from the lhc to a future collider - ucsbcharm.physics.ucsb.edu/people/incandel/incandela... · from...
TRANSCRIPT
Joe Incandela UC Santa Barbara
From the LHC to a Future ColliderCERN Theory InstituteFebruary 26, 2009
1
Acknowledgements
MARMOSET: Nima Arkani-Hamed et al. axXiv:hep-ph/0703088v1
OSET Tools team in CMS (from whom I got most of these slides):
Philip Schuster (SLAC), Natalia Toro (Stanford)
Sue Ann Koay, Roberto Rossin (UCSB)
2
Contents
Loss of information:
What’s left depends on what’s there
Making quick rough sketches:
Applying OSET Tools and metrics
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Hadron Colliders
Access broad range of constituent com energies
Large physics cross-section
Discovery machines …
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Good things come early…and late. Unbroken streak of discovery
opportunities: SPS & Tevatron Discoveries
SPS turn-on led to quick major discoveries
Not quite true at the Tevatron
SPS had a lot of data Already probed quite a bit
higher than the mean constituent com energy of ~100 GeV
Tevatron needed to ~match SPS integrated luminosity in order to probe a “new” energy domain And then discovered top!
Early discoveries have been followed by other important results at hadron colliders –but these have generally come late
Precision W&Z masses
Single topDi-bosonsMt ,MW
CDF & D0
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Discovery Machines Very high rate physics over a
very broad range of energies
The event-by-event cost Initial state parton flavors,
their energies, and polarizations unknown
Transverse energy-momentum conservation only
Triggering Very high rates means select a
very tiny fraction for readout.
Triggering adds significant complications to detector design and performance
Pile-up: A secondary issue for the most part at the LHC
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Hadron Colliders & New Physics Cost is quantifiable at LHC
E.g. for 2 2 processes, a variety of effects conspire to wash out detailed information.
Matrix elements can be replaced by simple parameterizations
Decays can often be well represented by phase space alone (especially early, when statistics are low)
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Introduce dimensionless variables X, xT
Dimensionless “Parton luminosity”
Differential Cross section
*arXiv:hep-ph/0703088v1
» is the z component momentum of com frame system (divided by ½ ECM)
d¾/dxT
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Final state mass asymmetry parameters ,
Where sb = com energy of the beams
Integration limits
Then:
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Next parameterize ME
As the sum of rational polynomials in X and
Then expand ds/dxT & ds/dy in D
Dimensionless Parton luminosities Integrated over com rapidity Homogeneous functions of ECM so
can approximate as:
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No n dependenceThis means that to O(D) there is no dependence of the shape of the transverse differential x-section on the angular variable
n only enters in the normalization
NB: (q+m 1)<0How good is this approximation?
Not only are additional terms suppressed by D, but also by 1/(1+xT
2) factors and Euler-Beta (B(m,n)) factors
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Shape invariance of d¾/dxT
M = 3
Consider |M|2¼Xm or |M|2¼ » n
Xm
» n
Normalized to equal areas
But the transverse distribution is invariant under changes in »dependence of |M|2 !
Shape of transverse distribution depends on Xm
as expected…
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Shape invariance of d¾/dyConsider |M|2¼ » n ,|M|2¼Xm , or |M|2¼Xm» n
Xm
»n
Xm»n
Shape of rapidity distribution invariant under changes in Xdependence of |M|2
and also for simultaneous Xm
and »n variations to good approx.
Dependence on »not surprising.
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Large mass asymmetries?
mc¼ 6 md ¢ = 0.5 see ~5% shift in peak and mean of d¾/dxT
One can model transverse and rapidity distributions independently See that d¾/dxT is well-modeled by leading order in X
to the ~ 5% level Without regard to » dependence.
The rapidity structure is usually fixed by the PDF’s with only a sub-leading correction in » from ME.
