cross sections and spin asymmetries in hadronic collisions

1

Cross Sections and Spin Asymmetries

in Hadronic Collisions

Jianwei QiuBrookhaven National Laboratory

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

January 6, 2010 Jianwei Qiu

January 6, 2010 Jianwei Qiu2

Outline

QCD and pQCD in hadronic collisions:

Cross sections and asymmetries:Role of the quantum interference or correlation

Factorization – predictive power of pQCD calculationExpansion 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


High energy scattering process:

High energy hadronic collisions

PP (Jet, π, γ, J/ψ,…)X, w/o polarization

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

In-state Out-state

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, ...


Scattering amplitude square – Probability – Positive definite A function of in-state and out-state variables: momentum, spin, …

Spin-averaged cross section:

Not necessary positive!Chance to see quantum interference directly

– Positive definite

Asymmetries or difference of cross sections:

Cross sections and asymmetries Cross section:


Connecting hadrons to QCD partons QCD confinement:

QCD parton dynamics Factorization - approximation:

Do not see partons in the detector!

Single active parton from each hadron!

(Diagrams with more active partons from each hadron!)

A Probability ~ A Product of probabilities!

2 2


PQCD factorization Collinear factorization:

Collinear on-shell active partons

Transverse-momentum dependent (TMD) factorization:

On-shell active partons

Not generally proved, but, used phenomenologically


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

Power correction is process dependent – non-universal! NLO is necessary


Questions

What have we learned from hadronic collisions?

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

can contribute to our knowledge of strong interaction in hadronic collisions?

NLO pQCD collinear factorization formalism has been very successful in interpreting data from high energy scattering

J-PARC could provide crucial tests of QCD in a regime whereNLO pQCD collinear factorization formalism has NOT been very successful


Unpolarized inclusive DIS – one hadron


Jet in hadronic collisions - two hadrons

Data and Predictions span 7 orders of magnitude!

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


Prediction vs CDF Run-II data

Highest ET jet !


Universal parton distributions Modern sets of PDFs with uncertainties:

Consistently fit almost all data with Q > 2GeV

xf(x,Q

2 )

x

Q2=10 GeV2 Q2=10 GeV2

xu

xd

xS(x0.05)

xG(x0.05)

NLO


Jet production at RHIC - two hadrons STAR:

NLO Calclation: Jäger, Stratmann, Vogelsang

PRL97, 252001(2006)


Inclusive single hadron at RHIC – 3 hadrons

PHENIX:

PRD76, 051106(2007)


Extending x coverage and particle type

BRAHMS:PRL98, 252001 (2007)

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


Direct photon at RHIC PHENIX:

Sakaguchi, 2008


Polarized inclusive DIS – one hadron Success of the NLO formalism:

−=Lg1


RHIC Spin Program Collider of two 100 (250) GeV polarized proton beam:

The asymmetry:

−=Lg1


RHIC Measurements on ΔGStar jet Phenix

π0

Small asymmetry leads to small gluon “helicity” distribution


Current status on ΔG Definition:

NLO QCD global fit - DSSV: PRL101,072001(2008)

Strong constraint on ΔG from


Large SSA in hadronic collisions Hadronic :

( )p p l Xp


One collinear parton per hadron in hard collision:

Helicity – flip quark mass term Generate the phase from the loop diagram αs

SSA in parton model

SSA vanishes in the parton model:

spin-dependence of parton’s transverse motion


QCD Collinear factorization approach is more relevant

– Expansion

Cross section with ONE large scale

Too large to compete! Three-parton correlation

SSA – difference of two cross sections with spin flip is power suppressed compared to the cross section

Sensitive to twist-3 multi-parton correlation functions Integrated information on parton’s transverse motion

Koike’s talk


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


Direct photon at fixed target energies

Another long standing problem:

Aurenche et al., PRD73, 094007(2007)


Higher order corrections beyond NLO:

where Threshold logarithms

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

Large high order corrections in power of αs


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 energyChance to probe QCD high order dynamics


