# Presentation: 778182

## Bs properties: Ms, s & s

- Avdhesh Chandra

_***for the  CDF and D***__***Ø collaborations***_

**Lattice QCD  Workshop 2007, Fermilab**

**Measurement of B****s**** properties helps in constraining unitary triangle and hence new physics.**

**In SM quark mixing (Q****2/3******** Q****-1/3****) is given by CKM matrix**

**  **

**Unitarity triangle equation for b-quark**

**Unitary Triangle for B****s**

## Bs  Mixing

**Schrödinger Equation:**

**b**

**s**

******b**

******s**

**M****12**** stems from the real part of the   box diagram, dominated by top**
******12**** stems from the imaginary part, dominated by charm**

**Diagonalization gives two physically observed “Light” and “Heavy” mass eigenstates**

**CP even**

**CP odd**

**B****s  ****Mixing**

***i.e.***** no CP *****violation***

**‘****squashed’ triangle ******** ‘flat’ triangle**

## Physical Quantities

** ********s**** = *****arg*****(-M****12****/********12****) ;   CP violation phase**
** ********M****s**** = M****H**** - M****L**** = 2|M****12****| ;   frequency of B****s****-********B****s**** oscillations**
** ********s**** = ********L**** - ********H**** = 2|********12****|cos********s**** ;   decay width difference**

**    ****Three physical quantities; **** M****12**** , |********12****|  and *****arg*****(-M****12****/********12****)**

**Other useful quantities:**
**a****fs**** = *****Im*****(********12****/M****12****) = (********12****/M****12****)sin********s**** = (********s****/********M****s****)tan********s**** ;   semileptonic CP asymmetry**
**A****mix****CP****(B****s********(J/********)****CP********)**** = ******** sin(-2********s****) ;   mixing induced CP asymmetries  **
**A****0**** A****||**** A******** ****; Linear**** polarization amplitudes in B****s********J/******** ******
******0**** ********||**** ************ ****; CP-conserving strong phases , *********i****** ********* *****arg*****(A*****i*****)**

**In recent years there is a big improvement in theory prediction of ********M****s**** , ********s**** & ********s**

**Physical Quantities**

**We can extract all the elements of mixing matrix, and other physical quantities, describe B****s**** system**

## For New Physics

******M****s**** = ********M****s****SM**** |********s****|  = (19.30 ******** 6.74)ps****-1****.|********s****|**
******s**** = 2|********12****|cos(********s****SM**** + ********s********) **
**       ****= (0.096 ******** 0.039)ps****-1****. **
**                        ****cos( (4.2 ******** 1.4).10****-3**** + ********s********) **
**...****. and others**

******s**** = (0.096 ******** 0.039) ps****-1**
******M****s**** = (19.30 ******** 6.74) ps****-1**
******s**** = (4.2 ******** 1.4).10****-3**

**a****fs**** = (2.06 ******** 0.57).10****-5**
******s****/********M****s**** = (49.7 ******** 9.4).10****-4**

**Theory Predictions**

**For New Physics**

**where**

***Im***** ********s**

***Re***** ********s**

**Note, angle ******** of the unitary triangle in B****s**** system;   ********s****=(2.0 ******** 0.5).10****-2**

**For SM ********s**** = 1;  while ********s******** ****is a physical CP phase**

_***hep-ph/0612167v2***_

******M****s**

******s****/********M****s**

**a****fs**

## The CDF & DØ Detector

**High tracking efficiency:**
**95%  |********| < 3**** (Silicon disks) **

**Excellent tracking & mass resolution**
**Silicon  |********| < 2**** , 90 cm long**
**96 layer drift chamber 44 to 132 cm **

**Triggered   Muon coverage**
** ****p****T**** > 1.5 GeV,   |********| < 1**

**Low  p****T****  Muon identification   **
** ****p****T**** > 1.5 GeV,   |********| < 2**

**The CDF & DØ Detector**

## Mixing frequency Measurement

**Mixing frequency Measurement**

## Overview

**For ******** = 0**

**One needs three ingredients:**
** ****B****s**** flavor at decay**
** ****B****s**** flavor at production**
** ****Good proper decay length resolution**

**Transverse decay length**

**Proper decay length**

- Tagging efficiency

- Proper decay length resolution

- Signal

- Background

- Dilution

**lepton**

**frag**

**PV**

**jet**

**B hadron**

**K**

**frag**

**B****s**

**K**

****

**D****s**

**SV**

***b***

*********b***

**L*****xy***

**Overview**

## DØ Bs candidates 

**Fully reconstructed hadronic and partially reconstructed hadronic and semileptonic B****s**** decays from ~2.4 fb****-1**

**44777**
**1663**
**249**
**18098**

**Decay Channels**

**N****sig**

**DØ B****s**** candidates **

**D****s****+ ****invariant mass**

**B****s****0 ****invariant mass**

**hadronic mode**

**D****s****+ ****invariant mass**

**semileptonic mode**

## CDF Bs candidates 

**From 5600 fully reconstructed hadronic, 3100 partially reconstructed hadronic, and 61500 partially reconstructed semileptonic B****s**** decays of ~1.0 fb****-1**

**CDF B****s**** candidates **

**semileptonic mode**

## Proper decay length resolution

******ct ****event by event, with scale factor**
** ****For partially reconstructed decays  **

**K from MC, for each decay channel**

**Proper decay length resolution**

## Initial state flavor tagging

**Opposite to reconstructed B****s**** side (due to b ,********b produciton)**

**On reconstructed B****s**** side (due to correlation between B****s**** flavor and the charge of fragmentation K)**

**Combine OST and SST if both present**
**Assume both independent**
**Combine SST and “Event charge” if both present  **
******q****i ****of all tracks on opposite side **
**Total: ********D****2**** = 4.5%**

