Baryon PT for Two-Boson Exchange Graph Vadim Lensky Johannes - PowerPoint PPT Presentation

Baryon χ PT for Two-Boson Exchange Graph Vadim Lensky Johannes Gutenberg Universität Mainz September 30, 2017 Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 1 / 31

Motivation Consider the γγ box at low energies (important corrections to ep scattering, µ atoms) χ PT — the low-energy EFT of QCD — is a suitable tool in this regime Remove the lepton line = ⇒ proton Compton scattering (CS) — wealth of exp. data Calculate CS in χ PT, confront data, make predictions for γγ box Extend to γ Z and γ W at low energies? Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 2 / 31

Outline χ PT framework 1 Results for nucleon Compton scattering and µ H 2 RCS VVCS VCS Lamb shift and HFS Some thoughts on extension to γ Z and γ W 3 Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 3 / 31

Outline χ PT framework 1 Results for nucleon Compton scattering and µ H 2 RCS VVCS VCS Lamb shift and HFS Some thoughts on extension to γ Z and γ W 3 Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 4 / 31

χ PT framework inlcude nucleons, photons, pions Weinberg, Gasser and Leutwyler, ... count powers of small momenta p ∼ m π numerically e ∼ m π / M N — count as p also include the Delta isobar Hemmert, Holstein, ... ∆ = M ∆ − M N is a new energy scale = ⇒ δ -counting: Pascalutsa, Phillips (2002) m π / M N , count ∆ ∼ p 1 / 2 if p ∼ m π � numerically δ = ∆/ M N ∼ complications due to the spin-3 / 2 field (consistent couplings etc.) two energy regimes: ω ∼ m π : n = 4 L − 2 N π − N N − 1 � 2 N ∆ + kV k ω ∼ ∆ : � n = 4 L − 2 N π − N N − N ∆ − 2 N 1 ∆ R + kV k Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 5 / 31

NLO: Born and π N Loops Born graphs responsible for low energy (Thomson) limit; point-like nucleon O ( p 2 ) and O ( p 3 ) (a.m.m. coupling) π 0 anomaly and π N loops leading-order contribution to polarisabilities : O ( p 3 ) Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 6 / 31

NNLO: Delta pole and π ∆ loops Delta pole and π ∆ loops different counting in different energy regimes Delta pole: O ( p 4 /∆ ) = O ( p 7 / 2 ) at ω ∼ m π ; O ( p ) at ω ∼ ∆ π ∆ loops: O ( p 4 /∆ ) = O ( p 7 / 2 ) at ω ∼ m π ; O ( p 3 ) at ω ∼ ∆ at ω ∼ ∆ one needs to dress the 1 ∆ R propagator i Σ = at ω ∼ ∆ corrections to γ N ∆ vertex are O ( p 2 ) = + + Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 7 / 31

Outline χ PT framework 1 Results for nucleon Compton scattering and µ H 2 RCS VVCS VCS Lamb shift and HFS Some thoughts on extension to γ Z and γ W 3 Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 8 / 31

Outline χ PT framework 1 Results for nucleon Compton scattering and µ H 2 RCS VVCS VCS Lamb shift and HFS Some thoughts on extension to γ Z and γ W 3 Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 9 / 31

Results: RCS observables Θ lab � 45 ° Θ lab � 60 ° Θ lab � 90 ° 20 15 covariant baryon calculation 10 VL, McGovern, Pascalutsa (2015) 5 d � � nb � sr � 0 VL, Pascalutsa (2009) 40 Θ lab � 120 ° Θ lab � 135 ° Θ lab � 180 ° d Σ NNLO ( O ( p 7 / 2 ) ) at ω ∼ m π 30 NLO ( O ( p 2 ) ) at ω ∼ ∆ 20 10 prediction of ChPT 0 0 50 100 150 0 50 100 150 0 50 100 150 E Γ � MeV � Θ lab � 45 ° Θ lab � 60 ° Θ lab � 90 ° 400 polarisabilities are seen 300 starting at ∼ 50 MeV 200 pion loops are important at low d � � nb � sr � 100 0 energies and around pion 200 Θ lab � 120 ° Θ lab � 135 ° Θ lab � 180 ° d Σ production threshold 150 Delta pole dominates in the 100 50 resonance region 0 0 100 200 300 0 100 200 300 0 100 200 300 E Γ � MeV � Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 10 / 31

