1. Predicting and measuring the total inelastic cross section at the LHC
Konstantin Goulianos
The Rockefeller University
Valparaiso, Chile   May 19-20, 2011

2. The total inelastic pp cross section at LHC K. Goulianos
Contents
1) Introduction gaps
2) Predicting the total s: st
3) Predicting the total-elastic s: sel
total-inelastic s: sinel = st-sel
4) Measuring the “visible”-inelastic s: sinelvis
5) Extrapolating to measured-inelastic s: sinelmeas
6) A Monte Carlo algorithm for the LHC - nesting
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

3. The total inelastic pp cross section at LHC K. Goulianos
1) Introduction gaps
diffraction, saturation and pp cross sections at LHC
2) Predicting the total s st
3) Predicting the total-elastic s sel
 total-inelastic s sinel = st-sel
4) Measuring the “visible”-inelastic s sinelvis
5) Extrapolating to measured-inelastic s sinelmeas
6) A Monte Carlo algorithm for the LHC nesting
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

4. The total inelastic pp cross section at LHC K. Goulianos
Why study diffraction?
Two reasons: one fundamental / one practical.
fundamental
practical: underlying event (UE), triggers, calibrations, acceptance, … the UE affects all physics studies at LHC sT
optical theorem
Im fel(t=0)
dispersion relations
Re fel(t=0)
measure sT & r-value at LHC:
check for violation of dispersion relations  sign for new physics
Bourrely, C., Khuri, N.N., Martin, A.,Soffer, J., Wu, T.T
Diffraction
saturation  sT
NEED ROBUST MC SIMULATION OF SOFT PHYSICS
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

5. MC simulations: Pandora’s box was unlocked at the LHC!
Presently available MCs based on pre-LHC data were found to be inadequate for LHC
MCs disagree in the way they handle diffraction
MC tunes: the “evils of the world” were released from Pandora’s box at the LHC
… but fortunately, hope remained in the box
 a good starting point for this talk!
Pandora's box is an artifact in Greek mythology, taken from the myth of Pandora's creation around line 60 of Hesiod's Works And Days. The "box" was actually a large jar (πιθος pithos) given to Pandora (Πανδώρα) ("all-gifted"), which contained all the evils of the world. When Pandora opened the jar, the entire contents of the jar were released, but for one – hope Nikipedia
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

6. CMS: observation of Diffraction at 7 TeV
(an early example of MC inadequacies)
• No single MC describes the data in their entirety
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

7. Diffractive gaps definition: gaps not exponentially suppressed
Particle production
Rapidity gap h f
Dh≈-ln x
ln MX2
ln s
No radiation
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

8. Diffractive pbar-p studies @ CDF
sT=Im fel (t=0)
Elastic scattering
Total cross section f f
OPTICAL
THEOREM
GAP h h SD DD
DPE
SDD=SD+DD
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

9. Basic and combined diffractive processes
gap DD SD
a 4-gap diffractive process
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

10. Regge theory – values of so & g?
KG-1995: PLB 358, 379 (1995)
Parameters:
s0, s0' and g(t)
set s0‘ = s0 (universal IP )
determine s0 and gPPP – how?
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

11. A complication …  Unitarity!
ds/dt ssd grows faster than st as s increases
 unitarity violation at high s
(similarly for partial x-sections in impact parameter space)
the unitarity limit is already reached at √s ~ 2 TeV
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

12. Sigma-SD vs sigma-total
sTSD vs sT (pp & pp) M
x,t p p’
 suppressed relative to Regge for √s>22 GeV sT sT
Factor of ~8 (~5)
suppression at
√s = 1800 (540) GeV
 RENORMALIZATION MODEL
KG, PLB 358, 379 (1995)
540 GeV
1800 GeV
CDF Run I results
√s=22 GeV
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

13. Single diffraction renormalized – (1 of/4)
KG  CORFU-2001: hep-ph/
KG  EDS 2009:
2 independent variables: t
color
factor
gap probability
sub-energy x-section
Gap probability  (re)normalize to unity
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

