# Presentation: 916204

## Heavy Flavors

- Sheldon Stone,
- Syracuse University

## Introduction

- “Heavy” flavors, defined as b & c quarks, not t, which is heavier, as the top doesn’t live long enough to form a meson and just decays ~100% directly to b quarks (In England we have “Heavy” flavo_u_rs)
- Charm is interesting in several special areas, but I will concentrate on b’s
- First I will discuss some specific b phenomenology and then point out why these studies are extremely important and interesting

## Some B Meson Decay Diagrams

- a) is dominant
- b) is “color suppressed”
- a) & b) are called “tree” level diagrams

## The Standard Model

- Theoretical Background
- Physical States in the Standard Model
- The gauge bosons: W±,  & Zo and the Higgs Ho
- Lagrangian for charged current weak decays
- Where

## The CKM Matrix

- Unitary with 9*2 numbers  4 independent parameters
- Many ways to write down matrix in terms of these  parameters

## The Basics: Quark Mixing & the CKM Matrix

- A, ,  and  are in the Standard Model fundamental constants of nature like G, or EM
-  multiplies i and is responsible for CP violation
- We know =0.22 (Vus), A~0.8; constraints on  & 

-           d               s              b

- u

- c

- t

- mass

- m
- a
- s
- s

## The 6 CKM Triangles

- From Unitarity
- “ds” - indicates rows or columns used
- There are 4 independent phases:  ( can be substituted for or as )

- 

- 

- 

- 

- 

- Area of each  = A26, the Jarlskog Invariant

## Both Vcb & Vub can be determined
    using diagram (a) when  W-→-
Can use either inclusive
   decays B→X-,  with B~10%or 
   exclusive B→D*-with B~6%
|Vcb|=(41.96±0.23±0.35±0.59)x10-3 inclusive

                                                  (see Kowalewski ICHEP 2006)
      Very well based theoretically (HQET)
Note difference is 2.6x10-3, much larger than quoted
    theoretical errors!

-     using diagram (a) when  W-→-
- Can use either inclusive
-    decays B→X-,  with B~10%or
-    exclusive B→D*-with B~6%
- |Vcb|=(41.96±0.23±0.35±0.59)x10-3 inclusive
-                                                   (see Kowalewski ICHEP 2006)
-       Very well based theoretically (HQET)
- Note difference is 2.6x10-3, much larger than quoted
-     theoretical errors!

- |Vcb|

## |Vub|

-  This is much more difficult because the b→u rate is so much smaller than b→c
- Inclusive decays are studied with severe cuts to reduce b→u background
- |Vub|=(4.49±0.19±0.27)x10-3
- For exclusive decays
-    use B→-(in
-    principle also -

- Again difference
- between
- inclusive &
- exclusive

## Measurements of Bo & BS mixing

## Bo-Bo Mixing

- Bo can transform to Bo, like neutral K’s
- The eigenstates of flavor, degenerate in pure QCD mix under the weak interactions. Let QM basis be {|1,|2} {|Bo,|Bo}, then

## Mixing Measurements 

- Diagonalizing we have
-    m= mBH-mBL=2|M12|, ~0
- R= prob BoBo/ prob BoBo
- First seen by ARGUS
- P(BoBo)=
-       0.5e-t•[1+cos(mt)]
- Must “tag” the flavor of the
-     of the decaying B at t=0
-     using the other B

## md Measurements

- md average
-  0.507±0.004 ps-1
- Accuracy better than 1%

## Bd Mixing in the Standard Model

- Relation between B mixing & CKM elements:
- F is a  known function, QCD~0.8
- BB and fB are currently determined only theoretically
- in principle, fB can be measured, but its very difficult, need to measure B- -
- Current best hope is Lattice QCD

## Bs Mixing in the Standard Model

- Measurement of  Bs mixing provides the ratio of Vtd/Vts which gives the same essential information as Bd mixing alone, but with much better control of theory parameters
- |Vtd|2=A24[(1-)2+2]
- |Vtd|2/ |Vts|2=[(1-)2+2]
- Circle in () plane centered at (1,0)
- To relate constraints on CKM matrix in terms of say  &  need to use theoretical estimates of                     =fBs2BBs/ fBd2BBd

## CDF Measurement of ms

- P(BSBS)=0.5X
- Se-St[1+cos(mSt)]
- It is useful to analyze the data as a function of a test frequency 
- g(t)=0.5 S
-       e-St[1+****cos(t)]
- CDF:
- D0 90% cl bounds

