[PPT] - The Radiative Return at - and B -Meson Factories PowerPoint Presentation

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The Radiative Return at Φ- and B-Meson Factories

KARLSRUHE–KATOWICE–VALENCIA

J. H. K¨

uhn

I Basic Idea II Monte Carlo Generators: Status & Perspectives III Charge Asymmetry and Radiative Φ-Decays (⇒ H. Czy˙ z) IV Nucleon Form Factor at B-Factories V Conclusions

(with H. Czy˙ z, A. Grzelinska, E. Nowak, G. Rodrigo)

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I BASIC IDEA

J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 2

photon radiated off the initial e+e− (ISR) reduces the effective energy of the collision dσ(e+e− → hadrons + γ) = H(Q2, θγ) dσ(e+e− → hadrons) ◮ measurement of R(s) over the full range

f energies, from threshold up to √s

◮ large luminosities of factories compensate α/π from photon radiation ◮ radiative corrections essential (NLO) ◮ advantage over energy scan (BES, CMD2, SND): systematics (e.g. normalization) only

nce

High precision measurement of the hadronic cross-section at DAΦNE, CLEO-C, B-factories

SLIDE 3

DAΦNE versus B-factories:

J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 3

configurations in the cms - frame 10 GeV

− e + e

γ

very hard photon: clear kine- matic separation between pho- ton and hadrons 1 GeV

π π + −

γ

no natural kinematic separation ➪ cuts to control FSR versus ISR ( two step process: e+e− → γ ρ(→ γππ) ⇒ see below )

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Rough estimates for rates:

J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 4

π+ π− γ : Eγ > 100MeV √s [GeV ]

L [fb−1] #events, θmin = 7◦

1.02 1.35 16 ·106 10.6 100 3.5 ·106 multi-hadron-events (R ≡ 2) √s = 10.6 GeV Q2-interval [GeV ] #events, θmin = 7◦ [ 1.5 , 2.0 ] 9.9 ·105 [ 2.0 , 2.5 ] 7.9 ·105 [ 2.5 , 3.0 ] 6.6 ·105 [ 3.0 , 3.5 ] 5.8 ·105

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Lowest order

J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 5

dσ dQ2

e+e− → γ + had(Q2)
= σ
e+e− → had(Q2)
× α

πs

s2+Q4

s(s−Q2)

log(s/m2

e) − 1

, no angular cut

s2+Q4 s(s−Q2) log

1+cos θmin

1−cos θmin

− s−Q2

s

cos θmin

⇒ differential luminosity:

dL dQ2

Q2, s
= α

πs

· · ·
L(at s)

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Basic Ingredients for Pion Formfactor

J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 6

◮ ISR pion form factor ➪ to be tested ◮ FSR radiation from point- like pions (probably

verestimated)

◮ additional radiation: collinear (EVA MC)

(Binner, JK, Melnikov)

r NLO calculation (PHOKHARA MC)

SLIDE 7

II MONTE CARLO GENERATORS

J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 7

P H OTONS FROM KARLSRUHE H ADRONICALLY R ADIATED

References etc. → http://cern.ch/german.rodrigo/phokhara

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J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 8

http://cern.ch/german.rodrigo/phokhara

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J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 9

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PHOKHARA 2.0: π+π−, µ+µ−, 4π

ISR at NLO: virtual corrections

to one photon events and two photon emission at tree level

2 2

γ γ γ γ

+ +

FSR at LO: π+π−, µ+µ−
tagged or untagged photons
modular structure

SLIDE 12

J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 12

QED CORRECTIONS AT LEPTONIC SIDE = ⇒ BASIC BUILDING BLOCK FOR ALL HADRONIC FINAL STATES

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PHOKHARA 3.0

J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 13

◮ specifically developed for π+π− (plus photons) ◮ allows for simultaneous emission of photons from initial and final state, including virtual corrections (interference neglected).

⇒ dominated by “two step process”: e+e− → γ ρ (→ γ ππ)

⇒ importance of ππγ as input for aµ

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J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 14

Large effect for Q2 < m2

ρ eliminated by suitable cuts

n π+π− configuration (suppress 2γ events )

a

✁

✂☎✄ ✁

180

✁

✂✝✆ ✁

180

✞

s = 1.02 GeV

e

✟

e

✠ ✡ ☛ ✟ ☛ ✠ ☞

(

☞

) Q2(GeV2)

d

✌

(IFSNLO) dQ2

✍

d

✌

(IFSLO) dQ2

✎

1

✏

9

✏

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✏

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✏

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✏

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✏

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✏

1

✏

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✏

12

✏

1

✏

08

✏

06

✏

04

✏

02

✑ ✏

02

50

✒ ✓ ✔✖✕ ✗ ✓

130

✒

no Mtr cut Mtr cut

c p

✕ ✘ ✙

p

✕ ✚

:

