Unlocking the Structure of New Physics at the LHC Natalia Toro - - PowerPoint PPT Presentation
Unlocking the Structure of New Physics at the LHC Natalia Toro hep-ph/0703088: Arkani-Hamed et al 0810.3921: Alwall, Schuster, NT work in progress: UCSB CMS group (special thanks: S.A. Koay) Hadron Collider 101 A x 1 , x
Natalia Toro
hep-ph/0703088: Arkani-Hamed et al 0810.3921: Alwall, Schuster, NT work in progress: UCSB CMS group (special thanks: S.A. Koay)
x1E1 x2E2 A B
x1, x2: fraction of beam energy carried by each parton
dσinc dVars = dx1 x1 dx2 x2 x1fg(x1, Q)x2fq(x2, Q)dˆ σ(qg → AB) dVars
x1E1 x2E2 A B
x1, x2: fraction of beam energy carried by each parton
dσinc dVars = dx1 x1 dx2 x2 x1fg(x1, Q)x2fq(x2, Q)dˆ σ(qg → AB) dVars
CM-frame boost ⇒multi-particle Lorentz invariants and pT’s
cm
CM boost
= dˆ s ˆ s d¯ y
uu gg u¯ u/ug
¯ y (CM boost)
arbit. scale
gg u¯ u/ug uu
¯ y (CM boost)
arbit. scale
(300 GeV)
(1 TeV)
To construct invariants, must pair/group particles. To pair, must know decay topology. Not known a priori. What can be learned from simpler pT’s? (and lower statistics) Edge/endpoint:
˜ q χ0
2
χ0
1
˜ ℓ q ℓ ℓ
Full reconstruction and mT2: Many more variables: – precision mass measurement at hadron colliders! ...100 fb-1
& counts are search variables → understood early. They suffice to build good hypotheses for mass spectra, cascades, then isolate decay modes for precision mass measurement.
Useful combinations:
HT = |pT |, ET = pT
1) HT bump ~ 1–2 x produced particle mass: 2) Locations of pT bumps ~ relative mass scales
(depends on decay chain, LSP mass)
pT , HT , ET
Lepton pT Leading jet pT
+lepton +jet
HT for Models with M=650–700 GeV (after cuts) HT (GeV)
relevant observables and address (subset of) theoretical questions.
(results from UCSB CMS group)
dσinc dVars = dx1 x1 dx2 x2 x1fg(x1, Q)x2fq(x2, Q)dˆ σ(qg → AB) dVars
parton cross-section
→parton luminosity
Simple and instructive to calculate pT distribution for 2→2 product with general matrix element:
parton E2
cm
CM boost
= dˆ s ˆ s d¯ y
s0 = 2M 2
( : threshold s)
y
s2 dσ dˆ tdˆ s = 1 ˆ s s2 ˆ s2 ρ(ˆ s, Q2)
s2 dˆ σ dˆ t
ρ(ˆ s, Q2) ∝ (ˆ s/Stot)−q
u¯ u ug uu gg
τ = ˆ s/Stot ρ(ˆ s/Stot, Q2)
Q2 = (500 GeV)2
(1 TeV)
(300 GeV)
∼ (1 − x)px−q
1 8π |M(ˆ s, ˆ t)|2
ˆ t = −1 2 [ˆ s(1 − ξ) − s0]
CM-frame Lorentz invariants: or or
ˆ s & ˆ t ˆ s & p2
T
related by:
“pure angular” variable linearly related to
→ good variable for M.E. expansion
ˆ s & ξ ξ ∼ β cos θCM : p2
T =
