Transcript michaels_defense - Physics

Mass and Spin from a
Sequential Decay with a Jet
and Two Leptons
Michael Burns
University of Florida
Advisor: Konstantin Matchev
Collaborators: KC Kong, Myeonghun Park
Contents
• New Physics and Sequential Decays
• Mass Determination
– Kinematical Endpoint Method
– Kinematical Boundaryline Method
• Spin Determination
– Chiral Projections
– Basis Functions
– Reparametrization
New Physics and Sequential Decays
“old” physics:
“new” physics, “DCBA”:
• At LHC: colored particle production (j), unknown energy and longitudinal
momentum (D)
• Assume OSSF leptons (ln, lf), missing transverse momentum (A)
• What is the new physics (assuming the chain “DCBA”)?
– What are the masses of A,B,C,D?
– What are their spins?
MASS
Method of Kinematical Endpoints
(arXiv:hep-ph/9907518, Figs. 1 and 4)
Use extreme kinematical
values of invariant mass.
(“model-independent”)
These values depend on
spectrum of A,B,C,D …
… however, the
dependence is
piecewise-defined.
Offshell B: Njl = 4
(e.g. JHEP09(2000)004 and JHEP12(2004)003)
Inversion and Duplication
These inversion
formulas use
the jll threshold!
• Experimental ambiguity
– Finite statistics, resolution -> “border effect”
– Background -> “dangerous feet/drops”
• Piecewise defintions: hmm… largely ignored
– Inversion formulae depend on unknown spectrum
– Ambiguity DOES occur!
picture of
a foot, just
for fun
Appendix: Example Duplication
Change columns to “Njl”
How to resolve?
We have a technique.
Two Variable Distribution: ---------MAIN POINT:
shapes of kinematical boundaries
reveal Region => no more piecewise
ambiguity (from perfect experiment).
Njl = 3
Njl = 2
Njl = 1
Njl = 4
Two Variable Distribution: -------We know the expression for
the hyperbola.
easy to see restricted
(
) distribution
SPIN
Spin Assignments
Assume q/qbar jet
Each vertex changes spin by (+/-)1/2
S = scalar
F = spinor
V = vector
Spins and Chiral Projections
IJ=11
IJ=12
IJ=21
IJ=22
Four helicity groupings, depending on RELATIVE
(physical) helicities of the jet and two leptons.
I: relative helicity b/w j and ln
J: relative helicity b/w ln and lf
spin of antifermion is “opposite of the spinor”?
-> four “basis functions”
“Near-type” Distributions
I will change mass-ratio coefficients to generic (no one cares).
etc.
The arrow subscripts
indicate the relative
helicities.
BOTH HELICITY
COMBINATIONS
CONTRIBUTE!
(Notice what happens
for equal helicity
contributions.)
(“near-type” applies in SM: top decay)
“Near-type” Distributions
Show plots?
Observable Spin Distributions
“cleverly” redefine spin basis functions (like change of basis)
Relevant coefficients are the following combinations of couplings:
Distribution decomposed into model-dependent (a, b, g) and model-independent (d)
contribution
etc.
I will rewrite this,
slightly simpler.
Observable Spin Distributions
Dilepton: purely “near-type” (nice)
Only one model-dependent parameter (for each spin case): a !!!
Get as much use out of this one as possible (as usual).
Jet-lepton: must include “near-type” and “far-type” together, piecewise defined
S fits to same a as L !!!
extra constraint
D gives charge assymtery; fits to
independent model parameters b and g
So, in addition to spin, get three measurements of the couplings through a, b, g
– extra model determination.
Example: SPS1a
We generated “data” from DCBA = SFSF, assuming
Dbg
La
Sa
The fits were determined by minimizing:
Other Spin Assignments
Dbg seems the most promising to discriminate the SPS1a model.
However, the most discriminating distribution depends on the masses and spins
of the true model.
Some models cannot even be discriminated, in principle (using our method).
(This does not imply that our method is bad; just general.)
