June 8, 2007 DSU 2007, Minnesota

Relic Density at the LHC

B. Dutta

In Collaboration With:

R. Arnowitt, A. Gurrola, T. Kamon, A. Krislock, D. Toback

Phys. Lett. B 639 (2006) 46; B 649 (2007) 73; To appear

Texas A&M University

The signal to look for: 4 jet + missing ET

SUSY in Early Stage at the LHC

Kinematical Cuts and Event Selection ET

j1 > 100 GeV, ETj2,3,4 > 50 GeV

Meff > 400 GeV (Meff ETj1+ET

j2+ETj3+ET

j4+ ETmiss)

ETmiss > Max [100, 0.2 Meff]

Phys. Rev. D 55 (1997) 5520

Example Analysis

SUSY scale is 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 of around 5% at WMAP Question:

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

Relic Density and Meff

We establish the dark matter allowed regions from the detailed features of the signals.

We accurately measure the masses.

We calculate the relic density and compare with WMAP.

Strategy

Minimal Supergravity (mSUGRA)Minimal Supergravity (mSUGRA)4 parameters + 1 sign

m1/2 Common gaugino mass at MG

m0 Common scalar mass at MG

A0 Trilinear couping at MG

tan <Hu>/<Hd> at the electroweak scale

sign() Sign of Higgs mixing parameter (W(2) = Hu Hd)

4 parameters + 1 signm1/2 Common gaugino mass at MG

m0 Common scalar mass at MG

A0 Trilinear couping at MG

tan <Hu>/<Hd> at the electroweak scale

sign() Sign of Higgs mixing parameter (W(2) = Hu Hd)

i. MHiggs > 114 GeV Mchargino > 104 GeVii. 2.2x104 < Br (b s ) < 4.5x104

iii.

iv. (g2)

Experimental Constraints

12900940 201

.h. ~

Dark Matter Allowed RegionsWe choose mSUGRA model. However, the

results can be generalized.

Neutralino-stau coannihilation region

Focus point region – the lightest neutralino has a larger higgsino component

A-annihilation funnel region – This appears for large values of m1/2

2

1CDM

+…

In the stau neutralino coannihilation region

01~

1~

20Δ

2

/Me

011

~~ MMM Δ

Griest, Seckel ’91

Relic Density Calculation

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

tan= 40, > 0, A0 = 0

011 ~~

GeV 155

011

~

MMM ~~

Can we measure M at colliders?

Coannihilation Region

SUSY Signals at the LHCIn Coannihilation Region of SUSY Parameter Space:

Soft

Soft

p p p

g~

q~

01

~

02

~

~

q

q~q

q

~ 01

~

02

~

p

g~

q~

01

~

02

~

~

1

~

q

q~q

q

~ 01

~

Soft

Hard Hard

Hard

Final state: 3/4 s+jets +missing energyUse hadronically decaying

GeV 155

011

~

MMM ~~

Soft

Trigger on the jets and missing ET

1. Sort τ’s by ET (ET1 > ET

2 > …) and use OS-LS method to extract pairs from the decays

2. Use counting method (NOS-LS) & ditau invariant mass (M) to measure mass difference M (between the lightest stau and the neutralino) and gluino mass

3. Measure the PT of the low energy to estimate the mass difference M

Three Observables

Since we are using 3 variables, we can measure M, Mgluino and the universality relation of the gaugino masses i.e. 1/2χ1/2χ1/2g 0.4m~M0.8m~M ,2.8m~M 0

102

~~~ ,

Mgluino measured from the Meff method may not be accurate for this parameter space since the tau jets may pass as jets in the Meff observable.

The accuracy of measuring these parameters are important for calculating relic density.

SUSY Parameters

high e

nergy

High Energy Proton-Proton collisions produce lots of Squarks and Gluinos which

eventually decay

Identify a special decay chain that can reveal M information

011 ~~ low energy

A Smoking Gun at the LHC?

Version 7.69 (m1/2 = 347.88, m0 = 201.1) Mgluino = 831

Chose di- pairs from neutralino decays with (a) || < 2.5(b) = hadronically-decaying tau

Nu

mb

er o

f C

oun

ts /

1 G

eV

(GeV) visM

ETvis(true) > 20, 20 GeV

ETvis(true) > 40, 20 GeV

ETvis(true) > 40, 40 GeV

GeV) 5.7(

011

02

M

~~~

062pont End

1143

4137

1264

1

01

02

.

.~.~.~

ET > 20 GeV is essential!

