Search for R-parity violatingSearch for R-parity violatingSupersymmetric effectsSupersymmetric effects

in the neutron beta decayin the neutron beta decay

N. Yamanaka(Osaka University)

2009 年 8 月 12日at KEK

In collaboration withT. Sato (Osaka univ.), T. Kubota (Osaka univ.)

arXiv:0908.1007 [hep-ph]

ContentsContents

• IntroductionIntroduction• Neutron beta decayNeutron beta decay• MSSM and R-parity violationMSSM and R-parity violation• Neutron Beta decay within RPVMSSMNeutron Beta decay within RPVMSSM• AnalysisAnalysis• SummarySummary

IntroductionIntroduction

Go beyond the Standard ModelGo beyond the Standard Model• Gauge group Gauge group SUSU(3)(3)CC××SUSU(2)(2)LL××UU(1)(1)YY

• 3 generations3 generations• 1 Higgs 1 Higgs SUSU(2)(2)LL doublet doublet

quarkleptongauge boson Higgs boson

Standard Model:Standard Model:

Reasons to go beyond the SM:Reasons to go beyond the SM:

Hierarchy problemsHierarchy problems Particle-antiparticle asymmetry (too many particles!)Particle-antiparticle asymmetry (too many particles!) No candidates of Dark Matter in SMNo candidates of Dark Matter in SM Evidence of neutrino oscillations (1998 Evidence of neutrino oscillations (1998 ～～ ))……

Approach to New PhysicsApproach to New PhysicsHigh energy approach:High energy approach:

Energy above the new physics threshold Energy above the new physics threshold ⇒ ⇒ create new particlescreate new particles

Ex: LHC (CERN)Ex: LHC (CERN)

Low enerLow energygy a apppproach:roach:

Very accurate experiments are now possible:Very accurate experiments are now possible: ⇒ ⇒ Observe the small discrepancy from SM by Observe the small discrepancy from SM by

precise measurements of low energy phenomenaprecise measurements of low energy phenomena

Phenomena:Phenomena:• EDMsEDMs• Decay phenomenaDecay phenomena• Muon g-2Muon g-2• … …

⇒ ⇒ Search for New physics beyond SMSearch for New physics beyond SM

Groups:Groups:• J-PARCJ-PARC• LANSCELANSCE• PSIPSI• ILLILL• … …

Neutron beta decayNeutron beta decay

New physics from beta decayNew physics from beta decayNeutron beta decay may involve many New PhysicsNeutron beta decay may involve many New Physics

Minimal supersymmetric standard model (MSSM)

R-parity violating MSSM

Left-Right symmetric model

Charged Higgs exchange

Leptoquark exchange

……

ee--

uudd

ee--

eeLL~~

~~ddRR

uu

ee--

dd

ee--

ObjectObjectR-parity violating MSSMR-parity violating MSSM contributes to the scalar contributes to the scalarinteraction at the interaction at the tree leveltree level !! !!

Investigate RPVMSSM contribution to the Investigate RPVMSSM contribution to the neutron beta decay.neutron beta decay.

Object:Object:

Recently,Recently,

• Measurement of Measurement of RR coefficient of the neutron beta decay coefficient of the neutron beta decay(Kozela (Kozela et alet al. (PSI), Phys.Rev.Lett.102, 2009). (PSI), Phys.Rev.Lett.102, 2009)

• Bound on Fierz interference term of the beta decayBound on Fierz interference term of the beta decay(Hardy & Towner, Phys. Rev. C 79, 055502, 2009)(Hardy & Towner, Phys. Rev. C 79, 055502, 2009)

⇒ ⇒ Both give Both give scalar interaction of the neutron beta decay of the neutron beta decay

Neutron beta decayNeutron beta decay

Neutron beta decayNeutron beta decayProcess:Process: ( ～ 100%)

Interaction Hamiltonian:Interaction Hamiltonian:

ee--

nn

ee--

pp

WW

V-A interaction:V-A interaction:Standard ModelStandard Model

ee--

ppnn

ee--

eeLL~~

Scalar interaction: Exotic!

Transition:Transition:

Angular correlationsAngular correlations

Decay distribution:

Angular dependence of the beta decayAngular dependence of the beta decay

Jackson, Treiman, Wyld, Nucl. Phys. 4, 206 (1957)

(no polarization)

(neutron polarization)

(e- polarization)

(neutron&e- polarization)

neutrino momentum & e- polarization: ⇒ new terms!!

