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

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

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3 epehX and Jlab E00-108 Jlab E00-108 experiment tried to detect duality in semi- inclusive reaction ep epX. 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 epepX? 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 epepX?

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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:

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

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

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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

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

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11 Answer 2: Choose large and compare measurement of various

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

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

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

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

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16 Summary The contributions to cross-section 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. We have not attempted to study the evolution of the ratio, A way to extract higher twist effect in fragmentation sector through is to choose large with various at the same z. that this ratio contains information of the higher twist effects in the fragmentation sector and should be studied in the future. as a function of z. However, we suggest

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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.edugxu@uh.edu or guahxu@cognifast.comguahxu@cognifast.com

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