Searches for spin-dependent short-range forces

Pinghan Chu Duke University/LANL

!Feb.13, 2015

1Colloquium@South Dakota School of Mines and Technology

Outline

• Spin-dependent short-range forces

• Polarized 3He

• Paramagnetic insulators

• Summary

2

Spin-dependent short-range force(SDSRF)

• Interaction between polarized particles and unpolarized particles

• Parity, Time-reversal violation • Axion or Axion-Like particles(ALPs)

• Axion is proposed to explain QCD CP-problem • Axion is also a dark matter candidate

r: distance between polarized and unpolarized particles gsgp : coupling strength of the force σ : spin λ : force interaction length mp : mass of polarized particles

V (r) =~2gsgp8⇡mp

(� · r)( 1

r�+

1

r2)e�r/�

3

J. E. Moody and Frank Wilczek, Phys. Rev. D 30, 130 (1984).

Baryon asymmetry of Universe

• Baryon asymmetry of Universe (BAU) :baryon/photon10^-104

Credit: NASA/CXC/M.Weiss

Baryon asymmetry of Universe and Charge-Parity violation

• Baryon asymmetry of Universe (BAU) :baryon/photon10^-10

• Sakharov proposed charge-parity(CP) violation as one of necessary ingredients(1967)

• CP violation has only been observed in kaon and B meson decays, which can be explained by Kobayashi-Maskawa mechanism (CKM matrix) in Standard Model(SM) : baryon/photon~10^-18

• Require CP violation beyond SM

• Electric dipole moment? Spin-dependent short-range forces?

Kobayashi Maskawa

5

Sakharov

Electric dipole moment

• Electric dipole moment (EDM) is the first moment of the charge distribution (ρ). • The EDM (vector) is parallel to the Spin (axial vector) direction. • A non-zero EDM violates the parity and time-reversal symmetries.

6

Spin - parity+

~

d =

Zdx

3⇢~x = dS

Spin - Time reversal+ - +

-+

• Quantum chromodynamics (QCD) allows for a CP-violating term

!

!

!

• Neutron electric dipole moment(EDM),|dn|<2.9x10-26 e cm

LCP�viol.

=↵s

4⇡✓ tr(G

µ⌫

Gµ⌫)

Strong-CP problem

M: quark mass matrix

very small

(by Chiral rotation)|dn| ⇠ 10�16|✓| e cm

✓ ⌘ ✓ + arg det M

✓ . 10�10

G : gluon field strength tensor

G : dual tensor of G

↵s : strong coupling constant

✓ : fundamental parameter

determined experimentally

7

• Peccei and Quinn proposed promoting θ to a dynamic field (Peccei-Quinn mechanism)

• Add a new global symmetry, axion field, that becomes spontaneously broken

• The θ term can be absorbed into the axion field a.

Axion

fa : axion decay constant which determines the strength of interaction of axion with SM particles

8

R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977).

✓ ! ✓ +a

fa

Experiments

• torsion pendulum

• neutron bound states on a mirror in the Earth’s gravitational field

• longitudinal and transverse spin relaxation

• precession frequency shift

• paramagnetic insulator (new idea!)

9

Torsion Pendulum• An oscillating force on a

torsion pendulum generates an oscillating twist which can be observed by an autocollimator.

• Magnetic field can be switched from the clockwise to counterclockwise orientation.

• SDSRF Signals: Change the different pendulum distances from the pole faces of magnet halves

• Limited by thermal noise

10

S. A. Hoedl, F. Fleischer, E. G. Adelberger, and B. R. Heckel, Phys. Rev. Lett. 106, 041801 (2011).

neutron bound states on a mirror in the Earth’s gravitational field

• Earth’s gravitational field and reflecting mirror form a potential well for neutrons

• Neutrons can only exist in a certain height because of the quantum bound state, which can be measured by absorber

• SDSRF is different for two spin states of neutrons, and modifies spatial wave function of neutrons 11

S. Baessler, et al., Phys. Rev. D 75 (2007) 075006.

longitudinal and transverse spin relaxation

• SDSRF can generate additional gradients and change spin-relaxation rate for polarized particles

12

C. B. Fu, T. R. Gentile, and W. M. Snow, Phys. Rev. D 83, 031504(R) (2011); A. K. Petukhov, G. Pignol, and R. Golub, Phys. Rev. D 84, 058501 (2011).

