# Presentation: 367777

## Title page

**CKM Matrix **
**Element **
**Magnitudes**

- K. R. Schubert, TU Dresden
- XXI Lepton - Photon Symposium
- Fermilab, 12 Aug 2003

- St. Model origin, invariants, and parametrisations of VCKM.
- |Vud|, |Vus|, |Vcd|, |Vcs|1 : Unitary?
- |Vcb|, |Vub|, |Vtd|, |Vts|, |Vcs|2 : Unitary? CP-violating?
- Parameter values without and with (K0) and sin2
- Many averaged results are my private guesses,
- many references will only be given in the later write-up of this talk.

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Yukawa Structure of the St. Model

- C(u)  and C(d) cannot be diagonalised simultanuously since Glashow
- married uL and dL into doublets. The difference of the two
- „rotations“ in family space which diagonalize C(u)  and C(d) is VCKM.

*V  *was introduced 1973 by M. Kobayashi
- and T. Maskawa; is called *V*CKM  since
- 1987 in recognition of N. Cabibbo 1963.
- St. Model allows arbitrary C(u)  and C(d)  ****** **
- Standard weak interaction is not CP-invariant.

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Invariants of the CKM matrix

- In ÕSt.Model,  (u and  (darbitrary  *V* not observable,
- Observables are, i. e. invariants under phase transformations
- 	     1)
-          	     2)
-          3 et al.)

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Slide 4

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vud

- Three sources:
- Super-allowed nuclear +-decays
- - decays of polarized neutrons
- + decay of the +

- K. R. Schubert, Seminar at LBL

- 26/7/00

## - decays of polarized neutrons:

- V and A transition because of 1/2+  1/2+. GV = GF |Vud|,
- but jA only partially conserved. Determine GA/GV  = experimentally!

- K. R. Schubert, Seminar at LBL

- 26/7/00

## 

- PDG 2003:  = -1.2695  0.0029
- (S = 2.0). n = (885.7  0.8) s

- |Vud| n = 0.9741  0.0020

- |Vud| Nucl = 0.9740  0.0005

- PERKEO-II (Abele 03, corrected) alone:

**SKY**

** ****P        A/A****raw ****- 1**
**0.989****	****0.02**
**0.97****	****   -**
**0.98****	****0.15**
**0.70****	****0.30**
**0.98****	****0.13**

- |Vud| n = 0.9717  0.0013

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Summary of Vud:

- _Prospects:_ PIBETA will not reach competitive precision, 0.0030 ?
- (Vud,Nucl) dominated by radiative corr.
- (Vud,n) dominated by experiment. New experiments are underway,
- PERKEO 03, „new PERKEO“ 05 , LANL, SNS, Gatchina/PSI
- _My average:_ (1) + (3) + (4) with S =1.3  

- |Vud|  = 0.9737  0.0007

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vus

- _Sources:_ Old Kl3 decays, new Kl3 decays,
- hyperon -decays,  decays

- K. R. Schubert, Seminar at LBL

- 26/7/00

## BNL-E865:  Aim K+  ++e-. Dedicated run for K+  0e+e during 

- New theoretical inputs
- increase Vus by + 0.2%  0.2%
- V. Cirigliano 2003:

- |Vus| old Kl3 = 0.2201  0.0024

- _BNL-E865:_  Aim K+  ++e-. Dedicated run for K+  0e+e during
- one week 1998, 0  e+e-Normalised to K+  +0, +00. Result:
-            BF(K+  0e+e) 	= (5.13  0.02  0.09  0.04)%
- 			= (1.053 0.024) **. **BF(old), 2.2
- =+(old)

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vus 3

- |Vus| Kl3,old = 0.22010.00160.0018
- |Vus| E865   = 0.22850.00230.0019
- using Cirigliano‘s f(0)(1+),
- 3.0  higher than old K+K0 average

- |Vus| Kl3,old+E865  = 0.2220  0.0019 (S=1.5)  0.0018

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Tau decays:

- Using ALEPH data and ms(2 GeV) = (105  20) MeV, Gamiz et al find
- Dominant error is experimental. Better measurements of rates
- _and mass moments_ would give _both_ ms and |Vus|.

- _Tau decays:_

- |Vus|  =    0.2179  0.0044exp  0.0009th

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vcd

- Old source: Production of dimuon
- pairs by neutrinos on nuclei

- = (0.41 **** 0.07) %                CDHS 1982

-  ***B**** *= 0.099 ****** **0.012    

- |Vcd| = 0.224  0.016

- with ***B*** = ***BF***(c +X):

- _Prospects:_ CLEO-c

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vcs

- Sources: (1)  decays of D mesons and
- (2) decays of real W ****

- Constituent quark models and QCD sumrules:
- f(0) = 0.7  0.1

- |Vcs| = 1.04  0.16

- 

- D+  K0 e+Ą and D0  K - e+Ą:

- 2nd method, much more precise, needs 3rd quark family,
- will be discussed later.

