1. Double spin asymmetry ALT in the production of photons, hadrons, and jets
Daniel A. Pitonyak
Department of Physics, Temple University
Supported by NSF (PHY )
JLab QCD Evolution Workshop 2012

2. Outline Collinear twist-3 formulation
Studies of ALT in other processes
ALT in N(P, ST) + N(P, )   (l) + X
ALT in N(P, ST) + N(P, )  C(l) + X (where C = h, jet)
Numerical results for ALT
Summary/Outlook
1/10/2019
Daniel A. Pitonyak

3. Collinear twist-3 formulation
Initially established for transverse SSAs (see, e.g., Efremov and Teryaev, Phys. Lett. B (1982); Qiu and Sterman, Nucl. Phys. B (1992))
For DSAs in processes such as A(P, ST) + B(P, )  C(l) + X
What contributions are possible for ? 
1/10/2019
Daniel A. Pitonyak

4. Possible twist-3 matrix elements (see, e.g., Zhou, et al., Phys. Rev. D (2010))
xP + kT X X
x1P + k1T
xP + kT P P  
0 in LC gauge  
Neglect kT
(with a twist-3 projection)
Neglect kT
1/10/2019
Daniel A. Pitonyak

5. F-type functions D-type functions 1/10/2019 Daniel A. Pitonyak x1P xP

6. Relations between F-type and D-type functions (see, e. g
Relations between F-type and D-type functions (see, e.g., Eguchi, et al., Nucl. Phys. B (2006))
where
(Note also that )
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Daniel A. Pitonyak

7. X
xP + kT P
0 in LC gauge using PV BC
in LC gauge 
Neglect kT
gT can be related to D-type functions through EOM (see, e.g., Efremov and Teryaev, Phys. Lett. B (1985); Jaffe and Ji, Nucl. Phys. B (1992))
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Daniel A. Pitonyak

8. Independent twist-3 functions OR
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Daniel A. Pitonyak

9. Studies of ALT in other processes
ALT in inclusive DIS
ALT in W boson decay from pp collisions (Metz and Zhou, Phys. Lett. B (2011))
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Daniel A. Pitonyak

10. ALT in l p  jet X (Kang, et al., Phys. Rev. D (2011))
ALT in Drell-Yan (Tangerman and Mulders, hep-ph/ (1994))
. . .
No process considered in the literature so far has involved a complete set of twist-3 functions
1/10/2019
Daniel A. Pitonyak

11. Involves a complete set of collinear twist-3 functions
ALT in N(P, ST) + N(P, )   (l) + X (Liang, Metz, DP, Schäfer, Song, and Zhou, accepted in Phys. Lett. B)
2 channels:
Involves a complete set of collinear twist-3 functions
1/10/2019
Daniel A. Pitonyak

12. ALT in N(P, ST) + N(P, )  C(l) + X
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Daniel A. Pitonyak

13. (Note that h.c. diagrams have not been shown)
Example: channel
(Note that h.c. diagrams have not been shown)
In general, imaginary parts cancel between different cut diagrams  left with PRINCIPAL VALUE part
= gluon attachment
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Daniel A. Pitonyak

14. Involves a complete set of collinear twist-3 functions
12 channels, over 200 diagrams
Involves a complete set of collinear twist-3 functions
1/10/2019
Daniel A. Pitonyak

15. Comments on the analytical results
Analog of the calculation of AUT in the same processes (Qiu and Sterman, Nucl. Phys. B (1992); Qiu and Sterman, Phys. Rev. D (1999); Kouvaris, et al., Phys. Rev. D (2006))
Derivative and non-derivative contributions to combine in the same compact form found in SSAs in direct photon and inclusive pion production (Qiu and Sterman, Nucl. Phys. B (1992); Kouvaris, et al., Phys. Rev. D (2006); Koike and Tanaka, Phys. Rev. D (2007))
Hard parts for are different  cannot combine into gT like in e.g. ALT for inclusive DIS
In principle, this process, in conjunction with other reactions, allows us to access a complete set of collinear twist-3 functions in a transversely polarized nucleon
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Daniel A. Pitonyak

16. Numerical results for ALT
Case 1: g as in de Florian, et al., Phys. Rev. D (2009)
Case 2: g = g
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Daniel A. Pitonyak

17. 1/10/2019
Daniel A. Pitonyak

18. Comments on the numerical results
ALT does not appear to exhibit the rise for large xF as seen in AUT
The observable is sensitive to g in a range not yet explored (sensitive to roughly x ~ 10-4)
Direct photon production shows the most promise of a measurable effect
Pion and jet production observables appear too small to measure
HOWEVER…
1/10/2019
Daniel A. Pitonyak

19. We have not calculated the numerical contribution from the 3-parton correlators (i.e., terms)  
Large effect 
Small effect
Extract information on 3-parton correlators
Measure large effect = evidence of another mechanism at work
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Daniel A. Pitonyak

20. Summary/Outlook
We have calculated ALT in the production of photons, hadrons, and jets in the collinear twist-3 framework
These processes allow one to study a complete set of twist-3 functions
Photon production shows promise to be a measurable effect; jet and pion production seem too small to measure
BUT, must obtain estimate on contribution from 3-parton correlators before a definite prediction can be made
Measurement at RHIC could extract info on 3-parton correlators or determine if another mechanism is at work; also gain access to g down to x ~ 10-4
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Daniel A. Pitonyak

21. Special thanks to Jefferson Lab and the Organizing Committee:
Alexei Prokudin,
Anatoly Radyushkin, Ian Balitsky, Leonard Gamberg,
Harut Avakian
Thank you
1/10/2019
Daniel A. Pitonyak