Very often |M|2¼Constant is adequate
Upshot The number of parameters accessible to LHC
experiments is substantially smaller than the number contained in a BSM theoryO
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Implications
Depends on what’s there. Some things are simple
21 heavy resonance, decaying to two leptons Spin 0,1,2 could be distinguished
Many new particles, including a DM candidate Full event reconstruction difficult Simple event variables difficult to interpret Spin information could be particularly difficult early
Nevertheless the data does retain much important information about masses and relationships among BSM and SM particles
Are we prepared ? Can we get some idea of the underlying spectrum and rates as data accumulates? For some things it would be useful to have an analysis tool
that takes the limitations of hadron colliders into accountOS
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What’s left?
Full Model16
Full model calculation
spinscouplingsoff-shell states…
*
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On Shell Effective Theory17
Full model calculation Parameterization
spinscouplingsoff-shell states…
branching ratios
All lines on-shell
~ constant
*
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Model to OSET example18
on- and off-shell massesseveral couplingscontrol both kinematics and rates
Production contributions:Associated production same-sign squarks, gauginos
SUSY ModelOSET
“blobs” represent dynamicsthat are parameterized by one rate and possibly an additional shape parameter
Off-shell particles do not appear;effects are present in the rates
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Another SUSY example19
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Another SUSY example20
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Can we really get away with |M|2 = Constant ?
gluino, kk-gluino pairs: Flat OSET versus full MEs21
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Very simpleO
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If the matrix element |M|2 varies smoothly over energy, while parton luminosities fall rapidly at threshold
reproduces well the kinematics of the hadron productionThis is indeed true for the gluino pair-production
In general find |M|2 = Constant is adequate
When/why does constant approximation fail?
The threshold or high-energy scaling of |M|2 is extreme in one limit or the other.
Examples:
Threshold suppression (e.g. p-wave scattering)
|M|2 =A+B(1-1/X)
Contact interactions
|M|2 =A+B(X-1)
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Slightly less simple
Threshold-suppressed and contact interactions24
p-wave dominated
Contact interaction
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Marmoset25
In this framework an OSET is defined by:A spectrum of new particles w/ given massesThe UEM(1) and SUC(3) gauge quantum numbersObservable production and decay modes
In terms of on-shell particlesA parameterized |M|2 for each vertex
MARMOSET is a Pythia based Monte Carlo tool which implementsthe parameterization
Blobs
2 → 1 Resonant production (straightforward)
2 → 2 Pair or associated production (discussed)
2 → 3 Production ( like higgs in VBF and tt)
1 → n Decay (phase space)
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OSETs in CMS26
Results of new physics searchesPhrase/answer structural questions:
Quantum numbersMass hierarchyDecay modes
Case studies, usage examplesGuidelines, cautions, caveats, issues, …Maps for BSM model → OSET
Systematization of:OSET constructionGoodness of “OSET fit”
Framework for a first understanding of BSM signals(complementary to full-model searches)
theorist experimentalistcommunications
More flexible/manageable complexity than full model
Model topologies → signatures, discriminating variablesModel constraints → further analysis directions
Training exercisesData challenges Workshops…
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Monte Carlo “scripting language”27
t
tt
t
duplo
duplo
OSET hypothesis
Quantum numbers / mass
Decay
duplo : charge=0 color=0 mass=
duplo
g g > duplo duplo : matrix 1
t tbar>
800New particle
Production
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=
|M|2 = fi(x)»j
f1=1, f2=(1-1/X), f3=(1-1/X)2
f4=(X-1), f5=(X-1)2
N1 : pdg=1000022 charge=0 color=0 mass=50 #stable
C1 : mass=143 color=0 charge=+3N2 : mass=143 color=0 charge=0N3 : mass=480 color=0 charge=0ER : mass=420 color=0 charge=-3
GL : mass=1400 color=8 charge=0 width=15.UL : mass=1230 color=3 charge=2 width=15.UR : mass=1100 color=3 charge=2 width=1.6
GL > UR ubarUL > C1 dUL > N2 uUR > N3 u
N3 > ER e+ ER > e- N2C1 > W+ N1N2 > Z0 N1
u g > GL UL $ sA
Partial OSET for a cascade in a SUSY model...
