QCD background for Higgs γγ · ¥ Higgs signal has a larger hqTi than the background (a prediction of qT resumma-tion) ¥ An efﬁcient qT-dependent likelihood analysis is possible

QCD background for Higgs → γγ

Pavel Nadolsky

Argonne National Laboratory

May 16, 2006

Pavel Nadolsky (ANL) QCD background for Higgs production May 16, 2006May 16, 2006 1

Transverse momentum (qT ) distributionsin pp

(−) → γγX

We use qT resummation to compute fully differential distributionsof prompt γγ pairs (including qT dependence) at NNLL accuracy

References

1. C. Balázs, E. Berger, P. N., C.-P. Yuan, hep-ph/06030372. C. Balazs, E. Berger, S. Mrenna, C.-P. Yuan, PRD 57, 6934 (1998)3. C. Balazs, P. N., C. Schmidt, C.-P. Yuan, PLB 489, 157 (2000)4. P. N., C. Schmidt, PLB 558, 63 (2003)

The results are implemented in a MC integrator program ResBos


SM Higgs boson search at the LHC

1

10

10 2

102

103

Higgs mass MH (GeV)

Sig

nal s

igni

fica

nce

H → γ γ + WH, ttH (H → γ γ ) ttH (H → bb) H → ZZ(*) → 4 l

H → ZZ → llνν H → WW → lνjj

H → WW(*) → lνlν

Total significance

5 σ

∫ L dt = 100 fb-1

(no K-factors)

ATLAS

¥ gg → H → γγ (via t-quark loop) isthe crucial and challenging searchmode for 115 < MH < 140 GeV

¥ QCD background processes forγγ production are complicated;must be understood forsuccessful Higgs discovery andmeasurement of Higgs crosssections

¥ An interesting QCD process onits own!


Higgs discovery significance is improved by...

Bruce Mellado, ATLAS Physics Workshop 07/06/05

Higgs -> 2gamma + 0 or 1 jetPreliminary

TDR-like analysis with NLO cross-sections

¥ ... NLO corrections¥ ... use of qT of γγ pair

as a discriminatingvariable

I Significanceincreased by20− 40%

¥ ... combination ofinclusive H → γγ andH → γγ + 1 jetanalyses

¥ ... optimization of γdetection and jetrejection


Higgs discovery significance is improved by...

Bruce Mellado, ATLAS Physics Workshop 07/06/05

Higgs -> 2gamma + 0 or 1 jetPreliminary

TDR-like analysis with NLO cross-sections

¥ ... NLO corrections¥ ... use of qT of γγ pair

as a discriminatingvariable

I Significanceincreased by20− 40%

¥ ... combination ofinclusive H → γγ andH → γγ + 1 jetanalyses

¥ ... optimization of γdetection and jetrejection


Knowledge of qT optimizes Higgs boson search(Abdullin et al., 1998; Balazs, P.N., Schmidt, Yuan; de Florian, Kunszt, 1999; Berger, Qiu, 2003)

M. Escalier, 2005; ResBos [2,3]

¥ At qT ¿ Q,(

dσdq2

T

)q2

T¿Q2≈ ∑∞

k=0 αks

[ckδ(~qT )

+q−2T ·∑2k−1

n=0 dnk lnn(Q2/q2T )

];

the large terms are summedto all orders in αs by means ofCollins-Soper-Sterman (CSS)resummation

¥ Higgs 〈qT 〉 is enhanced bya larger soft (Sudakov) factorand gluon PDF shapein gg → H scattering


Knowledge of qT optimizes Higgs boson search(Abdullin et al., 1998; Balazs, P.N., Schmidt, Yuan; de Florian, Kunszt, 1999; Berger, Qiu, 2003)

M. Escalier, 2005; ResBos [2,3]

¥ Higgs signal has a larger 〈qT 〉than the background(a prediction of qT resumma-tion)

¥ An efficient qT -dependentlikelihood analysis is possible


qT resummation for γγ production(QCD background)

¥ new PQCD corrections to production in direct qq̄ + qg andgg channels

¥ improved treatment of the fragmentation region

¥ improved model for nonperturbative resummedcontributions (A. Konychev, P. N., PLB 633, 710 (2006))

I non-pert. terms constrained by low-Q and Tevatron Z data

¥ automated matching at the ntuple level; optimizedMonte-Carlo integration

I new ResBos code is easy to use!


