from the lhc to a future collider - ucsbcharm.physics.ucsb.edu/people/incandel/incandela... · from...

Joe Incandela UC Santa Barbara

From the LHC to a Future ColliderCERN Theory InstituteFebruary 26, 2009

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)

Contents

Loss of information:

What’s left depends on what’s there

Making quick rough sketches:

Applying OSET Tools and metrics

Hadron Colliders

Access broad range of constituent com energies

Large physics cross-section

Discovery machines …

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

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

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)

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

Final state mass asymmetry parameters ,

Where sb = com energy of the beams

Integration limits

ApproximateO

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:

…and solveO

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

Shape invariance of d¾/dxT

Consider |M|2¼Xm or |M|2¼ » 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…

Shape invariance of d¾/dyConsider |M|2¼ » n ,|M|2¼Xm , or |M|2¼Xm» 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.

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

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

What’s left?

Full Model16

Full model calculation

spinscouplingsoff-shell states…

On Shell Effective Theory17

Full model calculation Parameterization

spinscouplingsoff-shell states…

branching ratios

All lines on-shell

~ constant

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

Another SUSY example19

Another SUSY example20

Can we really get away with |M|2 = Constant ?

gluino, kk-gluino pairs: Flat OSET versus full MEs21

Very simpleO

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)

Slightly less simple

Threshold-suppressed and contact interactions24

p-wave dominated

Contact interaction

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

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)

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…

Monte Carlo “scripting language”27

OSET hypothesis

Quantum numbers / mass

duplo : charge=0 color=0 mass=

g g > duplo duplo : matrix 1

t tbar>

800New particle

Production

|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

Another example of MARMOSET Input28

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

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

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

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.

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.

tt+jets

W+jets

Pseudo-data

pseudo-data – SM background

expectations

SIGNAL ≡

Neutral(stable)

Charged

3rd gen.

partners

1st, 2nd gen.

partners

―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%~

l (irrelevant)~

< 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

OSETTools

OSET ProcessS

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

Upper-bound:

The upper-bound is usually computed

simultaneously over multiple distributions

signal

800 GeV duplo

ET / HT

Upper-bound:

signal

800 GeV duplo

ET / HT

400 GeV duplo

Of course the processes

may fit much better with

different masses

OSET Rates

Masses=200,600,…

Upper-bound:

Upper-bound ≡

maximum number of

OSET events such

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

Upper-bound:

Upper-bound ≡

maximum number of

OSET events such

over bins where

signal > OSET)

SM-subtracted data

OSET template

OSET Process

σ(gu→gq)~~

σ(uu→

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

Upper-bound:

Upper-bound ≡

maximum number of

OSET events such

over bins where

signal > OSET)

SM-subtracted data

OSET template

OSET Process

σ(gu→gq)~~

σ(uu→

BR(q→qg)~~

best-fit OSET rate

parameters (cross-

OSET Model

Mass of particle 1

χ2 = 5.6

χ2 = 2.3

χ2 = 3.8

χ2 = 1.4

parameters for a

given set of mass

hypotheses

Fit to signal:

- Compare mass hypotheses

to locate most likely

spectrum

Goodness-of-fit:

OSET RatesP

parameters for a

given set of mass

hypotheses

Upper-bound: Fit to signal:

Upper-bound ≡

maximum number of

OSET events such

over bins where

signal > OSET)

SM-subtracted data

OSET template

OSET Process

σ(gu→gq)~~

σ(uu→

BR(q→qg)~~

best-fit OSET rate

parameters (cross-

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

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

distinction

between A

BSM Physics

Mass of particle 1

Mass o

f part

OSET A

OSET B

OSET C

“A > C > B > …”

Naïvely / Intuitively :

WORK IN PROGRESS

BSM Billboard

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

parameters for a

given set of mass

hypotheses

Fit to signal:

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).

signal

Fitted

fractions

(stacked)

Lead untagged ET

Lead tagged ET

Lead untagged ET

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).

tance (

Landscape of distance used in the fraction fit — 2D slices for each pair of OSETs

g1Ag2A

- 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

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

BUT…

How do we know what region falls within

the parabolic approximation?

Are we assured of there being exactly one

minimum?

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

BUT…

minimum?

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.

BUT…

minimum?

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.

BUT…

minimum?

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)

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‖)

leading jet ET

tion c

oeffic

leading b-jet ET

- 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.

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.

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)

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

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

*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:

MPT/Ch

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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