The QCD coupling from CLAS data A. Deur Thomas Jefferson National - PowerPoint PPT Presentation

The QCD coupling from CLAS data A. Deur Thomas Jefferson National Accelerator Facility 1 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

Outline • Coupling constants are not constant at high energy. Why is that? (why are they running?) Effective couplings. • For QCD, the perturbative definition of the coupling doesn’t work at low energy. Can we extend the effective coupling approach to low energy? • If so, can the CLAS data be used to get α s at low energy? • Now that we have some kind of coupling at low energy, is it useful? Does it work? • What do we learn from all this? 2 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

Effective couplings Force = coupling constant × charge 1 × charge 2 × f(r) 1 (2 static bodies) (for linear theories with massless force carriers) r 2 magnitude of the force ~amount of matter Faraday: 1/r 2 : weakening of the force flux as it spreads isotropically through space. Nowadays: manifestation in the coordinate space of the propagator of the force carrier. 3 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

Effective couplings Force = coupling constant × charge 1 × charge 2 × f(r) 1 r 2 Faraday: 1/r 2 : weakening of the force flux as it spreads isotropically through space. Nowadays: manifestation in the coordinate space of the propagator of the force carrier. e - e - Ex: Electron scattering: γ * Q 2 In momentum space, scattering amplitude ∝ propagator 1/Q 2 . ⇒ Potential in coordinate space ∝ FT(amplitude) ∝ 1/r. ⇒ Force ∝ 1/r 2 . 4 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

Effective couplings But is a first order approximation. ... Higher orders: (not in QED) f e a c b d (QED: Effect of other graphs cancel each The loop affects the propagator. others (“b+c=0”) or do not affect definition of coupling (d). More complicated for QCD) Force=coupling constant × charge 1 × charge 2 × f(r) 1 r 2 We keep f(r)=1/r 2 and fold the additional distance dependence in the coupling. ⇒ Effective coupling. Now depends on distance (i.e. energy) scale. Loops such as lead to infinite probability amplitudes. Theories need to be regularized and renormalized. ⇒ Coupling depends on method: renormalization scheme dependence. 5 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

The strong coupling α s (r) α s (r) is well understood at short distances where it is small ( α s ~0.1). (pQCD). Very active research to understand it at long distances where it is large ( α s ~1, non-perturbative domain). α s (r) at large distance, work done in collaboration with: V. Burkert, J-P Chen and W. Korsch (experimental). PLB 650 244 (2007), PLB 665 349 (2008) S. J. Brodsky and G. de Teramond (phenomenology). PRD 81 ,096010 (2010), PLB 750 , 528 (2015), PLB 757 , 275 (2016) arXiv:1604.04933 Review on α s with S. J. Brodsky and G. de Teramond. Prog. Part. Nuc. Phys. 90 1 (2016) 6 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

The strong coupling at short distances α s is not constant due to loops in gluon propagator: + + ... • α s becomes small at short distances (large Q 2 ) ⇒ Asymptotic freedom, pQCD. α s (Q 2 ) is well defined within pQCD. s • α s becomes large at long distances (necessary ingredient to quark confinement) 7 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

The strong coupling at short distances At low Q 2 ( ≲ 1GeV 2 ), pQCD cannot be used to define α s : If pQCD is trusted, α s →∞ for Q →Λ s . Contradict the perturbative hypothesis s 8 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

The strong coupling at short distances At low Q 2 ( ≲ 1GeV 2 ), pQCD cannot be used to define α s : If pQCD is trusted, α s →∞ for Q →Λ s . Contradict the perturbative hypothesis Definition and computation of α s at long distance? s 9 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

α s (r) at long distance (low Q 2 ) Prescription: Define effective couplings from an observable’s perturbative series truncated to first order in α s . G. Grunberg , PLB B95 70 (1980); PRD 29 2315 (1984); PRD 40 680(1989). Proposed for pQCD. We tentatively extend it to non-perturbative QCD. 10 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

α s (r) at long distance (low Q 2 ) Prescription: Define effective couplings from an observable’s perturbative series truncated to first order in α s . G. Grunberg , PLB B95 70 (1980); PRD 29 2315 (1984); PRD 40 680(1989). Ex: Bjorken sum rule: 1 M 2 α s α s + [a 2 ( α s )+4d 2 ( α s )+4f 2 ( α s )]+... ∫ ( g p 1 -g n 1 )dx ≙ Γ 1 p-n = g A (1- -3.58( ) 2 -...) π 6 π 9Q 2 Spin Higher twist structure Nucleon axial pQCD corrections. corrections. Related to functions. charge. ( Here in the MS confinement forces. scheme. 1 st order in α s is scheme independent ) 11 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

