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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.