** ****Using both opposite side and          same side**
** ****NN combination of the opposite side jet charge , kaon and lepton tags: ********D****2**** = 1.8 %**
** ****NN kinematic and identification variables of the kaon candidate, for same side tag ********D****2**** = 3.7% (had.) , 4.8% (semilep.)**

**Initial state flavor tagging**

**DØ **

**CDF **

## DØ Ms result 

**A parabolic fit to likelihood scan for ********Ms returns:**
**********M****s**** = 18.5 ± 0.9 ps****-1**
**3.1******** statistical significance**

******M****s ****(ps****-1****)**

**Combined amplitude scan**

**Sensitivity : 27.3 ps****-1**

**DØ ********M****s**** result **

## CDF Ms result 

******M****s**** = 17.77 ******** 0.10 (stat) ******** 0.07 (syst) ps****-1**** **
** ****5.4******** statistical significance**

**CDF ********M****s**** result **

## s & s from J/  

******s**** & ********s**** from J/******** ******** **

## Angular Distribution 

**B****s **** ********  V1 + V2 (J/******** + ********)   i.e.            Spin    0  ********  1+1        L= 0,1,2   **
** ****L = 0 and 2 corresponds to CP even;    L=1 CP odd**
**Angular distribution can be written in helicity basis , ****BUT****    generally ****Transversity basis is used to write angular distribution , where polar coordinates are defined in ****“J/******** rest frame”****  and  ****“******** rest frame”**

**Polarization Amplitudes**

**Angular Distribution **

## Polarization Amplitudes 

**Upper sign corresponds to:**** ****Time evolution of pure B****s****0**** ******** J/******** ******** ****at t=0**
**Lower sign corresponds to:**** ****Time evolution of pure********B****s****0**** ******** J/******** ******** ****at t=0 **

_***hep-ph/9804253  &  hep-ph/0012219***_

**Polarization Amplitudes **

** ******** ******** ****average decay width of  two physical eigenstates**
******1 ********2 ******** ****CP-conserving strong phase ; ~ |********| and 0**
**A****0****(0) , A****||****(0) ********CP-even linear polarization amplitude at t=0**
**A********(0) ********CP-odd linear polarization amplitude at t=0**

## For untagged 

**Adding up for all    B****s****0****   and  ********B****s****0**

** ****Assuming equal production rate of B****s****0**** and********B****s****0**** in *****p –************p***** collisions**
** ****All opposite terms go away;    Insensitive to ********M****s**** , but sensitive to ********s**

**For untagged **

## Results (no CP violation) 

**456 ******** 13 (stat) ******** 7 (syst)**

**Results (no CP violation) **

**454 ******** 21 (stat)       (syst)**

**0.12 ******** 0.09 (stat) ******** 0.02 (syst)**

**c********s ****(in ********m)**

******s  ****(in ps****-1****)**

******s********0**

## Results (s free)

******s**** = -0.79 ******** 0.56 (stat)         (syst)**

**Results (********s**** free)**

** ****above are close to SM values**
** ****results have 4-fold ambiguities**

** ****no numerical values are given**
** ****90 & 95% confidence curves are shown**

## Angular fit projections

**Angular fit projections**

## Semileptonic charge asymmetry

**Indirectly from time-integrated di-muon charge asymmetry**
**                            ****0.0064 ******** 0.0101**
**Directly from time-integrated charge asymmetry from B****s**** ******** ********D****s**** **
**                                   ****0.0245 ******** 0.0193 ******** 0.0035 **
**Combining above two measurement ****               **
**                                    ****   ****0.0001 ******** 0.0090**

**For measured value of ********M****s **
******s**** tan********s**** = 0.002 ******** 0.160 ps****-1**

**Semileptonic charge asymmetry**

## Constrained DØ results 

******s**** = 0.13 ******** 0.09 ps****-1**
******s**** = -0.70 **

**Constrained DØ results **

## Summary of numbers 

**17.77 ******** 0.10 ******** 0.07**

**18.56 ******** 0.89**

******s**** (in ps****-1****)**

**0.076         ******** 0.006**

**0.13 ******** 0.09**

******s**

**-0.70**** **

**Summary of numbers **

**DØ**** **

**CDF**** **

**Results are consistent with SM**

## Room for new physics 

**Room for new physics **

**Using measured values of ********M****s**** , ********s****, |********s****|/********M****s**** and a****s****fs**

**Still room for new physics, updated results will be important for existence of any deviation from SM ****stay tuned!**

***Im***** ********s**

***Re***** ********s**

******M****s**

******s****/********M****s**

**a****fs**

**Theoretical**

## Updated measurement with ~ 2 times data

Flavour tagging to BsJ/
 Relatively small error on physics parameters  (specially s)
 Helpful in resolving ambiguities

Required
 Better understanding of similar physics parameters from other source so BsJ/ can be benefited for example by BdJ/K* 
 Fixing strong phases from BdJ/K*

- Flavour tagging to BsJ/
** ****Relatively small error on physics parameters  (specially ********s****)**
** ****Helpful in resolving ambiguities**
- Required
** ****Better understanding of similar physics parameters from other source so B****s********J/******** can be benefited for example by B****d********J/********K* **
** ****Fixing strong phases from B****d********J/********K***

**Coming Soon... **

## Additional   Slides

## Amplitude Scan 

**Scan ****Δ****M****s****, for each value find**
** **
**                     **
**If sample frequency is ****Δ****M****s**** amplitude           **
**   ****otherwise **

**Amplitude Scan **

## un

**un**

**Large uncertainty cancels out**

**Bag parameter**

**Weak decay constant**

**From QCD **