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 zi into the “transformed” space

Mellin moments of : Threshold resummation:


Resummation for single hadron production

de Florian, Vogelsang, 2005 Resummed “coefficient” functions:p “Observed” partons

Unobserved recoil jet

where Correction to gggg:

Big enhancement factor:


Improvement from resummationE706

de Florian, Vogelsang, 2005

WA70


Improvement to direct photon production

Direct contribution:

Relatively small resummation effect:

Catani et al.; Sterman, Vogelsang; Kidonakis, Owens

for the Compton term

Fragmentation contribution:

Similar enhancement for gggg, but, gluon fragmentation function to photon is very small!


Drell-Yan at low QT – two scales Fixed-order collinear pQCD calculation:

LO Born

2 2

2 22 T

T

sF

T

n Qd d Cdyd

Q

yQ Qd p

2

Bornreal+viru

2

a0

22

l

2

t

with Q

T s WT

d ddQ O Q MdydQ dy

Note:

“integrated” QT distribution:

22

2

2

2

2

2 22 2

2

real+virutalreal+virutal

B

22

orn Born

Bo

0 0

2

2

2 2

2 2

n

2

r

1 2 1

exp

T

T

T

Q Q

T TT T

QTs s

F T FT

Q

Q

T

s

Q

TF

d ddp dpdydp d

Q

ydp

n Q pd dC dp C n Qdy p dy

d C n Qdy

Q

p p

p

=

Effect of gluon emission

Assume this exponentiates

“resummed” QT distribution – DDT formalism:

22 2

Bor

22 2

n

2

2 exp 0 TT

T

sF F

T

sQn Qd d C C n Q

dyd yQ

QdQ p p

as QT→0


CSS resummation formalism Experimental fact:

2 finite [neither n or ] as 0! 0 TT

ddyd

QQ

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


“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 QLarge phase space for the shower = large s

Jianwei Qiu35January 6, 2010

Power correction is very small, excellent prediction!

Examples with large QQiu and Zhang, PRL, 2001


Example with low Q large phase space

Berger, Qiu, Wang, 2005CEM with all order resummation of soft gluon shower

CDF Run-I D0 Run-II

A prediction


IF bmax ~ 0.3 1/GeV

Example with low Q small phase spaceQiu and Zhang, PRD, 2001


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


Resummed “helicity structure functions” Drell-Yan hadronic tensor:

EM current conservation:where are functions of and the choice of frame

for all values of even when Connection to inclusive cross section:

Difficulty for : No LO perturbative double logs!


Lam-Tung relation Normalized Drell-Yan angular distribution:

Lam-Tung relation:

J.C. Peng, 2008

Peng’s talk

TMD Boer-Mulders function:

Extending CSS resummationCollins, Qiu and Sterman

Boer’s talk


Heavy quarkonium production

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

Fact:

Basic production mechanism:

12 Q

rm

Coherent soft interaction

Quarkonium

Perturbative Non-perturbative

A

B

( )( ) , ,AB QQ

AB h Q hQQ QQ hstates

statesstate

QQQs

dd F p p p

d

=

Different models Different assumptions/treatments on how the heavy quark pair becomes a quarkonium?


Popular production models Color singlet model: Only pairs with right quantum number can become quarkonia Non-perturbative part ~ decay wave function squared

Color evaporation model: 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:

2/ / [ ] /

[/

]

(0)AB J J AB O cc JO

JM m OM yy y y =

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

Chang 1974, Einhorn and Ellis (1975), …

Fritsch (1978); Halzen; …

Bodwin, Braaten, Lapage (1994); …


CSM: Huge high order corrections


Polarization of quarkonium at Tevatron Measure angular distribution of μ+μ− in J/ψ decay

Normalized distribution:


Surprises from polarization measurements

Transverse polarization at high pT?NRQCD: Cho & Wise, Beneke & Rothstein, 1995, …