Yu. N. Pokotilovski, Phys. Lett. B 686, 114 (2010) A. Petukhov, G. Pignol, D. Jullien, and K. Andersen, Phys. Rev. Lett. 105, 3 (2010)

Polarized 3He

13

Experimental techniqueSpin in a magnetic field

•Change precession frequency •Depends on spin or direction, P, T violation

SDSRF

B←

Spin←SDSRF←

B←

Spin←SDSRF→P,T

V (r) / (� · r) VB(r) / (� · B)

V (r) / (� · r) P (V (r)) / (� ·�r)

T (V (r)) / (�� · r) 14

Experimental techniqueSpin in a magnetic fieldSDSRF

unpolarized mass

unpolarized mass

fout

fin

ΔfSDSRF=2∫V(r)dr3/h=fin-fout

B←

foutfin

(mass-in)

(mass-out)

Zeeman splitting

V (r) / (� · r) VB(r) / (� · B)

15

B←

Polarized 3He: Spin-exchange optical pumping

• Optical pumping Rubidium(Rb)

• Spin-exchange from Rb electron to 3He nucleus

Rb Rb

3He 3He

5p2P1/2

5s2S1/2

circularly polarized light 795nmcollisional decay

RbZeeman splitting

1640cm

7 amg

250μm

Phase I : setup• Polarize 3He using spin-exchange

optical pumping

• A long 3He cell (40cm) with window thickness: 250 μm

• Cell pressure : 7 amg

• Unpolarized mass: Macor ceramic

• Pickup coil B : magnetometer→normalize the frequency at pickup coil A

• Study systematics of the method using polarized 3He

17

Log|

g sgn p|

h (cm)

Mass (eV)

-30-28-26-24-22-20-18-16

10-3 10-2 10-1 100 101

10-510-410-3

100 cycles for each configuration ⇒∆fSDSRF=-0.003±0.005Hz

The sensitivity is close to the upper limit at the time

this work

Phase I : result

upper limit at the time

18

Sensitivity of frequency

19

�f / 1

TpmN

T: measurement time m: measurement cycles N: particle number

1

T2=

1

2T1+

8�2R4

175D|rBz|2

1

T1= D

|rBx

|2 + |rBy

|2

B20

• The sensitivity of frequency depends on measurement time

• T2: transverse relaxation time; precession decay rate; measurement time is proportional to it

• T1: longitudinal relaxation time; polarization decay rate; can be ignore for T2

• The equation is for a spherical cell; the coefficient is geometry-dependent

• T2 is inverse-proportional to magnetic field gradient square

ϒ:gyromagnetic ratio R:cell radius D:diffusion constant B0: holding field

McGregor, PRA, 41, 2631, 1990

• Measurement region is at the center of Helmholtz coil→increase the magnetic field uniformity

• Larger correction coil

• Larmor frequency : 23800Hz

• Two pickup coils (A, B) are put together

• Pickup coil B is used as a reference → fA’=fA-fB

• ΔfSDSRF=f’A,in-f ’A,out

Phase II : setup

20

Phase II : unpolarized mass

•Macor ceramic : magnetic susceptibility ~ same order of water •Salt water: 1.02%MnCl2(paramagnetic) + water(diamagnetic) → magnetic susceptibility ~ 0

21

Phase II : free induction decay(FID)

22

3He

pickup coil

RF coil

Helmholtz coil

y

xz

RFspin

spin

spin

B0

B0

2B1cos(ω0t)

2B1cos(ω0t)

Larmor frequency ω0 = γB0

1.

2.

3.

e�t/T2

B0

z

x

z

z z

z

Phase II : frequency determination

• Signals in time domain s(t) • Signals in frequency domain S(f) • Fourier transform by numerical integration

• Vary f (step: 10-6Hz)→ Maximum of S(f) → precession frequency

R(f) =

R10 cos(2⇡ft)s(t)dt,

I(f) =

R10 sin(2⇡ft)s(t)dt,

S(f) =

pR2

(f) + I2(f)

23

Yan, et. al. , Commun. Comput. Phys. 15, 1343-1351, 2014

Phase II : systematics

• fB is the magnetic field-dependent precession frequency (including holding field and possible effect from magnetic susceptibility of mass)

• fP is polarization-dependent frequency shift • fSDSRF is the frequency shift due to SDSRF

B←P←

B→P→

• Possible systematics • magnetic susceptibility of mass • polarization of 3He

• Flip magnetic-field and polarization of 3He in order to reduce the systematics

• Two configurations have longer T2

fB,P = f+± = fB ±�fP +�fSDSRF,

f�⌥ = fB ±�fP ��fSDSRF

24

�fSDSRF =1

2(f+� � f�+)

