Dipion Spectrum : e + e - annihilations and τ decays

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Dipion Spectrum : e + e - annihilations and τ decays. M. Benayoun LPNHE Paris 6/7. The Pion Form factor in e + e - and τ Data. Since the advent of τ data, disagreement with e + e - data - PowerPoint PPT Presentation

Transcript of Dipion Spectrum : e + e - annihilations and τ decays

  • Dipion Spectrum : e+e- annihilations and decaysM. Benayoun LPNHE Paris 6/7*M. Benayoun, e+ e- versus tau

    M. Benayoun, e+ e- versus tau

  • The Pion Form factor in e+e- and DataSince the advent of data, disagreement with e+e- dataLarge activity in identifying isospin symmetry breaking in both e+e- annihilation and decayDisagreement survived accounting for identified isospin breaking corrections!Is there a missing piece, a systematic effect (in e+e- or data) or new physics?M. Benayoun, e+ e- versus tau*

    M. Benayoun, e+ e- versus tau

  • The Latest Account

    Inv. Mass dependent missing effect

    M. Benayoun, e+ e- versus tau*M. Davier NP Proc. Supp. 169 (2007) 288

    M. Benayoun, e+ e- versus tau

  • The Latest Account

    Inv. Mass dependent missing effect !

    Is it isospin breaking?M. Benayoun, e+ e- versus tau*M. Davier NP Proc. Supp. 169 (2007) 288

    M. Benayoun, e+ e- versus tau

  • Possible Missing Effect : (--) MixingM. Benayoun, e+ e- versus tau*FFs New DataIsospin 1 part of Isospin 1 part of

    M. Benayoun, e+ e- versus tau

  • Possible Missing Effect : (--) MixingM. Benayoun, e+ e- versus tau*FFs New DataIsospin 1 part of Isospin 1 part of

    Isospin 0 part of 0 ?Can it be s-dependent?

    M. Benayoun, e+ e- versus tau

  • OUTLINEA VMD-like Model : HLS Model (briefly)Breaking of U(3)/SU(3) Symmetries (briefly)The Anomalous Sector (briefly)The Pion Form Factor in e+e- Annihilation and Decay (Isospin Breaking) Loop Transition Effects in e+e- : Physical 0, , Extended Data Sample submitted to fit, Why? Fit results & PlotsConclusions

    M. Benayoun, e+ e- versus tau*

    M. Benayoun, e+ e- versus tau

  • OUTLINEA VMD-like Model : HLS Model (briefly)Breaking of U(3)/SU(3) Symmetries (briefly)The Anomalous Sector (briefly)The Pion Form Factor in e+e- Annihilation and Decay (Isospin Brk) Loop Transition Effects in e+e- : Physical 0, , Extended Data Sample submitted to fit, Why? Fit results & PlotsConclusions

    M. Benayoun, e+ e- versus tau*

    M. Benayoun, e+ e- versus tau

  • The Pion form Factor in e+e- and Physics

    Without Symmetry Breaking :

    Isospin symmetry breaking: mass splittings +

    M. Benayoun, e+ e- versus tau*W. Marciano & A. Sirlin PRL 71 (1993) 3629V. Cirigliano G. Ecker & H. Neufeld PL B 513 (2001) 361

    M. Benayoun, e+ e- versus tau

  • The Pion form Factor in e+e- and Physics

    Without Symmetry Breaking :

    Isospin symmetry breaking : mass splittings +

    M. Benayoun, e+ e- versus tau*W. Marciano & A. Sirlin PRL 71 (1993) 3629V. Cirigliano G. Ecker & H. Neufeld PL B 513 (2001) 361 HLS

    M. Benayoun, e+ e- versus tau

  • The Pion form Factor in e+e- and Physics

    With Symmetry Breaking :

    Isospin symmetry breaking : mass splittings +

    M. Benayoun, e+ e- versus tau*W. Marciano & A. Sirlin PRL 71 (1993) 3629V. Cirigliano G. Ecker & H. Neufeld PL B 513 (2001) 361 (/W)V ??m2

    M. Benayoun, e+ e- versus tau

  • /W- TransitionsNo isospin breaking :

    Isospin symmetry breaking : component

    M. Benayoun, e+ e- versus tau*I and I componentsI component

    M. Benayoun, e+ e- versus tau

  • Transitions among vector fields at one loopAt tree level ideal fields mass eigenstatesAt one loop, the HLS Lagrangian piece

    induces transitions among ideal fieldsideal fields mass eigenstatesisospin symmetry breaking :

    M. Benayoun, e+ e- versus tau*

    M. Benayoun, e+ e- versus tau

  • Transitions among vector fields at one loopDefine the loops : = K+ K- , = K0 K0

    Then, beside self-masses : = + ~ 2(s) 0 always = - 0 by isospin brk = - ~ 1(s)

    M. Benayoun, e+ e- versus tauVVP Lagrangian K*K loops // Yang-Mills K*K*loops*f(s)

    M. Benayoun, e+ e- versus tau

  • The Modified Vector Mass Matrix I IIWith m2 = a g2 f2 and = zV No SU(3) Brk :: , No SU(2) Brk ::Blue : Loop effectsmagenta : SU(3) breaking red : isospin breaking*M. Benayoun, e+ e- versus tau

    M. Benayoun, e+ e- versus tau

  • Loop Corrections : ( , ) MixingI IIBlue : Loop effectsmagenta : SU(3) breaking red : isospin breaking*M. Benayoun, e+ e- versus tau

