Cross Sections and Spin Asymmetries
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Cross Sections and Spin Asymmetries in Hadronic Collisions. Jianwei Qiu Brookhaven National Laboratory. KEK theory center workshop on high-energy hadron physics with hadron beams KEK, Japan, January 6-8, 2010. Outline. Cross sections and asymmetries:.

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Cross Sections and Spin Asymmetries in Hadronic Collisions

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Cross Sections and Spin Asymmetries


Hadronic Collisions

Jianwei Qiu

Brookhaven National Laboratory

KEK theory center workshop on high-energy hadron physics with hadron beams KEK, Japan, January 6-8, 2010

Jianwei Qiu


  • Cross sections and asymmetries:

Role of the quantum interference or correlation

  • QCD and pQCD in hadronic collisions:

Factorization – predictive power of pQCD calculation

Expansion in inverse power of hard scale and in power of αs

  • Importance of NLO contributions in power of αs:

Resummation to all orders in αs

Resummation to all powers in power corrections

  • Asymmetries – leading power does not contribute:

Single spin asymmetry, transverse momentum broadening, …

  • Role of J-PARC facility in hadron physics

Jianwei Qiu

High energy hadronic collisions

  • High energy scattering process:

PP (Jet, π, γ, J/ψ,…)X,

w/o polarization



Momentum transfer Q=(PT, MJ/ψ, …) >> typical hadronic scale ~ 1/fm

  • Why these reactions?

  • Short-distance interaction – use of QCD perturbation theory

  • Important tests of our understanding of QCD

  • – role of high orders, resummation, power corrections, …

  • Important insights into proton structure

  • – parton densities, helicity distributions, multiparton correlations, …

  • Baseline for heavy-ion collisions, ...

Jianwei Qiu

Cross sections and asymmetries

  • Cross section:

Scattering amplitude square – Probability – Positive definite

A function of in-state and out-state variables: momentum, spin, …

  • Spin-averaged cross section:

  • Asymmetries or difference of cross sections:

– Positive definite

Not necessary positive!

Chance to see quantum interference directly

Jianwei Qiu

Connecting hadrons to QCD partons

  • QCD confinement:

Do not see partons in the detector!

  • Factorization - approximation:

QCD parton dynamics

Single active parton from each hadron!



(Diagrams with more active partons

from each hadron!)

A Probability ~ A Product of probabilities!

Jianwei Qiu

PQCD factorization

  • Collinear factorization:

Collinear on-shell active partons

  • Transverse-momentum dependent (TMD) factorization:

On-shell active partons

Not generally proved, but, used phenomenologically

Jianwei Qiu

Predictive power of pQCD factorization

  • Prompt photon production as an example:

Hard part:

  • Predictive power:

  • Short-distance part is Infrared-Safe, and calculable

  • Long-distance part can be defined to be Universal

  • Scale dependence – artifact of pQCD calculation

  • NLO is necessary

  • Power correction is process dependent – non-universal!

Jianwei Qiu


  • What have we learned from hadronic collisions?

NLO pQCD collinear factorization formalism has been very

successful in interpreting data from high energy scattering

  • What is special for J-PARC and what J-PARC

  • can contribute to our knowledge of strong

  • interaction in hadronic collisions?

J-PARC could provide crucial tests of QCD in a regime where

NLO pQCD collinear factorization formalism has NOT been very


Jianwei Qiu

Unpolarized inclusive DIS – one hadron

Jianwei Qiu

Jet in hadronic collisions - two hadrons

Inclusive Jet cross section at Tevatron: Run – 1b results

Data and Predictions span 7 orders of magnitude!

Jianwei Qiu

Prediction vs CDF Run-II data

Highest ET jet !

Jianwei Qiu

Q2=10 GeV2


Q2=10 GeV2







Universal parton distributions

  • Modern sets of PDFs with uncertainties:

Consistently fit almost all data with Q > 2GeV

Jianwei Qiu

Jet production at RHIC - two hadrons

  • STAR:

PRL97, 252001


NLO Calclation: Jäger, Stratmann, Vogelsang

Jianwei Qiu

Inclusive single hadron at RHIC – 3 hadrons


PRD76, 051106


Jianwei Qiu

Extending x coverage and particle type

Large rapidity p,K,p cross sections for p+p, s=200 GeV


PRL98, 252001 (2007)

