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QCD N06 - Monte Porzio Catone - 15/06/ SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione In Collaboration with M. Anselmino, U.D’Alesio, F. Murgia, A. Prokudin, C. Turk INFN – Sezione di Torino e Universita’ degli Studi di Torino

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2 QCD N06 - Monte Porzio Catone - 15/06/2006 Outline of the talk Azimuthal and PT dependences of hadrons in unpolarized SIDIS At small P T, (P T, <1 GeV/c) lowest order contributions + TMD distribution and fragmentation functions describe all data At large P T, (P T, >1 GeV/c) the usual pQCD higher order collinear contributions dominate We can explain the full range of experimental data New detailed predictions for azimuthal and P T dependences of hadrons produced at HERMES, COMPASS and JLab (6 GeV). Collins Fragmentation and Transversity Distribution Functions New experimental data from BELLE and Hermes allow us a comprehensive fit to determine the Collins fragmentation function and to give first indications on the Transversity distribution function. Analysis of A UT sin( S + h ) at Hermes and COMPASS and of A U /A L at BELLE.

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3 QCD N06 - Monte Porzio Catone - 15/06/2006 Lowest order term, d 0 : a virtual photon with momentum q strikes a quark with transverse momentum k _|_. The final detected hadron,has transverse momentum p _|_ with respect to the direction of the fragmenting quark from wich it originates, and transverse momentum P T with respect to the photon direction. This is the main source of hadrons with small P T. Azimuthal and PT dependences of hadrons in unpolarized SIDIS

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4 QCD N06 - Monte Porzio Catone - 15/06/2006 The first order term, d includes the processes in which the quark emits a hard gluon and those initiated by a gluon. Here the final quark can have a large transverse momentum, even starting from a collinear configuration. This term will dominate lepto-production of hadrons with P T larger than 1 GeV/c. The second order term, d 2, will be taken into account through the K factor

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5 QCD N06 - Monte Porzio Catone - 15/06/2006

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7 The modulation at small P T is a higher twist effect and decreases like1/Q for growing Q. Therefore we expect it to be smaller for ZEUS, where Q is huge, than for E665 ! We ignore the Collins and Boer-Mulders contribution: here is mainly arising from pQCD contributions.

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8 QCD N06 - Monte Porzio Catone - 15/06/2006 Predictions for forthcoming measurements HERMES Experiment Hydrogen target E e = GeV Since P T and Q 2 are very low, the perturbative effects obtained by including higher order corrections are negligible. and are a and are a direct consequence of the intrinsic transverse motion of partons inside the hadrons.

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9 QCD N06 - Monte Porzio Catone - 15/06/2006 Predictions for Jlab Predictions for COMPASS

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10 QCD N06 - Monte Porzio Catone - 15/06/2006 Spin asymmetries, Transversity and Collins fragmentation function Recent experimental data from BELLE, HERMES and COMPASS shed some light on the Transversity distribution function and on the Collins fragmentation function. Can we make a comprehensive analysis to extract information on both functions ?

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11 QCD N06 - Monte Porzio Catone - 15/06/2006 HERMES and COMPASS have measured the weighted asymmetry HERMES and COMPASS have measured the weighted asymmetry A UT sin( S+ h) as a function of x B, z h and PT. A UT sin( S+ h) as a function of x B, z h and PT. At first order in the (k _|_ /Q) expansion we have: At first order in the (k _|_ /Q) expansion we have:

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12 QCD N06 - Monte Porzio Catone - 15/06/2006 Fit to the HERMES data

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13 QCD N06 - Monte Porzio Catone - 15/06/2006 Description of COMPASS data (no fit)

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14 QCD N06 - Monte Porzio Catone - 15/06/2006 Predictions for JLab

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15 QCD N06 - Monte Porzio Catone - 15/06/2006 Description of BELLE data

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16 QCD N06 - Monte Porzio Catone - 15/06/2006 Description of BELLE data

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17 QCD N06 - Monte Porzio Catone - 15/06/2006 Description of BELLE data

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18 QCD N06 - Monte Porzio Catone - 15/06/2006 Description of BELLE data We can describe BELLE data Without any fit, by using the Collins function as obtained by fitting HERMES data and fixing The transversity function to be either g 1 or ½(f 1 +g 1 ). BELLE data prefer h 1 =g 1 !

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19 QCD N06 - Monte Porzio Catone - 15/06/2006 Description of BELLE data We can describe BELLE data without any fit, by using the Collins function as obtained by fitting HERMES data and fixing the transversity function to be either g 1 or ½(f 1 +g 1 ). BELLE data prefer h 1 =g 1 !

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20 QCD N06 - Monte Porzio Catone - 15/06/2006 Conclusions The Collins fragmentation function has been determined by fitting HERMES The Collins fragmentation function has been determined by fitting HERMES data on A UT. The transversity function was fixed to be either g 1 (x) or data on A UT. The transversity function was fixed to be either g 1 (x) or ½[g 1 (x)+f 1 (x)]. ½[g 1 (x)+f 1 (x)]. With this function we obtain an excellent description of COMPASS data With this function we obtain an excellent description of COMPASS data on the same asymmetry. on the same asymmetry. Predictions for JLab are given. Predictions for JLab are given. We then reproduce the BELLE asymmetry without fitting, and find that the We then reproduce the BELLE asymmetry without fitting, and find that the Collins function as obtained from the fit to HERMES data work really well, Collins function as obtained from the fit to HERMES data work really well, showing that the Collins function is universal. showing that the Collins function is universal. BELLE data prefer h 1 (x)=g 1 (x), giving us a first indication on the size of the BELLE data prefer h 1 (x)=g 1 (x), giving us a first indication on the size of the transversity function transversity function

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21 QCD N06 - Monte Porzio Catone - 15/06/2006 Future perspectives We are eagerly awaiting new data from BELLE. These will allow a reliable fit to fully determine the These will allow a reliable fit to fully determine the Collins function. Collins function. Then HERMES data can be used to fix the Transversity distribution. Transversity distribution. For a proper analysis we have to take into account all orders in the O(k _|_ /Q) expansion.

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