1 / 16

Soft-gluon resummation in Drell-Yan dilepton (and vector boson)

Soft-gluon resummation in Drell-Yan dilepton (and vector boson) production at small transverse momentum: spin asymmetries and a novel asymptotic formula. Hiroyuki Kawamura (RIKEN). RADCOR2007 in Florence Oct. 4 2007. PTP115(2006)667 NPB777 (2007)203 arXive:0709.1572.

Sharon_Dale
Download Presentation

Soft-gluon resummation in Drell-Yan dilepton (and vector boson)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Soft-gluon resummation in Drell-Yan dilepton (and vector boson) production at small transverse momentum: spin asymmetries and a novel asymptotic formula Hiroyuki Kawamura (RIKEN) RADCOR2007 in Florence Oct. 4 2007 PTP115(2006)667 NPB777 (2007)203 arXive:0709.1572 In collaboration with K.Tanaka (Juntendo Univ.) & J.Kodaira (KEK)

  2. Jiro Kodaira (1951-2006) RADCOR2005 in Shonan (Oct. 2005)

  3. Transversely polarized Drell-Yan process • tDY (RHIC, J-PARC, GSI,…) ♠ double spin asymmetry: • Transversity — twist-2, chiral-odd distribution function • No gluon contribution (→ NS-type evolution) • Not measured in inclusive DIS Future DY data can provide an direct access to δq.

  4. Double spin asymmetry at small QT • ATT for the “QT-integrated” cross sections at NLO RHIC (PP) : Martin, Shäfer, Stratmann,Vogelsang (’99) GSI (PP-bar ) : Shimizu, Sterman, Yokoya,Vogelsang (’05) (threshold resummation) Barone et al. (’06) • ATT(QT) at small QT • A bulk of dileptons is produced. • Soft gluon corrections are dominant :“universal” • →Extraction of δq(x) can be simpler. — resummation of “recoil logs” — spin asymmetry with soft gluon resummation

  5. QT distributions at LO Kodaira, Shimizu, Tanaka, HK (’06) • Drell-Yan process with transverse polarization φ: azimuthal angle of one of the leptons → phase space integral with φ dependence (difficult in D-dimension) ♠ soft/col. singularity appear only at QT=0. ex. D-dim. 4-dim. • QT distribution at LO Altarelli, Ellis,Greco,Martinelli (’84)

  6. NLL resummation for tDY Kodaira, Shimizu, Tanaka, HK (’06) Resummed part: double Mellin space pdf b : impact parameter • coeff. function • Sudakov factor LL NLL universal NLL • evolution op. Grazzini, de Florian (‘00)

  7. NLL resummation for tDY b ∟ C • “Minimal prescription” + NP function bL Landau pole Laenen, Kulesza, Vogelsang, Sterman, … (’99 - ) Bozzi, Catani, de Florian, Grazzini (’03 - ’07) • QT distribution at “NLL+LO” → “unitarity constraint”

  8. QT distributions Kodaira, Shimizu, Tanaka, HK (’06) • Input function Koike et al. (’96) Kumano et al. (’96) Vogelsang (’97) + NLO evolution (GRV98+GRSV00) pol. unpol. pp collision @ RHIC s = 200 GeV, Q = 5GeV, y=2, φ=0 with gNP=0.5GeV2

  9. Double-spin Asymmetries at small QT Kodaira, Tanaka, HK (’07) . pp collision @ RHIC pp collision @ J-PARC s = 200 GeV, Q=2-20 GeV, y=2,φ=0 s = 10 GeV, Q= 2-3.5 GeV, y=0,φ=0 large-x, (valence) x (sea) small-x, (valence) x (sea)

  10. Double-spin Asymmetries at small QT ppbar collision @GSI s = 10 GeV, Q= 2-6GeV, y=0,φ=0 large-x, (valence)2

  11. Double-spin Asymmetry at small QT • ratios of each component pp : s = 200 GeV, Q = 5GeV, y=2, φ=0 NLL+LO: XNLL+Y NLL: XNLL LL: XLL • → soft corrections are crucial. • → dominated by the resumed part. • Flat in the peak region↔ soft gluon corrections almost cancel. (universal) But! Some contributions still remain. What determines (or what can be obtained from) ATT(QT) ?

  12. Saddle point evaluation at NLL Kodaira, Tanaka, HK (’07) Observation: → saddle point evaluation • resummed part at QT=0 LL terms NLL terms • Around the saddle-point, the resummation formula is organized in terms of • a single parameter. ex. → up to NNLL corrections “degree-0” approximation Collins, Soper,Sterman (’85)

  13. Saddle point evaluation at NLL • Saddle point , • The saddle point is determined by LL terms. • (up to NNLL) • Result • Extends the conventional SP evaluation at LL level. Parisi, Petronzio (’79) Collins, Soper, Sterman (’85) → approaches the exact result in the asymptotic limit • Large corrections in ( … ) cancel in the asymmetry. • Evolution operator shifts the pdf scale —

  14. Asymptotic formula In the peak region, • pdf scale: for pp colisions. ⇒ • Simple but still contains the essential dynamics which determine . • Only depends on pdf at a fixed (x,μ) • → useful for extracting pdf from experimental data. LO Caution: The evolution from Q to b0/bSP is given by the NLL approximation of NLO evolution operator ↔ LO DGLAP kernel. NLO “mismatch” between resummation and fixed order

  15. Asymptotic formula vs. Numerical results • from the asymptotic formula vs. numerical results (1)SP-I : asymptotic formula (NLO pdfs + LO DGLAP for Q → b0/bSP) (2) SP-II : asymptotic formula (NLO pdfs at b0/bSP) (3) NB : numerical b-integration pp collision ppbar collision — “SP-I” coincides with ATT(QT) quite well in all cases. — For the J-PARC & GSI kinematics, “SP-II” also works well. (The difference between LO & NLO kernel is small at large-x.)

  16. Summary • ATT(QT) for Drell-Yan dilepton production at small QT —Soft gluon corrections are crucial. → QT resummation at NLL — NLL contribution enhances the asymmetry (for pp collisions). — Numerical study shows in the peak region. • The saddle-point evaluation at NLL → a novel asymptotic formula for — pdf at the fixed scale b0/bSP at a fixed x. • Can be useful to extract δq from the experimental data. • The analysis is general and applicable to other asymmetries, • such as ALL(QT) for vector boson production at RHIC.

More Related