1 QED corrections and the B Kπ puzzleifae2006/talks/FisicaSapore/Baracchini.pdf · Elisabetta...

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


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


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


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


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


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?


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


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


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


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


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


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...


able to reproduce the experimental pattern

correlated

=0.2 =0.07

=0.009

16Fit results on hadronic parameters


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


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