- 21>mS>17 ps-1

## Constraint on  plane

- Need to use theory value for
- Using both Vub/Vcb & B mixing
- In principle, could measure fB|Vub| using B-, but difficult: Belle “discovery” was “corrected” & Vub  error is significant, so use D decays

- See
- http://ckmfitter.in2p3.fr/

## Leptonic Decays: D(s)   +

- Leptonic Decays: D(s)   +

-    c and q  can annihilate, probability is  to wave function overlap
-   Diagram:

- _

- (s)

- or *cs*

## Measuring Charm at Threshold

- DD production at threshold: used  by Mark III,  and more recently by CLEO-c and BES-II.
- Unique event properties
- Only DD not DDx produced
- Ease of B measurements using "double tags“
- BA = # of A/# of D's
- Beam Constrained Mass

## Measurement of fD+

-  To find signal, look for events consistent with one  track opposite a D- tag with a missing 
-  Compute
- Find

## DS+→++,  →+ 

- DS+→++,  →+ Sum contains 100 ++ events for MM2 <0.2 GeV2
- Also, DS+→+,  →e+
- Weighted Average: fDs=280.1±11.6±6.0  MeV, the systematic error is mostly uncorrelated between the measurements
- Thus fDs/fD+=1.26±0.11±0.03
-     (CLEO-c)

## Comparisons with Theory

- CLEO-c data are consistent with most models, more precision needed, for both

## Measurements of CP Violating Angles

## Formalism of CP Violation

- CP Eigenstates:
- Because of mixing mass eigenstates are a superposition of a|Bo>+b|Bo> that obey the Schrödinger equation

## Bo CP Formalism II

- For CP not being conserved, instead of B1 & B2
- CP is violated if q/p  1
- Time dependence is given by

## Bo CP Formalism III

- This leads to the time evolution of flavor amplitudes as
- m=mH-mL,  L H  *(true for B**d**, not necessarily for B**s**)*
- Probability of a Bo decay is given by <Bo(t)|Bo(t)*> & is pure exponential in the absence of CP violation

## CP violation using CP eigenstates

- CPV requires the interference of two amplitudes. We use the direct decay for one amplitude and mixing for the other one
- Define
- A=<f|H|Bo>
- A=<f|H|Bo>
- |A/A|1 is evidence of CP violation in the decay amplitude (“direct” CPV)
- With mixing included, we have CPV if

## CP V using CP eigenstates II

- CP asymmetry
- for |q/p| = 1
- When there is only one decay amplitude, =1 then
- Time integrated

*good luck, maximum is –0.5*

## CPV using CP eigenstates III

- For Bd,
- Now need to add A/A
- for J/ Ks:

## Ambiguities

- Suppose we measure sin(2) using Ks, what does that tell us about ?
- Ans: 4 fold ambiguity- 
- Only reason >0, is Bk>0 from theory, and related theoretical interpretation of 

## B Kinematics at the Y(4S) (Babar & Belle)

- From Abe

- Asymmetric e+e-
- machines at Y(4S)

## Fit to t Distributions

- B0 tag

-  resolution, wrong tags

- B0 tag

## 2006: BaBar + Belle

- From Hazumi ICHEP 2006

##  (not sin2) measurements

- B0D*+D*Ks
- Time-dependent Dalitz analysis
- (T.Browder, A. Datta et al. 2000)
-  cos2 > 0
- (94%CL, model-dependent)

- B0Dh0 (h0 = 0 etc.)
- Time-dependent Dalitz analysis
-  cos2 > 0
- Belle: 98.3%CL
- (hep-ex/0605023, accepted by PRL)
- BaBar 87% CL
- (BABAR-CONF06/017)

- Preliminary

## CPV in Charmless B Decays

- Can have both tree & loop diagrams in +- (or +-)
- The weak phase in the tree graph is . The weak phase in the Penguin is different. Therefore, the Penguin can (and does) mess up CP via mixing in +-
- Penguin is unmasked by evidence of oo

*Tree*

*Penguin*

## CPV in B+-

- First done by BaBar confirmed by Belle
- Not a CP eigenstate, but final state is almost fully longitudinally polarized
- fL=0.978+0.024+0.015 (BaBar)
- However, Penguin pollution revealed at 3 level (BaBar):
- B()=( 1.2±0.4±0.3)x10-6
- B()=(23.5±2.2±4.1)x10-6

