Cross Sections and Spin Asymmetries in Hadronic

Scattering

Werner VogelsangBNL Nuclear Theory

KEK, 03/10/2007

Dedicated to Jiro

• QCD perturbation theory in hadronic collisions

• Some NLO phenomenology at RHIC

• Phenomenology of resummation in hadronic collisions

• Conclusions

Outline:

Jiro’s work has had a big impact onthe development of this area:

some of the early seminal papers of the field polarized-DIS & RHIC programs

QCD spin physics:

proposals and studies for processes at RHIC

open the door to beyond-LL resummation

QCD resummation:

brought young people into field

I. Introduction

pp jet Xpp Xpp X, …

Polarized and unpolarized protons

Such reactions :

0

10

20

30

40

50

60

70

80

90

1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

EastWestNorth

important tests of our understanding of QCD, need for higher orders, resummations, power corrections, …

important insights into proton structure

short-distance interaction perturbation theory

One prime example: at RHIC to measure

baseline for heavy-ion collisions, New Physics searches, …

short-distance:perturbation theory

universal pdf’s

: factorization/ren. scale

(good up to corrections suppressed as )

II. Some NLO phenomenology Example: pp at RHIC

K

RHIC

(Aversa et al.; de Florian)

Scales varied between pT/2 < < 2 pT

STAR

Jäger, Stratmann, WV

(NLO calculation assumes “narrow” jet cone)

Aurenche et al.; Baer et al.; Gordon, WV

−=Lg1

−=Lg1

The gluon distribution g

“axial anomaly” Altarelli et al.

Not much information until recently:

Ultimately: “global analysis” to really extract g and its integral

III. Phenomenology of resummation in hadronic scattering

A long-standing problem :

…well described by NLO at RHIC …but data much higher than NLO at fixed-target energies !

Aurenche et al.; Bourrely, Soffer

higher-order corrections beyond NLO ?

(without rapidity integration: )

Real emission inhibted Only soft/collinear gluons allowed

“threshold” logarithms

• convolution with PDFs :

emphasized, in particular as

• work began in the late ‘70sDokshitzer et al.; Parisi Petronzio;Collins, Soper, Sterman;Kodaira, Trentadue

threshold resummation

qT resummation

Sterman; Catani, Trentadue; …

= Resummation

• will spoil perturbative series - unless taken into account to all orders

• today : high level of sophistication

many other reactions in QCD

towards NNLL

Kidonakis, Sterman; Bonciani et al.;Catani, Mangano, Nason;Laenen, Oderda, Sterman;Catani, Grazzini, de Florian;Moch, Vogt, Vermaseren; Aybat, Dixon, Sterman;

“joint resummations” Li; Laenen, Sterman, WV

other formalisms Becher, Neubert; Ji, Ma, Yuan

Resummation usually done in “transform space”:

In our case, Mellin moments in

Exponentiation

• : soft-collinear emission off “observed” partons. LL+…

• J : collinear (soft/hard) emission off “unobserved” recoiling “jet” LL+…

• (int) : large-angle soft emission (matrix problem) NLL+…

Kidonakis, Sterman; Bonciani, Catani, Mangano, Nason; Aybat, Dixon, Sterman

Kodaira, Trentadue

Jet function:

expect large enhancement ! de Florian, WV

de Florian, WV

E706

(use “Minimal Prescription” of )Catani, Mangano, Nason, Trentadue

WA70

subleading terms important at collider energies

resummation effects much smaller

Application to prompt photons:

“direct” contributions:

“fragmentation” contributions:

Relatively small resum. effects

a bit like 0 production,but less gggg (because Dg

is smaller)

(Catani et al.; Sterman, WV; Kidonakis, Owens)

de Florian, WV

de Florian, WV

de Florian, WV

Application to jet production: de Florian, WV

Jet cone

• “ observed” jet: involves integration over jet mass

• “unobserved” jet: becomes massless at threshold

no double logs Kidonakis, Sterman

• can be explicitly verified by comparison to “analytical” NLO calculation in small-cone approximation Jäger, Stratmann,WV

Tevatron 1800 GeV RHIC 200 GeV

de Florian, WV

Drell-Yan @ J-PARC

Yokoya, WV

• good understanding of high-p cross sections at colliders

• gives confidence for analysis of spin asymmetries at RHIC

Conclusions

• progress in fixed-target regime through soft-gluon resummation

• generally, resummation techniques important with regard to hadron colliders: J-PARC to RHIC to Tevatron to LHC

• Jiro’s contributions crucial throughout this physics