Precision Cosmology at the Precision Cosmology at the LHCLHC

Bhaskar Dutta

Texas A&M University

Precision Cosmology at the LHC 125th August ’ 08

Cosmo 2008, Madison, Wisconsin

We are about to enter into an era of major discovery

Dark Matter: we need new particles to explain the content of the universe

Standard Model: we need new physics

Supersymmetry solves both problems!

Our best chance to observe SUSY is at the LHC

Future results from Planck, direct and indirect detection in tandem with the LHC will confirm a model

LHC: The experiment which directly probes TeV scale

Discovery Time…

The super-partners are distributed around the weak scale

Precision Cosmology at the LHC 2

The signal : jets + leptons + missing ET

SUSY at the LHC

(or l+l-, )

DM

DM

Colored particles get produced and decay into weakly interacting stable particles

High PT jet

High PT jet

[mass difference is large]

The pT of jets and leptons depend on the sparticle masses which are given by models

R-parity conserving

3Precision Cosmology at the LHC

Excess in ETmiss + Jets R-parity conserving SUSY

Meff Measurement of the SUSY scale at 10-20%.

Excess in Excess in EETTmissmiss + Jets + Jets

Hinchliffe and Paige, Phys. Rev. D 55 (1997) 5520

q

The heavy SUSY particle mass is measured by combining the final state particles

q

q

q01~

01~

g~g~

ETj1 > 100 GeV, ET

j2,3,4 > 50 GeV Meff > 400 GeV (Meff ET

j1+ETj2+ET

j3+ETj4+ ET

miss) ET

miss > max [100, 0.2 Meff]

Precision Cosmology at the LHC 4

SUSY scale can be measured with an accuracy of 10-20%

This measurement does not tell us whether the model can generate the right amount of dark matter

The dark matter content is measured to be 23% with an accuracy less than 4% at WMAP

Question:

To what accuracy can we calculate the relic density based on the measurements at the LHC?

Relic Density and Meff

Precision Cosmology at the LHC5

Measurement of Masses

We need to measure the masses of the particles.

Model parameters need to be determined to check the cosmological status. [Allanach, Belanger, Boudjema and Pukhov’04]

If we observe missing energy, then we have a possible dark matter candidate .

We want to make sure that we have the correct model to explain the dark matter content

Using the model parameters we calculate relic density and compare with WMAP, PLANCK data

6Precision Cosmology at the LHC

Goal:Goal:

7

2

1CDM

+ ….

A near degeneracy occurs naturally for light stau in mSUGRA.A near degeneracy occurs naturally for light stau in mSUGRA.

011

~~ MMM Δ011

~~ MMM Δ

fTMe k/Δ

2

01~

1~+ + ….

Co-annihilation (CA) Process

Co-annihilation (CA) ProcessGriest, Seckel ’91

Anatomy of Anatomy of annann

pbM

vann 1~~2

2

Precision Cosmology at the LHC

2GeV) 37(21/2

15020

2cE

m.m~m

In mSUGRA model the lightest stau seems to be naturally close to the lightest neutralino mass especially for large tan

For example, the lightest selectron mass is related to the lightest neutralino mass in terms of GUT scale parameters:

For larger m1/2 the degeneracy is maintained by increasing m0 and we get a corridor in the m0 - m1/2

plane.

The coannihilation channel occurs in most SUGRA models with non-universal soft breaking,

21/2

160201

m.~

m

Thus for m0 = 0, becomes degenerate with at m1/2 = 370 GeV, i.e. the coannihilation region begins at

0

1

~2

cE~

m1/2 = (370-400) GeV

Coannihilation, GUT Scale

Arnowitt, Dutta, Santoso’ 01

Precision Cosmology at the LHC 8

DM Allowed Regions in mSUGRABelow is the case of mSUGRA model.

However, the results can be generalized.

[Stau-Neutralino CA region]

[Focus point region]the lightest neutralino has a larger Higgsino component[A-annihilation funnel region]This appears for large values of m1/2

[Bulk region] is almost ruled out

9Precision Cosmology at the LHC

CA Region at tanCA Region at tan = 40 = 40

GeV 155011

~MMM ~~ GeV 155011

~MMM ~~

Can we measure M at colliders?Can we measure M at colliders?

