# Presentation: 563690

## Measurement of CP Violation and Search for New Physics in BsJ/ Decays with CDF 

- Luis Labarga Echeverría
- C.I.E.M.A.T.- U.A.M.
- 6/05/2008

- Measurement of CP Violation and Search for New Physics in BsJ/ Decays with CDF

- Juan Pablo Fernández Ramos
- C.I.E.M.A.T.
- 24/04/2008

## Introduction

## Beyond the Standard Model

- The search for physics beyond the standard model is pursued through a broad program of physics at the Tevatron
- Direct searches for evidence of new physics (SUSY ?)
- Indirect searches : check internal consistency of Standard Model
- CP violation in B0s meson system is an excellent way to search for new physics
- B-factories have stablished that, at leading order, NP effects, if existing, 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

## 

- It is an ingredient that may help to explain matter-antimatter asymmetry in the universe

- Bs0

- Rate of

- Rate of

- What Is what we measure?

- 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 CP violation?

## CP Violation in the Standard Model (S.M.)

- Described within framework of the CKM mechanism
-      where sinc = 0.23 = |Vus|
- Imaginary terms give rise to CP violation

- CP symmetry is broken in nature by the weak interaction
- Weak interaction Lagrangean is not invariant under CP transformation due to complex phases in mixing matrices that connect up-type with down-type fermions via W bosons

## Unitarity of CKM Matrix

- The S.M. does not fix the values of the CKM matrix elements, but it does imply certain fundamental restrictions that can be conveniently written as angles of unitary triangles (from requiring the CKM transformation matrix to be orthonormal). Two of these angles are the CP violation related and s.
- Can construct six unitary relations

- s  arg[-VtsVtb*/ VcsVcb*]  O(2)
- ~0.02 predicted tiny SM-CP phase!

-   arg[-VtdVtb*/VcdVcb*]= O(1)
-    sin(2)~0.7 [well measured]

- The angles sare related to CP violating asymmetries
- in B decays

- relates to the angle

- non-unitarity would imply contributions from unknown physics

##  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]

## +

- 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 mixing and decay amplitudes

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

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

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

- J/

- => sin (2s)

- -

##  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

## New Physics CPV in Bs0 Decays

- Under the existence of new physics ...
- In Bs0J/, we would measure 2s = (2sSM  sNP) ~ -sNP
- Observation of large CP phase in Bs0J/
- 	 unequivocal sign of new physics (new unknown contribution in the loop process? )

**+**

- unknown flavor structure

## Experiment Overview

## Introduction to the Tevatron

-  Tevatron is the world highest energy accelerator: pp ats=1.96TeV
-  Will take data until Sept 2009 (may be extended 1 year)
-  Expected integrated luminosity : ~ **6 - 7 fb****-1** until 2009
-  CDF has already **3 fb****-1**** **on tape [only 1.3 **fb****-1 **(tagged analysis) /               1.7 **fb****-1 **(untagged) fully analized]

- -

## 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.

## Basics of B Physics at the Tevatron

-  b-quarks produced in bb pairs. Lowest order s2 production:

- -

- -

-  Quarks fragment into hadrons: Bc- (bc), b(bdu), b+ (buu), b- (bdd)        [Tevatron exclusive], Bs0 (bs), B0(bd), B-(bu), also B*, B**, etc
-  Tevatron can be considered as a B factory

- -

- -

- -

- -

- -

- Vcb, Vub from for instance lifetime measurements
- Vtb, Vts, Vtd from for instance mixing and CP violation

-  (*) Extraction of these parameters from weak decay data is complicated by the fact that we do not observe free quarks but rather quarks confined inside colorless hadrons described by QCD

- Many interesting and essential measurements, good complement to e+e- B
- factories  fundamental test of the EW theory

-  The weak decay of quarks inside hadrons depends on fundamental parameters of the SM including elements of the CKM matrix. Studies of these decays leads to info. on (*)

