1

The Neutron Lifetime, the Big Bang and the

Spallation Neutron Source

Geoff GreeneUniversity of Tennessee / Oak Ridge National Laboratory

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Neutron Decay and Big Bang Nucleosynthesis

Measuring the Neutron Lifetime

The Spallation Neutron Source (SNS)

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The neutron Lifetime and the Standard Model

4

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Theoretical Framework for the Theory of Neutron Decay

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Theoretical Framework for the Theory of Neutron Decay

Question: How do we accommodate V-A (parity violation)

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Including V-A (“Parity Violation”)

A “Handed” Interaction Requires:

A VECTOR the “Push”and

An Axial Vector the “Twist”

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Including V-A (“Parity Violation”)

A “Handed” Interaction Requires:

A VECTOR the “Push”and

An Axial Vector the “Twist”

The relative sign of the vector and axial-vector determines the “handedness

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V-A in the “Ideal “Quark-Lepton Interaction

uγγγdeγγγνGH 5µµ5µµeweakweak −−= −“V-A”

Vector “minus” Axial Vector Means a “Left-Handed” Interaction

“vector” operator “axial-vector” operator

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Neutron Decay is a Bit More ComplicatedThe strongly interacting quarks within the neutron modify the

relative size of the vector and axial vector couplings

But since the strong interaction conserves parity, this does not change the relative phase (handedness),

It only changes the “pitch” of the “screw”

uγγgγgdeγγγνGH 5µAµV5µµeweakweak −−= −

If Neutron Decay is Purely Left-Handed, only two parameters completely describe it

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Theory SummaryOur interest in fundamental symmetry violation led us to examine neutron beta decay as a “model” system

If the Standard Model for the Electro-Weak Interaction is correct, only twoparameters, gA and gV, are required. (gA/gV can be thought of as the “pitch” of the screw)

The experimental challenge is to determine whether or not all the phenomenology in neutron beta decay can consistently be explained by twojust parameters.

If two parameters are not enough, something is wrong.This be an indication of something new…perhaps an indication of incomplete symmetry breaking!

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Phenomenology of Neutron Beta Decay

n

p

e

ν

epv

ppv

νpvnσr

n

p

e

ν

epv

ppv

νpvnσr

Momentum Must Be Conserved!

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Phenomenology of Neutron Beta Decay

n

p

e

ν

epv

ppv

νpvnσr

n

p

e

ν

epv

ppv

νpvnσr

V-A says that neutrinos arepurely “Left-Handed” with

1p −=⋅rrσ

Momentum Must Be Conserved!

Conservation of linear and angular momentum implies that there are strong correlations between the initial neutron spin and decay particle momenta.

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Correlations in Neutron Decay

Parity violation implies a rich phenomenology in neutron decay.V-A implies that All experimental Quantities can be related to

the axial and vector coupling constants gA and gV.

⎥⎦⎤

⎢⎣⎡ ⋅

+⋅

++⋅⋅

+∝υυ

υ υσστ E

BE

AEmb

EEa1)E(F1dW n

e

en

e

e

e

ee

n

pppp

⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=

V

A

2

V

A

gg31

gg1

a 0b =2

V

A

V

A

2

V

A

gg31

gg

gg

2A

⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛

−= 2

V

A

V

A

2

V

A

gg1

gg

gg

2B

⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛

=

V

A

2V

2A

gg

)g3g( +Neutron beta decay measurements give:

)g3g/(1 2V

2An +∝τ 0b =

2

V

A

V

A

2

V

A

gg1

gg

gg

2B

⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛

=

⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=

V

A

2

V

A

gg31

gg1

a)g3g/(1 2V

2An +∝τ

2

V

A

V

A

2

V

A

gg31

gg

gg

2A

⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛

−=

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The FREE neutron is unstable against beta-decay

τn ≈ 890 s

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Some Theoretical Implications the Neutron LifetimeCosmology:

The neutron lifetime sets the time scale over which nucleosynthesis occurs during the Big-Bang. The comparison of the neutron lifetime, the cosmological He/H (or D/H) ratio, and the number of neutrino species provides a prediction for the Universal Baryon Density. This is a critical component of the “Dark Matter Problem.”

