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Pion Scalar Form factor I

From dispersion theory:

From (7rIJI7r)(O), (KIJIK)(O) and the phases, w.e know the t dependence

J = uu + dd

. ~~+~~ ~~+~~

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o 0.3. / r~--- 0.3

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lIT K form factors Johan Bijnens 10 ,

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I

Pion Electromagnetic Form Factor I

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I

Kl3 Definitions and Vus

I

fo(t)

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f+(t) + 2 t 2f-(t)

mK - m7r

f+,o(t)

=

f+(O) (1 + A+,O~;) f+(O)

⁼⁼

1 + ^{. . .}

"

)

²

-m jK+7r° (O)

Leuwyler-Roos :0 - ⁼⁼ 1.022 In Progress

f+

^1r (O)

Corrections: use generalized formfactors Cirigliano et al" hep-phjOll0153

Scalar formfactor:

Usual

parametrization:

IVllsl: 8

Know theoretically

Short distance correction to G

F

from Marciano-Sirlin Ademollo-Gatto-Behrends-Sirlin theorem: (ms

- Isospin Breaking

Know experimentally 1+(0)

.

Radiative

Paramle1trllze

form-factor: is linear eoough tor f+(t) ?

I Vudl == 0.9734

:f: 0.0008

^{I Vusl} ⁼⁼ 0.2196 =Í= 0.0026

P DG2002:

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+

CV;Ld from neutron decay only * a bit worse)

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I

f+(t) Theory ~

f+(t) = 1 + f14)(t) + f16)(t)

(4) ( ) t

^r

f+ t = F2Lg + leeps

2 7r

116) (t) ==

8 Pion

electromagnetic Form factor:

JB, Talavera

L~

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0.00593 :l: 0.00043

- 4C~8

+ ^4C~o

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0.00022 :f: 0.00002

VMD: R~f

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^GeV2

fuI! result

1

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

N

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-0.2 -0.15 -0.1

-0.25

t [GeV2)

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I

ChPT fil 10 f+(t) I

::::}R+1 ==K 7r

-(4.7:1:0.5) 10-5 GeV2

(c+ ^{3.2 GeV-4)}

== 1.009 :1: 0.004 -

=}a+

=> A+

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1.2 1.18 1.16 1.14 1.12

1+(1) 1.1 1.08 1.06 1.04 1.02 1 0.98

0.08 0.1

0.02 0.04 0.06

t [GeV2]

o

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I

ChPT fit to f+(t) I

:::} RK 7r+1 == 1.2

-2.5 10-5

GeV2

1.15

3.2 GeV-4) c.IJR'lA íURt

^f+(t)

l ^fl ^X ^{E D} ^{'By CWPr}

^1.1

1.006 (c+

^-

::::} a + -

=*A+ == 0.0214 =Í= 0.0018

0.6 %

1.25

1.05

1

0.95

O 0.02 0.04 0.06 0.08 0.1 0.12

t [GeV2]

(22)

I fo(t) ~

8 F4 ( ^Cr2 t

'Ir

+8- _F4 ( 2Cr ₁₂

'Ir

- 8 t2

C

r F4 12 +

7r

fo(t)

Main Result: 1

Ó(O)

⁼⁼

-0.0080 :i: 0.OO57[loops] :f: O.OO28[L;] .

2

) 2

m7r

m;)

C~4) (m~

C~4) (m~ +

~(t) + ~(O)

+

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