Diapositiva 1

1
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.D69073002,2004 AIP
Conf.Proc.96440-46,2007 Work to appear soon
PHI PSI 08 Frascati April 10th 2008
Pablo Roig Pablo.Roig_at_ific.uv.es Instituto de
FÍsica Corpuscular CSIC-UVEG València (Spain)
2
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 TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
3
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
h1h2h33K,2p h, Kph
IMPROVING HADRONIZATION IN TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
4
HADRONIC DECAYS OF THE t LEPTON
nt
t-
W -
TmltHadrons(V-A)m eiSQCD0gt Si(Lorentz
Structure)i Fi(Q2,sj)
h1
. . .
Hadrons
QCD
hn
IMPROVING HADRONIZATION IN TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
5
HADRONIC DECAYS OF THE t LEPTON
nt
t-
W -
TmltHadrons(V-A)m eiSQCD0gt Si(Lorentz
Structure)i Fi(Q2,sj)
h1
. . .
Hadrons
QCD
hn
?
LQCD LQCD (qi,Gmags,mi)
IMPROVING HADRONIZATION IN TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
6
HADRONIC DECAYS OF THE t LEPTON
nt
t-
W -
TmltHadrons(V-A)m eiSQCD0gt Si(Lorentz
Structure)i Fi(Q2,sj)
h1
. . .
Hadrons
QCD
hn
PhT RcT
IMPROVING HADRONIZATION IN TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
7
HADRONIC DECAYS OF THE t LEPTON
nt
t-
W -
h1
h2
QCD
h3
Hadrons
(Kühn, Santamaría 90)(KS) (Gómez-Cadenas,
González-García, Pich 90) (GGP)
IMPROVING HADRONIZATION IN TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
8
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 TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
9
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 TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
10
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 TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
11
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
KK-p-
r0
?
?
V2m
K0
V1m
K-K0p0
K0
V1m
r-
V1m
K-p-p
V1m
K0
r-
V1m
K0p0p-
IMPROVING HADRONIZATION IN TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
12
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 TAUOLAPablo 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 TAUOLAPablo 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 TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
15
cPT The low-energy EFT of QCD
(Gasser Leutwyler 84, 85)
PGB
IMPROVING HADRONIZATION IN TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
16
Resonances PGB
(Ecker, Gasser, Pich, De Rafael 89) (Ecker,
Gasser, Leutwyler, Pich, De Rafael 89)
TOOLS RcT
Antisymmetric tensor formalism
(Gómez Dumm, Pich, Portolés 04)
VMD
(Ruiz-Femenía, Pich, Portolés 03)
(Gómez Dumm, Pich, Portolés, R. in progress)
IMPROVING HADRONIZATION IN TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
17
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 TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
18
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 TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
19
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 TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
20
t- ? (2K p)- nt
First work on this already in 90
(González-García, Gómez-Cadenas, Pich)
IMPROVING HADRONIZATION IN TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
21
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 TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
22
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 TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
23
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
TAU06. 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 TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
24
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
TAU06. 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 ee- ? KK p/h using ISR events.
Furthermore, their Dalitz-plot fit has allowed
to separate cleanly the I0,1 contributions.
Assuming CVC and comparing to ALEPH 99 allows
to derive (GV/GT) 0.1670.024 in t- ? (KK p)-
nt . Under CVC one can relate ee- data to the t
decay.
(Davier, Descotes-Genon, Höcker, Malaescu, Zhang
08)
IMPROVING HADRONIZATION IN TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
25
t- ? (2K p)- nt
(Gómez Dumm, Pich, Portolés, R. in progress)
Our work

1. Computation of the involved process within RcT(15
   couplings).
2. Brodsky-Lepage behaviour demanded to the Form
   Factors (6 couplings).
3. Computation and fit to Br(w?3p) completing (Pich,
   Portolés, Ruiz-Femenía 03). Use of some
   constraints from this work for ltVVPgt (3
   couplings).
4. Axial-form factor fixed by t?3p nt (2 couplings).
   (Gómez-Dumm, Pich, Portolés 04) (Cirigliano,
   Ecker, Eidemüller, Pich, Portolés 04).
5. Vector-form factor fixed thanks to BaBar data on
   ee- ? (KKp)- nt and ALEPH99s full t spectrum.

IMPROVING HADRONIZATION IN TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
26
t- ? (2K p)- nt
(Gómez Dumm, Pich, Portolés, R. in progress)
Our work

1. Computation of the involved process within RcT(15
   couplings).
2. Brodsky-Lepage behaviour demanded to the Form
   Factors (6 couplings).
3. Computation and fit to Br(w?3p) completing (Pich,
   Portolés, Ruiz-Femenía 03). Use of some
   constraints from this work for ltVVPgt (3
   couplings).
4. Axial-form factor fixed by t?3p nt (2 couplings).
   (Gómez-Dumm, Pich, Portolés 04) (Cirigliano,
   Ecker, Eidemüller, Pich, Portolés 04).
5. Vector-form factor fixed thanks to BaBar data on
   ee- ? (KKp)- nt and ALEPH99s 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 ee- scattering below 2 GeV.
IMPROVING HADRONIZATION IN TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
27
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
mnt
Vus, ms
IMPROVING HADRONIZATION IN TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati
28
CONCLUSIONS

• Current analyses of t- ? (3p-, KK-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 ee- ? KKp to fix our
  free parametres on the Vector Current sector. We
  will improve our analysis once t- ? KK-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, BESare 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 TAUOLAPablo Roig
(IFIC)
PHI PSI 08 Frascati