Stefan Leupold Interactions of light with light mesons

Interactions of light with light mesons

Stefan Leupold

Uppsala University

Light Meson Dynamics, Mainz, Feb. 2014

1 Stefan Leupold Interactions of light with light mesons Collaborators

Uppsala: Per Engstr¨om,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

2 Stefan Leupold Interactions of light with light mesons Table of Contents

1 What we are after

2 Transition form factors and two-gamma physics

3 Lagrangian approach

4 Dispersive approach to pion transition form factor

3 Stefan Leupold Interactions of light with light mesons Challenges of hadron (+nuclear) physics

structure of matter understand masses of hadrons

(also, e.g., mass ordering: mσ < mρ, 1440 < 1520) life times, branching ratios of hadron resonances form factors and intrinsic structure nature of hadrons (how much quark-antiquark? how much hadron-hadron? ...) (nuclei, neutron stars) new forms of matter high-precision frontier of standard model

4 Stefan Leupold Interactions of light with light mesons Challenges of hadron (+nuclear) physics

structure of matter new forms of matter non-qq¯ mesons (exotic quantum numbers, exotic decomposition, X/Y/Z states, glueballs, meson molecules, ...) non-3q baryons, di-baryons (∆ ∆ by WASA?), ... − (quark-gluon plasma, color superconductors, early universe, core of neutron stars) high-precision frontier of standard model

5 Stefan Leupold Interactions of light with light mesons Challenges of hadron (+nuclear) physics

structure of matter new forms of matter high-precision frontier of standard model determine parameters of standard model (light quark masses, CKM matrix, ...) traces of physics beyond standard model (rare decays, g 2 of muon, ...) −

6 Stefan Leupold Interactions of light with light mesons Challenges of hadron (+nuclear) theory

structure of matter new forms of matter high-precision frontier of standard model

from phenomenological models to real quantum field theories physical form factors instead of ad-hoc cutoff form factors do not neglect loops just because they are complicated assign degrees of importance to processes, diagrams (e.g. power counting, separation of relevant from irrelevant degrees of freedom) reliable uncertainty estimates treat unitarity/rescattering, analyticity serious We are not there yet!

7 background for physics beyond standard model e+ 0 + 0 rare pion decay π e e− π → e−

γ(k) kρ

g 2 of muon had + 5 permutations of the qi q3λ q − q2ν 1µ

µ(p) µ(p′)

Stefan Leupold Interactions of light with light mesons 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?

8 Stefan Leupold Interactions of light with light mesons 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 e+ 0 + 0 rare pion decay π e e− π → e−

γ(k) kρ

g 2 of muon had + 5 permutations of the qi q3λ q − q2ν 1µ

µ(p) µ(p′)

8 Stefan Leupold Interactions of light with light mesons Hadronic contribution to g 2 of the muon −

γ(k) kρ light-by-light scattering had + 5 permutations of the qi q 3λ q2ν q1µ

µ(p) µ(p′)

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) ( ) ( ) 0 , γ ∗ γ ∗ π (you’ve seen this before for rare pion decay), → ( ) ( ) ↔ γ ∗ γ ∗ 2π,... ↔ 9 Stefan Leupold Interactions of light with light mesons Shopping list for hadron theory and experiment

( ) ( ) transition form factors of pseudoscalars γ ∗ γ ∗ P 0 ↔ with P = π , η, η0,... , several interesting kinematical regions next slide (for pion) →

10 Stefan Leupold Interactions of light with light mesons 0 2 2 π γ∗(q )γ∗(q ) transition form factor → v s

2 qs

0 e− π

e− e+ e+

0 + + π e e−e e− → 2 qv π0 γγ e− → π0 e+

(figures from Bastian Kubis) 11 + 0 0 0 “two-gamma physics” γγ π π−, π π , π η, KK¯ ,... (cross relation to polarizability→ of the pion)

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

Stefan Leupold Interactions of light with light mesons Shopping list for hadron theory and experiment

