# Presentation: 005219

## Quark masses and quark mixing parameters – what’s next?

**Marina Artuso **
**Syracuse University**

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## The questions

- What are the values of the quark masses and quark mixing parameters?
- Are they consistent with the Standard Model?
- Within “beyond SM” theory, additional parameters may be pinned down by analyses geared towards CKM determination

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Quark Masses

- This is a good illustration of the interplay between fundamental parameters and QCD.
- QCD effects increase as quark mass becomes closer to QCD scale qcd  0.5 GeV.
- Theoretical tools:
- Lattice
- HQET
- Chiral perturbation theory

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## A pocket guide to quark masses

- Mass hierarchy is a striking feature

- Approximate values (GeV/c2)

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## The heaviest of all: mt

- CDF & D0 combined results

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Is the top quark special?

-  *m**t*  scale of the EW symmetry breaking:
- SUSY: large Yukawa coupling at Planck scale  ***t** (m**t **)* 1
- Higgs a *tt*  bound state? (Bardeen, Hill & Lindner)
- TeV II should bring error in mass determination down to 2 GeV!

- Marina Artuso Snowmass 2001

- July 3rd, 2001

##  mb and mc

- Non perturbative effects are important.
- Quark masses are “running”: important to define the scale at which they are evaluated.
- Pole mass ill defined
- “short distance masses” (potential subtracted,kinetic mass...)
- mq()

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Theory input on mb (sample of a vast literature)

- Important for Vc(u)b

-  expansion, semileptonic decay moments

- Jet observables sensitive to b mass(LEP)

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## mc

- Charmonium data (moments)mc= 1.350.05 GeV
- HQE (short distance definition):

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Quark Mixing

- 

- 

- weak eigenstates             VCKM           mass eigenstates

- Weak interaction couples weak eigenstates, not mass eigenstates: CKM matrix relates these two representations:

- CKM unitary  described by 4 parameters (3 real, 1 imaginary)

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## The CKM matrix in the Wolfenstein parameterization

- Good 3 in real part & 5 in imaginary part
- We know =0.22, A~0.8; we have constraints on  & strategy to pin them down under way

-   d                       s                           b

- u

- c

- t

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## The Unitarity Triangles

- “ds” - indicates rows or columns used
- There are 4 independent parameters, which can be used to construct the entire CKM

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## CKM magnitudes: present data

|   ud:  -decay
0.9739  0.0009 |    us: Ke
0.22000.0025 |  ub: bul &B( )l
 0.0035 0.001 |
| --- | --- | --- |
|  cd: dlcllX
0.224  0.016 |    cs: DKe,W Xc X
   0.97  0.11 |   cb: bcl, BDl
  0.041  0.003 |
|  td: Bd mixing
0.0083  0.0016 |    ts: Bs mixing
 0.04  0.01 |     tb: tbl
0.99  0.15 |

- - measured

- - assuming unitarity

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## In other words:

- We now know  the Wolfenstein parameters:
- A~0.8
- = 0.22
- We are working hard to over-constrain the  plane:
- Precision determination of Standard Model parameters?
- ‘Beyond the Standard Model’ effects
- Check validity of ‘new physics’ effective theories

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## A map of the ‘quark mixing’ hunt

- Improvements on the measurements of the sides will be achieved through the interplay between new precision data available and refinements of theoretical tools
- The angles ******will be determined studying 2-body hadronic  *B*-decays (rare):
*      **B****D***
- Help from (rare) *K* after 2005

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Experimental input

- The goal:
- measure all the **masses** and **mixing parameters** to challenge the Standard Model and find clues towards a more complete theory
- The challenge:
- QCD is the obstacle that nature has put on our “treasure hunt” of these fundamental parameters. We need a better understanding of  hadronic matrix elements to complete our program

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Experimental constraints

- Experimental information:
-  semileptonic decays of heavy flavored hadrons
- m in flavor oscillation of the B(d,s) mesons
- CP violation observables in B decays (*starting now)*
- CP violation observables in K decays
- Rare K decays
- The challenge: extract the fundamental parameters from data (we observe **hadrons**, not **quarks**!)

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Theory input 

**HQET** effective theory is valid when **m****q******
- applications to **exclusive decays**.
**Heavy Quark Expansion**
- application to inclusive properties (decay widths, total-semileptonic-moments of inclusive properties)
**Lattice Gauge Theory**, based on QCD but still on its way to precise calculations (although may be very close, more later..): the first theory to have both statistical and systematic errors!

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Vcb from BD*

- HQET:
-   The shape,       not a clearly predictable quantity, but is constrained by theoretical bounds and measured form factors

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## The parameter FD*(1) 

- Lim  FD*(1) = 1 as mb  ,
- FD*(1)=1+O(s/)+1/m2+1/m3 (no 1/m , Luke’s theorem)
- FD*(1) = 0.91±0.042, from Caprini, Uraltsev.....
- FD*(1) = 0.89±0.06, from Bigi (June 1999)
- Lattice QCD calculation is an important check.
**Jim Simone’s talk @ Lattice99** **F****D*********(1) = 0.935 ±0.035**, some errors not yet evaluated (quenching,cutoff)
- What is the meaning of the theoretical errors?