Particle Physics:A comparison between the neutron lifetime and neutron decay correlations provides an important test of the standard model, and provides a an insight into the origin of parity violation.

Astrophysics:The reaction which provides the dominant source of energy in the Sun (pp fusion) is governed by the same matrix element as neutron decay. The neutron lifetime is a key parameter of the solar models which are involved in the “Solar Neutrino Problem”

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Important Processes with the same Feynman Diagram as Neutron Decay

After D.Dubbers

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Review of Big-Bang Nucleosynthesis

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The Time Scale for the Big Bang (1)

TimeSince

Big Bang

<10-43s

~10-43s

~10-35s

~10-35s - 10-33s

T(K)

ρ(g/cm-3)

Quantum era Universe consists of “soup” of leptons & quarks

Grand Unification EraGravity separates from other Grand

Unified ForcesEnd of Grand UnificationStrong Force breaks symmetry w/ ElectroWeak Force.

Inflationary epoch Universe inflates by a factor of 1030 or more (“observable Universe”expands from size of an atomic nucleus to size of a pea).

1032K

1027K

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The Time Scale for the Big Bang (2)Time SinceBig Bang

~10-12s

~10-6s

0.01s

1 s

T(K)

ρ(g/cm-3)

Particle Era Electromagnetic force and Weak Force break symmetry.

Quark Hadron transition.Protons and neutrons (plus antiprotons and antineutrons) are formed from quarks - at this time the“matter’ particles have an excess of ~one in a billionover “antimatter” particles.

The Universe is expanding rapidly, scale is doublingevery 0.02s. As Universe expands it cools,

T ~ 1/R. Although the temperature is too low forProtons and neutrons to be created from the thermalenergy of the early universe reactions such as:νe + n p+ + e-

And vice-versa, maintain an equal number ofprotons and neutrons. As the temperature decreasesproton/neutron balance shifts in favor of lessmassive protons.

Weakly interacting neutrinos “decouple”from the rest of the Universe

1013K

1011K

1015K

4 x 109

1010K 4 x 105

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The Time Scale for the Big Bang (3)Time SinceBig Bang

15s

3 min

3 1/2 min

5 x 105 yr

T(K)

ρ(g/cm-3)

Temperature is below threshold for creation of electron/positron pairs e+/e- annihilate: e+ + e- γ + γ The Universe is “reheated”about 35% by annihilation.Era of NucleosynthesisNuclei can begin to hold together, e.g.p + n d + γAt this time the baryons are dividedinto about 87% protons 13% neutrons.

Era of Galaxy Formation

109K

108K

109 yr

3 x 109K

4000K

4 x 104

Era of Recombination nuclei &electrons “recombine to form atomsUniverse becomes transparent

End of Nuclear Reactions Neutrons havebeen “used-up” forming 4He Universeis now 80% H nuclei (p+) & 20% Henuclei

400

22......

p2HeHeHepHeHeD

nHeTDpTDDnHeDD

HeDpdnpepn

433

3

4

3

3

+→+

+→+

+→+

+→++→+

+→+

+→+++→

γ

γν

Some of the reactions in Big Bang Nucleosynthesis

23Temperature (109 K)ν’s decouple here

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The Cosmic He/H Ratio Depends upon three quantities:

1) The Cooling rate of the UniverseGiven by the heat capacity of the UniverseDetermined mainly by the number of “light particles” (m ≤ 1 MeV )Includes photons, electrons (positrons), neutrinos (x3)

2) The Rate at which Neutrons are decayingThe neutron lifetime

3) The rate at which nuclear interactions occurDetermined by the the logarithm of the density ofnucleons (baryons)

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)28.10(018.0N012.0log023.0228.0Y n10p −+++= τη νCosmic Helium Abundance

Number of Neutrino FlavorsNeutron Lifetime in Minutes

The Parameters of Big Bang Nucleosynthesis

Cosmic Baryon Density

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[ ] 023.0/)28.10(018.0Y264.0log nP10 −+−= τη

Cosmic Baryon Density

Neutron Lifetime in Minutes

Cosmic Helium Abundance

We can “invert” this line of reasoning. If we measure the Helium Abundance, the Neutron Lifetime, and if we know the Number of “light” Neutrinos is 3, We can determine the density of “ordinary” matter in the universe.

