# Presentation: 839376

## From Bjorken Scaling to pQCD---Experimental techniques from p-p collisions of the 1970’s with application to Au+Au collisions at RHIC

- M. J. Tannenbaum
- Brookhaven National Laboratory
- Upton, NY 11973 USA

- Nuclear Physics Seminar  Physics Department, BNL     December 7, 2004

## Bjorken Scaling in Deeply Inelastic Scattering and the Parton Model---1968

## BBK 1971

- S.M.Berman, J.D.Bjorken and J.B.Kogut, Phys. Rev. **D4**, 3388 (1971)

-  BBK calculated for p+p collisions, the inclusive reaction
-                       *A+B ****C + X*     when particle *C *has pT>> 1 GeV/c
-  The charged partons of DIS **must scatter electromagnetically ***“which may be viewed as a ***lower bound*** on the real cross section at large p**T**.”*

## CCR at the CERN-ISRDiscovery of high pT production in p-p 

-  e-6pT breaks to a power law at high pT with characteristic s dependence
-  Large rate indicates that partons interact strongly (>> EM) with other.
-  Data follow BBK scaling but with n=8!, not n=4 as expected for QED

-  F.W. Busser, *et al., *
- CERN, Columbia, Rockefeller Collaboration
-  Phys. Lett. **46B**, 471  (1973)

- Bj scaling  BBK scaling

## BBK scaling with n=8, not 4 Inspires Constituent Interchange Model

- Berman, Bjorken, Kogut, PR**D4**, 3388 (1971)

- xT=2pT/s

- n=4 for QED or vector gluon

- n=8 for quark-meson scattering by the exchange of a quark

- CIM-Blankenbecler, Brodsky, Gunion, Phys.Lett.**42B**,461(1972)

## State of the Art Fermilab 1977

- D. Antreasyan, J. Cronin, et al., PRL **38**, 112 (1977)

- Beautiful xT scaling at all 3 fixed target energies with n=8

- Totally Misleading--Not CIM or QCD but kT

## CCOR 1978--Discovery of “REALLY high pT>7 GeV/c” at ISR

- CCOR A.L.S. Angelis, et al, Phys.Lett. **79B**, 505 (1978)

- See also A.G. Clark, et al Phys.Lett **74B**, 267 (1978)

-  Agrees with CCR, CCRS (Busser) data for pT < 7 GeV/c.

-  Disagrees with CCRS fit pT > 7 GeV/c
-  New fit is:

## n(xT, s) WORKS n5=4++

- Same data Ed3/dp3(xT)   ln-ln plot

## ISR Expt’s more interested in n(xT,s) than absolute cross section

- cross sections vary by factor of 2

- Athens BNL CERN Syracuse Collaboration,  C.Kourkoumelis, et al Phys.Lett. **84B**, 279 (1979)

- But n(xT,s) agrees

## Status of ISR single particle measurements 1978

- kT is what made n=4++  n=8

## Status of QCD Theory in 1978

## LO-QCD in 1 slide

## QCD and Jets are now a cornerstone of the standard model

- Incredibly at the famous Snowmass conference in July 1982, many if not most people were skeptical
- The International HEP conference in Paris, three weeks later, changed everything.

## THE UA2 Jet-Paris 1982

- From 1980--1982 most high energy physicists doubted jets existed because of the famous NA5 ET spectrum which showed NO JETS. This one event changed everybody’s opinion.

## Also Paris 1982-Jets in ET distribution

- Also Paris 1982-Jets in ET distribution

- 1980 ICHEP-NA5 No Jets 7 orders of magnitude

## Also Paris1982-first measurement of QCD subprocess angular distribution using      0-0 correlations

- DATA: CCOR NPB 209, 284 (1982)

- Also Paris1982-first measurement of QCD subprocess angular distribution using      0-0 correlations

- QCD

## The leading-particle effect a.k.a. trigger bias

-  Due to the steeply falling power-law spectrum of the scattered partons, the inclusive particle pT spectrum is dominated by fragments biased towards large z. This was unfortunately called trigger bias by M. Jacob and P. Landshoff, Phys. Rep. **48C**, 286 (1978) although it has nothing to do with a trigger.

- Fragment spectrum given pTq

- Fragment spectrum given pT

## <ztrig>  measured at ISR

-  <ztrig> ~ 0.8-0.9 at ISR, n~ 11
-  <ztrig> xT scales

- DATA: CCOR NPB 209, 284 (1982)

- pTjet=pTtrig+1.5px

- 0.3 GeV/c<pT    || <0.7    ||< 60o

- ztrig=pTtrig/pTjet

## How everything you want to know about JETS was measured with 2-particle correlations

- CCOR, A.L.S.Angelis, et al Phys.Lett. **97B**, 163 (1980)   PhysicaScripta **19**, 116 (1979)

- pTt > 7 GeV/c vs pT

## kT is not a parameter, it can be measured

## Feynman Field & Fox to the rescue

## jT, kT, xE, pout definitions                       all in plane transverse to beam direction

-  kT is transverse momentum of a parton in a proton (2 protons)
-  xE=-pTpTt/|pTt|2 represents away jet fragmentation z
-  pout is component of away pT perpendicular to trigger pTt

- jT, kT, xE, pout definitions                       all in plane transverse to beam direction

******p****out********2**** =x****E****2********2 ******** k****Ty**** ********2**** + ******** j****Ty**** ********2********+ ******** j****Ty**** ********2**

## xE distribution measures fragmentation fn.

- xE distribution measures fragmentation fn.

