K form factors from a dispersive approach Emilie Passemar* - - PowerPoint PPT Presentation

Kπ

form factors from a dispersive approach

Emilie Passemar

Emilie Passemar* Indiana University/Jefferson Laboratory « Current and Future Status of the First-Row CKM Unitarity » Workshop UMass Amherst, Amherst, USA., May 17 2019

*Supported by NSF

Outline :

• 1. Introduction and Motivation
• 2. Dispersive representation of the Kπ form factors
• 3. Improvement: Combination of τ → Kπντ and Kl3 decays
• 4. Applications
• 5. Conclusion and outlook

2

• 1. Introduction and Motivation

Emilie Passemar

1.1 Precise test of the Standard Model

4

• Studying and Kl3 decays indirect searches of new physics,

several possible high-precision tests: Extraction of Vus

4

(0) Vus f

(0) f

Vus

? 2 2 2

1

ud us ub

V V V

• 0+0+

decays Kl3 decays Negligible (B decays)

Test of unitarity From Lattice QCD

• l

K l

• ,

l e

• K
• ,

l e

• W

us

V

/ 0 / 0

2 3

(0)V

l us K l K

N f I

• 3

2 / 0 / 0

8

1 , ( ), ( )

l K K

I dt F t f t f t m

• with

Emilie Passemar

• Studying and Kl3 decays indirect searches of new physics,

several possible high-precision tests: Extraction of Vus Knowledge of the two form factors:

5

• K

( ) s u K(p ) = ( ) ( )

K K K K K

p p p p p f t p p f t t t

• 2

2 2

( ) ( ) ,

K

t q p p p p

• 0,

0,

( ) ( ) (0) f t f t f

• vector

scalar

• l

K l

• ,

l e

• K
• ,

l e

• W

us

V

/ 0 / 0

2 3

(0)V

l us K l K

N f I

• 3

2 / 0 / 0

8

1 , ( ), ( )

l K K

I dt F t f t f t m

• with

1.1 Precise test of the Standard Model

Emilie Passemar 5

6 Emilie Passemar

1.2 Callan-Treiman Low Energy Theorem

Very precisely known from Br(Kl2/l2), (Ke3) and

• –

–

V 1 ( ) V (0) V (0) V

us K ud K K CT CT ud us

F F C f F f F r f

• ud

V

2 2 K

m m

• Bernard, Oertel, E.P., Stern’06
• Callan-Treiman theorem:
• In the Standard Model :
• In presence of new physics, new couplings :
• Ex:

Bernard, Oertel, E.P., Stern’06, ‘08

Bexp = 1.2446(41)

1 r =

( )

ln 0.2141(73)

SM

C =

1 r ≠

3

( 3.5 8).10

CT −

Δ = − ±

NLO value + large error bars in agreement with

Bijnens&Ghorbani’07 Kastner & Neufeld’08

+"

s,d ν ℓ u H+ s

7 Emilie Passemar

1.2 Callan-Treiman Low Energy Theorem

CT point

?

2

( )

K

t m mπ ⎡ ⎤ ⎡ ⎤ = − ⎣ ⎦ ⎣ ⎦

Physical Region

2 2 K K

m m

π π π π

⎡ ⎤ ⎡ ⎤ Δ = − ⎣ ⎦ ⎣ ⎦

8 Emilie Passemar

• SUSY loops

Z’, Charged Higgs, Right-Handed Currents,…. [E.g. Bernard et al’06,’07, Deschamps et al’09, Cirigliano et al’10, Jung et al’10, Buras et al’10…]

u

s

,e

• ,e
• W

us

V

g g

Test of New Physics :

1.3 Test of New Physics

9 Emilie Passemar

1.4 Kπ form factors

• accessible in Ke3 and K3 decays
• nly accessible in K3 (suppressed by ml2/MK2) + correlations

difficult to measure

• Data from Belle and BaBar on K decays (Belle II, SuperB soon!)