- -

-  High cross section  (**pp**  **bb** ) ~ 40 b at s = 2 TeV

- -

## Online B selection process

-  Huge background to the process  (**pp****bb**) in Tevatron: O(0.05 b)!
-  B hadrons are filtered online using selective triggers based on clear           signatures that overcome the QCD background
-  Our sample is selected by a Joriented dimuon trigger
-    BR(B J X) = 0.5 %;  BR(J6%

- B J X 0.5 %; J6%

- -

- -

- calorimeter

-  chamber

-  stub

-  Central tracker

-  Central track

-  Measurements :
-   Central tracking chamber:
-     - Track momentum
-     - Trajectory
-   Muon chambers:
-     - Trajectory (stub)
-  Require :
-    - Central track
-    - Muon stub
-    - Position and angle match between              central track and muon stub

## Bs0 travels ~ 450 m before decaying into  J/ and   

- 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)
- The sensitivity of the analysis to the CP-violating parameters depends on decay time, CP at decay, and initial flavor of Bs0 /Bs0
- Purpose: disentangle all these features

- _

## 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 (flavor tagging)
- 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)

- -

- CP-even  (*l *=0,2) and CP-odd (*l * =1) final states

## Signal and Lifetime Reconstruction 

## Bs0J/ Signal Selection

- N(Bs0) ~ 2000 in 1.35fb-1

- 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 and PID

## Bs0 Lifetime Reconstruction

- Bs0 Lifetime Reconstruction

-  Peak at 0 comes from prompt
-   J/(main source: Drell Yan)
-  Long lived tail is mostly our          Bs0J/ Signal

- Phys. Rev. Lett. 100, 121803 (2008)

## Angular Analysis of Final States

##   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 ()
- {A0,A||,A}: transition amplitude  < B0s | P > to each final state {P0,P||,P}
- {A0,A||,A}: transition amplitude  < B0s | P > to each final state {P0,P||,P}
-  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

**_**

**_**

## cos(

- cos(

- 

- cos(

- Transversity Angles
- (corrected for detector sculpting)

- The analytical relationships are detailed next ...

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

- A.S.Dighe, I.Dunietz, H.J.Lipkin, J.L.Rosner; EPJ C6  (1999) 647

## 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

##   Cross check sample: B0  J/( ) K*0(K)

-        c = 456 ± 6 (stat) ± 6 (syst) m
- 	|A0(0)|2  = 0.569 ± 0.009 (stat) ± 0.009 (syst)
- 	|A||║(0)|2 = 0.211 ± 0.012 (stat) ± 0.006 (syst)
- ║ = 2.96 ± 0.08 (stat) ± 0.03 (syst)
- 	 =    2.97 ± 0.06 (stat) ± 0.01 (syst)
- Results are in good agreement with Belle and BaBar results and errors are competitive !

- |A0(0)|2  = 0.556 ± 0.009 (stat) ± 0.010 (syst)
- 	|A║(0)|2 = 0.211 ± 0.010 (stat) ± 0.006 (syst)
- 	║ = 2.93 ± 0.08 (stat) ± 0.04 (syst)
- 	 =    2.91 ± 0.05 (stat) ± 0.03 (syst)

- Phys. Rev. D 76, 031102 ( 2007 )

-   Cross check sample: B0  J/( ) K*0(K)
- High-statistics test of angular efficiencies and fitter

- No width difference ( = 0)

- http://www-cdf.fnal.gov/physics/new/bottom/070830.blessed-BdPsiKS

## 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....

- -

## Overview of Flavor 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)

- opposite side

- same side

## Quantifying Tagging Power

- The statistical power of the tagging is quantified by  <D2typically 4.5 % as detailed next.