- xE ~ z/<ztrig>

- Dq(z)~e-6z

-  independent of pTt

- <ztrig>=0.85 measured*

- * but we did learn something new on this issue in PHENIX.

- See M. Jacob’s talk EPS 1979 Geneva

## CCOR 
2 vs x2E

- CCOR 
2 vs x2E

******p****out********2**** =x****E****2********2 ******** k****Ty**** ********2**** + ******** j****Ty**** ********2********+ ******** j****Ty**** ********2**

- CCOR, A.L.S.Angelis, et al Phys.Lett. **97B**, 163 (1980)

## jT is constant-independent of pTt and s Characteristic of jet fragmentation

- jT is constant-independent of pTt and s Characteristic of jet fragmentation

-  it took the e+ e- people several more years to get this correct---because they didn’t understand the seagull effect:  (jT < pT)

## kT varies with pTt and s--not intrinsic

- kT varies with pTt and s--not intrinsic

## We did (re)learn a few things at RHIC

-  FFF’s formula was really:
-  Jan Rak discovered this by insisting to rederive all the formulas, but it was in FFF’s paper.
- <zt> depends on pTa as well as pTt but may be too confusing for this talk

******p****out********2**** =x****E****2********2 ******** k****Ty**** ********z****t ********2**** + ******** j****t****Ty**** ********2********+ ******** j****a****Ty**** ********2**

-  CCOR NPB 209, 284 (1982)

## kT Phenomenology-I

## kT Phenomenology-II

## Early theoretical attempt to understand kT

- Early theoretical attempt to understand kT

-  Modern work falls under the subject  “resummation”

-  <kT>=3.5/2=2.5 GeV/c

## Gaussian Integrals-I

## Gaussian Integrals--II

## Conclusions from ISR

## A puzzle from RHIC: why does                   NLO-QCD fit the p-p 0 spectrum with no kT?

- A puzzle from RHIC: why does                   NLO-QCD fit the p-p 0 spectrum with no kT?

- Data: PHENIX PRL** 91**, 241803 (2003)
- Theory: W.Vogelsang, see B.Jager, A.Schafer, M.Stratmann,W.Vogelsang PR**D67**,054005(2003)

## kT and NLO are distinct---e.g. Drell Yan

- kT and NLO are distinct---e.g. Drell Yan

- A.S.Ito, et al, PRD23,604 (1981)

- J.K.Yoh, et al,                CFS, PRL **41**, 684 (1978)

- A.L.S.Angelis, et al,     CCOR, PLB **87**, 398 (1979)

## <pT>(=2kT) vs s in Drell-Yan

- CMOR, NPB348, 1 (1991)

## N.B.-- Lots of Drell-Yan Measurements at Colliders: all you need is luminosity.

- ISR

- CDF

## kT and NLO II

- ``Every final state in hard scattering carries the imprint of QCD dynamics at all scales.’’

-  For the only measurement of kT in direct photon production that I know of, see UA2 Collaboration, ZPC** 41**, 395 (1988)
-  They also measure cos* distribution for + Jet production and show that it is flatter than Jet+Jet (Compton-like).
-  L.Apanasevich, et al, PR **D59** 074007 (1999) doesn’t measure kT they derive it by kT-smearing NLO cross predicitons to agree with measurements. See also hep-ex/0407011.

- In George Sterman’s words 12/3/04:

## Application to RHIC

## RHIC pp spectra s=200 GeV nicely illustrate hard scattering phenomenology

- 0

- Good agreement with NLO pQCD
- this is no surprise for `old timers’ (like me) since as I just explained, single particle inclusive spectra were what proved QCD in the late 1970’s before jets.
**Reference for A+A and p+A spectra**
-  0 measurement in same experiment allows us the study of nuclear effect with less systematic uncertainties.

