Hadronic Decays of the TAU Lepton within RESONANCE CHIRAL THEORY ( R cT )

Hadronic Decays of the TAU Lepton within

RESONANCE CHIRAL THEORY (R)

Pablo Roig Garcés

[email protected]

Instituto de Física Corpuscular

CSIC-UVEG València (Spain)

XII Spring School “Bruno Touschek”

INFN LNF Frascati

FlaviAnet

• Hadronic decays of the lepton

• Tools : PT, RT, Large Nc (inspired)

• Recent past :

• Present:

• Immediate future : K

• Outlook :

SUMMARY:

(Gómez Dumm, Pich, Portolés ’04)

(Gómez Dumm, Pich, Portolés, R. ’07 to appear)

(h1h2h3)

in RTPablo Roig Garcés


XII Spring School “Bruno Touschek”FlaviAnet

• Hadronic decays of the lepton

• Tools : PT, RT, Large Nc (inspired)

• Recent past :

• Present:

• Immediate future : K

• Outlook :

SUMMARY:

(h1h2h3)



h1h2h3=3K,2




5( ) (1 ) ( )2F

CKM

GV 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| |

4nF

CKM

Gd V d L T T

M





5( ) (1 ) ( )2F

CKM

GV u u T

M

.

.

.Hadrons

-

hn

QCD



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

?2

2 ( 1) *2

| | 4

nFCKM

Gd V d L T T

M




W -

5( ) (1 ) ( )2F

CKM

GV u u T

M

.

.

.Hadrons

-

hn

QCD




EFT’sPT, R

22 ( 1) *

2| |

4nF

CKM

Gd V d L T T

M




W -

QCDLow energy expansion Intermediate region

PT c

2 2 2 2

2 2

, , , (4 ) R

p m p m

F M Tree level diagrams

Matching the OPE

(Gasser & Leutwyler ’84, ’85)

(‘t Hooft ’74, Witten ‘79)

EFT EFT

TOOLS: EFFECTIVE FIELD THEORIES

# 0-width resonances




QCD

PT c

2 2 2 2

2 2

, , , (4 ) R

p m p m

F M Tree level diagrams

Matching the OPE

(Gasser & Leutwyler ’84, ’85)

EFT EFT

TOOLS: EFFECTIVE FIELD THEORIES

Only one 8 (SRA)

Off-shell width

RT

(‘t Hooft ’74, Witten ‘79)

# 0-width resonances




Low energy expansion Intermediate region

TOOLS : PT (Gasser & Leutwyler ’84, ’85)




PT

2

2

2

2 2 2

,, ,

(4 ) ( )R

p m p m

F M

(Gasser, Leutwyler ’84, ’85)

08

008

0 8

† †

† †

† †

2( )

( )

0

1 4

2

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2 6

( )2 6

2

6

( )( ) exp , u ( ) ( )

2

2 ( ),

4

...

L R

K

x K

K K

i xu x i u i u u i u

i u u u u

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L u u

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B

F

L

r l

s

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p

L u

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( ),

7

4

9... ... ...

in the odd-intrinsic parity sectorWZW

i f u u

L

L L

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

†( , ) ( , )X h g X h g

TOOLS : RT (Ecker, Gasser, Pich, De Rafael ‘89)

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

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

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V V

d

ug

uM

d

M

g

0*8

0*08

* *0 8

2 6

( )2 6

2

6

K

x K

K

V

K

Antisymmetric tensor formalism

(Ruiz-Femenía, Pich, Portolés ’03)






VMDVMD

V

V

TOOLS : RT (Ecker, Gasser, Pich, De Rafael ‘89)

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




a

a

5

1

75

( ) ( ),

1

( ) (

2

))

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;

2 2 2

2 2

( , , ) [ , ] ...

;

( , , )

I

I


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

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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

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( , , ) , ...

( , ) , ...

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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

M

g

A

A V

TOOLS : RT (Gómez Dumm, Pich, Portolés ’04)

5

1

75

( ) ( ),

1

( ) (

2

))

1

4(

;

2 2 2

2 2

( , , ) [ , ] ...

;

( , , )

I

I


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

, ...

( , , ) , ...

( , ) , ...

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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

M

g




V

TOOLS : RT

v

(Ruiz-Femenía, Pich, Portolés ’03)

5

1

75

( ) ( ),

1

( ) (

2

))

1

4(

;

2 2 2

2 2

( , , ) [ , ] ...

;

( , , )

I

I


V

A

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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

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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

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( , , ) , ...

( , ) , ...

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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

M

g




V V

V

TOOLS : RT

5

1

75

( ) ( ),

1

( ) (

2

))

1

4(

;

2 2 2

2 2

( , , ) [ , ] ...

;

( , , )

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I


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A

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i

PR T WZW VJP VVP VP

V V

PP

iVJP

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L

A

VO

L L L L L

L

F G

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c c

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1

5

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54

1

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( , , ) , ...