14. Single diffraction renormalized – (2 of/4)
color
factor
Experimentally:
KG&JM, PRD 59 (114017) 1999
QCD:
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

15. Single diffraction renormalized - (3 of/4)
set to unity
 determine so
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

16. Single diffraction renormalized – (4 of/4)
 Pumplin bound obeyed at all impact parameters
grows slower than se
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

17. M2 distribution: data Regge data
 ds/dM2|t=-0.05 ~ independent of s over 6 orders of magnitude!
KG&JM, PRD 59 (1999)
Regge
data 1
Independent of s over 6 orders of magnitude in M2
M2 scaling
 factorization breaks down to ensure M2 scaling
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

18. Scale so and triple-pom coupling
Pomeron flux: interpret as gap probability
set to unity: determines gPPP and s0
KG, PLB 358 (1995) 379
Pomeron-proton x-section
Two free parameters: so and gPPP
Obtain product gPPP•soe / 2 from sSD
Renormalized Pomeron flux determines so
Get unique solution for gPPP
gPPP=0.69 mb-1/2=1.1 GeV -1
So=3.7±1.5 GeV2
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

19. Saturation “glueball” at ISR?
Giant glueball with f0(980) and f0(1500) superimposed, interfering destructively and manifesting as dips (???)
√so
See M.G.Albrow, T.D. Goughlin, J.R. Forshaw, hep-ph>arXiv:
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

20. Saturation at low Q2 and small-x
figure from a talk by Edmond Iancu
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

21. DD at CDF: comparison with MBR
gap probability
x-section
renormalized
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

22. Multigap cross sections, e.g. SDD
KG, hep-ph/
Gap probability
Sub-energy cross section
(for regions with particles)
5 independent variables
color
factor
Same suppression
as for single gap!
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

23. SDD in CDF: data vs MBR MC
Excellent agreement between data and NBR (MinBiasRockefeller) MC
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

24. Multigaps: a 4-gap x-section
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

25. Gap survival probability
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

26. The total inelastic pp cross section at LHC K. Goulianos
sSD and ratio of a'/e
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

27. The total inelastic pp cross section at LHC K. Goulianos
1) Introduction gaps
2) Predicting the total s st
3) Predicting the total-elastic s sinel
 total-inelastic s sinel = st-sel
4) Measuring the “visible”-inelastic s sinelvis
5) Extrapolating to measured-inelastic s sinelmeas
6) A Monte Carlo algorithm for the LHC nesting
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

28. The total inelastic pp cross section at LHC K. Goulianos
The total x-section
√sF=22 GeV
SUPERBALL MODEL
98 ± 8 mb at 7 TeV
109 ±12 mb at 14 TeV
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

29. The total inelastic pp cross section at LHC K. Goulianos
1) Introduction gaps
2) Predicting the total s st
3) Predicting the total-elastic s sinel
 total-inelastic s sinel = st-sel
4) Measuring the “visible”-inelastic s sinelvis
5) Extrapolating to measured-inelastic s sinelmeas
6) A Monte Carlo algorithm for the LHC nesting
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

30. Global fit to p±p, p±, K±p x-sections
PLB 389, 176 (1996)
Regge theory eikonalized
INPUT
el/tot slowly rising
RESULTS
negligible
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

31. The total-inelastic cross section
Small extrapolation to 7 TeV
sel=(sel/st)●st
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

32. st at LHC from CMG global fit
Born
Eikonal
LHC √s=14 TeV: 122 ± 5 mb Born, 114 ± 5 mb eikonal
 error estimated from the error in e given in CMG-96
Compare with SUPERBALL s(14 TeV) = 109 ± 6 mb
caveat: so=1 GeV2 was used in global fit!
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

