jets met atlas jamboree 2011

Searching for New Colored Statesat the Early LHC

Jay WackerSLAC

with Daniele Alves & Eder IzaguirrearXiv:1003.3886, 1008:0407, 1101:xxxx

ATLAS JamboreeBrookhaven National Lab

January 10, 2011

Simplified Models

First LHC Results and Their Implication

Going Forward to 1fb-1

Outline

Jets + MET Simplified Models

LHC is the New Energy Frontier(but you still need luminosity)

The first Jets+MET Search cameout with 70 nb-1 of integrated luminosity

ATLAS NOTEATLAS-CONF-2010-065

20 July, 2010

Early supersymmetry searches in channels with jets and missing

transverse momentum with the ATLAS detector

ATLAS collaboration

Abstract

This note describes a first set of measurements of supersymmetry-sensitive variables in

the final states with jets, missing transverse momentum and no leptons from the!s= 7 TeV

proton-proton collisions at the LHC. The data were collected during the period March 2010

to July 2010 and correspond to a total integrated luminosity of 70±8nb"1. We find agree-ment between data and Monte Carlo simulations indicating that the Standard Model back-

grounds to searches for new physics in these channels are under control.

ATLAS NOTEATLAS-CONF-2010-065

20 July, 2010

Early supersymmetry searches in channels with jets and missing

transverse momentum with the ATLAS detector

ATLAS collaboration

Abstract

This note describes a first set of measurements of supersymmetry-sensitive variables in

the final states with jets, missing transverse momentum and no leptons from the!s= 7 TeV

proton-proton collisions at the LHC. The data were collected during the period March 2010

to July 2010 and correspond to a total integrated luminosity of 70±8nb"1. We find agree-ment between data and Monte Carlo simulations indicating that the Standard Model back-

grounds to searches for new physics in these channels are under control.

[GeV]missTE

0 20 40 60 80 100 120 140 160 180 200

Entr

ies / 1

0 G

eV

-310

-210

-110

1

10

210

310

410

510

610

0 20 40 60 80 100 120 140 160 180 200-3

10

-210

-110

1

10

210

310

410

510

610 = 7 TeV)sData 2010 (

Monte CarloQCDW+jetsZ+jets

ttSU4 (x10)

-1L dt ~ 70 nb!

Three Jet Channel

ATLAS Preliminary

Amazing that such an early search is possible!

SU4 *10

SU4*10

g

!WB

q

!

HHh

400 GeV

100 GeV50 GeV

As light as possible inside of mSugraStill had to multiply it by 10 to be visible

But with 70nb-1, what should we expect?No other theories were explored

mSugra Review

m 12,m2

0, A0, Bµ, µ5 Parameters at the GUT Scale

2 4 6 8 10 12 14 16 18Log

10(Q/1 GeV)

0

100

200

300

400

500

600

Ma

ss

[Ge

V]

m0

m1/2

(µ2+m

0

2)1/2

squarks

sleptons

M1

M2

M3

Hd

Hu

Figure 7.4: RG evolution of scalar and gaugino mass parameters in the MSSM with typical minimalsupergravity-inspired boundary conditions imposed at Q0 = 2.5! 1016 GeV. The parameter µ2 + m2

Hu

runs negative, provoking electroweak symmetry breaking.

a reasonable approximation, the entire mass spectrum in minimal supergravity models is determinedby only five unknown parameters: m2

0, m1/2, A0, tan!, and Arg(µ), while in the simplest gauge-mediated supersymmetry breaking models one can pick parameters !, Mmess, N5, "F #, tan !, andArg(µ). Both frameworks are highly predictive. Of course, it is easy to imagine that the essentialphysics of supersymmetry breaking is not captured by either of these two scenarios in their minimalforms. For example, the anomaly mediated contributions could play a role, perhaps in concert withthe gauge-mediation or Planck-scale mediation mechanisms.

Figure 7.4 shows the RG running of scalar and gaugino masses in a typical model based on theminimal supergravity boundary conditions imposed at Q0 = 2.5 ! 1016 GeV. [The parameter valuesused for this illustration were m0 = 80 GeV, m1/2 = 250 GeV, A0 = $500 GeV, tan ! = 10, andsign(µ)= +.] The running gaugino masses are solid lines labeled by M1, M2, and M3. The dot-dashedlines labeled Hu and Hd are the running values of the quantities (µ2 + m2

Hu)1/2 and (µ2 + m2

Hd)1/2,

which appear in the Higgs potential. The other lines are the running squark and slepton masses,with dashed lines for the square roots of the third family parameters m2

d3, m2

Q3, m2

u3, m2

L3, and m2

e3

(from top to bottom), and solid lines for the first and second family sfermions. Note that µ2 + m2Hu

runs negative because of the e"ects of the large top Yukawa coupling as discussed above, providing forelectroweak symmetry breaking. At the electroweak scale, the values of the Lagrangian soft parameterscan be used to extract the physical masses, cross-sections, and decay widths of the particles, and otherobservables such as dark matter abundances and rare process rates. There are a variety of publiclyavailable programs that do these tasks, including radiative corrections; see for example [204]-[213],[194].