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## |Vcb| from BD*l

***Study w*****: *********w*****(CLEO)= 0.03; *********w*****(LEP) ********0.07**
**Fit each *****w*****-bin for (*****B************D*************l*********+*****D*************Xl*********+bgds)**
**CLEO limit: ********(slow ********)**
**LEP limit: *****D*************Xl********* level**
- Model of Leibovich, *et al.*
*    *PRD 57, 308 (1997)
- CLEO measures it, sees less

**CLEO 2001**
***F(1)|V******cb******|=*****(42.2 ******** 1.3 ******** 1.8)********10****-3 ********2****=1.61********0.09**

**5% total error on *****F(1)|V******cb******|***** **

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Vcb Exclusive Averages

**When taking out *****F(1*****),**
** ****LEP WG uses **
***  ******F(1*****)=0.88********0.05**
** ****CLEO uses**
**  *****F(1)=*****0.913********0.042**

**  **

**CLEO fits both a**** ****smaller **
***D*************Xl************  *****AND a**** ****larger ********2 ****than **
**LEP, & both are correlated **
**with**** *****F******D*******(1)|V******cb******|***

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## |Vcb| from inclusive  B Xc

- From B(BXcl) extract the experimental decay width:
- Compare with the theoretical prediction from Operator Product Expansion:

- Known phase space factors

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Another parameterization of inclusive semileptonic decays

- Using Operator Product Expansion & Heavy Quark Expansion, in terms of s(mb), , and the matrix elements 1 and 2
- These quantities arises from the differences
- From B*-B mass difference, 2 = 0.12 GeV2

- Marina Artuso Snowmass 2001

- July 3rd, 2001

##   determined from “Moments”

- Prediction on ******, ********1****  **from Lattice QCD** (**Kronfeld & Simone, hep-ph/0006345**.)**
******, ********1**** ****determined from **
- Measured hadronic spectral moments in *b****cl*
- Measured photon energy spectrum moments in *b****s*
- Measured lepton energy moments in *b****cl*
**New, preliminary CLEO data on 1,2 (3 close to be ready too).**

**A.Falk, M. Luke, & M. Savage,  **
**                    ****PRD53 (2491) 1996.**
**M. Gremm & A. Kapustin, **
**                      ****PRD55 (6934) 1997.**
**M. Voloshin, PRD51 (4934) 1995.**

******, ********1**

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## CLEO b sspectral moments

**Measure photon spectrum in lab-frame.**
**Convert to *****B***** rest frame.  MC accounts for smearing**
- Best match ***m******b******= *****4719±115***** *****MeV/*****c******2******; p******F****** = *****378±150 MeV**
**Extract moments (*****E************ > *****2.0 GeV)**

- Preliminary

******E************=2.345 ********0.030 ********0.010 GeV (1.3%)**

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## B Xcl  Hadronic Mass Moments

***B************ X******c************l************  *****Hadronic Mass Moments**

**Lepton (p>1.5 GeV)**
******-reconstruction: *****p*******
**Calculate recoil mass**
**Fit spectrum w/*****B************ ******Dl************, B************ ******D*************l************B ************ ******X******H******l***********(various models for *****X******H*****)**
******M****X****2 ****- M****D****2********, M****D**** is spin-averaged D, D********* mass**
******M****X****2****-M****D****2********= 0.287********0.065 GeV****2**
**2****nd**** moment: 0.63 ********0.17 GeV****4**

******M****X****2 ****- M****D****2******

**Second moments give consistent**
**results, but still theoretically shaky**.

**DATA**
**Fit**
**D**********l*******
**D*****l*******
**X****H*****l*******

- Marina Artuso Snowmass 2001

- July 3rd, 2001

**Notes:**
Width of the average MX spectrum is from our neglect of the last term and the neutrino energy-momentum resolution (~400 MeV?)

Heavy component includes six D** resonances with decay properties specified by ISGW2 form factors. And also includes non-resonant four body states such as B-> D pi ell nu and are decayed according to model of Goity and Roberts. 

