Exclusive b → s Transitions at the LHC
Patricia Ball
IPPP, Durham
1st LHCb Upgrade Workshop, Jan 11 2007
Why b → s?
b → sγ & b → s`+ `− are FCNC processes: not allowed at tree level in the
SM
in the SM, FNCN processes governed by GIM mechanism, induces
sensitivity to higher scales (mt , mW ) and CKM elements, in particular
Vts , Vtb (and Vtd for b → d transitions)
FCNC processes sensitive to physics beyond the SM, and BSM
amplitudes (possibly) comparable to those of SM
BSM models studied in literature: MSSM (of course!) (with and without R
parity), (universal) extra dimensions, left-right symmetric model, model
with 4 quark generations. . .
inclusive ↔ exclusive processes: exclusive wins at the LHC. . .
Patricia Ball
– p.1/21
Observables
B → K ∗γ
branching ratio
isospin asymmetry
CP asymmetry
B → K ∗ `+ `−
branching ratio
forward-backward asymmetry
helicity/transversity amplitudes (partially integrated over invariant
lepton mass)
Bs → ` + ` −
branching ratio
Patricia Ball
– p.2/21
B → K ∗γ
Patricia Ball
– p.3/21
Theory Framework
naive factorisation: A(B → V γ) = hV γ|Heff |Bi ∝ T1B→V (0)
QCD factorisation:
A(B → V γ) =
(Bosch/Buchalla 01)
8 X
X
λU Ci hV γ|QU
i |Bi
i=1 U =u,c
hV γ|QU
i |Bi =
T1B→V (0) TiI +
Z
1
0
dξ du TiII (ξ, u) φB (ξ) φ⊥
2;V (u) · e
λU : CKM factors
Ci , TiI,II : perturbative QCD quantities
T1 , φ B , φ ⊥
2;V : non-perturbative QCD quantities
QCD factorisation formula valid to leading order in 1/mb
Patricia Ball
– p.4/21
Theory Framework
Contributions at O(1/mb ):
b
b
D
D
B
V
q
B
V
q
(a)
q
(b)
weak annihilation
soft gluon emission
can be treated in QCDF
beyond QCDF, new method
developed by
Ball/Jones/Zwicky 06
relevant for B(B → ργ) and isospin
asymmetries
long-distance photon emission, beyond QCDF, relevant for B(B ± →
ρ± γ)
Patricia Ball
relevant for B(B → V γ) and
time-dependent CP
asymmetry
– p.5/21
Status of Branching Ratio
inclusive:
(Misiak et al. 06)
Bexp (B → Xs γ)|Eγ >1.6 GeV = (3.55 ± 0.26) × 10−4
Bth (B → Xs γ)|Eγ >1.6 GeV = (3.15 ± 0.23) × 10−4
exclusive:
(Ball et al. 06)
Bexp (B − → K ∗− γ) = (40.3 ± 2.6) × 10−6
Bth (B − → K ∗− γ) = (54.2 ± 13.2 (form factor) ± 6.7) × 10−6
space for some, but not much new physics (in Wilson coefficient C7 or
from new operators)
spin-flipped amplitudes (γR instead of γL ) not strongly constrained as
L/R amplitudes add incoherently
Patricia Ball
– p.6/21
Isospin Asymmetry
0
∗0
±
∗±
Γ(
B̄
→
K
γ)
−
Γ(B
→
K
γ)
∗
AI (K ) =
Γ(B̄ 0 → K ∗0 γ) + Γ(B ± → K ∗± γ)
(Kagan/Neubert 2002)
AI (K ∗ )
AI (K ∗ ) = (5.4 ± 1.0(µ) ± 0.6(NLO ↔ LO) ± 0.6(fB ) ± 0.6(other))%
= (5.4 ± 1.4)%
(Ball/Jones/Zwicky 06)
12.
10.
r = a6 /aSM
6
8.
6.
a6 = C5 + C6 /3
4.
2.
Sensitive to penguin operators!
0.