Figure 7.5 shows deliberately qualitative sketches of sample MSSM mass spectrum obtained fromthree di"erent types of models assumptions. The first is the output from a minimal supergravity-inspired model with relatively low m2

0 compared to m21/2 (in fact the same model parameters as used

for fig. 7.4). This model features a near-decoupling limit for the Higgs sector, and a bino-like !N1

LSP, nearly degenerate wino-like !N2, !C1, and higgsino-like !N3, !N4, !C2. The gluino is the heaviest

80

Bµ, µ! vEW = 246 GeV, tan!

Applying the above results to the special case of the MSSM, we will use the approximation thatonly the third-family Yukawa couplings are significant, as in eq. (5.2). Then the Higgs and third-familysuperfield anomalous dimensions are diagonal matrices, and from eq. (5.26) they are, at 1-loop order:

!Hu =1

16"2

!3y!t yt !

3

2g22 ! 3

10g21

", (5.37)

!Hd =1

16"2

!3y!byb + y!!y! ! 3

2g22 ! 3

10g21

", (5.38)

!Q3=

1

16"2

!y!t yt + y!byb !

8

3g23 ! 3

2g22 ! 1

30g21

", (5.39)

!u3=

1

16"2

!2y!t yt !

8

3g23 ! 8

15g21

", (5.40)

!d3=

1

16"2

!2y!byb !

8

3g23 ! 2

15g21

", (5.41)

!L3=

1

16"2

!y!!y! !

3

2g22 ! 3

10g21

", (5.42)

!e3=

1

16"2

!2y!!y! ! 6

5g21

". (5.43)

[The first and second family anomalous dimensions in the approximation of eq. (5.2) follow by settingyt, yb, and y! to 0 in the above.] Putting these into eqs. (5.23), (5.24) gives the running of thesuperpotential parameters with renormalization scale:

#yt "d

dtyt =

yt

16"2

#6y!t yt + y!byb !

16

3g23 ! 3g2

2 ! 13

15g21

$, (5.44)

#yb " d

dtyb =

yb

16"2

#6y!byb + y!t yt + y!!y! ! 16

3g23 ! 3g2

2 ! 7

15g21

$, (5.45)

#y! " d

dty! =

y!

16"2

#4y!!y! + 3y!byb ! 3g2

2 ! 9

5g21

$, (5.46)

#µ " d

dtµ =

µ

16"2

#3y!t yt + 3y!byb + y!!y! ! 3g2

2 ! 3

5g21

$. (5.47)

The one-loop RG equations for the gauge couplings g1, g2, and g3 were already listed in eq. (5.21). Thepresence of soft supersymmetry breaking does not a!ect eqs. (5.21) and (5.44)-(5.47). As a result ofthe supersymmetric non-renormalization theorem, the #-functions for each supersymmetric parameterare proportional to the parameter itself. One consequence of this is that once we have a theory thatcan explain why µ is of order 102 or 103 GeV at tree-level, we do not have to worry about µ being madevery large by radiative corrections involving the masses of some very heavy unknown particles; all suchRG corrections to µ will be directly proportional to µ itself and to some combinations of dimensionlesscouplings.

The one-loop RG equations for the three gaugino mass parameters in the MSSM are determinedby the same quantities bMSSM

a that appear in the gauge coupling RG eqs. (5.21):

#Ma " d

dtMa =

1

8"2bag

2aMa (ba = 33/5, 1, !3) (5.48)

for a = 1, 2, 3. It follows that the three ratios Ma/g2a are each constant (RG scale independent) up to

small two-loop corrections. Since the gauge couplings are observed to unify at Q = MU = 2 # 1016

GeV, it is a popular assumption that the gaugino masses also unify§ near that scale, with a value called

§In GUT models, it is automatic that the gauge couplings and gaugino masses are unified at all scales Q ! MU , becausein the unified theory the gauginos all live in the same representation of the unified gauge group. In many superstringmodels, this can also be a good approximation.

44

Applying the above results to the special case of the MSSM, we will use the approximation thatonly the third-family Yukawa couplings are significant, as in eq. (5.2). Then the Higgs and third-familysuperfield anomalous dimensions are diagonal matrices, and from eq. (5.26) they are, at 1-loop order:

!Hu =1

16"2

!3y!t yt !

3

2g22 ! 3

10g21

", (5.37)

!Hd =1

16"2

!3y!byb + y!!y! ! 3

2g22 ! 3

10g21

", (5.38)

!Q3=

1

16"2

!y!t yt + y!byb !

8

3g23 ! 3

2g22 ! 1

30g21

", (5.39)

!u3=

1

16"2

!2y!t yt !

8

3g23 ! 8

15g21

", (5.40)

!d3=

1

16"2

!2y!byb !

8

3g23 ! 2

15g21

", (5.41)

!L3=

1

16"2

!y!!y! !

3

2g22 ! 3

10g21

", (5.42)

!e3=

1

16"2

!2y!!y! ! 6

5g21

". (5.43)

[The first and second family anomalous dimensions in the approximation of eq. (5.2) follow by settingyt, yb, and y! to 0 in the above.] Putting these into eqs. (5.23), (5.24) gives the running of thesuperpotential parameters with renormalization scale:

#yt "d

dtyt =

yt

16"2

#6y!t yt + y!byb !

16

3g23 ! 3g2

2 ! 13

15g21

$, (5.44)

#yb " d

dtyb =

yb

16"2

#6y!byb + y!t yt + y!!y! ! 16

3g23 ! 3g2

2 ! 7

15g21

$, (5.45)

#y! " d

dty! =

y!

