.
  • domain assumption No CP violation in B0-B0 mixing.
    Stated in footnote [15] as an excellent approximation; underlies the time-dependent CP fit in Eq. 1.
  • ad hoc to paper The transverse polarization (TP) signal has S = C = 0 in the baseline CP fit.
    Section IV B 1: TP states are mixtures of CP-even and CP-odd; setting their CP violation to zero is a simplification. The impact is evaluated as a systematic uncertainty (Table VII).
  • domain assumption External inputs f00 = 0.4861 from HFLAV [51] and N(Upsilon(4S)) = (387 +/- 6) x 10^6 are correct.
    Used in Eq. 5 to convert signal yields to a branching fraction; uncertainties are propagated as systematics.
  • domain assumption The PDG values of tau_B0 and Delta m_d are used in the time-dependent PDF.
    Used in Eq. 11; the paper varies them by their quoted uncertainties as a systematic.
  • domain assumption The MC simulation correctly models signal and background distributions after the applied data-MC corrections.
    The entire PDF description (Table II) is based on MC templates and calibration factors; validated with control channels, but a residual mis-modeling is always possible. The paper attempts to cover this with data-MC mis-modeling systematics.

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Cite this review

Pith. "Pith review of Measurement of the branching fraction, polarization, and time-dependent $CP$ asymmetry in $B^0 \to \rho^+\rho^-$ decays and constraint on the CKM angle $\phi_2$." pith.science (2026). https://pith.science/paper/7ODJGLA7

@misc{pith2026241219624,
  author       = {Pith},
  title        = {Pith review of: Measurement of the branching fraction, polarization, and time-dependent $CP$ asymmetry in $B^0 \to \rho^+\rho^-$ decays and constraint on the CKM angle $\phi_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7ODJGLA7}},
  note         = {Machine review of arXiv:2412.19624}
}
abstract

We present a measurement of the branching fraction and fraction of longitudinal polarization of $B^0 \to \rho^+ \rho^-$ decays, which have two $\pi^0$'s in the final state. We also measure time-dependent {\it CP} violation parameters for decays into longitudinally polarized $\rho^+ \rho^-$ pairs. This analysis is based on a data sample containing $(387\pm6) \times 10^6$ $\Upsilon(4S)$ mesons collected with the Belle~II detector at the SuperKEKB asymmetric-energy $e^+e^-$ collider in 2019-2022. We obtain $\mathcal{B}(B^0\to\rho^+\rho^-) = (2.89 ^{+0.23}_{-0.22} {}^{+0.29}_{-0.27}) \times 10^{-5}, f_{L} = 0.921 ^{+0.024}_{-0.025} {}^{+0.017}_{-0.015}$, \mbox{$S = -0.26\pm0.19\pm0.08$}, and $C = -0.02\pm0.12^{+0.06}_{-0.05}$, where the first uncertainties are statistical and the second are systematic. We use these results to perform an isospin analysis to constrain the CKM angle $\phi_2$ and obtain two solutions; the result consistent with other Standard Model constraints is $\phi_2 = (92.6^{+4.5}_{-4.7})^\circ$.

Figures

Figures reproduced from arXiv: 2412.19624 by the authors.

Figure 1
Figure 1. Distribution of the FBDT classifier to distinguish [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Distributions for ∆E (top left), mπ±π0 (top center, top right), TC (bottom left), and cos θρ± (bottom center, bottom right). The points with error bars represent the data, the solid red curves show the sum of all contributions, the long-dashed blue curves show the LP signal, the short-dashed red curves show the TP signal, the short-dashed blue curves show the sum of LP and TP SCF, the dotted purple curves represent … view at source ↗
Figure 3
Figure 3. Distributions for ∆t of B 0 tag in 0.875 < r < 1.0 (left), ∆t of B 0 tag in 0.875 < r < 1.0 (center), and background-subtracted asymmetry using the sPlot technique [53]. The points with error bars represent the data and the curves show the fit result. The sWeights are calculated using ∆E, mπ±π0 , cosθρ± , and qr [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Probability (1−Confidence-Level) for the CKM angle ϕ2 based on combined inputs from the world averages [12] and our results of B → ρρ decays. The black dotted lines correspond to the 0.683 and 0.954 confidence levels. We subsequently combine our B0 → ρ +ρ − results wit…

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Reference graph

Works this paper leans on

68 extracted references · 42 canonical work pages

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    W. Altmannshofer, R. Harnik, and J. Zupan, JHEP 11, 202 (2013), arXiv:1308.3653 [hep-ph]

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    Correctly reconstructed Signal The ∆ E distribution is described by two bifurcated Gaussian functions with a common mean. The ρ± line- shape is modeled by a relativistic Breit-Wigner (BW) function given by A(m) = pπ m2 − m2 0 + im0Γ(m) F (pρ) F (p′ρ) F (pπ) F (p′π) , (9) Γ(m) = pπ p′π 3 m0 m Γ0 F (pπ) F (p′π) 2 , (10) where m0 and Γ 0 are the peak positio...

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    The lineshape of mπ±π0 is described by the sum of a linear function and a relativistic BW function

    Signal Self-crossfeed For self-cross-feed signal, the ∆E distributions are de- scribed by a bifurcated Gaussian function. The lineshape of mπ±π0 is described by the sum of a linear function and a relativistic BW function. The TC distribution is mod- eled by a linear function. A two-dimensional histogram template is used for cos θρ+ and cos θρ− , as these ...

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    Since continuum events also include ρ resonances, the mπ±π0 distributions are mod- eled by a sum of a relativistic BW function and a linear function

    Continuum For continuum events, the ∆E distribution is described by a quadratic function. Since continuum events also include ρ resonances, the mπ±π0 distributions are mod- eled by a sum of a relativistic BW function and a linear function. As there are correlations in the ∆ E-TC and mπ±π0 -cos θρ± distributions, one-dimensional histogram templates dependi...

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    The ∆ E-TC and mπ±π0 -cos θρ± distributions are modeled in the same way as continuum background

    Combinatorial BB backgrounds The ∆ E and mπ±π0 distributions are both described by quadratic functions. The ∆ E-TC and mπ±π0 -cos θρ± distributions are modeled in the same way as continuum background. These parameters are obtained from MC simulated samples except for the ∆ E shape. The ∆ E shape parameters and the yield for combinatorial BB background are...

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    rare peaking

    Peaking BB backgrounds The decay of B mesons to all-pion final states or to final states with pions and a kaon could peak in the fit observables. The peaking backgrounds are modeled indi- vidually, as summarized in Table II. The branching frac- tions used are measured values when possible and are listed in Table III. Most peaking backgrounds that are not ...

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    τ +τ − background The τ +τ − background is suppressed by the selec- tion with the TabNet classifier. The remaining events arise mostly from combinations of three decays: τ − → π−π+π−π0ντ , τ − → π−π0ντ , and τ − → π−π0π0ντ , which account for more than 90% of the τ +τ − back- ground. The ∆ E distribution for τ +τ − background is modeled by a quadratic fun...

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    Correctly reconstructed Signal Similar PDFs are used for the LP and TP signal events. Since the TP signal decay includes contributions from both CP-even and CP-odd states, our baseline fit as- sumes that CP-violating effects cancel out in the TP components; thus, in the PDF function for ∆ t, both S and C are set to zero. Possible nonzero values for the TP...

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Pith tools

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