W Helicity Analysis: Matrix Element Method Sensitivity and optimization using 0-tag events Jorge A. Pérez Hernández UAEM, México IPM Summer FNAL Supervisor: Ricardo Eusebi

J. A. Perez Hernandez, IPM Summer Intern FNAL 2 W Helicity Measurement Objective: To measure the W boson longitudinal fraction f 0. Technique: Matrix Element (ME). SM Prediction:  Right handed fraction f + ~0%  Longitudinal Fraction f 0 ~70%  Left Handed Fraction f - ~30%.

J. A. Perez Hernandez, IPM Summer Intern FNAL 3 ME Method: Likelihood, Part I The Likelihood function: 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) d n  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 4 ME Method: Likelihood, Part II Current Analysis: (Lepton + Jets Channel) Top quark decay: tt → W + b W - b → qqb l l b Select MC sample with a known value for f 0. (“ f 0 true ”) Set f + = 0. Calculate P signal,i ( f 0 ) and P background,i =const, for f 0 [0,1]. C s calculation: maximize likelihood for “ f 0 true”. Find the maximum for the final likelihood. The result is the measured value of f 0. (“ f 0 fit ”)

J. A. Perez Hernandez, IPM Summer Intern FNAL 5 ME Method: Linearity Linearity Plot: Repeat previous procedure for several “ f 0 true” values. Plot “ f 0 fit” vs “f 0 true”. Example: Fit straight line. Obtain intercept (p 0 ), and slope (p 1 ). f 0 True f 0 Fit NOTE: We use signal and background fractions expected for 1.7fb -1 data.

J. A. Perez Hernandez, IPM Summer Intern FNAL 6 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 f 0 fit,  f 0 and pull. Correct each PSE outcome by linearity parameters.

J. A. Perez Hernandez, IPM Summer Intern FNAL 7 ME Method: PSE’s, Part II Cross-check: signal number of events distribution for 500 PSE.

J. A. Perez Hernandez, IPM Summer Intern FNAL 8 Previous Results (for ≥1 tag sample) H t > 200GeV Signal Fraction = 86% Mean Error =0.089

J. A. Perez Hernandez, IPM Summer Intern FNAL 9 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 10 0 b-tag sensitivity 0 b-tag, H t >200: Signal Fraction=25%, Mean Error = f 0 Meanf 0 Errorf 0 Pull Compare with Mean Error = for ≥1 tag sample… 9% Improvement!

J. A. Perez Hernandez, IPM Summer Intern FNAL 11 H t Optimization Expected Uncertainty (Mean Error) vs H t Cut Minimum! H t Cut =275GeV We are currently investigating this point

J. A. Perez Hernandez, IPM Summer Intern FNAL 12 The Results ≥1 b-tag events (H t >200GeV):  Mean Error = b-tag events (H t >275GeV):  Mean Error = ≥1 and 0 b-tag events:  Mean Error= ≈10% Improvement! In the most sensitive W Helicity measurement

J. A. Perez Hernandez, IPM Summer Intern FNAL 13 Conclusions ~8% by including 0 b-tag sample. For the 0 b-tag sample, there is an H t cut which minimizes the f 0 mean error, namely, H t >275GeV.  Expected 10% improvement on f 0 mean error upon including 0 b-tag sample.

EPR Paradox & Bell’s Theorem J. A. Perez Hdez. Summer Interns Weekly Meeting, August 1 st, 2007

J. A. Perez Hernandez, IPM Summer Intern FNAL 15 Part I: EPR Paradox

J. A. Perez Hernandez, IPM Summer Intern FNAL 16 EPR Paradox: Proposed in 1935:  by A. Einstein, B. Podolsky, N. Rosen (Phys. Rev. 47, 777). Original paper can be found at:

J. A. Perez Hernandez, IPM Summer Intern FNAL 17 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! David Bohm

J. A. Perez Hernandez, IPM Summer Intern FNAL 18 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: realistBohr: orthodox

J. A. Perez Hernandez, IPM Summer Intern FNAL 19 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 20 Part II: Bell’s Theorem

J. A. Perez Hernandez, IPM Summer Intern FNAL 21 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: John S. Bell

J. A. Perez Hernandez, IPM Summer Intern FNAL 22 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 23 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 24 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.