( ) ( ) transition form factors of pseudoscalars γ ∗ γ ∗ P 0 ↔ with P = π , η, η0,... if invariant mass of dilepton around mass of a vector meson: relation to transition form factors of vector to pseudoscalar mesons ( ) 0 V Pγ ∗ with V = ρ , ω, φ, . . . ↔

12 Stefan Leupold Interactions of light with light mesons Shopping list for hadron theory and experiment

( ) ( ) transition form factors of pseudoscalars γ ∗ γ ∗ P 0 ↔ with P = π , η, η0,... if invariant mass of dilepton around mass of a vector meson: relation to transition form factors of vector to pseudoscalar mesons ( ) 0 V Pγ ∗ with V = ρ , ω, φ, . . . ↔ + 0 0 0 “two-gamma physics” γγ π π−, π π , π η, KK¯ ,... (cross relation to polarizability→ of the pion)

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

12 Stefan Leupold Interactions of light with light mesons 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

13 Stefan Leupold Interactions of light with light mesons Table of Contents

1 What we are after

2 Transition form factors and two-gamma physics

3 Lagrangian approach

4 Dispersive approach to pion transition form factor

14 Stefan Leupold Interactions of light with light mesons Transition form factor ω π0+ dilepton →

100 (P1) (P2) data and our Lagrangian approach stand. VMD NA60 show strong deviations from vector-meson dominance (VMD) 2 |

0 10 our approach describes data fairly ωπ

|F well except for large invariant masses close to phase-space limit (log plot!) 1 second experimental confirmation

0 0.2 0.4 0.6 desirable − ml+l [GeV]

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

15 Stefan Leupold Interactions of light with light mesons Transition form factor φ η+ dilepton → 10 2 |Fφη| θ = − 2° θ = + 2° VMD VEPP-2M

5 our Lagrangian approach deviates from VMD new data from KLOE will come 0 soon

-5 0.0 0.2 0.4 q [GeV] C. Terschl¨usen,S.L., M.F.M. Lutz, Eur.Phys.J. A48, 190 (2012)

16 Stefan Leupold Interactions of light with light mesons + 0 0 γγ π π−, π π → 300 60 Mark II + - Crystal Ball 0 0 Belle γγ → π π Belle γγ → π π CELLO Belle syst. error Belle syst. error 200 40 ] ] b b n n [ [

σ 100 σ 20

0 0 0.3 0.7 1.1 0.3 0.7 1.1 s1/2 [GeV] s1/2 [GeV]

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

overall 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)

17 Stefan Leupold Interactions of light with light mesons γγ to other meson pairs

, stay tuned for Matthias’ talk →

18 Stefan Leupold Interactions of light with light mesons Table of Contents

1 What we are after

2 Transition form factors and two-gamma physics

3 Lagrangian approach

4 Dispersive approach to pion transition form factor

19 Stefan Leupold Interactions of light with light mesons 0 2 2 π γ∗(q )γ∗(q ) transition form factor → v s

2 qs

0 e− π

e− e+ e+

0 + + π e e−e e− → 2 qv π0 γγ e− → π0 e+

(figures from Bastian Kubis) 20 Stefan Leupold Interactions of light with light mesons 0 2 π γ∗(q )γ transition form factor → v 2 qs

0 e− π

e− e+ e+

0 + + π e e−e e− → 2 qv 0 + 0 π γγ e− π π e− → π0 e+ e+ π− γ (figures from Bastian Kubis) 21 Stefan Leupold Interactions of light with light mesons 0 2 π γγ ∗(q ) transition form factor → s 2 qs 0 e− π ω(φ)

e+ γ 0 e− π

e− e+ e+

0 + + π e e−e e− → 2 qv π0 γγ e− → π0 e+

(figures from Bastian Kubis) 22 Stefan Leupold Interactions of light with light mesons Pion transition form factor — dispersive approach

+ 0 want prediction for e e− π γ (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 and decay widths ω/φ π0γ → − → − →

23 Stefan Leupold Interactions of light with light mesons + 0 Pion transition form factor (e e− π γ) → height between peaks is not 2 10 a fit!