( , ) , ...

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i

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i

i

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f u

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V

V V V V

V V

d

ug

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d

M

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5( ) (1 ) ( )2F

CKM

GV u u T

M

Hadrons

-

QCD

h1 h2 h3


1 2 3

1 2

0

1 2 3 1 2 1 2 3 12 2

1 2 1 2 3

1

1 1

2 2

5

2

2 3

3( ) ( ) ( )

( ) , ( ) , ( )

| |, ,

128(2 )F CKM

P V

p p p

Q Q Q Qp p p Q V g p p V g p p

Q Q

T V V QF i p p p

d G Vdsdt f I I I

h h h

F F

M

F

dQ

(Kühn, Santamaría ’90)(KS)

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




(Finkemeier, Mirkes ‘96)(FM)

W -

A

V

V V

V V

V

V

cigi di

i

GV, FV

F





v

v

v

v

a

a

a

a

a

RECENT PAST :




PRESENT:




Free

c1235, d123, c4, g4, g5

coming soon]

PRESENT:




Free

c1235, d123, c4, g4, g5

coming soon]

PRESENT:




Free

c1235, d123, c4, g4, g5

coming soon]

PRESENT:

XII Spring School “Bruno Touschek”FlaviAnet in RT

Pablo Roig GarcésInstituto de Física Corpuscular

coming soon]




PRESENT:

coming soon]

PRESENT:




Experiment # of pairs

LEP

CLEO

BABAR

BELLE

LHC

3·105

1·107

3·108

5·108

1·1012

coming soon]

PRESENT:

(I. Nugent TAU06)




PRESENT:

(I. Nugent TAU06)




Our Hadronic matrix elements

dataMC’s

IMMEDIATE FUTURE: K

• Computation of hadronic matrix element within RT

• Required Brodsky-Lepage behaviour to both the axial-vector and vector form factors: Constraints among the couplings

identical/compatible to those found for FA,FV in the 2K -modes

• Great sensitivity to the values of the K1 mass and on-shell width (axial-vector meson mixing)

• We plan to use this computation to help extract Vus and ms

• Agreement with BELLE to implement our expressions for the hadronic matrix element in their MC’s to analyze the data




IMMEDIATE FUTURE: K




(I. Nugent TAU06)

All contributions

Axial-VectorVector

IMMEDIATE FUTURE: K




(I. Nugent TAU06)

PreliminaryAll contributions

Axial-VectorVector

IMMEDIATE FUTURE: K




(I. Nugent TAU06)

Preliminary

1 11( )(1 )

1.27 0.3KK MK

M GeV GeV

All contributions

Axial-VectorVector

IMMEDIATE FUTURE: K




(I. Nugent TAU06)

Preliminary

Our Hadronic matrix elements

dataMC’s

All contributions

Axial-VectorVector

OUTLOOK: hhh

hhh

3

2K

K 2

2

K

3K




FA FVVus, ms m

( KK)

CONCLUSIONS• Current analyses of data using

TAUOLA have shown noticeable inconsistencies. We would like to improve the hadronic matrix elements in TAUOLA.

• We have studied these decays within RT with a Large NC-inspired model guided by QCD. (Preliminary study of 2 K-modes)

• Our results have been implemented in SHERPA (LHC and TEVATRON).

• LHC, BABAR, BELLE, BES…are promising facilities to test our predictions.

• The future looks even more promising and exciting: Vus, ms, m

and, of course, hadronization of QCD currents.




SKIPPED SLIDES







CLEO VERSION(F. Liu ‘03, CLEO-III ’04)

2 3

1

2 2iBV

i

F BWF

R

22 ,

, 2, ,

( , )( )

V AV A i

V A V A

MBW x s Q

M x i x x




(F. Liu ‘03, CLEO-III ’04)

(4),WZWL 2 0

1Q

2 3

1

2 2iBV

i

F BWF

R

CLEO VERSION




(F. Liu ‘03, CLEO-III ’04)

(4),WZWL 2 0

1Q

1.800.53QCD

2 3

1

2 2iBV

i

F BWF

R

CLEO VERSION







CLEO ‘04

NV/NA

1.5

This work 5

9

(Finkemeier, Mirkes ‘95)

0.4

PT at (p2) PT at (p4)

V AFA F4VFA

Yes

- -

ad-hoc

channels within RTK K




(Gómez-Cadenas, González-García,

Pich ’90)

SHERPA(Simulation of High Energy Reactions of PArticles)

•Institute for Theoretical Physics at TU Dresden (Germany)

•Group Leader : Frank Krauss

•Tevatron + LHC

•http://www.physik.tu-dresden.de/~krauss/hep

Insertion of our matrix elements for hadronic tau decays




RESULTS K+ K- -

2 ( )Q GeVXII Spring School “Bruno Touschek”FlaviAnet



Documents

Hadronic Decays of the TAU Lepton within RESONANCE CHIRAL THEORY ( R cT )