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:.
Brookhaven National Laboratory
KEK theory center workshop on high-energy hadron physics with hadron beams KEK, Japan, January 6-8, 2010
Role of the quantum interference or correlation
Factorization – predictive power of pQCD calculation
Expansion in inverse power of hard scale and in power of αs
Resummation to all orders in αs
Resummation to all powers in power corrections
Single spin asymmetry, transverse momentum broadening, …
PP (Jet, π, γ, J/ψ,…)X,
Momentum transfer Q=(PT, MJ/ψ, …) >> typical hadronic scale ~ 1/fm
Scattering amplitude square – Probability – Positive definite
A function of in-state and out-state variables: momentum, spin, …
– Positive definite
Not necessary positive!
Chance to see quantum interference directly
Do not see partons in the detector!
QCD parton dynamics
Single active parton from each hadron!
(Diagrams with more active partons
from each hadron!)
A Probability ~ A Product of probabilities!
Collinear on-shell active partons
On-shell active partons
Not generally proved, but, used phenomenologically
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 where
NLO pQCD collinear factorization formalism has NOT been very
Unpolarized inclusive DIS – one hadron
Jet in hadronic collisions - two hadrons
Inclusive Jet cross section at Tevatron: Run – 1b results
Data and Predictions span 7 orders of magnitude!
Prediction vs CDF Run-II data
Highest ET jet !
Universal parton distributions
Consistently fit almost all data with Q > 2GeV
Jet production at RHIC - two hadrons
NLO Calclation: Jäger, Stratmann, Vogelsang
Extending x coverage and particle type
Large rapidity p,K,p cross sections for p+p, s=200 GeV
PRL98, 252001 (2007)
Small asymmetry leads to small gluon “helicity” distribution
Strong constraint on ΔG from
Large SSA in hadronic collisions
SSA vanishes in the parton model:
Too large to compete!
Pion production at fixed target energies
Data is much higher
than NLO at fixed-target
Aurenche et al.; Bourrely, Soffer
Aurenche et al., PRD73, 094007(2007)
inhibits the real emission
while the soft /collinear gluon
emission is still allowed
The product of parton distributions strongly favor the region
where xx’ small, that is, enhances the region where
Threshold resummation – resum to all powers.
Sterman; Catani, Trentadue; …
Chance to probe QCD high order dynamics
Mellin moments of :
Resummation for single hadron production
de Florian,Vogelsang, 2005
Unobserved recoil jet
Big enhancement factor:
de Florian,Vogelsang, 2005
Relatively small resummation effect:
for the Compton term
Catani et al.; Sterman, Vogelsang;
Similar enhancement for gggg,
but, gluon fragmentation function
to photon is very small!
Drell-Yan at low QT – two scales
Effect of gluon
Assume this exponentiates
Particle can receive many finite kT kicks via soft gluon radiation
yet still have QT=0 – Vector sum!
impose 4-momentum conservation at each step of soft gluon
IF long b-space tail
is not important for
Large phase space for the shower = large s
Qiu and Zhang, PRL, 2001
Power correction is very small, excellent prediction!
CEM with all order resummation of soft gluon shower
Berger, Qiu, Wang, 2005
Qiu and Zhang, PRD, 2001
IF bmax ~ 0.3 1/GeV
NO CSS resummation proved for these “structure functions”!
The CSS formalism only proved for inclusive Drell-Yan
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”
where are functions of and the choice of frame
for all values of even when
No LO perturbative double logs!
J.C. Peng, 2008
Extending CSS resummation
Collins, Qiu and Sterman
Different models Different assumptions/treatments on
how the heavy quark pair becomes a quarkonium?
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
Chang 1974, Einhornand Ellis (1975), …
Fritsch (1978); Halzen; …
open charm threshold could become bound quarkonia
Bodwin, Braaten, Lapage (1994); …
NRQCD: Cho & Wise, Beneke & Rothstein, 1995, …
KT-fact: Baranov, 2002
CDF Collaboration, PRL 2007
Li, He, and Chao, Braaten and Lee, …
Zhang, Gao, Chao, PRL
Kfactor = 1.96
Kfactor = 1.34
Kfactor = 1.32
Kfactor = 4.15
Bodwin et al. hep-ph/0611002
Production rate of is larger than
all these channels:
Inclusive production in e+e-
Kiselev, et al 1994,
Cho, Leibovich, 1996
Yuan, Qiao, Chao, 1997
NRQCD model, were proved theoretically
Spectator interactions are suppressed by (1/pT)n
Factorization is necessary for the predictive power
Factorization: fragmentation contribution
Nayak, Qiu, Stermen, 2005
Cannot get fragmentation func. from PDFs or decay matrix elements
Connection to NRQCD Factorization
Power correction in 1/PT – direct production
Kang, Qiu and Sterman
Calculation of H(4) and evolution of D(4)
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
Twist = dimension of the operator – its spin
Matrix elements of twist-2 operators:
Matrix elements of high twist operators:
NO simple probability interpretation!
More interesting QCD dynamics!
Experiments measure hadrons and leptons, not partons!
Twist-n parton distribution/correlation:
High twist effects = power corrections
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
Single transverse spin asymmetry:
Transverse momentum broadening:
leads to negative
at low x and Q2
MRST, CTEQ PDF’s
have the same
Does it mean that we have no gluon for
x < 10-3 at 1 GeV?
Gribov, Levin, Ryskin, 83
Mueller, Qiu, 86, McLerran, Venugopalan, 94, …
Eskola, et al. 03
If an active parton xis small enough
the hard probe could cover several nucleons
in a Lorentz contracted large nucleus!
can interact with whole hadron/nucleus coherently.
The conclusion is frame
Gribov, Levin, Ryskin, 83
Mueller, Qiu, 86
McLerran, Venugopalan, 94, …
Proton is dilute enough
Use nuclear target!