MSSM and R-parity violationMSSM and R-parity violation

SupersymmetrySupersymmetrySymmetry between boson & fermion:

fermionfermion bosonboson ⇒ Each particle has a “super-partner”⇔⇔

⇒ Phenomenological extension of the SM!!

Minimal Supersymmetric Standard Model (MSSM):

⇒ ⇒ Gauge invariant, renormalizable,Gauge invariant, renormalizable, R-parity conservingR-parity conserving

particles particles s-particles s-particles

⇔⇔

Why SUSY?• SUSY cancels power divergences (Fine tuning)• SUSY can break the EW symmetry• Accurate GUT at 1016GeV• Dark matter, etc.

……

□□R parity violating lagrangian:□□R parity violating lagrangian:

R-parity violationR-parity violationR parity:R parity:

⇒Conservation of baryon and lepton number in MSSM.

RPVMSSM:RPVMSSM:

Add R-parity violating interactions to the MSSMAdd R-parity violating interactions to the MSSM

uudd

eeLL~~

LL or or BB violating violating

Neutron beta decayNeutron beta decaywithin RPVMSSMwithin RPVMSSM

Steps of calculationSteps of calculation

Beta decay within R parity violating MSSMBeta decay within R parity violating MSSMBeta decay within R parity violating MSSMBeta decay within R parity violating MSSM

Neutron Beta decay effective interactionNeutron Beta decay effective interactionNeutron Beta decay effective interactionNeutron Beta decay effective interaction

Angular correlation (coefficients)Angular correlation (coefficients)Angular correlation (coefficients)Angular correlation (coefficients)

Plan:Plan:

RPV lagrangian & limitsRPV lagrangian & limits

Barger, Giudice, Han, Phys. Rev. D409, 2987 (1989)Barbier et al., Phys. Rept. 420, 1 (2005)Faessler, Kovalenko, Simkovic, Phys. Rev. D58, 115004 (1998)

Coupl. Current upper bounds Sources

λ121 < 0.049 [meR] CC universality

λ131 < 0.062 [meR] decay ratio

λ’211 < 0.059 [mdR] decay ratio

λ’311 < 0.11 [mdR] / decay ratio

λ’111 < 1.3 x 10-4 [mq]2 [mg]1/2 double beta decay

λ’112 < 0.021 [msR] CC universality

λ’113 < 0.021 [mbR] CC universality

[…] : sfermion mass in unit of 100 GeV[…] : sfermion mass in unit of 100 GeV

~ ~

RPV lagrangian:RPV lagrangian:

uudd

eeLL~~

Yukawa interaction!!Yukawa interaction!!

Neutron beta decay withNeutron beta decay withR-parity violation R-parity violation SM contribution:SM contribution:

Selectron exchange diagram:Selectron exchange diagram:

Down squark exchange diagram:Down squark exchange diagram:

Absorbed in Vud ⇒ Neglect

~~ddRR

uu

ee--

dd

ee--

ee--

uudd

ee--

eeLL~~

ee--

dd

ee--

uu

WW

Effective interactionEffective interaction

(pseudoscalar interaction neglected due to non-relativistic approx)(pseudoscalar interaction neglected due to non-relativistic approx)

(CVC assertion)(CVC assertion)(Experiment)(Experiment)

Effective interaction constructed from quark amplitude:Effective interaction constructed from quark amplitude:

Vector, axial and scalar constants:Vector, axial and scalar constants:

(Our work)(Our work)

ResultResult V-A only (SM) RPV contribution

a (1-2) / (1+32) 0

b 0 R

A 2(1-) / (1+32) 0

B 2(1+) / (1+32) (me/Ee) R

D 0 0

G -1 0

H (me / Ee) (2-1) / (1+32) - R

K (2-1) / (1+32) R

L 0 I

N 2(me / Ee) (1-) / (1+32) - R

Q 2(1-) / (1+32) R

R 0 I

S 0 R

T 0 I

U 0 I

V -2(1+) / (1+32) 0

W 0 R

Approx. usedApprox. used::• Static approx. of nucleonStatic approx. of nucleon• Scalar & V-A interferenceScalar & V-A interference only only• O(mO(mee/M/MNN) neglected) neglected