Direct diphotons

The dominant production mode; evaluated here up to fullNLO/NNLL accuracy

Balazs, Berger, Nadolsky, Yuan, 2006

Collinearfragmentationmodel

Direct γγproduction(resummed)

¥ qg and ggchannels areenhanced atx ∼ Q2/s ¿ 1 bylarge gluon PDF

¥ qq̄ and qgchannels at NLO:Aurenche et al.; Bailey, Owens,Ohnemus

¥ gg channel at NLO:Balazs, PN, Schmidt, Yuan; deFlorian, Kunzst; Bern, De Freitas,Dixon; Bern, Dixon, Schmidt


gg → γγX in the qT → 0 limit

+ ...

¥ O(α3s ) 1-loop 5-leg (pentagon) diagrams

I are computed in the helicity amplitudeformalism

I numerically checked against the“sector decomposition” calculation(Binoth, Guillet, Mahmoudi)

I small-qT limit is derived at thematrix-element level using the splittingamplitude method

¥ 2-loop box diagrams are added atqT = 0; the full cross section is resummedin the qT → 0 limit


Fragmentation model

The qg fragmentation collinear singularity is removed bycombination of quasi-experimental and smooth-cone isolation

Balazs, Berger, Nadolsky, Yuan, 2006

Collinearfragmentationmodel

Direct γγproduction(resummed)

¥ sufficient fordescription ofsmallfragmentationcontributionsrelevant for theTevatron and LHC

¥ good agreementwith the Tevatrondata


qT resummation for γγ production(QCD background)

¥ new PQCD corrections to production in direct qq̄ + qg andgg channels

¥ improved treatment of the fragmentation region

¥ improved model for nonperturbative resummedcontributions (A. Konychev, P. N., PLB 633, 710 (2006))

I non-pert. terms constrained by low-Q and Tevatron Z data

¥ automated matching at the ntuple level; optimizedMonte-Carlo integration

I new ResBos code is easy to use!


Comparison with the CDF Run-2 data

pp_ → γγX, CDF Run-2, 207 pb-1

QT (GeV)

dσ/d

QT (

pb/G

eV)

∆Rcone = 0.4, ∆Rγγ > 0.3ResummedFinite-order

10-1

1

0 5 10 15 20 25 30 35 40

¥ The NLO prediction (blue)diverges at low qT

¥ The resummed prediction(red) agrees with the dataat all qT ; matches the NLOprediction at large qT


γγ production at the LHC

pp → γγX, √S = 14 TeV

qT (GeV)

dσ/d

q T (

pb/G

eV)

115 < Q < 130 GeV

ResummedResummed, qq

_+qg only

ET iso = 15 GeV

10-2

10-1

0 20 40 60 80 100 120

qq̄ : qg : gg = 30:50:20

(compare withqq̄ : qg : gg =70:20:10at the Tevatron)

O(α2s ) corrections to qg are

likely important(σNNLO/σNLO ∼ 20%?)




qT (GeV)

dσ/d

q T (

pb/G

eV)

115 < Q < 130 GeV


_+qg only

DIPHOX

ET iso = 15 GeV

10-2

10-1

0 20 40 60 80 100 120

¥ DIPHOX agrees with theresummation at large qT ;exhibits integrable logarithmicsingularities at qT < E iso

T (E isoT is

the isolation energy)

¥ RESBOS shows a milddiscontinuity at qT = E iso

T




qT (GeV)

dσ/d

q T (

pb/G

eV)

115 < Q < 130 GeV


_+qg only

DIPHOX

ET iso = 15 GeV

10-2

10-1

0 20 40 60 80 100 120


Q (GeV)

dσ/d

Q (

pb/G

eV)

qT < Q


_ + qg only

DIPHOX, qq_ + qg only

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

40 60 80 100 120 140 160 180 200 220 240


Conclusions

¥ Knowledge of qT distributions is important for Higgs bosonsearches

I Significance of H → γγ discovery is improved by includinginformation about qT distributions (ongoing ATLAS studies)

I The shape of dσ/dqT affects dσ/dQ and other observables

I Theory predictions for QCD γγ production are most reliable atE iso

T < qT < Q


Conclusions II

¥ Resummation predicts normalization and shape ofdσ/d3pγ1d3pγ2 for direct γγ production at NNLL/NLO.

¥ Large logs are resummed at qT ¿ Q

¥ At qT & Q, our results agree with NLO, as well as with DIPHOXcalculation within the fragmentation model uncertainty ofDIPHOX

¥ At qT < E isoT , fragmentation contributions are removed by

smooth-cone isolation

I no logarithmic singularities at qT 6= 0!

¥ Streamlined matching of resummed and NLO cross sections;optimized phase space integration


Conclusions II

¥ Resummation predicts normalization and shape ofdσ/d3pγ1d3pγ2 for direct γγ production at NNLL/NLO.