10Precision Cosmology at the LHC

Goal for CA-analysisGoal for CA-analysis

Establish the “dark matter allowed region” signal

Measure SUSY masses Determine mSUGRA parameters

Predict h2 and compare with CDMh2 11Precision Cosmology at the LHC

Smoking Gun of CA RegionSmoking Gun of CA Region

100%1~

Lu~

01χ~

02χ~

g~

97%

u

u

SU

SY

Mass

es

(CDM)

2 quarks+2 ’s+missing energy

Uni

que

kine

mat

ics

12

Low energy taus exist in theCA regionHowever, one needs to measure the model Parameters to predict theDark matter content in this scenario

Precision Cosmology at the LHC

Nu

mb

er o

f C

oun

ts /

2 G

eVppTT

softsoft Slope and Slope and MM

Slope of pT distribution of “soft ” contains ΔM information

Low energy ’s are an enormous challenge for the detectors

pT and M distributions in true di- pairs from neutralino decay

Precision cosmology at the LHC 13

Nu

mb

er o

f C

oun

ts /

1 G

eV

ETvis(true) > 20, 20 GeV

ETvis(true) > 40, 20 GeV

ETvis(true) > 40, 40 GeV

GeV) 5.7(

011

02

M

~~~

Arnowitt, Dutta, Kamon, Kolev, Toback PLB 639 (2006) PLB 639 (2006) 4646

14

We use ISAJET + PGS4PLB 639 (2006) 46PLB 639 (2006) 46

Precision Cosmology at the LHCArnowitt, Dutta, Kamon, Kolev, Toback

MM Distribution Distribution

Clean peak even for low M

We choose the peak position as an observable.We choose the peak position as an observable.

(GeV) visM (GeV) vis

M

15Precision Cosmology at the LHC

MM peak peak vs. vs. XX

Uncertainty Bandswith 10 fb-1

16Precision Cosmology at the LHC

Slope(pTsoft ) vs. X

Uncertainty Bandswith 10 fb-1

(GeV) ~gM

(GeV) 02

~M

17Precision Cosmology at the LHC

SUSY Anatomy

Mj

M

pT()

100%1~

Lu~

01χ~

02χ~

g~

97%

u

u

SU

SY

Mass

es

(CDM)

18

Meff

Precision Cosmology at the LHC

MMjj Distribution Distribution

2~

2~

2~

2~

~

02

01

02 11

M

M

M

MMM

qq

endj

M < Mendpoint

Jets with ET > 100 GeV

Mj masses for each jet

Choose the 2nd large value Mj

gluinosquark + j

“other” jet

We choose the peak position as an observable.We choose the peak position as an observable.

19Precision Cosmology at the LHC

MMjjpeakpeak vs. vs. XX

20Precision Cosmology at the LHC

4 j+E4 j+ETTmissmiss: M: Meffeff Distribution Distribution

ETj1 > 100 GeV, ET

j2,3,4 > 50 GeV [No e’s, ’s with pT > 20 GeV] Meff > 400 GeV (Meff ET

j1+ETj2+ET

j3+ETj4+ ET

miss [No b jets; b ~ 50%]) ET

miss > max [100, 0.2 Meff]

21Precision Cosmology at the LHC

At Reference PointMeff

peak = 1274 GeV

Meffpeak = 1220 GeV

(m1/2 = 335 GeV)Meff

peak = 1331 GeV(m1/2 = 365 GeV)

Arnowitt, Dutta, Gurrola, Kamon, Krislock, Toback, PRL, 100, (2008) 231802

Determination of tanDetermination of tan

Measuring Relic Density at the LHC 22

Determination of tan is a real problem

Instead, we use observables involving third generation sparticles: Meff(b) [the leading jet is a b-jet]

We can determine tan and A0 with good accuracy

This procedure can be applied to different SUGRA models

One way is to determine stop and sbottom masses and then solve for A0 and tan

