Formulating electroweak pion decays in functional methods and the - PowerPoint PPT Presentation

Formulating electroweak pion decays in functional methods and the influence of CP-violation. Walid Ahmed Mian Advisor: Axel Maas and Jan M. Pawlowski June 20th, 2017 W. Ah. Mian EW pion decay in FM June 20th, 2017 1 / 31

Outline Motivation 1 Quark Propagator with broken Flavor and CP-Violation 2 Bethe-Salpeter Equation of the weak pion decay 3 Conclusion 4 W. Ah. Mian EW pion decay in FM June 20th, 2017 2 / 31

Binary Neutron Stars Mergers System of binary neutron stars mergers Source of gravitational waves Possible outcome: neutron star or black hole Depends on neutrino backcoupling, magnetic field etc. (Y. Sekiguchi et al. PRL 107 (2011), 051102 (http://www.ligo.org/science/GW-Inspiral.php) O. L. Caballero arXiv:1603.02755 [nucl-th] Foucart et al. arXiv:1510.06398v2 [astro-ph] Rosswog et al. arXiv:0302301v1 [astro-ph] . . . ) W. Ah. Mian EW pion decay in FM June 20th, 2017 3 / 31

Binary Neutron Stars Mergers System of binary neutron stars mergers Source of gravitational waves Possible outcome: neutron star or black hole Depends on neutrino backcoupling, magnetic field etc. (Y. Sekiguchi et al. PRL 107 (2011), 051102 (http://www.ligo.org/science/GW-Inspiral.php) O. L. Caballero arXiv:1603.02755 [nucl-th] Foucart et al. arXiv:1510.06398v2 [astro-ph] Rosswog et al. arXiv:0302301v1 [astro-ph] . . . ) W. Ah. Mian EW pion decay in FM June 20th, 2017 3 / 31

Binary Neutron Stars Mergers System of binary neutron stars mergers Source of gravitational waves Possible outcome: neutron star or black hole Depends on neutrino backcoupling, magnetic field etc. (Y. Sekiguchi et al. PRL 107 (2011), 051102 (http://www.ligo.org/science/GW-Inspiral.php) O. L. Caballero arXiv:1603.02755 [nucl-th] Foucart et al. arXiv:1510.06398v2 [astro-ph] Rosswog et al. arXiv:0302301v1 [astro-ph] . . . ) W. Ah. Mian EW pion decay in FM June 20th, 2017 3 / 31

Binary Neutron Stars Mergers Micro physics influence gravitational waves Very high neutrino flux Super/Hyper-Kamiokande have good sensitivity Measurement shows the inner structure of the neutron star mergers (Y. Sekiguchi et al. PRL 107 (2011), 051102 O. L. Caballero arXiv:1603.02755 [nucl-th] Foucart et al. arXiv:1510.06398v2 [astro-ph] Rosswog et al. arXiv:0302301v1 [astro-ph] . . . ) (Foucart et al. arXiv:1510.06398v2 [astro-ph]) W. Ah. Mian EW pion decay in FM June 20th, 2017 4 / 31

Back Coupling Neutrinos Very dense matter ⇒ opaque for neutrinos Reaction inside the core (Foucart et al. arXiv:1510.06398v2 [astro-ph]) → p + e − ν e + n ← → n + e + ν e + p ← → e + + e − ν e + ν e ← ν e + ν e ← → γ Electroweak interactions play an important role Consider QCD + electroweak interactions non-perturbative W. Ah. Mian EW pion decay in FM June 20th, 2017 5 / 31

β -decay Full resolution of electroweak interactions is complicated β -decay captures the main features Look at the π ± -decay Electroweak interactions approximate by 4-Fermi-interaction Electroweak interactions violates parity No results on non-perturbative backcoupling of C and P violation First: Investigate the effects on the simplest object: Quark propagator Analyse influence through explicit http://hyperphysics.phy- astr.gsu.edu/hbase/particles/proton.html breaking term (A. Maas & W. M., EPJA (2017) 53 : 22 , arxiv:1611:08130) W. Ah. Mian EW pion decay in FM June 20th, 2017 6 / 31

