A PROPOSAL FOR IMPROVING THE H A D R O N IZATION OF Q C D CURRENTS IN TAU OLA

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

Pablo Roig [email protected]

Instituto de FÍsica Corpuscular

CSIC-UVEG València (Spain)

PHI PSI 08 Frascati

April 10th 2008

• Hadronic decays of the lepton • Kühn-Santamaría Model in TAUOLA• Tools : PT, Large Nc , RT

•

• Outlook :

SUMMARY:

(Gómez Dumm, Pich, Portolés, R. to appear)

(h1h2h3)

PHI PSI 08 FrascatiIMPROVING HADRONIZATION IN TAUOLA

Pablo Roig (IFIC)

• Hadronic decays of the lepton • Kühn-Santamaría Model in TAUOLA• Tools : PT, Large Nc , RT

•

• Outlook :

SUMMARY:

(Gómez Dumm, Pich, Portolés, R. to appear)

(h1h2h3) h1h2h3=3K,2


Pablo Roig (IFIC)

PHI PSI 08 Frascati

5( ) (1 ) ( )2F

CKMG V u u T

M

..

.Hadrons

W --

hn

QCD

h1T=<Hadrons|(V-A) eiSQCD|0>=

=i(Lorentz Structure)i Fi(Q2,sj)

HADRONIC DECAYS OF THE LEPTON

22 ( 1) *

2 | | 4

nFCKM

Gd V d L T TM

IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC)

PHI PSI 08 Frascati

5( ) (1 ) ( )2F

CKMG V u u T

M

..

.Hadrons

-

hn

QCD

h1

QCD= QCD (qi,Ga;gs,mi)

?

W -

T=<Hadrons|(V-A) eiSQCD|0>=


22 ( 1) *

2 | | 4

nFCKM

Gd V d L T TM



PHI PSI 08 Frascati

5( ) (1 ) ( )2F

CKMG V u u T

M

..

.Hadrons

-

hn

QCD

h1

PhTR

22 ( 1) *

2 | | 4

nFCKM

Gd V d L T TM

W -

T=<Hadrons|(V-A) eiSQCD|0>=




PHI PSI 08 Frascati

5( ) (1 ) ( )2F

CKMG V u u T

M

-

h3

QCD

h1

W -



h2

Hadrons

1 2 3

1 2 3 1 2 122 3

1 2 1 2 3

2 2

1 2

2 13

1

15

2 3

0

( ) ( ) ( )

( ) , ( )

| | , ,128(2 )

P

KM

V

F C

F F F F

p p p

Q Qp p p Q V g p p

Q

T V V Q i p p p

G Vd dsdt f I I IdQ M

h h h

(Kühn, Santamaría ’90)(KS)

(Gómez-Cadenas, González-García, Pich ’90) (GGP)


Pablo Roig (IFIC)

KÜHN-SANTAMARÍA MODEL

KS

PT O(p2)

Vector Meson Dominance

22

2 2 2 2( )

( )R

R

R R

MBW xM x i x x

?

PT O(p4)

Asymptotic behaviour ruled by QCD

(Kühn-Santamaría ‘90)

(Brodsky-Farrar ’73, B-Lepage ‘80)

(Gounaris-Sakurai ‘68)

(Sakurai ’69, Kühn & Wagner ’84, Pich ’87)


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)


Pablo Roig (IFIC)

K-S-like works & HADRONIZATION IN TAUOLA(Finkemeier, Mirkes ’95,’96)


A

V

a

V

V

v

1 2 3i p p p

1 2 122 3

( )Q Q

V g p pQ

2 21 2

2 2 2 2 2 2 2 21 1 2 2( ) ( )

R R

R R R R

M M

M x i x x M y i y y ,1R & 2R

obtained from:


Pablo Roig (IFIC)



A

V

a

Some allowed contributions are lacking:

V-exchanged missing in

K+K-- 0 V2

K*0 V1

K-K00 K*0 V1

- V1

K--+ V1K*0

K00- - V1


Pablo Roig (IFIC)



V

V

v

' 'V AM M

3 2V AMultiplets Multiplets

Our aim is to tackle an ambitious program for describing within a theoretical framework as close as possible to QCD the

considered decays.

' 'V A


Pablo Roig (IFIC)

QQCCDDLow energy expansion Intermediate region

PT c

2 2 2 2

2 2

, , , (4 ) R

p m p mF M Tree level diagrams

Matching the OPE

(Gasser & Leutwyler ’84, ’85)

(‘t Hooft ’74, Witten ‘79)

EFT PhT

TOOLS: EFFECTIVE FIELD THEORIES

# 0-width resonances


Pablo Roig (IFIC)

QQCCDD

PT c

2 2 2 2

2 2

, , , (4 ) R

p m p mF M Tree level diagrams

Matching the OPE

(Gasser & Leutwyler ’84, ’85)

EFT PhT

TOOLS: EFFECTIVE FIELD THEORIES

Only one 9 (SRA)Off-shell width

RT

(‘t Hooft ’74, Witten ‘79)

# 0-width resonances

Low energy expansion Intermediate region

(Peris, Perrottet, de Rafael ‘98)

(Gómez-Dumm, Pich, Portolés ‘00)


Pablo Roig (IFIC)

PT: The low-energy EFT of QCD (Gasser & Leutwyler ’84, ’85)

08

008

0 8

† †

† †

† †

2( )

0

1( )

44 2

2

2 6

( )2 6

26

( )( ) exp , u ( ) ( )2

2 ( ),

4...

