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LL2004 , April 25 - 30 `04

LL2004 , April 25 - 30 `04. Soft Gluon Effects in Transversely Polarized Drell-Yan Process Jiro Kodaira (Hiroshima). 1. Spin Projects at RHIC. 2. Transversely Polarized Drell-Yan. Works Done so far. 3. Calculation in D-dimension. Technical Problems. 4. q T Resummation.

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LL2004 , April 25 - 30 `04

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  1. LL2004 , April 25 - 30 `04 Soft Gluon Effects in Transversely Polarized Drell-Yan Process Jiro Kodaira (Hiroshima) 1.Spin Projects at RHIC 2.Transversely Polarized Drell-Yan Works Done so far 3.Calculation in D-dimension Technical Problems 4.qT Resummation With H.Kawamura (KEK) H.Shimizu (Hiroshima) K.Tanaka (Juntendo) Resummation at NLL Order 5.Results and Summary J.Kodaira (Hiroshima)

  2. Spin Projects at RHIC ● PDFs ● Asymmetry Measured at RHIC J.Kodaira (Hiroshima)

  3. What Theorists Can Contribute to Spin Projects Challengingbut Not so Easy (at least for me) ● New Idea, Process, Physics … Choice of final States ● ‘Brute Force’ Cal. of Known Process (QCD) Higher Order Corrections Today’s Subject : Transversely Polarized Drell-Yan J.Kodaira (Hiroshima)

  4. Transversely Polarized Drell-Yan δq(x): Ralston & Soper, Soffer’s Inequality, … Works Done so far 1.Anomalous Dimension One-Loop (Artru & Mekhfi) Two-Loop (Hayashigaki, Kanazawa & Koike, Kumano & Miyama, Vogelsang) 2. qT Integrated Cross Section Massive Gluon Regularization: Vogelsang & Weber (1993) Dimensional Reduction: Contogouris, Kamal & Merebashvili (1994) Relation between Schemes: Kamal (1996) Dimensional Regularization: Kamal (1998) No explicit Cal. 3. qT Un-integrated Cross Section Massive and Finite qT Only: Vogelsang & Weber (1993) J.Kodaira (Hiroshima)

  5. D-dimensional Calculation Transversely Polarized case dσ ∝ cos (2Φ) We Must Keep Azimuthal Angle Phase Space Integral : Difficult ● Massive Gluon, DRS, … ● D-dimension Result using Scheme Transformation ●ProjectionMethod by Mukherjee, Stratmann and Vogelsang (’03) We have integrated in D-dimension Directly! J.Kodaira (Hiroshima)

  6. Momentum, Invariant and Spin Two Particle Phase Space Three Particle Phase Space J.Kodaira (Hiroshima)

  7. Spin Dependent Cross Section Tree + Virtual One Gluon Emission We Reproduced the Known Result for Total Cross Section J.Kodaira (Hiroshima)

  8. qT Resummation qT Un-integrated Cross Section Edge of Phase Space Perturbative Parts: Free From Singularity BUT In Edge Region of Phase Space Large αS ln 2 ( Ratio of Two Scales) Appear Recoil or QTLogs →Resummation of Large Logs. to All Orders J.Kodaira (Hiroshima)

  9. Strategy (DS, DSW) Step 1. General Form for Cross Section (CSS) with J.Kodaira (Hiroshima)

  10. Step 2. Perturbative Expansion of A, B, C Step 3. NkLL Approximation A(1) → LL A(2), B(1), C(1) →NLL , …. Step 4. Compare General Form with Explicit Cal. Note: A(1) , A(2) , B(1) are Universal and we have checked (for A(2), use L.Trentadue and J.K. Reasoning) J.Kodaira (Hiroshima)

  11. One Loop Result （AEGM) J.Kodaira (Hiroshima)

  12. Results and Summary ● qT Integrated Cross Section Reproduce the Known Result ● qT Un-integrated Cross Section Numerical Problems 1. PDF Model Saturating Soffer’s Inequality (Vogelsang et al.) 2. Small b (CTTW) 3. Large b (CSS) with J.Kodaira (Hiroshima)

  13. Numerical Results S½ = 100 GeV , Q = 10 GeV , y = 0 qT Distribution Asymmetry (Expected) J.Kodaira (Hiroshima)

  14. Some Comments ●Things to be Done Numerical Calculation of Asymmetry Change Parameters : S½ , Q , … Inclusion of Z Boson …… ● We Should Examine Experimental Status Cross Section is “Small” with Fixed y!! Should Obtain y-integrated Cross Section Check Sensitivity to Non-Perturbative Effects …… J.Kodaira (Hiroshima)

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