Quantum numbers and masses
Decay ch
ann
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Another example of MARMOSET Input28
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Building a hypothesis for a spectrum of particles OSETs allow one to separate masses from rates OSETs are a sum of distinct processes Each process can be treated separately while at the same time
correlations can be included e.g. by constraining BRs to sum to unity
This is extremely useful: Allows one to construct a characterization of new signals in stages
The number of parameters is usually smaller than the number of processes Data can quickly constrain OSETs or
Can take into account specific theoretical guidance Examples: Assume a SM gauge structure for new particles Use particular BSM models to inspire choices of processes
…but not strictly necessary
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Some features
4 Experimentalists Input is a minimal set of parameters
Maps pretty transparently onto standard observables Allows one to focus on particle spectra
Characterizes data in a way that is fairly straightforward to communicate May allow one to make a statement like “the data behaves as if there are
N particles, with masses Mn, related by these m processes or as if there are K particles, with masses Mk…etc.”
4 Theorists ( I speculate…)
Such characterizations might be more useful/transparent than maps of allowed/excluded regions in multidimensional parameter spaces of very detailed models…
Could help to quickly focus on specific parameter choices in existing BSM models
Could help to motivate new models
But this does not at all mean that OSETs can replace full models in MC ! Quite the contrary, OSETs could be seen as a scouting device that can help focus studies with MC of full models.O
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Some Potential Benefits
Education Students (and others…) learn a lot playing with OSETs
CPU Because one generates & then fully simulates somewhat generic
processes for specific masses, these can be used over and over in different combinations, assuming different rates, etc. saving a lot of cpu…
Analysis design Can thus be used to study the efficacy of different selection
variables and analysis techniques on a wide array of processes with a wide variety of relative rates
Theorists can provide OSETs for their favorite models Experimentalists can run them, and return optimum mass/rate
parameters, and possibly some goodness of fit info to the theorists For model building or for calibrating parameter ranges in a model
(e.g. for use in a more detailed full MC study)OS
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Other uses, benefits, spin-offs
The best way to show what OSETs are about is to carry out an exercise of building an OSET characterization of a new signal mixed with SM backgrounds.
I don’t have time in a short talk to do this
Will briefly show an few things from case studies and describe some of the OSET tools we have in CMS.
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The process
Case Study: Jets + MET channel33
HT ≡ ∑ scalar ET of electrons, muons, jets
OSET analysis starts from an observed significant discrepancy with the SM.This particular blind study involved many variables, jet, b jet, lepton multiplicities etc.
QCD
tt+jets
W+jets
Pseudo-data
pseudo-data – SM background
expectations
SIGNAL ≡
GeV
even
ts /
100
GeV
even
ts /
100
GeV
GeV
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34
octet
Neutral(stable)
Charged
3rd gen.
partners
1st, 2nd gen.
partners
SUSY:
―Higgsino‖
800 GeV
600 GeV
200 GeV
OSET DeductionActual Model
g (563 GeV)~
q (805 GeV)~
b, t (650 GeV)~ ~
h (197 GeV)~
W (1 TeV)
b t h ~ 89%~
b h2~
l (irrelevant)~
<0.2%
SU
(2)
< 7.2%
First experience with OSETs 35
What made (quick) model-deduction possible?