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Unitarity check of the udsc matrix:

- Inputs:	|Vud|  = 0.9737  0.0007
- 	|Vus|  = 0.2210  0.0023
- 	|Vcd|  =   0.224  0.016
- 	|Vcs|  =     1.04  0.16

-              |Vud|2 + |Vus|2 	=  0.9969  0.0017	 -1.8 
-                 |Vcd|2 + |Vcs|2  	=      1.13  0.33	+0.4 
-                 |Vud|2 + |Vcd|2 	=  0.9983  0.0073	 -0.2 
-                 |Vus|2 + |Vcs|2  	=      1.13  0.33	+0.4 
-         |VudVcd| - |VusVcs| 	=  - 0.012  0.039	  0.3 
-         |VudVus| - |VcdVcs| 	=  - 0.018  0.040	  0.4 

- K. R. Schubert, Seminar at LBL

- 26/7/00

## = 0.2235  0.0033

- (  1.5 % )

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vcb

- Primary  information:
-  0.8%
- data from ALEPH, BABAR, BELLE, CDF, DELPHI, L3, OPAL, SLD
- Next information: ***BF***(B  lX)

- Source: Inclusive and exclusive
- semileptonic B-meson decays
- _Inclusive decays:_

- HFAG
- 07/03

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vcb 2

- 10.90  0.23

- Integral over spectrum  **** ***BF***,
- 98% b  c, 2% b  u,   *BF*(Vcb) = 1.1%, (Vcb) = 0.4%.

-                  h X  h l- ÅY
-                         l+X
-                            
- e+e-  (4S)  B sig B tag
-                                    
- Spectrum of        l- ÅX or Breco
- signal leptons:

**BELLE 5/fb**
**e****sig ****(e+********)****tag**

- 1982 spectrum given by ACCMM model, d/dpl = f(mb, mc, pF, s).
- Vcb with (Vcb)  10%. Today QCD, i.e. HQET and OPE:
- mb  «, pF  1, mc  substituted, and more parameters 2 , i i ...

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vcb 3

- Of special
- interest are
- the moments
- Mijk of *f .*   M000 :
- Bases are duality, HQET, OPE. _Local duality_ predicts results for more
- low moments like <mX2>= M100/M000, <(mX2)2>= M200/M000,<El>= M010/M000
- Comparing measurements and calculations of „low“ Mijk tests goodness
- of local duality and expansions, and determines 1, «, |Vcb|...
- OPE and duality are not valid „too locally“, i.e. „high“ moments and
- the full d3 are not determining 1, «,|Vcb|...

- HQET gives:

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Moment measurements:

- 				     CLEO, DELPHI, BABAR
- _DELPHI_ 2003 determines Mi00 by reconstructing B  D** levents
- from 34 M Z at LEP. <mX2 - mD2> = (0.6470.0460.093) GeV2,
- 		    Also results for M200, M300
- 2002 they obtained <El> = (1.3830.012 0.009) GeV, also M020, M030.
- They fit in two mass schemes,
- with MS scheme:
- With kinetic scheme:
- |Vcb| = 0.0429 (10.012sl0.019fit 0.010th)
***BF***(B  lX) readjusted to 10.9%

- _Moment measurements:_

- K. R. Schubert, Seminar at LBL

- 26/7/00

## CLEO 2001 results:

- full mx,El,q2 space, El*Different for CLEO and BABAR.
- 		   		     from El spectrum,

- _CLEO 2001 results:_

- |Vcb|(*) = 0.0414 (10.012sl
-              0.022fit 0.020th)
- (*) ***BF***(B  lX) re-adjusted to 10.9%

- |Vcb|(*) = 0.0418 (10.012sl
-               0.012fit 0.022th)
- No combined fit performed.

- <mX2 - mD2> (El >1.5 GeV ) 	      M010 (El >1.5 GeV) and
- =(0.2510.0230.062) GeV2	      M000 (>1.7 GeV) / M000 (>1.5 GeV)
- and <E> from b s

- K. R. Schubert, Seminar at LBL

- 26/7/00

## BABAR 2003 results:

- _BABAR 2003 results:_

- Moments M100 with
- El > 0.9 ... 1.6 GeV,
- obtained from 89 M BB
- with Btag fully reconstructed,
- e and in Bsignal, El > 0.9 GeV.
- mX,signal from fit to pmiss and mobs
- <mX2>  <mX2> using MC:
- 			       Obtained
- 			       moments
- 			             M100 :

- ~

- ~

- Very small
- model
- dependence!