Use them to constrain the form factors and especially

• K decays

Hadronic matrix element: Crossed channel

• ( )

f t

• 0( )

f t

f

us

V

K

• W

K

• W
• K

s u 0 = ( ) ( )

K K K K K

p p p p f s p p f s s s

• vector

scalar

2 2

( )

K

s q p p

• with

8

1.5 Parametrization of the Kπ form factors

• Taylor Expansion:

Ok for Kl3 but can not combine with tau data and large correlations

' " ,0 ,0 ,0 2 2

1 ( ) 1 ... 2 t t f t m m

p p p p

l l l l

+ + + + +

= + = + + +

Only slope accessible for the scalar FF

K

( ) s u K(p ) = ( )( ) ( )( )

K K

p f t p p f t p p

p µ p µ p µ

p g p g

+

• +

+ + +

• [Franzini, Kaon’08]

2 2

( ) ( ) ( )

s K

t f t f t f t m mp

+

• =

+ = +

• Normalisation: and

( ) ( ) (0) f t f t f

+ + +

= ( ) ( ) , (0)

s

f t f t f+ = = = =

Emilie Passemar 10

1.5 Parametrization of the Kπ form factors

• Taylor Expansion:

Ok for Kl3 but can not combine with tau data and large correlations

• Pole parametrization:

Ok for Kl3 but can not combine with tau data: will explode at the resonance mass! Ok for vector but not so obvious for scalar

' " ,0 ,0 ,0 2 2

1 ( ) 1 ... 2 t t f t m m

p p p p

l l l l

+ + + + +

= + = + + +

K

( ) s u K(p ) = ( )( ) ( )( )

K K

p f t p p f t p p

p µ p µ p µ

p g p g

+

• +

+ + +

• 2

2

( ) ( ) ( )

s K

t f t f t f t m mp

+

• =

+ = +

• Normalisation: and

( ) ( ) (0) f t f t f

+ + +

= ( ) ( ) , (0)

s

f t f t f f+ = = = =

Emilie Passemar

2 , ,0 2 ,

( )

V S V S

m f t m t

+

=

• with mV,S to be fitted from data

11

• 2. Dispersive representation of the Kπ form

factors

Emilie Passemar

2.1 Introduction

13

• Parametrization to analyse both Kl3 and

– Vector form factor: Dominance of K*(892) resonance

• K

m m

• 3 decays

l

K

2 ' '' 2 2

1 ( ) 1 ... 2 s s f s m m

• K

m m

• m

decays K

• ( )

( )

i i

f s BW s

• [GeV]

s

• f

s

• m

Emilie Passemar

2.1 Introduction

14 Emilie Passemar

• Parametrization to analyse both Kl3 and

– Scalar form factor: No obvious dominance of a resonance

3 decays l

K

2 ' '' 2 2

( ) 1 ... s s f s m m

• m
• K

m m

• K

m m

• [GeV]

s

decays K

• 0( )

? f s

• f

s

CT

• Parametrization to analyse both Kl3 and

τ Kπντ Use dispersion relations

• Omnès representation:
• unknown
• Subtract dispersion relation to weaken the high energy contribution of the
• phase. Improve the convergence but sum rules to be satisfied!

2.2 Dispersive representation for the form factors

f+,0(s) = exp s π ds' s' φ+,0(s') s'− s − iε

sth ∞

∫

⎡ ⎣ ⎢ ⎤ ⎦ ⎥

,0

: ( ) ( )

in K

s s s s

π

φ δ φ δ

+

< = < =

Kπ scattering phase

,0

: ( )

in

s s s φ+ ≥

,0 ,0

( ) ( )

as

s s φ φ φ φ π π

+ + + +

= = = = ±

( )

,0( )

1/ f s s

+

→ Brodsky & Lepage

( )

2 th K

s m mπ ≡ +

ϕ+,0(s) : phase of the form factor

Emilie Passemar 15

disc f 0,+(s) ⎡ ⎣ ⎤ ⎦ ∝ tℓ

I∗(s) f 0,+(s)

Unitarity:

For s<sin:K scattering phase extracted from the data

• Dispersion relation with n subtractions in :

Ø dispersion relation with 2 subtractions: 1 in s=0 and 1 in s=ΔKπ

2 parameters to fit to the data and

2.2 Dispersive representation

16

s

( ) ( )

,0 ,0 1

( ') ' ( ) exp ( ) ' '

th

n n n s

s s s ds f s P s s s i s s φ π ε π ε

∞ + + −

⎡ ⎤ ⎡ ⎤ − = + = + ⎢ ⎥ ⎢ ⎥ − − − − − ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦

∫

0( )

f s

f 0(s) = exp s Δ Kπ lnC + s − Δ Kπ

( )

π ds' s' φ0(s') s'− Δ Kπ

( ) s'− s − iε ( )

mK +mπ

( )

2

∞

∫

⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥

'

λ

ln ln ( )

K

C f

π

= Δ

Bernard, Oertel, E.P., Stern’06,’09

[Callan-Treiman] For s < sin: Kπ scattering phase extracted from the data

Buettiker, Descotes-Genon, & Moussallam’02

Emilie Passemar

1 parameter to fit to the data:

• Dispersion relation with n subtractions in :

Ø dispersion relation with 2 subtractions in s=0

1 parameter to fit to the data:

2.2 Dispersive representation

s

( ) ( )

,0 ,0 1

( ') ' ( ) exp ( ) ' '

th

n n n s

s s s ds f s P s s s i s s φ π ε π ε

∞ + + −

⎡ ⎤ ⎡ ⎤ − = + = + ⎢ ⎥ ⎢ ⎥ − − − − − ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦

∫

( ) f s

+

f +(s) = exp λ+

'

s mπ

2 + s2

π ds' s'2 φ+(s') s'− s − iε

( )

mK +mπ

( )

2

∞

∫

⎡ ⎣ ⎢ ⎤ ⎦ ⎥

Extracted from a model including 1 resonances K*(892) a la Gounaris-Sakourai

'

λ+

17

Bernard, Oertel, E.P., Stern’06,’09

Emilie Passemar

2.2 Dispersive Representation

18 Emilie Passemar

• Take the Kπ rescattering into account
• Allow to determine the slope and curvature of the form factors: only 2 param.
• Use the CT theorem for the scalar FF Write a twice substracted

dispersion relation for ln f(t) at t=0 and at the CT point for the scalar FF

• Does it improve the agreement with data?

CT point

?

2

( )

K

t m mπ ⎡ ⎤ ⎡ ⎤ = − ⎣ ⎦ ⎣ ⎦

Physical Region

2 2 K K

m m

π π π π

⎡ ⎤ ⎡ ⎤ Δ = − ⎣ ⎦ ⎣ ⎦ Bernard, Oertel, E.P., Stern’06, ‘09

2.3 Scalar form factor

• Scalar form factor:
• Phase used:

0( )

exp (ln ( ))

K

t f t C G t

p

é ù é ù =

• ê

ú ê ú D ë û ë û

with

( ) ( ) ( ) ( )( )

K

K K K t

t ds s G t s s s t

p

p p p p p

f p

¥

D D D D

• =
• D
• D
• ò

S

L

2 2

2.25 GeV 2.77 GeV

S

< L <

Maximal value for G(t) : does not exceed 20% of lnC ~ 0.20

(0) 0.0398 0.0040 G = ± = ±

2

( )

K

t m mp é ù é ù =

• ë

û ë û

Bernard, Oertel, E.P., Stern’06,’09

Emilie Passemar

2.3 Scalar form factor

• Scalar form factor:
• Form factor:

0( )

exp (ln ( ))

K

t f t C G t

p

é ù é ù =

• ê

ú ê ú D ë û ë û

with

( ) ( ) ( ) ( )( )

K

K K K t

t ds s G t s s s t

p

p p p p p

f p

¥

D D D D

• =
• D
• D
• ò

Bernard, Oertel, E.P., Stern’06,’09

Emilie Passemar

f+(t)

2.4 Vector form factor

• Vector form factor:
• Phase used:

with Maximal value for H(t) : H(t0) = (2.16 +/- 0.04 +/- 0.33) x 10-3 does not exceed 10% of Λ+ ~ 24 x10-3

Bernard, Oertel, E.P., Stern’06,’09

Emilie Passemar

2

( )

K

t m mp é ù é ù =

• ë

û ë û

1 2 3 4

t[GeV

2]

φ 1(t)

• ur model

aM=-7 10

• 3

aM=-7.5 10

• 3

π 2π 3π

2

( ) exp ( ( )) t f t H t mp

+ +

é ù é ù = L + ê ú ê ú ë û ë û

2 2

( ) ( ) ( )

