What can be learned from decays?Giulia Bampa

ContentsContents

2

3

How did previous physicists learn so much about weak interaction by analyzing the decays?

4

Why are we studying decays?Why are we studying decays?

• The analysis of decays is very important since it gives “real-world” tests of the theory

Does a particular decay - allowable in theory –

occur in practice?

‘If it is permitted, it must happen’ – or our theory is

incomplete

Do the decays we observe have the

characteristics we expect?

If they don’t, we need to figure out why

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The The mostmost famousfamous ββ-decay-decay• Alpha decay is mono-energetic and was already well understood by the

early 20th century:

• Simple conservation of the four-momenta was enough to predict that alpha decay is mono-energetic, and experiments confirmed this

• Against this background, one might have expected beta decay to be similar:

• In fact, experiments showed them to be characterized by an energy distribution – suggesting the existence of new particles which “share” the energy with the electrons: neutrinos (1930, W. Pauli)

pn

eE

e#

E

#

e particleexp

eepn

ParityParity violationviolation

6

• The ττ--θθ puzzle puzzle: the τ and the θ must be different particles since their spin-

parity are different; the τ and the θ are not different particles, since they have the

same masses and lifetimes.

!

0 , 3

0 , 2

exp

,0

P

PCJ

P

J

JP

ParityParity violationviolation

7

• The ττ--θθ puzzle puzzle: the τ and the θ must be different particles since their spin-

parity are different; the τ and the θ are not different particles, since they have the

same masses and lifetimes.

• In 1956 Lee and Yang suggested that θ and τ were different decay modes of the same particle (K-meson), and that parity was not conserved in the weak interaction

While the strong and electromagnetic interactions conserve While the strong and electromagnetic interactions conserve parity, parity,

weak interactions do not weak interactions do not !!

!

0 , 3

0 , 2

exp

,0

P

PCJ

P

J

JP

8

Fermi theoryFermi theory Analogy with the electromagnetic

interaction:

e

)( )( uuuuGM enpfi

eeppfi uuq

uuepjejeM

)1

( )()(2

22

e.m. charge

propagator Dirac spinors

interaction

First approximation:

POINT-LIKE interactionPOINT-LIKE interaction

9

5

5i

i

scalar (S)

vector (V)

tensor (T)

axial vector (A) pseudoscalar (P)

There is no a priori reason why the weak current should be a vector

current

Every covariant current is in principle a possible candidate

iO

NOTE that Fermi hypothesis cannot account for the parity violation… Perhaps not surprisingly, given that it had not yet been discovered!

] )1( [ ) (2 i

5 uOuuOuCG

M ienipifi

10

M.me Wu’s M.me Wu’s experimentexperiment ee NiCo 6028

6027

Parity violation

V-A interaction

low energy recoil

e e

low energy recoil

e e

high

energyrecoil

e

e

high

energyrecoil

e

e

right-handed electron

left-handed electron

right-handed electron

left-handed electron

S

VV

T

AA

cos1 cv

cos1 cv

cos1 31

cv

cos1 31

cv

cos1c

vI

1 2

5 uuG

M fi

ΛΛ0 0 vs nvs n

Neutron decay Lambda decay

11

d

u ee

W

s

u ee

W

e

uuuug

M edun 1 1

25

215

21

2

e

uuuug

M edsn 1 1

25

215

21

2

%100 epenBR 40 1014.032.8 epeBR

12

Cabibbo theoryCabibbo theory

ccw sdd sincos 98.0cos, 22.0sin CC

B. Povh, K. Ritz, C. Scholtz, F. Zetsche, Teilchen und Kerne, Springer-Verlag (1995)

are the eigenstates of the weak interaction wqare the eigenstates of the strong interaction

qwhere

00

10)( re whe 212

121charg iqqgJ LL

According to the Cabibbo theory,

…but although theory predicts the amplitude for the decay should be proportional to , experiment suggests a rate many orders of magnitude weaker!

The suppression of KThe suppression of K00μμ++μμ-- … …

13

K

s

u

Ws

d

0Z0K

cccc dsdsssdduuJ cossin)(sincos 22neutr

ΔS=1

cc cossin

%5.63expBR % 103.7 7

exp

BR

2216.0

10

01 re whe 33

neutr LL qqgJ

ΔS=1

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……and the and the existenceexistence of the charm of the charm quarkquark• In 1970 Glashow, Iliopoulos and Maiani solved this problem by

proposing the existence of a new quark which belongs to a “second generation” doublet

• According to the GIM mechanism,

…meaning the neutral current makes no contribution to strangeness-changing decays !

ww

GIM

w s

c

d

u

d

uwhere

ccw ds

c

s

c

sincos

cc

cc

dsdsdsds

ddssssddccuuJ

cossin)(

sin)(cos)( 220

Second order diagrams for KSecond order diagrams for K00

15

u-exchange graph c-exchange graph

If this decay is STRONGLY suppressed, why we have a finite value for the BR (and not an upper

limit)?

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Cabibbo-Kobayashi-Maskawa Cabibbo-Kobayashi-Maskawa matrixmatrix

b

s

d

VVV

VVV

VVV

b

s

d

tbtstd

cbcscd

ubusud

w

w

w

www b

t

s

c

d

u

bWtsbBB

lDBKlDXN

lXBlK

VVV

VVV

VVV

dd

ud

tbtstd

cbcscd

ubusud

decay

A less “theoretical” and more “experimental” CKM matrix:

E. Golowich (talk at II° Int. Conf. on B-physics and CP-Violation), arXiv:hep-ph/9706548v1

A new family of quarks (nice analogy with leptons!):

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00034.000004.0

312.078.0

332.064.0

309.080.0

300024.000023.0

999100.010)61.41(10)14.8(

10)21.42(00024.097296.00010.02271.0

10)09.096.3(0010.02272.097383.0

C. Amsler et al. (Particle Data Group), Physics Letters B667, 1 (2008)

132313231223121323122312

132313231223121323122312

1313121312

ccescsscesccss

csesssccessccs

escscc

Vii

ii

i

Standard parameterizationStandard parameterization:

where

ijijijij cs cos , sin

The factor δ is the so-called “Kobayashi-Maskawa phase”.

and 3,2,1, ji arethe family labels.

