IX International Workshop On Tau Lepton Physics Pisa, 19-22 September 06

1. IX International Workshop On Tau Lepton Physics Pisa, 19-22 September 06 Model-dependent electromagnetic corrections to → decay Gabriel López Castro Physics Department Cinvestav, México City

2. Necessity for radiative corrections Current precision in B(→)~O( 0.5% ), PDG 2006. Expected improvement at B factories. Current tests of the CVC Hypothesis: Superallowed 0+→0+transitions (at the 10-4 level). 2.9 discrepancy in B(→) [measured-CVC] 2.1 discrepancy in a,LO [ –e+e- based data] Up to 10% discrepancy in Fe+e-(s)/F(s)2 [KLOE data]

3. Isospin symmetry breaking • Isospin symmetry breaking : and (Cirigliano et al, 01,02) 1.02010.0003 (Marciano-Sirlin 88 Braaten-Li 90)

4. Kinematics  Virtual and real photon corrections to have an infrared safe result Kinematics of three-body decay (tree-level + virtual corrections) t=(p-p)2 =(p-+p0) 2 and u=(p- p-)2 Kinematics of four-body decay (real photon corrections)

5. Long-distance electromagnetic corrections Important for photon inclusive measurements (→+→)

6. Model-dependent contributions (Cirigliano et al, JHEP 2002) Resonant  and a1 exchange fixed by ChPT (Ecker et al, NPB, 1989) with form factors from (Guerrero-Pich, PRD, 1997; Kühn-Santamaria, ZPC, 1990) Anomalous axial couplings (Wess-Zumino, PLB, 1971; Witten, NPB, 1983) fixed by F. Not realistic for all energies, but expected to be small

7. Cirigliano et al, JHEP 2002 G0EM(t) G0EM(t)

8. Vector meson dominance model (Flores et al, PRD 2005; hep-ph/0608084)  Large q2 in  decays allows the production and decay of resonances  Couplings fixed from low-energy processes: →, l+l-, →, Γa1 , Weinberg sum rule (fa1)  Alternative calculation

10. Excluding the contribution of (782) meson

11. Corrections to the decay rate If photons with E 0 are discriminated 0(%)Cirigliano (MeV) This work 2002 Hard photon radiative events

12. Radiative → decays Can help to discriminate between two models

13. Hadron spectrum Photon spectrum

14. Effects of (770) magnetic dipole moment Electromagnetic  vertex, magnetic moment =(e/m) → →0 =100 =100 =1 =2 =3 =200 y=cos x=2E/m =200 GLC+toledo, PRD, 1999 Flores et al, PRD, 2005

15. Conclusions  Long-distance corrections to the spectrum to the dipion spectrum are smaller than in ChPT for t  0.6 GeV2. Effect in a(,  based) ~ -3.8x10-10 Long-distance corrections to the decay rate of O(-0.1%). Well below current (and future?) uncertainties. The decay rate, and the photon and 2 spectrum in → can be useful to discriminate between MDM and ChPT.

16. Sources of isospin breaking corrections (M. Davier et al EPJ C27, 2003)

17. Current best test of CVC Hardy and Towner, EPJ A25, 2005 0+ (A,Z+1)→0+ (A,Z)e+ 0+T_ 0+=2 Marciano & Sirlin, PRL 96, 2006

18. Isospin symmetry breaking Isospin symmetry (CVC): (s)= 0(s)  Isospin breaking: (s)0(s) and, 1.02010.0003 (Marciano-Sirlin 88 Braaten-Li 90)