- K. R. Schubert, Seminar at LBL

- 26/7/00

## CLEO 2003:

- BABAR fits HQET parameters
- in 3 schemes, here pole mass  ****
- quotes |Vcb| from 1S scheme:
- 0.0421(10.025exp 0.017th)

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Summary Vcb inclusive:

- Moment measurements
- of
- and HQET/OPE offer the potential
- to determine |Vcb| with  < 2%.
- _Duties for experiment:_
- Identify inconsistency areas.
- _for theory:_ Identify best scheme
- (1S ?), get terms with s/mb2
- and more 1/mb3 and s2 terms ...

- |Vcb|incl = 0.0429 (1  0.012sl  0.019fit  0.010th)	DELPHI, kin
- 	 0.0414 (1  0.012sl  0.022fit  0.020th)	CLEO m, pole mass
- 	 0.0418 (1  0.012sl  0.012fit  0.022th)	CLEO E, pole mass
- 	 0.0421 (1  0.025exp  0.017th)		BABAR, 1S
- My average:

- Ellipses
- with 1,
- exp. only

- |Vcb|incl = 0.0421  0.0013  (3.0%)

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Exclusive Vcb determination:

- _Exclusive V_cb_ determination:_

-                                                            from
- new results submitted to LP03 by DELPHI and BABAR
- both with full reconstruction
- DELPHI 3.4 M Z, 1688 ev. (e+),  BABAR 86 M (4S), 55700 (e+)
- Delicate background from D**.
- DELPHI uses hemisphere and
-    vertex separation to identify
-    extra tracks from Bsig
- BABAR uses cos **B,D*l**

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Advantage of BABAR: less background,

- of DELPHI: large acceptance also at q2max, i.e. w = 1. _Results:_

|  | DELPHI | BABAR |
| --- | --- | --- |
| 103|Vcb|.F(1) | 39.21.82.2 | 34.00.21.3 |
| A12 | 1.320.150.33 | 1.230.020.28 |
| BF(B0D*l)% | 5.900.220.48 | 4.680.030.29 |

- ~2  discrepancy

- e

- w 

- 1

- 1.5

- q2 

- 0

- 10 GeV2

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Summary for Vcb:

- _Summary for V_cb_:_

- ndof
- 

- |Vcb|**.**F(1) = 0.0367  0.0013 (S = 1.7)
- F(1) = 0.913             HQET                    |Vcb|incl =   0.0421  0.0013

- +0.030
- - 0.035

- |Vcb| = 0.0415  0.0011

- |Vcb|excl** **= 0.0402  0.0020

- K. R. Schubert, Seminar at LBL

- 26/7/00

## A 2 = 0.0415  0.0011

- (  2.7 % )

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vub

- _Source:_ Inclusive and exclusive
- semileptonic B-meson decays
- into charmless final states

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vub excl Babar

- _BABAR 2003:_
- B0  -e+
- B+  0e+
- high - El: 2.3-2.7 GeV
- low - El: 2.0-2.3 GeV
-        signals for -  ****

- Signal
- Crossfeed
- Downfeed
- bcl
- continuum
- is already
- subtracted

- K. R. Schubert, Seminar at LBL

- 26/7/00

## CLEO 2003:

- Detector hermeticity  „ reconstruction“
-  q2 and El >1.0 GeV (), >1.5 GeV ()
********Signals
- in q2 bins ****
- 			   white = signal
- 			   red = crossfeed
- 			   yellow = downfeed
- 			   green = continuum
- 			   black = bcl

- 0

- 

- 

- 

- 

- K. R. Schubert, Seminar at LBL

- 26/7/00

## CLEO

**CLEO**

**CLEO**

- 103 |Vub|

- 103 |Vub|

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Inclusive decays b ul

- from
- HFAG
- LP03

- new

- new

- Three methods
- 1)  El > 2.3 GeV, „endpoint“
- 2)  El > 1.0 GeV
-      and mX < 1.5 GeV,
-      requires tagged B,
-      less QCD-dependent.
- 3)  El > 1.0 GeV
-      and mX < 1.5 GeV
-      and q2 >12 GeV2,
-      requires tagged B
-      and high statistics.
-      needs even less QCD.

