High Energy Transverse Single-Spin Asymmetry Past, Present and Future

Transcription

1 High Energy Transverse Single-Spin Asymmetry Past, Present and Future Jianwei Qiu Brookhaven National Laboratory Stony Brook University

2 Transverse single-spin asymmetry (TSSA) q Consistently observed for almost 40 years! ANL 4.9 GeV BNL 6.6 GeV FNAL 20 GeV BNL 62.4 GeV q Definition: BNL 200 GeV s p Left Right

3 Transverse single-spin asymmetry (TSSA) q Consistently observed for almost 40 years!

4 q Early attempt: Cross section: Do we understand it? AB(p T, ~s) / Kane, Pumplin, Repko, PRL, 1978 m Asymmetry: q AB(p T,~s) AB(p T, ~s ) = / s p T q What do we need? Too small to explain available data! A N / i~s p (~p h ~p T ) ) i µ p hµ s p p 0 h Need a phase, a spin flip, enough vectors q Vanish without parton s transverse motion: A direct probe for parton s transverse motion, Spin-orbital correlation, QCD quantum interference

5 Current understanding of TSSAs q Symmetry plays important role: Inclusive DIS Single scale Q Parity Time-reversal A N = 0 q One scale observables Q >> Λ QCD : Collinear factorization Twist-3 distributions SIDIS: Q ~ P T DY: Q ~ P T ; Jet, Particle: P T q Two scales observables Q 1 >> Q 2 ~ Λ QCD : TMD factorization TMD distributions SIDIS: Q>>P T DY: Q>>P T or Q<<P T

6 How collinear factorization generates TSSA? q Collinear factorization beyond leading power: p, ~s k (Q, ~s) / t 1/Q 2 Expansion Too large to compete! Three-parton correlation q Single transverse spin asymmetry: Efremov, Teryaev, 82; Qiu, Sterman, 91, etc. (s T ) / T (3) (x, x) ˆT D(z)+ q(x) ˆD D (3) (z,z)+... T (3) (x, x) / D (3) (z,z) / Qiu, Sterman, 1991, Kang, Yuan, Zhou, 2010 Integrated information on parton s transverse motion! Needed Phase: Integration of dx using unpinched poles

7 Twist-3 distributions relevant to A N q Two-sets Twist-3 correlation functions: No probability interpretation! Kang, Qiu, 2009 q Twist-2 distributions: Role of color magnetic force! Unpolarized PDFs: Polarized PDFs: q Twist-3 fragmentation functions: See Kang, Yuan, Zhou, 2010, Kang 2010

8 Interpretation of twist-3 correlation functions q Measurement of direct QCD quantum interference: T (3) (x, x, S? ) / Qiu, Sterman, 1991, Interference between a single active parton state and an active two-parton composite state q Expectation value of QCD operators: apple Z hp, s (0) + (y ) P, si hp, s (0) + (y ) P, si? s T dy 2 F + (y 2 ) apple Z hp, s (0) + hp, s (0) + ig? s T dy 2 F + (y 2 ) 5 (y ) P, si (y ) P, si How to interpret the expectation value of the operators in RED?

9 A simple example q The operator in Red a classical Abelian case: Qiu, Sterman, 1998 q Change of transverse momentum: q In the c.m. frame: q The total change: Net quark transverse momentum imbalance caused by color Lorentz force inside a transversely polarized proton

10 Collinear twist-3 contribution to A N d (s T ) d (s T ) d ( s T ) SGP T FT (x, x) SFP T FT (0,x),... G FT (0,x),... Sivers-type function Also tri-gluon correlators at SGP

11 Collinear twist-3 contribution to A N d (s T ) d (s T ) d ( s T ) SGP T FT (x, x) H FU (x, x) SFP T FT (0,x),... G FT (0,x),... H FU (0,x),... Boer-Mulders-type function

12 Collinear twist-3 contribution to A N d (s T ) d (s T ) d ( s T ) SGP T FT (x, x) H FU (x, x) SFP T FT (0,x),... G FT (0,x),... H FU (0,x),... Ĥ(z),H(z), ĤFU(z,z 1 ),... Collins-type function

13 Collinear twist-3 contribution to A N d (s T ) d (s T ) d ( s T ) SGP T FT (x, x) H FU (x, x) SFP T FT (0,x),... G FT (0,x),... H FU (0,x),... Ĥ(z),H(z), ĤFU(z,z 1 ),... q Early work (before 2013): Assumed that SGP (Sivers-type) dominates the twist-3 contribution to TSSAs in: p " + p! (x F,p T )+X Qiu, Sterman (1991, 98) ² Growth in x F ² Slow fall off in p T

14 Collinear twist-3 contribution to A N d (s T ) d (s T ) d ( s T ) Negligible Kanazawa & Koike (2000)

15 Collinear twist-3 contribution to A N d (s T ) d (s T ) d ( s T ) Negligible Kanazawa & Koike (2000) q Twist-3 fragmentation contribution: Important Metz & Pitonyak (2013)