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The Cosmic Helium Abundance “YP” vs the Baryon Density

Density of “Normal Matter”(protons & neutrons)

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A Brief Digression on the Mass of the Universe

From Big Bang Nucleosynthesis, we conclude that, averagedover the entire universe, there are a few protons per cubic meter.

Is this a lot, or this it a little?

The only sensible way to answer this question is to respond:

Compared to What?

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A Scale for the Density of the Universe

From red-shift observations we know that the Universe is in a state of (nearly) uniform expansion. If the density of the Universe is sufficiently high, this expansion will come to a stop and a universal collapse will ensue.If the density of the Universe is sufficiently low, it will expand forever.The critical density of the universe is given by the Hubble constant H, and the Gravitational constant G

We define:GH

83 2

critical πρ =

critical/ ρρΩ =

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An Upper Limit for Ω

If Ω were sufficiently large, the universe could NOT have attained its apparent age (1/H) without collapsing.

Very simple arguments based on the fact that the universe is here and still expanding today indicate that:

Ωtotal < 2.5

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By simply counting the number of stars and galaxies we can get

0.005 ≤ Ωtotal

A Lower Limit for Ω

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Ω is NOT necessarily constant over time

If Ω >1 at any time, Then Ω will continue to grow larger with time

If Ω <1 at any time, Then Ω will tend toward zero with time

Only if Ω = 1 EXACTLY, will it stay constant for all time

We observe that Ω is NOW not too far from 1 (0.01 < Ω < 2.5). Thus:

Ω was EXTREMELY close to 1 early in the big bang ( |Ω-1|≤10-16)

This raises the “Fine Tuning” question:

If Ω was so very nearly equal to 1, Isn’t it reasonable that it equals 1?

For a many compelling reasons (fine tuning, inflation, CMB,…),

We strongly believe that Ω = 1 EXACTLY

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The “Preposterous” Universe

~3% “Ordinary” Matter

~30% “Dark” Matter

~67% “Dark Energy”

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Neutron lifetime provides a measurement of the CosmicBaryon Density:

This can be compared with the determination from theCosmic Microwave Background:

The largest uncertainty to the nuclear theory of BBNis the experimental value of the neutron lifetime.

)%7.03.3( ±=ΩB

)%1.03.2( ±=ΩB

critical

BaryonB ρ

ρ≡Ω

BBN

CMB

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Determination of the Neutron Lifetime

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Measurement of the Neutron Lifetime

nt

eNN τ−= 0

n

NdtdN

τ=−

“Bottle” MethodAn ensemble of “ultracold” neutrons is confinedin a material or magnetic bottle. The population in the bottle decreases as:

“Beam Method”

A detector counts neutron decay products froma well defined volume traversed by a neutron beamwith known neutron density. The decay rate in the volume will be:

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The NIST Penning Trap Lifetime Experiment

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The NIST Penning Trap Lifetime Experiment“Opening the Trap”

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Error Budget (all entries in seconds)

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Ultracold Neutrons and Neutron Bottles

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At low energies S-wave scattering dominates, phase shift is given by ( )cohkb1cot −

=δ

bcoh

For “random” well depths and “random” well size, it is unlikely to obtain a positive coherent scattering length:

bcoh critical range for bcoh<0

πλ cohbNn

2

1−=

Index of refraction is therefore <1 for most nuclei *

*In the vicinity of A~50 (V,Ti,Mn) nuclear sizes are such that bcoh<1 and thus n>1

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Neutron Index of Refraction

πλ

2Nb1n coh

22 −= ncos crit =ϕ

For sufficiently large neutron wavelength, λ, n=0 and cosφcrit =90°

This implies that neutrons will be reflected at ALL ANGLES!