- The tagging of an event can be
- f Right Sign (RS) if assigned “sign” = true “sign” (B0s or B0s)
- of Wrong Sign (WS)
- Inconclusive (NT)

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

- -

## Opposite Side Flavor Tagging (OST)

- -

- -

- Tagging in the opposite side identifies the flavor of the other    B-hadron produced in the event's final state.
- Submethods

- Lepton tagging (SET,SMT): searches lepton (either an electron or a muon) in the other side coming from the semileptonic decay of the other B. The charge of this lepton is correlated with the flavor of the B hadron. E.g.: a l comes from a transition b-> q l     (i.e.,   a B0 ,B0s meson or a B-)
- Jet charge tagging (JQT): exploits the fact the sign of the sum of the charges (weighted by their momentum) of the jet is the same as the b quark that produces that jet.

## Input to the Dilution function:  

- Input to the Dilution function:
- JQT: total jet charge (track-pT weighted)
- SET, SMT: PID likelihood  pTrel

- Where the “low” Dilution comes from? :     - some OS b outside acceptance region
-   - detector reconstruction effects
-   - fragmentation effects in the JQT
-   - b  c transitions in SET and SMT
-   - B oscillations
-   - others

-  = 96  1%
-  √<D2>= 11 2 %
-  <D2> = 1.1 %

- B0s , B0s  sample

- _

## Same Side Kaon Tagging (SST)

- Among candidate tracks:
-       1. close to B meson
- R =  < 0.7
-       2. pT > 350 MeV/c
-       3. coming from PV: |d0 /| < 3
-    choose the one with highest NN prob. output (based on pLrel ,pTrel rel. to         **p****B**** + p****track** direction & particle ID)

- Tag on the leading fragmentation particle
- (LPF); in a B0s event is almost always a Kaon

- Same Side Kaon Tagging (SST)

- B+ or B0 can not be used to calibrate since
- there the LFP is with large probability a 

- Where the Dilution comes from ? :
- - detector reconstruction effects
- - fragmentation fluctuations
- - PID limitations
- - others

- - need to rely on MC                                 - cross checked in mixing (B0s  Ds+ )
- - particle ID by ToF and dE/dx helps

- B0s , B0s  sample

- _

-  = 50  1%
-  √<D2>= 27 4%
-  <D2> = 3.5 %

## 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 factorized in:

*f**s* : signal fraction (fit parameter)

## Ps(m|m) : Gaussian N(m,m)        

*P**s**(m*|***m**) *: Gaussian N(*m,****m*)
*P**b**(m) *:  1st order polynomial

- Measured quantities that enter in the fit and their probability function (I)
- reconstructed mass of Bs0 ,Bs0 and its error, decay time and its error, transversity angles, flavor tag decision, dilution D

- Mass: discriminate signal against background

## -

- reconstructed mass of Bs0 ,Bs0 and its error, decay time and its error, transversity angles, flavor tag decision, dilution D

- Angles:                             Separate CP-even from  CP-odd final states

- ={-1,0,+1}: tag decision
- D: event-per-event dilution
- (****): detector effects obtained from MC
****

- Decay-time:                      Lifetime of each CP and  flavor state

- convolve time dependence with Gaussian proper time resolution function with mean of 0.1 ps and RMS of 0.04 ps

- Bs0

- Bs0

*P**b **( t | ****t **) *: delta function at t = 0 + one (two) exponentials for
-                    t < 0 (t > 0)  Gaussian resolution function

*P**b **(****) = P**b**(cos ****T**) P**b**(****T **) P**b**(cos** ****T **) ;* *P**b*’s from sidebands events

- _

## Measured quantities that enter in the fit and their probability function (III)

- TTagging :  flavor of initial state

- reconstructed mass of Bs0 ,Bs0 and its error, decay time and its error, transversity angles, flavor tag decision, dilution D

##  Parameters in 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

-  1. Untagged analysis (do not use information on                production flavor)                 arXiv:0712.2348; PRL 100, 121803 (2008)
- and
-  2. Tagged analysis                     arXiv:0712.2397, accepted by PRL
- sconfidence region
-     s confidence interval
-          (quote results with and without external theory constraints)

