PoS(SPIN2018)123 https://pos.sissa.it/ ∗ Speaker. The crisis arose some 30periment years on ago polarized following DIS. results Since of then a manyare European people too have naive, Collaboration pointed yet out ex- papers that continue the toinvolved arguments appear in involved giving devoted a to precise “the statement spin of crisis". the We spin explain sum the rule subtleties and clarify why there is really no crisis. ∗ Copyright owned by the author(s) under the terms of the Creative Commons c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). 23rd International Spin Physics Symposium -10-14 SPIN2018 September, 2018 - Ferrara, Italy Imperial College London Elliot Leader [email protected] The Non-existence of the Spin Crisis PoS(SPIN2018)123 ) at 2 p 1 Q (1.1) (2.2) (1.2) (2.1) , Γ as the x ( 2 1 interpre- Q g Elliot Leader arises because 0 ) a 3 scheme, at leading / over naive N M MS , ≈  Q MS S M C ∆ Hence a measurement of dependence of ) 2 2 . Nonetheless papers keep appear- Q Q )( ( 0 of the singlet SU(3) current. Now the Q a ( 0 -decay. a 4 3 . β Q z + dx S ) x Q MS NS ∑ ( , where the p 1 C ) = g ∆ 2 1 1 ) N z Q 0 8 ( S Z ?????? a A crisis in the parton model: Where, oh where is the 0 1 3 ]). = ≡ 2 there is no such crisis 2 p 1 + Why Mauro Anselmino and E.L. published a paper in response / Γ 3 1 a  1 12 is scheme dependent. In the ) = 2 p 1 30 years ago Γ Q bound state of 3 massive ( p , 1 = 2 Γ M  is effectively a measure of a 2 ]. 2 Nucleon Q 1 [ are the known singlet and non-singlet Wilson coefficients. can be obtained from neutron and hyperon 8 , C 3 ∆ a The Model of the nucleon had offered a fairly successful description of the nucleon and The controversy began some decades ago when the European Muon Collaboration (EMC) The quantity of interest is the first moment of the spin-dependent structure function are matrix elements of non-singlet SU(3) currents and 8 , 3 The nucleon corresponds to the groundan state, s-state. and for In any the reasonably behavedno simplest potential OAM non-relativistic this (orbital case, will angular for be momentum). theZ-direction constituents Hence, in for an a s-state, nucleon the at quarks rest, have say polarized in the positive twist, valid for where the a the baryon resonances: ing referring to “The proton spin crisis" . 1. The naive interpretation of the EMC results values of However, it has long been understood that to the results of the EMCproton’s experiment spin? entitled Because people have forgotten that the belief in a spin-crisis emerged from an published results of theirconstituents experiment of on the polarized proton could fully notproton inclusive provide had DIS, enough spin angular 1/2. which momentum And suggested to so explain that the the fact that the Spin Crisis tation of the EMC experiment. (Forsee a the modern review summary of of Kuhn, the Chen situation and and access Leader to [ the literature, 2. Theoretical interpretation of the EMC polarized DIS experimental results In NLO the expression for some value of Q the singlet current has to be renormalized, and it is customary and convenient to choose PoS(SPIN2018)123 (2.6) (4.3) (4.1) (4.2) (2.3) ) to hold ?? Elliot Leader 1, giving rise to the as to which operators  0 a ) s ∆ . + ii ii s 2 (2.4) z G z , ! Thus failure of Eq. ( ∆ / controversy ˆ ii L 2 1 G z G can Q hh ˆ ˆ L L = ) + ( + hh hh d ii ∆ + + G z proton z ˆ + ii S ii S z q z , d hh ˆ . L , especially in the case of the massless . = ∆ 1 (2.5) 1 # q can + hh i ˆ # L ¯ = q z 2 = i ii + ¯ S ]). q z hh 0 q z 0 ) + ( h 4 S a ˆ G a L u h ¯ + q ∆ ∆ ∑ ¯ hh q G , i.e. a function of ∑ + ) + + + ∆ 2 0 i + u q z a ii Q i + ∆ S q z ( q z 1 2 ( 0 ˆ h 0 S S a a h q ≡ = hh 2 1 ∑ 0 and later experiments confirmed that q ∑ " 2 1 = = ≈ " ∆Σ 2 0 1 2 2 1 a = = 0 , equal to a because the right hand side is a fixed number, whereas the left hand side ) parton model. However, naive there is no other source of angular momentum one expects ] and the review by Leader and Lorcé [ if 3 Clearly a correct relation between the spin of a nucleon and the angular momentum of its The sum rule relating the angular momentum (AM) of its constituents to the AM of the proton beyond the naive level cannot possibly be true constituents should include their OAMmuch and more a complicated contribution than from it the sounds, . because Unfortunately there this is is some cannot, in principle, be used to infer that there is a spin3. crisis. The