ˆ tˆ u − M 4 ˆ s
1 ˆ s
⇒ dp2
T dˆ
s = ξdˆ tdˆ s
s2 dσ dˆ tdˆ s = s2 s2 ρ(ˆ s, Q2)|M|2
ρ(ˆ s, s0) ≈ A(ˆ s/Stot)−q
ˆ t = −1 2 [ˆ s(1 − ξ) − s0]
CM-frame Lorentz invariants: or or
ˆ s & ˆ t ˆ s & p2
T
related by:
“pure angular” variable linearly related to
→ good variable for M.E. expansion
ˆ s & ξ ξ ∼ β cos θCM : p2
T =
ˆ tˆ u − M 4 ˆ s
s2 dσ dp2
T
= 1 ξ
s 1 ξ dˆ s ˆ s
⇒ dp2
T dˆ
s = ξdˆ tdˆ s
s0 + 4p2
T
s0 + 4p2
T
Stot Stot
s2 dσ dˆ tdˆ s = s2 s2 ρ(ˆ s, Q2)|M|2
ρ(ˆ s, s0) ≈ A(ˆ s/Stot)−q
ˆ t = −1 2 [ˆ s(1 − ξ) − s0]
CM-frame Lorentz invariants: or or
ˆ s & ˆ t ˆ s & p2
T
related by:
“pure angular” variable linearly related to
→ good variable for M.E. expansion
Expand near threshold
(usually dominated by low m, n)
ˆ s & ξ ξ ∼ β cos θCM : p2
T =
ˆ tˆ u − M 4 ˆ s
s2 dσ dp2
T
= 1 ξ
s 1 ξ dˆ s ˆ s
|M|2 =
s/s0)mξn
⇒ dp2
T dˆ
s = ξdˆ tdˆ s
s0 + 4p2
T
s0 + 4p2
T
Stot Stot
s2 dσ dˆ tdˆ s = s2 s2 ρ(ˆ s, Q2)|M|2
ρ(ˆ s, s0) ≈ A(ˆ s/Stot)−q
s0 + 4p2
T
Stot
s2 dσ dp2
T
= s0 Stot −q
m,n
Cm,n dˆ s ξˆ s(ˆ s/s0)m−q−2ξn
ˆ t = −1 2 [ˆ s(1 − ξ) − s0]
CM-frame Lorentz invariants: or or
ˆ s & ˆ t ˆ s & p2
T
related by:
“pure angular” variable linearly related to
→ good variable for M.E. expansion
Expand near threshold
(usually dominated by low m, n)
ˆ s & ξ ξ ∼ β cos θCM : p2
T =
ˆ tˆ u − M 4 ˆ s
s2 dσ dp2
T
= 1 ξ
s 1 ξ dˆ s ˆ s
|M|2 =
s/s0)mξn
⇒ dp2
T dˆ
s = ξdˆ tdˆ s
s0 + 4p2
T
s0 + 4p2
T
Stot Stot
s2 dσ dˆ tdˆ s = s2 s2 ρ(ˆ s, Q2)|M|2
ρ(ˆ s, s0) ≈ A(ˆ s/Stot)−q
s0 + 4p2
T
Stot
s2 dσ dp2
T
= s0 Stot −q
m,n
Cm,n dˆ s ξˆ s(ˆ s/s0)m−q−2ξn
ˆ s/s0 = 1 + 4p2
T /s0
1 − ξ2
≈ 1
= s0 Stot −q
m,n
Cm,n
1 − ξ2 (1 − ξ2)−m+q+2ξn × (1 + 4p2
T /s0)m−q−2
ˆ t = −1 2 [ˆ s(1 − ξ) − s0]
CM-frame Lorentz invariants: or or
ˆ s & ˆ t ˆ s & p2
T
related by:
“pure angular” variable linearly related to
→ good variable for M.E. expansion
Expand near threshold
(usually dominated by low m, n)
ˆ s & ξ ξ ∼ β cos θCM : p2
T =
ˆ tˆ u − M 4 ˆ s
s2 dσ dp2
T
= 1 ξ
s 1 ξ dˆ s ˆ s
|M|2 =
s/s0)mξn
⇒ dp2
T dˆ
s = ξdˆ tdˆ s
s0 + 4p2
T
s0 + 4p2
T
Stot Stot
s2 dσ dˆ tdˆ s = s2 s2 ρ(ˆ s, Q2)|M|2
ρ(ˆ s, s0) ≈ A(ˆ s/Stot)−q
s0 + 4p2
T
Stot
s2 dσ dp2
T
= s0 Stot −q
m,n
Cm,n dˆ s ξˆ s(ˆ s/s0)m−q−2ξn shape independent of n
ˆ s/s0 = 1 + 4p2
T /s0
1 − ξ2
≈ 1
= s0 Stot −q
m,n
Cm,n
1 − ξ2 (1 − ξ2)−m+q+2ξn × (1 + 4p2
T /s0)m−q−2
“Shape invariance” Arkani-Hamed et al, hep-ph/0703....
pT variables are useful because they are simple, single-particle Lorentz invariants and insensitive to production matrix element!
