# Presentation: 448921

##  sin (2s) status from CDF 

- Juan Pablo Fernández Ramos
- C.I.E.M.A.T.
- 05/09/2008
- Workshop : Beyond 3SM generation

## Introduction

## Beyond the Standard Model

- CP violation in B0s meson system is an excellent way to search for new physics
- B-factories have established that, at tree level, NP effects, if existing in B0, B+decays, have a magnitude < O(10%). However, there exists an important corner not explored by them: the B0s system
- CP violation in B0s  predicted to be extremely small in the SM.
- Contribution from new physics could come through the enhancement of loop processes

- look at any **difference** in properties like decay rate, angular decomposition of the amplitude, etc **between** a decay and its “mirror image” resulting from C and P transformations

- What Is what we measure?

##  Neutral Bs system 

-  Neutral Bs system

- Experimentally accessible

-  The magnitude of the box diagram gives the oscillation frequency ms= mH - mL ≈ 2|M12| ;      ms = 17.77  0.12 ps-1 (CDF)

-  Mass eigenstates have different decay widths (lifetimes)
-  = L – H ≈ 2|12| cos s ;     = 0.07 0.04 ps-1 [A.Lenz et al, JHEP06(2007)072]

-  The phase of the diagram gives the complex number q/p = e-i s where s = arg (-M12/)  [ CP-violating phase]

-  Mixing phase – sensitive to NP

## CP Violation in the S.M. (Bs0 J/

- sSM  2arg[-VtsVtb*/ VcsVcb*]

- CP violation phase s in SM is predicted to be very small

- The chance to observe CP violation comes from interference between decay-only and decay-through-mixing amplitudes

- The CP phase between the two decay paths appears via the factor sin(2s)

**B****s****0**

- J/

## Experiment Overview

## Introduction to the CDF II detector

-  	      CDF II detector includes (**relevant to this analysis**)
-  Central tracking: silicon vertex detector surrounded by a drift chamber
-  pT resolution pT/pT = 0.0015 pT
-  vertex resolution ~ 25 m
-  Particle identification (PID): dE/dx ~1.5 separation for K/pi with p>2 GeV and TOF ~2  K/pi with p<1.5-1.8 GeV.
-  Good e and  identification by calorimeters and muon chambers

-   → excellent mass and vertex rec.

-  Excellent performance of Tevatron accelerator
-  CDF has already **4 fb****-1**** **on tape
-  Expect 6-8 fb-1 by end of the run 2
-  This analysis uses 2.8 **fb****-1 **(but
- equivalent to 2.0 fb-1, no PID 2nd half )

## Overview of Bs0 J/ Decay

- Bs0 travels ~ 450 m before decaying into  J/ and 
-  Spin-0 Bs0 decays to spin-1 J/ and spin-1 
-  final states with *l* = 0, 2 (CP-even) and *l*  =1 (CP-odd)
- Maximum sensitivity to phase (sin 2s) depends on decay time re-solution and separation of CP at decay and initial flavour of Bs0/Bs0
- Purpose: disentangle all these features and measure the phase

- Overview of Bs0 J/ Decay

- Overview of the decay

- Measure decay time from flight length

## Measurement Strategy

- Reconstruct Bs0  J/( ) ( KK)
- Use angular properties of the J/  decay to separate angular momentum states which correspond to CP eigenstates
- Identify initial state of Bs meson (flavour tagging) and thus separate time evolution of Bs0 and Bs0 to maximize sensitivity to CP asymmetry (sin 2s)
- Perform un-binned maximum likelihood fit to extract signal parameters of interest (e.g. s, L)

- _

## Bs0J/ Signal Selection

- N(Bs0) ~ 3200 ( with PID expect ~3800 )

- Use an artificial neural network (ANN) to efficiently separate signal from background
- ANN training
- Signal from Monte Carlo reconstructed as it is in data
- Bkg. from J/ sidebands
- Variables used in network
- Bs0:  pT and vertex prob.
- J/: pT and vertex prob.
-  :  mass and vertex prob.
- K,K:  pT (NO PID)

## Angular Analysis of Final States

- Maximum sensitivity to phase if *CP-*even* and CP-*odd states are separated

## cos(

-   Alternatively to the S,P,D-wave states one can use the “transversity              basis”: three independent components that use the vector mesons                polarizations w.r.t. their direction of motion (pol.states P0,P||,P

- cos(

- 

** ** the “transversity angles” (T,T,T) are sensitive to the polarizations

- Angular correlations in decay products  separation of  CP-components.

- cos(

## Flavor Tagging

- We have a  sample of
*B**0**s**    **and**     **B**0**s **→ **J/**** ****      ( J/****→μ****+**μ****- ****→K**+**K**- **) *
- of known decay-time and CP.
- It will help to know whether a meson or an anti-meson was produced in the *pp* interaction...

