p-p, p/d-A, and A-A Collisions: Probing “partonic” matterProf. Brian A. Cole.Columbia University

5th International Conference on Physics and Astrophysics of Quark Gluon Plasma

A very incomplete, highly biased (by my interests) perspective on hard scattering in p-p, p-A, A-A collisions at RHIC.

I will focus on conceptual issues and will only use data as needed to make my points.

My apologies in advance for all of the beautiful data I will not be able to show.

An Embarassment of Riches•The first 4 years of RHIC operation have brought

– Au-Au collisions at s = 20, 64, 130, 200 GeV– d-Au collisions at s = 200 GeV– (polarized) p-p collisions at s = 200 GeV– Now in the middle of Cu-Cu at s = 200 GeV

•The resulting data have dramatically extended an already wealthy data-set on strong interactions under various conditions.

•We are also blessed with a rich physics program– (strongly coupled?) quark-gluon plasma– quark/gluon interactions in a “medium”– physics of hadronization– Saturation /CGC– Hard scattering & application of pQCD at modest pT

– …

The Focus of this Talk•A complete discussion of the above physics topics and the application to all of the available p-p, p/d-A, A-A data from the last 30 years would be daunting …

•To keep this talk manageable and to provide it focus, I will concentrate on hard processes:– Single high-pT hadron production

– Hadron-hadron (h-h) jet/di-jet induced correlations– Prompt photon production

•And from these partially address:– Hard scattering & issues in the application of pQCD

to data at RHIC energies. – quark/gluon interactions in a “medium”– Saturation /CGC

Hard Scattering in p-p Collisions

•Factorization: separation of into– Short-distance physics: – Long-distance physics: ’s

p-p di-jet Event

STARSTAR

a/A

b/B

A

B

ab̂

From Collins, Soper, Sterman Phys. Lett. B438:184-192, 1998

Single High-pt Hadron Production

•NLO calculation agrees well with PHENIX 0 spectrum (!?)– BUT, FF dependence ?– Lore: KKP better for gluons – Calc. Includes resummation!

KKP

Kretzer

data vs pQCDdt

d

z

QzD

QxQxdxdxdp

dE

c

abcaBbaAaba

ˆ),,(

),,(),,(

2

/

2/

2/3

3

0

Phys. Rev. Lett. 91, 241803 (2003)a/A

b/B

A

B

ab̂

D(z)

But QCD is not Nearly So Simple …•Initial and final state radiation leads to QCD evolution– Parton distributions– Fragmentation func’s

•Well-controlled (infrared safe) evolution depends on cancellation of real and virtual radiation.

•Why does this matter?– Radiation broadening of transverse momenta– Phase space restrictions can inhibit the real/virtual

cancellation. High pT hadron production at large xT (low s). Heavy quark production at low transverse momenta.

Application of pQCD vs s

•How well does NLO pQCD work as we go down in energy from RHIC ?

•Clearly describes data more poorly for decreasing s.– And for more

forward production.

•Also, sensitivity to factorization scale also grows.

Soffer and Bourrely, Eur. Phys. J. C36:371-374,2004

Threshold re-summation

•Re-summation that “fixes” problem with phase-space limit improves agreement with data at lower s.

•Much smaller (but non-zero) effect for RHIC at mid-rapidity.

•But, what about at forward rapidity??

Forward Production at RHIC

•NLO pQCD works well at RHIC even at large xF

•But still ~40% scale uncertainty (=pT vs =pT/2) !

•Calculation by Vogelsang also agrees with data– Role of

resummation?

Soffer and Bourrely, Eur. Phys. J. C36:371-374,2004

p-p Prompt Production (Fixed target)

•NLO pQCD also needs corrections to match fixed-target data.

•E706 claims that intrinsic kT ~ 1 GeV is needed to match pQCD to data.

•With incorporation of soft gluon recoil and threshold resummation, much better description of the data.

Laenen, Sterman, Vogelsang, Phys.Rev.Lett.84:4296 (2000)

PHENIX: 200 GeV p-p Prompt Prod.

•See parallel session talk by Stephan Bathe

•Background removed via combination of:– (Jet) isolation cuts 0 decay tag– Statistical subtraction

•Spectrum and yield well-described by NLO pQCD (w/ threshold & recoil resummation)

•~ 15% scale uncertainty above 5 GeV/c

Hard Scattering Rates (1)•Go back to nucleon-nucleon collisions:

– parton flux parton flux parton-

parton

•Why does this even work ?

