Search for Medium Range Force bySearch for Medium Range Force bya Precision Measurement ofa Precision Measurement of

Neutron Scattering Cross SectionNeutron Scattering Cross Section

Tatsushi ShimaResearch Center for Nuclear Physics, Osaka University

The 4th International Workshop on Nuclear and Particle Physics at J-PARC(NP08), Mito, 5-7 Mar 2008

Introduction Why neutron? Small angle scattering with gas target Simulations Summary

Test of Inverse-Square Law of GravityTest of Inverse-Square Law of Gravity

Reference: Coy, Fischbach, Hellings, Standish, & Talmadge (2003)

LaboratoryLake

Tower

Earth-LAGEOS

LAGEOS-Lunar

Lunar Precession Planetary

λ : range in units of m

PotentialPotential

( ) ( ) ( ) !"

#$%

& '(=(+'= ))/exp(1(

r

mMGrVrrVrV ggG )*

exotic interaction (Yukawa-type)Newtonian

Large Extra Dimension (Alkani-Hamed, Dimopoulos, Dvali)

Radion-mediated force

Moduli coupling (exchange of string-theory scalars)

Axion exchange

Multi-particle exchange (axions, ν-ν, etc.)

Vacuum-energy scenarios (“fat graviton” model)

Theoretical models:

Constraint on Non-Newtonian Gravity inConstraint on Non-Newtonian Gravity in Sub-millimeter Range Sub-millimeter Range

) (

))/exp(1(

l

mMGV

lVV

g

gG

!"=

"+= #$

ADD (n=2, MN=1TeV)

[pm] 2.3 4

m][ 5.1 3

!"=

!"=

#

µ#

n

n

Torsion-balance experimentsTorsion-balance experiments

Hoyle et al. PRD70, 042004 (2004)Kapner et al. PRL98, 021101 (2007)

Atomic Force MicroscopyAtomic Force Microscopy

R.S. Decca et al. PRL94, 240401 (2005)

Van der Waals force is dominant at l < ~10µm ;

4

0

8

3

l

cUC

!

"

h#=

Electric polarizability of atoms; α0 ~ 10-24 cm3

NeutronNeutron ; αn ~ 10-42 cm3

BackgroundBackground

(Casimir-Polder)

( )( ) ( )[ ]

( ) ( ) ( )!!!

!!!"

GGNeneeneNN

GGeneN

FaaFZaZFaaa

FaZFaad

d

222222

2

+++#

++=$

aN ; nuclear scattering amplitudeane ; neutron-electron scattering amplitudeaG ; gravitational scattering lengthZ ; atomic number of targetFe(θ) ; form factor for atomic electronFG(θ) ; gravitational form factor

aG ∝ α

Search for New Intermediate-range Force Search for New Intermediate-range Force via Neutron Scattering via Neutron Scattering Greene & Gudkov

Zimmer & KaiserFrank, Isacker & Gómez-Camacho

( )

2

2

2

2

2

2

2sin8

1

1

4

!!!!!

"

#

$$$$$

%

&

+!"

#$%

&'!

"

#$%

& ''=

( )

*

+),

n

n

nG

Ec

cm

MmG

d

d

h

Cross SectionCross Section

G : coupling constant of Newtonian gravityα : coupling constant of LED gravityλ : range of non-Newtonian gravityΜ : target massmn : neutron rest mass

Experimental SetupExperimental Setup

Neutron Energy Spectrum atNeutron Energy Spectrum atJ-PARC/JSNS/BL05/High-intensity branchJ-PARC/JSNS/BL05/High-intensity branch

En [meV]

!n [/cm

2/meV/s/MW]

0 10 20 30

0.2

0.4

0.6

0.8

1("108)

1A 1 meV 2

!="= &qEn

Forward scattering (Δq~0.01Å-1) ⇒ λ ~10nm

Monte Carlo Simulation;Monte Carlo Simulation; Velocity Distribution of Scattered Neutrons Velocity Distribution of Scattered Neutrons

Initial10K100K300K1000K

vn [m/s]

Probability (a.u.)

vn(initial)=630±80 m/s Target: Ar (1atm)

0 400 800 1200 1600 2000

0.004

0.008

0.012

Counting rate; Counting rate; ArAr σN(36Ar)=77.90 bσN(40Ar)=0.421 b

λ=10nm, α=1024

Non-Newtonian Gravity (!=10nm, "=1024)

40Ar; nuclear elastic36Ar; nuclear elasticDirect

Scattering Angle [deg.]

Count Rate [ /s/0.1deg.]

Ar, T=100K

0 2 4 6 8 10 12101

102

103

104

105

106

Counting rate; Counting rate; XeXe σN(natXe)=2.96 bσN(124Xe)=0.141 b

λ=10nm, α=1024

Non-Newtonian Gravity (!=10nm, "=1024)

124Xe; nuclear elastic natXe; nuclear elasticDirect

Scattering Angle [deg.]

Count Rate [ /s/0.1deg.]

Xe, T=200K

0 2 4 6 8 10 12 14 16100

101

102

103

104

124124Xe(n,n) cross sectionXe(n,n) cross section

Sensitivity Sensitivity (2year measurement, 95% C.L.)(2year measurement, 95% C.L.)

SummarySummary

Slow neutron is an ideal probe for testing the inverse-square law of the Newtonian gravity in the sub-micrometer range.

Small-angle scattering of slow neutron with

noble gas atom is a simple way to search for exotic

intermediate-range forces.

Experiments with enriched targets of 36,40Ar and 124,natXe

are planned at the high-intensity branch of

the J-PARC/JSNS/BL05 beam line.

Models of Exotic Intermediate-Range ForcesModels of Exotic Intermediate-Range Forces

Large Extra Dimension (Alkani-Hamed, Dimopoulos, Dvali)

Radion-mediated force

Moduli coupling (exchange of string-theory scalars)

Axion exchange

Multi-particle exchange (axions, ν-ν, etc.)

⇒ power-law potential

Vacuum-energy scenarios (“fat graviton” model)

Hierarchy problems ; ▪ MEW ~ 100GeV ⇔ MPl ~ 1019GeV

▪ G ~ 10-36 αEM

Gravity in d=N space ;

11

21 ,)(!!

="

!=NNNNN

M

hcG

r

mmGrF

Continuity at r=R ;n

Plank

n

R

RGG !

"

#$%

&= +33

Large Extra Dimension modelLarge Extra Dimension model Alkani-Hamed, Dimopoulos, Dvali (ADD)

Size of compact space R is so large as G3 << GN, but is smaller than experimentally surveyed range (~1mm).

Atomic Form FactorAtomic Form Factor

( )!"#

>>

<<$

%1

1

A 10for 0

A 01.0for 1

&

&

q

qqF

-

e

( ) 1A 01.0at 998.0

!=" &qqFe

More precisely,