# Presentation: 063392

## Status of Transverse Spin Physics

- Feng Yuan
- RBRC, Brookhaven National Laboratory

## Transverse spin physics at RHICII and eRHIC

- Double transverse spin asymmetry
- A_TT for Drell-Yan, jet, hadron, etc. to measure the quark transversity
- Single transverse spin asymmetry
- Various TMD physics (additional information on nucleon structure) see more in Gamberg’s talk
- Sivers function (PDF)
- Collins function (FF)
- ...

## What’s Single spin asymmetry?

- Single Transverse Spin
- Asymmetry (SSA)

- Final state particle is
- Azimuthal symmetric

- No hadronic single spin asymmetry
- Associated with SL

- Transverse plane

## Single Spin Asymmetry

- Its strong tied with the quark orbital angular momentum
- We have beautiful data
- Nontrivial QCD dynamics, and fundamental test of the factorization, and the universality of PDFs, FFs,...

## Transverse spin physics: a Renaissance

- Single transverse spin asymmetry has long been observed in high energy hadronic reactions (late 70’s and 80’s)
- Naïve Parton model fails to explain large Single transverse spin asymmetry (G. Kane et al, PRL41, 1978), we have to go beyond to understand the large SSAs
- Many activities in recent years

## SSAs in “Ancient” age: fixed target exp.

**Hadron production in p****"****p**
**Adams, et al., PLB264 (1991)**

**hadron production in p****"****p**
**A. Bravar et al.,E704, PRL77(1996)**

## SSAs in Modern era: RHIC

**Central rapidity!!**

- BRAHMS preliminary

- STAR

- PHENIX

**Large SSA continues at **
**Collider experiments!!**
**(Also in *****ep***** DIS exp.)**

## Why Does SSA Exist? 

**Single Spin Asymmetry requires**
**Helicity flip**: one must have a reaction mechanism for the hadron to change its helicity (in a cut diagram)
**A phase difference****:** the phase difference is needed because the structure S ·(p × k) violate the naïve time-reversal invariance

## Naïve parton model fails?

- If the underlying scattering mechanism is hard, the naïve parton model generates a very small SSA: (G. Kane et al, 1978),
- It is in general suppressed by αSmq/Q
- We have to go beyond this naïve picture

## Two mechanisms in QCD

- Spin-dependent transverse momentum dependent (TMD) function
- Sivers 90
- Brodsky,Hwang,Schmidt, 02 (FSI)
- Gauge Property: Collins 02;Belitsky-Ji-Yuan,NPB03
- Factorization: Ji-Ma-Yuan,PRD04;Collins,Metz,04
- Twist-3 quark-gluon correlations (coll.)
- Efremov-Teryaev, 82, 84
- Qiu-Sterman, 91,98

**P**

**Sivers function ****»**** S****?****¢**** (P****£****k****?****)**

## Regions 

- Twist-three: the single inclusive hadron production in pp, require large PT, SSA is suppressed by 1/Pt
- TMD: low PT, require additional hard scale like Q2 in DIS and Drell-Yan, PT<<Q, SSA survives in Bjorken limit
- Overlap: QCD<< Pt<<Q, unifying these two

## Recent theoretical developments(twist-three)

- Complete formalism for single inclusive hadron production in pp collision has been derived, including the derivative and non-derivative terms

**Qiu, Sterman, 91, 98**
**Kouvaris,Qiu,Vogelsang,Yuan, 06**
**See also Koike, et al., 06,07**

## Twist-3 Fit  to data

- E704

- STAR

**Kouvaris,Qiu,Vogelsang,Yuan, 06**

- RHIC

- BRAMHS

## Compare to 2006 data from RHIC

**J.H. Lee, SPIN 2006**

## A unified picture for SSA

- In DIS and Drell-Yan processes, SSA depends on Q and transverse-momentum P
- At large P, SSA is dominated by twist-3 correlation effects
- At moderate P, SSA is dominated by the transverse-momentum-dependent parton distribution/fragmentation functions
- The two mechanisms at intermediate P generate the same physics!
-                **Ji-Qiu-Vogelsang-Yuan,Phys.Rev.Lett.97:082002,2006**

## Testable prediction at RHIC

- Initial state vs. final state interactions
- “Universality”: fundamental QCD prediction

- HERMES

*********

*********

**Drell-Yan**

**DIS**

## Experiment SIDIS vs Drell Yan

-   ***0.1        0.2        0.3   x***

**0**

**0**

**Experiment SIDIS vs Drell Yan**
** **

- HERMES Sivers Results

- RHIC II  Drell Yan Projections

- Markus Diefenthaler
- DIS Workshop
- Munich, April 2007

- _http://spin.riken.bnl.gov/rsc/_

## Proposed by Boer-Vogelsang
Pheno. studies: Vogelsang-Yuan 05; 
   Bomhof-Mulders-Vogelsang-Yuan 07
Initial state and/or final state interactions?
Bacchetta-Bomhof-Mulders-Pijlman: hep-ph/0406099, hep-ph/0505268, hep-ph/0601171, hep-ph/0609206
Qiu-Vogelsang-Yuan, arXiv:0704.1153; 0706.1196
Collins-Qiu, arXiv:0705.2141 
Mulders, et al., 07?
Factorization? Universality?

- Pheno. studies: Vogelsang-Yuan 05;
-    Bomhof-Mulders-Vogelsang-Yuan 07
- Initial state and/or final state interactions?
- Bacchetta-Bomhof-Mulders-Pijlman: hep-ph/0406099, hep-ph/0505268, hep-ph/0601171, hep-ph/0609206
- Qiu-Vogelsang-Yuan, arXiv:0704.1153; 0706.1196
- Collins-Qiu, arXiv:0705.2141
- Mulders, et al., 07?
- Factorization? Universality?