1000 cycles for each configuration ⇒∆fSDSRF, ceramic=(2.6±1.7)×10-5 Hz

∆fSDSRF, salt water=(-0.8±2.6)×10-5 Hz

•Ceramic is consistent with zero within 1.5 σ •Salt water is consistent with zero within 1 σ •The sensitivity is better than the upper limit at the time around the axion window (2cm-20μm)

num

ber o

f cyc

les

0

50

cycle0 200 400 600 800 1000

(Hz)

srf

f6

-0.005

0

0.005

(Hz)srf f6-0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.0040

50

cycle0 200 400 600 800 1000

(Hz)

srf

f6 -0.005

0

0.005

0.01

Phase II : result

axion window

salt water

ceramic

Log|

g sgn p|

h (cm)

Mass (eV)

-30-28-26-24-22-20-18-16

10-3 10-2 10-1 100 101

10-510-410-3

25

Phase III: Improvements

• Configuration

• Reduce cell window thickness

• Heavier mass density

• Mass shape

• Uniform magnetic field

26

• Use masses at two ends of the cell

• SDSRFs have opposite direction but the magnetic fields are similar.

• Reduce the systematics from flipping magnetic field/polarization of 3He

Phase III : Configuration

fSDSRF →

27

fSDSRF ← fSDSRF →

28

oven

mass

cellmass

Phase III : Cell

29

• Use a short 3He cell (5 cm) with window thickness 150 μm

• Heavier mass:

• BGO, Copper, Lead, gallium,etc

• Shaped mass

• A pocket on the mass fits cell window

• Closer to polarized 3He from unpolarized mass

Phase III : MassfSDSRF ←

30

shaped mass can match the cell window

Phase III : Magnetic field

31

• Improve magnetic field uniformity → improve transverse relaxation time as well as frequency sensitivity

Phase III : Magnetic field

32

Compensation coils (square Helmholtz coils) : compensate Earth’s fields

Holding coil (Helmholtz coils): provide holding field

Gradient coils (Maxwell coils and Golay coils): compensate gradient fields

Compensating Earth’s Fields

• 3 pairs of square Helmholtz coils to compensate Earth’s fields

33

34

• A gradient-field Maxwell coil(dBz/dz)

•Golay (saddle) coil (dBz/dx, dBz/dy)

Phase III : Gradient coils

Phase III : Gradient coils

35

Phase III : sensitivity

Log|

g sgn p|

h (cm)

Mass (eV)

-30-28-26-24-22-20-18-16

10-3 10-2 10-1 100 101

10-510-410-3

!Blue:  Tullney  et  al.,  PRL  111,  100801  (2013)  Green:    Bulatowicz  et.  al.,PRL  111,  102001(2013)  Magenta:  Zheng,  et.  al.,  PRD  85,  031505  (2012)  Orange:  Chu,  et.  al.,  PRD  87,  011105  (2013)  Red:  Phase-­‐III  projecNon,  10-­‐6  Hz  assumed      

• Use heavier masses, e.g., BGO

• Use a shaped mass → the mass can be closer to the cell window

• Assume a sensitivity can reach 10-­‐6  Hz  (a  factor  of  20  improvement)

axion window

36

Collaboration

• Duke/LANL: P.-H. Chu

• Duke University: H. Gao, B. Lalremruata, G. Laskaris, X. Li, Y. Zhang, W. Zheng

• Indiana University: A. Dennis, R. Khatiwada, K. Li, E. Smith, W. M. Snow, H. Yan

• Shanghai Jiaotong University: C. B. Fu

37

New Idea: Paramagnetic insulators

38

Paramagnetism

39http://www.themagnetguide.com/magnetic-materials.html

• spin in a magnetic field

• magnetization of a sample containing N spinsV = �µ ·B;Em = ��~mB µ = �S

Magnetic field coupling with spin can induce magnetization

M = N�~⌃

Im=�Im exp(�~mB/kT )

⌃

Im=�I exp (�~mB/kT )

• F. L. Shapiro’s proposal

!

!

!