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Cold NeutronsCharacterized by a thermal velocity comparable to T~20K

v ≈ 500 m/sEk ≈ 5 meVλ ≈ 5 Å

Cold NeutronsCharacterized by a thermal velocity comparable to T~20K

v ≈ 5 m/sEk ≈ 100 neVλ ≈ 500 Å

Material Bottle Veff ≈ 200 neV for Ni, Be, Cu, …Magnetic Bottle mv2 ≈ 2µnB for B ~ 1 TeslaGravitational Well mv2 ≈ mgh for h ~ 1 meter

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888.4 3.1 n sτ = ±

[V. Nesvizhevsky, A. Serebrov et al., JETP 75 (1992) 405]

PNPI Rotating Spherical Bottle

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The Systematic Concern with UCN Bottles

Loss rate in Bottle with material walls:

Neutrons can be lost to absorption on walls, up-scattering on walls, escape through gaps in the wall.

holesscatterupabsorbdecaybottle τττττ11111

+++=−

These effects are velocity dependent, not well understood, and depend strongly on trace contamination on walls

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887.6 3 n sτ = ±[W. Mampe et al., NIM A284 (1989) 111]

“MAMBO” Ultracold Neutron Bottle

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stat syst885.4 0.9 0.4 n sτ = ± ±

[S. Arzumanov, L. Bondarenko et al., NIM A 440 (2000) 511]

Double Bottle with Neutron Loss Monitors

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Measurements of the Neutron Lifetime

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Measurements of the Neutron Lifetime prior to 2005

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Current Situation

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What Next

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Improving the error on the NIST Beam Experiment

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Neutron Detection Using Absolute Calorimetry

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Improving the error on the NIST Beam Experiment

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Current Situation

Reduce this x2-3

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Magnetic Trapping of Ultra Cold Neutrons

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S. N. Dzhosyuk, C. E. H. Mattoni, D. N. McKinsey, L. Yang and J. M. DoyleHarvard University

P. R. Huffman and A. K. ThompsonNIST, Gaithersburg

R. GolubHMI, Berlin

S. K. Lamoreaux, G. GreeneLos Alamos National Laboratory

K. J. CoakleyNIST, Boulder

Magnetic Trapping of Ultracold Neutrons[P. Huffman, et. al, Nature, 403, no.6765, 2000]

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Ioffe-Type Magnetic Trap

0

0.5

1

1.5

-1.5 0 1.5r (cm)

-30 -20 -10 0 10 20 30

-1.50.01.5

Z (cm)

00.5

11.5

-30 -20 -10 0 10 20 30Z (cm)

figure courtesy J. Doyle

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Wonderful Property #2

Production of Ultra Cold Neutrons in Superfluid Helium

0

5

10

15

20

0 10 20Momentum Q ( in nm -1 )

p 2

2m

Elementary Excitationsin Liquid Helium

ph

• Neutrons of energy E ≈ 0.95 meV(11 k or 0.89 nm) can scatter in liquidhelium to near rest by emission of asingle phonon.

• Upscattering by absorption of an 11 kphonon is a UCN loss mechanism. Butpopulation of 11 K phonons is suppressed by a large Boltzman Factor: ~ e–11/T

where T~200 mk

Golub and Pendlebury (1977)

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Detection of Trapped Neutrons

liquid helium2He *

e–

γ – 80nm

g – 430nm

TPB

• Recoil electron creates an ionization track in the helium.

• Helium ions form excited He2* molecules (ns time scale)in both singlet and triplet states.

• He2* singlet molecules decay, producing a large prompt(< 20 ns) emission of extreme ultraviolet (EUV) light.

• EUV light (80 nm) is converted to blue using the organicfluor TPB (tetraphenyl butadiene).

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Magnet form

Racetrack coil

Cupronickel tube

Acrylic lightguide

TPB-coated acrylic tube

Solenoid

Neutron shielding Collimator

Beam stop

Trapping region

figure courtesy J.Doyle

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Recent Results FromThe Harvard/NIST/LANL/HMI Neutron Lifetime Expt.

Figure Courtesy of Paul Huffman