L R

K

x K

K K

i xu x i u i u u i u

s ip u uF

B

L

r

u u

f uF u u F u

F u u

u u u uL

l

L

L4

2

( ),

7 9 ... ... ...

in the odd-intrinsic parity sectorWZW

L Li f u u

L

PGB

(3) (3) (3)L R VSU SU SU

†( , ) ( , )X h g X h g


Pablo Roig (IFIC)

(Ecker, Gasser, Pich, De Rafael ‘89)

(Ecker, Gasser, Leutwyler, Pich, De Rafael ‘89)

2

4

( ) ( )

5

1

,

1

( ) (

5

( )

1

7

)

;

2 2 2

2 2

( , , ) [ , ] ...

;

( , , )

I

I

P kinR T V A V A VAP

V

A

iVAP

i

PR T WZW VJP VVP VPP

V V

A

i

P

iVJP

i V V

i

L L L L L

if u uV V

A

V A V

F G

A

V

F f

O

L L L L

OM

c cM

j

L

L

L

L

L

L

5

5

1

1

4

1

, ...

( , , ) , ...

( , ) , ...

iVVP

i

iVPPP

i V V

i

i

f u

O u

V

V V V V

V V

d d

g gO u uM M

L

L

0*8

0*08

* *0 8

2 6

( )2 6

26

K

x K

K

V

K

Antisymmetric tensor formalism

(Ruiz-Femenía, Pich, Portolés ’03)

(Gómez Dumm, Pich, Portolés ’04)

(Gómez Dumm, Pich, Portolés, R. in progress)

Resonances+ PGB

VMDVMD

TOOLS : RT


Pablo Roig (IFIC)

V

TOOLS : RT

5

1

75

( ) ( ),

1

( ) (

2

))

1

4(

;

2 2 2

2 2

( , , ) [ , ] ...

;

( , , )

I

I

P kinR T V A V A VAP

V

A

iVAP

i

PR T WZW VJP VVP VP

V V

PP

iVJP

i V V

A

i

i

V V

L L L L L L

iL f u u

L f

L

A

VO

L L L L L

L

F G

F

c c

A V A

V jOM M

1

5

1

54

1

, ...

( , , ) , ...

( , ) , ...

iVVP

i

iVPPP

i

i

i

V V

f u

L O u

L O

V

V V V V

V V

d

ug uM

d

Mg

V

v V V

A V

V

a

A

(Ecker, Gasser, Pich, De Rafael ‘89)

(Ecker, Gasser, Leutwyler, Pich, De Rafael ‘89) ,…

Resonances+ PGB

V

a A

Vv

A

V

V V

V V

V

V

cigi di

i

GV, FV

F

v

v

v

v

a

a

a

a

a

RT APPLIED


Pablo Roig (IFIC)

A

V

V V

V V

V

V

cigi di

i

GV, FV

F

v

v

v

v

a

a

a

a

a

RT APPLIED


Pablo Roig (IFIC)

24 24 couplingscouplings


Pablo Roig (IFIC)

First work on this already in ’90 (González-García, Gómez-Cadenas, Pich)


Pablo Roig (IFIC)

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.



Pablo Roig (IFIC)

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).





Pablo Roig (IFIC)



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.





Pablo Roig (IFIC)



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 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 (V/T) = 0.167+0.024 in Under CVC one can relate e+e- data to the decay.(Davier, Descotes-Genon, Höcker, Malaescu, Zhang ‘08)




Pablo Roig (IFIC)

1. Computation of the involved process within RT(15 couplings).

2. Brodsky-Lepage behaviour demanded to the Form Factors (6 couplings).

3. Computation and fit to Br(3) completing (Pich, Portolés, Ruiz-Femenía ‘03). Use of some constraints from this work for <VVP> (3 couplings).

4. Axial-form factor fixed by 3(2 couplings). (Gómez-Dumm, Pich, Portolés ‘04) (Cirigliano, Ecker, Eidemüller, Pich, Portolés ‘04).

5. Vector-form factor fixed thanks to BaBar data on e+e- and ALEPH’99’s full spectrum.

Our work: (Gómez Dumm, Pich,

Portolés, R. in progress)


Pablo Roig (IFIC)

1. Computation of the involved process within RT(15 couplings).

2. Brodsky-Lepage behaviour demanded to the Form Factors (6 couplings).

3. Computation and fit to Br(3) completing (Pich, Portolés, Ruiz-Femenía ‘03). Use of some constraints from this work for <VVP> (3 couplings).

4. Axial-form factor fixed by 3(2 couplings). (Gómez-Dumm, Pich, Portolés ‘04) (Cirigliano, Ecker, Eidemüller, Pich, Portolés ‘04).

5. Vector-form factor fixed thanks to BaBar data on e+e- and ALEPH’99’s full spectrum.

Our work: (Gómez Dumm, Pich,

Portolés, R. in progress)

Thus, we can concentrate on improving the most challenging aspect in 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.


Pablo Roig (IFIC)

OUTLOOK: hhh

hhh

3

2K

K 2

2

K

3K

FA FV

Vus, ms

m

Vus, ms Vus, ms

CONCLUSIONS• Current analyses of 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 RT with a Large NC-inspired model guided by QCD.

• We have used BaBar data on e+e- to fix our free parametres on the Vector Current sector. We will improve our analysis once data are published.

• We aim to improve our off-shell a1 width in order to revisit .

• 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, mand, of course,

hadronization of QCD currents.


Pablo Roig (IFIC)

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A PROPOSAL FOR IMPROVING THE H A D R O N IZATION OF Q C D CURRENTS IN TAU OLA

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