0.25
0.75
1.25
1.75
r
Patricia Ball
– p.7/21
Time-Dependent CP Asymmetry
(Atwood/Gronau/Soni 97, Grinstein/Pirjol 05, Ball/Zwicky 06)
b → sγ is actually either bR → sL γL (with, in the SM, a helicity factor mb )
or bL → sR γR (with, in the SM, a helicity factor ms ):
γ dominantly left-polarised, γR suppressed by ms /mb
entails a small time-dependent CP asymmetry (interference of γL /γR
amplitudes):
Γ(B̄ 0 (t) → K̄ ∗0 γ) − Γ(B 0 (t) → K ∗0 γ)
ACP =
Γ(B̄ 0 (t) → K̄ ∗0 γ) + Γ(B 0 (t) → K ∗0 γ)
= −(2.2 ± 1.5+1
−0 )%
ms
≈ −2
sin(2β) sin(∆mB t)
mb
(K ∗ , K̄ ∗ observed as CP eigenstate KS π )
helicity suppression removed by NP if spin flip can occur on virtual line
(e.g. left-right symmetric model, MSSM)
Patricia Ball
O – p.8/21
Time-Dependent CP Asymmetry
(Atwood/Gronau/Soni 97, Grinstein/Pirjol 05, Ball/Zwicky 06)
Not for LHCb!?
Patricia Ball
– p.8/21
Theory Prospects for 2010
small improvement of inclusive theory error (dominated at present by
non-perturbative effects)
improvement of exclusive theory error requires input from lattice
calculations (unquenched) — planned
improvement of prediction for isospin asymmetry requires including
radiative corrections — can be done, given enough manpower
Patricia Ball
– p.9/21
B → K ∗ `+ `−
Patricia Ball
– p.10/21
Observables
B(B → Xs`+` )
HFAG
August 2006
π`+ `−
π 0 `+ `−
π + `+ `−
CLE O
Belle
BABA R
PDG2006
New A vg.
+ −
Kl l
Kµ +µ−
NP extraction from B(B → K ∗ `+ `− )
hampered by hadronic (form factor)
uncertainties
better consider ratios:
Γ(B → Kµ+ µ− )
R=
= 1.0000 ± 0.0001
+
−
Γ(B → Ke e )
Ke+ e−
K 0 e+ e−
K + µ+ µ −
K 0 µ+ µ−
(Hiller/Krüger 04)
K + e+ e−
+ −
∗
K (892)l l
enhanced by large tan β
K ∗ (892)µ+ µ−
K ∗ (892)0 µ+ µ−
or asymmetries:
K ∗ (892)+ µ+ µ−
K ∗ (892)e+ e−
forward-backward asymmetry AF B
K ∗ (892)0 e+ e−
K ∗ (892)+ e+ e−
has a zero in SM, position largely
independent of form factors
sl+ l−
sµ+ µ−
se+ e−
transverse asymmetries
0.0
Patricia Ball
5.0
Branching Ratio x 106
10.0
– p.11/21
Spin Amplitudes
B 0 → K ∗0 (→ K − π + )`+ `− : differential distribution:
d4 Γ ∝ I(s, θl , θK ∗ , φ)dsd cos θl d cos θK ∗ dφ depends on 4 spin amplitudes:
A⊥ , A k , A 0 , A t
Patricia Ball
O – p.12/21
Spin Amplitudes
Can construct various observables: e.g. forward-backward asymmetry AF B
and
−2Re(Ak A∗⊥ ) (2)
|A2⊥ | − |Ak |2
(1)
transverse asymmetries: AT (s) =
, AT (s) = 2
.
2
2
2
|Ak | + |A⊥ |
|Ak | + |A⊥ |
Patricia Ball
O – p.12/21
Spin Amplitudes
To what accuracy can these amplitudes be measured at LHCb/upgrade?
Patricia Ball
– p.12/21
1
0.8
0.6
0.4
0.2
-0
-0.2
-0.4
-0.6
-0.8
-1
0
1.4
b)
a)
1.2
1
FL
A FB
Current Experimental Status of Asymmetries
0.8
0.6
0.4
0.2
2
4
6
0
0
8 10 12 14 16 18 20
2
q 2 (GeV /c 4 )
AFB (bkg-sub)
FB Asymmetry, BaBar 06
2
4
6
8 10 12 14 16 18 20
2
q 2 (GeV /c 4 )
Longitudinal polarisation fraction
1
0.5
0
-0.5
-1
0
2
4
6
8
10
12
14
16
2
q
18
20
2
GeV /c
2
FB Asymmetry, Belle 06
Patricia Ball
– p.13/21
Theory Framework (Beneke/Feldmann/Seidel 01/04)
similar to B → K ∗ γ : QCD
factorisation, include
non-factorisable radiative
corrections
only valid to leading order in 1/mb
and for small q 2 : otherwise, QCD
factorisation breaks down
charm resonances cause
amplitude to diverge for
q 2 → 4m2c ; restrict calculations to
q 2 < 3m2c ≈ 6 GeV2
position of zero of AF B shifted
upon LO → NLO
Patricia Ball
– p.14/21
Theory Homework
most analyses leading order in 1/mb & use heavy-quark-symmetry
relations between form factors
(Beneke/Feldmann/Seidel 01/04, Ali/Kramer/Zhu 06)
subleading form factor effects?
