# Presentation: 661905

## Introduction to Flavor Physics in and beyond the Standard Model

- Enrico Lunghi
- References:
- The BaBar physics book, http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-r-504-TOC-pdf.pdf
- B physics at the Tevatron: Run II and beyond, hep-ph/0201071
- The Discovery potential of a Super B Factory, hep-ph/0503261

*Lecture 3/4*

## Outline

-  Summary of the previous lecture
-  CP violation: meson mixing, classification of CPV effects
-  Examples: sin(2), sin(2), 

## Main points from lecture 2

## Effective Hamiltonian approach

- perturbative  integrate out:

- dependence on external states (possibly non-perturbative)

- not dependent on
- the external states

## Advantage 1: improved perturbation theory

- A generic amplitude at the 1-loop level looks like:
-      where
- We can write
- Using the fact that A(if) is  independent, we can write a RGE for C(), whose solution resums all these logarithms:
- Now we can choose                        in order to minimize the logs in               and                     to minimize the logs in                 :

## Advantage 2: separation of short and long distance

- The Wilson coefficients do not depend on the external states
- Since the matrix elements of the various operators are dominated by large distance physics, new physics can enter only by:
- modifying the Wilson coefficients
- inducing new operators

- SM

- Supersymmetry

- SUSY at large tan()

## CP Violation

## Introduction

- CPV appears only in weak interactions and together with flavor changing interactions
- The CPV phase in the Standard Model is large

## CP violation in meson decays

- CPV in mixing
-       if                  , it is possible to measure CPV in decays to final states accessible only to      or
- CPV in decay
- CPV in the interference of decays with and without mixing

- from CKM

- from QCD

## Meson mixing

- Let’s consider two states that at t = 0 are pure       and       :
- CPT:
-       Hermiticity:
- The mass eigenstates are (                          ):

- mass matrix

- decay matrix

## Time evolution of weak eigenstates

- The time evolution of these states is:
- Let us consider a state that is a pure B0 at t = 0:
- At some time t it will be:
- Expressing everything in terms of the weak eigenstates:

## Time evolution of weak eigenstates cont’d

-      where
- CPV in mixing:

- Time evolution of weak eigenstates *cont’d*

## Meson mixing parameters 

- Dispersive and absorbitive parts of B=2 diagrams yield M12 and 12
-  Explicit solution of the eigenvalue equation for M-i /2 are:
- These expressions are valid for any kind of meson mixing: K, D, Bd and Bs

## The B mixing case

- In the B mixing system, there is empirical evidence for:
- In general                     , because the former stems from final states that are common to      and
- Bs case.
-       Experimental evidence shows that
- Bd case.
-       Decays to final states common to      and       have BR in the 10-3 range.
-       We can assume that their combined effect will be in the 10-2 range:
-       Using                                   we obtain:

## The B mixing case cont’d

- The B mixing case *cont’d*

## Time-dependent decay rates

- Given a final state f, let us introduce the two amplitudes
-       and                             , and the quantity:
- Master equations:

## The three types of CP violation

- There are three quantities that drive CPV effects:
- CPV in mixing:
- CPV in decay:
- CPV in the interference between decay and mixing:

## CPV in mixing

- The mass eigenstates are not CP eigenstates
- An example is the neutral semileptonic decay asymmetry to wrong sign leptons:
- Large hadronic uncertainties in the calculation of 12

## CPV in decay

- In charged B decays this is the only source of CP asymmery
- We need two amplitudes with different weak and strong phases:
- We need the amplitude ratio and the difference of strong phases: both are difficult to calculate

## CPV in the interference between decay and mixing

- Similar to CPV in decay: the two amplitudes are                  and
- In the limit                 we have:

## Flavor specific decays and

- Let us consider a final state accessible to      but not to
- Examples are                        and
- The time dependent rates are:
- The asymmetry is:
- Used to measure

## Untagged B mesons and 

- Let us consider the time evolution of an equal admixture of       and
- Useful to extract information on  and f at hadronic machines

- can be eliminated if the total
- branching ratio is known

## Calculation of M12

- B=2 transitions need to go through a W loop  short distance physics is involved
- As usual we write an effective Hamiltonian that captures the SD physics:

- NLO Wilson coefficient: C()

- Local operator: Q()

## Calculation of M12 cont’d

- Now we must specify the external states:
- From lattice-QCD we obtain:
- Putting everything together:

- theory uncertainty

## Calculation of M12 cont’d

- Mass difference:
- Mixing parameter:

- up to corrections proportional to 12/M12

## Calculation of 12

- 12 is the absorbitive part of the                 amplitude: it originates from decays that are common to       and
- In formulae:

## Calculation of 12 cont’d

- At leading order we have:
- Note that:

## Calculation of the amplitudes (Af)

- We are plagued by non-perturbative QCD effects
- In general we must take matrix elements of a decay effective Hamiltonian:
- If only one operator contributes (                    ):
- If all the Wilson coefficients come with the same phase (    ):

- Form factors
- QCD factorization
- Lattice QCD

## Examples

## The final state is a CP eigenstate (with eigenvalue -1)

- This process is mediated by both tree and penguin operators:
- The last term is doubly suppressed:

- penguin pollution

## There is a problem:                    and  

- There is a problem:                    and
- Ks is the lighter mass eigenstate:
- Interference between                           and                           is only possible through K mixing:
- Putting everything together:
- and the time dependent CP asymmetry is

## Slide 32

## This process is mediated by penguin operators only:

- The last term is only CKM suppressed:

- penguin pollution

- penguin pollution

## This process is mediated by both tree and penguin operators:

- Is the last term suppressed?

- penguin pollution

- The time-dependent CP asymmetry is:
- What do we get from experiments (Belle & BaBar)?

- !!!!

## Solutions:

- use effective theories to calculate
- use SU(3) flavor symmetry to relate BK and B
- isospin analysis
- Up to isospin breaking corrections we can describe
-      in terms of two isospin amplitudes
- At the end of the day we are able to eliminate r and extract sin(2)

## Slide 37

## Analysis is identical to the  case 

- Analysis is identical to the  case
- Experimental measurements have larger errors
- The constraint on  is stonger!

## Slide 39

## The decays                            and                            are both allowed and have similar CKM suppression (                                             ):

- The CP eigenstates of the neutral D mesons are:

## It is possible to identify the neutral D in the final state:

- It is possible to identify the neutral D in the final state:
-       or       are identified by semileptonic decays containing a + or a -, respectively
- DCP§ are identified by final states that are CP eigenstates
- Using the following four observables, we can extract 
- 	where                          and

## Slide 42