Rare B meson decays - mathieu trocmé

II- Physical Background 15
0 * + −
+
II.4- The B → K π & B → K π decays:
A way to measure the CKM matrix elements (or to measure the angles of the unitary
triangle) is to measure the asymmetric parameter ACP . This is proportional to the difference
between the branching ratio BR of a B meson decay – i.e. the likelihood the decay happens –
and that of the conjugate process. For instance, if the decay studied is of the form:
B → X + Y , the conjugate process will be: B → X + Y and the asymmetric parameter will
be such that: ACP ∝ BR{
B → X + Y}
− BR{
B → X + Y } . Formally, the asymmetric parameter
is defined as the ratio of the difference of the conjugate decays branching ratios to their sum,
that is:
A CP
BR
=
BR
0
* −
{ B → X + Y}
− BR{
B → X + Y }
{ B → X + Y}
+ BR{
B → X + Y }
0 * + −
* − +
The B decay studied in this project is B → K π so its conjugate is B → K π .
Distinguishing two conjugate neutral B mesons and ensuring they come from the same Y(4S)
is not a trivial task. Actually, this would require a whole other project. Thus, no calculation of
the asymmetric parameter was required. The aim of this project was only to determine a
global branching ratio for the two conjugate decays simultaneously. This corresponds to the
denominator of A CP .
0
Let us consider the B decay first. To detemine an accurate branching ratio for this
* +
decay, the K decay into a +
0
π and a K S is of special interest. Indeed, the final state
produced consists of three particles and is referred to as a three body charmless state
− + 0
+
−
0
( π π K where π = ud
, π = ud
, and K S = ds
, no charm quark)
S
But other physical processes occur, namely:
B
0 * + −
→ K π
B
0 * + −
→ K π
0
K S
+
π
( K
( K
0
S
0
L
π )
+ −
π
π )
+ −
π
+ 0 −
( K π ) π
0