# Presentation: 087965

## Single Transverse Spin Asymmetries

**      **
**Single Transverse Spin Asymmetries**

**Jianwei Qiu**
***Iowa State University***

**RBRC Workshop on**
**Single Spin Asymmetries**
**June 1 – 3, 2005**
**Brookhaven National Lab, Upton, NY**

- Jianwei Qiu, ISU

- June 1, 2005

## Outline

** ****Single spin asymmetry before QCD**
** ****Single spin asymmetry within the collinear **
**    ****factorization – high twist matrix elements**
** ****K****T****- factorization – Sivers and Collins effects**
** ****Connection between high twist matrix elements **
**    ****and Sivers and Collins functions**
** ****Open questions**

**Outline**

- Jianwei Qiu, ISU

- June 1, 2005

## Single Spin Asymmetry – definition

- Jianwei Qiu, ISU

- June 1, 2005

## Symmetry and Single Spin Asymmetry

** ****Even though cross section               is finite, single**
**    ****spin asymmetries can ****vanish**** if  the polarized cross**
**    ****sections are ****independent of spin directions**** due to**
**    ****the ****fundamental symmetries**** of the interactions**** **

** ****A****L**** vanishes for Parity conserved interactions:**

- Jianwei Qiu, ISU

- June 1, 2005

## Single transverse spin asymmetry before QCD

** ****Almost 40 years ago, ****A****N**** in inclusive DIS was proposed**
**    ****by Christ and Lee to test the Time-Reversal invariance:**

** ****In the approximation of one-photon exchange, **
** ****A****N**** of inclusive DIS ****vanishes**** if Time-Reversal **
** ****is invariant for EM and Strong interactions**
**               ****N. Christ and T.D. Lee, Phys. Rev. 143, 1310 (1966)**

- Jianwei Qiu, ISU

- June 1, 2005

## AN = 0 for inclusive DIS

** ****DIS cross section:**

** ****Leptionic tensor is symmetric:****    *****L******μν****** = L******ν******μ***

** ****Hadronic tensor:**

** ****Polarized cross section:**

** ****P and T invariance:**

- Jianwei Qiu, ISU

- June 1, 2005

## Large AN in hadronic collisions

******process:  only ****one**** hadron is transversely polarized:**

******Large asymmetries A****N**** **
**    ****observed in hadron **
**    ****collisions:**
**   ****decay of ********    **
**    ****production of ********’s**

- FNAL - E704

- Jianwei Qiu, ISU

- June 1, 2005

## Single spin asymmetry correspondsto a T-odd triple product

- Jianwei Qiu, ISU

- June 1, 2005

## Single transverse spin asymmetry – AN

**in the parton model**

** ****the operator for *****δ******q***** has even ****γ****’s             quark mass term   **
** ****the phase requires an imaginary part             loop diagram **

**  ****transverse spin information at leading twist – transversity:**

**PQCD calculable partonic parts should not depend on light current quark mass – ****singals a high twist effect in pQCD**** **

- Jianwei Qiu, ISU

- June 1, 2005

## Single transverse spin asymmetry – AN

**in collinear factorization approach**

** ****Leading twist PDF with transverse hadron spin:**

** ****need an even number ********’s:**

**Twist-3 matrix elements**

**An extra transverse index**
**    ****extra gluon (its polarization)**
**    ****extra vector direction **

- Jianwei Qiu, ISU

- June 1, 2005

## High twist contribution to AN

**    ****a quark-gluon composite state**

** ****Observed hadron momentum provides the ****3****rd**** vector**

**Q: pQCD factorization beyond leading twist?**

**High twist contribution to A****N**

- Jianwei Qiu, ISU

- June 1, 2005

## Multiple scales in hadronic collisions

**(3)**

**(2)**

**(1)**

**Hard collision:                Q >> ****Λ****QCD **
**Gluon shower:                ****<k****T****>****dynamic ****~ F[Q****2****,log(s/Q****2****)]**
**Hadron wave function:  <k****T****>****intrinsic ****~ 1/fm ~ ****Λ****QCD **

** ****PQCD factorization:**
**    ****(1) Perturbative                 IR safe ****single ****hard **
**                                               ****partonic “cross section”**
**    ****(2) Leading log                  DGLAP evolution of PDFs**
**    ****(3) Nonperturbative          PDFs**