• gadolinium gallium garnet (GGG)

• |de|=(−5.57±7.98±0.12)×10−25e·cm

• Eu0.5Ba0.5TiO

• |de|<6.05x10-25 ecm

electron EDM

40

F.L. Shapiro, Usp. Fiz. Nauk., 95 145 (1968) [Soc. Phys. Usp. 11, 345 (1968)]

Y. J. Kim et al. arXiv:1104.4391

S. Eckel, A. O. Sushkov, and S. K. Lamoreaux Phys. Rev. Lett. 109, 193003 (2012)

E field coupling with electron EDM of sample can induce additional magnetization

~d = d~s

s

Original proposal for eEDM• The system is put in

low temperature and low magnetic field environment

• Magnetization induces a flux in pickup coils

• Detect magnetization using a SQUID

• Run E field at AC mode; flip E field direction at frequency of 1 Hz (in order to cancel out background magnetic fields)

41

Y. J. Kim et al. arXiv:1104.4391

Proposal for spin-dependent short-range forces

• Any force coupling with spins can induce additional magnetization

• Modulate spin-dependent short-range forces

42

Proposal for spin-dependent short-range forces

• Advantage : unpolarized mass can be as close as possible to the surface of paramagnetic insulator; this experiment can be sensitive for the force range < 1mm

43

insulator

paramagnetic

mass

insulator

paramagnetic

mass

pickup coils

mass-out mass-in

Conceptual design• The whole system is

installed in low magnetic environment

• The whole system is in dilution refrigerator

• Pickup coil surrounds the detector mass (GGG)

• Source mass (BGO)

• SQUID is coupled with the pickup coil

44

Source mass (BGO)

Detector mass (GGG)

Dilution refrigerator mixing chamber plate

Pickup coil

SQUID sensor

Magnetic shielding

Sensitivity

45

• Assume the gap between mass and paramagnetic insulator is 1 μm

• Monte Carlo integration

• Generate points in unpolarized mass and detector sample; calculate the potential

• Sum all randomly generated points, normalize it and calculate the magnetization

Sensitivity

46

• Based on parameters in Y. J. Kim et al. arXiv:1104.4391 • This method is extremely sensitive for the force range less

than 10-4 m

Blue: Hoedl, et al., Phys. Rev. Lett. 106, 041801 (2011) Red short dash: Leslie and Long, Phys. Rev. D 89 114022 (2014)

Challenges

• Magnetic impurity

• Move masses in a dewar at low-temperature; vibration

• Gap between mass and paramagnetic insulator

47

• B. A. Dobrescu and I. Mocioiu, J. High Energy Phys. 11, 005 (2006)

!

!

!

• CPT and Lorentz violating forces

Other spin-dependent exotic forces

48

V4+5(r) =~2

8⇡mef?(� · (~v

c⇥ r))(

1

r�+

1

r2)e�r/�

V12+13(r) =~8⇡

fv(� · ~v)(1r)e�r/�

v: velocity of unpolarized particle relative to polarized particle

49

V4+5 V12+13

donut shape

Collaboration

• Duke University/LANL: P.-H. Chu

• Indiana University: J. Long, E. Weisman, C.-Y. Liu, A. Holley

50

Summary• Spin-dependent short-range forces are possible

sources for T-reversal violation and dark matter

• Polarized 3He and paramagnetic insulator can be used to search for spin-dependent short-range forces for nucleons and electrons, respectively

• Improvement of techniques may lead new discovery of physics

This work is supported by Duke University, Indiana University, IU STARS program, Department of Energy : DE- FG02-03ER41231, National Science Foundation : PHY-1068712

51

Backup slides

52

53

Magnetic field scan

• Fluxgate magnetometer

• 3-axis stepping motor

Magnetic field scan

• Magnetic field gradient can be smaller than 0.1 mG/cm by tuning gradient coils

00.5

11.5

22.5

00.5

11.5

22.50.5

1

1.5

2

2.5

3

x(inch)

Gradient (mG/cm)

y(inch)

z(in

ch)

Phase III: old cell, Pablum

56

Pablum

BA

laser

(B,S)=(-,+)

• Use old cell to test

• lenght = 20cm

• window thickness = 150 μm

57

58

Ａ Ｂ

current status

59

T2 can be quite long, but the signal is not stable

Freq(Hz)14440 14441 14442 14443 14444 144450

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Channal BChannal B

Strong-CP problem

tr(Gµ⌫Gµ⌫) ⇠ ~EG · ~BG

in QCDCP ( ~EG · ~BG) = � ~EG · ~BG

! e�i↵�5

! e�i↵�5

✓ ! ✓ + 2↵

•Chiral rotation

•Similar to QED

•Physics must be invariant under transformation of dummy integration variable ψ •For vanishing quark mass, θ-term can be rotated away and becomes unphysical. •Physical invariant quantity

✓ ⌘ ✓ + arg det M

generating functional:

L = ✓g2s

32⇡2tr(Gµ⌫G

µ⌫)

! L = m✓ i�5

Z[J ] =

ZD D ei

Rd

4x✓

g2s32⇡2 tr(Gµ⌫G

µ⌫)

60

axion

ϕ : a complex scalar field ψ : massless quark y : Yukawa coupling

• Lagrangian

•Peccei-Quinn Symmetry •L is invariant under global Chiral U(1)PQ transformation

! e�i↵�5 , ! e�i↵�5 ,�! e�2i↵�

L = @µ�†@µ�+ µ2�†�� �(�†�)2 + i 6 D + y� R L + h.c.