K

t

m t ds s H t s s t

p

p

j p

¥

=

• ò

2.4 Vector form factor

• Vector form factor:
• Form factor:

Bernard, Oertel, E.P., Stern’06,’09

Emilie Passemar

f+(t)

• 0.5
• 0.25

0.25 0.5 t [GeV]

2

0.4 0.8 1.2 1.6 2 |f+(t)|

Λ+

pole

Λ+

ΝΑ48

with

2

( ) exp ( ( )) t f t H t mp

+ +

é ù é ù = L + ê ú ê ú ë û ë û

2 2

( ) ( ) ( )

K

t

m t ds s H t s s t

p

p

j p

¥

=

• ò

• 3. Combining Kl3 and τ → Kπντ to improve the

Kπ

form factors determination

Emilie Passemar

3.1 Kπ form factors from τ → Kπντ and Kl3 decays

24

• Fit to the τ → Kπντ decay data

– from Belle [Epifanov et al’08] (BaBar?) – Normalization disappears by taking the ratio fit independent of Vus

1

K events tot w K

d N N b d s

π π

Γ ∝ Γ

bin width with

2 2 events bins N

N N

τ

τ τ

χ σ ⎛ ⎞ ⎛ ⎞ − = ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠

∑

Number of events/bin dΓ Kπ d s = GF

2mτ 3

32π 3sCK

2 SEW f+(0)Vus 2 1 − s

mτ

2

⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

1 + 2s mτ

2

⎛ ⎝ ⎜ ⎞ ⎠ ⎟ qKπ

3 (s) f+(s) 2 + 3Δ Kπ 2

4s qKπ (s) f0(s)

2

⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 1

K K

d d s

π π

Γ Γ

Emilie Passemar

• Dispersion relation with n subtractions in :

Ø dispersion relation with 3 subtractions: 2 in s=0 and 1 in s=ΔKπ Callan-Treiman

Ø dispersion relation with 3 subtractions in s=0

3.2 Dispersive representation for the FFs

s

( ) ( )

,0 ,0 1

( ') ' ( ) exp ( ) ' '

th

n n n s

s s s ds f s P s s s i s s φ π ε π ε

∞ + + −

⎡ ⎤ ⎡ ⎤ − = + = + ⎢ ⎥ ⎢ ⎥ − − − − − ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦

∫

0( )

f s

( ) ( ) ( )( )

( )

2

2 2 '

( ') ' ' ' ' ln ln ( ) exp

K

K K K K K m m K

s s s f s s m s d C s s s i C s s

π

π π π π π π π π π π π

φ ε λ π

∞ +

⎡ ⎤ ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ Δ − Δ − Δ ⎛ ⎞ ⎛ ⎞ = + = + − Δ − + ⎢ ⎥ ⎢ ⎥ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ Δ Δ Δ Δ ⎢ ⎥ ⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎣ − Δ − Δ − ⎦ −

∫

Bernard, Boito, E.P.’11

Emilie Passemar

( ) f s

+

( )

( )

( )

2

2 3 2 2 ' '' '2 3

1 ( ) exp + ( ' ' ' 2 ' )

K

m m

s s s f s ds s s s i m m s

π

π π π π

π φ λ λ λ λ λ ε

+ + + + + + ∞ + +

− ⎡ ⎤ ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ ⎢ ⎥ ⎢ ⎥ = − + ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ ⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ ⎣ ⎦ −

∫

Extracted from a model including 2 resonances K*(892) and K*(1414) Boito, Escribano, Jamin’09,’10 Jamin, Pich, Portolés’08

25

Bernard’14

• Model for ϕ+(s):

Modeling of the phase

Emilie Passemar

K∗−(892)

π−

K0

=

π−

K0

K∗−(892)

π−

K0

K∗−(892)

˜ H(s)

+ · · · +

! f+(s) = mK*

2 −κ K* Re !

