New Physics Beyond the Standard Models with...

New Physics Beyond theStandard Models with SolarNeutrinos

Annelise Malkus

June 2007

Trento, Italy

ECT*

Outline

• Standard Solar Neutrino Model

• Standard MSW

• Where Can We See New Physics?

• New Models

• Conclusions

Solar Neutrino SpectrumB

ahcall, Sere

nelli, A

pJ, 6

2 1, L 85 (2 00

5 )

Radial DistributionF

igure 6

.1 in Ne

utrino A

stro physic s,

J.N. B

ahcall

Electron Density

€

245NAe−10.54 t /Rsun / cm3

Standard MSW

€

i ∂∂t

ψe

ψx

=

ϕ(t) Λ

Λ −ϕ(t)

ψe

ψx

€

ϕ(t) =12GFNe (t) −

δm2

4Ecos(2θv )

Λ =δm2

4Esin(2θv )

Solar +KamLANDGlobalAnalysis

Balantekin & Yuksel, J.Phys. G 29, 665 (2003).

What I Used

€

δm2 = 8.0 ×10−5eV 2

€

sin2(2θv) = 0.86

W.M. Yao et al. (Particle Data Group), J. Phys. G 33, 1(2006) (URL:http://pdg.lbl.gov)

Electron Neutrino Survival Probability

Standard MSW Effect

Where Can We See New Physics?

• Adiabatic Solution

• Resonance€

P(ν e →ν e ) =12

+12cos(2θv ) cos(2θi) source

€

=12

+12cos(2θv )

−ϕ(t)Λ +ϕ 2(t)

source

€

ϕ(t) resonance =12GFNe(t) −

δm2

4Ecos(2θv) = 0

′ ϕ (t) resonance =ϕ(t) resonance + δϕ

=12GFNe(t) −

δm2

4Ecos(2θv) + δϕ = δϕ

Right Here!

Introduction to New Models

• New Interactions

• Mass-Varying Neutrinos

• Long Range Leptonic Forces– Scalar

– Vector

– Tensor

• Solar Density Fluctuations

New Interactions

€

LNSI = −2 2GF (ν αγρνβ )(εαβff L f Lγ

ρ ˜ f L + εαβf˜ f RE f Rγ

ρ ˜ f R ) + h.c.

€

ϕ(t) =12GFNe (t)[1+ ε11]−

δm2

4Ecos(2θv )

Λ =δm2

4Esin(2θv ) +

12GFNe (t)ε12

€

εij = εiju Nu

Ne

+ εijd Nd

Ne

A. Friedland, C. Lundardini andC. Pena-Garay, Phys. Lett. B594, 347 (2004)

Modify Phi

Modify Lambda

Mass-Varying Neutrinos

Cosmic Coincidence Problem:

Use another “coincidence” to help:

Neutrinos couple to dark energy with scalarfield, acceleron.

R. Fardon, A.E. Nelson and N. Weiner, JCAP 0410 005 (2004)[arXiv;astro-ph/0309800]

€

ρCDM ~ ρΛ

€

ρν ~ ρΛ

Mass-Varying Neutrinos

€

i ∂∂t

ψe

ψx

=

12E

U m1 −M1(t)( )2 M3(t)2

M3(t)2 m2 −M2(t)( )2

U

† +2 2GFNe (t)E 0

0 0

ψe

ψx

€

Mi(t) = µiNe (t)Ne (t0)

k

€

ϕ(t) =12GFNe (t) − (m2 −M2(t))2

cos(2θv)2E

+ 2M3(t)2sin(2θv)2E

Λ = 2M3(t)2 cos(2θv ) −

(m2 −M2(t))2

4Esin(2θv )

V. Barger, P. Huber, D. Marfatia, Phys. Rev. Lett. 95 211802 (2005)


€

m1 = 0m2 = 0.0089eVµ1 = 0µ2 = 0.0077eVµ3 = i0.0022eV

Forces Couple to Lepton Number

Universal Function

Long Range Leptonic Forces

€

W (t) = Ne(ρ)0

Rsun

∫ e− ρ− t /λ

ρ − td3ρ

M.C. Gonzales-Garcia, P.C. deHolanda, E. Masso and R.Zukanovich Funchal, arXiv:hep-ph/0609094

Long Range Leptonic Forces

Scalar

€

ϕ(t) = 2GFNe (t)

+12E

m12 cos2θv − 1

2( ) + m22 sin2θv − 1

2( ) −m1ksW (t)cos2θv −m2ksW (t)sin2θv +

ks2W 2

2

Λ =12E

(m2 −m1)(m2 + m1 − ksW (t))cosθv sinθv[ ]