– simple analysis can’t distinguish
convolved with y distribution have similar shape
|M|2 ∼ (ˆ s/s0)mξn, ρ(ˆ s) ∼ ˆ s−q
for
dσ dp2
T
∼ (1 + p2
T /M 2)m−q−2
Typical pT~0.5 M
–
can be stripped out & still do meaningful analysis
any description of positive signal at LHC
detector response w/o full knowledge of model Lagrangian
reach compared to no. of parameters
know intermediate spins.
Specialize to models like SUSY – pair production, no fully-reconstructed decays
First three: On-Shell Effective
Theory – hep-ph/0703088
Much less detail than full Lagrangian – but even at this level data can be ambiguous...
Mass
χ0
1
χ0
2
+2j +2j +jet
˜ g ˜ qL,R σ˜
q˜ q, σ˜ q˜ g ≪ σ˜ g˜ g
χ0
1
χ0
2
+2j +2j +jet
˜ g ˜ qL,R m˜
q − m˜ g ≫ m˜ g
⇓
can ignore squarks
m˜
q − m˜ g ≪ m˜ g
⇓
can ignore squarks
jet from squark decay very soft
Extreme spectra well described by fewer particles –> can’t resolve squark mass in these cases
q q
G
G
q q q q q
/Z(∗)
G G
G G G q
ℓ ℓ
G
q q q
Q Q
Q Q Q
ℓ ℓ
Q
q
Two decay modes populate 0, 2, 4 leptons, flavor correlation Just 2 flavor-uncorrelated leptons distinguishable
q q q q q
G G
G G G q ℓ ℓ q G q
*
ℓ or ν ν or ℓ
q q q
Q Q
Q Q Q q ν ℓ ℓ ℓ Q
q q q q q
G G
G G G q ℓ ℓ q G q
*
ℓ or ν ν or ℓ T T
ℓ ν
Many handles: frequency of n-lepton events, flavor & sign correlations.
but....
Counts: Kinematic distributions:
Points: Model with very complicated cascades:
ℓ/ν 500 GeV 380 GeV 140 GeV 115 GeV ˜ ℓ/˜ ν ˜ W 0,± ˜ h
W (Z) ℓ/ν ℓ/ν
Red/Green: One-stage fit
(2ℓ, W, Z, prompt)
assume SUSY!):
(Excellent approximation: info. erased by PDF integration)
(Overlapping processes)
range of SUSY (etc.) models well (in pT’s, some m’s)
broadly applicable, and transparent*
complex production/decay modes
From gluon partner:
q q q q q
W/Z(∗)
G G
G G G
σG
q
*
ℓ ℓ q G q
*
ℓ or ν ν or ℓ
BW /BZ BLSP Bℓℓ Bℓν
MI (ML) MLSP MG
Masses
From quark partner:
q q q
*
Q Q
Q Q Q
W/Z(∗)
q
*
ℓ or ν ν or ℓ ℓ ℓ
BW /BZ BLSP Bℓℓ Bℓν σQ
Q
Masses
MI (ML) MLSP MQ
*on or off-shell
[Alwall, Schuster, Toro 0810.3921]
From quark partner: From gluon partner:
t t G G
q q
G
b b
G G
Bbb Btt Bqq σG
MLSP MG
Masses
q
b
T
σQ σB σT
T T
Q Q
Q
B B
B
MLSP
Masses
MQ/T/B
Different structures / different patterns of b-tag multiplicity [Alwall, Schuster, Toro 0810.3921]
1) Which colored particles dominate production? 2) What color-singlet decay channels are present, and in what fractions? Models with one produced species, one-stage cascade decay (produced species either G or Q). 3) How b-rich are the events? G: Produce gluon partners that decay to qq, bb, or tt +LSP Q: Pair-produce parters of q12, b, and t
Quark partner Q Gluon partner G
_ _
_
Either
[Alwall, Schuster, Toro 0810.3921]
Leptonic Heavy flavor
Good agreement in many, not all distributions & well-defined best-fit parameters – Discrepancies hint at (specific!) additional structure, but extensions can’t be fully constrained
underway)
LM* – “first, do no harm”
Design searches around individual topologies, with more softer
(work in progress by UCSB CMS group)
24
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(after hadronic search cuts: lepton veto, 3 or more jets)
–S.A. Koay
Fit gg, ug, and uu production fractions (and masses, by eye) from HT, jet pT
~~ ~~ ~~
“Do no harm” : search
discover LM1 as well as an LM1-optimized search (generator-level comparison)
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Extreme case: LM0 (significant stop production and cascade decays)
–S.A. Koay
20
MET/HT very sensitive to cascade shape, most discrepant
Affects efficiency of search cuts, but minor impact on distributions after cuts
Design cuts for sensitivity to processes with more/ fewer jets, wide range of spectra.