HKπ (0) + Re ! HKη(0)

( ) + βs

D mK*,Γ K*

( )

− βs D mK*',Γ K*'

( )

⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥

K∗(892)

K∗(1410)

D mn,Γ n

( ) = mn

2 − s −κ n

Re ! H

∑

− imnΓ n(s)

with

tanδ Kπ

P ,1/2 = Im !

f+(s) Re ! f+(s)

Boito, Escribano, Jamin’09,’10 Jamin, Pich, Portolés’08

26

Bernard’14

Fit to the τ Kπντ decay data + Kl3 constraints

Bernard, Boito, E.P.’11

Emilie Passemar

1

K events tot w K

d N N b d s

π π

Γ ∝ Γ

27

Bernard’14

3.3 Determination of the form factors

28

• Results of the fits:

Bernard, Boito, E.P.’11 Antonelli, Cirigliano Lusiani, E.P.’13 Very accurate determination of K*(892)!

Emilie Passemar

3.4 Kπ form factors from τ → Kπντ and Kl3 decays

• Precise extraction of Kπ scattering phase and good determination of K*

and PDG : and

• Callan-Treiman test or lattice QCD test (FK/Fπ and f+(0))
• Vus from τ → Kπντ:

:

• Prediction of the strange Brs and Vus
• Use of the form factors for CPV tests, etc.

Emilie Passemar

*

892.02 0.21 MeV

K

m = ± = ±

*

46.300 0.426 MeV

K

Γ = ±

*

891.66 0.26 MeV

K

m = ± = ±

*

50.8 0.9 MeV

K

Γ = ±

2

(0)V

K u K s

N I f

τ

τ τ π τ πν + →

Γ =

( )

, ( ), ( )

K

I ds F s f s f s

τ +

= ∫

with

29

3.5 Kπ phase shift

30

NB: BRs measured by B factories are systema4cally smaller than previous measurements

Kπ I=1/2 P-wave scattering phase

τ→ πν

K*π threshold threshold parameters

• Emilie Passemar

5

Tau data

τ Kπντ

Boito, Escribano & Jamin’10

See also lattice QCD Dudek et al. Wilson et al.’14

• 4. Applications

Emilie Passemar

• Decay rate master formula

4.1 Extraction of Vus from τ → Kπντ

f+ 0

( )Vus = 0.2141 ± 0.0014IK ± 0.0021exp

Vus = 0.2212 ± 0.0027

f+ 0

( ) = 0.9677 27 ( )

Emilie Passemar

BR τ → K 0π −ντ

( ) = 0.416 ± 0.008

( )%

Belle’14

Γ τ → Kπντ γ ⎡ ⎣ ⎤ ⎦

( ) = GF

2mτ 5

96π 3 CK

2 SEW τ

Vus

2 f+ K 0π − (0) 2

IK

τ

1+ δ EM

Kτ + δ

!

SU(2) Kπ

⎛ ⎝ ⎞ ⎠

2

ew

1.0201 S =

Marciano & Sirlin’88, Braaten & Li’90, Erler’04

( )

EM

0.15 0.2 %

K τ

δ = − ± IK 0

τ = 0.50432 ± 0.01721

Antonelli, Cirigliano, Lusiani, E.P.’13 FLAG’19 Nf = 2+1

32

• Decay rate master formula
• Result of fit to Kl3 + τ Kπντ and Kπ scattering data including

inelasticities in the dispersive FFs

4.1 Extraction of Vus from τ → Kπντ

f+ 0

( )Vus = 0.2141 ± 0.0014IK ± 0.0021exp

Vus = 0.2212 ± 0.0027

f+ 0

( ) = 0.9677 27 ( )

Emilie Passemar

Γ τ → Kπντ γ ⎡ ⎣ ⎤ ⎦

( ) = GF

2mτ 5

96π 3 CK

2 SEW τ

Vus

2 f+ K 0π − (0) 2

IK

τ

1+ δ EM

Kτ + δ

!

SU(2) Kπ

⎛ ⎝ ⎞ ⎠

2

Antonelli, Cirigliano, Lusiani, E.P.’13

f+ 0

( )Vus = 0.2163 ± 0.0014

Bernard’14 FLAG’19 Nf = 2+1

33

0.21 0.21 0.22 0.22 0.23 0.23 0.24 0.24 0.25 0.25

Vus

τ -> Kν absolute (+ fK) τ -> Kπντ decays (+ f+(0), FLAG) τ branching fraction ratio Kl2 /πl2 decays (+ fK/fπ) τ -> s inclusive Our result from Belle BR τ decays Kaon and hyperon decays Kl3 decays (+ f+(0)) Hyperon decays τ -> Kν / τ -> πν (+ fK/fπ)

From Unitarity Flavianet Kaon WG’10 update by M.Moulson CKM’18 BaBar & Belle HFAG update by A.Lusiani Tau’18

Emilie Passemar 34

NB: BRs measured by B factories are systematically smaller than previous measurements

• Modes measured in the strange channel for :

s τ →

HFAG’12

~70% of the decay modes crossed channels from Kaons!