- -0.013

## CPV in B+- II

- Constraints on 

## Results on 

## : B±DoK± decays, Do Ks

- Can have CPV in B decays
-    Just need two interfering
-    amplitudes
- For the B- decay:
-    A(B-DoK-) AB
-    A(B-DoK-) ABrBe*i*(B-)
- Use modes where the Do is indistinguishable from the Do. Then use Daltiz plot analysis to find  see A. Giri et al., [hep-ph/0303187]

##  from BDoK-, Do Ks

- d2 ln L/d2

- sensitivity

- Belle first saw a
- clear difference
- Now data show a smaller effect

## Poor Constraints on 

- See
- http://www.utfit.org/

## Putting It All Together: Status

- Global fit using all available inputs
- K is from CP violation in Ko system

## Reasons for Further B Physics Studies

- There is New Physics out there: Standard Model is violated by the Baryon Asymmetry of Universe & by Dark Matter
- I will show that B physics will be crucial towards interpreting New Physics found at the LHC

## The Enigma of Baryogenesis

- When the Universe began, the Big Bang, there was an equal amount of matter & antimatter
- Now we have most matter. How did it happen?
- Sakharov criteria
- Baryon (B) number violation
- Departure from thermal equilibrium
- C & CP violation

## Sakharov Criteria All Satisfied

- B is violated in Electroweak theory at high temperature, B-L is conserved (need quantum tunneling, powerfully suppressed at low T)
- Non-thermal equilibrium is provided by electroweak phase transition
- C & CP are violated by weak interactions. However the violation is too small!
- nB-nB/n = ~6x10-10, while SM can provide only ~10-20
- Therefore, there **must** be new physics

## Dark Matter

- Discovered by Zwicky in 1933 by measuring rotation curves of galaxies in the Coma cluster

- Also gravitational lensing of galaxy clusters

- Is dark matter composed of
- Supersymmetric particles?

## The Hierarchy Problem

- Physics at the Planck scale ~1019 GeV is much larger than at the ~100-1000 TeV electroweak scale, requires delicate cancellations between fundamental quantities and quantum corrections.
- New Physics is needed to solve this problem

## Loop Diagrams - Penguins

- Effects of New Particles on B Decays
- These decays are suppressed, so New Particles can show enhanced effects

## MSSM Measurements, from Hinchcliff & Kersting (hep-ph/0003090)

- MSSM Measurements, from Hinchcliff & Kersting (hep-ph/0003090)

- Contributions to Bs mixing

- CP asymmetry  0.1sincossin(mst), ~10 x SM

## Supersymmetry

- Supersymmetry contains      squarks and sleptons.
- Squark mass matrixes        contain information on     SUSY breaking      mechanisms &/or GUT scale interactions.
- Quark flavor changing neutral current processes, e.g. BS or D0 mixing, are sensitive to the off-diagonal elements of the squark mass matrix.

## Examples

- T.Goto,Y.O.Y.Shimizu,Y.Shindou,and M.Tanaka,2003

- SM

- BS mixing

- CP Violation in BS

- From Okada ICHEP 2006

- SUSY GUT & BS Mixing

## SO(10)ala’ Chang, Masiero & Murayama hep-ph/0205111

- Large mixing between  and  (from atmospheric  oscillations) can lead to large mixing between bR and sR.
- This does not violate any known measurements
- Leads to large CPV in Bs mixing, deviations from sin(2) in Bo Ks and changes in the phase 

- ~

- ~

## New Physics Effects in Some Different Models

*Different models give different patterns* (2003 SLAC WS Proceedings)

## Possible Size of New Physics Effects

- From Hiller hep-ph/0207121

## bs Transitions (Penguins)

- In SM t in loop dominates and CP asymmetry should be equal to that in J/Ks

-  Other objects in loop, new virtual particles,
-    could interfere
-  So this process is sensitive to new physics

## CPV Measurements In bs 

- We  cannot just average these modes, but ....
- <S>=sin2
-                  =0.50±0.06
- S=.52±.05-.68±.03 = -0.16 ±0.06
- Does u & c parts of Penguin contribute? Yes but S >0, ~0.1
- New Physics???

## Electroweak penguins BK(*)+-

-  With *l*+*l*- pair, can have either pseudoscalar or vector mesons
-  New physics can affect both rates and kinematic distributions.

