1. Sides and Angles of the Unitarity Triangle
Soeren Prell
Iowa State University
High-energy Physics in the LHC Era
3rd International Workshop
January 4-8, 2010
Valparaiso, Chile

2. Sides and Angles of the Unitarity Triangle (S.Prell)
The CKM Matrix
V connects quark mass eigenstates to weak interaction eigenstates and thus describes coupling strength of quarks to charged current weak interaction
V first suggested by M. Kobayashi and T. Maskawa in 1973 to explain CP violation in Kaon mixing (Physics Nobel Prize 2008, shared with Y. Nambu); called VCKM to acknowledge N. Cabibbo i
W - j
GFVij
quark transition
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

3. The CKM Matrix
In 3-generation Standard Model CKM matrix is a unitary 3x3 matrix
Values of Vij not predicted by SM
Invariants under quark field rotations are observables (e.g. |Vij|2,VijVik*VlkVlj*)
VCKM has only 4 independent parameters
Search for physics beyond the SM by testing unitarity of CKM matrix !
Wolfenstein’s
parameterization
d s b u c t
point out symmetry perfect, except for Vub and Vtd
… reflects size of
matrix elements
(areas of squares
proportional to |Vij|2)
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

4. The (B) Unitarity Triangle
Vud, Vcd and Vtb are well known:
Vud from nuclear β decays,
Vcd (= Vus) from Kaon decays,
Vtb  1 from Vub and Vcb
Determine Vub, Vcb, Vtd
and Vts with B decays
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

5. CKM Matrix Element Magnitudes
Vub e-
Vud
Vus ν b Bd u
All 1st and 2nd row matrix elements
are most precisely determined from
leptonic and semi-leptonic decays π
Vcb e-
Vcd
Vcs ν b Bd c D
Vtd
Vts
Vtb b d b s Bd t Bd Bs t Bs t t d b s b
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

6. Vcb from B → D(*)lν decays
B →D*lν results
arXiv:
Experiments fit differential B → D(*)lν decay rate for |Vcb|F(1) and |Vcb|G(1) using HQET-based form factor parameterizations
B → D(*) form factor normalizations from lattice calculations
Prelim. result from Belle with B- →D*0lν EPS’09, arXiv: , not yet included in average):
PRD77, (2008)
PRL100, (2008)
PRD79, (2009)
Update plot
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

7. Vcb from inclusive B → Xclν decays
Inclusive rate Γ(B → Xclν) can be described by expansion in powers of 1/mb (HQET, OPE)
Non-perturbative corrections up to O(1/mb3) are determined from inclusive distributions in B decays (Elep and mhad in B → Xclν and Eγ in B → Xsγ decays)
Comment on error estimate
BaBar, arXiv:
mhad in
B → Xclν
HFAG, Winter 2009
p*l > 0.8 GeV
(~2.3σ larger than Vcb from excl. decays)
My average (S = 2.3)
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

8. Vub from B → π l ν decays
PRL101, (2008)
PLB648, 139 (2007)
arXiv:0812:1414
PRL101, (2008)
Experiments determine |Vub||f+(q2)| from measured B → π l ν rate
|f+(q2)| calculated from theory (LQCD (LCSR) at high (low) q2)
arXiv:0812:1414
PRL99, (2007)
PRL98, (2007)
arXiv:0812:1414
FNAL/MILC + BaBar data, PRD79,
(2009): 3.38 ± 0.36
Error dominated by f+(0) calculation
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

9. Vub from inclusive B→Xu l ν decays
Vub (B→πlν)
I can’t average theories, will use
|Vub|incl = (4.20 ±0.28)x10-3 (BLNP)
arXiv:
PRL100, (2008)
Challenges
mb5-dependence of Γ(B→Xulν)
b →c background: Γ(B→Xclν)/ Γ(B→Xulν)~50
Select B→Xulν enhanced region in phase sp.
use shape function from B→Xsγ Eγ-spectrum and theory to extrapolate rate to full PS
New Belle multivariate analysis
Reconstruct other B in hadronic mode
Covers about 90% of B→Xulν PS
Check slide
arXiv:
Vub from incl. B→Xulν syst. higher (~1-2σ) than from B→πlν decays
My average
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