Problem: Stop creates a background for sbottom and …

...2

...2

)cot(

)cot(

R

L

ttt

ttQ

mAm

Amm

E.g., stop mass matrix:

3 j+1b+E3 j+1b+ETTmissmiss :M :Meffeff

((bb)) DistributionDistribution

ETj1 > 100 GeV, ET

j2,3,4 > 50 GeV [No e’s, ’s with pT > 20 GeV] Meff

(b) > 400 GeV (Meff

(b) ET

j1=b+ETj2+ET

j3+ETj4+ ET

miss [j1 = b jet]) ET

miss > max [100, 0.2 Meff]

23Precision Cosmology at the LHC

Meff(b)peak = 1122 GeV

(m1/2 = 365 GeV)At Reference PointMeff

(b)peak = 1026 GeV

Meff(b)peak = 933 GeV

(m1/2 = 335 GeV)

MMeffeff((bb)) can be used to determine A0 and tan even

without measuring stop and sbottom masses

Arnowitt, Dutta, Gurrola, Kamon, Krislock, Toback, Arnowitt, Dutta, Gurrola, Kamon, Krislock, Toback, Phys. Rev. Lett. 100, (2008) 231802Phys. Rev. Lett. 100, (2008) 231802

Observables

SM+SUSY Background gets reduced

NN

•Ditau invariant mass: M

• Jet-- invariant mass: Mj

• Jet- invariant mass: Mj

• PT of the low energy • Meff : 4 jets +missing energy• Meff(b) : 4 jets +missing energy

Since we are using 7 variables, we can measure the model parameters and the grand unified scale symmetry (a major ingredient of this model)

1.Sort ’s by ET (ET1 > ET

2 > …)• Use OSLS method to extract pairs from the

decays

All these variables depend on masses => model parameters

24Precision Cosmology at the LHC

7 Eqs (as functions of SUSY parameters)

)~,~(

)~,~,,~(

)~,~,,~ (

)~,~,~(

)~,(

)~,~,(

6peakeff

01

025

(2)peak2

01

024

(2)peak1

01

023

(2)peak

012

01

021

peak

L

Lj

Lj

Lj

qgfM

MqfM

MqfM

qfM

MfSlope

MfM

Invert the equations to Invert the equations to determine the massesdetermine the masses

Determining SUSY Masses (10 Determining SUSY Masses (10 fbfb11))

1 ellipse

)91.5( 8.09.5/

)19.3( 2.01.3/

0.26.10

;19141;15260

;21831 ;25748

01

02

01

02

~~

~~

~~

~~

theoryMM

theoryMM

M

MM

MM

g

g

gqL

10 fb-1

25

Phys. Rev. Lett. 100, (2008) 231802Phys. Rev. Lett. 100, (2008) 231802

Meff(b) = f7(g, qL, t, b)~ ~ ~ ~

Measurement of Dark Matter Content at the LHC

GUT Scale SymmetryWe can probe the physics at the Grand unified theory (GUT) scale

The masses , , unify at the grand unified scale in SUGRA models

01

~

m1/2

mas

s

MZMGUTLog[Q]

g~

01

~02

~

02

~ g~

Gaugino universality test at ~15% (10 fb-1)

Another evidence of a symmetry at the grand unifying scale!

Use the masses measured at the LHC and evolve them to the GUT scale using mSUGRA

[1] Established the CA region by detecting low energy ’s (pT

vis > 20 GeV)

[2] Determined SUSY masses using:M, Slope, Mj, Mj, Meff

e.g., Peak(M) = f (Mgluino, Mstau, M , M )

[3] Measure the dark matter relic density by determining m0, m1/2, tan, and A0

DM Relic Density in mSUGRADM Relic Density in mSUGRA

01

~02

~

27Precision Cosmology at the LHC

Determining mSUGRA ParametersDetermining mSUGRA Parameters

),tan,,()(

),(

),tan,,(

),(

002/14eff

02/13eff

002/12

02/11

AmmXbM

mmXM

AmmXM

mmXM j

?tan

?

?

?

0

2/1

0

A

m

m

),tan,( 02/102

~01

AmmZh

)fb (??? ???/ 12~

2~ 0

101

hh

28Precision Cosmology at the LHC