## BK(*)+-:  Lepton F-B Asymmetry 

- BK(*)+-:  Lepton F-B Asymmetry

- Lepton angular
- distribution in
*l**l* rest frame

- hep-ex/0508009

- Belle: lepton

- 386 M BB

- SM

- NP scenarios

- But large
- errors &
- somewhat
- contradictory
- data from
- BaBar

## Constraints on New Physics

- Next to Minimal Flavor Violation construction
- Assume NP in tree decays is negligible
- Is there NP in Bo-Bo mixing?
- Use Vub, ADK, SK, S, md, ASL =
-    semileptonic asymmetry
- Fit to , rd, d (or h, )

- _[Agashe](http://xxx.lanl.gov/find/hep-ph/1/au:+Agashe_K/0/1/0/all/0/1)__**, **__[Papucci](http://xxx.lanl.gov/find/hep-ph/1/au:+Papucci_M/0/1/0/all/0/1)__**, **__[Perez](http://xxx.lanl.gov/find/hep-ph/1/au:+Perez_G/0/1/0/all/0/1)_**, & **_[Pirj](http://xxx.lanl.gov/find/hep-ph/1/au:+Pirjol_D/0/1/0/all/0/1)__[o](http://xxx.lanl.gov/find/hep-ph/1/au:+Pirjol_D/0/1/0/all/0/1)__**l**_** hep-ph/0509117**

## New Physics Constraints

- Amplitudes ~20% of SM still allowed in any region, more near 0o
- Still a lot of room for New Physics in Bd system

- h

- 

## BS System

- New Physics almost unconstrained

##  in BS Decays

-  = L- H, where  of “light” vs “heavy”
-  In Bd system  is small, driven by common channels for Bo & Bo (i.e. )
- BSDS+(*) DS-(*), where CP+ outweighs CP- BS (recall CDF measured mS), CDF & D0 have measurements, order of B(B→D(*)DS(*))~10%
- Recall
-  =2|12|cosS, where S is the CP violating phase in BS mixing, expected to be tiny in SM ~-22=-.04 rad but effected by NP
- Can measure  using  measurements

## Measuring  Phase of BS mixing

- CP violation in BS mixing
- f = ±1, depending on f= CP+ or CP -
- Contrast with Bo
- (Bof)~e-t/[1+Adircosmt+sinmt]

## Measuring  Without Flavor Tagging

- Sum
- Some sensitivity to  without flavor tagging

## Measuring  with BSJ/ (or )

- BSJ/ (where  or o) is a CP eigenstate similar to BoJ/ KS. However, detecting the  is difficult for some hadron collider detectors
- J/ is not a CP eigenstate, but is very useful in all experiments. Must take into account different spins: S, P, D.
- ∴use Transversity analysis
- Most sensitivity expected using flavor tagged analysis

## D0 Untagged Analysis

- D0 has 978±45 events
- S=-0.79±0.56±0.01 (rad)
- S=0.17±0.09±0.04 ps-1
- 025±0.13

## Future Experiments

## B experiments at the LHC

- LHCb: first dedicated b experiment at a hadron collider, the LHC
- Excellent vertexing
- Excellent particle id
- Super B? Two efforts, one at Frascati and SuperBelle in Japan

- LHCb

- CMS

- ATLAS

## LHCb Projections

- K*
-    2 fb-1

- (0.02 rad)

## Also ATLAS & CMS

- ATLAS
- CMS

- BSJ/

## Will There Be a Super-B e+e- Machine?

- Two proposals currently being pursued to make L~1036, ~100 times current B factories
- Super Belle at KEK
- Linear-B scheme

**IP**

- LER Bunch compressor and FF

- HER Bunch compressor and FF

- LER

- HER

- LER injection

- HER injection

## Conclusions

- Much has been learned about the structure of matter & fundamental forces in nature using flavor decays; contributions from several generations of experiments at e+e-, fixed target and hadron colliders
- b & c decays will be used as incisive probes of New Physics. These effects appear in loops. We already are probing the TeV scale. Flavor decays will be ever more important in understanding the nature of NP effects found at the LHC or Tevatron (i.e. SUSY, Extra Dimensions, Little Higgs etc...)
- The next few years will see more results from BaBar, Belle, CDF & D0, but only Belle will remain post 2009
- LHCb will be the first dedicated B physics experiment at a Hadron Collider. ATLAS & CMS also have B physics capability. There may be a Super B factory, possibly at KEK or at Frascati