## CLEO Vcb from bcl, bs

**Using**
- B(B ***X**c** l *)=(10.390.46)% (CLEO, PRL76 (1570) 1996 )
-  = (1.548 0.032) psec (PDG)
- 0 = (1.653 0.028) psec (PDG)
- f+-/f00 = 1.04  0.08 (CLEO, hep-ex/0006002)
******(*****b************cl*********) = ( 0.427 ******** 0.020 ) ******** 10****-10**** MeV**
**|*****V******cb*****|= (40.5  ********  0.9  ********  0.9  ********  0.8)  ******** 10****-3**** **

******exp**

******,***** ************1 *********exp**

**1/*****M******B*****3**

**3.7% total error**

- Marina Artuso Snowmass 2001

- July 3rd, 2001

##  , 1 from b sB Xclmoments

**moments**

- Preliminary

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## A note of caution 

- Discrepancy between hadronic mass moments and El moments
- Taking Mx estimates only:
-  MB-mb(POLE)= 0.330.020.08 GeV mb=4.97 0.10 GeV
- 1=-0.130.010.06 GeV2

**CLEO**

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Inclusive bcl

** ****5%? common theoretical error**

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## |Vcb| Summary

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## bul

**Similar to *****b**********cl********* BUT *****BR(b**********ul***********) ~ 2********10****-3 ****!**
**Experimentally: few evts, swamped w/ *****b**********cl*******
**LEP expmts use inclusive analysis**
- LEP |*V**ub*| avg has 10% statistical error
- HQE uncertainty (5%) + duality/modeling unc. (12%)
- Systematics from identifying & separating *b**u, b**c*
- Systematics from non-*b**u,***non-*b**c *suppression
**CLEO uses “********-recon.” for *****B **********l**********l*******
- Statistical error of 4%
- Form-factor model uncertainty of 17%

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## |Vub| from LEP using hadronic mass cut

- Analyses of ALEPH, DELPHI & L3
- Look for bu 
- Use likelihood that hadron tracks come from b decay: vertex info, pt....
- Eliminate identified kaons (DELPHI only)
- Mass < MD  b  u some assumption on Mu needed

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Vub from  and 

- Vub from  and 

- 
- 

- bc backrounds

- bu backrounds
- & cross-feeds

- bu backrounds
- & cross-feeds

**CLEO**

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Bd Mixing: md 

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Bs Mixing

***B******s***** too heavy to be produced @ ********(4S)**
** **LEP, SLC, Tevatron
** ****Near maximal mixing observed**
-  *m**s * unlike *B**d*
* *Oscillations not yet definitively seen  due to large frequency; hard to measure
-  Only get lower limit on *m**s*, even when combining all expmts

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## ms World Average

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## sin 2

**sin 2******

**0.34 ******** 0.21   BaBar**
**0.58 ******** 0.34   Belle**
**0.79 ******** 0.43   CDF**
**0.84 ******** 0.93   ALEPH**
**  ****3.2 ******** 2.0     OPAL**
**World Average: 0.48 ******** 0.16**

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## sin 2

**sin 2******

**0.34 ******** 0.21   BaBar**
**0.58 ******** 0.34   Belle**
**0.79 ******** 0.43   CDF**
**0.84 ******** 0.93   ALEPH**
**  ****3.2 ******** 2.0     OPAL**
**World Average: 0.48 ******** 0.16**

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## “95% CL” w/sin2 Constraint

- From A. Hocker, et al. hep-ph/0104062

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## A road map to progress

- milestones in the experimental program
- large data sets accumulated at e+e- b-factories and Tevatron
- large data sets accumulated at dedicated b-experiments at hadron colliders (BTeV-LHCb)
- results from rare K decays
- Milestones in theoretical program:
- Precision unquenched lattice gauge calculations available
- Further checks/refinements in HQE/HQET

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Milestone I ( end of pre-LHC era)

- e+e- b-factories will have a few hundred fb-1 data sets
- sin2 error down to 0.05 (500 fb-1)
- CDF/D0 will have ~15 fb-1
- Better measurements of sin2 from Ks
- Plans to measure ms,
- Unquenched lattice calculations of some key parameters with *O*(few %) accuracy checked by precision charm data (CLEO-c)
- Other QCD based effective theories checked to a few % (CLEO, b-factories)

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Milestone II (BTeV and LHCb)

- Precision studies of Bd,u, Bs
- BTeV projections in **1 year**

| Observable | Precision |
| --- | --- |
| sin2 from BKs() | 0.025 |
|  from B  | <  50 |
| from Bs DsK | <  70 |
| from B DK | <  100 |
| from B K | <  50(+th error) |

- Precision studied for angles, sides can be studied too

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## CKM and quark mass hierarchies

- Observation: both the quark masses and mixing parameters follow a hierarchical structure  exploring this connection may provide some clues to a dynamical origin of masses (H. Fritzsch)
- investigation of the consequences of specific textures of the mass matrices:

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## CKM and quark mass textures- an example

- origin of flavor via spontaneously broken U(2) symmetry Barbieri,Hall,Romanino

- Marina Artuso Snowmass 2001

- July 3rd, 2001

## Conclusion: a glimpse at the new millennium

**The unitarity triangle will be checked**

**The mechanism of electroweak symmetry breaking will be unfolded**** **

**The mystery of flavour will be unfolded**

- Marina Artuso Snowmass 2001

- July 3rd, 2001