– In principle should include interference of all different fock states …

– But, large momentum transfer (Q2) to one parton “selects” it out of the superposition.

z

QzD

td

dQxfQxfdxdx

dp

d chcdabNbNaba

NNhard

),(

ˆ),(),(

2/2

2/2

1/2

... qqqqqgggqqqggqqqgqqq

Hard Scattering Rates (2) •Why is there no spatial dependence in:

–parton flux parton flux parton-parton ?

Crude attempt at answer:

•Suppose we imagine some parton density dist. in nucleon, (z,r), w/ z integral:

•Then:

•But for large Q2, interaction is point-like:

– Then only depends on # partons, not (z,r).

–But double parton scattering (measured at Tevatron) is sensitive to (z,r).

),()(

rzdzrt

1,2,

22,1,2,1, )()(

rbr

hard

rd

drtrtrdrdbd

)(22

rrd

d

212,1,2,1, )()( nnrtrtrdrdhard

Hard Scattering Rates (3)

•Now apply above to nuclei: (z,r) A(z,r).

–

•Where:–

–

•Then – with

•Now, apply point-like cross-section:– ??

?

•Yes, if is constant over the spatial region where is appreciable– Otherwise corrections are needed …

AB rbrBBAABA

ABhard rd

dbrtbrtrdrdbN

,,

2,,,, )2/()2/()(

),'(),'(|)'|,'()','('),( 1,,1,,, rzzrzrdzdrrzzrzrdzdrz AAAA

)()()( 1,,1,, rtrTrdrt AAAA

)2/()2/(

,|)(||)(|)()()(

1,,2,,

22,1,2,1,,,,,

brrbrrr

rrd

drtrtrdrdrTrTrdrdbN

AB

BBAABAABhard

NNhardAB

NNhardABAAA

ABhard bTbrTrTrdbN )()()()( ,,,

)()( ,, BBAA rTrT

)( rt

Hard Rates in p/d/A-A Collisions

•TAB is nucleon-nucleon (time-integrated) luminosity

– As every good experimentalist knows:

– So, it is common to define:

– Then,

•Then, for example, we can define:

•But, this introduces an unnecessary apparent dependence on a quantity that we don’t measure.

– The RHIC experiments measure not .

•Why does this matter?

– Because it confuses physicists outside the field.

– It sometimes confuses physicists inside the field.

e.g. the treatment of diffractive cross-section !

dtNcoll L

ABNNinel

ABcoll TN

pphard

ABcoll

ABhard NNbN )(

3

3

3

3

/

1

dpNd

E

dpNd

E

NR pp

AA

AAcoll

AAdA

3

3

dp

dE

pp3

3

dp

NdE

pp

A-A Hard Scattering Rates•Parton flux density “thickness”

–

•For point-like interactions:

– dNhard / dA product of nuclear T’s

– Integrate over transverse area

– Then

– Nbinary (also known as Ncoll) is fiction

no successive nucleon-nucleon scattering !

Just a convenience (pure number not fm-

2)

),()(

rzdzrT nucleon

A

rT

b

|)(||)(|)( rbTrTrdbT BAAB

binary

NNhardNN

inelAB

NNhard

AB

NNhard

ABhard N

dp

dnbT

dp

dnbT

dp

d

dp

dn2222

)()(

•There is, however, a real issue with the treatment of diffractive part of p-p inelastic cross-section.

•The problem is that TAB must be averaged over b– For a range of b that matches applied centrality cuts.

•“Typical” Method:– Relate centrality measure to Npart (including fluctuations)

– Monte-Carlo nucleon locations for two “model” nuclei Using Woods-Saxon nuclear density distributions

– Calculate Npart for A-B collision:

Two nucleons scatter if

– Then, use Npart(b), including fluctuations, to relate centrality cut range to b distribution.

– Calculate TAB averaged over that b distribution.

What about Diffraction Anyway?

NNinelb 12

What About Diffraction Anyway? (2)

•The above approach is basically a classical reduction of Eikonal approximation in quantum mechanics.– For a short-range, strongly absorptive optical potential.

•Kopeliovich (Phys. Rev.C68:044906,2003) has argued– The diffractive contribution to is not correctly handled

using the above-described approach.

– Because diffraction is a quantum-mechanical interference between interacting & non-interaction parts of proton WF.

•One problem with diffraction is that it’s description is simplest in the arcane language of Regge theory.– But an article (Phys. Rev. D18:1696,1978) by Pumplin, Miettinen

shows how to understand diffraction using language of partons.

•My personal opinion: – I think Kopeliovich has a valid argument that must be addressed.

– However, the argument should only affect peripheral collisions.

