Interactions of light mesons with photons Stefan Leupold Uppsala - - PowerPoint PPT Presentation

Stefan Leupold Interactions of light mesons with photons

Interactions of light mesons with photons

Stefan Leupold

Uppsala University

Meson 2014, Cracow, May/June 2014

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Stefan Leupold Interactions of light mesons with photons

Collaborators

Uppsala: Per Engstr¨

• m, Bruno Strandberg (now Glasgow),

Hazhar Ghaderi, Carla Terschl¨ usen GSI: Igor Danilkin (now JLAB), Matthias Lutz Bonn: Franz Niecknig, Martin Hoferichter (now Bern), Sebastian Schneider, Bastian Kubis

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Stefan Leupold Interactions of light mesons with photons

Table of Contents

1

Transition form factors and two-gamma physics

2

Lagrangian approach

3

Dispersive approach to pion transition form factor

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Stefan Leupold Interactions of light mesons with photons

Reactions of hadrons with (virtual) photons

Why is it interesting? explore intrinsic structure of hadrons

form factors to which extent does vector meson dominance hold?

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Stefan Leupold Interactions of light mesons with photons

Reactions of hadrons with (virtual) photons

Why is it interesting? explore intrinsic structure of hadrons

form factors to which extent does vector meson dominance hold?

background for physics beyond standard model rare pion decay π0 → e+e−

π0 e− e+

g − 2 of muon

µ(p) γ(k) kρ had + 5 permutations of the qi µ(p′) q1µ q2ν q3λ

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Stefan Leupold Interactions of light mesons with photons

Hadronic contribution to g − 2 of the muon

light-by-light scattering

µ(p) γ(k) kρ had + 5 permutations of the qi µ(p′) q1µ q2ν q3λ

γ∗γ∗ ↔ hadron(s) is not directly accessible by experiment ֒ → need good theory with reasonable estimate of uncertainty

(ideally an effective field theory)

֒ → need experiments to constrain such hadronic theories true for all hadronic contributions: the lighter the hadronic system, the more important

(though high-energy contributions not unimportant for light-by-light)

֒ → γ(∗)γ(∗) ↔ π0 (you’ve seen this before for rare pion decay), γ(∗)γ(∗) ↔ 2π, . . .

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Stefan Leupold Interactions of light mesons with photons

Shopping list for hadron theory and experiment

transition form factors of pseudoscalars γ(∗)γ(∗) ↔ P with P = π0, η, η′, . . . ֒ → several interesting kinematical regions next slide (for pion)

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Stefan Leupold Interactions of light mesons with photons

π0 → γ∗(q2

v)γ∗(q2 s ) transition form factor qv

2

qs

2

e− e+ e+ e− π0

π0 → e+e−e+e−

e− e+ π0

π0 → γγ

(figures from Bastian Kubis)

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Stefan Leupold Interactions of light mesons with photons

Shopping list for hadron theory and experiment

transition form factors of pseudoscalars γ(∗)γ(∗) ↔ P with P = π0, η, η′, . . . if invariant mass of dilepton around mass of a vector meson: relation to transition form factors of vector to pseudoscalar mesons V ↔ Pγ(∗) with V = ρ0, ω, φ, . . .

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Stefan Leupold Interactions of light mesons with photons

Shopping list for hadron theory and experiment

transition form factors of pseudoscalars γ(∗)γ(∗) ↔ P with P = π0, η, η′, . . . if invariant mass of dilepton around mass of a vector meson: relation to transition form factors of vector to pseudoscalar mesons V ↔ Pγ(∗) with V = ρ0, ω, φ, . . . “two-gamma physics” γγ → π+π−, π0π0, π0η, K ¯ K, . . .

(cross relation to polarizability of the pion)

֒ → has triggered a lot of experimental activity, in particular MesonNet (WASA, KLOE, MAMI, HADES, . . . )

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Stefan Leupold Interactions of light mesons with photons

Two complementary approaches

Lagrangian approach

use only hadrons which are definitely needed (here: lowest nonets of pseudoscalar and vector mesons) sort interaction terms concerning importance, essentially based on large-Nc include causal rescattering/unitarization for reactions

(I. Danilkin, L. Gil, M. Lutz, Phys.Lett. B703, 504 (2011))

long-term goal: obtain sensible estimates of uncertainties

dispersive approach

include most important hadronic inelasticities use measured (and dispersively improved) phase shifts (2-body) use Breit-Wigner plus background for narrow resonances (n-body, n > 2) error estimates from more vs. less subtracted dispersion relations

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Stefan Leupold Interactions of light mesons with photons

Table of Contents

1

Transition form factors and two-gamma physics

2

Lagrangian approach

3

Dispersive approach to pion transition form factor

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Stefan Leupold Interactions of light mesons with photons

Transition form factor ω → π0+ dilepton

1 10 100 0.2 0.4 0.6 |Fωπ0|2 ml+l− [GeV] (P1) (P2)

• stand. VMD

NA60

data and our Lagrangian approach show strong deviations from vector-meson dominance (VMD)

• ur approach describes data fairly

well except for large invariant masses close to phase-space limit (log plot!) second experimental confirmation desirable

