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Cross Sections and Spin Asymmetries in Hadronic Collisions

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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

Jianwei Qiu

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

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 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!

2

2

(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

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

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

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

Jet production at RHIC - two hadrons

- STAR:

PRL97, 252001

(2006)

NLO Calclation: Jäger, Stratmann, Vogelsang

Jianwei Qiu

Inclusive single hadron at RHIC – 3 hadrons

- PHENIX:

PRD76, 051106

(2007)

Jianwei Qiu

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

Direct photon at RHIC

- PHENIX:

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:

PRL101,072001(2008)

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

energies!

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

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

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

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

where

- Correction to gggg:

Big enhancement factor:

Jianwei Qiu

Improvement from resummation

E706

WA70

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 gggg,

but, gluon fragmentation function

to photon is very small!

Jianwei Qiu

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

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

“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

CDF Run-I

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

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

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:

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

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

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

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

- 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

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

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

- 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

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

independent

Jianwei Qiu

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