✓

15

✒

e

✛

e

✜ ✢ ✣ ✛ ✣ ✜ ✤

(

✤

) Q2(GeV2)

d

✥

(IFSNLO) dQ2

✦

d

✥

(ISRNLO) dQ2

✧

1 1

★

9

★

8

★

7

★

6

★

5

★

4

★

3

★

05

★

04

★

03

★

02

★

01

✩ ★

01

✩ ★

02

✩ ★

03

✩ ★

04

r measure photon

SLIDE 15

Experimental Perspectives

J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 15

KLOE

= ⇒ TALK BY STEFAN M¨ ULLER ◮ ππ pion form factor

BABAR, BELLE

higher Q2 available ⇒ measurement of R(Q2) from threshold up to at least 5 GeV. Examples: ◮ 3π ◮ 4π± ◮ K K ππ ◮ K K K K ◮ J/Ψ

SLIDE 16

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J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 16

M3π (GeV/c2) events/(2.5 MeV/c2)

500 1000 1500 0.8 0.9 1.0

M3π (GeV/c2) events/(25 MeV/c2)

100 200 300 1.2 1.4 1.6 1.8

The background-subtracted 3π mass spectrum for masses between 0.70 and 1.05 MeV/c2 (plot on the left) and for masses from 1.05 to 1.80 MeV/c2 (plot on the right). BaBar

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J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 17

M3π (GeV/c2) Cross section (nb)

2 4 6 8 1.5 2 2.5 3

The e+e− → π+π−π0 cross section measured by BaBar (filled circles), by SND (open circles), and DM2 (open triangles). BaBar

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J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 18

BaBar

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CMD2 04 SND 03 CMD2 95 SND 02 ND CMD2 98 DM1

✁
✂

✄ ☎ ✁ ☎ ✂ ☎ ✆ ✝ ✞ ✟ ✠☛✡ ☞ ✌ ✍ ✎ ✏ ✑ ✒ ✓ ✔ ✕ ✖✗✘ ✗ ✖✗ ✗ ✗ ✙ ✘ ✗ ✙ ✗ ✗ ✚ ✘ ✗ ✚ ✗ ✗ ✛ ✘ ✗ ✛ ✗ ✗ ✜ ✘ ✗ ✖ ✚ ✗ ✗ ✖ ✜ ✗ ✗ ✖ ✢ ✗ ✗ ✖✣ ✗ ✗ ✖ ✗ ✗ ✗ ✚ ✗ ✗ ✜ ✗ ✗ ✢ ✗ ✗ ✣ ✗ ✗ ✗

BABAR SND 02 ND DM1

✤ ✥ ✤ ✦ ✧ ★ ✥ ★ ✦ ★ ✩ ✪ ✫ ✬ ✭ ✮ ✯ ✰ ✱ ✲ ✳ ✴ ✵ ✶ ✷ ✸ ✹✺ ✺ ✺ ✻✼ ✺ ✺ ✻✽ ✺ ✺ ✻ ✾ ✺ ✺ ✻ ✻ ✺ ✺ ✻✺ ✺ ✺ ✿ ✼ ✺ ✺ ✿ ✽ ✺ ✺ ✿ ✾ ✺ ✺ ✿ ✻✺ ✺ ✿ ✽ ✿ ✾ ✿ ✻ ✿ ✺ ✼ ✽ ✾ ✻ ✺ ❀ ✻

BaBar

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J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 20

✂✁☎✄ ✆ ✝ ✞✠✟ ✡☞☛ ✞✠✟ ✌ ✍

GeV

✎ ✏ ✆ ✞✑ ✟ ✒✓

GeV

✔ ✕ ✔ ✖ ✗ ✘ ✕ ✘ ✖ ✘ ✙✛✚ ✝ ✚ ✍

✄

✜ ✄ ✢ ✝ ✣ ✔ ✤ ✍ ✥ ✦ ✥ ✧ ★ ✩ ★ ✪ ✫ ✬ ✭ ✮ ✯ ✰ ✱ ✲ ✳✵✴ ✶ ✳ ✴ ✷ ✳✵✴ ✸ ✳ ✹ ✴ ✺ ✹ ✴ ✶ ✹ ✴ ✷ ✹ ✴ ✹ ✹ ✶ ✹ ✴ ✹ ✹✻ ✹ ✴ ✹ ✹ ✷ ✹ ✴ ✹ ✹✼ ✹ ✴ ✹ ✹ ✸ ✹ ✴ ✹ ✹ ✳ ✹

M(π+π-) (GeV/c2) events/(25 MeV/c2)

100 200 0.5 1 1.5

BaBar

SLIDE 21

PHOKHARA 4.0

J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 21

µ+µ−γ with FSR at NLO
vacuum polarisation can be switched on
nucleon pair production included

SLIDE 22

III Charge Asymmetries and Radiative Φ-Decays

J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 22

(H. Czy˙ z, A. Grzelinska, JK, hep-ph/0412239)