16"2

#4y!!y! + 3y!byb ! 3g2

2 ! 9

5g21

$, (5.46)

#µ " d

dtµ =

µ

16"2

#3y!t yt + 3y!byb + y!!y! ! 3g2

2 ! 3

5g21

$. (5.47)

The one-loop RG equations for the gauge couplings g1, g2, and g3 were already listed in eq. (5.21). Thepresence of soft supersymmetry breaking does not a!ect eqs. (5.21) and (5.44)-(5.47). As a result ofthe supersymmetric non-renormalization theorem, the #-functions for each supersymmetric parameterare proportional to the parameter itself. One consequence of this is that once we have a theory thatcan explain why µ is of order 102 or 103 GeV at tree-level, we do not have to worry about µ being madevery large by radiative corrections involving the masses of some very heavy unknown particles; all suchRG corrections to µ will be directly proportional to µ itself and to some combinations of dimensionlesscouplings.

The one-loop RG equations for the three gaugino mass parameters in the MSSM are determinedby the same quantities bMSSM

a that appear in the gauge coupling RG eqs. (5.21):

#Ma " d

dtMa =

1

8"2bag

2aMa (ba = 33/5, 1, !3) (5.48)

for a = 1, 2, 3. It follows that the three ratios Ma/g2a are each constant (RG scale independent) up to

small two-loop corrections. Since the gauge couplings are observed to unify at Q = MU = 2 # 1016

GeV, it is a popular assumption that the gaugino masses also unify§ near that scale, with a value called

§In GUT models, it is automatic that the gauge couplings and gaugino masses are unified at all scales Q ! MU , becausein the unified theory the gauginos all live in the same representation of the unified gauge group. In many superstringmodels, this can also be a good approximation.

44

etc. The first and second family squarks and sleptons with given gauge quantum numbers remainvery nearly degenerate, but the third-family squarks and sleptons feel the e!ects of the larger Yukawacouplings and so their squared masses get renormalized di!erently. The one-loop RG equations for thefirst and second family squark and slepton squared masses are

16!2 d

dtm2

!i= !

!

a=1,2,3

8Ca(i)g2a|Ma|2 +

6

5Yig

21S (5.56)

for each scalar "i, where the"

a is over the three gauge groups U(1)Y , SU(2)L and SU(3)C , withCasimir invariants Ca(i) as in eqs. (5.28)-(5.30), and Ma are the corresponding running gaugino massparameters. Also,

S " Tr[Yjm2!j

] = m2Hu

! m2Hd

+ Tr[m2Q ! m2

L ! 2m2u + m2

d+ m2

e ]. (5.57)

An important feature of eq. (5.56) is that the terms on the right-hand sides proportional to gauginosquared masses are negative, so! the scalar squared-mass parameters grow as they are RG-evolved fromthe input scale down to the electroweak scale. Even if the scalars have zero or very small masses atthe input scale, they can obtain large positive squared masses at the electroweak scale, thanks to thee!ects of the gaugino masses.

The RG equations for the squared-mass parameters of the Higgs scalars and third-family squarksand sleptons get the same gauge contributions as in eq. (5.56), but they also have contributions dueto the large Yukawa (yt,b," ) and soft (at,b," ) couplings. At one-loop order, these only appear in threecombinations:

Xt = 2|yt|2(m2Hu

+ m2Q3

+ m2u3

) + 2|at|2, (5.58)

Xb = 2|yb|2(m2Hd

+ m2Q3

+ m2d3

) + 2|ab|2, (5.59)

X" = 2|y" |2(m2Hd

+ m2L3

+ m2e3

) + 2|a" |2. (5.60)

In terms of these quantities, the RG equations for the soft Higgs squared-mass parameters m2Hu

andm2

Hdare

16!2 d

dtm2

Hu= 3Xt ! 6g2

2 |M2|2 !6

5g21 |M1|2 +

3

5g21S, (5.61)

16!2 d

dtm2

Hd= 3Xb + X" ! 6g2

2 |M2|2 !6

5g21 |M1|2 !

3

5g21S. (5.62)

Note that Xt, Xb, and X" are generally positive, so their e!ect is to decrease the Higgs masses as oneevolves the RG equations down from the input scale to the electroweak scale. If yt is the largest ofthe Yukawa couplings, as suggested by the experimental fact that the top quark is heavy, then Xt willtypically be much larger than Xb and X" . This can cause the RG-evolved m2

Huto run negative near

the electroweak scale, helping to destabilize the point Hu = Hd = 0 and so provoking a Higgs VEV (fora linear combination of Hu and Hd, as we will see in section 7.1), which is just what we want.† Thusa large top Yukawa coupling favors the breakdown of the electroweak symmetry breaking because itinduces negative radiative corrections to the Higgs squared mass.

The third-family squark and slepton squared-mass parameters also get contributions that dependon Xt, Xb and X" . Their RG equations are given by

16!2 d

dtm2

Q3= Xt + Xb !

32

3g23 |M3|2 ! 6g2

2 |M2|2 !2

15g21 |M1|2 +

1

5g21S, (5.63)

!The contributions proportional to S are relatively small in most known realistic models.†One should think of “m2

Hu” as a parameter unto itself, and not as the square of some mythical real number mHu

. Sothere is nothing strange about having m2

Hu< 0. However, strictly speaking m2

Hu< 0 is neither necessary nor su!cient

for electroweak symmetry breaking; see section 7.1.