**PHENIX (p+p) PRL 91, 241803 (2003)**

**Notes:**
Add to boxes; Thermal e-6pT independent of sqrt s, Hard varies strongly with sqrts.

## Inclusive single hadron high pT spectra in p-p all s

- Inclusive single hadron high pT spectra in p-p all s

## xT scaling in p-p collisions x~0.05-0.10

- xT

##   -A DIS at AGS (1973)--Hard-Scattering is pointlike 

- M. May, et al, (M.Murtagh, T.Kirk, MJT) PRL **35**, 407 (1975)

## M. May, et al.,

## High pT in A+B collisions---TAB Scaling

- High pT in A+B collisions---*T**AB* Scaling

- view along beam axis

-  For point-like processes, the cross section in p+A or A+B collisions compared to p-p is simply proportional to the relative number of pointlike encounters
-  A for p+A, AB for A+B for the total rate
-  TAB the overlap integral of the nuclear profile functions, as a function of impact parameter b

- looking down

**Notes:**
In the last bullet mention Nbinary=Tab X \sigma_int, so Nbinary or Ncoll scaling

## What really Happens: for p+A RA > 1! 

- The anomalous nuclear enhancement a.k.a. the Cronin effect--
- due to multiple scattering of initial nucleons (or constituents)

- Known since 1975 that yields increase as   A,    > 1

- J.W. Cronin et al.,Phys. Rev. **D11**, 3105 (1975)
- D. Antreasyan et al.,Phys. Rev. **D19**, 764 (1979)

- =1.150.01

**Notes:**
Give power of alpha on this plot.

## For A+A: RAA1 before RHIC

-  The importance of comparison data!

## RAA at RHIC--Suppression to at least 10 GeV/c

- PHENIX, PRL 91 (2003) 072301

- Binary scaling

- Participant scaling

- Factor 5

**Large suppression in central AuAu - Never seen previously!!  A breakdown of QCD???**

**Peripheral AuAu - consistent with N****coll**** scaling (large systematic error)**

## PHENIXSemi-Inclusive 0 Au+Au sNN=130 and 200 GeVvs pT

**Peripheral 60 -- 80%**

**Central 0-10%**

- S.S.Adler, et al, PRC **69**, 034910 (2004)

## Same data vs xT on log-log plot

## n(xT) point-by-point 200/130

-  0 xT scales in both peripheral and central Au+Au with same value of n=6.3 as in p-p
-  (h+ + h-)/2 xT scales in peripheral same as p-p but difference between central and peripheral is significant

## xT scaling of direct  in p-p

- PHENIX preliminary, K.Okada, H. Torii, et al, SPIN 2004, JPS2004

## Recall 0: n=5.1 works better for xT> 0.2

## xT scaling with Jets at the Tevatron a failure of QCD?

- xT scaling with Jets at the Tevatron a failure of QCD?

- _Ratio of Scaled Cross Sections 630/1800_

-  Exp’t       n4= 0.448       n=4.45
-  Theory    n4= 0.559       n=4.56
-  Either just outside or just touching the systematic errors?

- J.Huston,  Proc. ICHEP98, World Scientific also see CDF qcd www pages and   	         G.C.Blazey & B.L.Flauger, ARNPS **49**, 633 (99)

## Slide 55

## Backup with PHENIX highlights

## Central Spectrum is suppressed---is this due to a shift caused by energy loss

## RAA  : High PT Suppression to at least 10 GeV/c

-  PRL 91 (2003) 072301

- Binary scaling

- Participant scaling

- Factor 5

**Large suppression in central AuAu - close to participant scaling at high P****T**

**Peripheral AuAu - consistent with N****coll**** scaling (large systematic error)**

## Cronin effect observed in d+Au at RHIC sNN=200 GeV

- PHENIX preliminary 0 d+Au vs centrality for DNP2003

## Nuclear modification factor: sNN dependence for A+B collisions

- Nuclear modification factor: sNN dependence for A+B collisions

**A.L.S.Angelis** PLB 185, 213 (1987)
- WA98, EPJ C 23, 225 (2002)
- PHENIX, PRL 88 022301 (2002)
- D.d'E. PHENIX Preliminary QM2002

- CERN: Pb+Pb (sNN ~ 17 GeV),  (sNN ~31 GeV): **all previous msmts B+A**-Cronin enhancement

- Ncollision scaling
- Npart scaling

- RAA ~  0.4
-                           RAA~0.2

- RAA ~  2.0

- RAA ~1.5

- RHIC Au+Au sNN=130 and 200 GeV HUGE SUPPRESSION---Major Discovery 2001-2

## Spectra are suppressed for more central collisions---is this due to a shift caused by energy loss?

- RAA(pT)=constant for pT> 4
-  d/pTdpT is pT-8.1

-  pT for d/dpT

## |kTy| from pp and dAu

- z =0.75  taken as constant

- kT-broadening increases with pTtrig as as at lower s
- no difference in dAu and pp!
- need lots more data in both pp and p(d)+Au

##  |jTy| and z |kTy| in Au+Au

-  |jTy| and z |kTy| in Au+Au

- (2.5pTtrigg4.0)(1.0pTassoc2.5)

- PHENIX preliminary QM2004

## UA2 results on cos* and kT in direct 

- R. Ansari, et al, UA2, ZPC **41**, 395 (1988)