– I/we don’t know how big any systematic error might be.

ppinel

Coherence in p/d-A Collisions•View in nucleus rest frame:

– For mid-rapidity jet with mass MT:

Relative to nucleus, y=5.4

E pL = MT cosh(y) 100 MT

– Also, Jet formation time: ~1/ MT

Lorentz boost: = cosh(y) 100

– Giving jet formation length (LF)

LF = 20 GeV fm / MT•From this simple analysis we can conclude:

– All for the “action” for mid-rapidity particle production (and forward) occurs along the straight path of the incoming nucleon.

– Even high-pT and heavy quark production processes may be affected by coherence in the multiple scattering process.

•New at RHIC: (semi) hard cross-section large enough for multiple (semi) hard scattering.– Transverse broadening (Cronin effect) + “shadowing” + …

text

STAR d-Au High-pT Charged

•Beware:

– Top plot is RdA

– Bottom plot is Rcp

•Strong enhancement in charged hadron production at =0.

•Enhancement larger for baryons than for mesons.

– Ks similar to

similar to

PHENIX d-Au 0 vs Centrality

•Small Cronin effect (not expected to be large)•It is now known that preliminary data suffer from small trigger bias (central will go peripheral ).

PHENIX d-Au Production

•PHENIX sees small Cronin effect– Approx. consistent within errors with STAR Ks result – Enhancement seen in charged (baryons) all the more striking!

PHOBOS: d-Au h RdA

•Clearly the “enhancement” of charged hadron production in d-Au depends on rapidity ().

• dependence suggests suppression for >1

nucl-ex/0406017, PRC in press nucl-ex/0406017, PRC in press

BRAHMS: d-Au RdA or Rcp vs

•BRAHMS also sees suppression of (h-) yields at larger (beware “isospin” effect for =2.2, =3.2)

•Suppression increases for more central collisions.

PHENIX d-Au Forward/Backward h

•PHENIX observes similar trend in hadron spectra– Suppression relative to “expected” TAB scaling

– Suppression greater for more central collisions– Suppression NOT confined to large only!

Forward Suppression (CGC ??)• Kharzeev, Kovchegov, Tuchin (Phys.Lett.B599:23-31,2004)

•Evolution from enhancement (Cronin effect) at mid-rapidity to suppression at forward rapidity.

•h- RdA modified by charge bias in p-p coll’s.

•Rcp less sensitive.

But, Vitev and Qiu: Higher Twist Effect

•“Higher Twist”: – multiple exchanges between

projectile & target.

•Vitev & Qiu: coherent multiple scattering

Effective rescaling of x of parton from deuteron.

Interpreting Forward Suppression

•(How) different are CGC and coherent multiple scattering approaches?– In target rest frame (appropriate gauge) the CGC

appears as coherent multiple scattering in nucleus.– But analyzed in very specific framework (dipole)– Evolution (due to radiation) of interacting partons is

crucial to forward suppression – otherwise CGC just produces a Cronin effect.

– Is there any way to connect the two approaches Cryptic note in Vitev, Qiu about leading twist

shadowing …

•But, Kopeliovich (hep-ph/0501260): suppression is due to radiation.

•Hwa, Yang, Fries: effect is due to recombination.

Di-hadron Azimuthal () Correlations

•jT represents hadron pT relative to jet

•kT represents the di-jet momentum imbalance

•“y” implies projection onto transverse plane.

yTj

yTj

Jet

yTk

(di)jet h-h Correlations in d-Au / p-p

•STAR version of “shock and awe” (and I mean it!)

h-Λh-Λ

K0s-hh-h

STAR preliminary

d+Au200 GeV

pt (trig

)

From Dan Magestro, Hard Probes 2004 talk

STAR d-Au -h Correlations

•Photons dominantly from 0 decay– Reflect 0 direction

•Assume Gaussian distribution for hadron jT•Study how jT depends on pT of hadrons

– Away from phase space boundaries jT constant.

RM

S j

T (

not

j Ty)

PHENIX d-Au/p-p, - h, Correlations

•“Trigger” pion pT > 5 GeV/c

•Four different associated hadron pT bins

•Clearly see role of constant jT, contribution from kT

0.4-1 GeV/c1-2 GeV/c

2-3 GeV/c 3-5 GeV/c

PHENIX preliminary

p-pd-Au

Alternative Method for Studying (di)jets

•By measuring pout pair-by-pair, more directly see the shape of the jT/kT dist’s.