46


16!2 d

dtm2

!i= !

!

a=1,2,3

8Ca(i)g2a|Ma|2 +

6

5Yig

21S (5.56)



S " Tr[Yjm2!j

] = m2Hu

! m2Hd

+ Tr[m2Q ! m2

L ! 2m2u + m2

d+ m2

e ]. (5.57)



Xt = 2|yt|2(m2Hu

+ m2Q3

+ m2u3

) + 2|at|2, (5.58)

Xb = 2|yb|2(m2Hd

+ m2Q3

+ m2d3

) + 2|ab|2, (5.59)

X" = 2|y" |2(m2Hd

+ m2L3

+ m2e3

) + 2|a" |2. (5.60)


andm2

Hdare

16!2 d

dtm2

Hu= 3Xt ! 6g2

2 |M2|2 !6

5g21 |M1|2 +

3

5g21S, (5.61)

16!2 d

dtm2

Hd= 3Xb + X" ! 6g2

2 |M2|2 !6

5g21 |M1|2 !

3

5g21S. (5.62)





16!2 d

dtm2

Q3= Xt + Xb !

32

3g23 |M3|2 ! 6g2

2 |M2|2 !2

15g21 |M1|2 +

1

5g21S, (5.63)







46


16!2 d

dtm2

!i= !

!

a=1,2,3

8Ca(i)g2a|Ma|2 +

6

5Yig

21S (5.56)



S " Tr[Yjm2!j

] = m2Hu

! m2Hd

+ Tr[m2Q ! m2

L ! 2m2u + m2

d+ m2

e ]. (5.57)



Xt = 2|yt|2(m2Hu

+ m2Q3

+ m2u3

) + 2|at|2, (5.58)

Xb = 2|yb|2(m2Hd

+ m2Q3

+ m2d3

) + 2|ab|2, (5.59)

X" = 2|y" |2(m2Hd

+ m2L3

+ m2e3

) + 2|a" |2. (5.60)


andm2

Hdare

16!2 d

dtm2

Hu= 3Xt ! 6g2

2 |M2|2 !6

5g21 |M1|2 +

3

5g21S, (5.61)

16!2 d

dtm2

Hd= 3Xb + X" ! 6g2

2 |M2|2 !6

5g21 |M1|2 !

3

5g21S. (5.62)





16!2 d

dtm2

Q3= Xt + Xb !

32

3g23 |M3|2 ! 6g2

2 |M2|2 !2

15g21 |M1|2 +

1

5g21S, (5.63)







46

Gaugino Masses

Scalar Masses

mSugra and “Gaugino Mass Unification”

mg : mW : mB = !3 : !2 : !1 ! 6 : 2 : 1

g

!W

B

q

!

HH

h

Most models look like this

A shocking lack of diversity

mSugra and “Gaugino Mass Unification”

mg : mW : mB = !3 : !2 : !1 ! 6 : 2 : 1

g

!W

B

q

!

HHh

Most models look like this

A shocking lack of diversity

Figure 7: (Top) Identity of the nLSP. (Bottom) nLSP-LSP mass splitting as a function of the LSPmass, with the identity of the nLSP as labeled. Both assume flat priors.

26

5 for 1st 2 Generations

The Phenomenological MSSM

m2q,m

2uc ,m2

dc ,m2!,m2

ec

5 for 3rd Generationsmg,mW ,mB , µ 4 for *-ino masses

At, Ab, A! 3 for A-termsm2

hu,m2

hd, Bµ 3-1 for Higgs Sector

Figure 7: (Top) Identity of the nLSP. (Bottom) nLSP-LSP mass splitting as a function of the LSPmass, with the identity of the nLSP as labeled. Both assume flat priors.

26

Berger, Gainer, Hewett, Rizzo 2008

How to parameterize this without using a CPU-Century?

Real models have dozens of parameters

Sometimes small/reasonable perturbationscan make huge differences in the visibility of a model

Need to simplify and abstract models

Need to cover signature space better

Captures specific models

Simplified Models

Easy to notice & explore kinematic limits

Limits of specific theories

Not fully model independent, but greatly reduce model dependence

Removes superfluous model parameters

Only keep particles and couplings relevant for searches

Add in relevant modification to models (e.g. singlets)

Including ones that aren’t explicitly proposed

Masses, Cross Sections, Branching Ratios (e.g. MARMOSET)

Still a full Lagrangian description

(Effective Field Theories for Collider Physics)

Hides Similarities Between Theories

MSSM Universal Extra DimensionsHigh Cut-Off Low Cut-Off

Large Mass Splittings Small Mass Splittings

Similar in spirit, radically different in practice

Color octet that decay into missing energy

g

wb 60 GeV

120 GeV

400 GeVb1w1

g1

400 GeV410 GeV460 GeV

Simplified Models



Outline


Solution to Hierarchy Problem

Jets + MET

Dark Matter

Fewest requirements on spectroscopy

If the symmetry commutes with SU(3)C,new colored top partners

note twin Higgs exception:

Wimp Miracle: DM a thermal relic ifmass is 100 GeV to 1 TeV

Usually requires a dark sector,frequently contains new colored particles

Doesn’t require squeezing in additional states to decay chains

SU(3)C1 ! SU(3)C2 ! Z2

(e.g. Split Susy)

Simplified ModelsDirect Decays

g

!