    M. Benayoun, e+ e- versus tau

  • Isospin Breaking : (, , ) MixingI IIBlue : Loop effectsmagenta : SU(3) breaking red : isospin breaking*M. Benayoun, e+ e- versus tau

    M. Benayoun, e+ e- versus tau

  • The Mass Matrix Eigen System Expect : Then solve for the eigensystem perturbatively :

    and : M. Benayoun, e+ e- versus tau*

    M. Benayoun, e+ e- versus tau

  • From Ideal To Physical Fields I

    : Real analytic matrix functionfulfills Unitarity Condition*M. Benayoun, e+ e- versus tau

    M. Benayoun, e+ e- versus tau

  • From Ideal To Physical Fields IIMass term derived from the eigenvalues of M2(s) : Leading order propagators become *M. Benayoun, e+ e- versus tau(Self masses include subtraction polynomials)

    M. Benayoun, e+ e- versus tau

  • V Couplings *At leading order : term unchanged *s-dependent and couplings generated*M. Benayoun, e+ e- versus tau

    M. Benayoun, e+ e- versus tau

  • V Couplings *At leading order : term unchanged

    *s-dependent and couplings generated*M. Benayoun, e+ e- versus tauOrsay Phase 90 at peak

    M. Benayoun, e+ e- versus tau

  • V Couplings In terms of Ideal Fields

    Becomes

    With

    M. Benayoun, e+ e- versus tau*

    M. Benayoun, e+ e- versus tau

  • Vector Meson Couplings to /W (/W) V transitions : constant + (PP,VP) loops = + loop term : disp. relation (subtractions)tree terms :

    M. Benayoun, e+ e- versus tau*

    M. Benayoun, e+ e- versus tau

  • Vector Meson Coupling to /W (/W) V transitions : constant + (PP,VP) loops = + loop term : disp. relation (subtractions)tree terms :

    M. Benayoun, e+ e- versus tau*I and I components of 0

    M. Benayoun, e+ e- versus tau

  • Parameter FreedomIf only using the pion form factor (e+e-,) the parameter freedom is far too large:a (HLS), g , zA , m2 (4)Subtraction polynomials in : (~ 8) Too many parameters, too few structuresSolution : extend the fitted data sample: more information, less correlations

    M. Benayoun, e+ e- versus tau*

    M. Benayoun, e+ e- versus tau

  • The Extended Data SampleAdd anomalous decay modes VP, P :

    Price : x, zT, zV, zA for 14 modes for free for free + 4 measured data :: Total 18 add. data

    M. Benayoun, e+ e- versus tau*M.B.,L.D. ,S.E, V.I. & H.OC, PR D 59 (1999) 114027M.B, H.OC EPJ C22 (2001) 503

    M. Benayoun, e+ e- versus tau

  • The Main GuessMain Guess Proof of Principle 18 Decay Modes + Pion FF in e+e- annihilation

    Fully reconstruct The Pion FF in decay (improvement of parameter fit values)M. Benayoun, e+ e- versus tau*

    M. Benayoun, e+ e- versus tau

  • The 2 contributions to fitsM. Benayoun, e+ e- versus tau*

    Data Set (#data points)Full Data FitNo dataNo Spacelike DataDecays (18+1)11.1311.5211.48New Timelike (127+1)128.1122.0125.8Old Timelike (82+1)59.154.755.2Spacelike (59+2)65.755.289.8/(59) ALEPH (33)23.942.3/(33)20.8 CLEO (25+1)26.126.2/(25)29.72/dofProbability313.8/331 74%257.7/274 75%238.8/272 93%

    M. Benayoun, e+ e- versus tau

  • The 2 contributions to fitsM. Benayoun, e+ e- versus tau*

    Data Set (#data points)Full Data FitNo dataNo Spacelike DataDecays (18+1)11.1311.5211.48New Timelike (127+1)128.1122.0125.8Old Timelike (82+1)59.154.755.2Spacelike (59+2)65.755.289.8/(59) ALEPH (33)23.942.3/(33)20.8 CLEO (25+1)26.126.2/(25)29.72/dofProbability313.8/331 74%257.7/274 75%238.8/272 93%

    M. Benayoun, e+ e- versus tau

  • The 2 contributions to fitsM. Benayoun, e+ e- versus tau* DATA OUTSIDE FIT : 2 distance to prediction

    Data Set (#data points)Full Data FitNo dataNo Spacelike DataDecays (18+1)11.1311.5211.48New Timelike (127+1)128.1122.0125.8Old Timelike (82+1)59.154.755.2Spacelike (59+2)65.755.289.8/(59) ALEPH (33)23.942.3/(33)20.8 CLEO (25+1)26.126.2/(25)29.72/dofProbability313.8/331 74%257.7/274 75%238.8/272 93%

    M. Benayoun, e+ e- versus tau

  • The 2 contributions to fitsM. Benayoun, e+ e- versus tau*Spacelike data OUTSIDE FIT

    Data Set (#data points)Full Data FitNo dataNo Spacelike DataDecays (18+1)11.1311.5211.48New Timelike (127+1)128.1122.0125.8Old Timelike (82+1)59.154.755.2Spacelike (59+2)65.755.289.8/(59) ALEPH (33)23.942.3/(33)20.8 CLEO (25+1)26.126.2/(25)29.72/dofProbability313.8/331 74%257.7/274 75%238.8/272 93%

    M. Benayoun, e+ e- ve