- Jianwei Qiu, ISU

- June 1, 2005

## Perturbative QCD factorization – (I)

** ****Perturbative pinch poles:**

** ****Perturbative factorization:**

**Parton state of momentum, **
***k*****, lives much longer than **
**the time of hard collision:**
**              ****|*****k*****2****|<<|Q****2****|**

**Remove soft interactions between different time scales**

- Jianwei Qiu, ISU

- June 1, 2005

## Perturbative QCD factorization (II)

** ****Collinear factorization:**

**Provides systematic **
**ways to quantify high **
**order corrections**** **

** *****K******T *****–factorization **

**No all-order proof of *****k******T***** – factorization for an arbitrary *****k******T***** **

**Factorization fails beyond the next-to-leading powers **
**in hadronic collisions**

**Leading Twist**

**Power corrections**

**perturbative**

**Long lived parton state**

- Jianwei Qiu, ISU

- June 1, 2005

## AN from polarized twist-3 correlations

******Factorization:**

******Twist-3 correlation functions:**

**A****N**** from polarized twist-3 correlations**

- Jianwei Qiu, ISU

- June 1, 2005

## Single spin asymmetry within the    collinear factorization

**Single spin asymmetry within the****    collinear factorization**

** ****Generic twist-3 factorized contributions**

**Even  ********’s !**

**Even  ********’s !**

**Provides hadron spin dependence**

**transversity**

**Calculated by Qiu and Sterman, Phys. Rev. D, 1999**
**Calculated by Kanazawa and Koike, Phys. Lett. B, 2000**

- Jianwei Qiu, ISU

- June 1, 2005

## Leading twist-3 contribution to AN

** ****Minimal approach (within the collinear factorization):**

****

- Jianwei Qiu, ISU

- June 1, 2005

## Predictive power of the factorization approach

- Jianwei Qiu, ISU

- June 1, 2005

## What is the T(3)(x)?

- Jianwei Qiu, ISU

- June 1, 2005

## What the T(3) (x) tries to tells us?

** ****Consider **
**    ****a classical **
**    ****(Abelian) **
**    ****situation:**

- Jianwei Qiu, ISU

- June 1, 2005

## Model for TF(x,x)

** *****T******F****** *****(*****x,x*****) tells us something about quark’s transverse **
**    ****motion in a transversely polarized hadron**

**One parameter and one sign!**

** ****It is non-perturbative, has unknown ****x****-dependence**

- Jianwei Qiu, ISU

- June 1, 2005

## Numerical results – (I)(compare apples with oranges)

**Qiu and Sterman**
**Phy. Rev. D, 1999**

- Jianwei Qiu, ISU

- June 1, 2005

## Numerical results – (II)(compare apples with oranges)

**Qiu and Sterman**
**Phy. Rev. D, 1999**

- Jianwei Qiu, ISU

- June 1, 2005

## Numerical results – (III)(comparison with RHIC data)

** ****Comparison with  **
**     ****STAR data **
** ****Too small P****T**** value **
**     ****to be comfortable**
**    ****for initial state twist-3**
** ****See Koike’s talk on**
**    ****final state twist-3**
** ****New data from STAR,**
**    ****BRAHMS, PHENIX **

- Jianwei Qiu, ISU

- June 1, 2005

## Twist-3 vs KT approach

******Twist-3 contribution in collinear factorization**
**    ****– ****leading corrections from parton correlation (a minimal approach)**

******Effect of non-vanish parton k****T ****(when k****T**** ~ p****T****):****  **

***M*********Non-perturbative scale, e.g.,**
**       ****di-quark mass, ...**

- Jianwei Qiu, ISU

- June 1, 2005

## Sivers’ functions

** ****Sivers’ functions:**

**Sivers’ functions are connected to a polarized hadron beam**

**Sivers’ functions are T- odd, but do not need another T- odd**
**function to produce nonvanish asymmetries – the extracted**
**proportional factor is T- odd, proportional to A****N**** **

