Definitions of Physics and Resolution Variables for Various Fitting Modes

Last Update: 10-Sep-05
Original Version: 22-Jul-05

Index

Definitions
Physics Function Variables
Resolution Function Variables

Definitions for Below

For logL fits
- Data(hist): event var's used to fill data histograms
- Pred(fit): event var's used to construct PDFevt
- Pred(hist): loop over var ranges to get var's used to fill prediction histograms.
  Integrate over ranges of other (than plotted) var's * PDF(var) in constructing pred. histo
For chi2 fits
- Data: event var's used to fill data asymmetry histogram (used as data input to chi2 and for display)
- Pred: loop over VPDL range (same VPDL used for each source) to construct pred asymmetry histogram (used as pred input to chi2 and for display)
Histograms for logL Fits (alt_evt)
- Loop over bins of all variables in constructing prediction histograms
- This is why non-plotted variables include a PDF(var) in the physics function definition
- Requires an alternate event structure for fits using VPDL - signalled by flag alt_evt
Variable Qualifiers
- true(tr): unsmeared variable for this event
- smear(sm): smeared variable for this event
- def: default value for variable - e.g. M(def) = M(Bs)
- src: value of this variable assuming a specified source (not using source info stored w/ event)
- bin: indicates that the variable in question is a loop variable rather than a variable from an event
- conv: indicates that the variable in question is a convolution variable - integrated over in PDFevt
- sm/bin-cnv: for fits using Resolution convolution, input to PDFevt is the smeared or bin Lxy/VPDL, but input to the Physics function uses Lxy/VPDL(conv) that is looped over
VPDL: defined depending on Mode (see below)
σ(Lxy) & σ(vpdl) in Physics Functions
- σ(Lxy-evt/bin) is only used for Lxy(smear) cases in the 0-lifetime component
- σ(vpdl-evt/bin) is used for VPDL(smear) cases in the 0-lifetime component of logL(VPDL) fits
- only <σ(vpdl)> is used for VPDL(smear) cases in the 0-lifetime component of chi2 fits

Physics Function Variables

Mode	phys_ind_x	phys_ind_k	phys_ind_tag	phys_ind_err	phys_ind_ptm	phys_ind_mass
True ct0 - logL: Nunm/mix Histos vs ct0
Data(hist)	ct0(true)	---	Tag(true)	---	---	---
Pred(fit)	ct0(true)	1	Tag(true)	---	1	1
Pred(fit)	o ct0(true) = c evt[ind_t0]
Pred(hist)	ct0(bin)	1	Tag(bin)	---	1	1
True ct0 - chi2: Asym histo's vs. ct0
Data	ct0(true)	---	Tag(true)	---	---	---
Data	o ct0(true) = c evt[ind_t0]
Pred	ct0(bin)	1	Tag(bin)	---	1	1

Pt(B) - logL(Lxy): Nunm/mix histo's vs Lxy
Data	Lxy(tr/sm)	---	Tag(tr/sm)	---	---	---
Pred(fit)	Lxy(tr/sm-cnv)	1	Tag(tr/sm)	σ(Lxy-evt)	Pt(B-evt)	M(src)
Pred(fit)	o Pt(B-evt) = Pt(m-evt) / K(true)
Pred(hist)	Lxy(bin-cnv)	1	Tag(bin)	σ(Lxy-bin)	Pt(B-bin)	M(src)
fit should be identical to ct0(logL) if using Lxy(true) and Tag(true)
Pt(B) - logL(VPDL): Nunm/mix histo's vs VPDL
Data	VPDL(tr/sm)	---	Tag(tr/sm)	---	---	---
Data	o VPDL(tr/sm) = M(def) Lxy(tr/sm) / Pt(B) o Pt(B) = Pt(m) / K(true)
Pred(fit)	VPDL(tr/sm-cnv)	1	Tag(tr/sm)	σ(vpdl-evt)	1	1
Pred(fit)	o VPDL(sm) = M(src) Lxy(sm) / Pt(B)
Pred(hist)	VPDL(bin-cnv)	1	Tag(bin)	σ(vpdl-bin)	1	1
Pred(hist)	o σ(vpdl-bin) = from PDF(errVPDL) histo
fit not should be identical to ct0(chi2) if using VPDL(true) and Tag(true) b/c of M(def) in VPDL(true)
Pt(B) - chi2: Asym histo's vs VPDL
Data	VPDL(tr/sm)	---	Tag(tr/sm)	---	---	---
Data	o VPDL(tr/sm) = M(def) Lxy(tr/sm) / Pt(B) o Pt(B) = Pt(m) / K(true)
Pred	VPDL(bin-cnv)	1	Tag(bin)	<σ(vpdl)>	1	1
fit not should be identical to ct0(chi2) if using VPDL(true) and Tag(true) b/c of M(def) in VPDL(true)

