Relic Density at the LHC

B. Dutta

In Collaboration With:

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

Phys.Lett.B639:46,2006, hep-ph/0608193 (Phys. Lett.B), To appear

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 less than 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

Dark Matter Allowed Regions

Neutralino-stau coannihilation region

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

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

We choose mSUGRA model. However, the results can be generalized.

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 at LHC

In 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

15 - 5 ~ )~~( 0

11 MFinal state: 3/4 s+jets +missing energy

Signals

2. Use Counting Method (NOS-LS) & Ditau Invariant Mass (M) to measure mass difference

Use Hadronically Decaying and construct 3 observables

1.Sort τ’s by ET (ET1 > ET

2 > …) and use

OS-LS method to extract pairs from the decays

3. Measure the PT of the low energy

Observables

Since we are using 3 variables, we can measure M, Mgluino and the universality relation of the gaugino masses i.e. 1/2χ~1/2χ~1/2g~

0.4m~M,0.8m~M ,2.8m~M 01

02

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

Version 7.69 (m1/2 = 347.88, m0 = 201.06) 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

~~~

0162

141143

441137

116264

1

01

02

.endpont

.~.~.~

ET > 20 GeV is essential!

Mvis in ISAJET

EVENTS WITH CORRECT FINAL STATE : 1 + 3j + ETmiss

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

ETmiss > 100 GeV, ET

j1 > 100 GeV, ETmiss + ET

j1 > 400 GeV

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

PT > 40, 40, 20 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

Extracting Pairs from Decays02

~EETTmissmiss + 1j+ 1j ++ 33 Analysis PathAnalysis Path

ETmiss + 1j + 3 Analysis

Much smaller SM background, but a lower acceptance

[1] ISAJET + PGS sample of ETmiss, 1 jet and at least 3 taus with pT

vis > 40,

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

ETjet1 > 100 GeV, ET

miss > 100 GeV, ETjet1 + ET

miss > 400 GeV

[2] Select OS low di-tau mass pairs, subtract off LS pairs

Note: fj = 0% 1.6 counts/fb1

Small dependence on the uncertainty of fj

3 +1 Jet

Next: combine NOS-LS and M values to measure M and Mgluino simultaneously

Counts drop with Mgluino

Mass rises with Mgluino

M/M ~15% and Mgluino/Mgluino ~6%

3 +1 Jet (contd)

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)

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

PT STUDY

Slope of the soft PT distribution has a M dependence

Phys.Lett. B639 (2006) 46, hep-ph/06031280

1~~

Slope of PT distribution contains ΔM Information.

PTsoft in ISAJET

OS

OS-LS

LS

GeVM

GeVM

g 831

6.10

~

[1] ETmiss , at least 2 jets, at least 2 ’s with PT

vis > 20, 40 GeV

[2] = 50% , fake rate 1%

[3] Cuts: ETjet1 > 100 GeV, ET

jet2 > 100 GeV, ETmiss > 180 GeV

ETjet1 + ET

jet2 + ETmiss > 600 GeV

ETmiss + 2j + 2Analysis: PT

soft

Can we still see the dependence of the PT slope on M using OS-LS Method?

GeV 015

GeV 610

GeV 75

GeV 3260

GeV 831

02

.M

.M

.M

.M

M

~

g~

PT Study

Measuring M from the PT Slope

Luminosity = 40 fb-1

Slope of PT

PT does not depend on the mass or the mass 02

~M

gM ~

How accurately can M be measured for our reference point?

Considering only the statistical uncertainty:

We can measure M to ~ 6% accuracy at 40 fb-1 & ~ 12% accuracy at 10 fb-1 for mass

of 831 GeV.

g~

Slope of PT M

Can parameterize the our observables as functions of M, , &

NOS-LS , to first order, does not depend on mass. A large increase or decrease

in mass is needed to obtain a point that lies outside the error bars Cross-Section is dominated by the gluino mass

02

~02

~

gM ~ 02

~M

Model Parameters

2~

2

~

2

~

2~

~

1

01

02

1

02

11

M

M

M

MMM end

Model Parameters

CONTOURS OF CONSTANT VALUES ( L = 40 fb-1 )

• Intersection of the central contours

provides the measurement of M,

, &

• Auxilary lines determine the 1

region

• 1st order test on Universality

gM ~ 02

~M

Testing Gaugino 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)

Determination of m0 and m1/2

M and Mgluino (for fixed A0 and tan)

Determination of

201h~

h2/h2 ~ 7% (for A0=0, tan=40)

201h~

h2/h2 ~ 7% for A0=0, tan=40

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