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Single Diffractive Higgs Production at the LHC *

Maria Beatriz Gay Ducatibeatriz.gay@ufrgs.br

DIFFRACTION 2010 – OTRANTO, ITALY, 10 – 15 SEPTEMBER

* Work with G. G. Silveira, M. M. Machado and M. V. T. Machado

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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

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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

Motivation

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LHC opens a new kinematical region:

CM Energy in pp Collisions: 14 TeV 7x Tevatron Energy

Luminosity: 10 – 100 fb-1 10 x Tevatron luminosity

MotivationThe TEVNPH Working Group, 1007.4587 [hep-ph]

Evidences show new allowed mass range excluded for Higgs Boson production

Tevatron exclusion ranges are a combination of the data from CDF and D0

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Introduction

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

Diffractive structure function

Gap Survival Probability (GSP)

MBGD, M. M. Machado and M. V. T. Machado, PRD

What is the Pomeron ?

Cross sections at NLO

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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

Single diffractive Higgs production

Rapidity gaps

Regge factorization

Heyssler et al, 9702.286 [hep-ph]

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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

Two rapidity gaps

Regge factorization

DPE Higgs production P. D. Collins, An Introduction to Regge Theory and High Energy Physics

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o Focus on the gluon fusion

o Main production mechanism of Higgs boson in high-energy pp collisions

o Gluon coupling to the Higgs boson in SM

triangular loops of top quarks

Higgs production D. Graudenz et al. PRL 70 (1993) 1372

Lowest order to gg contribution

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Diagrams

Higgs production in gq and qq collisions

Vertex corrections

Real gluon radiation

o At NLO, these processes could occur

Quark considered top (high mass)

Possible background expected for high pT

BBgg

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Lowest order

parton cross section expressed by the gluonic width of the Higgs boson

gg invariant energy squared

Partonic cross section M. Spira et al. 9504378 [hep-ph]

dependence

Quark Top

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LO hadroproduction Lowest order two-gluon decay width of the Higgs boson

Gluon luminosityPDFs MSTW2008

Lowest order proton-proton cross section

Renormalization scale

s invariant pp collider energy squared

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QCD Corrections

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

M. Spira et al. 9504378 [hep-ph]

Three contributions

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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

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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

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Delta functionso Contributions from gluon radiation in gg, gq and qq scattering

o Dependence of the parton densities

o Renormalization scale

QCD coupling in the radiative corrections and LO cross sections

renormalization scale μ

factorization scale M

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d functions

F+

usual + distribution

Considering only the heavy-quark limit

Region allowed by Tevatron combination

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Diffractive cross section

Normalization

Gluon distributions in the proton

β=xxIP

Single diffractive

H1 parametrization (2006)

Double Pomeron Exchange

Gluon distributions in the Pomeron

Gluon distributions (i ) in the Pomeron IPPomeron flux

MSTW (2008)

H1 parametrization

• Range of data

0.0043 < z < 0.8

• In this work, FIT B.

• z is the momentum fraction of the Pomeron

A. Aktas et al, Eur. J. Phys. J. C48 (2006) 715

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Gap

• Absorptive corrections by Multiple Pomeron Scattering

• <|S|2> gap survival probability (GSP)

• A(s,b) diffractive process amplitude

• PS(s,b) probability that no inelastic interactions occurs between

remains particles

Gap Survival Probability (GSP)

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22

2

|b)A(s,|bd

s)(b,P|b)A(s,|bd|>S|

s

Comparison between GLM and KKMR models

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Single diffraction

• ρ variable gives the renormalization/factorization

scale dependence

• Predictions to inclusive and diffractive cross sections at LO in agreement with other

theoretical predictions

Heyssler et al, arXiv:hep-ph/9702286

M. Spira et al. 9504378 [hep-ph]

NLO cross sections ~ 1.7 greater than LO cross sections

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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 %

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Higgs production as ρ function (LO)ρ σInc

(pb)

σDiff

(pb)

σKKMR

(pb)

σGLM

(pb)

Rdiff

(%)

RKKMR

(%)

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 0.21 0.013 0.017 2.43 0.15 0.19

4.0 6.21 0.16 0.010 0.014 2.48 0.15 0.19

Single Diffraction

KKMR = 6 %

GLM = 8 %

Heyssler et al, arXiv:hep-ph/9702286

ρ σInc

(pb)

σDiff

(pb)

σKKMR

(pb)

σGLM

(pb)

Rdiff

(%)

RKKMR

(%)

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 0.025 0.0065 0.0015

0.40 0.010 0.023ρ = μ / MH

DPE

KKMR = 2.6 %

GLM = 6 %

Boonekamp et al, arXiv:hep-ph/0406061

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Higgs production as ρ function (NLO)

ρ σInc

(pb)

σDiff

(pb)

σKKMR

(pb)

σGLM

(pb)

Rdiff

(%)

RKKMR

(%)

RGLM

(%)

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 0.022 2.48 0.15 0.19

ρ σInc

(pb)

σDiff

(pb)

σKKMR

(pb)

σGLM

(pb)

Rdiff

(%)

RKKMR

(%)

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 0.009 0.022

Single Diffraction

KKMR = 6 %

GLM = 8 %

DPE

KKMR = 2.6 %

GLM = 6 %

ρ = μ / MH

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Conclusions

• 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 ~ 2.5 %

DPE ~ 0.5 %

SD ~ 50 - 70 fb DPE ~ 3 – 6 fb γ γ 0.1 fb

γp 0.08 fb MBGD, G. G. Silveira PRD 78 113005 (2009)

• Theoretical predictions

Inclusive

Single Diffractive

Double Pomeron Exchange

Higgs production at LHC energies at

LO and NLO

Very small diffractive ratios to Higgs Mass ~ 150 GeV

at NLO without GSP