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Cracking the Unitarity Triangle — A Quest in B Physics —. Masahiro Morii Harvard University University of Arizona Physics Department Colloquium 7 October 2005. Outline. Introduction to the Unitarity Triangle The Standard Model, the CKM matrix, and CP violation

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Cracking the unitarity triangle a quest in b physics

Cracking the Unitarity Triangle— A Quest in B Physics —

Masahiro Morii

Harvard University

University of Arizona Physics Department Colloquium

7 October 2005


  • Introduction to the Unitarity Triangle

    • The Standard Model, the CKM matrix, and CP violation

    • CP asymmetry in the B0meson decays

  • Experiments at the B Factories

  • Results from BABAR and Belle

    • Angles a, b, g from CP asymmetries

    • |Vub| from semileptonic decays

    • |Vtd| from radiative-penguin decays

  • Current status and outlook

The Unitarity Triangle




Results presented in this talk are produced by the BABAR, Belle, and CLEO Experiments,the Heavy Flavor Averaging Group, the CKMfitter Group, and the UTfit Collaboration

M. Morii, Harvard

What are we made of



What are we made of?

  • Ordinary matter is made of electrons and up/down quarks

    • Add the neutrino and we have a complete “kit”

    • We also know how they interact with “forces”




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Simplified standard model











Note W± can “convert”u↔ d, e↔ n









Simplified Standard Model

  • Strong force is transmitted by the gluon

  • Electromagnetic force by the photon

  • Weak force by the Wand Z0bosons
















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Three generations

1st generation

2nd generation

3rd generation

Three generations

  • We’ve got a neat, clean, predictive theory of “everything”

  • Why 3 sets (= generations) of particles?

    • How do they differ?

    • How do they interact with each other?

It turns out there are two “extra” copies of particles

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A spectrum of masses

Particle mass (eV/c2)

A spectrum of masses

  • The generations differ only by the masses

     The structure is mysterious

  • The Standard Model has no explanation for the mass spectrum

    • All 12 masses are inputs to the theory

    • The masses come from the interaction with the Higgs particle

      • ... whose nature is unknown

      • We are looking for it with the Tevatron, and with the Large Hadron Collider (LHC) in the future

The origin of mass is one of the most urgent questions in particle physics today

Q = 1 0 +2/3 1/3

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If there were no masses
If there were no masses

  • Nothing would distinguish u from c from t

    • We could make a mixture of the wavefunctions and pretend it represents a physical particle

  • Suppose W connects u↔ d, c↔ s, t↔ b

    • That’s a poor choice of basis vectors

M and N are arbitrary33 unitary matrices

Weak interactions between u, c, t, and d, s, b are “mixed” by matrix V

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Turn the masses back on
Turn the masses back on

  • Masses uniquely define u, c, t, and d, s, b states

    • We don’t know what creates masses We don’t know how the eigenstates are chosen M and N are arbitrary

    • V is an arbitrary 33 unitary matrix

  • The Standard Model does not predict V

    • ... for the same reason it does not predict the particle masses

or CKM for short

Cabibbo-Kobayashi-Maskawa matrix

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Structure of the ckm matrix
Structure of the CKM matrix

  • The CKM matrix looks like this 

    • It’s not completely diagonal

    • Off-diagonal components are small

      • Transition across generations isallowed but suppressed

  • Matrix elements can be complex

    • Unitarity leaves 4 free parameters, one of which is a complex phase

There seems to be a “structure”separating the generations

This phase causes “CP violation”

Kobayashi and Maskawa (1973)

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What are we made of again
What are we made of, again?

  • Dirac predicted existence of anti-matter in 1928

    • Positron (= anti-electron) discovered by Anderson in 1932

  • Our Universe contains (almost) only matter

    • Translation: he would like the laws of physics to be different for particles and anti-particles



I do not believe in the hole theory, since I would like to have the asymmetry between positive and negative electricity in the laws of nature (it does not satisfy me to shift the empirically established asymmetry to one of the initial state) Pauli, 1933 letter to Heisenberg

Are they?

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C p and t symmetries
C, P and T symmetries

  • Three discrete symmetries of Nature

    • Laws of physics are symmetric under C, P, and T

      • Not true: weak interactions do not respect C and P

    • Laws of physics are really symmetric under CP and T

      • Wrong again: CP violation discovered in KLdecays

  • CP violation makes matter and anti-matter different

    • The SM does this with the complex phase in the CKM matrix

Wu et al., 1957

Christenson et al.1964

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Truth the whole truth
Truth, the whole truth

Is the CKM mechanism the whole story of CP violation?

