w helicity analysis: matrix element method sensitivity and optimization using 0-tag events jorge a....

W Helicity Analysis:Matrix Element Method

Sensitivity and optimization using 0-tag events

Jorge A. Pérez Hernández

UAEM, MéxicoIPM Summer Intern @ FNAL

Supervisor: Ricardo Eusebi

J. A. Perez Hernandez, IPM Summer Intern FNAL

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W Helicity Measurement

Objective: To measure the W boson longitudinal fraction f0.

Technique: Matrix Element (ME).

SM Prediction: Right handed fraction f+ ~0%

Longitudinal Fraction f0 ~70%

Left Handed Fraction f- ~30%.

J. A. Perez Hernandez, IPM Summer Intern FNAL

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ME Method: Likelihood, Part I

))1(),((),,( ,0,1

0 ibackgroundsbkgisignals

Nevents

is PCAffPCffCL

•The Likelihood function:

),()()(),;(),(

1),;( 21210

00, yxWqfqfdqdqffyd

ffffxP n

obsisignal

W(x,y) is the probability that a parton level set of variables y will be

measured as a set of variables x (parton level corrections)

dn is the differential cross section: LO Matrix element

f(q) is the probability distribution than a parton will have a

momentum q

•The matrix element (for each event):

J. A. Perez Hernandez, IPM Summer Intern FNAL

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ME Method: Likelihood, Part II

•Current Analysis: (Lepton + Jets Channel)

•Top quark decay: tt → W+ b W- b → qqbllb

•Select MC sample with a known value for f0. (“f0 true”)

•Set f+ = 0.

•Calculate Psignal,i(f0) and Pbackground,i=const, for f0 [0,1].

•Cs calculation: maximize likelihood for “f0 true”.

•Find the maximum for the final likelihood. The result is the measured value of f0. (“f0 fit”)

))1(),((),,( ,0,1

0 ibackgroundsbkgisignals

Nevents

is PCAffPCffCL

J. A. Perez Hernandez, IPM Summer Intern FNAL

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ME Method: Linearity•Linearity Plot:

•Repeat previous procedure for several “f0 true” values.

•Plot “f0 fit” vs “f0 true”. Example:

•Fit straight line. Obtain intercept (p0), and slope (p1).

f0 True

f 0 F

it

NOTE:

We use signal and background fractions expected for 1.7fb-1 data.

1

0,0,0 p

pff fittrue

1

,0,0 p

ff fittrue

slopep

interceptp

1

0

J. A. Perez Hernandez, IPM Summer Intern FNAL

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ME Method: PSE’s, Part I Run PSE’s.

With number of events as seen in data Using expected fractions of signal and

background.

From each PSE we get f0 fit, f0 and pull.

Correct each PSE outcome by linearity parameters.

fit

truefit

f

ffPull

,0

,0,0

J. A. Perez Hernandez, IPM Summer Intern FNAL

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ME Method: PSE’s, Part II

Cross-check: signal number of events distribution for 500 PSE.

J. A. Perez Hernandez, IPM Summer Intern FNAL

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Previous Results (for ≥1 tag sample)

Ht > 200GeV

Signal Fraction =

86% Mean Error =0.089

J. A. Perez Hernandez, IPM Summer Intern FNAL

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The Question

Is there any improvement on the sensitivity of the ME

Analysis by adding the 0 b-tag sample?

J. A. Perez Hernandez, IPM Summer Intern FNAL

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0 b-tag sensitivity

0 b-tag, Ht>200: Signal Fraction=25% , Mean Error = 0.1916

f0 Mean f0 Error f0 Pull

Compare with Mean Error = 0.089 for ≥1 tag sample… 9% Improvement!

J. A. Perez Hernandez, IPM Summer Intern FNAL

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Ht Optimization Expected Uncertainty (Mean Error) vs Ht Cut

Minimum!

