Scale uncertainties in - PowerPoint Presentation

Slide1

Scale uncertainties in ggF->Higgs(+jets)

J. Huston, S. Ellis, B.

MelladoSlide2

Scale uncertainty

The Higgs cross section depends on the renormalization scale

m

R and factorization scale mFConsider default values for these two scales, mo,F and mo,R and expand around these valuesCan write the NLO Higgs cross section (actually any NLO cross section) near the reference scales as…where the explicit logarithmic dependences have been factorized out; the b and c variables will depend on the kinematicsIn general, there will be a saddle point, where the local slope as a function of mR,mF is zeroAround the saddle point, can write the scale dependence asSlide3

Consider inclusive jet production

Some 1-D slices

NLOJET++ with

ApplgridSlide4

Use logarithmic scales

b

road saddle

point regiontypical scale choice (pT

jet) is not atthe saddle pointbut scale uncertainty choicesinclude itSlide5

Saddle points

For

c

F>0,cR<0 and cF,|cR|>>|cRF|, the saddle point axes are aligned with the plot axes, as shown at the top rightAt higher pT values, cRF<0 and cF,|cR|<<|cRF|, the saddle position rotates by about 45oThe saddle position also depends on jet size and on rapidity (somewhat)In any case, the perturbative series is well-behaved for inclusive jet production, leading to stable predictions at NLO, using a scale related to the

pT of the jet …except perhaps when you go very far forwardSlide6

2-D plots for ggF for Higgs

The NNLO scale dependence looks similar to that for low

p

T inclusive jet production, steep at low values of mR, shallow in mFNote that there is no saddle point at NLO; it looks similar to LO for inclusive jet productionihixsSlide7

ggF at NNLO

Note that the location of the saddle point is at ~(0.15m

H

,0.24mH), i.e. outside of the range of uncertainties typically taken into account when using a scale of either mH or 0.5 mHSaddle point ~23.1pb compared to 20.7pb for mH/2Slide8

ggF at NNLO

Now consider a 450

GeV

Higgs produced by ggFThere’s some rotation of the saddle region as you would expect from the jet analysisSaddle point also moves to smaller mFSlide9

Babis at GGI

Points out that series is not well-behaved and that even NNLO might not be enough for precision predictions

~N3LO prediction peaks near a scale of

mHiggsBut normalization has not been determined; likely to have some additional positive correctionsI don’t really understand the ~NNNLOcurve. Very large change in predicted cross section at low scales.claims that 5% precision might be achievable at NNNLO. good progress in the calculation, so maybe we don’t have toolong to waitSlide10

Now look at Higgs+1 jet at NLO

This is for inclusive requiring only a 20

GeV

/c cut on the jet; behavior is monotonic and no saddle point is present; scale uncertainties are large and ill-definedSlide11

Higgs+1 jet at NLO

This plot was generated using MCFM running on a 5X5 grid of scale choices for

m

R and mFWhat we’re trying to understand is how well we can define the scale uncertainties for Higgs+jets in a region where ggF dominates, use the measured cross section to pin down that cross section, and then translate that to the region where we are trying to measure the contribution of VBFCan we define a region where ggF dominates and where the scale dependence is better-behavedSlide12

mF dependence

As we have seen, the

m

F dependence is much flatter than the mR dependenceMostly because ggF probes the gluon distribution in the region around the inflection pointFor the higher x values probed in the VBF region, this will change somewhatSlide13

Higgs + 1 jet

No cuts on photons or jets (other than jet

p

T cuts shown)I said the scale behavior of the Higgs+1 jet cross section was worrisomeThe behavior of the NLO cross section becomes non-monotonic as the jet pT requirement increasesSlide14

Higgs+1 jet: yjet

Apply selection cuts on photons

Require |

yjet|<4.5pTjet>25 GeV/cNon-monotonic behavior only when jet rapidity is largeWe need Higgs+1 jet at NNLOLuckily that will happen in 2013Slide15

What about Higgs+2 jets?

The 1-D plot is shown here

Much better behavior than either inclusive Higgs (at NNLO) or Higgs+1 jet (at NLO) Slide16

Higgs + 2 jets-2D

p

T

jet>20 GeV/c; |yjet|<5Slide17

Higgs + 2 jets-2D

Cutoff at 2000

fb

to look at peak in more detailSlide18

Higgs + 2 jets 2D

Add a few cross section points at lower

mR

scaleSlide19

Higgs + 2 jets-2D

Cutoff at 2000

fb

to look at peak in more detail(mH,mH)s~3400 fbspeak

~4000 fbSlide20

gg->Higgs + >= 2 jets

r

ed=

Dyjj>1green=Dyjj>2blue=Dyjj>3from top to bottom for each Dy, lines show mjj

>0,100, 200,300,400, 500 GeVThis is Dy>3,mjj>400

GeV, closest to VBF cutsCross sections for scales of 12.6 GeV

(and sometimes for 25.2 GeV) are negativeFor VBF-like cuts, scales of mHiggs lead to peak cross sectionCross section uncertainties on the order of 20%

p

T

jet

>25

GeV

/cSlide21

Higgs + 2 jets (after VBF cuts)

Cross section again peaks at a scale of

m

Higgs, so taking a factor of 2 up or down results in <20% scale uncertaintyStill need to look at 2D scale plotsSlide22

Summary

The hope is to incorporate some of this information into Bruce’s note

Steve Ellis, myself, and

Pavel Starovoitov are writing a note/paper on scale dependence for inclusive jet production incorporating the detailed information we have for that processWould be nice to try for an analytic understanding of the b and c parameters for both jet production and Higgs(+jets) productionSlide23

Look for saddle point position (dijets)

Position of saddle point

Black circles 0-0.3

Red squares 0.3-0.8Green triangles 0.8-1.2Blue triangles 1.2-.21Magenta crosses 2.1-2.8Slide24

mR

increases with y*/

y

maxBlack circles 0-0.3Red squares 0.3-0.8Green triangles 0.8-1.2Blue triangles 1.2-.21Magenta crosses 2.1-2.8y*=(yj1-yj2)/2Slide25

mF

increases with y

*/

ymaxBlack circles 0-0.3Red squares 0.3-0.8Green triangles 0.8-1.2Blue triangles 1.2-.21Magenta crosses 2.1-2.8Note: maybe no true saddle points at high y* and high mass, so script has trouble finding them; there are still flat places