Jianwei Qiu

Direct photon at RHIC


Sakaguchi, 2008

Jianwei Qiu

Polarized inclusive DIS – one hadron

  • Success of the NLO formalism:

Jianwei Qiu

RHIC Spin Program

  • Collider of two 100 (250) GeV polarized proton beam:

  • The asymmetry:

Jianwei Qiu

RHIC Measurements on ΔG

Star jet

Phenix π0

Small asymmetry leads to small gluon “helicity” distribution

Jianwei Qiu

Current status on ΔG

  • Definition:

  • NLO QCD global fit - DSSV:


Strong constraint on ΔG from

Jianwei Qiu

Large SSA in hadronic collisions

  • Hadronic :

Jianwei Qiu

SSA in parton model

  • One collinear parton per hadron in hard collision:

  • Helicity – flip quark mass term

  • Generate the phase from the loop diagram αs

SSA vanishes in the parton model:

  • spin-dependence of parton’stransverse motion

Jianwei Qiu

Cross section with ONE large scale

Too large to compete!

Three-parton correlation

  • QCD Collinear factorization approach is more relevant

  • SSA – difference of two cross sections with spin flip

  • is power suppressed compared to the cross section

– Expansion

  • Sensitive to twist-3 multi-parton correlation functions

  • Integrated information on parton’s transverse motion

Koike’s talk

Jianwei Qiu

Pion production at fixed target energies

  • A long standing problem:

Data is much higher

than NLO at fixed-target


Aurenche et al.; Bourrely, Soffer

Jianwei Qiu

Direct photon at fixed target energies

  • Another long standing problem:

Aurenche et al., PRD73, 094007(2007)

Jianwei Qiu

Large high order corrections in power of αs

  • Higher order corrections beyond NLO:

Threshold logarithms


  • Threshold logarithm is a consequence of the rapidity

  • integration of the generic perturbative term:


The limit:

inhibits the real emission

while the soft /collinear gluon

emission is still allowed

Jianwei Qiu

Enhanced by steep falling parton flux

  • Convolution with parton distributions:


  • Partonic flux:

The product of parton distributions strongly favor the region

where xx’ small, that is, enhances the region where

  • Solution:

Threshold resummation – resum to all powers.

Sterman; Catani, Trentadue; …

  • Threshold resummation is particularly important for

  • J-PARC energy

Chance to probe QCD high order dynamics

Jianwei Qiu

Threshold resummation – Single scale

  • Resummation is usually done in a “transformed” space:

  • Express energy (or momentum) conservation δ-function as

  • Individual zi-integration transform the function of ziinto the

  • “transformed” space

  • Threshold resummation:

Mellin moments of :

Jianwei Qiu

Resummation for single hadron production

  • Resummed “coefficient” functions:

de Florian,Vogelsang, 2005

“Observed” partons

Unobserved recoil jet


  • Correction to gggg:

Big enhancement factor:

Jianwei Qiu

Improvement from resummation



de Florian,Vogelsang, 2005

Jianwei Qiu

Improvement to direct photon production

  • Direct contribution:

Relatively small resummation effect:

for the Compton term

Catani et al.; Sterman, Vogelsang;

Kidonakis, Owens

  • Fragmentation contribution:

Similar enhancement for gggg,

but, gluon fragmentation function

to photon is very small!

Jianwei Qiu

Drell-Yan at low QT – two scales

  • Fixed-order collinear pQCD calculation:


  • “integrated” QT distribution:

Effect of gluon


Assume this exponentiates

  • “resummed” QTdistribution – DDT formalism:

as QT→0

Jianwei Qiu

CSS resummation formalism

  • Experimental fact:

  • Why?

    Particle can receive many finite kT kicks via soft gluon radiation

    yet still have QT=0 – Vector sum!

  • Subleading logarithms are equally important at QT=0

  • Solution:

    impose 4-momentum conservation at each step of soft gluon


Jianwei Qiu

“b”-space resummation

  • The formula:

  • “b”-space distribution – perturbative at small b:

  • Predictive power:

IF long b-space tail

is not important for

the b-integration

Large Q

Large phase space for the shower = large s

Jianwei Qiu

Examples with large Q

Qiu and Zhang, PRL, 2001

Power correction is very small, excellent prediction!