β -decay Full resolution of electroweak interactions is complicated β -decay captures the main features d ν Look at the π ± -decay Electroweak interactions approximate by 4-Fermi-interaction Electroweak interactions violates parity No results on non-perturbative backcoupling of C and P violation First: Investigate the effects on the simplest object: Quark propagator e u Analyse influence through explicit breaking term (A. Maas & W. M., EPJA (2017) 53 : 22 , arxiv:1611:08130) W. Ah. Mian EW pion decay in FM June 20th, 2017 6 / 31

β -decay Full resolution of electroweak d ν interactions is complicated β -decay captures the main features Look at the π ± -decay Electroweak interactions approximate by 4-Fermi-interaction Electroweak interactions violates parity No results on non-perturbative e u backcoupling of C and P violation First: Investigate the effects on the ↓ simplest object: Quark propagator Analyse influence through explicit breaking term (A. Maas & W. M., EPJA (2017) 53 : 22 , arxiv:1611:08130) W. Ah. Mian EW pion decay in FM June 20th, 2017 6 / 31

Quark Propagator Symmetry breaking ⇒ More involved tensor structure Pure QCD: P ( p 2 ) = ˜ A ( p 2 ) i / p + ˜ B ( p 2 )1 1 Parity violation: p γ 5 + ˜ P ( p 2 ) = ˜ p + ˜ 1 + ˜ A ( p 2 ) i / B ( p 2 )1 C ( p 2 ) i / D ( p 2 ) γ 5 Flavor and parity violation: p γ 5 + ˜ P AB ( p 2 ) = ˜ p + ˜ 1 + ˜ A AB ( p 2 ) i / B AB ( p 2 )1 C AB ( p 2 ) i / D AB ( p 2 ) γ 5 W. Ah. Mian EW pion decay in FM June 20th, 2017 7 / 31

Quark Propagator and its inverse Pure QCD: P − 1 ( p 2 ) = − A ( p 2 ) i / p + B ( p 2 )1 1 P ( p 2 ) = ˜ A ( p 2 ) i / p + ˜ B ( p 2 )1 1 A ( p 2 ) Z ( p 2 ) A ( p 2 ) = ˜ A 2 ( p 2 ) p 2 + B 2 ( p 2 ) = p 2 + M 2 ( p 2 ) B ( p 2 ) M ( p 2 ) ˜ B ( p 2 ) = A 2 ( p 2 ) p 2 + B 2 ( p 2 ) = p 2 + M 2 ( p 2 ) Wavefunctionrenormalization and Massfunction: M ( p 2 ) = B ( p 2 ) 1 Z ( p 2 ) = A ( p 2 ) A ( p 2 ) W. Ah. Mian EW pion decay in FM June 20th, 2017 8 / 31

Quark Propagator and its inverse Flavor and parity violation: p γ 5 + D AB ( p 2 ) γ 5 P − 1 AB ( p 2 ) = − A AB ( p 2 ) i / p + B AB ( p 2 )1 1 + C AB ( p 2 ) i / p γ 5 + ˜ P AB ( p 2 ) = ˜ p + ˜ 1 + ˜ A AB ( p 2 ) i / B AB ( p 2 )1 C AB ( p 2 ) i / D AB ( p 2 ) γ 5 Complicated and very lengthy relation: A AB = ˜ ˜ A AB ( A CD , B CD , C CD , D CD ) W. Ah. Mian EW pion decay in FM June 20th, 2017 9 / 31

Tree-level Propagator 1 w p 2 i / P 0 , uu ( p 2 ) = ( m 2 d + (1 − 2 g 2 w ) p 2 ) i / p + m u ( m 2 d + p 2 )1 1 + 2 g 2 p γ 5 � � N ( p 2 ) g w P 0 , ud ( p 2 ) = ( m u m d − p 2 ) i / p − ( m u + m d ) p 2 1 1 − ( m u m d + p 2 ) i / p γ 5 � � N ( p 2 ) − g w ( m u − m d ) p 2 γ 5 N ( p 2 ) d ) p 2 + (1 − 4 g 2 N ( p 2 ) = m 2 d m 2 u + ( m 2 u + m 2 w ) p 4 Pseudo scalar channel of the mixed propagator (tree-level) is proportional to mass splitting W. Ah. Mian EW pion decay in FM June 20th, 2017 10 / 31

