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Unitary triangle angles

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  • Provide world averages for measurements related to the angles of the Unitarity Triangle. In particular, we provide world averages of measurements of time-dependent CP violation, and related parameters. We also prepare averages of time-independent measurements that have a clean relation to the UT angles (especially in the B→DK system).
    • α ≡ φ2
      • from time-dependent CP asymmetries in b → uu-bar d decays, like Bd → π+π, (ρπ)0, ρ+ρ, a1+−π−+, …
      • extraction of α ≡ φ2 via isospin analysis, or interpretation of Dalitz plot parameters
    • β ≡ φ1
      • from time-dependent CP asymmetries in
        • b → cc-bar s decays, like Bd → J/ψ KS, J/ψ K*, D*+D* KS, …
        • colour-suppressed b → cu-bar d decays, like Bd → D π0
        • b → cc-bar d decays, like Bd → J/ψ π0, D(*)+D(*), …
        • hadronic b → s penguin decays, like Bd → φ KS, η′ KS, KS KS KS, K+K KS, …
        • hadronic b → d penguin decays, like Bd → KS KS, … (*)
        • radiative b → s γ penguin decays, like Bd→ KS π0 γ, … (*)
      • extraction of sin(2β) ≡ sin(2φ1) from the Bd → J/ψ K0 system
      • resolution of the ambiguity in 2β ≡ 2φ1
    • γ ≡ φ3
      • from time-dependent CP asymmetries in b → cu-bar d/uc-bar d decays, like Bd → D(*)−+π+−, …
      • extraction of constraints on |sin(2β+γ)| ≡ |sin(2φ13)| from the above
      • from time-dependent CP asymmetries in b → cu-bar s/uc-bar s decays, like Bs → Ds−+K+−, …
      • extraction of constraints on γ−2βs from the above
      • from rates and asymmetries in b → cu-bar s/uc-bar s decays, like B±→ D(*)K(*)±, …
      • extraction of constraints on γ ≡ φ3 from the above
    • φs
      • from time-dependent CP asymmetries in b → cc-bar s decays of the Bs meson, like Bs → J/ψφ, …

    (*) These measurements are listed under the β ≡ φ1 category as much for convenience as for physical reasons.

  • Identify common experimental and theoretical uncertainties and treat them coherently in the averages. Rescale the measurements if updated input parameters are available.
  • In cases where effective UT angles are measured
    no attempts are made to derive the fundamental quantities, if this requires input from QCD calculations.
  • If straightforward, an interpretation of the results is given.


Averages are updated around the times of major conferences; speakers at such events are encouraged to contact the HFLAV CP(t)/UT group members listed below in order to obtain the latest results which may not yet be posted officially. Requests for updates between major conferences are also welcome, though satisfaction cannot be guaranteed.


Date Comments
PDG & Spring 2021 Averages for the Winter conferences (Moriond, etc.) and PDG 2021
Summer 2018 Averages for the Summer 2018 conferences, ICHEP 2018 (South Korea), CKM2018 (Germany) etc.
Winter 2018 Averages for the Winter 2018 conferences, Moriond 2018 (Italy) etc.
Summer 2017 Averages for the Summer 2017 conferences, EPS 2017 (Italy), LP 2017 (China) etc.
Summer 2016 Averages for the Summer 2016 conferences, ICHEP 2016 (USA), CKM 2016 (India) etc.
Winter 2016 Averages for the Winter 2016 conferences, Moriond 2016 (Italy) etc.
Summer 2015 Averages for the Summer 2015 conferences, EPS 2015 (Austria), LP 2015 (Slovenia) etc.
Winter 2015 Averages for the Winter 2015 conferences, Moriond 2015 (Italy), etc.
Summer 2014 Averages for the Summer 2014 conferences, ICHEP 2014 (Spain), etc.
Winter 2014 Averages for the Winter 2014 conferences, Moriond (Italy), etc.
Summer 2012 Averages for the Summer 2012 conferences, ICHEP, Australia & CKM2012, USA, etc.
Moriond 2012 Averages for the Winter 2012 conferences, Moriond (Italy), etc.
Summer 2011 Averages for the Summer 2011 conferences, EPS 2011 (France), Lepton Photon 2011 (India) etc.
Winter 2011 Averages for the Winter 2011 conferences, Moriond (Italy), Beauty 2011 (Netherlands), FPCP2011 (Israel) etc.
Summer 2010 Averages for the Summer 2010 conferences, ICHEP2010 (France) etc.
Winter 2010 Averages for the Winter 2010 conferences, Moriond (Italy), FPCP2010 (Italy) etc.
Summer 2009 Averages for the Summer 2009 conferences, EPS 2009 (Poland), LP2009 (Germany) etc.
Winter 2009 Averages for the Winter 2009 conferences, Moriond 2009 (Italy), FPCP 2009 (USA) etc.
Summer 2008 Averages for the Summer 2008 conferences, ICHEP 2008 (USA), CKM2008 (Rome) etc.
Winter 2008 Averages for the Winter 2008 conferences, Moriond 2008 (Italy), FPCP2008 (Taiwan) etc.
Summer 2007 Averages for the Summer 2007 conferences, EPS-HEPP 2007 (Manchester, UK) and Lepton Photon 2007 (Daegu, Korea)
Winter 2007 Averages for the Winter 2007 conferences, Moriond 2007, (Italy) etc.
Summer 2006 Averages after the Summer 2006 conferences, ICHEP 2006, Moscow (Russia)
Winter 2006 Averages after the Winter 2006 conferences, Moriond (etc.) 2006
Summer 2005 Averages after the Summer 2005 conferences, LP 2005, Uppsala (Sweden) and EPS-HEPP 2005, Lisboa (Portugal).
Winter 2005 Averages after Winter 2005 conferences, Moriond 2005.
Summer 2004 Averages after the Summer 2004 conferences, ICHEP 2004, Bejing (China) and FPCP 2004, Daegu (Korea).
Winter 2004 Averages after Winter 2004 conferences, Moriond 2004.
PDG 2004 Averages for PDG 2004 update.
Published results only; therefore fewer measurements used than for Summer 2003 averages.
Summer 2003 Averages for Lepton-Photon 2003, FNAL
Winter 2003 Averages for FPCP 2003, Paris

Members of the Sub-Group

   Contact Persons       Experiment   
Tim Gershon (*) BABAR and LHCb
Matthew Kenzie LHCb
Kenkichi Miyabayashi Belle
Diego Tonelli Belle II

(*)Primary contact of this group

Past members: David Asner, Angelo Carbone, Gianluca Cavoto, Hal Evans, Owen Long, Yoshi Sakai, Achille Stocchi, Karim Trabelsi.

Email to the entire group at