Double spin asymmetry ALT in the production of photons, hadrons, and jets Daniel A. Pitonyak Department of Physics, Temple University Supported by NSF (PHY-0855501) JLab QCD Evolution Workshop 2012

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

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

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

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

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 ) 1/10/2019 Daniel A. Pitonyak

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)) 1/10/2019 Daniel A. Pitonyak

Independent twist-3 functions  OR 1/10/2019 Daniel A. Pitonyak

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)) . . . + 1/10/2019 Daniel A. Pitonyak

ALT in l p  jet X (Kang, et al., Phys. Rev. D (2011)) ALT in Drell-Yan (Tangerman and Mulders, hep-ph/9408305 (1994)) . . . No process considered in the literature so far has involved a complete set of twist-3 functions 1/10/2019 Daniel A. Pitonyak

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

ALT in N(P, ST) + N(P, )  C(l) + X 1/10/2019 Daniel A. Pitonyak

(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 1/10/2019 Daniel A. Pitonyak

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

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 1/10/2019 Daniel A. Pitonyak

Numerical results for ALT Case 1: g as in de Florian, et al., Phys. Rev. D (2009) Case 2: g = g 1/10/2019 Daniel A. Pitonyak

1/10/2019 Daniel A. Pitonyak

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

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 1/10/2019 Daniel A. Pitonyak

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 1/10/2019 Daniel A. Pitonyak

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