1. Work done in collaboration with D. Gómez-Dumm, A. Pich, J. Portolés
A PROPOSAL FOR IMPROVING THE HADRONIZATION OF QCD CURRENTS IN TAUOLA
Work done in collaboration with D. Gómez-Dumm, A. Pich, J. Portolés
See Phys.Rev.D69:073002,2004 ; AIP Conf.Proc.964:40-46,2007 ; Work to appear soon
PHI PSI 08
Frascati
April 10th 2008
Pablo Roig
Instituto de FÍsica Corpuscular
CSIC-UVEG València (Spain)

2. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
SUMMARY:
Hadronic decays of the t lepton
Kühn-Santamaría Model in TAUOLA
Tools : cPT, Large Nc , RcT
t-  (2K p)- nt
Outlook :
(Gómez Dumm, Pich, Portolés, R. to appear)
t-  (h1h2h3) - nt
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

3. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
SUMMARY:
Hadronic decays of the t lepton
Kühn-Santamaría Model in TAUOLA
Tools : cPT, Large Nc , RcT
t-  (2K p)- nt
Outlook :
(Gómez Dumm, Pich, Portolés, R. to appear)
t-  (h1h2h3) - nt
h1h2h3=3K,2p h, Kph
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

4. HADRONIC DECAYS OF THE t LEPTONnt t-
W -
Tm=<Hadrons|(V-A)m eiSQCD|0>=
=Si(Lorentz Structure)i Fi(Q2,sj) h1 .
QCD
Hadrons hn
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

5. HADRONIC DECAYS OF THE t LEPTONnt t-
W -
Tm=<Hadrons|(V-A)m eiSQCD|0>=
=Si(Lorentz Structure)i Fi(Q2,sj) h1 .
QCD
Hadrons ? hn
LQCD= LQCD (qi,Gma;gs,mi)
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

6. HADRONIC DECAYS OF THE t LEPTONnt t-
W -
Tm=<Hadrons|(V-A)m eiSQCD|0>=
=Si(Lorentz Structure)i Fi(Q2,sj) h1 .
QCD
Hadrons hn
PhT: RcT
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

7. HADRONIC DECAYS OF THE t LEPTONnt t-
W - h1 h2
QCD h3
Hadrons
(Kühn, Santamaría ’90)(KS)
(Gómez-Cadenas, González-García, Pich ’90) (GGP)
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

8. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
KÜHN-SANTAMARÍA MODEL
(Kühn-Santamaría ‘90)
PT O(p2)
PT O(p4)
(Sakurai ’69, Kühn & Wagner ’84, Pich ’87)
Vector Meson Dominance KS
Asymptotic behaviour ruled by QCD
(Brodsky-Farrar ’73, B-Lepage ‘80) ?
(Gounaris-Sakurai ‘68)
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

9. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
KÜHN-SANTAMARÍA-like MODELS & TAUOLA
(Decker, Mirkes, Sauer, Was ‘92)
(Decker, Mirkes ‘92)
(Decker, Finkemeier, Mirkes ’93)
(Decker, Finkemeier ’93, ‘94)
(Decker, Finkemeier, Heiliger, Jonsson ‘94)
(Finkemeier, Mirkes ’95,’96)
(Finkemeier, Kühn, Mirkes ‘96)
(Mirkes, Urech ‘97)
(Kühn, Mirkes, Willibald ‘97)
(Jadach, Was ’90, ‘93)
(Jadach, Kühn, Was ‘90)
(Jezabeck, Was, Jadach, Kühn ‘90)
(Jadach, Was, Decker, Kühn ‘90)
(Bondar, Eidelman, Milstein, Pierzchala, Root, Was, Worek ‘02)
(Golonka, Kersevan, Pierzchala, Richter-Was, Was, Worek ‘06)
(Kühn, Was ‘06)
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

10. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
K-S-like works & HADRONIZATION IN TAUOLA
(Finkemeier, Mirkes ’95,’96)
(Finkemeier, Kühn, Mirkes ‘96)  A V
a m    V V
v m  
c,1R & 2R obtained from:
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

11. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
K-S-like works & HADRONIZATION IN TAUOLA
(Finkemeier, Mirkes ’95,’96)
(Finkemeier, Kühn, Mirkes ‘96) 
Some allowed contributions are lacking: A V
a m
  
V-exchanged
missing in
K+K-p- r0  
V2m
K*0
V1m
K-K0p0
K*0
V1m r-
V1m
K-p-p+
K*0
V1m r-
V1m
K0p0p-
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

12. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
K-S-like works & HADRONIZATION IN TAUOLA
(Finkemeier, Mirkes ’95,’96)
(Finkemeier, Kühn, Mirkes ‘96)  V V
v m  
Our aim is to tackle an ambitious program for describing within a theoretical framework as close as possible to QCD the considered decays.
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

13. TOOLS: EFFECTIVE FIELD THEORIES
QCD
EFT
PhT
Low energy expansion
Intermediate region
cPT
1/Nc
(Gasser & Leutwyler ’84, ’85)
(‘t Hooft ’74, Witten ‘79)
 # 0-width resonances
Tree level diagrams
Matching the OPE
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

14. TOOLS: EFFECTIVE FIELD THEORIES
QCD
EFT
PhT
Low energy expansion
Intermediate region
cPT
1/Nc
RcT
(Gasser & Leutwyler ’84, ’85)
(‘t Hooft ’74, Witten ‘79)
(Peris, Perrottet, de Rafael ‘98)
 # 0-width resonances
Only one 9 (SRA)
Tree level diagrams
Off-shell width
(Gómez-Dumm, Pich, Portolés ‘00)
Matching the OPE
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

15. cPT: The low-energy EFT of QCD
(Gasser & Leutwyler ’84, ’85)
PGB
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

16. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
Resonances+ PGB
TOOLS : RcT
(Ecker, Gasser, Pich, De Rafael ‘89)
(Ecker, Gasser, Leutwyler, Pich, De Rafael ‘89)
Antisymmetric tensor formalism
(Gómez Dumm, Pich, Portolés ’04)
VMD
(Ruiz-Femenía, Pich, Portolés ’03)
(Gómez Dumm, Pich, Portolés, R. in progress)
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

17. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
Resonances+ PGB
TOOLS : RcT
(Ecker, Gasser, Pich, De Rafael ‘89)
(Ecker, Gasser, Leutwyler, Pich, De Rafael ‘89) ,… V V V j
v m
a m j A A j
a m A V j V
v m j V V j V j j j
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

18. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
RcT APPLIED     F
a m
a m      V V
GV, FV
a m 
a m      i A V
a m    gi  ci  di  V V V V 
v m
v m 
v m
v m      
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

19. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
RcT APPLIED     F
a m
a m      V V
GV, FV
a m 
a m      i A V
24 couplings
a m    gi  ci  di  V V V V 
v m
v m 
v m
v m      
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

20. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
t-  (2K p)- nt
First work on this already in ’90 (González-García, Gómez-Cadenas, Pich)
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

21. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
t-  (2K p)- nt
First work on this already in ’90 (González-García, Gómez-Cadenas, Pich)
The phenomenological approach of KS-like works (Finkemeier and Mirkes ’95, ‘96) do not include all possible contributions for the exchanged resonances and depend noticeably on the excited resonances parameters.
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

22. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
t-  (2K p)- nt
First work on this already in ’90 (González-García, Gómez-Cadenas, Pich)
The phenomenological approach of KS-like works (Finkemeier and Mirkes ’95, ‘96) do not include all possible contributions for the exchanged resonances and depend noticeably on the excited resonances parameters.
CLEO (Liu ’03, CLEO ‘04) could not fit their data using FM expressions and reshaped the model violating the normalization of the WZ term (i.e. low-energy QCD).
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

23. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
t-  (2K p)- nt
First work on this already in ’90 (González-García, Gómez-Cadenas, Pich)
The phenomenological approach of KS-like works (Finkemeier and Mirkes ’95, ‘96) do not include all possible contributions for the exchanged resonances and depend noticeably on the excited resonances parameters.
CLEO (Liu ’03, CLEO ‘04) could not fit their data using FM expressions and reshaped the model violating the normalization of the WZ term (i.e. low-energy QCD).
BaBar presented their data on these modes in TAU’06. However the plot of the spectral function vs. invariant mass of the hadronic system was not at the Proc. (Nugent ‘06) and they have not submitted the paper yet.
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

24. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
t-  (2K p)- nt
First work on this already in ’90 (González-García, Gómez-Cadenas, Pich)
The phenomenological approach of KS-like works (Finkemeier and Mirkes ’95, ‘96) do not include all possible contributions for the exchanged resonances and depend noticeably on the excited resonances parameters.
CLEO (Liu ’03, CLEO ‘04) could not fit their data using FM expressions and reshaped the model violating the normalization of the WZ term (i.e. low-energy QCD).
BaBar presented their data on these modes in TAU’06. However the plot of the spectral function vs. invariant mass of the hadronic system was not at the Proc. (Nugent ‘06) and they have not submitted the paper yet.
BaBar has recently (BaBar ‘07) published very precise data on e+e-  KK p/h using ISR events. Furthermore, their Dalitz-plot fit has allowed to separate cleanly the I=0,1 contributions. Assuming CVC and comparing to ALEPH ’99 allows to derive (GV/GT) = in t-  (KK p)- nt . Under CVC one can relate e+e- data to the t decay.
(Davier, Descotes-Genon, Höcker, Malaescu, Zhang ‘08)
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

25. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
t-  (2K p)- nt
(Gómez Dumm, Pich, Portolés, R. in progress)
Our work:
Computation of the involved process within RcT(15 couplings).
Brodsky-Lepage behaviour demanded to the Form Factors (6 couplings).
Computation and fit to Br(w3p) completing (Pich, Portolés, Ruiz-Femenía ‘03). Use of some constraints from this work for <VVP> (3 couplings).
Axial-form factor fixed by t3p nt (2 couplings). (Gómez-Dumm, Pich, Portolés ‘04) (Cirigliano, Ecker, Eidemüller, Pich, Portolés ‘04).
Vector-form factor fixed thanks to BaBar data on e+e-  (KKp)- nt and ALEPH’99’s full t spectrum.
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

26. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
t-  (2K p)- nt
(Gómez Dumm, Pich, Portolés, R. in progress)
Our work:
Computation of the involved process within RcT(15 couplings).
Brodsky-Lepage behaviour demanded to the Form Factors (6 couplings).
Computation and fit to Br(w3p) completing (Pich, Portolés, Ruiz-Femenía ‘03). Use of some constraints from this work for <VVP> (3 couplings).
Axial-form factor fixed by t3p nt (2 couplings). (Gómez-Dumm, Pich, Portolés ‘04) (Cirigliano, Ecker, Eidemüller, Pich, Portolés ‘04).
Vector-form factor fixed thanks to BaBar data on e+e-  (KKp)- nt and ALEPH’99’s full t spectrum.
Thus, we can concentrate on improving the most challenging aspect in t decays into three mesons: The axial-vector form factors and, specifically, the off-shell width of the a1.
Easy to extend to the e+e- scattering below 2 GeV.
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

27. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
OUTLOOK: t-  (h1 h2 h3 )- nt
h1 h2 h3 FA FV 3p
2K p
K 2p
2p h
p K h 3K
Vus, ms
Vus, ms
Vus, ms
mnt
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati

28. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
CONCLUSIONS
Current analyses of t-  (3p-, K+K-p-) nt data using TAUOLA have shown theoretical inconsistencies. We would like to improve the hadronic matrix elements in TAUOLA and PHOKARA.
We have studied these decays within RcT with a Large NC-inspired model guided by QCD.
We have used BaBar data on e+e-  KKp to fix our free parametres on the Vector Current sector. We will improve our analysis once t-  K+K-p- nt data are published.
We aim to improve our off-shell a1 width in order to revisit t-  3p- nt.
Our results have been implemented in SHERPA (LHC and TEVATRON) and may be used by the B-factories.
LHC, BABAR, BELLE, BES…are promising facilities to test our predictions.
The future looks even more promising and exciting: Vus, ms, mnt and, of course, hadronization of QCD currents.
IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC)
PHI PSI 08 Frascati