Experimental value V-A only (SM) RPV contribution

a -0.103 ± 0.004 -0.105 0

b (Hardy & Towner) 0 5.12 x 10-3

A -0.1173 ± 0.0013 -0.117 0

B 0.981 ± 0.004 0.988 6.50 x 10-3 x (me/Ee)

D (-2.8 ± 6.4 ± 3.0 ) x 10-4 0 0

G -1 0

H 0.105 x (me/Ee) -5.12 x 10-3

K 0.105 5.12 x 10-3

L 0 5.12 x 10-3

N 0.056 ± 0.011 ± 0.005 0.117 x (me/Ee) -6.50 x 10-3

Q 0.117 6.50 x 10-3

R 0.008 ± 0.015 ± 0.005 0 6.50 x 10-3

S 0 6.50 x 10-3

T 0 -6.50 x 10-3

U 0 -6.50 x 10-3

V -0.988 0

W 0 -6.50 x 10-3

AnalysisAnalysis

Survey of superallowed Fermi Survey of superallowed Fermi transitiontransition

J.C. Hardy, I.S. Towner, Phys. Rev. C79, 055502 (2009)J.C. Hardy, I.S. Towner, Phys. Rev. C79, 055502 (2009)

In 0In 0++→→00++ transition, effect of (real part of) scalar transition, effect of (real part of) scalarinteraction shows up in Fierz interference terminteraction shows up in Fierz interference term

Corrected Ft valueCorrected Ft value(isospin symmetry breaking correction(isospin symmetry breaking correctionand radiative corrections)and radiative corrections)

CVC assertion CVC assertion ⇒ ⇒ Vector interaction not renormalizedVector interaction not renormalizedFt Ft identicalidentical in nuclear medium for 0 in nuclear medium for 0++→→00++ transition transition

Fierz interference term Fierz interference term ⇒ ⇒ limit to Re(Cs) !!limit to Re(Cs) !!

Test of CVC:Test of CVC:

Test of CVC with 20 superallowed 0Test of CVC with 20 superallowed 0++→→00++ beta decay. beta decay.

RR coefficient coefficient

Experimental status:Experimental status:

Final state interaction:Final state interaction:

Kozela Kozela et al.et al.(PSI), PRL102 (2009)(PSI), PRL102 (2009)Rexp = 0.008 ± 0.011 ± 0.005

Rfsi = 0.00086 × me/pe

RRSMSM ≦ ≦ 1010-14-14 Herczeg, Phys. Rev. D56 (1997)Herczeg, Phys. Rev. D56 (1997)

SMSM FSIFSI RPVRPV

1010-14-14 1010-4-4 1010-2-2

Jackson, Treiman, Wyld, Nucl. Phys. 4, 206 (1957)Jackson, Treiman, Wyld, Nucl. Phys. 4, 206 (1957)

ExpExp

RR correlation: correlation:

SM:SM:

Sensitive to the imaginary part of Cs

New boundsNew boundsR coefficient from Kozela et al. Hardy & Towner’s work

Source value R = 0.008 ±0.011 ± 0.005 bF/ 2 = 0.0011 ± 0.0013

Cs /Cv -0.0184±0.0253 ± 0.0115 0.0011±0.0013

1i1’*i11 / [meL]2 -0.012±0.017±0.008 (imaginary) (7.2±8.5) x 10-4 (real)

(plot with all m(plot with all mSUSYSUSY= 100 GeV)= 100 GeV)

Current limit:Current limit:

SummarySummary

We have investigated the R-parity violatingcontribution to the neutron beta decay.

The following new constraints were established:

Future prospectsFuture prospectsDD coefficient: coefficient:

V-A only (SM)V-A only (SM) 00Fsi Fsi O(10O(10-5-5))RPVMSSMRPVMSSM 0 (tree level, O(m0 (tree level, O(mee/m/mnn) contribution neglected !)) contribution neglected !)

L, S, T, U, W L, S, T, U, W coefficients:coefficients:

Zero in V-A only (SM), but RPV contributions existZero in V-A only (SM), but RPV contributions existS,T,U,W are direct probe of the real part of scalar interaction!!

Loop contribution:Loop contribution:

Non-scalar interactions at the one-loop level.Non-scalar interactions at the one-loop level. ⇒ ⇒ Possibility of large contribution to some angular correlations?Possibility of large contribution to some angular correlations?

d u

W

e-e

_