10. Vtd and Vts
Experimental input: Bd0Bd 0 and Bs0Bs 0 oscillation frequencies
CDF, PRL 97, (2006)
D0, PRL 97, (2006)
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

11. Vtd and Vts From neutral B0d(s) mixing Improved lattice results:
From radiative B decays: BR(B → ργ) / BR(B → K*γ)
Improved lattice results:
(HPQCD, PRD 80, (2009))
Some theoretical errors
cancel in the ratio:
(errors dominated by theoretical uncertainties)
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

12. UT Apex from Vub, Vcb, Vts and Vtd
UT from full fit including
CKM phases
Explain CL regions
Measurements of the Unitarity Triangle sides are theoretically limited !
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

13. CKM Phases and Unitarity Triangle Angles
d s b u c t γ β βs
Phases in Wolfenstein convention (areas of squares proport. to |argVij|)
Convention-independent definition:
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

14. Sensitivity to CKM Phases from Interference
KS(Ф) c b
d(s) s
B(s)0
J/ψ t
V*td(s)
2β(s) from BB box diagrams
no weak phase in decay amplitudes
2α = 2(π – β – γ)
from BB box diagram followed by b → u decay γ
from charged B b → u decay c b
d(s) s
B(s)0
J/ψ
KS(Ф) t d b B0
V*td u
π - π+
V*ub d b u B0
π - π+
Vub
Time-dependent analyses to measure mixing-induced CP-asymmetries: s b u c B+ D0 K+ u b c s B+ K+ D0
Vub
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

15. β from b →(cc) s decays
Theor. clean measurement of |S| = sin2β with B → J/ψ K0, J/ψ K*, ψ(2S)KS, ηcKS, & χc1KS by BaBar and Belle
BaBar, PRD 79, (2009)
statistically limited
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

16. β from b → s(qq ) penguin loop decays
BaBar, PRD 79,  (2009)
In SM penguin decay amplitude is dominant and has same weak phase as b→c(cs) amplitude
expect to measure |S| = sin(2b)
SM contributions from suppressed diagrams expected to be small (Dsin(2b) = sin(2beff)- sin(2b) ~ )
Penguin decays with b → s (qq ) loop sensitive to New Physics from heavy particles
New Physics contributions could cause large D sin(2b)
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

17. β from b → s(qq) penguin loop decays
CP asymmetries measured by B factories in 9 different b → s (qq) modes
All measurements of sin2βeff consistent with sin2βb→c(cs)
C’s consistent with zero
Naïve average sin2βeff of all b → s (qq) modes used to be ~3σ lower than sin2β (~2004), now ~1σ
Some modes (ФK0, η’K0, K0K0K0) believed to have relatively small theoretical uncertainties
My average for clean modes
Theoretically
clean modes
(1.3σ away from sin2β)
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

18. a from B0 → pp g Sππ  sin2aeff = sin2(a + d )
Optimal Case:
Two sizeable amplitudes (P/T ~ 0.3) :
b → u “tree”
b → d “penguin” g
PRL 98, (2007)
Sππ  sin2aeff = sin2(a + d )
Excluded
at 95% CL
Determine d from
isospin analysis
(Gronau & London, PRL 65, 3381 (1990))
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

19. Sides and Angles of the Unitarity Triangle (S.Prell)
a from B → pp, rr, rp
• VV decay B → rr
separate isospin analysis for each polarization amplitude
fortunately, longitudinal polarization dominant (>90%)
Small penguin contribution in B → rr
New measurement of BR(B+ → r+r0) from BaBar stretches isospin triangles
2008
2009
PRL 102, (2009)
Excluded by
other constraints
Also prelim. BaBar result from a1π and K1π EPS’09, arXiv: )
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