  • CP violation must explain how much matter is in the Universe

    • What’s predicted by the CKM mechanism is not enough... by several orders of magnitude

  • The Standard Model runs into self-inconsistency at higher energies (1-10 TeV)  New Physics must exist to resolve this

    • Almost all theories of New Physics introduce new sources of CP violation (e.g. 43 of them in SUSY)

The CKM mechanism is almost certainly an incomplete explanation of CP violation

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The unitarity triangle
The Unitarity Triangle

  • V†V = 1 gives us

    • Experiments measure the angles a, b, g and the sides

This one has the 3 terms in the same order of magnitude

A triangle on the complex plane

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The ut 1998 2005

95% CL

The UT 1998 2005

  • We did know something about how the UT looked in the last century

    • By 2005, the allowed region for the apex has shrunk to about 1/10 in area

The improvements are due largely to the B Factoriesthat produce and study B mesonsin quantity

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Anatomy of the b 0 system







Anatomy of the B0 system

  • The B0 meson is a bound state of b and d quarks

    • They turn into each other spontaneously

    • This is called the B0-B0 mixing

Indistinguishable from the outside

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Time dependent interference
Time-dependent Interference

  • Starting from a pure |B0 state, we’d get

  • Suppose B0 and B0 can decay into a same final state fCP

    • Two paths can interfere

    • Decay probability depends on:

      • the decay time t

      • the relative complex phase between the two paths

Ignoring the lifetime

50-50 mix


t = 0

t = t

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The golden mode
The Golden Mode

  • Consider

    • Phase difference is

Direct path

Mixing path

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Time dependent cp asymmetry
Time-dependent CP Asymmetry

  • Quantum interference between the direct and mixed paths makes and different

  • Define time-dependent CP asymmetry:

    • We can measure the angle of the UT

  • What do we have to do to measure ACP(t)?

    • Step 1: Produce and detect B0 fCP events

    • Step 2: Separate B0 from B0

    • Step 3: Measure the decay time t



B Factory

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B factories
B Factories

  • Designed specifically for precision measurements of the CP violating phases in the CKM matrix



Produce ~108B/year by colliding e+ and e− with ECM = 10.58 GeV

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Slac pep ii site





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Asymmetric b factory

Step 1:

Reconstruct the signal B decay

Step 2:

Identify the flavorof the other B

Decay products often allow us to distinguishB0 vs. B0

Step 3:Measure Dz Dt

Asymmetric B Factory

  • Collide e+ and e− withE(e+) ≠ E(e−)

    • PEP-II: 9 GeV e− vs. 3.1 GeVe+ bg = 0.56

Moving in the lab




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Detectors b a b ar and belle
Detectors: BABAR and Belle

  • Layers of particle detectors surround the collision point

    • We reconstruct how the B mesons decayed from their decay products



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B a b ar picture
BABAR picture

“Rear” view of BABARnear completion.

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J y ks event
J/y KS event

Red tracks are from the other B,which was probably B0

A B0 → J/yKS candidate (r-fview)

p −

p −


p +

Pions from

p +


p +


Muons from

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Cpv in the golden channel
CPV in the Golden Channel

  • BABAR measured in B0 J/y+ KS and related decays

227 million events



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Three angles of the ut
Three angles of the UT

  • CP violation measurements at the B Factories give

Precision of b is 10 times better than a and g

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Ckm precision tests
CKM precision tests

  • Angle measurements agree with the Standard Model

    • But is it all?

  • We’ve measured b precisely, but a and g are much harder

    • One good measurement doesn’t test consistency

The CKM mechanism is responsible for the bulk of the CP violation in the quark sector

Next steps

  • Measure b with different methods that have different sensitivity to New Physics

  • Measure the sides




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Penguin decays
Penguin decays

  • The Golden mode is

  • Consider a different decaye.g.,

    • b cannot decay directly to s

    • The main diagram has a loop

    • The phase from the CKM matrix is identical to the Golden Mode

  • We can measure angle b in e.g.B0 f + KS



top is the main contributor

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New physics in the loop
New Physics in the loop

  • The loop is entirely virtual

    • W and t are much heavier than b

    • It could be made of heavier particlesunknown to us

  • Most New Physics scenarios predictmultiple new particles in 100-1000 GeV

    • Lightest ones close to mtop = 174 GeV

    • Their effect on the loop can be as big as the SM loop

    • Their complex phases are generally different

Comparing penguins with trees is a sensitive probe for New Physics

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Strange h ints
Strange hints

  • Measurements show a suspicious trend

    • Naive average of penguins give sin2b = 0.50  0.06

    • Marginal consistency from the Golden Mode(2.6s deviation)

Penguin decays

Golden Mode

Need more data!