16 Collinear twist-3 contribution to A N q Fragmentation + QS (fix through Sivers function): Kanazawa, Koike, Metz, Pitonyak PRD 89(RC) (2014)

17 Test QCD at twist-3 level Kang, Qiu, 2009 q Scaling violation DGLAP evolution: Te Kqq K q,f (f ) TeG,F = (d) TeG,F (f ) Te G,F (d) Te G,F (x, x + x2, µ, st ) qq (f ) KGq (d) KGq K (f ) Gq K (d) Gq Kq K (f ) KqG q q K q (f f ) (f ) KG K K (f ) G Kq (d) qg K (f d) q KGG q KGG (df ) (dd) KGG (f ) G (d) G K KGG (d) KG (f ) qg (d) KqG (f ) q G K (d) q G KG (f f ) G KG (df ) KG G (dd) KG G (f d) G qk (f f ) GG K (f d) GG K (f f ) G G K (df ) GG K (dd) GG K (df ) (dd) G GK G G q (, + 2 ; x, x + x2, s ) Teq,F (d) G Kq K (f d) G G Z DGLAP for f2: Evolution for f3: q,f (f ) TeG,F (d) TeG,F (f ) Te G,F d q Evolution equation consequence of factorization: Factorization: Te Z (d) Te G,F d 2

18 Evolution kernels an example q Quark to quark: Kang, Qiu, 2009 Cut vertex and projection operator in LC gauge q Feynman diagram calculation: Z Z d d 2 T q,f (, + 2 ) Z Z d d 2 T q,f (, + 2 ) Z Z d Z µ 2 F dk 2 T k 2 T apple CA 2 s 2 T q,f (x, x) d 2 T q,f (, + 2 ) Z µ 2 F dk 2 T k 2 T apple CA 2 s 2 T q,f (x, x) + virtual loop diagrams

19 Current understanding of TSSAs q Symmetry plays important role: Inclusive DIS Single scale Q Parity Time-reversal A N = 0 q One scale observables Q >> Λ QCD : Collinear factorization Twist-3 distributions SIDIS: Q ~ P T DY: Q ~ P T ; Jet, Particle: P T q Two scales observables Q 1 >> Q 2 ~ Λ QCD : TMD factorization TMD distributions SIDIS: Q>>P T DY: Q>>P T or Q<<P T Brodsky et al. explicit calculation with m q =\=0

20 Semi-inclusive DIS (SIDIS) q Process: e(k)+n(p)! e 0 (k 0 )+h(p h )+X q Natural event structure: In the photon-hadron frame: P ht 0 Semi-Inclusive DIS is a natural observable with TWO very different scales Q P ht & QCD Localized probe sensitive to parton s transverse motion q Collinear QCD factorization holds if P ht integrated: d h!h 0 / f/h dˆ f!f 0 D f 0!h 0 (z) z = P h p q p y = q p k p q Total c.m. energy : s p =(p + q) 2 Q 2 apple 1 xb x B Q2 x B

21 Single hadron production at low p T q Unique kinematics - unique event structure: Briet frame: Large Q 2 virtual photon acts like a wall vs High energy low p T jet (or hadron) - ideal probe for parton s transverse motion! q Need for TMDs, if we observe p T ~ 1/fm: Z 1 1 d 4 k a H(Q, p T,k a,k b ) ka 2 + i" ka 2 T (k a, 1/r 0 ) i" Z applez dx 1 1 x d2 k a? H(Q, p T,ka 2 =0,k b ) dka 2 ka 2 + i" ka 2 T (k a, 1/r 0 ) i" Can t set k T ~ 0, since k T ~ p T TMD distribution

22 QCD factorization for SIDIS q Factorization: Ji, Ma, Yuan q Low P ht TMD factorization: q High P ht Collinear factorization: SIDIS(Q, P h?,x B,z h )=Ĥ(Q, P h?, s ) q P ht Integrated - Collinear factorization: SIDIS(Q, x B,z h )= H(Q, s ) f D f!h + O f D f!h + O 1 Q 1, 1 P h? Q

23 Factorized Drell-Yan cross section q TMD factorization ( q? Q ): The soft factor,, is universal, could be absorbed into the definition of TMD parton distribution q Collinear factorization ( q? Q ): + O(1/Q) q Spin dependence: The factorization arguments are independent of the spin states of the colliding hadrons same formula with polarized PDFs for γ*,w/z, H 0

24 How TMDs generate spin asymmetry? q Sivers effect Sivers function: Hadron spin influences parton s transverse motion q Collin s effect Collin s function: Transversity Parton s transverse spin affects its hadronization q Separation of different effects? Best in SIDIS, at EIC

25 Transition from low p T to high p T q Two-scale becomes one-scale: A N (Q 2,p T ) p T Q p T Q Q s p T TMD Collinear Factorization q TMD factorization to collinear factorization: Ji,Qiu,Vogelsang,Yuan, Koike, Vogelsang, Yuan Two factorization are consistent in the overlap region: QCD p T Q A N finite requires correlation of multiple collinear partons No probability interpretation! New opportunities!