4.2 Vus using info on Kaon decays and τ Kπντ

35

4.2 Vus using info on Kaon decays and τ Kπντ

• (0.713 ± 0.003)%

(0.471 ± 0.018)% (0.857 ± 0.030)% (2.967 ± 0.060)%

• Antonelli, Cirigliano, Lusiani, E.P. ‘13
• Longstanding inconsistencies

between τ and kaon decays in extraction of Vus seem to have been resolved !

• R. Hudspith, R. Lewis, K. Maltman,
• J. Zanotti’17
• Crucial input:

τ → Kπντ Br + spectrum

need new data

Vus = 0.2229 ± 0.0022exp ± 0.0004theo

36

4.2 Vus using info on Kaon decays and τ Kπντ

• (0.713 ± 0.003)%

(0.471 ± 0.018)% (0.857 ± 0.030)% (2.967 ± 0.060)%

• Antonelli, Cirigliano, Lusiani, E.P. ‘13
• Longstanding inconsistencies

between τ and kaon decays in extraction of Vus seem to have been resolved !

• R. Hudspith, R. Lewis, K. Maltman,
• J. Zanotti’17
• Crucial input:

τ → Kπντ Br + spectrum

need new data

Vus = 0.2229 ± 0.0022exp ± 0.0004theo

|

us

|V

0.22 0.225 , PDG 2016

l3

K 0.0010 ± 0.2237 , PDG 2016

l2

K 0.0007 ± 0.2254 CKM unitarity, PDG 2016 0.0009 ± 0.2258 s incl., Maltman 2017 → τ 0.0004 ± 0.0022 ± 0.2229 s incl., HFLAV 2016 → τ 0.0021 ± 0.2186 , HFLAV 2016 ν π → τ / ν K → τ 0.0018 ± 0.2236 average, HFLAV 2016 τ 0.0015 ± 0.2216

HFLAV

Spring 2017

37

4.3 Callan-Treiman theorem and test of new physics

Emilie Passemar

Very precisely known from Br(Kl2/l2), (Ke3) and

• –

–

V 1 ( ) V (0) V (0) V

us K ud K K CT CT ud us

F F C f F f F r f

• ud

V

2 2 K

m m

• Bernard, Oertel, E.P., Stern’06

66 Emilie Passemar

• Callan-Treiman theorem:
• In the Standard Model :
• In presence of new physics, new couplings :

Experiment Ke3+Kµ3 ln C NA48’07 (Kµ3 alone) 0.144(14) KLOE’08 0.204(25) KTeV’10 0.192(12) NA48 (preliminary) ?

Bernard, Oertel, E.P., Stern’06, ‘08

Bexp = 1.2446(41)

1 r =

( )

ln 0.2141(73)

SM

C =

1 r ≠

3

( 3.5 8).10

CT −

Δ = − ±

NLO value + large error bars in agreement with

Bijnens&Ghorbani’07 Kastner & Neufeld’08 /NA62’18

0.184(15)

• 5. Conclusion and outlook

Emilie Passemar

Conclusion and outlook

• Kπ form factors (shape and normalization) are an important input in the

determination of Vus

• In this talk we discussed the determination of the shape of the vector and scalar

form factors using a dispersive approach Main input: Kπ scattering phase-shifts. Unknown: Kπ phase in the inelastic region source of systematic uncertainty

• Possible improvement comes from combining τ → Kπντ and Kl3 decays

model of the phase at higher energies Will allow to reduce the large 2π band in the inelastic region

• It would be great to have more precise data from Tau sector
• Many possible applications:

– Vus extraction from Kl3 and τ → Kπντ data – Callan-Treiman test of the Standard Model and New Physics

• It would be great to have lattice information on the shape of these FFs

Emilie Passemar 40

• 6. Back-up