33. The total inelastic pp cross section at LHC K. Goulianos
Secs. 4 & 5
1) Introduction gaps
2) Predicting the total s st
3) Predicting the total-elastic s sinel
 total-inelastic s sinel = st-sel
4) Measuring the “visible”-inelastic s sinelvis
5) Extrapolating to measured-inelastic s sinelmeas
6) A Monte Carlo algorithm for the LHC nesting
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

34. Visible/total inelastic cross sections
ATLAS
Pre-Moriond 2011
ATLAS-CONF Feb 
with pythia (phojet) extrapolation
Post-Moriond 2011
arXiv: v1
CMS (DIS-2011), also post-Moriond 2011
visible svtxinel=59.9±0.1(stat)±1.1(syst)±2.4(Lumi)
(range due to uncertainty in MC extrapolation)
Prediction: stinel=71±6 mb
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

35. The total inelastic pp cross section at LHC K. Goulianos
1) Introduction gaps
2) Predicting the total s st
3) Predicting the total-elastic s sinel
 total-inelastic s sinel = st-sel
4) Measuring the “visible”-inelastic s sinelvis
5) Extrapolating to measured-inelastic s sinelmeas
6) A Monte Carlo algorithm for the LHC nesting
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

36. Diffraction in PYTHIA – (1 of/3)
some comments:
1/M2 dependence instead of (1/M2)1+e
F-factors put “by hand” – next slide
Bdd contains a term added by hand - next slide
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

37. Diffraction in PYTHIA – (2 of/3
note:
1/M2 dependence
e4 factor
Fudge factors:
suppression at kinematic limit
kill overlapping diffractive systems in dd
enhance low mass region
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

38. Diffraction in PYTHIA – (3 of/3)
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

39. Monte Carlo Strategy for the LHC
sT  from SUPERBALL model
optical theorem  Im fel(t=0)
dispersion relations  Re fel(t=0)
sel
sinel
differential sSD  from RENORM
use nesting of final states (FSs) for
pp collisions at the IP­p sub-energy √s' sT
optical theorem
Im fel(t=0)
dispersion relations
Re fel(t=0)
Strategy similar to that employed in the MBR (Minimum Bias Rockefeller) MC used in CDF based on multiplicities from: K. Goulianos, Phys. Lett. B 193 (1987) 151 pp
“A new statistical description of hardonic and e+e− multiplicity distributions “
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

40. Monte Carlo algorithm - nesting
Profile of a pp inelastic collision
no gap
gap
gap t
h'c
evolve every cluster similarly
ln s'
final state
from MC
w/no-gaps
Dy‘ > Dy'min
Dy‘ < Dy'min
generate central gap
EXIT
repeat until Dy' < Dy'min
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

41. The total inelastic pp cross section at LHC K. Goulianos
SUMMARY
Introduction
Diffractive cross sections
basic: SDp, SDp, DD, DPE
combined: multigap x-sections
ND  no-gaps: final state from MC with no gaps
this is the only final state to be tuned
The total, elastic, and inelastic cross sections
Monte Carlo strategy for the LHC – “nesting”
derived from ND
and QCD color factors
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

42. The total inelastic pp cross section at LHC K. Goulianos
BACKUP
BACKUP
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

43. RISING X-SECTIONS IN PARTON MODEL
(see E. Levin, An Introduction to Pomerons,Preprint DESY ) y f
Emission spacing controlled by a-strong
 sT : power law rise with energy
~1/as
a’ reflects the size of the emitted cluster,
which is controlled by 1 /as and thereby is related to e y f
Forward elastic scattering amplitude
assume linear t-dependence
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

44. Dijets in gp at HERA from RENORM
K. Goulianos, POS (DIFF2006) 055 (p. 8)
Factor of ~3 suppression
expected at W~200 GeV
(just as in pp collisions)
for both direct and resolved components
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

45. Diffraction in MBR: DPE in CDF
Excellent agreement between data and MBR
 low and high masses are correctly implemented
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos

46. The total inelastic pp cross section at LHC K. Goulianos
The end
the end
Valparaiso Symposium, May 2011
The total inelastic pp cross section at LHC K. Goulianos