Ht Cut =275GeV

We are currently investigating this point

J. A. Perez Hernandez, IPM Summer Intern FNAL

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The Results ≥1 b-tag events (Ht>200GeV):

Mean Error = 0.089

0 b-tag events (Ht>275GeV): Mean Error = 0.188

≥1 and 0 b-tag events:

Mean Error=081.0

189.0

1

089.0

12/1

22

≈10% Improvement!In the most sensitive W Helicity

measurement

J. A. Perez Hernandez, IPM Summer Intern FNAL

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Conclusions

~8% by including 0 b-tag sample. For the 0 b-tag sample, there is an Ht

cut which minimizes the f0 mean error, namely, Ht>275GeV. Expected 10% improvement on f0 mean

error upon including 0 b-tag sample.

EPR Paradox & Bell’s Theorem

J. A. Perez Hdez.

Summer Interns Weekly Meeting, August 1st, 2007

J. A. Perez Hernandez, IPM Summer Intern FNAL

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Part I: EPR Paradox

J. A. Perez Hernandez, IPM Summer Intern FNAL

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EPR Paradox:

Proposed in 1935: by A. Einstein, B. Podolsky, N. Rosen

(Phys. Rev. 47, 777). Original paper can be found at:

http://www.drchinese.com/David/EPR.pdf

J. A. Perez Hernandez, IPM Summer Intern FNAL

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EPR Paradox, Simplified (by Bohm):

Pi meson decay:0 → e- + e+ Linear Momentum conserved →

If 0 was at rest, then e-, e+ will fly off in opposite directions.

Angular Momentum conserved → Singlet configuration:

total spin = 0, half & half (on average) → they’re correlated! IMPORTANT: quantum mechanics doesn’t

predict which combination you’ll get on any particular decay!

2

1

David Bohm

J. A. Perez Hernandez, IPM Summer Intern FNAL

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EPR Paradox: Realist vs Orthodox

If you measure e+ spin (e.g., ↑), then you’ll immediately know e- spin (e.g., ↓)!!

The electron

really had spin ↓

since it was

created… It’s just

quantum

mechanics didn’t

know about it!

No—The act of measurement produced the spin of the electron… the wave function collapsed!

Einstein: realist Bohr: orthodox

J. A. Perez Hernandez, IPM Summer Intern FNAL

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EPR Paradox: Conclusion

Assuming locality, EPR showed quantum mechanics was incomplete:

Instantaneous wave function collapse implies “spooky action-at-a-distance” (Einstein’s words for non-locality)…

Thus EPR supported locality and concluded quantum mechanics was incomplete…

…And therefore, quantum mechanics

needs additional parameters (hidden

variables) in order to give a complete

description of reality.

J. A. Perez Hernandez, IPM Summer Intern FNAL

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Part II: Bell’s Theorem

J. A. Perez Hernandez, IPM Summer Intern FNAL

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Bell’s Theorem: Hidden variable theories: The wave function

is not the whole story – some other quantity (or quantities), , is needed in addition to , to characterize the state of a system fully.Theoretical physicists were happily proposing hidden variable theories, until…

1964: John Stewart Bell proved that any local hidden variable theory is incompatible with quantum mechanics.

1964, baby!

Bell’s original paper can be found at: http://www.drchinese.com/David/Bell_Compact.pdf

John S. Bell

J. A. Perez Hernandez, IPM Summer Intern FNAL

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Bell’s Inequality“Bell’s paper is a gem: brief,

accessible, and beautifully written” – David J. Griffiths The main result obtained by

J. S. Bell was this (math won’t be discussed here):

If Bell’s inequality holds, then EPR are right and QM is not only incomplete but downright wrong;

But…

If Bell’s inequality is violated, then EPR are wrong, and QM is complete…and non-local.

J. A. Perez Hernandez, IPM Summer Intern FNAL

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Bell’s Inequality: The experiment

1982: A. Aspect, J. Dalibard, and G. Roger test experimentally Bell’s inequality (Phys. Rev. Lett. #49, 91).

The results were in excellent agreement with the predictions of QM, and clearly violated Bell’s inequality.

J. A. Perez Hernandez, IPM Summer Intern FNAL

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Bell’s Theorem: Conclusions

It spelled the demise of realism. Demonstrated that nature itself is fundamentally nonlocal.

Nevertheless, there are two types of nonlocality: Causal (energy transport, information transmission,

special relativity causal absurdities) Ethereal (e.g., entanglement, there’s no transmission

of information, the only effect is the correlation between data)

Nature is “ethereally” nonlocal.