α s (r) at long distance (low Q 2 ) Prescription: Define effective couplings from an observable’s perturbative series truncated to first order in α s . G. Grunberg , PLB B95 70 (1980); PRD 29 2315 (1984); PRD 40 680(1989). Ex: Bjorken sum rule: 1 M 2 α s α s + [a 2 ( α s )+4d 2 ( α s )+4f 2 ( α s )]+... ∫ ( g p 1 -g n 1 )dx ≙ Γ 1 p-n = g A (1- -3.58( ) 2 -...) π 6 π 9Q 2 Spin Higher twist structure Nucleon axial pQCD corrections. corrections. Related to functions. charge. ( Here in the MS confinement forces. scheme. 1 st order in α s is scheme independent ) 12 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

α s (r) at long distance (low Q 2 ) Prescription: Define effective couplings from an observable’s perturbative series truncated to first order in α s . G. Grunberg , PLB B95 70 (1980); PRD 29 2315 (1984); PRD 40 680(1989). Ex: Bjorken sum rule: 1 M 2 α s α s + [a 2 ( α s )+4d 2 ( α s )+4f 2 ( α s )]+... ∫ ( g p 1 -g n 1 )dx ≙ Γ 1 p-n = g A (1- -3.58( ) 2 -...) π 6 π 9Q 2 Spin Higher twist structure Nucleon axial pQCD corrections. corrections. Related to functions. charge. ( Here in the MS confinement forces. scheme. 1 st order in α s is scheme independent ) α g1 1 ⇒ Γ 1 p-n ≙ g A (1- ) π 6 α g1 = “ α s in the g 1 scheme” i.e. α s obtained using the Bjorken sum ∫ g p-n 1 dx. 13 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

α s (r) at long distance (low Q 2 ) Prescription: Define effective couplings from an observable’s perturbative series truncated to first order in α s . G. Grunberg , PLB B95 70 (1980); PRD 29 2315 (1984); PRD 40 680(1989). Ex: Bjorken sum rule: 1 M 2 α s α s + [a 2 ( α s )+4d 2 ( α s )+4f 2 ( α s )]+... ∫ ( g p 1 -g n 1 )dx ≙ Γ 1 p-n = g A (1- -3.58( ) 2 -...) π 6 π 9Q 2 Spin Higher twist structure Nucleon axial pQCD corrections. corrections. Related to functions. charge. ( Here in the MS confinement forces. scheme. 1 st order in α s is scheme independent ) α g1 1 ⇒ Γ 1 p-n ≙ g A (1- ) π 6 This means that short distance pQCD effects and long distance confinement forces are now folded into the definition of α s . Analogy with the original coupling constant becoming an effective coupling when short distance quantum effects are folded into its definition. 14 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

α s (r) at long distance (low Q 2 ) Advantages of extracting α s from the Bjorken Sum Rule: Bjorken sum rule: simple perturbative series. Data (CLAS!) exist at low, intermediate, and high Q 2 . p-n in the unmeasured Q 2 → 0 and Rigorous Sum Rules dictate the behavior of Γ 1 Q 2 →∞ regions. ⇒ We can obtain α g1 at any Q 2 . 15 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

α g1 from the Bjorken Sum data Bjorken sum Γ 1 p-n measurement ! 1p-n pQCD leading twist 0.2 0.15 JLab EG1-DVCS 0.1 JLab EG1b JLab RSS JLab E94010/EG1a JLab EG1a DESY HERMES 0.05 SLAC E143 SLAC E155 CERN COMPASS (2015) 0 0 1 2 3 4 5 A. Deur et al. PRD 90, 012009 (2014) Q 2 (GeV 2 ) 16 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

α g1 from the Bjorken Sum data Bjorken sum Γ 1 p-n measurement ! 1p-n pQCD leading twist 0.2 0.15 JLab EG1-DVCS 0.1 JLab EG1b JLab RSS JLab E94010/EG1a JLab EG1a DESY HERMES 0.05 SLAC E143 SLAC E155 CERN COMPASS (2015) 0 0 1 2 3 4 5 A. Deur et al. PRD 90, 012009 (2014) Q 2 (GeV 2 ) 17 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016

α g1 from the Bjorken Sum data Bjorken sum Γ 1 p-n measurement ! 1p-n ! g1 (Q)/ " pQCD leading twist 0.2 1 � ! g1 / " DESY HERMES ! g1 / " CERN COMPASS ! g1 / " SLAC E142/E143 ! g1 / " SLAC E154/E155 0.15 ��� ! g1 / " JLab RSS ! g1 / " CERN SMC α g1 1 p-n = g A (1- ) Γ 1 JLab EG1-DVCS π 6 ��� 0.1 JLab EG1b JLab RSS JLab E94010/EG1a JLab EG1a ��� DESY HERMES 0.05 SLAC E143 SLAC E155 CERN COMPASS (2015) ��� 0 ! g1 / " JLab CLAS (2008) ! g1 / " JLab CLAS (2014) ! g1 / " Hall A/CLAS 010 -1 � 0 1 2 3 4 5 � � 1 � � � A. Deur et al. PRD 90, 012009 (2014) Q 2 (GeV 2 ) Q (GeV) Q 2 (GeV 2 ) 18 A. Deur CLAS Col. Meeting 11/02/16 Wednesday, November 2, 2016