20. g from B- → D(*)K- Decays
Rates of B± → D (*) K± decays are sensitive to γ through inter ference of b → c and b → u transitions
Need states accessible to D(*)0 and D(*)0
Several neutral D (*) final states investigated by B factories and CDF
EPS’09
3.4 σ
GLW : CP eigenstates (pp, KK,etc.)
Gronau & London, PLB 253, 483 (1991);
Gronau & Wyler, PLB 265, 172 (1991)
ADS: Flavor DCSD states (Kp)
Atwood, Dunietz, & Soni, PRL 78, 3257 (1997),
Atwood, Dunietz, & Soni, PRD 63, (2001)
GGSZ: 3-body decays (KSpp, KSKK)
Giri, Grossman, Soffer, & Zupan, PRD 68, (2003)
Bondar, PRD 70, (2004)
New BaBar measurement with first evidence for ADS signal B- → DK-
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

21. g from B- → D (*) K- Decays
• B- → D (*)K- decays with 3-body Dalitz analysis of D → KSπ π, D → KSKK most sensitive to γ
Belle: updated Dalitz analysis including D*0 → D0γ
Poluektov
@ EPS’09
Add comment on model error in BaBar analysis
2008 (prelim.)
2009 (prelim.)
Also, from time-dependent
B → D (*)K/p analyses:
2β+γ = (± 90 ± 32)o
Model error can be reduced to ~2o using CLEO-c
measurements of ψ(3770)→DD (PRD 80, (2009))
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

22. UT from Angles α, β, γ (and εK)
Define epsilonK
All measurements of the Unitarity Triangle angles are statistically limited !
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

23. βs from Bs → J/ψ Ф decays
• D0 and CDF measure βs with angular dependent fit to decay time distributions of Bs → J/ψ Ф
Simultaneous fit for ΔΓs and βs
SM predicts βs very small (~0.02)
sensitive to new physics in Bs mixing
Prospects
D0 and CDF working on updates with x samples
LHCb sensitivity with 0.5 fb-1: σ(βs) = 0.02
New physics in BsBs mixing
CDF/PHYS/BOTTOM/CDFR/9787, DØ Note 5928-CONF
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

24. Sides and Angles of the Unitarity Triangle (S.Prell)
Global CKM Fit
Other constraints
All constraints
CKM angles
Consistency of angles
Consistency of angles and sides from global fit
Overall good fit (CKMFitter: global p-value 45%)
~2σ tension between sin2β and εK / Vub
correction to εK will make it worse (Buras, Guadagnoli, PRD78, (2008))
Replace CKM fitter plot
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

25. Sides and Angles of the Unitarity Triangle (S.Prell)
Rare Decay: B → τ ν
Decay B → τ ν is sensitive to Vub
Decay proceeds via W annihilation in SM
also sensitive to new physics (e.g. charged Higgs)
B → τ ν event reconstruction at B factories
Tagging B side
Full reconstruction of B in hadronic (D(*)π/ρ, etc.) or semi-leptonic mode (D(*)lv)
Signal B side
Charged tracks
Missing energy due to ν’s
Require (no) additional energy in EM calorimeter (Eextra,EECL)
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

26. BR(B → τ ν) Measurements
Semileptonic tag (arXiv: )
preliminary
10x signal
Revise world average (cite reference, check HFAG)
Belle
Hadronic tag
Semileptonic tag
BaBar
World average
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

27. Unitarity Triangle consistency ?
~2.4σ discrepancy between direct BR(B → τ ν) measurements and global UT analysis
Theoretical uncertainty from fB is removed in BR(B → τ ν) / Δmd
discrepancy remains at ~2.5σ (only remaining theoretical error is 12% from B bag factor)
Effect of charged Higgs
W. Hou, PRD 48, 2342 (1992)
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

28. Sides and Angles of the Unitarity Triangle (S.Prell)
Conclusions
Many new measurements regarding quark flavor mixing in the last few years constrain the Unitarity Triangle with increasing precision
CKM mechanism proven to be dominant mechanism for quark mixing
describes all current experimental results in quark mixing and CP violation (including measurements of CKM matrix elements (Vud, Vus, Vcd, Vcs, Vtb) not covered in this talk)
Some intrinsic discrepancies need to be resolved
Vcb and Vub (incl. vs excl. decays)
A few interesting “tensions” at the 2-3 σ level should be monitored closely in the future
β (J/ψ K0) vs εK and Vub
B → τν vs β (J/ψ K0) βs
Expect significant impact from upcoming experiments (LHCb, Super B factories) and improved theory/lattice calculations mostly on improving γ, βs, Vub, Vtd / Vts
Importance for direct searches at LHC, flavor structure of new physics
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

