precision cosmology at the lhc
DESCRIPTION
Precision Cosmology at the LHC. Bhaskar Dutta Texas A&M University. Cosmo 2008, Madison, Wisconsin. 25 th August ’ 08. Discovery Time…. We are about to enter into an era of major discovery. Dark Matter: we need new particles to explain the content of the universe. - PowerPoint PPT PresentationTRANSCRIPT
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
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