“Three hard jets” “~5 hadronic jets”
(Effect of cascade depends on C+ mass)
Even more/softer jets
(not visible – ignore for now)
Fixed cuts: lepton veto, 3 jets Optimize Jet pT, HT, MET cuts for sensitivity to A/B
topologies over wide mass range
Leptonic search effort underway...
Search Generally Present Generally
Sensitivity (and eventually exclusion) can be quoted in terms
section, mg, mu, and mC+, mLSP Models with similar topologies don’t require separate searches. If topology is dissimilar, motivation to search for it is clear. Ensure sensitivity to multiple topologies
~ ~ ~
Applying deltaPhi cuts to every jet makes search insensitive to longer cascades – dangerous if they dominate!
And for wide range of mass splittings!
Crude “Simplified Models” from earlier are general starting point for analysis. Example:
– what do they tell us? – how do we move beyond them? – what do we learn from simplified model fits “inside,” but not
OSOF (e+µ-) OSSF (e+e-) ZCand SSOF (e+µ+) SSSF (e+e+)
5 params and 3 independent counts in 2-lepton data (under-constrained) Additional constraint from 0-, 1
AMBIGUITY: W goes to 1 lepton (30%)
Hard to distinguish W’s from combination of direct and one-lepton cascade
Parameters that fit counts, HT, pT(lepton):
ambiguity – affects conclusions! big syst. effect on masses, xsec some branching ratios more stable than others
Theorist on the outside can estimate these from 1,2-lepton data... but given large systematics, we’re likely to make mistakes combining channels reliably
Counts, jet kinematics reproduced well!
(also jet pT plots, MET...)
(2-lepton plots) (1-lepton plots)
Cannot reproduce the data with these models (or with tops). Robustly demonstrating this is hard, but provides STRONG EVIDENCE for more complex source of soft, flavor-uncorrelated leptons.
Lepton pT OSSF (e+e-) invariant mass Opposite-flavor (eµ) invariant mass
Q/G weak LSP
+leptons/W/Z +jets
Q/G weak LSP weak’
(only believable if studied by experimentalists)
error) ...on-shell slepton and charginos.
See if this can be confirmed from kinematics – dilepton invariant mass should have an EDGE (this is sub-dominant source
jump out but this motivates looking harder)
Q/G weak LSP slepton Q/G weak LSP slepton
? I can find SUSY models with both hierarchies, see if any of them are consistent with larger set of distributions in data...
flavor works well. Not flavor-universal!
G weak LSP slepton
+ light flavor + heavy flavor (G decay could have intermediate on-shell Q’s)
flavor works well. Not flavor-universal!
G weak LSP slepton
+ light flavor + heavy flavor (G decay could have intermediate on-shell Q’s)
three SUSY ideas
gluino weak LSP slepton stop squarks
top dominates because stop is lighter
gluino weak H LSP slepton stop & squarks
top dominates because it has biggest coupling
~ gluino weak H LSP slepton
top dominates because stop is lighter
~ stop squarks
Hadron colliders swallow a lot of information! Sharpen the question: “What can be probed?” Two natural classes of simplification: – insensitivity to production matrix element – smearing-together of decay chains Used at CMS to generalize some SUSY searches Basis for observable properties of new physics will assist in making sense of a discovery