p-p, p/d-A, and A-A Collisions: Probing “partonic” matter Prof. 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 p-p di-jet Event STAR • Factorization: separation of into • Short-distance physics: • Long-distance physics: ’s From Collins, Soper, StermanPhys. Lett. B438:184-192, 1998
Single High-pt Hadron Production data vs pQCD KKP Kretzer Phys. Rev. Lett. 91, 241803 (2003) • NLO calculation agrees well with PHENIX 0 spectrum (!?) • BUT, FF dependence ? • Lore: KKP better for gluons • Calc. Includes resummation!
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 Soffer and Bourrely, Eur. Phys. J. C36:371-374,2004 • 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.
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 Soffer and Bourrely, Eur. Phys. J. C36:371-374,2004 • 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?
p-p Prompt Production (Fixed target) Laenen, Sterman, Vogelsang, Phys.Rev.Lett.84:4296 (2000) • 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.
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.
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).
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 …
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 !
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)
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?
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.
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” + …
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 hRdA nucl-ex/0406017, PRC in press nucl-ex/0406017, PRC in press • Clearly the “enhancement” of charged hadron production in d-Au depends on rapidity (). • dependence suggests suppression for >1
BRAHMS: d-Au RdAor 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. Jet
(di)jet h-h Correlations in d-Au / p-p K0s-h h-h pt(trig) d+Au200 GeV STAR preliminary From Dan Magestro, Hard Probes 2004 talk • STAR version of “shock and awe” (and I mean it!)
STAR d-Au -h Correlations RMS jT (not jTy) • 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.
PHENIX d-Au/p-p, - h, Correlations PHENIX preliminary 1-2 GeV/c 0.4-1 GeV/c 2-3 GeV/c 3-5 GeV/c • “Trigger” pion pT > 5 GeV/c • Four different associated hadron pT bins • Clearly see role of constant jT, contribution from kT d-Au p-p
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. Pout Pout Jet PHENIX, From J. Jia, DNP’04 Talk Radiative tails pp PHENIX Preliminary
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 1 + (g pQCD direct x Ncoll) / gphenix backgrd Vogelsang NLO 1 + (g pQCD direct x Ncoll) / gphenix backgrd Vogelsang, mscale = 0.5, 2.0 1 + (g pQCD direct x Ncoll) / (gphenix pp backgrd x Ncoll) • See “expected” high-pT photon production rate • “Clincher” for high-pT suppression. • Initial hard scatterings occur at expected rate. 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, Phys.Rev.C70:037901,2004 PHENIX nucl-ex/0408007 • 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” ??
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 …