29. Sides and Angles of the Unitarity Triangle (S.Prell)
Back-up Slides
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

30. Vud from nuclear β Decays
• 0+→0 + super-allowed nuclear β-decays within same isospin multiplet (pure V decays)
Error on rad.corrections ∆RV reduced x2 (Marciano and Sirlin, PRL 96, (2006))
Still dominant (syst.) error on Vud
Other Vud measurements compatible, but (7-10 x) less precise
n lifetime (error dominated by gA, most precise τn measurement 6σ away from earlier results), π decay (stat. limited)
Towner & Hardy,
PRC 79, (2009)
Before nucleus-
dependent corrections …
GF from μ decay
New Penning-trap
measurements of
decay energies
… and after
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

31. } Vus from K → πlν (Kl3) (experimental input, theory input)
Preliminary measurements τ(KL) and
τ(KS) (KLOE, cf. Kaon’09,
EPS’09) not yet in average
dominated by KL lifetime }
RBC-UKQCD, PRL
100, (2008)
Vus from τ decays
Prelim. BaBar measurement (ICHEP’08) of BR(τ→Kν)/BR(τ →πν) gives |Vus|=0.2255(23)
Rate of incl. τ → s decays (CKM’08) gives |Vus| = ± (exp) ± (theo); σ smaller than |Vus| from Kl3
Palutan Kaon ‘09
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

32. Vus / Vud and combined fit
Palutan Kaon ‘09
Ratio Vus / Vud can be determined independently from ratio of K → μν (KLOE, PLB 632, 76 (2006)) and π → μν decay rates
HPQCD-UKQCD,
PRL100, (2008)
From fit to Vud, Vus and Vud / Vus:
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

33. Sides and Angles of the Unitarity Triangle (S.Prell)
Vcd from v scattering
Di-muon production by neutrino on nuclei
Semi-leptonic decay D →π l ν
Dominated by D →π form factor
My average
CLEO-c, arXiv:
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

34. Sides and Angles of the Unitarity Triangle (S.Prell)
Vcs from D and Ds Decays
Semi-leptonic D decay D → K l ν
Dominated by D → K form factor
Leptonic Ds decays Ds →(μ,τ) ν
New measurements of from CLEO-c
decay constant f(Ds) from LQCD calculation
CLEO-c, arXiv:
[PRD 79, (2009),
PRD 79, (2009)]
My average
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

35. Unitarity of udcs Matrix
Cannot predict 3rd family
(Vub too small to matter)
(equal error contribution
to 1st row unitarity check)
Constraints on New Physics
Scalar currents (charged Higgs)
4th quark generation
|VuD| < 95% CL
Exotic μ decays
BR(Exotic μ decays) < 95% CL (~7x better than bound on μ+ → e+VeVμ)
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

36. Sides and Angles of the Unitarity Triangle (S.Prell)
K. Trabelsi for CKMFitter at Beauty 2009
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

37. Vtb from weak top production
From weak “single top” production cross-section in pp collisions at the Tevatron
Does not assume unitarity
5σ observations by CDF and D0
σ = pb [CDF, arXiv: ]
σ = 3.9 ± 0.9 pb [D0, arXiv: ]
CDF: |Vtb| = 0.91 ± 0.11(exp) ± 0.07(theo)
D0: |Vtb| = 1.07 ± 0.12
0.91+/-0.08
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

38. CKM matrix unitarity check
Magnitudes of CKM
matrix elements
fulfill unitarity well
From Vcb and Vts
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

39. Mixing-induced CP violation2 2 Af Af B0
fCP
B 0
fCP
B 0 Af B0 Af
Difference in decay
rate for B0 and B0
 CP Violation
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)

40. Measurement Technique for TDCPVs
B-Flavor
tagging z B
tag
Coherent BB production (p-wave) B0 B0
Reconstruction of B decays to exclusive final states
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell)