1
Elisabetta Baracchiniin collaboration with
M. Ciuchini, G.Isidori, M. Pierini, L. Silvestrini
Incontri di Fisica delle Alte Energie
QED corrections and
the B Kπ puzzle
2The two sources of BK puzzle
R=[BRBd
0K −BR Bd0 K−
BRBK 0BRB− K0−]B
B d0
Rc=2 [BRBK 0BRB−K −0BRBK 0BRBd
− K 0−]
Rn=12[
BRBd0 K−BR Bd
0K −
BR Bd0K 00BR Bd
0 K 00]
ACP K−≈ACP K
0
Rc−Rn≈0
calculated from HFAG
0.85 ± 0.06
1.01 ± 0.09
0.81 ± 0.08
theoretically expected
HFAG ACP
+=0.12 ± 0.02 A
CP+0= 0.04 ± 0.04
1 ) BR's seem to violate isospin
2 ) Expected correlation among (SAME SIGN)
proposed solution:NP in Electroweak Penguins
as a source of isospin breaking(Buras et al. hepph/0402112)
QCD factorization [hepph/0308039]SCET [hepph/0510241,hepph/0601214]pQCD at LO [hepph/0508041]all predict SAME SIGN
not observed by experiment
but QED was never considered yet
Elisabetta Baracchini IFAE 2006
3Outline
Two sources for a puzzle:BR seems to violate isospin
Account for QED corrections as a source of isospin breaking
theoretical issue experimental issue
CP Asymmetries
Isospin analysis of BK modes
Conclusions
Elisabetta Baracchini IFAE 2006
4Radiative correctionsTheoretical issue
Why: given the reached experimental precision, we have to take EM effects into account for a consistent analysis
In an ideal world where we could measure everything, in presence of charged particles we would anyway have to deal with
P1 P 2
incl E max= H P1 P2n ∣∑ E E max =P1 P 2P1 P 2nE
max
where Emax is the intrinsic energy resolution of the instrument with which we're investigating the process, or else the minimum energy for which we can distinguish
the photon
intrinsic and unavoidable feature of QED
P1 P 2
incl E max=P1 P 2
0 GP1 P2Emax
this is the amplitude needed in phenomenologythis is the amplitude needed in phenomenology
Elisabetta Baracchini IFAE 2006
5
Photoninclusive width
P1 P 2=
12 M H
∫ dP1 P2∣AP1 P2
1BP1 P2m
2 O2...O n∣2
P1 P 2nEmax=
12 M H
∫E E max dP1 P2n ∣AP 1 P2n∣2=
12 M H
∫ dP1 P2∣AP1 P 2
∣2 I P1 P2m
2 , Emax
I P 1 P2m
2 ,Emax =∫E E max
d3k23 2 E
∑spins
∣AH P1 P2AH P1 P2
∣2
OEmax
M H
need to be calculated at same order in perturbation theory
m is infrared regulator neededby the QED calculation
how to calculate? for heavy mesons hadronic decays
not possible from full theory
Elisabetta Baracchini IFAE 2006
use scalar QED because interested in soft photon spectrum
6Scalar QED calculation at O(short remind: for a neutral scalar decaying into two charged scalars
pb
p1q
p2
p1pb
p1
q
p2
p2
p2
p1
q
p2 q
p1 q
p1 + q
p2 q
A1 A2 doesn't give any relevant contribution because of Low theorem or gauge invariance
Virtual diagrams
Real emission diagrams
selfenergy vertex correction
Aireal=AP1 P 2
−ie0i
piq2−mi2i
piqpi
i=1,2
A self−en=AP1 P 2[1
ip2−m0
2i ie0
2 p]
ie02 p=ie0
2∫ d D q2D
−iq−m
2i 2p−q
ip−q 2−m0
2i 2p−q
A vert=AP1 P2ie 0
2∫ d D q
2D−i
q−m2i
i 2p1q
p1q2−m12i
−i2p2−q
p2−q2−m22i
for a charged scalar
into a neutral and a charged scalar
guess similar diagrams
and formulas
Elisabetta Baracchini IFAE 2006
7
G12E max=1[b12 ln
M H2
m2
H 12
2b12 ln
m2
4 Emax2F12N12 ]
2=[1−r1r 22][1−r 1−r 2
2] r i=M i
M H
120 =
16M H
∣AHP1 P2∣2
Scalar QED calculation at O() (II)IR divergences > photon mass m
UV divergences> dimensional regularizationpointlike weak coupling renormalized in MS scheme
here lies the true electroweak amplitude!!