Mvis in ISAJET

EVENTS WITH CORRECT FINAL STATE : 2 + 2j + ETmiss

APPLY CUTS TO REDUCE SM BACKGROUND (W+jets, …)

ETmiss > 180 GeV, ET

j1 > 100 GeV, ETj2 > 100 GeV, ET

miss + ETj1 + ET

j2 > 600 GeV

ORDER TAUS BY PT & APPLY CUTS ON TAUS: WE EXPECT A SOFT AND A HARD

PTall > 20 GeV, PT

1 > 40 GeV

LOOK AT PAIRS AND CATEGORIZE THEM AS OPPOSITE SIGN (OS) OR LIKE SIGN (LS)

OS: FILL LOW OS PT HISTOGRAM WITH PT OF SOFTER

FILL HIGH OS PT HISTOGRAM WITH PT OF HARDER

LS: FILL LOW LS PT HISTOGRAM WITH PT OF SOFTER

FILL HIGH LS PT HISTOGRAM WITH PT OF HARDER

LOW OS

HIGH OS

LOW LS

HIGH LS

LOW OS-LS

HIGH OS-LS

02

~EETTmissmiss + 2j + + 2j + 22 Analysis PathAnalysis Path

ETmiss + 2j + 2 Analysis

[1] ISAJET + ATLFAST sample of ETmiss, 2 jets, and at least 2 taus with

pTvis > 40, 20 GeV and = 50%, fake (fj ) = 1%. Optimized cuts :

ETjet1 > 100 GeV; ET

jet2 > 100 GeV; ETmiss > 180 GeV; ET

jet1 + ETjet2 + ET

miss > 600 GeV

[2] Number of SUSY and SM events (10 fb1):Top : 115 eventsW+jets : 44 eventsSUSY : 590 events

top SUSYMgluino = 830 GeVM = 10.6 GeV)

EETTmissmiss + 2j+ 2j ++ 22 AnalysisAnalysis

A small M can be detected in first few years of LHC.

10-20 fb110-20 fb1

+5%

5%

[Assumption] The gluino mass is measured with M/Mgluino = 5% in a separate analysis.

22 : Discovery Luminosity: Discovery Luminosity

Also, get more events

for large M

01

~~

Slope of PT

distribution contains ΔM Information

Slope of PT

distribution is largely unaffected

by Gluino Mass

Low energy ’s are an

enormous challenge for the detectors

PT Distribution of our softest

•Look at the mass of the - in the events

•Can use the same sample to subtract off the non-2 backgrounds Clean peak!

Larger M: More events Larger mass

peak

Clean peak Even for low M

More Observables

10.6)M 830,M for (ResultsG~ • The slope of the PT

distribution of the t’s only depends on the M

• The event rate depends on both the Gluino mass and M

• Can make a simultaneous measurement

An important measurement

without Universality

assumptions!

Results for ~300 events(10 fb-1 depending on the

Analysis)

Measurement of M and Gluino Mass

Peak of M

M

M1

M

M1MM 2

~

2~

2~

2~

~

1

01

02

102

As the neutralino

masses rise the Mtt peak

rises

Peak of M

g~tyUniversali

χ~M M, fromM to M measured Compare

tsmeasuremen ussimultaneo make to sobservable 3 all Use

02χ

~02

}~15 GeV or ~3%

g~χ~M17.0~M

AssumeOnly

01

Universal scenario?

g~χ~M17.0~M

assumes only Analysis

01

Results for ~300 events(10 fb-1 depending on the

Analysis)

GeV) 10.6M GeV, 830Mfor (Results

uslysimultaneo M and M M,

measure toSlope and M Events, Use

G~

χ~g~ 02

g~χ~

g~χ~

M17.0~M and

M32.0~M

assumes Analysis

01

02

} ~15 GeV or ~2%}

~0.5 GeV or ~5%

Assuming Universality

M and Mgluino m0 and m1/2

(for fixed A0 and tan

We determine m0/m0 ~ 1.2% and m1/2/m1/2 ~2 % (for A0=0, tan=40) (at 10 fb-1)

Determination of m0 and m1/2

M and Mgluino (for fixed A0 and tan)

201h~

h2/h2 ~ 7% (10 fb-1)(for A0=0, tan=40)

201h~Determination of Relic

Density

h2/h2 ~ 7% for A0=0, tan=40 (10 fb-1)

Analysis with visible ET > 20 GeV establishes stau-

neutralino coannihilation region

2 analysis: Discovery with 10 fb1 M/M ~ 5% , mg/mg ~ 2% using Mpeak, NOS-LS and pT

The analyses can be done for the other models that don’t suppress 2

0 production.

Meff will establish the existence of SUSY

Different observables are needed to establish

the dark matter allowed regions in SUSY model at the LHC

Universality of gaugino masses can be checked

Conclusion

Backups

ETmiss + 2j + 2 Analysis

[1] ISAJET + ATLFAST sample of ETmiss, 2 jets, and at least 2 taus with

pTvis > 40, 20 GeV and = 50%, fake (fj ) = 1%. Optimized cuts :

ETjet1 > 100 GeV; ET

jet2 > 100 GeV; ETmiss > 180 GeV; ET

jet1 + ETjet2 + ET

miss > 600 GeV

[2] Number of SUSY and SM events (10 fb1):Top : 115 eventsW+jets : 44 eventsSUSY : 590 events

top SUSYMgluino = 830 GeVM = 10.6 GeV)

A small M can be detected in first few years of LHC.

10-20 fb110-20 fb1

2 Analysis : Discovery Luminosity

+5%

5%[Assumption] The gluino mass is measured with M/Mgluino = 5% in a separate analysis.

Negligible fjdependence