Mass Measurements Mass Measurements mSUGRAmSUGRA

M peak, Meff(b)peak …. Sensitive to A0 , tanmandm1/2

Mjpeak, Meff

peak …. Sensitive to m0, m1/2

29Precision Cosmology at the LHC

Determining mSUGRA ParametersDetermining mSUGRA Parameters

),tan,,(

),(

002/14)(

eff

02/13eff

AmmfM

mmfMb

),tan,,(

),(

002/12

02/11

AmmfM

mmfM j

Solved by inverting the following functions:

140tan

160

4350

5210

0

2/1

0

A

m

m

10 fb-1

),tan,( 02/102

~01

AmmZh

1fb 10 L

1fb 50 )fb 30( %6/ 12~

2~ 0

101

hh

30

Phys. Rev. Lett. 100, (2008) 231802Phys. Rev. Lett. 100, (2008) 231802

Precision Cosmology at the LHC

)fb 30( %10/ 1~~ 0

101

pp

Focus Point (FP)Focus Point (FP)m0 is large, m1/2 can be small, e.g., m0= 3550 GeV, m1/2=314 GeV, tan=10, A0=0

31

M(gluino) = 889 GeV, ΔM(χ3

0- χ10) = 81 GeV,

ΔM(χ20- χ1

0) = 59 GeV, ΔM(χ3

0- χ20) = 22 GeV

Br(g → χ20 tt) = 10.2%

Br(g → χ20 uu) = 0.8%

Br(g → χ30 tt) = 11.1%

Br(g → χ30 uu) = 0.009%

~~

~~

---

-

Precision Cosmology at the LHC

)( OSDFOSSF eee )( OSDFOSSF eee

)( OSDF e )( OSDF e

)OSSF( ee )OSSF( ee

M(ll) (GeV)

Eve

nts

/GeV

GeV 59)()( 01

02 ~M~M GeV 59)()( 0

102 ~M~M GeV 81)()( 0

103 ~M~M GeV 81)()( 0

103 ~M~M

32

Dilepton Mass at FP

Tovey, PPC 2007; Baer, Barger, Salughnessy, Summy, Wang , PRD, 75, 095010 (2007),Crockett, Dutta, Flanagan, Gurrola, Kamon, Kolev, VanDyke, 08;

Precision Cosmology at the LHC

33

Determination of masses: FP

Relic density calculation depends on , tan and m1/2

All other masses are heavy!

mm1/21/2 and tan and tan can be solved from can be solved from

M(gluino), ΔM (χM(gluino), ΔM (χ3300- χ- χ11

00) and ΔM (χ) and ΔM (χ2200- χ- χ11

00))

Errors of : M(gluino), ΔM (χ30- χ1

0) ΔM (χ20- χ1

0)300 fb-1 4.5 % 1.2% 1.7%

Higher jet, b-jet, lepton multiplicity requirement increase the signal over background rate

Chargino masses can be measured! Work in Progress…Precision Cosmology at the LHC

tan 22% 0.1%

Bulk RegionThe most part of this region in mSUGRA is experimentally (Higgs mass limit, bs ) ruled out

mSUGRA point:

The error of relic density: 0.108 ± 0.01(stat + sys)

sparticle

mass

97.2

398

189

607

533

End pts value error

mll 81.2 0.09

Mlq((max) 365 2.1

Mlq(min) 266.9 1.6

Mllq(max) 425 2.5

Mllq(min) 207 1.9

M(max) 62.2 5.0

Relic density is mostly satisfied by t channel selectron, stau and sneutrino exchange

Perform the end point analysis to determine the masses

01

~

02

~

l~

g~

uL

~

m0=70; A0=-300m1/2=250; >0;tan=10;

[With a luminosity 300 fb-1, edge controlled to 1 GeV]

Nojiri, Polsello, Tovey’05

~Includes: (+0.00,−0.002 )M(A); (+0.001, −0.011) tan β; (+0.002,−0.005) m(2)

Precision Cosmology at the LHC

Accuracy of tanAccuracy of tan

35

The accuracy of determining tan is not so good if we do not have staus in the final states.

E.g., raise m0

The final states contain Z, Higgs, staus

Lahanas, Mavromatos, Nanopoulos, Phys.Lett.B649:83-90,2007.

Dilaton effect creates new parameter space

Precision Cosmology at the LHC

2200 DecayDecay Branching RatiosBranching Ratios