DSEs DSEs: Equation of motion for the correlation functions Pure QCD: − 1 − 1 = + d 4 q � P − 1 ( p 2 ) = P − 1 (2 π ) 4 g γ ν S νµ ( q − p ) P ( q 2 )Γ µ ( p , q ) + 0 Rainbow-Truncation gS νµ ( q − p )Γ µ ( p , q ) ∝ α (( p − q ) 2 ) S 0 ,νµ ( q − p ) γ µ W. Ah. Mian EW pion decay in FM June 20th, 2017 11 / 31

DSEs DSEs: Equation of motion for the correlation functions Pure QCD: − 1 − 1 = + d 4 q � P − 1 ( p 2 ) = P − 1 (2 π ) 4 g γ ν S νµ ( q − p ) P ( q 2 )Γ µ ( p , q ) + 0 Rainbow-Truncation gS νµ ( q − p )Γ µ ( p , q ) ∝ α (( p − q ) 2 ) S 0 ,νµ ( q − p ) γ µ W. Ah. Mian EW pion decay in FM June 20th, 2017 11 / 31

Maris-Tandy Coupling 2 πγ m [1 − exp ( − q 2 t )] α ( q 2 ) = π ω 6 Dq 4 e − q 2 m 2 ω 2 + ln[e 2 − 1 + (1 + q 2 QCD ) 2 ] Λ 2 12 Λ QCD =0 . 234 GeV 10 ω =0 . 4 GeV 8 D =0 . 93 GeV 6 m t =1 . 0 GeV 4 12 γ m = 2 11 N c − 2 N f 0 12 1e-06 1e-04 1e-02 1 100 10000 1e+06 1e+08 = p 2 [GeV 2 ] 11 · 3 − 2 · 2 ( P. Maris and P. C. Tandy, PRC 60, 055214 (1999)) W. Ah. Mian EW pion decay in FM June 20th, 2017 12 / 31

Wavefunctionrenormalization 1 chiral up 0.95 down strange charm 0.9 bottom top 0.85 Z ( p 2 ) 0.8 0.75 0.7 0.65 0.6 1e-06 0.0001 0.01 1 100 10000 1e+06 p 2 [GeV 2 ] W. Ah. Mian EW pion decay in FM June 20th, 2017 13 / 31

Massfunction 1 chiral up 0.1 down strange M ( p 2 ) [GeV] 0.01 0.001 0.0001 1e-05 1e-06 1e-07 1e-08 1e-06 0.0001 0.01 1 100 10000 1e+06 p 2 [GeV 2 ] W. Ah. Mian EW pion decay in FM June 20th, 2017 14 / 31

DSEs   − 1 − 1             = +               Weak interaction: Non-vanishing diagonal elements By inversion: Quark propagators of different flavor influence each other W. Ah. Mian EW pion decay in FM June 20th, 2017 15 / 31

Axial channel chiral 0.2 g w =0 g w =0.01 0 g w =0.1 Positive in UV g w =0.2 -0.2 g w =0.3 ~(p 2 ) [1/GeV 2 ] g w =0.4 -0.4 -0.6 -0.8 Negative in IR C Existence of a transition scale -1 -1.2 -1.4 10 -6 10 -4 10 -2 10 2 10 4 10 6 10 8 1 p 2 [GeV 2 ] W. Ah. Mian EW pion decay in FM June 20th, 2017 16 / 31

Axial channel m u =2.3MeV and m d =4.8MeV, g w =10 -5 1x10 -10 up down 0 -1x10 -10 ~(p 2 ) [1/GeV 2 ] -2x10 -10 Same behavior as in the chiral limit -3x10 -10 C -4x10 -10 -5x10 -10 -6x10 -10 10 -6 10 -4 10 -2 10 2 10 4 10 6 10 8 1 p 2 [GeV 2 ] W. Ah. Mian EW pion decay in FM June 20th, 2017 17 / 31

Axial channel m u =2.3MeV and m d =4.8MeV, g w =5x10 -5 2x10 -8 up down 1x10 -8 ~(p 2 ) [1/GeV 2 ] 0 -1x10 -8 Existence of a threshold strength: Qualitative change -2x10 -8 C -3x10 -8 -4x10 -8 10 -6 10 -4 10 -2 10 2 10 4 10 6 10 8 1 p 2 [GeV 2 ] W. Ah. Mian EW pion decay in FM June 20th, 2017 18 / 31