Branching ratio and helicity amplitudes for L b L (pK) g decays ( L spin = 3/2)

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:

2

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

5

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)

LHCb

B fa

ctor

ies

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

du

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

du

b

du

b

uu

pK

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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


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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)


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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 matrix element:

b

(p, s)

(q,)

(p´,s´)

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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


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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!

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 + QCDb Polarization = 20%

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Combined measurements1 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

Documents

Branching ratio and helicity amplitudes for L b L (pK) g decays ( L spin = 3/2)