Scalar polarisabilities: status �� �� �� �� �� �� � � � � � � � � � � � � � � �� �� �� �� �� �� ���� ���� ���� ���� ���� ���� ����� ����� ����� ����� ����� ����� � ����� ����� �� ��� � � � ����� ���� �� ��� � � � ����� ���� �� ��� � � � ����� ���� �� ��� � � � ����� ���� �� ��� � � � ����� ���� �� ��� � � �� ��� ��� ��� ��� ��� �� �� �� �� �� ��������� ��� �� �� �� �� �� �� � � � � � ���� � � � � � � � � � � � � � � � � � � � � ���������� � � � � � � � � � � �� �� �� �� �� �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� �� �� �� �� �� �� �� ��� ��� ��� ��� �� �� �� �� �� �� �� �� �� �� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� � ����� ����� �� ��� � � � ����� ���� �� ��� � � � ����� ���� �� ��� � � � ����� ���� �� ��� � � � ����� ���� �� ��� � � � ����� ���� �� ��� � � for the proton, χ PT calculations somewhat differ from other extractions (in particular, TAPS value) there are hints that the issue might be due to exp. data Krupina, VL, Pascalutsa, in preparation neutron polarisabilities are less well constrained — there is no free neutron target Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 11 / 31

Outline χ PT framework 1 Results for nucleon Compton scattering and µ H 2 RCS VVCS VCS Lamb shift and HFS Some thoughts on extension to γ Z and γ W 3 Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 12 / 31

VVCS forward VVCS amplitude ǫ ′∗ · � T ( ν, Q 2 ) = f L ( ν, Q 2 ) + ( � ǫ ) f T ( ν, Q 2 ) ǫ ′∗ × � ǫ ′∗ − � ǫ ) g TT ( ν, Q 2 ) − i � q ] g LT ( ν, Q 2 ) ǫ ) × ˆ + i � σ · ( � σ · [( � low-energy expansion of the amplitude is f T ( ν, Q 2 ) f B T ( ν, Q 2 ) + 4 π � Q 2 β M 1 + ( α E 1 + β M 1 ) ν 2 � = + . . . L ( ν, Q 2 ) + 4 π ( α E 1 + α L ν 2 ) Q 2 + . . . f L ( ν, Q 2 ) f B = TT ( ν, Q 2 ) + 4 πγ 0 ν 3 + . . . g TT ( ν, Q 2 ) g B = g LT ( ν, Q 2 ) g B LT ( ν, Q 2 ) + 4 πδ LT ν 2 Q + . . . = ν -dependent terms can be treated as functions of Q 2 and related to moments of nucleon structure functions Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 13 / 31

VVCS: results Proton Neutron 20 Α E1 �Β M1 � 10 � 4 fm 3 � 15 15 NLO/LO [ O ( p 4 /∆ ) / O ( p 3 ) ] 10 10 VL, Alarcón, Pascalutsa (2014) 5 5 HB χ PT O ( p 4 ) 0 0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Kao, Spitzenberg, Vanderhaeghen (2003) 4 4 IR O ( p 4 ) Α L � 10 � 4 fm 5 � 3 3 Bernard, Hemmert, Meissner (2003) 2 2 covariant χ PT O ( ǫ 3 ) 1 1 Bernard, Epelbaum, Krebs, Meissner (2013) MAID 0 0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Q 2 � GeV 2 � Q 2 � GeV 2 � Proton Neutron 3 HB and IR do not provide adequate 2 2 1 description Γ 0 � 10 � 4 fm 4 � 0 1 � 1 0 covariant χ EFT works much better, � 2 � 1 especially in γ 0 (HB is off the scale there) � 3 � 2 � 4 δ LT puzzle: difference between the two � 3 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.00 0.05 0.10 0.15 0.20 0.25 0.30 covariant calculations (the one of Bernard 3.0 2.5 2.5 ∆ LT � 10 � 4 fm 4 � et al. contains π ∆ loops subleading in our 2.0 2.0 1.5 counting) 1.5 1.0 1.0 data on δ LT from JLab expected 0.5 0.5 0.0 0.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Q 2 � GeV 2 � Q 2 � GeV 2 � Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 14 / 31

Outline χ PT framework 1 Results for nucleon Compton scattering and µ H 2 RCS VVCS VCS Lamb shift and HFS Some thoughts on extension to γ Z and γ W 3 Vadim Lensky (U. Mainz) Electroweak Box Workshop September 30, 2017 15 / 31