Dyson-Schwinger Equations approach to pseudoscalar poles - PowerPoint PPT Presentation

Dyson-Schwinger Equations approach to pseudoscalar poles contribution to HLbL piece of a m Pablo Roig work done in collaboration with Adnan Bashir & Khépani Raya ( to appear soon ) p 0 TFF DSE input from h c/b TFF 2 nd Plenary Workshop of the Muon g-2 Theory Initiative 18-22 June 2018, Helmholtz-Institut Mainz, Germany

p 0 TFF from Dyson-Schwinger equations K. Raya, L. Chang, A. Bashir, J. J. Cobos-Martínez, L. X. Gutiérrez-Guerrero, C. D. Roberts, P. C. Tandy Phys.Rev. D93 (2016) no.7, 074017 Without ERBL evolution Rainbow-ladder truncation + ERBL evolution of the p Lepage, Brodsky ‘80 Bethe-Salpeter amplitude CELLO data CLEO data BaBar data Belle data 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

p 0 TFF from Dyson-Schwinger equations K. Raya, L. Chang, A. Bashir, J. J. Cobos-Martínez, L. X. Gutiérrez-Guerrero, C. D. Roberts, P. C. Tandy Phys.Rev. D93 (2016) no.7, 074017 As a result of solving DSE, we end up with a numerical solution for the p 0 TFF. 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

p 0 TFF from Dyson-Schwinger equations K. Raya, L. Chang, A. Bashir, J. J. Cobos-Martínez, L. X. Gutiérrez-Guerrero, C. D. Roberts, P. C. Tandy Phys.Rev. D93 (2016) no.7, 074017 As a result of solving DSE, we end up with a numerical solution for the p 0 TFF. But how can we parametrize it analytically to compute the p 0 pole contribution to a m ? 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

p 0 TFF from Dyson-Schwinger equations K. Raya, L. Chang, A. Bashir, J. J. Cobos-Martínez, L. X. Gutiérrez-Guerrero, C. D. Roberts, P. C. Tandy Phys.Rev. D93 (2016) no.7, 074017 As a result of solving DSE, we end up with a numerical solution for the p 0 TFF. But how can we parametrize it analytically to compute the p 0 pole contribution to a m ? We first tried using LMD+V (Knecht & Nyffeler’02, Jegerlehner & Nyffeler’09) but it was not good enough to fit the data 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

p 0 TFF from Dyson-Schwinger equations K. Raya, L. Chang, A. Bashir, J. J. Cobos-Martínez, L. X. Gutiérrez-Guerrero, C. D. Roberts, P. C. Tandy Phys.Rev. D93 (2016) no.7, 074017 As a result of solving DSE, we end up with a numerical solution for the p 0 TFF. But how can we parametrize it analytically to compute the p 0 pole contribution to a m ? We first tried using LMD+V (Knecht & Nyffeler’02, Jegerlehner & Nyffeler’09) but it was not good enough to fit the data We decided to include an additional multiplet of resonances ( LMD+V+V’ ) and it worked. (K. Raya, A. Bashir & P. Roig) 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

p 0 TFF from Dyson-Schwinger equations K. Raya, L. Chang, A. Bashir, J. J. Cobos-Martínez, L. X. Gutiérrez-Guerrero, C. D. Roberts, P. C. Tandy Phys.Rev. D93 (2016) no.7, 074017 As a result of solving DSE, we end up with a numerical solution for the p 0 TFF. But how can we parametrize it analytically to compute the p 0 pole contribution to a m ? We first tried using LMD+V (Knecht & Nyffeler’02, Jegerlehner & Nyffeler’09) but it was not good enough to fit the data We decided to include an additional multiplet of resonances ( LMD+V+V’ ) and it worked. (K. Raya, A. Bashir & P. Roig) It also gave us a chance to improve the BL limit when the non-asymptotic photon is not real . 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

