Higher Twist Effect in Fragmentation Sector And Its Experimental Extraction.

1. Higher Twist Effect in Fragmentation Sector And Its Experimental Extraction. Ed. Hungerford, Larry Pinsky, Guanghua Xu, University of Houston, TX. Introduction Duality phenomenon in ep → e’X and its explanation ep→e’hX and Jlab E00-108 Duality in parton fragmentation sector. e+e- → h+X ep→e’hX Summary

2. Introduction • Duality phenomenon in ep → e’X and its explanation The discussion about duality in inclusive e-p scatterings can be explained by higher twist effect in parton structure sector. 2

3. ep→e’hX and Jlab E00-108 Jlab E00-108 experiment tried to detect duality in semi-inclusive reaction ep→e’pX. Semi-inclusive reaction contains information from both structure and fragmentation sector. • Questions: • Q1: Does duality exist in parton fragmentation sector? • Q2: How can one isolate the information of fragmentation sector from ep→e’pX? • Q3: Appealing to factorization, could the scale relating to the parton structure sector have different value from the scale relating to the parton fragmentation sector in ep→e’pX? 3

4. Duality in parton Fragmentation Sector We will mainly study e+e- → h+X and e-p → h+X in the following. We will, first, carry out twist expansion for the processes and, then, discuss their experimental extractions. The main difference between semi-inclusive and inclusive reaction is: 4

5. Step 1: • Step 2: Use of the fact that • Step 3: Changing to A gauge invariant 5

6. 6

7. Step 4: and light-cone expansion. Twist expansion • Step 5: Light-cone gauge • “Step 6: The definition of the twist of an invariant matrix element of a light-cone bilocal operator. 7

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9. Answer 1: • The fragmentation functions can also be expanded in terms of contributions of operators of various twists. • The phenomenon of duality can appear if the signs of the coefficients of the higher twist contributions are not positive definite. • Such experiments are straightforward in e+e- collisions, where one can compare the cross sections of hadron, h, production at fixed z for various 9

10. Comparing to e+e- Similarity: Difference: contain information of both parton structure and parton fragmentation sectors. 10

11. Answer 2: • Choose large and compare measurement of various 11

12. Answer 3: • In e-p • In e-p: • In e+e- • Universality of P: 12

13. effect is significant. At Jlab beam energies, Working in the lab frame 13

14. The small cross-section at can be avoided by lowering the beam energy. 14

15. Experimentally measurable quantities: The angles and play roles in determining at Jlab beam energies. Therefore, it is important to measure these quantities. 15

16. Summary cross-section • The contributions to can be expanded as contributions of operators with various twists. Experimental extraction of higher twist contributions can be carried out by comparing measurements of cross-sections vs. z at various . • A way to extract higher twist effect in fragmentation sector through with various is to choose large at the same z. • We have not attempted to study the evolution of the ratio, as a function of z. However, we suggest that this ratio contains information of the higher twist effects in the fragmentation sector and should be studied in the future. 16

17. My Contact Information Guanghua Xu Physics Department University of Houston 4800 Calhoun Road Houston, TX 77204 Ph.: (713)743-3723 or (281)324-9398 gxu@uh.eduor guahxu@cognifast.com 17