€

ks(e) =g02

4π=10−44

€

m1 = 0

Vector

€

ϕ(t) =12GFNe (t) −

δm2

4Ecos(2θv ) + kvW (t)

Λ =δm2

4Esin(2θv )

€

kV (e) =g12

4π=10−52

Tensor

€

ϕ(t) =12GFNe (t) −

δm2

4Ecos(2θv ) − Eν kT (e)W (t)

Λ =δm2

4Esin(2θv )

€

kT (e) = meg22

4π=10−60eV −1

Solar Density Fluctuations

€

Ff (t) = 0

Ff (t)Ff ( ′ t ) = 2τδ(t − ′ t )

€

ϕ(t) =12GFNe (t) −

δm2

4Ecos(2θv ) +

GF

2β Ne(t) Ff (t)

Λ =δm2

4Esin(2θv)

F.N. Loreti and A.B. Balantekin,Phys. Rev. D 50 4762 (1994)[arXiv:nucl-th/9406003];

A.B. Balantekin and H. Yuksel,Phys. Rev. D. 68, 013006 (2003)[arXiv:hep- ph/0303169


€

θv = 0.523δm2 = 8.2 ×10−5eV 2

Summary

• Many new models contain similarformulation:

• This is visible at ~1 MeV, independentof model

€

′ ϕ (t) =ϕ(t) + δϕ

How Can We Detect This?

SNO +

References1. Bahcall, Serenelli, ApJ, 621, L85 (2005)

2. Figure 6.1 in Neutrino Astrophysics, J.N. Bahcall

3. Solar+KamLAND parameter space

4. SNO Salt + KamLAND

5. PDG(2007)

6. A. Friedland, C. Lundardini and C. Pena-Garay, Phys. Lett. B594, 347 (2004)

7. V. Barger, P. Huber, D. Marfatia, Phys. Rev. Lett. 95 211802(2005); R. Fardon, A.E. Nelson and N. Weiner, JCAP 0410005 (2004) [arXiv;astro-ph/0309800]

8. M.C. Gonzales-Garcia, P.C. deHolanda, E. Masso and R.Zukanovich Funchal, arXiv:hep-ph/0609094

9. F.N. Loreti and A.B. Balantekin, Phys. Rev. D 50 4762 (1994)[arXiv:nucl-th/9406003]; A.B. Balantekin and H. Yuksel, Phys.Rev. D. 68, 013006 (2003) [arXiv:hep-ph/0303169]

DickensIt was the best of times, it was the worst of times, it was

the age of wisdom, it was the age of foolishness, itwas the epoch of belief, it was the epoch ofincredulity, it was the season of Light, it was theseason of Darkness, it was the spring of hope, it wasthe winter of despair, we had everything before us,we had nothing before us, we were all going direct toheaven, we were all going direct the other way - inshort, the period was so far like the present period,that some of its noisiest authorities insisted on itsbeing received, for good or for evil, in the superlativedegree of comparison only.

Grueling Detail-Solving Evolution

• For all hermitianmatrices, we candiagonalize, usingeither the adiabaticapproximation ornumerically

• Otherwise, we mustsolve completelynumerically

€

ψ(t + Δt) =Ue−iΔtDU†ψ(t)€

Dadiabatic =− ϕ 2 + Λ 0

0 ϕ 2 + Λ

€

D =UHU†

U =cosθm −sinθmsinθm cosθm

cos(2θm ) ≡−ϕ

ϕ 2 + Λ

sin(2θm ) ≡Λ

ϕ 2 + Λ

Survival Far From Origin

• Average over behavior at large t

€

ψ(t0) =10

ψ(t0,E) 2Rsun

Grueling Detail-Hermite Weights

• Approximate radialdistributions asgaussiandistributions, with

• Each process, j, isproduced on adifferentdistribution. €

ψ(E) j =

Wi ψ t j +xiσ j

Rsun ,E

i∑

Wii∑

€

σ j,rj

Grueling Detail-Weighting by Flux

• For each process, j, the flux of neutrinosvaries by energy

€

ψ(E) total =

ψ(E) jΦ jj=Be,B ,pp∑

Φ jj=Be,B ,pp∑

Toys-Polytropic Sun

€

P(t) = Kρ1+1/n (t)

SNO Salt and KamLAND [4]

Joint analysis of the solarneutrino dataincluding final SNOsalt results along withthe most recentKamLAND data

How Can We Detect This?

• SNO +

Solar Density Fluctuations

β is the percent fluctuation€

∂∂t

zyx

= −20 0 ϕ

0 k − Λ

−ϕ Λ k

zyx

€

k =GF2 Ne (t)

2β 2τ

€

z = 2 ν e *ν e −1

y = 2Im ν µ *ν e

x = 2Re ν µ *ν e

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