¥ Large logs are resummed at qT ¿ Q

¥ At qT & Q, our results agree with NLO, as well as with DIPHOXcalculation within the fragmentation model uncertainty ofDIPHOX

¥ At qT < E isoT , fragmentation contributions are removed by

smooth-cone isolation

I no logarithmic singularities at qT 6= 0!

¥ Streamlined matching of resummed and NLO cross sections;optimized phase space integration

Accurate predictions for future measurements at the Tevatronand LHC!


Backup slides


Universality of nonperturbative contributions

A. Konychev, P. N., PLB 633, 710 (2006)Nonperturbative Gaussian smearing a(Q)

5 10 20 50 100 200Q @GeVD

0

0.2

0.4

0.6

0.8

1

1.2

a@G

eV

2D

E288E605

CDF ZD0 ZR209

b max = 1.5 GeV-1

a2 = 0.19 GeV2

¥ qT factorization: initial-statenonperturbative contributions(∼“intrinsic” 〈k2

T 〉 ≡ a) followuniversal quasi-linear dependenceon ln Q; this expectation isconfirmed by the global analysis ofDrell-Yan and Z boson data

¥ the observed ln Q dependence agrees with therenormalon/lattice estimate

¥ at Q ∼ MZ , soft NP corrections dominate over collinear NPcorrections

¥ the model is employed to predict γγ cross sections


Resummation vs. CDF Run-2 data (PRL 95, 022003 (2005))


QT (GeV)

dσ/d

QT (

pb/G

eV)

∆Rcone = 0.4, ∆Rγγ > 0.3ResummedFinite-order

10-1

1

0 5 10 15 20 25 30 35 40

¥ The NLO prediction (blue)diverges at small qT

¥ The resummed prediction(red) agrees with the data at allqT ; matches the NLO predictionat large qT




qT (GeV)

dσ/d

q T (

pb/G

eV)

∆Rcone = 0.4, ∆Rγγ > 0.3

ResummedDIPHOX, ET

iso = 1 GeV

DIPHOX, ET iso = 4 GeV, µF = Q/2

10-1

1

0 5 10 15 20 25 30 35 40

The large-qT “shoulder” in thedata occurs atQ . 25 GeV, Q . qT , ∆ϕ < π/2The DIPHOX cross section¥ agrees with NLO RESBOS for

the nominal E isoT = 1 GeV, same

µF

¥ reproduces the “shoulder”for E iso

T = 4 GeV, smaller µF

N for E isoT = 4 GeV, the 1-fragmentation cross section increases by 400%




qT (GeV)

dσ/d

q T (

pb/G

eV)

∆Rcone = 0.4, ∆Rγγ > 0.3

ResummedDIPHOX, ET

iso = 1 GeV


10-1

1

0 5 10 15 20 25 30 35 40

The large-qT “shoulder” in thedata occurs atQ . 25 GeV, Q . qT , ∆ϕ < π/2The DIPHOX cross section¥ agrees with NLO RESBOS for

the nominal E isoT = 1 GeV, same

µF

¥ reproduces the “shoulder”for E iso

T = 4 GeV, smaller µF

N for E isoT = 4 GeV, the 1-fragmentation cross section increases by 400%




qT (GeV)

dσ/d

q T (

pb/G

eV)

∆Rcone = 0.4, ∆Rγγ > 0.3

ResummedDIPHOX, ET

iso = 1 GeV


10-1

1

0 5 10 15 20 25 30 35 40

¥ Other large corrections areknown to contribute at Q . qT(not in the existing theorycalculations)

¥ The CDF “shoulder” is a low-Qeffect, not relevant for the LHCHiggs searches

N can be removed by aqT ≤ Q cut


Azimuthal angle separation ∆ϕ


∆ϕ (rad)

dσ/d

(∆ϕ)

(pb

/rad

)

∆Rcone = 0.4, ∆Rγγ > 0.3

RESBOS, ET iso = 1 GeV

µF = Q (lower), Q/2 (upper)

DIPHOX, ET iso = 1 GeV


10-1

1

10

0 0.5 1 1.5 2 2.5 3

pp_ → γγX, √S = 1.96 TeV

∆ϕ (rad)

dσ/d

(∆ϕ)

(pb

/rad

)

∆Rcone = 0.4, ∆Rγγ > 0.3

RESBOS, ET iso = 1 GeV

µF = Q (lower), Q/2 (upper)DIPHOX, ET

iso = 1 GeV


QT < Q

10-1

1

10

0 0.5 1 1.5 2 2.5 3


Documents

QCD background for Higgs γγ · ¥ Higgs signal has a larger hqTi than the background (a prediction of qT resumma-tion) ¥ An efﬁcient qT-dependent likelihood analysis is possible