Identify and classify 20 decays

Dutta, Gurrola, Kamon, Krislock, Lahanas, Mavromatos, Nanopoulos, arXiv:0808.1372Dutta, Gurrola, Kamon, Krislock, Lahanas, Mavromatos, Nanopoulos, arXiv:0808.1372

Observables involving Z and Higgs

We can solve for masses by using the end-points

Precision Cosmology at the LHC

Observables

Higgs + plus jet + missing energy dominated region:

Effective mass: Meff (peak): f1(m0,m1/2)

Effective mass with 1 b jet: Meff (b) (peak): f2(m0,m1/2, A0, tan)

Effective mass with 2 b jets: Meff (2b) (peak): f3(m0,m1/2, A0, tan)

Higgs plus jet invariant mass: Mbbj(end-point): f4(m0,m1/2)

4 observables=> 4 mSUGRA parameters

However there is no stau in the final states: accuracy for determining tan will be less

Precision Cosmology at the LHC

39

Error with 1000 fb-1

Observables…

Precision Cosmology at the LHC

Determining mSUGRA ParametersDetermining mSUGRA ParametersSolved by inverting the following functions:

1839tan

950

15440

50472

0

21

0

A

m

m

/

),tan,( 02/102

~01

AmmZh

1fb 1000 L

%~h/h ~~ 1502201

01

)tan(

)tan(

)(

)(

00214peak )(

eff

00213peak )(

eff

0212peakeff

0211point end

A,,m,mXM

A,,m,mXM

m,mXM

m,mXM

/bb

/b

/

/jbb

1000 fb-1

40Precision Cosmology at the LHC

2 tau + missing energy dominated regions:

Solved by inverting the following Observables:

340tan

450

6600

23440

0

21

0

A

m

m

/

),tan,( 02/102

~01

AmmZh

%~h/h ~~ 192201

01

)tan(

)tan(

)(

)(

00214peak

00213peak )(

eff

0212peakeff

0211(2)peak

A,,m,mXM

A,,m,mXM

m,mXM

m,mXM

/

/b

/

/j

500 fb-1

For 500 fb-1 of data

Dutta, Gurrola, Kamon, Krislock, Lahanas, Mavromatos, Nanopoulos, arXiv:0808.1372Dutta, Gurrola, Kamon, Krislock, Lahanas, Mavromatos, Nanopoulos, arXiv:0808.1372 Precision Cosmology at the LHC

Conclusion

Signature contains missing energy (R parity conserving) many jets and leptons : Discovering SUSY should not be a problem!

Once SUSY is discovered, attempts will be made to connect particle physics to cosmology

Based on these measurement, the dark matter content of the universe will be calculated to compare with WMAP/PLANCK data.

Four different cosmological motivated regions of the minimal SUGRA model have distinct signatures

The CA region can be established by detecting low energy ’s (pT

vis > 20 GeV)

Determine SUSY masses using: M, Slope, Mj, Mj, Meff

e.g., Peak(M) = f (Mgluino, Mstau, M , M ) Gaugino universality test at ~15% (10 fb-1)

Measure the dark matter relic density by determining m0, m1/2, tan, and A0 using Mj, Meff, M, and Meff

(b)

We obtain:

Conclusion…Conclusion…

01

~02

~

43

)fb 30( %6/ 12~

2~ 0

101

hh

Precision Cosmology at the LHC

Focus point region also determines the parameters with high accuracy

Concusion…For large m0, when staus are not present, the mSUGRA parameters can still be extracted, but with less accuracy

It is also possible to determine nonuniversal model Parameters, ,

This analysis can be applied to any SUSY model

)1( 120

2

1mmH

)1( 220

2

2mmH

We can use new observables, Meff(2b), Meff(t) etc