Standard Model → BSM constraints (charge conservation, small rate of flavor violation, …)
Minimal addition of new content (a negotiable assumption)
Factorization into subsets of salient signatures
Hypothesized topologies new signatures and searches
Number of parameters (masses, branching ratios, …) << full model
+ O(many)
Monte Carlo “scripting” :EffortlessWait-less
to simulate hypotheses
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OSETTools
36
OSET ProcessS
tra
tegy
Masses=200,600,…
- Determine if a given
process is important
- Indicate regions that
require contributions
from other processes
Upper-bound:
Pa
ram
ete
r D
ete
rmin
atio
n
Pa
ram
ete
r D
ete
rmin
atio
nS
tra
tegy
- Determine if a given
process is important
- Indicate regions that
require contributions
from other processes
Upper-bound:
Upper-bound ≡
maximum number of
OSET events such
that χ2 ~ 3σ (summed
over bins where
signal > OSET)
SM-subtracted data
OSET template
OSET Process
40
Upper-bound:
- Determine if a given
process is important
- Indicate regions that
require contributions
from other processes
The upper-bound is usually computed
simultaneously over multiple distributions
HT
signal
800 GeV duplo
ET / HT
41
Upper-bound:
HT
- Determine if a given
process is important
- Indicate regions that
require contributions
from other processes
signal
800 GeV duplo
ET / HT
400 GeV duplo
Of course the processes
may fit much better with
different masses
OSET Rates
+
+
Pa
ram
ete
r D
ete
rmin
atio
nS
tra
tegy
Masses=200,600,…
- Determine if a given
process is important
- Indicate regions that
require contributions
from other processes
Upper-bound:
Upper-bound ≡
maximum number of
OSET events such
that χ2 ~ 3σ (summed
over bins where
signal > OSET)
SM-subtracted data
OSET template
OSET Process
- Extract best-fit model
parameters for a
given set of mass
hypotheses
Fit to signal:
OSET RatesP
ara
mete
r D
ete
rmin
atio
nS
tra
tegy
- Determine if a given
process is important
- Indicate regions that
require contributions
from other processes
Upper-bound:
Upper-bound ≡
maximum number of
OSET events such
that χ2 ~ 3σ (summed
over bins where
signal > OSET)
SM-subtracted data
OSET template
OSET Process
σ(gu→gq)~~
σ(uu→
gg)
BR(q→qg)~~
~~
Minimize discrepancy
between signal and OSET
model histograms, to find
best-fit OSET rate
parameters (cross-
sections, branching ratios)
- Extract best-fit rate
parameters for a
given set of mass
hypotheses
Fit to signal:
OSET RatesP
ara
mete
r D
ete
rmin
atio
nS
tra
tegy
- Determine if a given
process is important
- Indicate regions that
require contributions
from other processes
Upper-bound:
Upper-bound ≡
maximum number of
OSET events such
that χ2 ~ 3σ (summed
over bins where
signal > OSET)
SM-subtracted data
OSET template
OSET Process
σ(gu→gq)~~
σ(uu→
gg)
BR(q→qg)~~
~~
Minimize discrepancy
between signal and OSET
model histograms, to find
best-fit OSET rate
parameters (cross-
sections, branching ratios)
OSET Model
+
+
Mass of particle 1
Ma
ss o
f p
art
icle
2
+
++
+
+
+
χ2 = 5.6
χ2 = 2.3
χ2 = 3.8
χ2 = 1.4
- Extract best-fit rate
parameters for a
given set of mass
hypotheses
Fit to signal:
- Compare mass hypotheses
to locate most likely
spectrum
Goodness-of-fit:
OSET RatesP
ara
mete
r D
ete
rmin
atio
nS
tra
tegy
- Determine if a given
process is important
- Indicate regions that
require contributions
from other processes
- Extract best-fit rate
parameters for a
given set of mass
hypotheses
Upper-bound: Fit to signal:
Upper-bound ≡
maximum number of
OSET events such
that χ2 ~ 3σ (summed
over bins where
signal > OSET)
SM-subtracted data
OSET template
OSET Process
σ(gu→gq)~~
σ(uu→
gg)
BR(q→qg)~~
~~
Minimize discrepancy
between signal and OSET
model histograms, to find
best-fit OSET rate
parameters (cross-
sections, branching ratios)
OSET Model
- Compare mass hypotheses
to locate most likely
spectrum
Goodness-of-fit:
Fit paraboloid shape
function (expansion
around minimum) to
locate best-fit masses
Each mass-grid point is
the minimum χ2/NDOF
of rate-parameter fits
Ra
nkin
g O
SE
T M
od
els
OSET A > OSET B iff χ2min(A) < χ2
min(B)
OSET X iff χ2min(X) > 5σ
OSET A ~ OSET B iff χ2min(A) - χ2
min(B) < δ
• Statistical fluctuations should not spuriously
rank one model ahead of another
• Models should not be artificially favored
because they have more free parameters
that can be dialed to reduce χ2 (or χ2/NDOF)
Pseudo-
experiment
spread with
OSET A used
to generate
pseudo-signal
δ : such that ∫>δ ~ 10%
χ2min(A) – χ2
min(B)0
No
distinction
between A
and B
BSM Physics
+
+
Mass of particle 1
Mass o
f part
icle
2 +
+
OSET A
OSET B
OSET C
+
+
“A > C > B > …”
Naïvely / Intuitively :
WORK IN PROGRESS
BSM Billboard
BSM Billboard
Fin
Additional Information
Leaving spin out of the first pass:
Minimal impact on physics modeling; topology much more important.
Even so, systematics of this approximation can & should be determined in practice, along with other effects
Primary particle production spin can effect ME. This is modeled by an OSET
Spin correlation in decay chains (hard to see at low statistics when topology uncertain) can be included in an extension
Spin51
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- Extract best-fit model
parameters for a
given set of mass
hypotheses
Fit to signal:
+1σ
-1σ
When we have the set of
most significant processes,
we can fit for their fractions
the usual way (minimizing
distance between signal and
summed templates).
g2
g2A
g1A
signal
Fitted
fractions
(stacked)
Lead untagged ET
Lead tagged ET
Lead untagged ET
HT×
53
- Extract best-fit model
parameters for a
given set of mass
hypotheses
Fit to signal: The contours of the Minuit2 fit
are used as error bars. But pay
attention to the contour plots
for they contain more
information about flat
directions (similar processes).
dis
tance (
arb
itra
ry u
nits)
g1A
Landscape of distance used in the fraction fit — 2D slices for each pair of OSETs
g1Ag2A
g2
g2
g2A
54
- Compare mass hypotheses to
locate most likely spectrum
Goodness-of-fit:
For a specific set of
mass hypotheses
(at this point of the
mass grid): record
how well we can fit
the three processes
to explain signal.
Goodness-o
f-fit
For each particular model:
The goodness-of-fit (for the various processes)
as we vary the mass parameters can be used
to locate the most probable mass spectrum.
Mass 1
Mass 2
Contours of
parabolic fit
interpolating
between points
in (possibly
coarse) grid
Refine grid after
roughly locating
minimum
55
BUT…
How do we know what region falls within
the parabolic approximation?
Are we assured of there being exactly one
minimum?
- Compare mass hypotheses to
locate most likely spectrum
Goodness-of-fit:
―Salame‖ fit
The (mostly) green mesh are the 1-
D slice fits to the shape function:
a + b x + c x2
e.g. Particular cell in a 3-mass parameter space
If a slice is convex (c < 0), it
likely does not belong to an
N-D minimum — an
expansion around a minimum
must have positive 2nd order
derivatives.
Omit these points from N-D fit
56
BUT…
How do we know what region falls within
the parabolic approximation?
Are we assured of there being exactly one
minimum?
- Compare mass hypotheses to
locate most likely spectrum
Goodness-of-fit:
―Salame‖ fitThe 1-D minima form N ―planes‖ that
are close to the principal axes of the N-
D parabola around the global minimum. The intersection of all these
planes are a none-too-shabby
estimator for the global minimum.
57
BUT…
How do we know what region falls within
the parabolic approximation?
Are we assured of there being exactly one
minimum?
- Compare mass hypotheses to
locate most likely spectrum
Goodness-of-fit:
―Salame‖ fit
If a slice is convex (c < 0), it
likely does not belong to an
N-D minimum — an
expansion around a minimum
must have positive 2nd order
derivatives.
Omit these points from N-D fit
For a better estimator, we can also use the
1-D fits to more correctly seed the N-D fit.
58
BUT…
How do we know what region falls within
the parabolic approximation?
Are we assured of there being exactly one
minimum?