b±0=1−1
2 ln
11−
1 2 =1r 122 −r2 1
2
virtual contributions real contributions
UV renormalization scale dependence (cancels out in the
product 012G12(E))
summing real and virtual corrections, IR log
divergences cancels out and G(E
max) ln( M∝ H/ E
max )
need to know Emax
b−=12−
4−12−2
22 2
8ln
11−
1 2
General formulasvalid for neutral>charged+chargedand charged>charged+neutral modes
“Bond” factor for the two cases
E.B. & G. Isidori hepph/0508071
Elisabetta Baracchini IFAE 2006
8
Unfortunately, in the real world....Experimental issue
in current experiment spectrum of soft photons in Bh1h
2 is
unobserved
in general, need MC to interpret data from rare decays: two approaches
no MC simulation of brehmsstrahlung no clear knowledge of what is assumed (i.e. Belle and CLEO)
data include events with radiated photons: are they assigned to signal or background by the fit?
MC simulation of brehmsstrahlung (PHOTOS) need to be very careful to quote the measure BR in a consistent way (i.e. BaBar)
need a clear definition of the imposed cut on photon energy how much are we confident in PHOTOS performances?
Elisabetta Baracchini IFAE 2006
9In the real world...what BaBar does with PHOTOS
In MC generate a decay channel plus any number of bremsstrahlung photons in full spectrum region allowed by phase space
Impose cuts on data sample and then account for the efficiency as obtained from the MC this means taking into account all the photons and quoting
BR(Bh+h+ any kinematically allowed brehmsstrahlung photons)
i.e. Emax= MBm
h+m
h
not very useful for phenomenology extrapolation of nonradiative BR(Bh+h) clear only for small energies of radiated photons (scalar QED valid up to O(Emax/M
B))
not really clean even experimentally efficiency estimated from MC simulation which is said to reproduce scalar QEDwhat to do?
choose a variable clearly related to Emax
(i.e. )
define data sample as events matching the requirement account for the efficiency as obtained on THIS data sample now X=E
max and your quoting
E=E B∗−s /2
∣E∣X
BRB hh−n ∣E E max
Elisabetta Baracchini IFAE 2006
need to estimate fromMC the difference between a E cut
and a E cut
10In the real world...what you can do with BaBar results
As a cut |E|< X is used in the analysis, just need to remove from the quoted BR the efficiency related to it
Waiting for BaBar to do that, in the meanwhile can estimate the effect through the p.d.f used to parametrize E
For the BK modes correct only K+ and K0+ do not correct K00 (no charged particles) and K+E tail completely dominated by 0 )
With these values the following ratios are obtained:
compatible with zero!!
BR 4sBB−/BR 4s B0 B0having corrected also all BR for the ratio
Elisabetta Baracchini IFAE 2006
11
⟨KI=1 /2∣H effI=0∣B⟩∝P
⟨KI=1 /2∣H effI=1∣B ⟩∝T 1
Knowing how to remove QED as a source of isospin breaking...
Isospin analysis of Kπ modesThe operators of any dimensionsix effective Hamiltonian contributing to
BK decays (even allowing for NP) carry isospin I=0 or I=1
We can then introduce a minimal set of matrix elements with defined isospin quantum numbers:
⟨KI=3/2∣H effI=1∣B ⟩∝T 3
linear combination of different amplitudes different
combinationsof CKM terms
need additional complex parameters to describe the B meson decays
see next slides
chosen real for phase convention
complex parameters
Elisabetta Baracchini IFAE 2006
12Inclusion of Electroweak Penguinsstarting from the effective Hamiltonian for b s transitions H eff=
GF
2∑
i
V CKMi C iQi
Due to |C7,8
| << |C9,10
|, neglect Q7 and Q
8
see hepph/0601233
Introduced for historical reasons (replacements
e.m.)