p 0 TFF from Dyson-Schwinger equations K. Raya, L. Chang, A. Bashir, J. J. Cobos-Martínez, L. X. Gutiérrez-Guerrero, C. D. Roberts, P. C. Tandy Phys.Rev. D93 (2016) no.7, 074017 As a result of solving DSE, we end up with a numerical solution for the p 0 TFF. But how can we parametrize it analytically to compute the p 0 pole contribution to a m ? We first tried using LMD+V (Knecht & Nyffeler’02, Jegerlehner & Nyffeler’09) but it was not good enough to fit the data We decided to include an additional multiplet of resonances ( LMD+V+V’ ) and it worked. (K. Raya, A. Bashir & P. Roig) It also gave us a chance to improve the BL limit when the non-asymptotic photon is not real . LMD+V+V’ can be of interest for lattice Colls. in order to parametrize their data. 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ (LMD+V corresponds to N=2) 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ (LMD+V corresponds to N=2) It corresponds to N=3, LMD+V+V’ 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ (LMD+V corresponds to N=2) It corresponds to N=3, LMD+V+V’ First row corresponds to LMD+V 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ (LMD+V corresponds to N=2) It corresponds to N=3, LMD+V+V’ First row corresponds to LMD+V It can be rewritten as (Knecht & Nyffeler’02) 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ 0 0 (to fulfil QCD asymptotics ) 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ ABJ anomaly : 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ Allows for (seeming) small violations due to data non being asymptotic ABJ anomaly: Fully asymmetric BL : 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ Allows for (seeming) small violations due to data non being asymptotic ABJ anomaly: Fully asymmetric BL: Symmetric asymptotic limit ( Novikov et. al. ): 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ Allows for (seeming) small violations due to data non being asymptotic ABJ anomaly: Fully asymmetric BL: Symmetric asymptotic limit ( Novikov et. al. ): If subleading corrections are taken into account: We obtain a larger (and opposite in sign) value 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ ABJ anomaly: Fully asymmetric BL: Symmetric asymptotic limit ( Novikov et. al. ): 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ ABJ anomaly: Fully asymmetric BL: Symmetric asymptotic limit ( Novikov et. al. ): The BL limit must not change when the non-asymptotic photon is virtual : 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ ABJ anomaly: Fully asymmetric BL: Symmetric asymptotic limit ( Novikov et. al. ): The BL limit must not change when the non-asymptotic photon is virtual : 2 ~ M V1 2 ,-0.9 c 12 M V1 2 ] works remarkably well, since the dominant region is around Q 0 2 ~ M r 2 . However, c21 ͼ [-1.1 c 12 M V1 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ ABJ anomaly: Fully asymmetric BL: Symmetric asymptotic limit ( Novikov et. al. ): The BL limit must not change when the non-asymptotic photon is virtual : 2 ~ M V1 2 ,-0.9 c 12 M V1 2 ] works remarkably well, since the dominant region is around Q 0 2 ~ M r 2 . However, c21 ͼ [-1.1 c 12 M V1 From the subleading terms , we get 2 ~ M r 2 Approximately satisfied (within 9%) for Q 0 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ ABJ anomaly: Fully asymmetric BL: Symmetric asymptotic limit ( Novikov et. al. ): The BL limit must not change when the non-asymptotic photon is virtual: 2 ~ M V1 2 ,-0.9 c 12 M V1 2 ] works remarkably well, since the dominant region is around Q 0 2 ~ M r 2 . However, c21 ͼ [-1.1 c 12 M V1 From the subleading terms, we get 2 ~ M r 2 Approximately satisfied (within 9%) for Q 0 It is seen, a posteriori, that M V2,3 can be identified with M r ’ , M r ’’ 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’ 2 ) because we are dealing with p 0 pole contributions 2 ,Q 2 No other corrections enter P(Q 1 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m

(K. Raya, A. Bashir & P. Roig) p 0 TFF & LMD+V+V’, fit results 2 nd Plenary Workshop of the Muon g-2 Theory Initiative HLbL DSE approach to P poles in a m