Jianwei Qiu

Example with low Q large phase space


D0 Run-II

A prediction

CEM with all order resummation of soft gluon shower

Berger, Qiu, Wang, 2005

Jianwei Qiu

Example with low Q small phase space

Qiu and Zhang, PRD, 2001

IF bmax ~ 0.3 1/GeV

Jianwei Qiu

Drell-Yan lepton angular distributions

  • The observable:

  • “Helicity structure functions”:

NO CSS resummation proved for these “structure functions”!

The CSS formalism only proved for inclusive Drell-Yan

  • Idea:

Connect the resummation of these structure functions to

the resummation of the inclusive Drell-Yan cross section

– helper: EM gauge invariance

Berger, Qiu, Rodriguez, 2007

Jianwei Qiu

Resummed “helicity structure functions”

  • Drell-Yan hadronic tensor:

where are functions of and the choice of frame

  • EM current conservation:

for all values of even when

  • Connection to inclusive cross section:

  • Difficulty for :

No LO perturbative double logs!

Jianwei Qiu

Lam-Tung relation

Peng’s talk

  • Normalized Drell-Yan angular distribution:

  • Lam-Tung relation:

  • TMD Boer-Mulders function:

Boer’s talk

J.C. Peng, 2008

Extending CSS resummation

Collins, Qiu and Sterman

Jianwei Qiu

Coherent soft interaction






Different models Different assumptions/treatments on

how the heavy quark pair becomes a quarkonium?

Heavy quarkonium production

  • Fact:

After more than 35 years, since the discovery of J/y, we still have not been able to fully understand the production mechanism of heavy quarkonia

  • Basic production mechanism:

Jianwei Qiu

Popular production models

  • Color singlet model:

Chang 1974, Einhornand Ellis (1975), …

  • Only pairs with right quantum number can become quarkonia

  • Non-perturbative part ~ decay wave function squared

  • Color evaporation model:

Fritsch (1978); Halzen; …

  • All colored or color singlet pairs with invariant mass less then

    open charm threshold could become bound quarkonia

  • Non-perturbative part = one constant per quarkonium state

  • NRQCD model:

Bodwin, Braaten, Lapage (1994); …

  • All colored or color singlet pairs could become quarkonia

  • Power expansion in relative velocity of heavy quark pairs

  • Non-perturbative part = one matrix element per QQ state

Jianwei Qiu

CSM: Huge high order corrections

Jianwei Qiu

Polarization of quarkonium at Tevatron

  • Measure angular distribution of μ+μ− in J/ψ decay

  • Normalized distribution:

Jianwei Qiu

Surprises from polarization measurements

  • Transverse polarization at high pT?

NRQCD: Cho & Wise, Beneke & Rothstein, 1995, …

KT-fact: Baranov, 2002

CDF Collaboration, PRL 2007

Jianwei Qiu

Exclusive production in e+e-

Li, He, and Chao, Braaten and Lee, …

  • Double charm production:


  • Possible resolution for J/ψ+ηc:

Zhang, Gao, Chao, PRL

Kfactor = 1.96

  • NLO correction:

  • Relativistic Correction:

Kfactor = 1.34


Wave func:

Kfactor = 1.32


Kfactor = 4.15

Bodwin et al. hep-ph/0611002

Jianwei Qiu




Production rate of is larger than

all these channels:

combined ?

Inclusive production in e+e-

  • Charm associated production:

Kiselev, et al 1994,

Cho, Leibovich, 1996

Yuan, Qiao, Chao, 1997

  • Ratio to light flavors:

  • Message:

Jianwei Qiu






  • None of the factorized production models, including

    NRQCD model, were proved theoretically

  • Factorization of NRQCD model fails for low pT

  • Factorization of NRQCD model might work for large pT

Spectator interactions are suppressed by (1/pT)n

Factorization is necessary for the predictive power

Jianwei Qiu




Factorization: fragmentation contribution

Nayak, Qiu, Stermen, 2005

  • Fragmentation contribution at large PT

  • Fragmentation function – gluon to a hadron H (e.g., J/ψ):

Cannot get fragmentation func. from PDFs or decay matrix elements

Jianwei Qiu

  • IR safe

  • gauge invariant and universal

  • independent of the direction of the Wilson lines


Connection to NRQCD Factorization

  • Proposed NRQCD factorization:

  • Proved pQCD factorization for single hadron production:

  • Prove NRQCD Factorization

To prove:

  • Status: Have not been able to prove or disprove this!