Not needed and can be rewritten in terms of:
Q9=32Q1
suu−Q 1scc 3Q1
scc−12
Q3s
Q10=32Q2
suu−Q2scc 3Q2
scc−12
Q4s
contributing to I=1parts of V
ub V
us
amplitude, but with different weak
phase. Relevant for CP asymmetries
contributing to I=0penguin V
tb V
ts
amplitude. Change its size but with a reduced impact
(~ae.m.
suppression)
Q±=Q1±Q2
2
C±=C1±C2
C±EW=C9±C10
the effective Hamiltonian becomes
with
Elisabetta Baracchini IFAE 2006
13Inclusion of Electroweak Penguins (II)C
EW /C≈C−EW /C−
equal at LO and broken by O(s
e.m.log)
0.00565 0.00564
H eff≃GF
2{V ub
∗ V us [1EW CQsuu−Q
scc1−EW C−Q−suu−Q−
scc ]−V tb∗ V ts H I=0} EW≡−
32
CEW
C
V tb∗ V ts
V ub∗ V us
H eff I=1
H eff I=1−
different CKM coefficients
Assuming no NP at tree level and no NP in EWP (NP doesn't break SU(2)), any NP amplitude can be reabsorbed
into the definition of P and P
in general and will transform in a different wayunder CP conjugation
⟨KI=1 /2,3 /2∣H effI=0,1∣B ⟩ ⟨KI=1 /2,3 /2∣H eff
I=0,1∣B ⟩
T 1=V ub V us∗ {1EW
∗ t 1 e i1
1−EW∗ t1
−e i1−
}T 1=V ub∗ V us{1EW t 1
e i1
1−EW t1−e i1
−
}
T 3=V ub V us∗ {1EW
∗ t31−EW
∗ t 3−}
P=∣V tb V ts∣P e iP P=∣V tb V ts∣P e iP
T 3=V ub∗ V us{1EW t3
1−EW t 3−}
writing out explicitly the CKM coefficients, our parameters will be:
B decays B decaysElisabetta Baracchini IFAE 2006
14
ABK0=−P−T 1T 3
2 ABK 0=PT 12 T 3
AB0K−=P−T 1T 3
2 AB0K00=−PT 12 T 3
Isospin fit to B K modes (SM+NP)
similar decomposition for the B and B
with the substitution
P P
fit to the 10 parameters
with 8 inputs (BR, ACP
and S00
)
and the assumption
not used as input ACP K00
P , p , P ,P , t 1 ,1
, t1− ,1
− , t 3 , t 3
− and fixed to the UTfit analysis output
predicted whitin ~1 from exp. results
T 1 T 1 T 3 T 3
fit result in terms of BR, ACP
and S00 t 3
− / t 30.5
Elisabetta Baracchini IFAE 2006
the only (and very weak) model dependent assumption
15Relations among asymmetries
NOT correlated
Puzzle solved?...in agreement with NLO pQCD
calculation [hepph/0508041]where “fat” penguin with a
relevant strong phase is included...
Elisabetta Baracchini IFAE 2006
able to reproduce the experimental pattern
correlated
=0.2 =0.07
=0.009
16Fit results on hadronic parameters
Elisabetta Baracchini IFAE 2006
P
P
t+1
t1
t+3
t3
17ConclusionsTwo sources for the BK puzzle: ratios of BRs
and
A
cp
First step: remove EM correction as a source of isospin breaking
need for proper treatment of QED both in the data analysis and in phenomenological application of measured quantities
obtain using nonradiative BR
Second step: isospin fit to Kmodes able to include dominant EWP without additional hadronic matrix element
able to reproduce relation between asymmetries and to predict A(K00)
puzzle solved allowing a “fat” penguin with a relevant strong phase?
Rc−Rn≈0
Elisabetta Baracchini IFAE 2006
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