## Untagged analysis

-  Dependence on production flavor cancels out

-  Suited for precise measurement of width-difference and average lifetime (maximum sensitivity obtained when assuming a given value for s)
-  Marginally sensitive to CP-violation

## Untagged analysis: results

- Bs0 mean lifetime and width difference
*(CP conservation assumption: 2****s** = 0) *
-  = 1/ = 2 / (L+H) =ps
- L- ps-1(best measurement to date )

- picture consistent with SM expecteation

- Phys. Rev. Lett. 100, 121803 (2008)

## Untagged analysis: results

- Due to symmetries in the likelihood 4 solutions are possible in (2s- plane; in particular can not determine simultaneously the sign of 2sand 

- (2s , ) confidence region

- Marginal sensitivity to CP violation

- P region by= || cos s

- where |12|= 0.048  0.018

- A.Lenz, U.Nierste JHEP 06, 072 (2007)

## Tagged analysis

-  Likelihood expression has double minima due to symmetry
-    2s   – 2s ,    –║  2 – ║     – 

- s- Likelihood profile

- Likelihood function non gaussian
- There is no parabolic minima can’t quote point estimate!
- Quote confidence region

-  Study effect of tagging using
-    pseudo-experiments
-  s → -s no longer a symmetry

- using profile likelihood ratio ordering with rigorous frequentist inclusion of systematic uncertainties (a la Feldman-Cousins)

## 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.

- Exclude a given s- pair if it can be excluded for any choice of the 20+ nuisance parameters within 5 of their estimated values. This corresponds to evaluating a 27-dimensional confidence region (in all physics and nuisance parameters) and then project it into the 2-dimensional space of interest.

## 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 15%, corresponding to 1.5

- strong phases
- can separate
- the two minima

- Confidence region with profile-Lilkelihood Ratio ordering and rigorous frequentist inclusion of systematic uncertainties.

- arXiv:0712.2397

## s 1D Intervals

-  treated as a nuisance parameter
- 2s   [0.32, 2.82] at 68% CL
- Constraining |12|= 0.048  0.018 in  = |12|cos s ,
- ,  from BaBar's B0  J/ K*0 and on equal B0s and B0 lifetimes
- 2s   [0.40, 1.20] at 68% CL

- A.Lenz, U.Nierste JHEP 06, 072 (2007)

- PRD 76, 031102 (2007)

- Constrain strong phases

- Constrain lifetime and strong phases

## DØ Results

-  DØ 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                   constrained result
- 	2s Є [0.40,1.20] @ 68% CL

- DØ Results

- t would be great if DØ  would show that this number
-  and its uncertainty have the coverage properties desired.

## Future

-  Shown results 1.3 fb-1, but 3 fb-1 already on tape to be analyzed soon
-  Expect 6-8 fb-1 by the end of the run 2
-  Analysis to be improved and optimized:
-      - ~30% statistics from other triggers
-      - better flavor tagging
-      - signal optimization based on
- 	expected statistical errors
-  If s is indeed large CDF results
-     (together with the other experiment
-     DØ) have good chance to prove it
-  CPV in Bs system is one of the main topics in LHCb B Physics program
- → will measure s = -2s with great precision

## Conclusions

## Conclusions 

-  Significant regions in s space are ruled out
-  Best measurements of Bs decay width difference and of the best lifetime measurements
-  Both CDF and DØ observe 1-2 sigma s deviations from SM predictions
-  Interesting to see how these effects evolve with more data

- Conclusions

## Back up

## CDF and D0 plan to make a more appropriate “internal combination” for the near future

- _[http://arxiv.org/pdf/0803.0659](http://arxiv.org/pdf/0803.0659)_

- UTFit collaboration has done first attempt to combine results and claim a 3 deviation
- from SM expectation:

## Difference in direct CP violation between charged and neutral B meson decays BELLE; Nature 452(2008)332

_**Difference in direct CP violation between charged and neutral B meson decays**_** ****BELLE****; Nature 452(2008)332**

## 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

## 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