• C. Terschl¨

usen, S.L., Phys. Lett. B691, 191 (2010)

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Stefan Leupold Interactions of light mesons with photons

Transition form factor φ → η+ dilepton

• 5

5 10 0.0 0.2 0.4 q [GeV] |Fφη|2 θ = − 2° θ = + 2° VMD VEPP-2M

• ur Lagrangian approach deviates

from VMD new data from KLOE will come soon

• C. Terschl¨

usen, S.L., M.F.M. Lutz, Eur.Phys.J. A48, 190 (2012)

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Stefan Leupold Interactions of light mesons with photons

γγ → π+π−, π0π0

Mark II Belle CELLO Belle syst. error

γγ → π+π-

σ [nb]

100 200 300 s1/2 [GeV] 0.3 0.7 1.1

Crystal Ball Belle Belle syst. error

γγ → π0π0

σ [nb]

20 40 60 s1/2 [GeV] 0.3 0.7 1.1

dashed black lines: tree level, blue lines: with coupled-channel rescattering of two pseudoscalar mesons

• verall good description, room for improvement concerning f0(980)

at high energies spin-2 mesons are missing

I.V. Danilkin, M.F.M. Lutz, S.L., C. Terschl¨ usen, Eur.Phys.J. C73, 2358 (2013)

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Stefan Leupold Interactions of light mesons with photons

γγ → π0η

Crystal Ball Belle Belle syst. error

γγ → π0η

σ [nb]

20 40 60 s1/2 [GeV] 0.7 0.95 1.2

Crystal Ball Belle Belle syst. error

γγ → π0η

σ [nb]

20 40 60 s1/2 [GeV] 0.7 0.95 1.2

dashed black line: tree level, blue line: with coupled-channel rescattering of two pseudoscalar mesons a0(980) dynamically generated

I.V. Danilkin, M.F.M. Lutz, S.L., C. Terschl¨ usen, Eur.Phys.J. C73, 2358 (2013)

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Stefan Leupold Interactions of light mesons with photons

γγ → K +K −, K 0 ¯ K 0, ηη (pure predictions)

ARGUS

γγ → K+K-

σ [nb]

15 30 45 s1/2 [GeV] 1 1.1 1.2

T ASSO CELLO

γγ → K0K0

σ [nb]

10 20 30 s1/2 [GeV] 1 1.1 1.2

γγ → ηη

Belle

σ [nb]

1.5 3 4.5 s1/2 [GeV] 1.1 1.15 1.2

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Stefan Leupold Interactions of light mesons with photons

Table of Contents

1

Transition form factors and two-gamma physics

2

Lagrangian approach

3

Dispersive approach to pion transition form factor

16

Stefan Leupold Interactions of light mesons with photons

π0 → γ∗(q2

v)γ∗(q2 s ) transition form factor qv

2

qs

2

e− e+ e+ e− π0

π0 → e+e−e+e−

e− e+ π0

π0 → γγ

(figures from Bastian Kubis)

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Stefan Leupold Interactions of light mesons with photons

π0 → γ∗(q2

v)γ transition form factor qv

2

qs

2

e− e+ e+ e− π0

π0 → e+e−e+e−

e− e+ π0

π0 → γγ

π0 e− e+ π+ π− γ

(figures from Bastian Kubis)

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Stefan Leupold Interactions of light mesons with photons

π0 → γγ∗(q2

s ) transition form factor qv

2

qs

2

π0 γ e− e+ ω(φ)

e− e+ e+ e− π0

π0 → e+e−e+e−

e− e+ π0

π0 → γγ

(figures from Bastian Kubis)

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Stefan Leupold Interactions of light mesons with photons

Pion transition form factor — dispersive approach

want prediction for e+e− → π0γ (up to ≈ 1 GeV) ֒ → dominant inelasticities:

I = 1: e+e− → π+π− → π0γ I = 0: e+e− → π0π+π− → π0γ

required input for I = 1:

pion phase shift and pion form factor measured strength of amplitude π+π− → π0γ chiral anomaly

(M. Hoferichter, B. Kubis, D. Sakkas, Phys.Rev. D86 (2012) 116009)

input for I = 0 (three-body!):

dominated by narrow resonances ω, φ ֒ → use Breit-Wigners plus background for amplitude ֒ → fit to e+e− → π+π−π0

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Stefan Leupold Interactions of light mesons with photons

Pion transition form factor (e+e− → π0γ)

0.5 0.6 0.7 0.8 0.9 1 1.1 10

• 3

10

• 2

10

• 1

10 10

1

10

2

VEPP-2M CMD-2

σ(q)e+e−→π0γ[nb] q[GeV]

unsubtracted dispersion relation uncertainty estimate from quality of ω/φ → π0γ

Schneider et al., PRD86, 054013

can be extended to decay region π0 → γ e+e− and to spacelike region final aim: double virtual transition form factor ֒ → relevant for g − 2 and π0 → e+e−

• M. Hoferichter, B. Kubis, S.L., F. Niecknig and S. P. Schneider, in preparation

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Stefan Leupold Interactions of light mesons with photons

