Applications of chiral perturbation theory: electromagnetic - PowerPoint PPT Presentation

Applications of chiral perturbation theory: electromagnetic properties of baryons Astrid N. Hiller Blin Johannes Gutenberg-Universit¨ at Mainz hillerbl@uni-mainz.de Thursday 31 st August, 2017

Contents 1 Motivation: What can we learn from EM probes? 2 Framework: Why do we need ChPT? 3 (Only) a few interesting results ♣ Compton scattering and polarizabilities ♣ Virtual photons and form factors

Photon beams Electromagnetic interactions provide clean probes of the inner structure of hadrons ◮ Low photon energies ( ∼ 100 MeV): Compton scattering ◮ Slightly higher ( � 140 MeV): pion photoproduction Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 1

Photon beams Electromagnetic interactions provide clean probes of the inner structure of hadrons ◮ Low photon energies ( ∼ 100 MeV): Compton scattering ◮ Even higher: start feeling resonance production Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 1

Virtual photons ◮ E.g. elastic electron scattering e − e − b ◮ For all these processes we focus on: small external momenta/momentum transfer Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 2

Non-perturbative QCD vs. chiral perturbation theory E γ ≈ O ( m π ) ⇒ α s = O ( 1 ) Perturbative QCD breaks down = ⇒ EFT: expansion around other parameters Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 3

Non-perturbative QCD vs. chiral perturbation theory E γ ≈ O ( m π ) ⇒ α s = O ( 1 ) Perturbative QCD breaks down = ⇒ EFT: expansion around other parameters Chiral perturbation theory: m π p ext ◮ Small masses, momenta ( 1 GeV , 1 GeV ≪ 1): :combined expansion ◮ New degrees of freedom: : ✭✭✭✭✭✭✭✭✭ ❤❤❤❤❤❤❤❤❤ ✭ quarks and gluons = ⇒ mesons and baryons ❤ Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 3

Lagrangians of ChPT Lowest-order meson Lagrangian ∼ p 2 ext , m 2 π φφγ = F 2 � � L ( 2 ) ∇ µ U ∇ µ U † + χ + 4 Tr 0 Lowest-order baryon Lagrangian ∼ p ext + D + F � ¯ � � ¯ B γ µ { u µ , B } γ 5 � � ¯ B γ µ [ u µ , B ] γ 5 � L ( 1 ) B ( i / φ B γ = Tr D − m ) B 2 Tr 2 Tr Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 4

Inclusion of the spin-3/2 resonances The spin-3 / 2 states couple strongly to the spin-1/2 octet baryons Pascalutsa et al., Phys. Rept. 437 (2007) 125 Geng et al., Phys. Lett. B 676 (2009) 63 √ ∆ φ B = − i 2 C B ab ε cda γ µνλ ( ∂ µ ∆ ν ) dbe ( D λ φ ) ce + H.c. L ( 1 ) ¯ F 0 M ∆ 3 i e g M B ab ε cda Q ce ( ∂ µ ∆ ν ) dbe ˜ F µν + H.c. L ( 2 ) ¯ √ ∆ γ B = − 2 m ( m + M ∆ ) Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 5

Matching a diagram to a specific order � O = 4 L + kV k − 2N π − N N − N ∆ · ? π , spin-1/2 baryon ∼ p − 1 ◮ Propagators: meson ∼ m − 2 ext ◮ Spin-3/2 baryon: new scale δ = M ∆ − m N ≈ 0 . 3 GeV > m π ◮ ( δ/ m p ) 2 ≈ ( m π / m p ) = ⇒ far from resonance mass: ? = 1 2 Pascalutsa and Phillips, Phys. Rev. C 67 (2003) 055202 ◮ Close to resonance mass: p ext ∼ δ = ⇒ ? = 1 Hemmert et al., Phys. Lett. B 395 (1997) 89 Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 6

Renormalization ◮ Loop diagrams: divergences and power counting breaking terms 1 1 e.g. terms ∝ p 2 at O ( p 3 ) ǫ = and 4 − dim Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 7

Renormalization ◮ Loop diagrams: divergences and power counting breaking terms 1 1 e.g. terms ∝ p 2 at O ( p 3 ) ǫ = and 4 − dim ◮ Fully analytical = ⇒ match with Lagrangian terms ◮ Low-energy constants of these terms a priori unknwon Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 7

Renormalization ◮ Loop diagrams: divergences and power counting breaking terms 1 1 e.g. terms ∝ p 2 at O ( p 3 ) ǫ = and 4 − dim ◮ Fully analytical = ⇒ match with Lagrangian terms ◮ Low-energy constants of these terms a priori unknwon ◮ EOMS-renormalization prescription: Gegelia and Japaridze, Phys. Rev. D 60 (1999) 114038 ◮ MS absorbs L = 2 ǫ + log ( 4 π ) − γ E into LECs ◮ Also subtracts PCBT by redefinition of LECs ◮ Usually converges faster than other counting schemes (relativistic or not) Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 7

Compton scattering and polarizabilities Hiller Blin, Gutsche, Ledwig and Lyubovitskij Phys. Rev. D 92 (2015) 096004 arXiv: 1509.00955 [hep-ph]

Polarizabilities u u d u d |E|=0 |E|>0 u ◮ In EM field: hadrons deformed due to charged components ◮ Size of deformation: related to polarizabilities ◮ Experiment: Compton scattering off hadron targets Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 8

