Conformal Finite Size Scaling of Conformal Finite Size Scaling of - PowerPoint PPT Presentation

Conformal Finite Size Scaling of Twelve Fermion Conformal Finite Size Scaling of Conformal Finite Size Scaling of Flavors Chik Him Wong Twelve Fermion Flavors Twelve Fermion Flavors Outline Background Conformality Controversy Simulation Setup Spectroscopy Analysis Fitting under Chik Him Wong conformal hypothesis with FSS Fitting scaling function with physical model Lattice Higgs Collaboration (LHC): Fitting general scaling function using B-form Zoltán Fodor $ , Kieran Holland ∗ , spline functions Julius Kuti † , Dániel Nógrádi − , Conclusion Chik Him Wong † †: University of California, San Diego *: University of the Pacific $: University of Wuppertal -: Eötvös University LATTICE 2012 1 / 19

Outline Outline Conformal Finite Size Scaling of Twelve Fermion Flavors Chik Him Wong Outline Background Background Conformality Controversy Conformality Controversy of N f = 12 SU ( 3 ) Fundamental Simulation Setup Simulation Setup Spectroscopy Analysis Spectroscopy Analysis Fitting under conformal Fitting under conformal hypothesis with Finite Size Scaling study hypothesis with FSS Fitting scaling function with physical model Fitting scaling function with physical model Fitting general scaling function using B-form spline functions Fitting general scaling function using B-form spline functions Conclusion Conclusion Outstanding Problems Future Plans 2 / 19

Conformality Controversy of Conformality Controversy of Conformal Finite Size Scaling of N f = 12 SU ( 3 ) Fundamental N f = 12 SU ( 3 ) Fundamental Twelve Fermion Flavors Chik Him Wong Outline Is N f = 12 SU ( 3 ) Fundamental inside Conformal Window? Background Conformality Controversy Simulation Setup Spectroscopy Analysis Fitting under conformal hypothesis with FSS Fitting scaling function with physical model Fitting general scaling function using B-form Previously. . . spline functions Conclusion Likely: T. Appelquist et al, A. Deuzeman et al,A Hasenfratz et al, Y. Aoki et al Not Likely: X.-Y. Jin et al, Z. Fodor et al Latest findings of our group: Finite Size Scaling Conformal scenario is Inconsistent and Suspect 3 / 19

Conformality Controversy of Conformality Controversy of Conformal Finite Size Scaling of N f = 12 SU ( 3 ) Fundamental N f = 12 SU ( 3 ) Fundamental Twelve Fermion Flavors Chik Him Wong Outline Is N f = 12 SU ( 3 ) Fundamental inside Conformal Window? Background Conformality Controversy Simulation Setup Spectroscopy Analysis Fitting under conformal hypothesis with FSS Fitting scaling function with physical model Fitting general scaling function using B-form Previously. . . spline functions Conclusion Likely: T. Appelquist et al, A. Deuzeman et al,A Hasenfratz et al, Y. Aoki et al Not Likely: X.-Y. Jin et al, Z. Fodor et al Latest findings of our group: Finite Size Scaling Conformal scenario is Inconsistent and Suspect 3 / 19

Conformality Controversy of Conformality Controversy of Conformal Finite Size Scaling of N f = 12 SU ( 3 ) Fundamental N f = 12 SU ( 3 ) Fundamental Twelve Fermion Flavors Chik Him Wong Outline Is N f = 12 SU ( 3 ) Fundamental inside Conformal Window? Background Conformality Controversy Simulation Setup Spectroscopy Analysis Fitting under conformal hypothesis with FSS Fitting scaling function with physical model Fitting general scaling function using B-form Previously. . . spline functions Conclusion Likely: T. Appelquist et al, A. Deuzeman et al,A Hasenfratz et al, Y. Aoki et al Not Likely: X.-Y. Jin et al, Z. Fodor et al Latest findings of our group: Finite Size Scaling Conformal scenario is Inconsistent and Suspect 3 / 19

Conformality Controversy of Conformality Controversy of Conformal Finite Size Scaling of N f = 12 SU ( 3 ) Fundamental N f = 12 SU ( 3 ) Fundamental Twelve Fermion Flavors Chik Him Wong Outline Is N f = 12 SU ( 3 ) Fundamental inside Conformal Window? Background Conformality Controversy Simulation Setup Spectroscopy Analysis Fitting under conformal hypothesis with FSS Fitting scaling function with physical model Fitting general scaling function using B-form Previously. . . spline functions Conclusion Likely: T. Appelquist et al, A. Deuzeman et al,A Hasenfratz et al, Y. Aoki et al Not Likely: X.-Y. Jin et al, Z. Fodor et al Latest findings of our group: Finite Size Scaling Conformal scenario is Inconsistent and Suspect 3 / 19