<K> - logL(Lxy): Nunm/mix Histos vs Lxy
Data	Lxy(tr/sm)	---	Tag(tr/sm)	---	---	---
Pred(fit)	Lxy(tr/sm-cnv)	<K(src)>	Tag(tr/sm)	σ(Lxy-evt)	Pt(m-evt)	M(src)
Pred(hist)	Lxy(bin-cnv)	<K(src)>	Tag(bin)	σ(Lxy-bin)	Pt(m-bin)	M(src)
<K> - logL(VPDL): Nunm/mix Histos vs VPDL
Data	VPDL(tr/sm)	---	Tag(tr/sm)	---	---	---
Data	o VPDL(tr/sm) = M(def) Lxy(tr/sm) / Pt(m)
Pred(fit)	VPDL(tr/sm-cnv)	<K(src)>	Tag(tr/sm)	σ(vpdl-evt)	1	1
Pred(fit)	o VPDL(tr/sm) = M(src) Lxy(tr/sm) / Pt(m)
Pred(hist)	VPDL(bin-cnv)	<K(src)>	Tag(bin)	σ(vpdl-bin)	1	1
<K> - chi2: Asym Histos vs VPDL
Data	VPDL(tr/sm)	---	Tag(tr/sm)	---	---	---
Data	o VPDL(tr/sm) = M(def) Lxy(tr/sm) / Pt(m)
Pred	VPDL(bin-cnv)	<K(src)>	Tag(bin)	<σ(vpdl)>	1	1

Convolute over K - logL(Lxy): Nunm/mix Histos vs Lxy
Data	Lxy(tr/sm)	---	Tag(tr/sm)	---	---	---
Pred(fit)	Lxy(tr/sm-cnv)	K(conv)	Tag(tr/sm)	σ(Lxy-evt)	Pt(m-evt)	M(src)
Pred(hist)	Lxy(bin-cnv)	K(conv)	Tag(bin)	σ(Lxy-bin)	Pt(m-bin)	M(src)
Convolute over K - logL(VPDL): Nunm/mix Histos vs VPDL
Data	VPDL(tr/sm)	---	Tag(tr/sm)	---	---	---
Data	o VPDL(tr/sm) = M(def) Lxy(tr/sm) / Pt(m)
Pred(fit)	VPDL(tr/sm-cnv)	K(conv)	Tag(tr/sm)	σ(vpdl-evt)	1	1
Pred(fit)	o VPDL(tr/sm) = M(src) Lxy(tr/sm) / Pt(m)
Pred(hist)	VPDL(bin-cnv)	K(conv)	Tag(bin)	σ(vpdl-bin)	1	1
Convolute over K - chi2: Asym Histos vs VPDL
Data	VPDL(tr/sm)	---	Tag(tr/sm)	---	---	---
Data	o VPDL(tr/sm) = M(def) Lxy(tr/sm) / Pt(m)
Pred	VPDL(bin-cnv)	K(conv)	Tag(bin)	<σ(vpdl)>	1	1

Resolution Function Variables

Mode	res_ind_dx	res_ind_err
logL(Lxy) Fits
Pred(fit)	Lxy(smear) - Lxy(conv)	σ(Lxy-evt)
Pred(hist)	Lxy(bin) - Lxy(conv)	σ(bin)
logL(VPDL) Fits
Pred(fit)	VPDL(smear) - VPDL(conv)	σ(VPDL-evt)
Pred(fit)	o VPDL(smear) = M(src) Lxy(smear) / Pt(m)
Pred(hist)	VPDL(bin) - VPDL(conv)	σ(VPDL-bin)
chi2 Fits
Pred(fit)	VPDL(smear) - VPDL(conv)	<σ(vpdl)>
Pred(fit)	o VPDL(smear) = M(src) Lxy(smear) / Pt(m)
Pred(hist)	VPDL(bin) - VPDL(conv)	<σ(vpdl)>