101 [nb] can be extended to decay γ 0 π 0 + → 0 − region π γ e e− and to e 10 + e

) →

q spacelike region ( σ 10-1 VEPP-2M CMD-2 final aim: double virtual 10-2 transition form factor

-3 , relevant for g 2 and 10 0.5 0.6 0.7 0.8 0.9 1 1.1 → 0 + − q[GeV] π e e− →

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

24 Stefan Leupold Interactions of light with light mesons 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

25 Stefan Leupold Interactions of light with light mesons 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

+ 0 0 ω γ π π− , ω γ π π → → more (differential) data needed and also φ instead of ω (better data situation)

26 Stefan Leupold Interactions of light with light mesons Rare ω decays into 2π γ

2 20

18

16 + ω π π−γ: → 14 only upper limit Events/ 20 MeV/c 12

10

8 0 0 ω π π γ: 6 → 5 4 , branching ratio: 6.6 10− → · 2 , differential data from CMD2 0 → (Akhmetshin et al., 250 300 350 400 450 500 550 600 650 700 M(π0π0), MeV/c2 Phys.Lett.B580, 119 (2004)) histograms are simulations with an in- termediate rho (full) or sigma meson (dotted)

27 Stefan Leupold Interactions of light with light mesons

backup slides

28 Stefan Leupold Interactions of light with light mesons 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 Λ mV in denominator → hard  , expansion in derivatives/momenta over Λhard → depends on chosen representation 29 Stefan Leupold Interactions of light with light mesons Examples for interaction terms

relevant, e.g., for ω 3π and ω πγ∗ → → both can proceed directly or via πρ∗ some unsuppressed interaction terms ε tr V µν, V λα uβ
, µναβ { ∇λ } µ ν µν +
i f tr(Vµν [u , u ]) , f tr V fµν some suppressed interaction terms (the direct ones)

f µναβ λ 2 ε tr( Vλµ uν uα uβ) , Λhard ∇ f µναβ λ + 2 ε tr( Vλµ, fνα uβ) . Λhard {∇ }

Λhard: hadrogenesis gap or (here also O.K.) mass of excited vector mesons 30 Stefan Leupold Interactions of light with light mesons hadrogenesis conjecture

spectrum at large Nc argnssconjecture hadrogenesis . P J =0±, 1±,...

Λhard other observed mesons below Λhard are supposed mass to be dynamically generated, gap i.e. meson molecules

P J =1−

P J =0−

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

31 Stefan Leupold Interactions of light with light mesons Rare pion decay — status

e+ π0

e−

0 + 8 B(π e e−) = (6.46 0.33) 10− (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 → 0 ( ) ( ) π γ ∗ γ ∗ ↔

32 Stefan Leupold Interactions of light with light mesons g 2 of the muon — status −

290 290

10 +

− µ

10 240 240

× + + µ−

Theory KNO (1985) µ µ Theory (2009)

190 190 -11659000) µ a ( 140 140 Anomalous Magnetic Moment µ+

1979 1997 1998 1999 2000 2001 Average CERN BNL Running Year

Jegerlehner/Nyffeler, Phys. Rept. 477, 1 (2009) 33 Stefan Leupold Interactions of light with light mesons g 2 of the muon — theory − Largest uncertainty of standard model: hadronic contributions

γ(k) k γ ρ

had + 5 permutations of the qi q 3λ q2ν q1µ had

µ µ µ(p) µ(p′) vacuum polarization light-by-light scattering α2 α3 ∼ ∼

34 Stefan Leupold Interactions of light with light mesons 0 + Transition form factor ω π + µ µ− →

100 (P1) corresponding differential (P2) stand. VMD NA60 decay rate: 9 param. set (P1) 8 param. set (P2) ] stand. VMD -1 NA60 7 2 GeV |

0 10 -6 6 ωπ [10 2 |F − 5 µ + µ 4 / dm − µ

+ 3 µ 0 2 ω−>π Γ 1 d 1

0 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0 0.2 0.4 0.6 mµ+µ− [GeV] − ml+l [GeV]

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

35