Jianwei Qiu

Leading power in MH/PT

  • Cross section is given by the fragmentation contribution:

  • partonic part should be infrared safe for all powers in αs:

  • fragmentation functions obey the DGLAP evolution

  • Only difference from single pion production is the

  • fragmentation functions

  • Should only apply to the region where PT >> MH

  • Can we do better at lower PT?

Power correction in 1/PT – direct production

Jianwei Qiu

Factorization for heavy quarkonium production

  • Factorized cross section:

Kang, Qiu and Sterman

  • Expect the first two terms to dominate:

  • H(4) are IR safe and free of large logarithms

  • D(4) are fragmentation functions of 4-quark operators

Qiu, 1990

  • Urgent projects:

Calculation of H(4) and evolution of D(4)

Jianwei Qiu

“Direct” production of heavy quark pairs

  • Removal of fragmentation logarithms:

Project the factorized formula to the state

H(4) are free of large logarithms

– absorbed into the PDFs and fragmentation functions

  • All partonic hard parts are evaluated at PT:

Smooth transition from high PT to PT ~ MH

Need “new” non-perturbative fragmentation functions

Jianwei Qiu

Summary and outlook

  • QCD has been very successful in interpreting data in

  • high energy collisions

  • However, the successful collinear factorization formalism

  • has difficulties to explain phenomena at fixed target

  • energies, where high order pQCD corrections, so as

  • new types of QCD dynamics become important.

  • J-PARC facility could make crucial contributions to our

  • understanding of QCD and strong interaction via

  • measurements of single hadron, photon, dilepton,

  • heavy quarkonium, and etc. as well as asymmetries of

  • these reliable observables

Thank you!

Jianwei Qiu

Backup transparencies

Jianwei Qiu

High twist matrix elements

  • Matrix elements of parton operators:

Twist = dimension of the operator – its spin

  • Parton distributions and helicity distributions:

Matrix elements of twist-2 operators:


Probability interpretation

  • Multi-parton correlation functions:

Matrix elements of high twist operators:


NO simple probability interpretation!

More interesting QCD dynamics!

Jianwei Qiu

Cross section and power corrections

  • Cross section with a large momentum transfer:

Power expansion:

  • QCD confinement:

Experiments measure hadrons and leptons, not partons!

  • Factorization – connecting partons to hadrons:

Twist-n parton distribution/correlation:

High twist effects = power corrections

Jianwei Qiu

“Enhance” the power corrections

  • Calculable high twist effects are in general “small”:

If the 1st power correction is large, immediate question is

what is the size of the next power corrections

High twist effects are small for fully inclusive cross section

  • Observables – leading power term vanishes:

  • Observables – large power corrections – resummation:

Single transverse spin asymmetry:

, …



Transverse momentum broadening:

Jianwei Qiu

Negative gluon distribution at low x, Q2?

  • NLO global fitting

    leads to negative

    gluon distribution

    at low x and Q2


have the same


Does it mean that we have no gluon for

x < 10-3 at 1 GeV?


Jianwei Qiu

Recombination prevents negative gluon

  • Small-xgluons are not

  • localized ina Lorentz

  • contractednucleon



  • Gluon recombination

  • Recombination slows

  • down Q2-evolution

  • Prevents the distribution

  • to be negative

Gribov, Levin, Ryskin, 83

Mueller, Qiu, 86, McLerran, Venugopalan, 94, …

Eskola, et al. 03

Jianwei Qiu

Hard probe at low x

  • Hard probe – process with a large momentum transfer:

  • Size of a hard probe is very localized and much smaller

  • than a typical hadron at rest:

  • But, it might be larger than a Lorentz contracted hadron:

If an active parton xis small enough

the hard probe could cover several nucleons

in a Lorentz contracted large nucleus!

Jianwei Qiu

Frame dependence?

  • In target rest frame:

  • If , the q-qbar state of the virtual photon

    can interact with whole hadron/nucleus coherently.

The conclusion is frame


Jianwei Qiu

Parton saturation

Gribov, Levin, Ryskin, 83

Mueller, Qiu, 86

  • Saturation: Radiation = Recombination


McLerran, Venugopalan, 94, …

  • Saturation scale:

Proton is dilute enough

Use nuclear target!

  • How to approach the

  • saturation region?

  • How to treat the

  • saturation in QCD?

Jianwei Qiu

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