- Maximum sensitivity to phase if *B**0**s*  and *B**0**s *separated

- _

- _

## Overview of Flavour Tagging

- Output: decision (*b*-quark or *b*-quark) and the quality of that decision

- b quarks generally produced in pairs at Tevatron
- Tag either the b quark which         produces the J/(SST), or the     other b quark (OST)

- same side

- SST: exploits the charge/species correlations with associated particles produced in fragmentation that results in the reconstructed meson
- OST: exploits the decay products of the other *b*-hadron in the event

## Quantifying Tagging Power

- The statistical power of the tagging is quantified by  <D2typically 4.8 % as detailed next.

- To quantify tagging  we use:
- fficiency   tagged / Ntotal = (NRS+NWS)/(NRS+NWS+NNT)
- “Dilution”   D = Ptag – Pmistag = (NRS-NWS)/(NRS+NWS)

-  = 96  1%
-  √<D2>= 11 2 %
-  <D2> = 1.2 %

-  = 50  1%
-  √<D2>= 27 4%
-  <D2> = 3.6 %

- SST

- OST

- 1. Using B± (OST)

- 2. In the B0s mixing  (SST)

- Each tag decision comes with an dilution estimate
- (event-per-event dilution), validated:

- [used in 1st half only]

## Un-binned Likelihood Fit

- We have a  sample of
* **B**0**s**  **and**     **B**0**s  **→  **J/**** **** (J/****→μ****+**μ****-**, ****→K**+**K**-**) *
- of “known” decay-time, CP and production flavor.
- But this information is not know on a per-candidate basis.     Wrap it up in a fit.

- _

## Overview of fit

- Single event likelihood decomposed and fac-
- torized in:

- Measured quantities that enter in the fit and their PDFs
- reconstructed mass of Bs0 ,Bs0 and its error, decay time and its error, transversity angles, flavour tag decision, dilution D

- Parameters in the fit : the relevant ones : s , 
- plus many nuisance parameters: mean width LH,
- | A(0)|2, | A||║(0)|2,  | A0(0)|2 ,  = arg(A||║ A0*), = arg(A   A0*)  ...

- _

## Results                                

- 
- newsconfidence region  (CDF, 2.8 **fb****-1**, ~2 **fb****-1 **equiv.)
-     news confidence interval (CDF, 2.8 **fb****-1 **, ~2 **fb****-1 **equiv.)
-   [the results are not intended to be published, just an update for ICHEP, next publication: PRD in winter with full PID and ~4 **fb****-1**]
-      combined CDF and D0 (from previous measurements,                 Phys. Rev. Lett. 100, 161802 [2008, CDF 1.35 **fb****-1**] and                     arXiv:0802.2255  [hep-ph, 2008, D0 2.8 **fb****-1**])

- oth CDF and D0 have published their 1st determination of bounds on mixing-induced CP violation in Bs0  J/ references bellowToday I will show :

## Likelihood

- These yield multiple solutions with non-Gaussian uncertanties, biased estimates, etc
- Point estimate irrealistic quote confidence region

- using profile likelihood ratio ordering with rigorous frequentist inclusion of systematic uncertainties

## Probabilistic method has to provide proper coverage 

- 2D-Likelihood contour

- Profile-Likelihood Ratio ordering
- (a la Feldman-Cousins)

- Does _**not**_** **has coverage: the resulting confi-dence region does not contain the true value with desired CL independently of true value

- Above procedure has been corrected to have right coverage

- Excludes a given s- pair if it can be excluded for any choice of the 20+ nuisance parameters within 5 of their estimated values

- F-C guarantees coverage at quoted C.L. Accounts for non-asymptotic behavior of likelihood, i.e. log(L) non-parabolic, and possible large fluctuations of L shape from experiment-to-experiment

**Example of 2D-L contour vs Profile-L Ratio ordering for the 1.35 fb****-1**** CDF result**

- Phys. Rev. Lett. 100, 161802

- Phys. Rev. Lett. 100, 161802 (2008)

## Flavor Tagged 2s -  Confidence Region

- Assuming the SM, the probability of observing a fluctuation as large or larger than what observed in data is 7%, corresponding to 1.8

- Confidence region with profile-Likelihood Ratio ordering and rigorous frequentist inclusion of systematic uncertainties.   2D region is projection of a multidimensional region in the space of all (27) fit parameters

- Expect to shrink further once PID will be available for full dataset

## s 1D Intervals

- Assuming no CP violation (s  = 0), we also measure
-       cs = 459 ± 12 (stat) ± 3 (syst) μm
-       s  = 0.02 ± 0.05 (stat) ± 0.01 (syst) ps-1
-       and the transversity amplitudes
-               |A||(0)|2 = 0.241 ± 0.019 (stat) ± 0.007 (syst)
-               |A0(0)|2 = 0.508 ± 0.024 (stat) ± 0.008 (syst)

-  treated as a nuisance parameter
- s   [0.28, 1.29]
-     at 68% CL

## Reminder : DØ published Results

-  DØ observes a fluctuation consistent with CDF
-  Chooses to quote the results in     terms of s = -2s             (**arXiv:0802.2255)**
-  DØ quotes a point-estimate with        strong phases constrained from
*    **B**0* → *J/ψK***0*
-  This makes the result dependent        on theoretical assumptions
-  Can be compared to CDF                   published constrained result
- 	2s Є [0.40,1.20] @ 68% CL

- Reminder : DØ published Results

## Tevatron combination

- Combine CDF and D0 iso-CL  regions with no constrains and previously checked for coverage (a’ la HFAG):
********σconsistency with SM.