Summary

meson (transition) form factors and two-photon reactions allow access to intrinsic structure of hadrons ֒ → quark structure, polarizabilities, ... in addition input for standard-model baseline calculations for rare decays (π0) and high-precision determinations (muon’s g − 2) ֒ → we are sharpening our theory tools to improve the accuracy of predictions

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Stefan Leupold Interactions of light mesons with photons

Instead of an outlook

From two- to three-gamma physics yet another contribution to light-by-light scattering: γ∗ → ω → 3γ(∗) ֒ → related to scattering amplitude (dispersion theory) γ ω → π π → γ γ i.e. to decays ω → γ π+ π− , ω → γ π0 π0 more (differential) data needed and also φ instead of ω (better data situation)

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Stefan Leupold Interactions of light mesons with photons

Rare ω decays into 2π γ

ω → π+π−γ:

• nly upper limit

ω → π0π0γ: ֒ → branching ratio: 6.6 · 10−5 ֒ → differential data from CMD2

(Akhmetshin et al., Phys.Lett.B580, 119 (2004))

2 4 6 8 10 12 14 16 18 20 250 300 350 400 450 500 550 600 650 700

M(π0π0), MeV/c2 Events/ 20 MeV/c2

histograms are simulations with an in- termediate rho (full) or sigma meson (dotted)

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Stefan Leupold Interactions of light mesons with photons

backup slides

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Stefan Leupold Interactions of light mesons with photons

How we sort interactions/diagrams

without assigning importance to anything:

infinitely many interaction terms (with more and more derivatives) infinitely many loop diagrams

large-Nc framework (Nc = number of colors)

֒ → loops are suppressed note: we resum loops from rescattering, s-channel ֒ → sorting scheme applies to scattering kernel (potential), not to scattering amplitude

for interaction terms:

ensure appropriate Nc scaling by dimensionful decay constant f ∼ √Nc to ensure pertinent dimension of interaction term in Lagrangian: ֒ → assume large scale Λhard ≫ mV in denominator ֒ → expansion in derivatives/momenta over Λhard depends on chosen representation

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Stefan Leupold Interactions of light mesons with photons

Examples for interaction terms

relevant, e.g., for ω → 3π and ω → πγ∗ both can proceed directly or via πρ∗ some unsuppressed interaction terms εµναβ tr

• {V µν, ∇λV λα} uβ

, i f tr(Vµν [uµ, uν]) , f tr

• V µν f +

µν

• some suppressed interaction terms (the direct ones)

f Λ2

hard

εµναβ tr(∇λVλµ uν uα uβ) , f Λ2

hard

εµναβ tr({∇λVλµ, f +

να} uβ) .

Λhard: hadrogenesis gap or (here also O.K.) mass of excited vector mesons

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Stefan Leupold Interactions of light mesons with photons

hadrogenesis conjecture

spectrum at large Nc hadrogenesis conjecture

Λhard JP = 0±, 1±, . . . . . . mass gap JP = 1− JP = 0−

• ther observed mesons

below Λhard are supposed to be dynamically generated, i.e. meson molecules

• C. Terschl¨

usen, S.L., M.F.M. Lutz, Eur.Phys.J. A48, 190 (2012)

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Stefan Leupold Interactions of light mesons with photons

Rare pion decay — status

π0 e− e+

B(π0 → e+e−) = (6.46 ± 0.33) · 10−8 (KTeV, 2007) 3 σ deviation between experiment and standard model

Dorokhov/Ivanov, Phys. Rev. D75, 114007 (2007) (but controversial among theorists!)

for point-like pion QED loop is divergent ֒ → process is sensitive to hadronic transition form factor of pion π0 ↔ γ(∗)γ(∗)

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Stefan Leupold Interactions of light mesons with photons

g − 2 of the muon — status

290 240 190 140 140 190 240 290 1979 CERN Theory KNO (1985) 1997 µ+ 1998 µ+ 1999 µ+ 2000 µ+ 2001 µ− Average Theory (2009) (aµ-11659000)× 10−10 Anomalous Magnetic Moment BNL Running Year

Jegerlehner/Nyffeler, Phys. Rept. 477, 1 (2009)

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Stefan Leupold Interactions of light mesons with photons

g − 2 of the muon — theory

Largest uncertainty of standard model: hadronic contributions

µ γ had µ

µ(p) γ(k) kρ had + 5 permutations of the qi µ(p′) q1µ q2ν q3λ

vacuum polarization light-by-light scattering ∼ α2 ∼ α3

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Stefan Leupold Interactions of light mesons with photons

Transition form factor ω → π0 + µ+µ−

1 10 100 0.2 0.4 0.6 |Fωπ0|2 ml+l− [GeV] (P1) (P2)

• stand. VMD

NA60

corresponding differential decay rate:

1 2 3 4 5 6 7 8 9 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 dΓω−>π0µ+µ− / dmµ+µ−2 [10-6 GeV-1] mµ+µ− [GeV]

• param. set (P1)
• param. set (P2)
• stand. VMD

NA60

theory: C. Terschl¨ usen, S.L., Phys. Lett. B691, 191 (2010) data: NA60, Phys. Lett. B 677, 260 (2009)

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