- Compare mass hypotheses to
locate most likely spectrum
Goodness-of-fit:
―Salame‖ fit
The N-D fit (gray
surface) successfully
ignores points that can’t
reasonably lie within the
region where the
parabolic expansion is
valid (empty circles)
59
Qu
ality - Correlated variables
Suppose a naïve graduate student performs a 10-histogram fit with:
ET + HT + HT + HT + HT + HT + HT + HT + HT + HT
Unfairly weighted, wrong degrees-of-freedom count
… but it can happen to you too:
Principal components analysis:
Diagonalize to a de-correlated basis
Remove redundant variables- Non-discriminating
variables (―garbage‖)
HT
leading jet ET
ET+HT
corr
ela
tion c
oeffic
ient
1
0
leading b-jet ET
60
- Correlated variables
- Non-discriminating
variables (―garbage‖)
OSET 1
OSET 2
OSET 3
Fractions reported by fitter
Number of non-
discriminating plots
Inclusion of non-discriminating
plots (i.e. where all hypotheses
have the same shape) tends to
wash out the information in
such a way that the fractions
are biased towards equal
numbers — unless we have
perfect (∞ statistics) templates.
Metric for sorting plots according to
discriminating power — examining the
trend as we increase template statistics
provides even more information.
Qu
ality
Introduction to OSETs (I)What is an OSET?
Easiest to explain starting from a full model, e.g. for SUSY
Production: replace 2→2 matrix element with constant
(variation permits study of systematic effects from modeling)
Decay: replace 1→2 matrix element with constant; same for 1→3 if intermediate state is off-shell
The approximation is useful because it eliminates dependence on parameters that are poorly constrained by data (at least early on)
It is valid because kinematics is mostly controlled by phase space.
61O
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Introduction to OSETs (II)
A set of particles, with quantum numbers and masses, and corresponding decay chains; the production cross-sections and branching ratios
What defines an OSET?
Marmoset – a simple Pythia-based generator for any OSET – is interfaced in CMSSW. You specify production and decay modes, it generates and organizes events so that cross-section/branching ratio (re-)weighting can be done.
In principle, can extend to more powerful generators (MadGraph & Alpgen implementations in progress...)
How do I simulate an OSET?
(+ next-order improvements for extreme kinematics & study of systematics)
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Correlations among final states
OSETs have predictive power!Consistently weighting according to branching ratios is important to get the physics right
Parameterize with branching ratios (very important!)63
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W & Z Masses and production rates were predicted
Signals stood out “like being hit on the head with a hammer”
Interpretation was unambiguous
Top Signal was a bit harder to dig out (initially a counting experiment)
and less straightforward to interpret but…
We knew it had to be “somewhere”
Production and decay properties were predicted
Higgs Like top – for a given mass, we know its production and decay
properties in the SM and alternative BSMs. For some masses, counting experiments may be the first sign.
Or maybe like W & Z –the signal could appear as a striking mass peak
New Physics (NP) Don’t know what to expect. Theory provides examples, some are
compelling, none are guaranteed ...
Past versus future discoveries*R
ecen
t P
ast
Fu
ture
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*M.L.M. http://arxiv.org/abs/0802.0026v2
Thresholds & Shape Invariance
➔Simple, universal corrections to constant ME!
Caveats:Correct PDFs necessaryLarge final state mass asymmetry requires careTransverse momentum-rapidity correlations not included
Homogeneity of PDF inand
See: hep-ph/0703088 for detail...
(one piece dominatesnear threshold)
Angular variable:
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QGL
SL
MPT/Ch
N2*
NL*
heavier LH squark hard to constrain; trade-off between squark fraction and W fraction(important mode to search for and study)
don’t know where W’s come from (but we have evidence that there are some with b’s)More study needed to confirm this hypothesis...
...
The underlying model
Some evidence for tops: b-modes, and evidence for W’s. See comments below.Attempt at top reconstruction for these topologies a good next step...
Need to study tau structure.Well-motivated sub-dominant modes (like prompt decays of triplet) need to be studied further...
Already, the structure is emerging
* New neutral particles (see prev. slide) motivated by observed decay products
“2-Day” OSET (~100 pb-1)66
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