**10****3**** ****|V****ub****|**

- K. R. Schubert, Seminar at LBL

- 26/7/00

## BELLE:

- 29 M(4S),
- (a) BeX
- (b) continuum
- and bc subtracted
***BF ***(B eXu) = ***BF ***(2.3 < El < 2.6 GeV) / fu(CLEO)
- |Vub| = (3.99  0.17stat  0.16sys  0.59th) 10 –3

- (a)

- (b)

- K. R. Schubert, Seminar at LBL

- 26/7/00

## mX Result of BABAR:

- 89 M(4S), 32 k events with
- (4S) BrecoBsig, El >1 GeV, Breco ****
- reconstruct mX in Bsig lX  ****

- Using the shape function 
-                 |Vub| = (4.62  0.28stat  0.27sys  0.40shf   0.26Vub) 10 –3

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Summary for Vub,incl:

- _Summary for V_ub,incl_:_

- |Vub|incl = (4.26 **** 0.13 **** 0.50) 10 –3

- No discussion of mX-q2 method here.
- Best prospects in the future because
- of smallest dependence on HQET
- parameters. Take them from Vcb data?
- HFAG does not yet present an average for |Vub|incl.
- My weighted inclusive mean:

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vtd

- Source: md of B0B0 Oscillations

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vts

- |Vts|**.**|Vtb| > 0.033

- from
- HFAG
- LP03

- from BsBs oscillations
- and b  s penguins
- ms >0 since s = (- fdd)/fs > 0.
- ms >14.4/ps (95% CL)   ****

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vcs again

- was 1.04  0.16
- using ( D  Ke)

- Decays of real W-bosons at LEP-2 increase precision:
- only using that there are five quarks with m(q) < m(W) 

- |Vcs| = 0.995 ± 0.014

- _Prospects:_ Check by CLEO-c

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Unitarity check of the full CKM matrix:

-           |Vud|2 + |Vus|2 + |Vub|2	= 0.9969 ± 0.0017	 -1.8 
-           |Vcd|2 + |Vcs|2 +  |Vcb|2	=   1.042 ± 0.029	+1.5 
- |VudVcd | - |VusVcs| ± |VubVcb|	= - 0.002 ± 0.016	  0.1 

- |Vud| = 0.9737 ± 0.0007    |Vub| = 0.0038 ± 0.0005
- |Vus| = 0.2210 ± 0.0023    |Vcb| = 0.0415 ± 0.0011
- |Vcd| =   0.224 ± 0.016	  |Vcs| =   0.995 ± 0.014

- The observed CKM matrix magnitudes fulfill unitarity reasonably well.
-  All processes which we call „weak“ can be described by the
- Standard weak interaction in which the CKM matrix is necessarily unitary.

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Assuming Unitarity :

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vtd again

- |Vtb|2 = 1 - |Vcb|2 - |Vub|2         	  |Vtb| = 0.99913 ± 0.00009
- 				  |Vtd| = (9.2 ± 1.4 ± 0.5) 10 –3
- |Vts|2 = |Vcb|2 + |Vub|2  - |Vtd|2   	   |Vts| = 0.0406 ± 0.0023

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vtd ff

- ¿

- md alone

- md and overoptimistic ms

- md and ms < 20/ps
- used in this talk

- |Vtd| :

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vub in the rho-eta plane

- ¿

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vtd+Vub

- ¿

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Vtd+Vub+fit

- ¿

- From magnitudes alone: _There is CP violation in the St. Model;_
- but the point (É,¿) = (0.37, 0) is only excluded with 2 .

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Final fit

- ¿

- É = 0.21 ± 0.08 ± 0.05,  ¿ = 0.34 ± 0.04 ± 0.02

- (K0)

- sin2

- Including CP violation measurements into
- the unitarity fit:

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Parameter values before and after the unitarity fit:

- ms = (14 - 39) / ps, 95%CL

- |Vub| = (3.82 **** 0.37) 10 -3

- K. R. Schubert, Seminar at LBL

- 26/7/00

## Summary:  

- Assuming „unitarity“, i. e. no New Physics, and including (K0), sin2:
- Hirarchy of magnitudes 1, , 2, 3 _was_ also a hirarchy of precision.
- No longer now, A2 is already better known than A.

- 	       Rich experimental and theoretical progress
- in the determination of CKM matrix magnitudes.
- _Experimental problems:_ GA/GV(n), (Kl3), F(1).|Vcb| ...
- _Important inputs missing:_ ms, (t) ...
- _More statistics_ will help |Vcb|incl and |Vub|

- _Summary:__  _

- K. R. Schubert, Seminar at LBL

- 26/7/00