Summary
• Mass determination:
– We have inversion formulas using jll threshhold.
– We identified the ambiguous endpoint Regions.
– We devised the kinematical boundaryline method, which
resolves the ambiguity (ideally).
• Spin determination:
– We devised a method that allows the model-dependent
parameters to float.
– We found a convenient spin basis for these floating
parameters.
– We identified the problem scenarios (fakers).
APPENDICES
Appendix: tree-level production
• Assuming extra conserved quantum number
and 2 to 2 production:
– SM in s-channel
• Gluon (SU(3) => dominant?)
• Electroweak
• Higgs (Yukawa => suppressed by SM vertex?)
– BSM in t-channel
• New color octet (e.g. gluino, KK gluon?)
• New color triplet (e.g. squark, KK quark?)
• New color singlet (e.g. gaugino, KK photon?)
Draw some diagrams.
Appendix: Backgrounds
• SM
– ISR, Z->dilepton, tau->lepton
• Other BSM
– Multiple resonances, alternative processes
• Combinatoric
– Which lepton? Which jet?
Draw some diagrams.
Appendix: OF Subtraction (leptons)
desired signal:
chi20 - chi10 = 68 GeV
event selection: 2 OSSF
leptons and four “pT-hard” jets
(ATLAS TDR 1999 Figs. 20-9 and 20-10)
(Hinchliffe, Paige, Shapiro, Soderqvist, Yao, LBNL-39412, Figs. 15 and 16)
basically same as above
Appendix: ME Subtraction (jets)
jet+lepton distribution
desired signal:
(different from ours)
squark - sneutrino = 284 GeV
(Nurcan Ozturk (for ATLAS), arXiv:0710.4546v2, Fig. 2)
event selection: one lepton
and two “pT-hard” jets
Appendix: threshold formulae
Appendix: Regions & Configurations
in rest-frame of C:
(1,.) and (5,.)
(2,.)
(3,.)
(4,.) and (6,.)
independently of frame:
in (.,1)
in rest-frame of B:
Appendix: Dangerous Feet/Drops
(arXiv:hep-ph/0510356, Fig. 10)
Background
Background
Appendix: Inversion Variables
Appendix: Duplication Maps
Appendix: HiLo Points
For Njl = 1,2,3
Appendix: 2D hi vs lo Distribtuions for
Duplicated Points
Maybe zoom
in to pdf before
copying to
show points?
Appendix: jll Hyperbola
Appendix: 2D jll vs. ll Distribtuions for
Duplicated Points
Maybe zoom
in to pdf before
copying to
show points?
Appendix: Chirality vs. Helicity
What to say?
(It still confuses me.)
Appendix: particle/antiparticle fraction
???
???
I have to find a reference.
Appendix: “Near-type” Basics
C’B’A’ = { SFS , SFV , FSF , FVF , VFS , VFV }
One of either I or J is irrelevant. C’B’A’fbfa = { CBAlnlf , DCBjln }. Only the
relative helicity between fa and fb is important.
Chiral projections allow helicities to be selected by the couplings (because
f’s are massless), so that matrix element can be spin-summed.
Spin dependence requires either:
- chiral imbalance (gL/=gR) at both vertices, or
- B’=V.
Appendix: “Near-type” Width
Show basic calculations:
Spin sums and contractions,
Narrow width approximation,
Appendix: “Near-type” with ClebschGordan
Show basic calculations:
Clebsch-Gordan Coefficients
Appendix: the “far-type” log behavior
Whereas the “near-type” distributions are polynomials in m2, the “far-type”
distributions (not presented), in addition to being more complicated, generally
have some logarithmic m2-dependence. This can actually be easily “motivated”.
Show near vs. far.
Show Jacobian stuff.
Appendix: Fakers
FSFV always fakes FSFS.
FSFS can also fake FSFV for some mass spectra. The only condition is:
I just need to fill this in (also for FVFS/FVFV).
Maybe I will show the plots for FSFV data.