Theoretical approach ◮ Amplitude expansion around low photon energy ω ◮ O ( ω 0 ) : total charge ◮ O ( ω 1 ) : anomalous magnetic moment ◮ O ( ω 2 ) : α E and β M ◮ O ( ω 3 ) : spin-dependent polarizabilities γ i Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 9

Theoretical approach ◮ Amplitude expansion around low photon energy ω ◮ O ( ω 0 ) : total charge ◮ O ( ω 1 ) : anomalous magnetic moment ◮ O ( ω 2 ) : α E and β M ◮ O ( ω 3 ) : spin-dependent polarizabilities γ i ◮ Forward spin polarizability γ 0 ◮ response to deformation relative to spin axis ◮ photon scattering in extreme forward direction Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 9

Theoretical approach ◮ Amplitude expansion around low photon energy ω ◮ O ( ω 0 ) : total charge ◮ O ( ω 1 ) : anomalous magnetic moment ◮ O ( ω 2 ) : α E and β M ◮ O ( ω 3 ) : spin-dependent polarizabilities γ i ◮ Forward spin polarizability γ 0 ◮ response to deformation relative to spin axis ◮ photon scattering in extreme forward direction ◮ Theory: Hemmert et al., Phys. Rev. D 57 (1998) 5746 � ǫ µ M SD µν ǫ ∗ ν ∂ ǫ ∗ )] = − i � γ 0 [ � σ · ( � ǫ × � � ∂ω 2 4 π ω � ω = 0 Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 9

Experimental extraction ◮ Sum rule: Gell-Mann et al., Phys. Rev. 95 (1954) 1612 � ∞ d ωσ 3 / 2 ( ω ) − σ 1 / 2 ( ω ) γ 0 = − 1 4 π 2 ω 3 ω 0 σ 3 / 2 ( σ 1 / 2 ) : photon and target helicities are (anti)parallel Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 10

Experimental extraction ◮ Sum rule: Gell-Mann et al., Phys. Rev. 95 (1954) 1612 � ∞ d ωσ 3 / 2 ( ω ) − σ 1 / 2 ( ω ) γ 0 = − 1 4 π 2 ω 3 ω 0 σ 3 / 2 ( σ 1 / 2 ) : photon and target helicities are (anti)parallel ◮ Experiment: Pasquini et al., Phys. Lett. B 687 (2004) 160 γ p 0 = [ − 1 . 01 ± 0 . 08(stat) ± 0 . 10(syst) ] · 10 − 4 fm 4 ◮ Dispersion relations: Drechsel et al., Phys. Rept. 378 (2003) 99 0 = [ − 1 . 1 ± 0 . 4 ] · 10 − 4 fm 4 and γ n γ p 0 = [ − 0 . 3 ± 0 . 2 ] · 10 − 4 fm 4 Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 10

Experimental extraction ◮ Sum rule: Gell-Mann et al., Phys. Rev. 95 (1954) 1612 � ∞ d ωσ 3 / 2 ( ω ) − σ 1 / 2 ( ω ) γ 0 = − 1 4 π 2 ω 3 ω 0 σ 3 / 2 ( σ 1 / 2 ) : photon and target helicities are (anti)parallel ◮ Experiment: Pasquini et al., Phys. Lett. B 687 (2004) 160 γ p 0 = [ − 1 . 01 ± 0 . 08(stat) ± 0 . 10(syst) ] · 10 − 4 fm 4 ◮ Dispersion relations: Drechsel et al., Phys. Rept. 378 (2003) 99 0 = [ − 1 . 1 ± 0 . 4 ] · 10 − 4 fm 4 and γ n γ p 0 = [ − 0 . 3 ± 0 . 2 ] · 10 − 4 fm 4 ◮ First goal is to reproduce these values theoretically ◮ Then extend the theoretical model to predict ⇒ hyperons polarizabilities of not yet measured states = Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 10

Renormalization ◮ ∞ and PCBT: do not enter pieces ∼ ω 3 relevant for γ 0 ◮ Leading order for γ 0 = ⇒ no unknwon LECs ◮ Results independent of renormalization or unknown LECs ⇓ pure predictions of ChPT Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 11

Results with different covariant ChPT models γ 0 [10 - 4 fm - 4 ] ◇ Proton Neutron ● 3 ● SU(2) ■ ● ■ our SU(3) results 2 ■ ◆ SU(2) Δ 1 ▲ our SU(3) Δ results ◆ 0 ▼ Experiment ○ ◆ ○ Disp. Rel. - 1 ▼○ ▲ ▲ - 2 SU ( 2 ) : Bernard et al., Phys. Rev. D 87 (2013) 054032 SU ( 2 ) with ∆ : Lensky et al., Eur. Phys. J. C 75 (2015) 604 Experiment : Pasquini et al., Phys. Lett. B 687 (2004) 160 Dispersion relations : Drechsel et al., Phys. Rept. 378 (2003) 99 Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 12

Results for the hyperons γ 0 [ fm − 4 10 − 4 ] Σ + Σ 0 Ξ 0 Σ − Λ Ξ − Our full model -2.30(33) 0.90 0.47(8) -1.25(25) 0.13 -3.02(33) ◮ g M not well known ◮ We estimate it from electromagnetic decay width Γ ∆ → γ N g M = 3 . 16 ( 16 ) ◮ Thursday 31 st August, 2017 SFB School 2017 A. N. Hiller Blin, JGU Mainz 13