MASS

color octet majorana fermion (“Gluino”)

neutral majorana fermion (“LSP”)

THREE-BODY

gq

q q

!01

Directly Decaying Gluino

Study one decay mode g ! qq!0

Keep masses and total cross section freem!0mg !(pp! ggX)

g!W

B

q

!

HH

h

gq

qj

j

ET/!0gq

qj

j

ET/ !0 q! q!

g!W

B

q

!

HH

h

Br = 100% Br ! 10%

Gluino Mass (GeV)

0 100 200 300 400 500 600

Sq

ua

rk M

as

s (

Ge

V)

0

100

200

300

400

500

600

-1DØ Preliminary, 0.96 fb

<0µ=0, 0

=3, A!tan

UA

1

UA

2

LEP

CD

F IB

DØ

IA

DØ IB

no mSUGRA

solution

CD

F II

What are the current limits?

Hard to interpret...

Electrically Neutral Colored ParticlesWeak model independent limits

3

Total Statistical Uncertainty

Experimental Statistical Uncertainty

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Fit"Data

Data!SM"

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Fit"Data

Data!SM # 25 GeV gluino"

0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24"0.10

"0.05

0.00

0.05

0.10

1"T

RelativeUncertainty

FIG. 1: Theoretical prediction versus aleph data at lep 1for the standard model and the standard model with a 25GeV gluino. The total statistical uncertainty band includestheoretical statistical uncertainty from the Monte Carlo usedto generate the NNLO fixed-order thrust distribution.

models are shown in Figure 1, where it is clear that themodel with the gluino is systematically worse.

To properly scan over masses, we must specify howto handle the thresholds. First, consider the totalhadronic cross section, !had. The exact leading or-der dependence of !had on the new particle mass canbe extracted from [28]. For m < µ, the contributionto the total cross section is proportional to !!had =

"2s(µ)

!#V (m2

Q2 ) + #R(m2

Q2 ) + 1

4log(m2

µ2 )", where #V is the

virtual contribution which vanishes at m = ! and #R

is the real emission contribution which vanishes for m >Q/2. The explicit log compensates the µ-dependence of"s and is necessary to have a smooth m " 0 limit. Wewill use this exact expression !!had for the new physicscontribution to !had in Eq. (1), but observe that, asshown in [28], it is well approximated for 0 < m < Qby the leading power in m2/Q2. Actually, it is notclear whether the experiments would have included de-cay products of real gluinos in their event selection for thethrust distribution, so in the spirit of providing a model-independent bound, we allow !!had to scan between 0and the cross section for !nf additional massless fla-vors. This variation is included in the uncertainty banddescribed below.

The exact contributions of massive colored states tothe jet, soft, and hard functions are not known, but sincethe same loops and real-emission diagrams are relevantfor them as for !!had, it is likely that the result wouldbe similar to that of !!had. Thus, we assume the leadingpower is linear in m2/µ2

h for the hard function, m2/µ2j for

the jet function, and m2/µ2s for the soft function. That is,

we take H,#j and #s to interpolate between the expressionfor nf = 5 + !nf flavors at m = 0 and nf = 5 flavorsat the relevant threshold. This removes any remainingdiscontinuity in the thrust distribution, and should be a

0 10 20 30 40 50 600.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Mass !GeV"

$n f

FIG. 2: Bounds on light colored particles from lep data. Thedarker region is completely excluded at 95% confidence. Thelighter region is an uncertainty band including estimates ofvarious theoretical uncertainties.

good approximation to the (unknown) exact result. Ina similar vein, the matching correction, r($) in Eq. (2),formally takes place at the hard scale Q. However, itdepends on nf and would be discontinuous as m crossesQ unless the discontinuity is removed by inclusion of ex-plicit mass corrections. We use an interpolation also lin-ear in m2/Q2 for this e"ect. Using this model for themass thresholds, in lieu of the exact result, introducessome theoretical uncertainty. To account for that un-certainty, we explore some variations of the model andinclude the errors in our final bound, as described below.

With this treatment of the threshold e"ects, the thrustdistribution is smooth and can be compared with thedata for each m and !nf . We perform a combined fit tothe aleph [22] and opal [24, 25] data sets from 91.2#206GeV [26, 27]. The fit regions used are 0.1 < $ < 0.24for lep 1 , and 0.04 < $ < 0.25 for aleph lep 2 and0.05 < $ < 0.22 for opal lep 2 . The data are cor-rected bin-by-bin for hadronization and bottom/charmmass e"ects using pythia. We perform a least-squaresfit of the theoretical prediction to the corrected data, us-ing errors which include both the experimental statisticalerrors and the statistical errors of the NNLO fixed-ordercalculation, rescaled by 1.5, as described above. For thestandard model, the %2 is 85.7 for 78 degrees-of-freedom.For each value of m and !nf , we minimize %2 and com-pute the maximum likelihood ratio as compared with thestandard model. The resulting 95% C.L. bound is shownin Figure 2. For !nf = 3, the limit is meg > 52.5 GeV.For a real gluino (with the appropriate group theory fac-tors di"ering from !nf = 3 at higher orders), the bounddi"ers by 0.03 GeV.