## Future

-  Shown results 2.8 fb-1, but 4 fb-1 already on tape to be analysed soon
-  Expect 6-8 fb-1 by the end of the run 2
-  Analysis to be improved and optimized:
-      - better flavour tagging
-      - calibrated PID
-      - more statistics from other triggers
-  If s is indeed large CDF results
-      have good chance to prove it
-  CPV in Bs system is one of the main topics in LHCb B Physics program
- → will measure mixing phase with great precision

## Conclusions

## Conclusions 

-  First update on larger dataset confirms old result and provides tighter constraints ( 15% to 7% agreement with SM), although several ingredients are still in the works
-  Best measurements of Bs decay width difference and one of the best lifetime measurements
-  Both CDF and DØ observe 1-2 sigma s deviations from SM predictions. SM agreement reduces to 2.2 when combined.
-  Interesting to see how these effects evolve with more data

- Conclusions

## Slide 28

## Un-binned Likelihood Fit

- Fit with separate PDFs for signal and background
- Ps(m|m) – Single Gaussian fit to signal mass
- Ps(ct, ****, |D, ct) – Probability forBs0/Bs0
- Pb(m) – Linear fit to background mass distribution
- Pb(ct| ct) – Prompt background, one negative exponential, and two positing exponentials
- Pb(****) – Empirical background angle probability distributions
- Use scaled event-per-event errors for mass and lifetime fits and event-per-event dilution

## s in Untagged Analysis

- fits on simulated samples

- a) Dependence on one parameter in the likelihood vanishes for some values of other parameters:

- - Fit for the CPV phase
-  Biases and non-Gaussian estimates in pseudo-experiments
-  Strong dependence on true values for biases on some fit parameters.

- b) L invariant under two transformations:
- 	→ 4 equivalent minima

- e.g., if ΔΓ=0, δ┴  is undetermined

## Angular Probability Distribution: time evolution 

- General relation for B-> VV

- Bs0

- Bs0

- A0, A||,A: transition amplitudes to a given polarization state at t=0

- anti*-B**0**s*

- Time dependence appears in *T, *
*U, V*. Different for Bs0  and Bs0

**** = {cos T, T, cos T}

- f(ρ):  angular distribution for a given polarization state

## Angular Probability Distribution: time evolution 

- Terms with ms dependen-ce; they are different for different initial state flavor

- CP asymmetry

- Knowledge of *B**0**s* mixing frequency needed(well measured by CDF-D0)

- Angular Probability Distribution: time evolution

- = arg(A||║ A0*), = arg(A   A0*) are the phases of A|| and A  relative to A0

## Systematics

- - Systematic uncertainties studied by varying all nuisance parameters +/- 5  from observed values and repeating LR curves (dotted histograms)
-  Nuisance parameters:
-  lifetime, lifetime scale factor uncertainty,
-  strong phases,
-         - transversity amplitudes,
-         - background angular and decay time
- 	parameters,
-         - dilution scale factors and tagging
- 	efficiency
-         - mass signal and background
- 	parameters
-         - ...
-  - Take the most conservative curve (dotted
- 	red histogram) as final result

##  CP violating phases : s   vs  s  

- s = 2s= 2arg [-VtsVtb*/ VcsVcb*] ~ 4.4o  (SM) phase of *b**→**ccs*                      transition that accounts for interference of decay and mixing+decay
-    s= arg[-M12/12] ~ 0.24o (SM)
- 	arg[M12 ]= arg(VtbVts*)2  matrix element that connects matter to                antimatter through oscillation.
- 	arg[12 ] =  arg[(VcbV*cs)2 + VcbV*csVubV*us + (VubV*us)2] width               of matter and antimatter into common final states.

-  Both SM values experimentally unaccessible by current experiments     (assumed zero). If NP occurs in mixing:
-          s = sSM + sNP ~ sNP
-           2s = 2 sSM – sNP ~ -sNP
-   standard approximation:  s  = -2βs

##   B  VV (our Bs0  J/   but also  B0  J/ K*0  ,  ... ) decay to              two CP even states (S-wave or D-wave) and one CP odd (P-wave)  

-   Alternatively to the S,P,D-wave states one can use the “transversity              basis”: the three independent components in which the vector mesons        polarizations w.r.t. their direction of motion are:
-               - longitudinal (0)
-          - transverse but parallel to each other ()
-          - transverse but perpendicular to each other ()
- Each final pol.state P0,P||,P has transition amplitude A0,A||,A;<B0s|P> = A
-   The < B0s,phys(t) | P > = A(t)  are convolutions of decay and oscillation functions

- CP even

-              _Oscillations_                                 _Intermediate “final” state (J/___                       _Final State_

- CP odd

- CP even

- CP odd

## Slide 36