Non-naive interpretation should be used to represent the (See [ implying, naively, . The EMC experiment gave spin crisis in the ( 4. Expression based on the canonical (can) version of the angular momentum Hence is, looks totally intuitive; can’t be incorrect! It is usually written in the Jaffe-Manohar form : but more correctly it should read : Spin Crisis renormalization scale. Now PoS(SPIN2018)123 ≈ G is G (6.1) (4.4) (4.5) (5.1) ∆ ∆ 0. = Elliot Leader + A DANGER! , but that the sum 0 or 2 Q = 0 . A 0 = + A ii| z , ii z G can , . , ˆ L 0 0 G Bel ˆ = = hh J 0 + hh A A + 0 + 2 the angular momentum sum rule becomes, = / ii Gauge + Gauge z 1 , A + ii| ii| q Bel z z 3 ii| , , ˆ L z , G can hh G can ˆ ˆ S q can S + ˆ L hh hh ii hh q z is not. = ˆ = S + ii G hh G z , G ∞ ∆ ∆ = ∆ G can 2 1 → S + hh P 0 . There are suggestions about how to measure the orbital AM terms, 2 a are also not gauge invariant. Thus all the gauge non-invariant operators 1 2 G , q = GeV ˆ L 2 1 10 ≈ 2 Q can be measured and seems to be relatively small, but not negligible, typically ] indicate significant contributions to the proton spin from the gluons (28%) and from the 32 for . 5 G 0 ∆ ± What appeared to be a spin crisis in the parton model, 30 years ago, was a consequence of a Finally for a fast moving proton with helicity All of the above utilized the canonical version of the angular momentum operators. There is 29 . In this case theoperators total are AM gauge of invariant theresults and [ gluons can is thus not be split studied into relatively spin simply and on orbital a parts. lattice. Also, Beautiful here, the orbital AM of the up,contributions from down the and constituents can strange at quarks leastof (48%). be any estimated sort via of So, lattice crisis. in calculations, there the is Belinfante no hint version, where the 7. Conclusions misinterpretation of the results of the European Muon Collaboration experiment on polarized deep appearing in the Jaffe-Manohar sum rule should be evaluated in the gauge also a perfectly good sum rule based on the Belinfante version of the operators: Spin Crisis But is the Jaffe-Manohar form reallya gauge identical invariant to quantity the but original canonicalHowever one form??? can show that or, as the nucleon momentum Moreover the operators 5. Rigorous statement of AM sum rule It should not be forgotten thatis each not. individual term in is actuallyNow a function of 0 but as yet there are noterms experimental results. and thus So to the challenge check is whetheris to the or find sum is a rule not way holds. a to spin Only measure crisis. then the orbital will one be able to6. claim that A there different version of the sum rule in contrast to the naive result PoS(SPIN2018)123 , Prog. ]. , , Elliot Leader 1203.6388 (2011) 164 [ Quark and Glue Momenta and Angular LATTICE2011 PoS 4 , ]. ]. . models the spin of the nucleon is built up largely from the Spin Structure of the Nucleon - Status and Recent Results ]. (1988) 239 1101.5956 0812.3535 [ A CRISIS IN THE PARTON MODEL: WHERE, OH WHERE IS THE [ quarks, and the smallness of the spin contribution of the partonic C41 The angular momentum controversy: What’s it all about and does it matter? (2009) 1 1309.4235 Z.Phys. , partonic constituent quark 63 (2011) 096012 (2013) [ On the controversy concerning the definition of quark and gluon angular momentum D83 .... Phys.Rept. Momenta in the Proton — a Lattice Calculation Phys.Rev. PROTON’S SPIN? Part. Nucl. Phys. [4] E. Leader and C. Lorce, [2] S. E. Kuhn, J. P. Chen and E. Leader, [5] K. Liu, M. Deka, T. Doi, Y. Yang, B. Chakraborty et al., spins of its constituents. This is not truequarks for is not unreasonable, givenand that that they the certainly gluons, too, possesssum carry orbital rule some angular it angular momentum momentum. is ashave known well, In experimental from the results usual experiment about canonical that theabsolutely form the no quark of basis and gluon the for gluon spin spin the assertion orbital isMoreover that an angular non-negligible, there alternative momentum, version is but of a so the we nucleon spin thatcan spin sum do there be crisis. rule not measured based is on on yet Belinfante a operators, lattice, where likewise, all shows terms absolutely no signs ofReferences a crisis. [1] E. Leader and M. Anselmino, [3] E. Leader, Spin Crisis inelastic scattering. This was caused bypartonic a failure quarks. to distinguish In adequately between constituent and