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Branching ratio and helicity amplitudes for b (pK) decays ( spin = 3/2)
Combined work of:Gudrun Hiller (Dortmund UNI), the Bearer of the Light
Thomas Schietinger (PSI), the ScholarMathias Knecht and Federica Legger (EPFL), the water
Carriers
Theoretical physics for experimentalists:
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Outline
Once upon a time: the electromagnetic penguin bs the photon polarization (theory and
experiment) my thesis results & open questions
The mighty quest for spin = 3/2: Branching ratio for b (pK)
the tools: Mathematica Helicity amplitudes Sensitivity to photon polarization
Summary and outlook
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Motivations Standard Model (SM): best description of known
elementary particles and their interactions: passed all experimental tests up to now; still one missing particle, the Higgs boson.
However... 19 (!!!) free parameters; gravity is not included.
Quest for new physics in the quark sector: CKM picture is very successful
but we still know little about b s, d transitions !
quarks
leptons
ud
cs
tb
ee
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The electromagnetic penguin bs
New physics in the decay rate : are there any contribution from supersymmetric particles? the measured bs branching fraction is compatible with SM
prediction Theory: BF(bs) [10-6]= 357 ± 30
Experiment: BF(bs) [10-6]= 355 ± 24 +9-10 ± 3
from HFAG (combined measurements by Belle, BaBar, CLEO) Need other observables to test the SM...
Gambino, Misiak, NPB 611 (2001) 338
http://www.slac.stanford.edu/xorg/hfag/rare
b
s
u,c,t
W
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b
s
u,c,t
W
The W boson only couples to a left-handed s quark
Left-handed photon (to conserve ang. momentum)
“Naïve” SMAtwood, Gronau, Soni, PRL 79, 185 (1997)
Photon polarization:
pure 2-body decay: right-handed components of the order of r = ms/mb
Grinstein, Grossman, Ligeti, Pirjol, PRD 71, 011504 (2005)
SM + QCD when considering bs + gluons right-handed components may be up to 10-15% explicit calculations only for BK*B
The electromagnetic penguin bs
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Photon polarization measurements
Melikov, Nikitin, Simula, PLB 442, 381 (1998)
Grossman, Pirjol, JHEP06, 029 (2000)
Atwood, Gronau, Soni, PRL 79, 185 (1997)
Mannel, Recksiegel, JPG: NPP 24, 979 (1998)
LHC
bB
fact
ori
es
Knecht, Schietinger, PLB 634, 403 (2006)
Gronau, Pirjol, PRD 66, 054008 (2002)
B-B interference
First measurements of K* polarization in B->K*l+l- by Belle/Babar
e+e- conversion
Exp. status Theor. Refs.
Latest world averagesin2 = 0.0 ± 0.3
Higher K* resonances
Difficult to disentangle resonance structure (Babar, hep/0507031)
Gronau, Grossman, Pirjol, PRL 88, 051802 (2002)
Charmonium res. interference
No results so far...
b-baryons Hiller, Kagan, PRD 65, 074038 (2002)
Exploit ang. correlations between polarized initial state and final state. Under study at LHCb (F.Legger, M. Knecht) Legger, Schietinger,
PLB 644 (2007) xxx
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Polarized b baryons decays
s
d u
b
d
u
b
Hiller, Kagan, PRD 65, 074038 (2002)
If initial state is polarized: exploit angular correlations between initial and final
states only possible with b baryons feasible at hadron colliders
Mannel, Recksiegel, JPG: NPP 24, 979 (1998)
Case study: b ((1115) p)
Long distance contributions from internal W exchange, or vector meson cc contributions are expected to be small
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Polarized b (1115) decays
Angular distributions
depend on photon polarization
PB = b polarization p = weak decay
parameter
Evtgen= 1PB = 1
cos, b rest frame cosp, rest frame
b (1115)
(fit) = 1.036 (theory) = 1
p (fit) = 0.679p (theory) = 0.642
b (1115)
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However...
From the experimental point of view the decay b (1115) is quite hard to observe (c = 7.89 cm)
Can we probe the photon polarization in heavier resonance decays?
b ((X) pK)
what do we need? Branching ratios for b (X) Angular distributions for spin = 1/2, 3/2
spin > 3/2: helicity states > observables
s
d
u
b
d
u
b
u
up
K
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(X) resonance spectrum
16901670
spin = 1/2 spin = 3/21520
Invariant pK mass spectrum obtained with: BR(b (X) ), calculated rescaling BR(b (1115) )
with a kinematical factor, assuming the same form factors and no spin dependence for all (X) resonances.
PDG 2004
Legger, Schietinger, PLB 644 (2007) xxx
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Helicity formalism for b (pK)
Photon helicity = ±1, helicity = ±1/2 2 helicity amplitudes
Photon angular distribution
Proton angular distribution flat because of P conservation
J = 1/2
Photon helicity = ±1, helicity = ±1/2, ±3/2 4 helicity amplitudes
Photon angular distribution
J = 3/2
Legger, Schietinger, PLB 644 (2007) xxx
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depends on the asymmetry of b spin with respect to photon momentum
and can be factorized into the photon helicity parameter and the strong parameter
can be extracted from the proton angular distribution
b (pK) decays(J = 3/2)
Legger, Schietinger, PLB 644 (2007) xxx
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The photon helicity can be probed in decays involving resonances of spin 3/2 by measuring 3/2 and
Can we get a better estimate of the BR ? Include at least the spin dependence Form factors will have to be measured
Can we get an estimation of ?