T L

T L

=

CDF Collaboration, PRL 2007

KT-fact: Baranov, 2002


Li, He, and Chao, Braaten and Lee, …

LO

Possible resolution for J/ψ+ηc:

Exclusive production in e+e-

Double charm production:

NLO correction: Relativistic Correction:

Kfactor = 1.96

Kfactor = 1.34X-section:Wave func: Kfactor = 1.32

Kfactor = 4.15

Bodwin et al. hep-ph/0611002

Combined:

Zhang, Gao, Chao, PRL


Charm associated production:

Kiselev, et al 1994,Cho, Leibovich, 1996Yuan, Qiao, Chao, 1997

Ratio to light flavors:

Production rate of is larger thane e J ccy

Message:

,e e J ggy , ...e e J qqy combined ?

all these channels:

Inclusive production in e+e-

Belle:NRQCD: 0.07 pb

Belle:


Factorization None of the factorized production models, including NRQCD model, were proved theoretically Factorization of NRQCD model fails for low pT

NRQCD

PQCD Quantuminteference

Factorization of NRQCD model might work for large pTSpectator interactions are suppressed by (1/pT)n

Factorization is necessary for the predictive power


Fragmentation contribution at large PT 2 2

2

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

Nayak, Qiu, Stermen, 2005

Factorization: fragmentation contribution

Cannot get fragmentation func. from PDFs or decay matrix elements


Connection to NRQCD Factorization Proposed NRQCD factorization:

Proved pQCD factorization for single hadron production:

Prove NRQCD FactorizationTo prove:

with IR safe gauge invariant and universal independent of the direction of the Wilson lines

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


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


Factorization for heavy quarkonium production

Factorized cross section:

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

Kang, Qiu and Sterman

Qiu, 1990

Urgent projects:Calculation of H(4) and evolution of D(4)


“Direct” production of heavy quark pairs

Removal of fragmentation logarithms:

All partonic hard parts are evaluated at PT:

Project the factorized formula to the state

H(4) are free of large logarithms – absorbed into the PDFs and fragmentation functions

Smooth transition from high PT to PT ~ MH

Need “new” non-perturbative fragmentation functions


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!

55

Backup transparencies


56

Matrix elements of parton operators:


Twist = dimension of the operator – its spin

High twist matrix elements

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!

57January 6, 2010 Jianwei Qiu

Factorization – connecting partons to hadrons:

Twist-n parton distribution/correlation:

High twist effects = power corrections

QCD confinement:Experiments measure hadrons and leptons, not partons!

Cross section and power corrections

Cross section with a large momentum transfer:Power expansion:


“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:Single transverse spin asymmetry:

Transverse momentum broadening:

Observables – large power corrections – resummation:

, , , …


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!

Negative gluon distribution at low x, Q2?


Recombination prevents negative gluon

Small-x gluons are not localized in a Lorentz contracted nucleon

Data

Gluon recombination

Gribov, Levin, Ryskin, 83

Recombination

Recombination slows down Q2-evolution

Prevents the distribution

to be negativeMueller, Qiu, 86, McLerran, Venugopalan, 94, …Eskola, et al. 03

61

Hard probe – process with a large momentum transfer:2

QCD with q Q q

Size of a hard probe is very localized and much smaller than a typical hadron at rest:

1 2 fm~ RQ

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

or equivalently1 1 1 2 0.1 2cR xm

px

Q xp mR

If an active parton x is small enoughthe hard probe could cover several nucleons

in a Lorentz contracted large nucleus!


Hard probe at low x


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

Frame dependence?


Saturation: Radiation = RecombinationEstimate:

Gribov, Levin, Ryskin, 83Mueller, Qiu, 86

Saturation scale:

Proton is dilute enough

How to approach the saturation region?

How to treat the saturation in QCD?

Use nuclear target!

McLerran, Venugopalan, 94, …

Parton saturation

cross sections and spin asymmetries in hadronic collisions

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