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

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

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Outline

  • 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


Cross sections and spin asymmetries in hadronic collisions

High energy hadronic collisions

  • High energy scattering process:

PP (Jet, π, γ, J/ψ,…)X,

w/o polarization

In-state

Out-state

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 spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

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!

2

2

(Diagrams with more active partons

from each hadron!)

A Probability ~ A Product of probabilities!

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

Questions

  • 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

successful

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Unpolarized inclusive DIS – one hadron

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

Prediction vs CDF Run-II data

Highest ET jet !

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Q2=10 GeV2

NLO

Q2=10 GeV2

xf(x,Q2)

xu

xG(x0.05)

xd

xS(x0.05)

x

Universal parton distributions

  • Modern sets of PDFs with uncertainties:

Consistently fit almost all data with Q > 2GeV

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Jet production at RHIC - two hadrons

  • STAR:

PRL97, 252001

(2006)

NLO Calclation: Jäger, Stratmann, Vogelsang

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Inclusive single hadron at RHIC – 3 hadrons

  • PHENIX:

PRD76, 051106

(2007)

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Extending x coverage and particle type

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

  • BRAHMS:

PRL98, 252001 (2007)

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Direct photon at RHIC

  • PHENIX:

Sakaguchi, 2008

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Polarized inclusive DIS – one hadron

  • Success of the NLO formalism:

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

RHIC Spin Program

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

  • The asymmetry:

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

RHIC Measurements on ΔG

Star jet

Phenix π0

Small asymmetry leads to small gluon “helicity” distribution

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Current status on ΔG

  • Definition:

  • NLO QCD global fit - DSSV:

PRL101,072001(2008)

Strong constraint on ΔG from

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Large SSA in hadronic collisions

  • Hadronic :

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

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 sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

Pion production at fixed target energies

  • A long standing problem:

Data is much higher

than NLO at fixed-target

energies!

Aurenche et al.; Bourrely, Soffer

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Direct photon at fixed target energies

  • Another long standing problem:

Aurenche et al., PRD73, 094007(2007)

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Large high order corrections in power of αs

  • Higher order corrections beyond NLO:

Threshold logarithms

where

  • Threshold logarithm is a consequence of the rapidity

  • integration of the generic perturbative term:

with

The limit:

inhibits the real emission

while the soft /collinear gluon

emission is still allowed

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Enhanced by steep falling parton flux

  • Convolution with parton distributions:

where

  • 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


Cross sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

Resummation for single hadron production

  • Resummed “coefficient” functions:

de Florian,Vogelsang, 2005

“Observed” partons

Unobserved recoil jet

where

  • Correction to gggg:

Big enhancement factor:

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Improvement from resummation

E706

WA70

de Florian,Vogelsang, 2005

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

Drell-Yan at low QT – two scales

  • Fixed-order collinear pQCD calculation:

Note:

  • “integrated” QT distribution:

Effect of gluon

emission

Assume this exponentiates

  • “resummed” QTdistribution – DDT formalism:

as QT→0

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

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

    resummation

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

“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


Cross sections and spin asymmetries in hadronic collisions

Examples with large Q

Qiu and Zhang, PRL, 2001

Power correction is very small, excellent prediction!

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Example with low Q large phase space

CDF Run-I

D0 Run-II

A prediction

CEM with all order resummation of soft gluon shower

Berger, Qiu, Wang, 2005

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Example with low Q small phase space

Qiu and Zhang, PRD, 2001

IF bmax ~ 0.3 1/GeV

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

Coherent soft interaction

A

Quarkonium

B

Perturbative

Non-perturbative

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


Cross sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

CSM: Huge high order corrections

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Polarization of quarkonium at Tevatron

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

  • Normalized distribution:

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

Exclusive production in e+e-

Li, He, and Chao, Braaten and Lee, …

  • Double charm production:

LO

  • Possible resolution for J/ψ+ηc:

Zhang, Gao, Chao, PRL

Kfactor = 1.96

  • NLO correction:

  • Relativistic Correction:

Kfactor = 1.34

X-section:

Wave func:

Kfactor = 1.32

Combined:

Kfactor = 4.15

Bodwin et al. hep-ph/0611002

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Belle:

NRQCD:

Belle:

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


Cross sections and spin asymmetries in hadronic collisions

PQCD

Quantum

inteference

NRQCD

Factorization

  • 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


Cross sections and spin asymmetries in hadronic collisions

2

2

2

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


Cross sections and spin asymmetries in hadronic collisions

  • IR safe

  • gauge invariant and universal

  • independent of the direction of the Wilson lines

with

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


Cross sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

“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


Cross sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

Backup transparencies

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

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 sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

“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


Cross sections and spin asymmetries in hadronic collisions

Negative gluon distribution at low x, Q2?

  • NLO global fitting

    leads to negative

    gluon distribution

    at low x and Q2

MRST, CTEQ PDF’s

have the same

features

Does it mean that we have no gluon for

x < 10-3 at 1 GeV?

No!

Jianwei Qiu


Recombination prevents negative gluon

Recombination prevents negative gluon

  • Small-xgluons are not

  • localized ina Lorentz

  • contractednucleon

Data

Recombination

  • 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


Cross sections and spin asymmetries in hadronic collisions

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


Cross sections and spin asymmetries in hadronic collisions

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

independent

Jianwei Qiu


Cross sections and spin asymmetries in hadronic collisions

Parton saturation

Gribov, Levin, Ryskin, 83

Mueller, Qiu, 86

  • Saturation: Radiation = Recombination

Estimate:

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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