Conformality Controversy of Conformality Controversy of Conformal Finite Size Scaling of N f = 12 SU ( 3 ) Fundamental N f = 12 SU ( 3 ) Fundamental Twelve Fermion Flavors Chik Him Wong Outline Is N f = 12 SU ( 3 ) Fundamental inside Conformal Window? Background Conformality Controversy Simulation Setup Spectroscopy Analysis Fitting under conformal hypothesis with FSS Fitting scaling function with physical model Fitting general scaling function using B-form Previously. . . spline functions Conclusion Likely: T. Appelquist et al, A. Deuzeman et al,A Hasenfratz et al, Y. Aoki et al Not Likely: X.-Y. Jin et al, Z. Fodor et al Latest findings of our group: Finite Size Scaling Conformal scenario is Inconsistent and Suspect 3 / 19

Simulation Setup Simulation Setup Conformal Finite Size Scaling of Twelve Fermion Flavors Chik Him Wong Action: Tree-level Symanzik-Improved gauge action with Outline Staggered N f = 12 Fundamental fermions Background HMC algorithm with multiple time scales and Omelyan integrator Conformality Controversy Simulation Setup Autocorrelations monitored by time histories of Fermion Spectroscopy condensate,plaquette and correlators Analysis β ≡ 6 / g 2 = 2 . 20, which is in the Weak Coupling regime Fitting under conformal hypothesis with FSS V 12 4 m 0 . 02, m 0 . 01, V 16 4 Fitting scaling function 2 with physical model we are here Fitting general scaling 1 m function using B-form ψψ � spline functions a 3 � ¯ 1/2 Conclusion our simulations here 1/4 1/8 intermediate intermediate phase phase 1 . 2 1 . 4 1 . 6 1 . 8 2 . 0 2 . 2 2 . 4 β . β C. Schroeder et al A. Hasenfratz et al 4 / 19

Simulation Setup Simulation Setup Conformal Finite Size Scaling of Twelve Fermion Flavors Chik Him Wong Action: Tree-level Symanzik-Improved gauge action with Outline Staggered N f = 12 Fundamental fermions Background HMC algorithm with multiple time scales and Omelyan integrator Conformality Controversy Simulation Setup Autocorrelations monitored by time histories of Fermion Spectroscopy condensate,plaquette and correlators Analysis β ≡ 6 / g 2 = 2 . 20, which is in the Weak Coupling regime Fitting under conformal hypothesis with FSS V 12 4 m 0 . 02, m 0 . 01, V 16 4 Fitting scaling function 2 with physical model we are here Fitting general scaling 1 m function using B-form ψψ � spline functions a 3 � ¯ 1/2 Conclusion our simulations here 1/4 1/8 intermediate intermediate phase phase 1 . 2 1 . 4 1 . 6 1 . 8 2 . 0 2 . 2 2 . 4 β . β C. Schroeder et al A. Hasenfratz et al 4 / 19

Simulation Setup Simulation Setup Conformal Finite Size Scaling of Twelve Fermion Flavors Chik Him Wong Action: Tree-level Symanzik-Improved gauge action with Outline Staggered N f = 12 Fundamental fermions Background HMC algorithm with multiple time scales and Omelyan integrator Conformality Controversy Simulation Setup Autocorrelations monitored by time histories of Fermion Spectroscopy condensate,plaquette and correlators Analysis β ≡ 6 / g 2 = 2 . 20, which is in the Weak Coupling regime Fitting under conformal hypothesis with FSS V 12 4 m 0 . 02, m 0 . 01, V 16 4 Fitting scaling function 2 with physical model we are here Fitting general scaling 1 m function using B-form ψψ � spline functions a 3 � ¯ 1/2 Conclusion our simulations here 1/4 1/8 intermediate intermediate phase phase 1 . 2 1 . 4 1 . 6 1 . 8 2 . 0 2 . 2 2 . 4 β . β C. Schroeder et al A. Hasenfratz et al 4 / 19

Simulation Setup Simulation Setup Conformal Finite Size Scaling of Twelve Fermion Flavors Chik Him Wong Action: Tree-level Symanzik-Improved gauge action with Outline Staggered N f = 12 Fundamental fermions Background HMC algorithm with multiple time scales and Omelyan integrator Conformality Controversy Simulation Setup Autocorrelations monitored by time histories of Fermion Spectroscopy condensate,plaquette and correlators Analysis β ≡ 6 / g 2 = 2 . 20, which is in the Weak Coupling regime Fitting under conformal hypothesis with FSS V 12 4 m 0 . 02, m 0 . 01, V 16 4 Fitting scaling function 2 with physical model we are here Fitting general scaling 1 m function using B-form ψψ � spline functions a 3 � ¯ 1/2 Conclusion our simulations here 1/4 1/8 intermediate intermediate phase phase 1 . 2 1 . 4 1 . 6 1 . 8 2 . 0 2 . 2 2 . 4 β . β C. Schroeder et al A. Hasenfratz et al 4 / 19