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The sides

To measure the lengths of thetwo sides, we must measure|Vub| ≈ 0.04 and |Vtd| ≈ 0.08

The smallest elements – not easy!

Main difficulty: Controlling theoretical errors due to hadronic physics

Collaboration between theory and experiment plays key role

The sides






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V ub the left side
|Vub| – the left side

  • |Vub| determines the rate of the b utransition

    • Measure the rate of b uvdecay ( = e or m)

    • The problem: b cv decay is much faster

    • Can we overcome a 50 larger background?

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Detecting b u v
Detecting b → uℓv

  • Use mu << mc difference in kinematics

    • Signal events have smaller mX  Larger E and q2

E = lepton energy

q2 = lepton-neutrino mass squared

u quark turns into 1 or more hardons

mX = hadron system mass

Not to scale!

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Figuring out what we see
Figuring out what we see

  • Cut away b cv  Lose a part of the b uvsignal

    • We measure

  • Predicting fC requires the knowledge of the b quark’s motion inside the B meson  Theoretical uncertainty

    • Theoretical error on |Vub| was ~15% in 2003

  • Summer 2005:

    • What happened in the last 2 years?

Cut-dependentconstant predictedby theory

Total buv rate

Fraction of the signal that pass the cut

HFAG EPS 2005 average

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Progress since 2003
Progress since 2003

  • Experiments combine E, q2, mX to maximize fC

    • Recoil-B technique improves precisions

    • Loosen cuts by understanding background better

  • Theorists understand the b-quark motion better

    • Use information from b sg and b  cn decays

    • Theory error has shrunk from ~15% to ~5% in the process

Fully reconstructedB hadrons


b  cvbackground



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Status of v ub
Status of |Vub|

  • |Vub| has been measured to 7.6%

    • c.f. sin2b is 4.7%

  • Fruit of collaboration between theory and experiment

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V td the right side
|Vtd| – the right side

  • Why can’t we just measure the t d decay rates?

    • Top is hard to make

  • Must use loop processes where b  t d

    • Best known example: mixing combined with mixing

    • Dmd= (0.509  0.004) ps−1

    • mixing is being searched for at Tevatron (and LEP+SLD)

      • Dms > 14.5 ps-1 at 95 C.L. (Lepton-Photon 2005)

B0 oscillation frequency

Bs oscillation frequency

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Radiative penguin decays
Radiative penguin decays

  • Look for a different loop that does b  t d

    • Radiative-penguin decays

    • New results from B Factories:

95% C.L.


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Impact on the ut
Impact on the UT

  • From the radiative-penguin measurements

    • Comparable sensitivities to |Vtd|

      • Promising alternative/crosscheck to the B0/Bs mixing method

limits from the B0/Bs mixing

Need more data!

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The ut today
The UT today

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The ut today1
The UT today

  • The B Factories have dramaticallyimproved our knowledge of theCKM matrix

    • All angles and sides measuredwith multiple techniques

  • Bad news: the Standard Model lives

    • Some deviations observed  require further attention

    • New Physics seems to be hiding quite skillfully

  • Good news: the Standard Model lives!

    • New Physics at ~TeV scale affect physics at low energies

    • Precision measurements at the B Factories place strong constraints on the nature of New Physics

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B factories and new physics
B Factories and New Physics

  • In addition to the angles and the sides of the UT, we explore:

    • rare B decays into Xsg, Xs+-, tn

    • D0 mixing and rare D decays

    • lepton-number violating decays

  • Even absence of significant effects contributes to identifying NP

    • If we measure them precisely enough

Two Higgs doublet model

Allowed byBABAR data

mH (GeV)

b sg

B tn

Some of the best limits on NP come from rare B decays


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  • The B Factories will pursue increasingly precise measurements of the UT and other observables over the next few years

  • Will the SM hold up?

    • Who knows?

  • At the same time,we are setting a tightweb of constraints on what New Physics can or cannot be

What the B Factories achieve in the coming years will provide a foundation for future New Physics discoveries

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