To account for the theoretical uncertainty, we includean uncertainty band (the light shaded region in Figure 2).This subsumes the following variations: (i) Removingthe lowest bins from each data set in the fit. (ii) Not

Limits come from event shape variables at LEP(e.g. Thrust)

Kaplan, Schwartz 2008

Model Independent Constraints

V. GLUINO EXCLUSION LIMITS

A. No Cascade Decays

For the remainder of the paper, we will discuss how model-independent jets + ET! searchescan be used to set limits on the parameters in a particular theory. We will focus specificallyon the case of pair-produced gluinos at the Tevatron and begin by considering the simplifiedscenario of a direct decay to the bino. The expected number of jets depends on the relativemass di!erence between the gluino and bino. When the mass di!erence is small, the decayjets are very soft and initial-state radiation is important; in this limit, the monojet searchis best. When the mass di!erence is large, the decay jets are hard and well-defined, sothe multijet search is most e!ective. The dijet and threejet searches are important in thetransition between these two limits.

As an example, let us consider the model spectrum with a 340 GeV gluino decayingdirectly into a 100 GeV bino. In this case, the gluino is heavy and its mass di!erence withthe bino is relatively large, so we expect the multijet search to be most e!ective. Table IIIshows the di!erential cross section grids for the 1-4+ jet searches for this simulated signalpoint. The colors indicate the significance of the signal over the limits presented in Table II;the multijet search has the strongest excesses.

Previously [28], we obtained exclusion limits by optimizing the ET! and HT cuts, whichinvolves simulating each mass point beforehand to determine which cuts are most appropri-ate. This is e!ectively like dealing with a 1" 1 grid, for which a 95% exclusion corresponds

Out[27]=

XX

100 200 300 400 5000

50

100

150

Gluino Mass !GeV"

BinoMass!GeV

"

FIG. 4: The 95% exclusion region for DO! at 4 fb!1 assuming 50% systematic error on background.The exclusion region for a directly decaying gluino is shown in light blue; the worst case scenariofor the cascade decay is shown in dark blue. The dashed line represents the CMSSM points andthe “X” is the current DO! exclusion limit at 2 fb!1.

15

Tevatron Reach

4 fb-1

2! sensitivity

g ! Bjj

g ! !Wjj ! (Bjj)jj

mg>! 120 GeV

A 50 GeV gluino is “ruled out”!

Alwall, Le, Lisanti, Wacker 2008

Sample theory

These were “best case scenario numbers” mg = 210 GeV mB = 100 GeV

Assumed no missed discoveries

HT ! 150 GeV E" T ! 100 GeVHT ! 300 GeV ET" ! 225 GeV

BG

Signal Signal

BG (w/o QCD)(w/o QCD)

Tevatron never searched in physics parameter space

e.g.

Possibility for light gluinos lurking

Alw

all, Le, Lisanti, Wacker 2008

Simplified Models



Outline


Set limit on !(pp! ggX) "

usually most effective3+j + ET!

2

Cut Topology 1j + ET! 2+j + ET! 3+j + ET! 4+j + ET!1 pT1 > 70GeV > 70GeV > 70GeV > 70GeV

2 pTn " 30GeV > 30GeV(n = 2) > 30GeV(n = 2, 3) > 30GeV(n = 2# 4)

3 ET! EM > 40GeV > 40GeV > 40GeV > 40GeV

4 pT ! " 10GeV " 10GeV " 10GeV " 10GeV

5 !!(jn, ET! EM) none [> 0.2, > 0.2] [> 0.2, > 0.2, > 0.2] [> 0.2, > 0.2, > 0.2, none]

6 ET! EM/Me! none > 0.3 > 0.25 > 0.2

NPred 46+22!14 6.6 ± 3.0 1.9 ± 0.9 1.0 ± 0.6

NObs 73 4 0 1

"(pp$ ggX)#|95% C.L. 663 pb 46.4 pb 20.0 pb 56.9 pb

TABLE I: Searches in [1] used to set limits in this article. The 95% C.L. on the production cross section times e"ciency of thecuts, "(pp$ ggX)#, derive from folding in the uncertainties in the luminosity and background.

which can be generated by integrating out a color tripletscalar. The lifetime of g is approximately

!g !(mg "m!)5

4!"4(2)

which leads to a prompt decay so long as " <# 10 TeVfor mg

># m! + 10 GeV. There is no a priori relationbetween the masses of " or g. " may be very light withoutany constraints arising from LEP, and the only modelindependent constraint on g is that it should be heavierthan 51 GeV.

Models with approximate g-" mass degeneracy are par-ticularly challenging for jet plus ET$ searches. In this case,the decay products of g are soft and not particularly spec-tacular. In the degenerate limit, the most e#cient wayto detect g production is by looking for radiation of addi-tional jets along with the pair of g. At the Tevatron, pairproduced g’s plus radiation gives rise to events with lowmultiplicity jets plus ET$ . In particular, monojet searchescan be e$ective at discovering these topologies [8]. How-ever, monojet searches are typically exclusive and placepoor bounds away from the degenerate limit. For in-stance, CDF places a second jet veto of ET j2 % 60 GeVand a third jet veto of ET j3 % 20 GeV [20]. As themass di$erence between g and " increases, the e#ciencyof such cuts diminishes. In the non-degenerate limit,the most suitable searches have higher jet multiplicity.However, the cuts applied on the monojet and multi-jet searches performed are su#ciently strong that theyleave a gap in the coverage of the intermediate mass-splitting region [8]. The present bound on mg only ex-tends above 130 GeV for m!

<# 100 GeV. The LHC crosssection for gluinos just above this limit is of the order ofa few nanobarns. Therefore, limits can be improved withremarkably low luminosity and early discovery is poten-tially achievable. Unfortunately, no excesses are observedin [1], so only new limits can be inferred.

In this work, the e#ciencies of the cuts applied byATLAS’ recent search are extracted through a MonteCarlo study. These e#ciencies depend on mg and m!

and are necessary to calculate limits. The signal is

calculated using MadGraph 4.4.32 [9], matching partonshower (PS) to additional radiation generated throughmatrix elements (ME) using the MLM PS/ME match-ing prescription from [10]. In the region where g and" are nearly-degenerate, the additional radiation is cru-cial in determining the shape of the ET$ distribution andhence how e#ciently the signal is found. A matchingscale of Qcut = 100 GeV is adopted for the signal andthe matrix elements for the following subprocesses aregenerated: 2g + 0j, 2g + 1j and 2g + 2+j. When per-forming MLM matching all higher multiplicity jet eventsare generated through parton showering.

The parton showering is performed in PYTHIA 6.4 [11].PYTHIA also decays g & qq", hadronizes the events andproduces the final exclusive events. These events are thenclustered using a cone-jet algorithm with R = 0.7 withPGS4 [12] which also performs elementary fiducial vol-ume cuts and modestly smears the jet energy using theATLAS-detector card.

ATLAS’ search does not use proper ET$ in their analy-sis, instead it uses missing energy at the electromagneticscale, ET$ EM. The relation between ET$ and ET$ EM isshown in Fig. 7 of [13] and is approximated as

ET$ EM !ET$

1.5"HT /2100 GeV, (3)

where HT is the sum of the energies of the jets in theevent. This e$ectively raises the ET$ cut to approximately50 GeV.

In order to validate this modeling of ET$ EM, the SU4mSUGRA model shown in [1] is reproduced. The SUSYLes Houches Accord parameter card [14] for SU4 is cre-ated with a spectrum calculated with SuSpect 2.41 [15]which matches the spectrum reported in [16] to 5% accu-racy. The decay card for SU4 is calculated with SDECAY[17], interfaced with SUSY-HIT [18], and finally the crosssections are generated with MadGraph and decayed, show-ered and hadronized in PYTHIA. The total SUSY produc-tion cross section is normalized to the NLO value usedin [1] in order to compare e#ciencies and shapes of dis-tributions.

Estimates of ATLAS ICHEP ReachCan 70nb-1 improve Tevatron results?

mg

!pp!

gg(nb)

100 200 300 4000.001

0.01

0.1

1

10

100

How many color octets can you make with!(pp! gg) = 20 pb

Prospino

! = 1%

! = 10%

! = 100%

160 GeV

250 GeV

360 GeV

Can get above the Tevatron’s current boundswith reasonable efficiencies

?

Need to calculate efficiencies(the hard part)

We need to know what fraction ofthe events from a given theory pass the cuts

Madgraph Pythia PGS! ! ! Cutsg ! 2j !0

1

(MLM matched)

pp! gg+ " 2j

Do this for each (mg, m!) pairEfficiency is the fraction of events that passed the cuts

Validated PGS to about 15% accuracy

A look at how PS/ME matching alters the signal150 GeV particle going to 140 GeV LSP and 2 jets

In rest frame of each gluino: two 5 GeV “jets” and a LSP with 3 GeV momentum

j1j2

B

g

A look at how PS/ME matching alters the signal150 GeV particle going to 140 GeV LSP and 2 jets

In rest frame of each gluino: two 5 GeV “jets” and a LSP with 3 GeV momentum

j1

j2

j3

j4

BB

gg

ET!

j1

j2

j3j4

Parton level Detector level

Totally invisible: faked by QCD with !

sBG " 20 GeV

j1j2

B

g

Give the gluino big boost!

j1

j2

j3

j4

gg

B

B

j1

j2

ET!

Jets merge and MET points in direction of jetMore energy, but looks like jet mismeasurement

pT g ! mg

Radiate off additional jet

q q

g gg

j1

j2

j3

j4

gg

B

B

j5

j1

j2

ET!j3

Unbalances momentum of gluinos

Need to calculate the spectrum of radiation

reliably

Putting it all together

200 pb

300 pb

500 pb

1 nb

2 nb

100 pb

Tevatron

!prod = 3!" NLO-QCD

!prod = !" NLO-QCD

!prod = 0.3 !" NLO-QCD


mSUGRA

g ! !qq

Sample theory

There could have been discoveries!

contours =!no-matching

lim

!matchinglim

! 1

2

1

0.3

0.2

0.1

0.03

21

0.3

0.2

0.1

0.03

Higher multiplicities affected more

Generally increases sensitivity

PS/ME Matching on Signal

Degenerate region can have limits altered by O(1)

Efficiencies are over estimated with jet vetos

1

-0.1

0.3

2

0.1

-0.05

Simplified Models



Outline


Looking towards future analysesCurrent plans are for a single multijet search

m!±=m!0+mW±

Tevatron

300 pb

500 pb

1 nb

2 nb

200 pb

!prod = 3!" NLO-QCD

!prod = !" NLO-QCD



mSUGRA

Maximize reach for highest mass gluino discovery

Should maximize sensitivity to smallest cross section for all masses

e.g. if only 10% of the decays are visible

Still need to be sensitive to light objects with small cross sections/branching ratios

Cuts & Optimization

• Generated signal for a wide range of masses , and the four decay modes discussed

mg m!

• Estimated sensitivities for cuts on several kinematic variables,

ET! , HT , pTi , Me! " ET! + ! pTi ,ET!Me!

,pTi

ET!

Hard to beat missing and visible energy

Stuck with combined cuts onET! , HT

7 TeV BackgroundsSoon to be available at LHCBackgrounds.com

! "

#4+Jets B

ackgrounds

Match ATLAS MC Work Reasonably Well

ttQCD

WZ

Combined

fb/2

5G

eV

Include 30% systematic error on BG Estimates

Simplified Models for this study

Direct Decays

g

!

MASS



THREE-BODY

gq

q q

!01

TWO-BODY

g

g

!01


One-Step Cascade Decays

g

!

MASS

!±

m!± = m!+ (mg + m!)



electroweak majoranafermion (“Wino”)

12

gq

W (!)q q

!01!2


Two-Step Cascade Decays

g

!

MASS

!±

m!± = m!+ (mg + m!)



electroweak majoranafermion (“Wino”)

!!neutral majorana fermion (“Higgsino”)

12

m!! = m!+ (m!± + m!)12

gq

W (!)W (!)q q

!01!2!3

Hunting for Optimal Cuts

QUESTION: Is there a single cut whose sensitivity is close to optimal for all masses and decay modes?

ANSWER: No

Want to have good coverage for all these models

for all kinematic ranges

Want to minimize:!lim(cut)

!optimal lim

cut

spac

e

mod

el s

pace

model space

!lim

!opt

Hunting for Optimal CutsTASK: Find the minimum set of cuts on MET and HT whose combined reach is close to optimal (within a given accuracy) for all models.

cut 1 cut 2

1.3

1

Hunting for Optimal Cuts

mg! ! "

m"!

"# HT#

g

!

mg! ! "

m"!

"

# HT#

g

!

mg! ! "

m"!

"

# HT#

g

!

mg! ! "

m"!

"

# HT#

g

!

within 10% of optimal



E.g.,reach of the search region

ET! "150 GeV& HT!750 GeV

2-body 3-body

Multiple Search Regions• minimal set of cuts (multiple search regions) whose combined reach

is within optimal to a given accuracy

for all masses and decay modesfor three luminosity scenarios: 10 pb-1, 100 pb-1, 1 fb-1

• size of the set depends on the optimal accuracy✦ 5% O( 30 cuts )✦ 10% O( 16 cuts )✦ 30% O( 6 cuts )✦ 50% O( 4 cuts )

• not sensitive to exact values of the cuts• only comprehensive when combined

combined reach

within 30% of optimalMultiple Search Regions

• 6 search regions necessary:

Dijet high MET

Trijet high MET

Multijet moderate MET

Multijet high MET

Multijet low MET

Multijet very high HT

ET! > 500 GeV, HT > 750 GeV

ET! > 450 GeV, HT > 500 GeV

ET! > 100 GeV, HT > 450 GeV

ET! > 150 GeV, HT > 950 GeV

ET! > 250 GeV, HT > 300 GeV

ET! > 350 GeV, HT > 600 GeV

combined reach


cut ch MET HT

2+j 500 750

3+j 450 500

4+j 100 450

4+j 100 650

4+j 150 950

4+j 250 300

4+j 350 600

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"

# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#mg

! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"# HT#

mg! ! "

m"!

"

# HT#Multiple Search Regions

g

!

g

!

g

!

g

!

2-body 3-body

Multijet high MET

Designing Optimal Regions

• Choice of multiple search regions depends upon

• Not something a theorist should be designing too closely

• Scans are expensive for experiments, providing benchmark theories saves effort

• backgrounds • detector efficiencies & acceptances• how good is good enough• etc

• We’ve done rough exploration of corners of parameter space looking for

List of Benchmark Models

• Chosen to maximize differences in how they appear in given searches

• Simple and easy to define

• Consistent theories on their own

m!± = m!0 + x(mg !m!0)

Lots more to be done

• This work focused on pair produced colored octets

color triplets (radiate less - different search regions for compressed spectra?)

• Important to look at other possibilities:

monojet signatures not from radiation (e.g., squark-neutralino associate production, resonantly produced composite gluon to gluon + invisible)

multijet signatures with no missing energy (very different story)

resonant production

• Joint effort in this direction: http://lhcnewphysics.org

other channels (heavy flavor - in progress w/SLAC ATLAS group)

http://lhcnewphysics.org

http://lhcnewphysics.org

Summary• Searches for new colored states with jets+MET signatures are

promising with the LHC data of next year

• Benchmark driven searches are suboptimal (and too model dependent)

• Reach can be highly improved by:

less model dependent parametrizations (simplified models)

multiple search region strategy

advantage: sensitive to a large range of phase space

advantage: combined reach is very close to optimal in the whole parameter space of models

2011 is the year for discoveries

Lots of work to be donehttp://LHCNewPhysics.org

201020112012201320142015

M201020112012201320142015

d log M

dt

Mass Reach as function of time

http://LHCNewPhysics.org

http://LHCNewPhysics.org

jets met atlas jamboree 2011

Education