** ****Polarized SIDIS cross section:**

- Jianwei Qiu, ISU

- June 1, 2005

## Collins’ functions

** ****Collins’ functions:**

**Collins’ functions are connected to the unpolarized **
**Fragmentation contributions to a hadron**

**Collins’ functions are T- odd, need another T- odd function to **
**produce nonvanish asymmetries**

** ****Polarized SIDIS cross section:**

- Jianwei Qiu, ISU

- June 1, 2005

## KT - Factorization

** ****Factorization requires a separation of perturbative **
**    ****hard scale from nonperturbative hadronic scale  **
**            ****a physical hard scale, Q, much larger than the k****T**

**Q ~ p****T**** >> k****T**

** ****k****T****-factorization measures parton k****T ****directly****, while**
**    ****twist-expansion gives ****integrated**** k****T**** information**
** ****No formal proof of k****T****-factorization for hadronic**
**    ****collisions at k****T**** ~ p****T**** **

** ****k****T****-factorization works for semi-inclusive DIS and **
**    ****Drell-Yan, or others with a large scale Q **

- Jianwei Qiu, ISU

- June 1, 2005

## Semi-inclusive deeply inelastic scattering

**Breit frame:**

**Two scale problem: Q****2****=-q****2****, p****T**

** ****Fixed order pQCD:**

** ****Sudakov resummation:**

** ****Single spin asym:**
** ****low p****T**** data sensitive to parton k****T**

**If P is anti-parallel to p**

- Jianwei Qiu, ISU

- June 1, 2005

## Intrinsic vs dynamical kT

**In q-P frame, if **

** ****we can neglect**

**in partonic part **

** ****But, we cannot neglect**

** ****One can define k****T****-dependent and gauge invariant **
**    ****parton distributions**
** ****Soft interaction between the hadrons can spoil**
**    ****factorization**

**S**

** ****Sudakov resummation (done in b- or k****T****-space) resums**
**    ****dynamical k****T**** from gluon shower**
** ****Parton orbital motion is more relevant to the ****intrinsic k****T**** **

**Intrinsic vs dynamical k****T**

- Jianwei Qiu, ISU

- June 1, 2005

## Open questions – (I)

** ****How much overlap between k****T****-approach at low p****T**
**    ****and twist expansion at high p****T****? **

** ****What these nonperturbative functions try to tell us?**
**    “****direct k****T****”  vs  “k****T**** – moments”**

- Jianwei Qiu, ISU

- June 1, 2005

## Open questions – (II)

**    ****and the others, how to separate dynamical k****T**** from **
**    ****intrinsic k****T ****?**
** ****How Sivers and Collins functions are affected by **
**    ****the process dependent gluon shower (resummation)?**
** ...**

**Open questions – (II)**

** **

** ****If there is no K****T**** – factorization, how universal are **
**    ****Sivers and Collins functions?**

- Jianwei Qiu, ISU

- June 1, 2005

## Backup transparencies

- Jianwei Qiu, ISU

- June 1, 2005

## Collinear approximation is important

**With collinear approximation:**

****

**=**

**In general, matrix elements with different cuts are not equal:**

**IR safe**

- Jianwei Qiu, ISU

- June 1, 2005

## When does the factorization lose its predictive power?

**At the time when the nonperturbative functions **
**lose their universality******

******For final-state fragmentation:**

**Factorization breaks if the fragmentation**
**took place ****inside**** the hadronic medium**

**If the lifetime of the parton state of momentun  *****k***** **
**is ****shorter**** than the medium size**

**Lifetime:**

- Jianwei Qiu, ISU

- June 1, 2005

## Asymmetries

******Double longitudinal spin asymmetries:**

**Reduce under parity to:**

******Double transverse spin asymmetries:**

******Single longitudinal spin asymmetries:**

******Single transverse spin asymmetries:**

- Jianwei Qiu, ISU

- June 1, 2005

## Measure Sivers’ and Collins’ functions

** ****SIDIS:**

** ****Collins functions:**

- Jianwei Qiu, ISU

- June 1, 2005

## Seperate Sivers’ and Collins’ functions

**Seperate Sivers’ and Collins’ functions**

- Jianwei Qiu, ISU

- June 1, 2005

## Initial success of RHIC pp runs

******************cross section measured **
**    ****over ****8**** order of magnitude**
**    ****[PRL 91, 241803 (2003)]**

******Good agreement with NLO**
******pQCD calculation at ****low *****p******T***

-  Can be used in interpretation
-     of spin-dependent results

- 9.6% normalization error not shown

- Jianwei Qiu, ISU

- June 1, 2005