FeaturesFeatures:

1. in the limit of where !

2. the phase-term is responsible for all CP-violating phenomena in flavor changing processes in the standard model

s

d

s

d

w

w cossin

sincos 0

1212

12122313

Cabibbo 12

NumbersNumbers:

18

19

PrincipalPrincipal features offeatures of D-mesonsD-mesons

P Anti-Pquark.-const.

Rest mass [MeV]

S C BLifetime

[s]

D+ D- cd1869.4

0+1

0 10.6x10-13

D0 D0 cu1864.6

0+1

0 4.2x10-13

D+s D-

s cs 1969+1

+1

04.7x10-13

C. Amsler et al. (Particle Data Group), Physics Letters B667, 1 (2008)

CBSY 31

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LeptonicLeptonic and rare and rare decaysdecaysThe possible decays are:

eq eD ,,

eD0

00 and , DeeD

ehllhllhDD s ,,,

21

llD

lluc

Why are they interesting?

• They are expected to be very rare in the standard model

some slides ago, we see that the K0 decay is strongly suppressed by the GIM!

• Lepton family number violation is strictly forbidden

Flavor-changing neutral currents Flavor-changing neutral currents (FCNC)(FCNC)

dD

0Z

d

c

u

l l

We are looking for

There are two different diagrams which contribute to the :

Theoretical calculations (QCD…) provide this order of magnitude for the branching ratio:

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A. Freyberger et al., Phys. Rev. Lett. 76, 17 (1996)

lluc

8

.10

theorucBR

23

D0 detector at FERMILABD0 detector at FERMILAB

ppTeV 96.1s

Projection End view of the collision, with charged particle tracks in the silicon detector, the energy deposited in the calorimeters, and possibly hits in the muon detectors.

The inner part, with the concentric circles, shows the locations, to scale, of the tracking detectors. The outer concentric ring is a histogram of deposited energies

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Analysis of the dataAnalysis of the data

V. Abazov et al., Phys. Rev. Lett. 100, 101801 (2008)

4

5

5

6

1019.086.2

101.30.9

1028.055.4

108.08.5

BR

BR

BR

BR

,,, where, XX

Check of the detectorCheck of the detector

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D

In order to check this detector, we can focus on a “known” reaction:

V. Abazov et al., Phys. Rev. Lett. 100, 101801 (2008)

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V. Abazov et al., Phys. Rev. Lett. 100, 101801 (2008)

610syst6.0stat5.08.1 DBR

From the last graph, it is possible to extract the branching ratio:

BRDBR

DBR

f

f

Dn

Dn

sss

Dc

Dc

s

The yield ratio is related to the branching ratio by:

which is consistent with expected value given by the product of

61026.086.1 BRDBR

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610syst6.0stat5.08.1 DBR

From the last graph, it is possible to extract the branching ratio:

BRDBR

DBR

f

f

Dn

Dn

sss

Dc

Dc

s

The yield ratio is related to the branching ratio by:

which is consistent with expected value given by the product of

61026.086.1 BRDBR

…what would have happened if it wasn’t consistent?

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Now, we search for the continuum decay of D+ mediated by FCNC interactions, eliminating the condition on the dimuon invariant mass.

09.2

BRDBR

DBR

6109.3 DBR

V. Abazov et al., Phys. Rev. Lett. 100, 101801 (2008)

This is ≈ 500 times above the SM expected rate .

Conclusions of the experimentConclusions of the experiment

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This is the most stringent limit to date in a decay c u μ+ μ-

It’s 500 times above the Standard Model expected rate

SM pass the test!

Other models can be ruled out

little Higgs model, SUSY, etc

SummarySummary

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We saw the “step-by-step” historical evolution of the theory for the weak interaction and the fundamental role played by fundamental role played by the studies on decaysthe studies on decays

We analyze a present experimentpresent experiment in the c-sector

ReferencesReferences

• S. Bianco, F. Fabbri, D. Benson, I. Bigi, A Cicerone for the Physics of Charm, hep-ex/0309021 (2008)

• C. Amsler et al. (Particle Data Group), Phys. Lett. B667, 1 (2008)

• V. Abazov et al., Phys. Rev. Lett. 100, 101801 (2008)

• W. E. Burcham, M. Jobes, Nuclear and Particle Physics, Prentice Hall (1979)

• B. Povh, K. Rith, C. Scholz, F. Zetsche, Particles and Nuclei, Springer (1996)

• H. Frauenfelder, Subatomic Physics, Prentice-Hall (1974)

… and of course, Wikipedia!

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2 ,1 ,0' 1

1' 0 1,0

1 0 ,1

lS

lSS

JJJJJ

f

ff

fdfi

How to handle with the JHow to handle with the JPP

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1. Let’s take a very common reaction:

2. If the parity is conserved, I would aspect:

3. Consider also the conservation of J:

4. Consider the total asymmetry

5. ...and then, give a number for

nnd

'2 ln

llnpfi relrel

d

rel

So called “intrinsic parity”Parity related to the relative motion

τ-θ