= ⇒ talk by Henryk Czy˙ z

SLIDE 23

IV NUCLEON FORM FACTORS

J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 23

(with Czy˙ z, Nowak, Rodrigo, hep-ph/0403062)

Q2 4m2

N accessible at B-factories

⇒ study e+e− → γ N ¯ N (with N = p or n) hadronic current: Jµ = −ie · ¯ u(q2)

F N

1 (Q2) γµ − F N 2 (Q2)

4mN [γµ, / Q]

v(q1) ,

Q = q1 + q2 , q = (q1 − q2)/2

r

GM = F1 + F2 , GE = F1 + Q2 4m2 F2

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J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 24

Separation of |GM|2 and |GE|2 through angular distribution: LµνHµν = (4πα)3 Q2 (1 + cos2 θγ) (1 − cos2 θγ) × 4

|GN

M|2 (1 + cos2 ˆ

θ) + 1 τ |GN

E |2 sin2 ˆ

θ

ˆ

θ = angle of nucleon with respect to γ-direction in hadronic rest frame

valid for s/Q2 ≪ 1, corrections and “optimal frame” → hep-ph/0403062
Similarity to e+e− → N ¯

N : dσ dΩ = α2βN 4Q2

|GN

M|2 (1 + cos2 θ) + 1

τ |GN

E |2 sin2 θ

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J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 25

✁

✂ ✄☎✝✆ ✞✟ ✠☛✡ ☞ ☎ ✌ ✍ ✎✑✏✓✒ ✔ ✏ ✍ ✄✕ ☎ ✌ ✞ ✌ ✍ ✎✗✖ ✍ ✄ ✘ ✞ ✌ ✙ ✖ ✚ ✛ ✠☛✡ ☞ ✟ ✞ ✌ ✍ ✎✗✖ ✍ ✄ ✞ ✞ ✌

At least one photon satisfies:

✜ ☎ ✌ ✍ ✎✗✏✓✒ ✔ ✏ ✍ ✄ ✞ ☎ ✌ ✡ ✢ ✡ ✣ ✤ ✥ ✦ ✥ ✧ ★ ✩

(GeV

✩

)

✪ ✫ ✪ ✬ ✭ ✮ ✯ ✰ ✱ ✲ ✳ ✴ ✵ ✶ ✄☎ ✷ ✕ ✘ ✸ ✞ ✛ ✄☎ ✣ ✹ ✄☎ ✣ ✺ ✄☎ ✣ ✻ ✄☎ ✣ ✼ ✄☎ ✣ ✽ ✄☎ ✣ ✾

e+e− → p¯ p γ implementation in PHOKHARA (large rates ∼ 400 evt/10MeV around 4GeV2)

SLIDE 26

Angular distributions of nucleon

J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 26

✂✁ ✄ ☎✝✆ ✂✞ ✟ ✠ ✄ ✡☛✌☞ ✍✎ ✑✏ ✒

4.5

✏

✒ ✓ ✔ ✕ ✓ ✔

5

✏

✒ ✓ ✖ ☛ ✗ ✔ ✘ ✆✚✙ ✛ ✆ ✔ ✡ ✍ ☛ ✗ ✎ ✍ ✗ ✔ ✘✢✜ ✔ ✡ ✍ ✍ ✗ ✏ ✣ ✏ ✤ ✥ ✦ ✧ ✦ ★ ✩✪✫ ✬ ✘ ✭ ✮ ✯ ✭ ✰ ✱ ✲ ✳ ✴ ✵ ✶

(nb)

✡ ☛ ☞ ✍ ☛ ✷ ☛ ☞ ✍ ✷ ✡ ✸✺✹ ✡ ☛ ✤ ✻ ✼ ☞ ✍ ✹ ✡ ☛ ✤ ✻ ✼ ✹ ✡ ☛ ✤ ✻ ✽ ☞ ✍ ✹ ✡ ☛ ✤ ✻ ✽✺✹ ✡ ☛ ✤ ✻ ✍ ☞ ✍ ✹ ✡ ☛ ✤ ✻ ✍✺✹ ✡ ☛ ✤ ✻ ✾ ☞ ✍ ✹ ✡ ☛ ✤ ✻ ✾ ✹ ✡ ☛ ✤ ✻ ✖ ☞ ✍ ✹ ✡ ☛ ✤ ✻

hadronic rest frame (two choices for GM/GE)

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J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 27

similar results for neutron pair production
NLO corrections from ISR included (corrections ∼ 1–2%)
no FSR

thousands of events around 4–5 GeV2 several events up to 7–8 GeV2

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V Conclusions

J.H. K¨ uhn The Radiative Return at Φ- and B-Meson Factories 28

continuous development of PHOKHARA

⇒ radiative corrections (completed for ISR) ⇒ more channels ⇒ cooperation between theory and experiment crucial

charge asymmetry as analysis tool
nucleon form factors:

GE and GM can be measured for a wide range of Q2 central issue: hadronic form factors !