2 form factors in QCDF, 7 in full QCD
charm loop corrections ∼ ΛQCD mb /m2c — not included
treat as in B → V γ ?
Consistent treatment of all b → s using the same theory input?
Patricia Ball
– p.15/21
Spin-Flipped Currents in SUSY (Lunghi/Matias 06)
NP via new operator O70 ∝ s̄σµν PL bF µν (SM has O7 ∝ s̄σµν PR bF µν )
NP ↔ gluino-squark loops
(1,2)
integrated transverse asymmetries AT not very sensitive to hadronic
form factors and NLO QCD factorisation corrections
Patricia Ball
1
4.25
0.75
4
0.5
3.75
0.25
AT 1,2
BR HB -> Xs ΓL ´ 104
4.5
3.5
0
3.25
-0.25
3
-0.5
2.75
-0.75
-0.4 -0.2 0 0.2 0.4
Ceff7' HΜb L
AT 1
AT 2
NLO
-0.2 -0.1 0 0.1
Ceff7' HΜb L
0.2
– p.16/21
! "
5
FB Asymmetry in B → K ∗``
resonances
4
0.4
purely SD
contrib.
3
MIA (C 7>0, C10>0)
0.2
MIA (C 7<0, C10>0)
SUGRA
SUGRA (C 7 <0)
MIA (C 7<0)
-0.2
1
SM+FF uncertainties
15
20
0
2
4
6
10
8
#
&
'
%$
5
SUGRA, MIA (C 7>0)
-0.4
0
0
SM
*)(
2
0
MIA
part of hadronic uncertainties cancels in FB asymmetry
Patricia Ball
– p.17/21
FB Asymmetry in B → K ∗``
Belle data (presented by J. Berryhill (BaBar), Moriond 06):
Patricia Ball
O – p.18/21
FB Asymmetry in B → K ∗``
Belle data (presented by J. Berryhill (BaBar), Moriond 06):
The fitted values for A7,9,10 may actually be wrong: QCD factorisation does
not work at large q 2 (1/mb exansion breaks down).
Better to rely on data at small q 2 < 8 GeV2 only, where theory is under better
control.
Patricia Ball
O – p.18/21
FB Asymmetry in B → K ∗``
Belle data (presented by J. Berryhill (BaBar), Moriond 06):
In any case, a reanalysis using recent form factor updates and a clean separation of leading and sub-leading (in 1/mb ) terms would be timely & useful.
(Ball/NN/Zwicky, planned)
Patricia Ball
– p.18/21
Bs → µ + µ −
Patricia Ball
– p.19/21
Bs → µ + µ −
GIM and helicity suppressed in SM, predicted BR: 4 × 10−9
current experimental bound: 8 × 10−8 (CDF)
SUSY Higgs penguins enhance BR with tan6 β
(Dedes 03)
Patricia Ball
O – p.20/21
Bs → µ + µ −
GIM and helicity suppressed in SM, predicted BR: 4 × 10−9
current experimental bound: 8 × 10−8 (CDF)
SUSY Higgs penguins enhance BR with tan6 β
2006 bound
Still a factor of 20 for
NP to hide!
(Dedes 03)
Patricia Ball
heavy Higgs
O – p.20/21
Bs → µ + µ −
GIM and helicity suppressed in SM, predicted BR: 4 × 10−9
current experimental bound: 8 × 10−8 (CDF)
SUSY Higgs penguins enhance BR with tan6 β
The ultimate Higgs penguin: Bs → eµ:
Higgs induced FCNC + Higgs mediated lepton flavour violation!
Current bound on BR: 6 × 10−6 (CDF).
Patricia Ball
– p.20/21
Summary & Prospects
exclusive b → sγ, µ+ µ− very versatile NP discovery/constraints channel
for LHCb
good (theory-robust) observables:
isospin and CP asymmetry in B → K ∗ γ
foward-backward asymmetry in B → K ∗ `+ `−
transversity asymmetries
homework for theorists:
form factors (this appears to be a time-invariant statement. . . )
include effect of charm loops
question to experimentalists:
measurement of spin/helicity amplitudes in B → K ∗ `+ `− ?
Patricia Ball
– p.21/21