•See non-Gaussian tails – expected due to hard radiation.

pp

Radiative tails

PHENIX, From J. Jia, DNP’04 Talk

PHENIX Preliminary

JetPout

Pout

Explicit Treatment of Radiation

•Conclude: large radiative component to di-jet kT

– Also see Vitev, Qiu : Phys.Lett.B570:161-170,2003.

• Without accounting for radiation initial parton intrinsic kT ~ 2 GeV/c (RMS).

• After accounting for radiation ~ 1 GeV/c

Analysis of STAR di-hadron distribution by Boer & Vogelsang,

Phys. Rev. D69 094025, 2004

di-jet broadening in d-Au?

•No apparent indication of increased kT.

•But these data are not yet sensitive enough.

•New publication from PHENIX with more results soon …

HI Collisions: Parton Energy Loss

•Medium-induced radiation process is coherent with the “normal” vacuum radiation.– Energy loss is a “higher-twist” affect also– Explicitly used by Wang et al to relate energy loss

in heavy ion collisions to cold nucleus modification of fragmentation in e-A collisions.

– The parton loses energy during fragmentation.Radiation may interact with the medium.

The oft-used GLV diagram

PHENIX: Au-Au High-pT Suppression

•Observed suppression is ~ flat with pT

•Even for non-central collisions !

•Problem for “corona” description ?

PHENIX: Direct Photon Production

•See “expected” high-pT photon production rate

•“Clincher” for high-pT suppression. Initial hard scatterings occur at expected rate.

1 + ( pQCD direct x Ncoll) / ( phenix pp backgrd x Ncoll)

1 + ( pQCD direct x Ncoll) / phenix backgrd Vogelsang NLO

1 + ( pQCD direct x Ncoll) / phenix backgrd Vogelsang, mscale = 0.5, 2.0

PHENIX Preliminary PbGl / PbSc Combined

High-pT (un) Suppression: Baryons

•Clear evidence from all data that high-pT baryons are less suppressed than mesons.– Usually interpreted in terms of coalescence.

•But, also see significant enhancement of baryons in d-Au collisions– Also coalescence ?

Coalescence/Recombination in d-Au

•Hwa and Yang argue that coalesence can produce observed d-Au baryon excess.

•But PHENIX observes same strength of jet correlations for leading protons & pions.

•“Correlated coalescence” ??

Hwa and Yang, Phys.Rev.C70:037901,2004

PHENIX nucl-ex/0408007

Recombination

•Hwa has argued that one can view jet fragmentation as a recombination process.

It may be reasonable that the same jet correlations can be observed in (e.g.) p-p and d-Au

Even when recombination produces significant modification (e.g.) of the baryon yield.

•But: This sounds to me more like an effect of coherent multiple scattering– Is baryon enhancement different higher-twist effect?

•One way to test/constrain recombination model– Perform measurements with and without detected

spectator neutron.– Can reduce the produced particle density while

keeping scattering length ~ fixed.

Summary•I have shown you a small fraction of data available from RHIC on p-p, d-Au collisions.

•p-p and d-Au data are absolutely essential benchmarks for high-pT/hard physics @ RHIC.

•pQCD works well at RHIC, but – Significant disagreement using different FF.– Soft gluon re-summation is included in the

“standard” comparisons of PHENIX data to pQCD.– Resummation clearly more important @ 62 GeV.

•pQCD calculations are entering (have entered) a new era of precision.– Resummation techniques are clearly complicated

but much progress has been made.– (How) does nucleus modify these contributions?

Summary (2)•d-Au measurements show interesting phenomena

– Weak Cronin effect in pions at mid-rapidity– Strong Cronin effect for baryons– Strong suppression of forward hadron production.

•Clearly the pT distributions evolve continuously with rapidity over a large rapidity range.– Weak Cronin effect at mid-rapidity an accident

•Interpretation of the forward suppression unclear.– CGC, coherent mult. scattering, Sudakov suppression,

recombination, …– This is not a good state of affairs …Need discriminating tests of models

•Baryon enhancement in d-A from recombination?– Personally, I am skeptical …

Summary (3)

•p-p/d-Au studies of jet correlations are providing stringent calibration of Au-Au jet measurements.

Essential because jet correlation measurements are starting to provide unique probes of medium.

•High-pT measurements at RHIC are possibly the best calibrated HI probe ever. – Unidentified hadrons, identified hadrons, direct , …

•But, we still have much to do– Testing role of saturation at in d-Au crucial to

understanding Au-Au initial conditions.

Whatever produces the y/-dependence in d-Au must also affect Au-Au collisions.

– We must improve our understanding of baryons …