26 Broken universality for TMDs q Definition: q Gauge links: SIDIS: DY: q Process dependence: Collinear factorized PDFs are process independent

27 Modified universality q Parity Time reversal invariance: q Definition of Sivers function: q Modified universality: Same function, but, opposite sign! q The sign change = Critical test of TMD factorization! Same applies to TMD gluon distribution Spin-averaged TMD is process independent

28 Sivers asymmetries from SIDIS q From SIDIS (HERMES and COMPASS) low Q: Non-zero Sivers effects Observed in SIDIS! Visible Q 2 dependence Major theory development in last few years Drell-Yan A N : COMPASS, RHIC run 17 th, Fermilab Drell-Yan,

29 A surprise story for TMDs q Fit the same low energy data Sivers function: q Very different predictions for A N at a higher energy: A N ( 1/3) W y A N W y

30 A surprise story for TMDs q Fit the same low energy data Sivers function: q Very different predictions for A N at a higher energy: A N ( 1/3) W y A N W y

31 Evolution equations for TMDs q Collins-Soper equation: b-space quark TMD with γ + Boer, 2001, 2009, JI, Ma, Yuan, 2004 Idilbi, et al, 2004, Kang, Xiao, Yuan, 2011 Aybat, Collins, Qiu, Rogers, 2011 Aybat, Prokudin, Rogers, 2012 Idilbi, et al, 2012, Sun, Yuan 2013, q RG equations: q Evolution equations for Sivers function: CS: RGs:

32 Sivers function q Sivers function: Differ from PDFs! Need non-perturbative large b T information for any value of Q! q What is the correct Q-dependence of the large b T tail? Q =μ with b max 1/2 GeV 1 g f/p (x, b T )+g K (b T )ln Q Q 0 apple g 1 + g 2 ln Q 2Q 0 + g 1 g 3 ln(10x) b 2 T Nonperturbative form factor Is the log(q) dependence sufficient? Choice of g 2 & b * affects Q-dep. The form factor and b * change perturbative results at small b T!

33 Q-dependence of the form factor q Q-dependence of the form factor : Konychev, Nadolsky, 2006 F NP (b, Q) =a(q 2 ) b 2 HERMES At Q ~ 1 GeV, ln(q/q 0 ) term may not be the dominant one! F NP b 2 (a 1 + a 2 ln(q/q 0 )+a 3 ln(x A x B )+...)+... Power correction? (Q 0 /Q) n -term? Better fits for HERMES data?

34 Parton k T at the hard collision q Sources of parton k T at the hard collision: Gluon shower P h P Confined motion xp, k T ` P h z,k0 T `0 Emergence of a hadron hadronization q Large k T generated by the shower (caused by the collision): ² Q 2 -dependence linear evolution equation of TMDs in b-space ² The evolution kernels are perturbative at small b, but, not large b The nonperturbative inputs at large b could impact TMDs at all Q 2 q Challenge: to extract the true parton s confined motion: ² Separation of perturbative shower contribution from nonperturbative hadron structure not as simple as PDFs

35 What controls the b-space distribution? q Features of perturbative calculation at small-b: Qiu, Zhang, 2001 b T Ff/P (b T,Q) q b-space distribution, and its Q and s dependence: Z-production Drell-Yan Upsilon p s =1.8 TeV p s = 27.4GeV p s =1.8 TeV

36 Small contribution from large-b T q Preserve calculated result at small b T : Qiu, Zhang, 2001 d resum AB!Z dq 2 T / Z 1 0 db J 0 (q T b) bw(b, Q) Intrinsic power corrections, g 1,g 2, All parameters, are fixed by the continuity of the W and its derivatives at b max excellent predictive power for observables with the saddle point at small enough b sp Leading twist Dynamical power corrections

37 Phenomenology Z 0 at the LHC Kang, Qiu, 2012 CMS pp-data NLO perturbative Resummed Same code Updated to CTEQ6 Effectively no non-perturbative uncertainty!

38 Phenomenology Higgs Berger, Qiu, 2003 Effectively no non-perturbative uncertainty!

39 Proposal from Collins and Roger q Resummed large b T behavior: Collins and Rogers, arxiv: g f/p (x, b T )+g K (b T )ln Q Q 0 apple g 1 + g 2 ln Q 2Q 0 + g 1 g 3 ln(10x) b 2 T Nonperturbative form factor + O(b 4 T )

40 Summary q QCD factorization/calculation have been very successful in interpreting HEP scattering data q What about the hadron structure? Not much! < 1/10 fm q Transverse spin opens up a new domain to test QCD dynamics and new observables for extracting partonic structure q Collinear and TMD factorization give complementary descriptions of QCD dynamics more work needed for TMDs q A new TMD Topical Collaboration was formed with theory, phenomenology and lattice efforts! Thank you!

41 Backup slices

42 Scaling violation of twist-3 correlations? ² Follow DGLAP at large x ² Large deviation at low x (stronger correlation) Kang, Qiu, PRD, 2009