1. Single Diffractive Higgs Production at the LHC *
Maria Beatriz Gay Ducati
DIFFRACTION 2010 – OTRANTO, ITALY, 10 – 15 SEPTEMBER
* Work with G. G. Silveira, M. M. Machado and M. V. T. Machado

2. Outlook Motivation Diffractive Physics Higgs production at LO
Higgs production at NLO
Inclusive and diffractive cross section
Pomeron Structure Function
Multiple Pomeron Scattering
Results
Conclusions

3. Motivation
Compute single diffractive and Double Pomeron Exchange (DPE) production of the Standard Model Higgs Boson
Considering diffractive factorization formalism
Parametrization for the Pomeron Structure Function
H1 Collaboration (2006)
Cross section computed at NLO accuracy
Gluon fusion process
leading mechanism to the Higgs boson production
Gap survival probability
rescattering corrections due to spectator particles
Single diffractive ratio computed for proton-proton collisions at the LHC
Estimations for the single and DPE events in the LHC kinematical regime

4. Motivation The TEVNPH Working Group, 1007.4587 [hep-ph]
LHC opens a new kinematical region:
CM Energy in pp Collisions: 14 TeV x Tevatron Energy
Luminosity: 10 – 100 fb x Tevatron luminosity
Evidences show new allowed mass range excluded for Higgs Boson production
Tevatron exclusion ranges are a combination of the data from CDF and D0

5. Introduction What is the Pomeron ? Diffractive structure function
MBGD, M. M. Machado and M. V. T. Machado, PRD
Diffractive processes rapidity gap
Exchange of a Pomeron with vacuum quantum numbers
Pomeron with substructure DPDFs
Diffractive distributions of quarks and gluons in the Pomeron
What is the Pomeron ?
Diffractive structure function
Gap Survival Probability (GSP)
Cross sections at NLO

6. Single diffractive Higgs production
Heyssler et al, [hep-ph]
Single diffraction in hadronic collisions
One of the colliding hadrons emits Pomeron
Partons in the the Pomeron interact with partons from the another hadron
Absence of hadronic energy in the final state
Regge factorization
Rapidity gaps

7. DPE Higgs production Double Pomeron Exchange in hadronic collisions
P. D. Collins, An Introduction to Regge Theory and High Energy Physics
Double Pomeron Exchange in hadronic collisions
Both colliding hadrons emit Pomeron
Partons in the the Pomerons interact with each other
Absence of hadronic energy in the final state
Regge factorization
Two rapidity gaps

8. Higgs production Focus on the gluon fusion
D. Graudenz et al. PRL 70 (1993) 1372
Focus on the gluon fusion
Main production mechanism of Higgs boson in high-energy pp collisions
Gluon coupling to the Higgs boson in SM
triangular loops of top quarks
Lowest order to gg contribution

9. At NLO, these processes could occur
Diagrams
At NLO, these processes could occur
Quark considered top (high mass)
Possible background expected for high pT
Higgs production in gq and qq collisions
Vertex corrections
Real gluon radiation

10. Partonic cross section
M. Spira et al [hep-ph]
Lowest order
parton cross section expressed by the gluonic width of the Higgs boson
Quark Top
gg invariant energy squared
dependence

11. LO hadroproduction
Lowest order two-gluon decay width of the Higgs boson
PDFs MSTW2008
Gluon luminosity
Lowest order proton-proton cross section
Renormalization scale
s invariant pp collider energy squared

12. QCD Corrections Three contributions M. Spira et al. 9504378 [hep-ph]
Involve virtual corrections for the subprocess and the radiation of
gluons in the final state
Higgs boson production gluon-quark collisions and quark
annihilation
Subprocesses contribute to the Higgs production at the same order of αs
Virtual corrections modify the lowest-order fusion cross section by a
coefficient linear in αs

13. NLO Cross Section Gluon radiation two parton final states
Invariant energy in the channels
New scaling variable supplementing and
The final result for the pp cross section at NLO
Renormalization scale in αs and the factorization scale of the parton densities to be fixed properly

14. NLO Cross Section
Coefficient contributions from the virtual two-loop
corrections
Regularized by the infrared singular part of the cross section for real gluon emission
Infrared part
Finite τQ dependent piece
Logarithmic term depending on the renormalization scale μ

15. Delta functions
Contributions from gluon radiation in gg, gq and qq scattering
Dependence of the parton densities
renormalization scale μ
factorization scale M
Renormalization scale
QCD coupling in the radiative corrections and LO cross sections

16. d functions F+ usual + distribution
Considering only the heavy-quark limit Region allowed by Tevatron combination

17. Diffractive cross section
Single diffractive
Double Pomeron Exchange
Gluon distributions in the Pomeron
Normalization
Gluon distributions in the proton
MSTW (2008)
H1 parametrization (2006)
Pomeron flux
Gluon distributions (i ) in the Pomeron IP

18. H1 parametrization Range of data 0.0043 < z < 0.8
A. Aktas et al, Eur. J. Phys. J. C48 (2006) 715
Range of data
< z < 0.8
In this work, FIT B.
z is the momentum fraction of the Pomeron

19. Gap Survival Probability (GSP)
Absorptive corrections by Multiple Pomeron Scattering
<|S|2> gap survival probability (GSP)
Gap
A(s,b) diffractive process amplitude
PS(s,b) probability that no inelastic interactions occurs between
remains particles
Comparison between GLM and KKMR models 19 19

20. Single diffraction
M. Spira et al [hep-ph]
Heyssler et al, arXiv:hep-ph/
ρ variable gives the renormalization/factorization scale dependence
Predictions to inclusive and diffractive cross sections at LO in agreement with other theoretical predictions
NLO cross sections ~ 1.7 greater than LO cross sections

21. Double Pomeron Exchange
DPE cross sections as Higgs mass function
Significant reduction of the diffractive cross section when applied the GSP
Difference about a factor 2 between GLM and KKMR models
Cross section and PDFs evaluated at NLO
KKMR = 2.6 %
GLM = 6 %

22. Higgs production as ρ function (LO)
σInc
(pb)
σDiff
σKKMR
σGLM
Rdiff
(%)
RKKM R
RGLM
0.5
13.18
0.52
0.031
0.042
3.95
0.24
0.32
1.0
10.04
0.26
0.016
0.021
2.59
0.16
0.21
1.5
8.65
0.013
0.017
2.43
0.15
0.19
4.0
6.21
0.010
0.014
2.48
Single Diffraction
KKMR = 6 %
GLM = 8 %
Heyssler et al, arXiv:hep-ph/ ρ
σInc
(pb)
σDiff
σKKMR
σGLM
Rdiff
(%)
RKKM R
RGLM
0.5
13.18
0.07
0.0021
0.0047
0.60
0.016
0.036
1.0
10.04
0.042
0.0011
0.0025
0.42
0.011
0.025
1.5
8.65
0.033
0.0086
0.0020
0.38
0.010
0.023
4.0
6.21
0.0065
0.0015
0.40
DPE
KKMR = 2.6 %
GLM = 6 %
ρ = μ / MH
Boonekamp et al, arXiv:hep-ph/

23. Higgs production as ρ function (NLO)
σInc
(pb)
σDiff
σKKMR
σGLM
Rdiff
(%)
RKKMR
RGL M
0.5
22.01
0.87
0.052
0.069
3.95
0.24
0.32
1.0
16.77
0.43
0.026
0.034
2.59
0.16
0.21
1.5
14.45
0.35
0.022
0.028
2.43
0.15
0.19
4.0
10.37
0.27
0.017
2.48
Single Diffraction
KKMR = 6 %
GLM = 8 % ρ
σInc
(pb)
σDiff
σKKMR
σGLM
Rdiff
(%)
RKKM R
RGLM
0.5
22.01
0.12
0.0033
0.0064
0.57
0.015
0.030
1.0
16.77
0.06
0.0017
0.0040
0.40
0.010
0.024
1.5
14.45
0.05
0.0013
0.0031
0.36
0.009
0.022
4.0
10.37
0.04
0.0011
0.0024
0.38
DPE
KKMR = 2.6 %
GLM = 6 %
ρ = μ / MH

24. Very small diffractive ratios
Conclusions
Inclusive
Single Diffractive
Double Pomeron Exchange
Higgs production
at LHC energies at
LO and NLO
Theoretical predictions
Estimate for cross sections as a function of Higgs Mass and ρ = μ/MH
Diffractive ratio computed using hard diffractive factorization and absorptive corrections
Values of diffractive LO cross section in good agreement with other theoretical predictions
Different predictions to NLO cross sections using two GSP models (KKMR and GLM)
Feasible value of cross sections for both GSP models
SD ~ fb
DPE ~ 3 – 6 fb
γ γ
0.1 fb γp
0.08 fb
Very small diffractive ratios
to Higgs Mass ~ 150 GeV
at NLO without GSP
SD ~ 2.5 %
MBGD, G. G. Silveira PRD (2009)
DPE ~ 0.5 %