- Alternative: Dijet-correlation at RHIC?

## The asymmetry can be related to that in DIS, in leading power of q?/Pt,universality of the parton distributions?

- qTDIS--- Sivers function from DIS
-     q?--- imbalance of the dijet
-     Hsivers depends on subprocess

**Qiu,Vogelsang,Yuan, 07**

## Questions...

- To what extend the factorization breaks down?
- Does a modified (weak) factorization hold if a general factorization breaks?
- Universality will be an issue
- ...
- More rigorous works need to be done to draw any conclusion
- Experiments at RHIC and future eRHIC can help us to answer these questions

## Collins effects 

- An important ingredient to extract the quark transversity distribution
- Its universality property has attracted many theoretical and experimental investigations
- Metz 02, Collins-Metz 02, 04
- Boer-Mulders-Pijlman, 03
- Gamberg-Goldstein, ...
- HERMES and Belle experiments, PRL 05-06

## Simple model a la Collins 93

- Phase information in the vertex
- Collins-93

**Universality of the Collins Function!!**

## One-gluon exchange (gauge link)?

- Metz 02, Collins-Metz 04:
- Universality of the Collins function!!

## Similar arguments for pp collisions

**Conjecture: the Collins function will be the same as e^+e^- and SIDIS**

- Vogelsang, Yuan, to appear

## Open questions 

- Universality for the SSA in the time-like region (fragmentation)
- Experiments at Belle, RHIC, eRHIC are crucial
- Link with the quark-gluon correlation in the fragmentation process
- Koike et al., 00-06
- Scale(Q^2)-dependence of all these SSAs

## Summary

- We are in the early stages of a very exciting era of transverse spin physics studies, where the future RHICII and eRHIC will certainly play very important roles
- We will learn more about nucleon structure from these studies, especially for the quark orbital motion

## What can we learn from SSA

**Quark Orbital Angular Momentum**
-     e.g, Sivers function ~ the wave function amplitude with nonzero orbital angular momentum!
-    Vanishes if quarks only in s-state!

**Ji-Ma-Yuan, NPB03**
**Brodsky-Yuan, PRD06**

## Take Drell-Yan as an example(with non-zero transverse momentum q?)

- Take Drell-Yan as an example(with non-zero transverse momentum q?)

- We need a loop to generate a phase

**Twist-three Correlations**
- Efremov-Teryaev, 82, 84
- Qiu-Sterman, 91,98

**Kane et al., hard parton model**

**+**

**+**

**+**

**-**

**+**

**+**

**+**

**-**

## Further factorization (q?<<Q)

- Further factorization (q?<<Q)

- The collinear gluons dominate

**Twist-three Correlations**
- Efremov-Teryaev, 82, 84
- Qiu-Sterman, 91,98

**Transverse Momentum Dependent distributions**
- Sivers, 90, Collins, 93,02
- Brodsky-Hwang-Schmidt,02
- Ji-Qiu-Vogelsang-Yuan,06

**q****?****<<Q**

## New challenge from STAR data (2006)

**Talks by Ogawa and Nogach in SPIN2006**

## Some comments

- It’s difficult to explain this pattern in the current theoretical approaches
- One possible reason could be the partial cancellation between the favored and disfavored contribution to Pi^0 production
- Check with the charged pions?

## Final Results

- P? dependence
- Which is valid for all P? range
- SSA is suppressed by 1/Pt at large Pt

- Sivers function at low P?

- Qiu-Sterman Twist-three

## Extend to all other TMDs: large Pt power counting

- kt-even distributions have the same dependence on kt
- kt-odd distributions are suppressed at large kt
- Power Counting Rule
-       kt-even: 1/kt2
- 		 kt-odd:   1/kt4

## SIDIS cross sections at large Pt

**1/P****t****2**

**1/P****t****4**

**1/P****t****3**

**1/P****t****5**

## Transition from Perturbative region  to Nonperturbative region?

- Compare different region of P?

**Nonperturbative TMD**

**Perturbative region**

## More over

- At low P?¿ Q, the second term vanishes, use the Sivers function only
- P?-moment of the asymmetry can be calculated from twist-three matrix element
- In SIDIS, for the Sivers asymmetry

- Boer-Mulders-Tangelmann, 96,98

## Compare to the HERMES data

- TF from the fit to single inclusive hadron data
- _[Kouvaris](http://www-spires.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Kouvaris,%20Chris%22)_**-**_[Qiu](http://www-spires.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Qiu,Jian-Wei%22)_**-**_[Vogelsang](http://www-spires.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Vogelsang,%20Werner%22)_**-**_[Yuan](http://www-spires.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Yuan,%20Feng%22)_, hep-ph/0609238
- This comparison is very nontrivial, because the SSA in DIS depends on final state interactions, whereas in hadronic collision both initial and final state interactions contribute
- Indicate the consistency of SSAs in DIS and hadron collisions

**not corrected for acceptance **
**and smearing**

- See also, Efremov, et al., PLB612,233 (20005)

## A new way to study higher-twist quark-gluon correlation functions?

- Large pt SIDIS certainly will provide information on higher-twist distributions
- Pt-weighted azimuthal asymmetries will also give constraints on these distributions
- Systematic analysis has to be done
- Evolution, NLO corrections, ...
- It indeed opens a new window for studying  higher-twsit quark-gluon correlations in SIDIS