Open questions
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Electromagnetic dipole operators:
long distance effects non perturbative
approach (HQET)
Wilson coefficients: C7, C7’ short distance Fermi theory (point-like
interactions)
The effective hamiltonian:
Decay amplitude for b (1520)
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The effective hamiltonian:
Decay amplitude for b (1520)
The matrix element:
b
(p, s)
(q,)
(p´,s´)
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The effective hamiltonian:
Decay amplitude for b (1520)
The matrix element:
Find and !!
u(p,s) = Dirac spinor to describe the b (spin 1/2)Rarita-Schwinger (RS) spinor to describe the (spin 3/2)
Dirac spinor
Polarization vector
1/2 1 = 3/2
Rarita, Schwinger, Phys Rev 60(1941) 61
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Conditions
Gauge invariance
On-shell photon
Equations of motion(EOM)
RS spinors
Main actors:
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and
Ansatz:
We define the tensor (antisymmetric in and ):
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and
Ansatz:
On-shell photon!
Reabsorbed in B and C using EOM
We define the tensor (antisymmetric in and ):
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and
We define the tensor (antisymmetric in and ):
Ansatz:
On-shell photon!
Reabsorbed in B and C using EOM
Contracting with q
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and
Form factors
(5) is related to (5) through the identity:
it is straightforward to obtain (ask Mathias) :
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Spin averaged matrix element
To evaluate the BR we need:
where
Writing explicitely the spinor indices!
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Spin averaged matrix element
Sum over spins:Aliev, Ozpineci, hep-ph/0406331
We finally obtain:
To calculate the trace we use:with the TRACER package
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Trace evaluation
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Trace evaluation
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Branching Ratio
In the limit
f2
BR (b 0 ~ 7·10-5
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HFAG ICHEP 2006
From B+ and B0 radiative decays, and dedicated form factors studies, BR should have the same order of magnitude
K*(892) = vector K1(1270) = axial vectorK1(1400) = axial vector K2*(1430) = tensor
S. Veseli, M.G. Olsson, Z. Phys. C 71 (1996) 287
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Helicity amplitudes
We use the b rest frame:
b
p´=(E´,0,0,E)q=(E,0,0,-E)
z
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Helicity amplitudes
The amplitudes A3/2 (A1/2 ) result from a b-baryon with
h = 1/2 (h = +1/2) and a photon with Jz = +1
Photon polarization vectors:
Jz in b rest frame:
polarization vectors:
helicity
RS spinor Dirac spinor
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Helicity amplitudes: results
In the limit and f1~f2
Right-handed photon
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Helicity amplitudes: naïve picture
b
Opposed b and b spin -> suppressed ~ O(1/mb)
Left-handed photon = SM
b
s
M. Suzuki, J. Phys. G: Nucl. Part. Phys. 31 (2005) 755
b
b
s
Spin flip b vs sQuark level:
b
s
Spin flip b vs
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Sensitivity to the photon polarization
Photon polarization:
b Polarization = 20%10k (1520) events (~3 yrs LHCb running)3 significance
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Conclusions and outlook
The BR(b ) has been calculated in the framework of HQET
form factors will need to be measured
Helicity amplitudes for the decay b have been evaluated
straightforward extension to decay involving JP
= 3/2+ resonances, by replacing C ’7-> -C ’7
Still to do: work out a better estimate of the Lb polarization
(Some) theoretical models and calculations are (also) accessible to experimentalists!
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Backup slides
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b production at LHC:
bb cross section in pp collision = 500 b 10% of produced bb hadronize in baryons b dominates (90%) b produced with transversal polarization
Expectations are PB ~ 20%
ATLAS plans to measure it with a statistical precision better than 1%
p1 p2
bn
Ajaltouni, Conte, Leitner, PLB, 614 (2005) 165
Feasibility of Beauty Baryon Polarization Measurement in b Jdecay channel by ATLAS – Atlas note 94-036 PHYS
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Photon polarization
b (1670) selected evts.transversally polarized b)
efficiency corrected (from unpolarized decays)
from data, the correction can be obtained from B K* decays
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Sensitivity on |r| measurement
Values of |r| that can be probed from single measurements
Getting close to the SM expected range, becomes interesting if NP!
1 year, 3 5 years, 3
SM naive
SM + QCD
SM naive
SM + QCD
b Polarization = 20%
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Combined measurements
1 year, 3 5 years, 3
SM naive
SM + QCD
Combining measurement increases range by a few percent at most
(X) measurements have good sensitivity (in case (1115) turns out to be difficult)
b Polarization = 20%
SM naive
SM + QCD
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Dependence on b polarization
If only the photon asymmetry is measured, a polarization of at least 20% is needed to have good sensitivity
b (X) b (1115) 1 year