� =fa + ⇢p

2eia/fa

•Spontaneous breaking of U(1)PQ leads to massless pseudo-scalar goldstone boson - axion

61

axion✓ ! ✓ + 2↵,

a

fa! a

fa� 2↵

• The physical invariant quantity becomes

✓ +a

fa

•The kinetic term :

@µ�†@µ� =

1

2@µa

†@µa+ ...

•The mass term :

L = �m cos

a

fah ¯ i ! L =

m

2f2a

h ¯ ia2

62

• QCD vacuum effects (instanton) is minimized a <ā>=0

• Nontrivial potential around <ā>=0 provides a small mass for axion, as a Goldstone boson

• The mass

!

!

• Couple to photons

axion

ma =m⇡f⇡f⇡

pmumd

mu +md⇡ 0.6meV ⇥ 1010GeV

fa

La�� = �1

4gaFµ⌫ F

µ⌫ = ga ~E · ~B

63

Ultralight Hidden-Sector Particles

• Hidden-sector U(1) gauge bosons

• For example, in E8xE8, the second E8 may be broken and produce non-Abelian and U(1) group

64

Very weakly interacting subelectronvolt particles(WISP)

• neutrinos have masses in the subelectronvolt range

• vacuum energy of universe, ρA~meV

• candiates: axion, axion-like particles(ALPs)

• often arise as Nambu-Goldston bosons associated with breakdown of global symmetry

65

Bounds from stellar evolution

• easily escape from stars

• contribute to total energy loss of stars

• depend on volume-to-surface factor

• WISP emission shortens normal burning phase

• prolongs intermediate (red-giant) phase

66

Bounds from stellar evolution

• For standard QCD axion, the axion window is • 10-6< ma<10-2 eV • lower bound : Cosmological limits (overclose) • upper bound : Neutrino burst (couple to nucleons)

(SN1987a)

67

Bounds from stellar evolution

• For ALPs, • Horizontal branch (HB) stars in globular clusters (couple to photons) • gamma burst and neutrino burst

68

Bound from Big Bang Nucleosynthesis

• T<1 MeV, p+e−→n+νe becomes ineffective • n/p~1/7, depends on the rate of cosmic expansion

H(ρ). ρ is total energy density of all particles • ρ➚, pn freeze-out occurs sooner and n/p→1/2 • Abundance of neutron, confined into 4He, can be

measured ➜ nonstandard energy density ρx. • Effective number of extra thermal neutrino

Neff

⌫,x

⌘ 4

7

30

⇡2T 4⇢x

= �0.6+0.9�0.8

69

Bounds from Cosmic Microwave Background (CMB)

• Related to T~0.1 eV. Repond for blackbody shape freeze at T~keV.

• γ+...→WISP+... depletes photons in a frequency-dependent way

• Constraint for different kinds of WISP(ALP, MCP, hidden photons,etc)

70

Dark Matter in Universe

71

Axion as cold dark matter

• T< GeV, below the hadronic scale(QCD phase transition), axion obtains mass ma

• Current bound ma<1.2eV

⌦ah2 = a(

fa1012GeV

)1.175✓2i

0.5 < a < few,

✓i ⇠ O(1)

⌦CDMh2 ⇠ 0.1

if fa ⇠ 1012GeV,ma ⇠ 10µeV

72

String at TeV

• Mass hierarchy problem (why gravity is muc weaker?)

• Supersymmetry: its breaking scale cannot be larger than a few TeV.

• Gravity propagates in all dimensions

• The parallel dimension length can be as large as 10-18 m (TeV -1)

• The transverse dimension can vary from 10-14 to 10-3 m, depending on number (6 to 2) 73

Short-range force

• Deviation from Newton’s law: 1/r2+n

• New scalar force in the sub-millimeter range: SUSY breaking, mΦ~10-4-10-6 eV and mSUSY~1-10 TeV, λ~ 10-3-10-5 m

• Non-universal repulsive force, mediated by abelian gauge fields

74

• The relative precession frequencies of Hg and Cs magnetometers as a function of the position of two 475 kg lead masses with respect to an applied magnetic field

A. N. Youdin, D. Krause, Jr., K. Jagannathan, L. R. Hunter, and S. K. Lamoreaux, Phys. Rev. Lett. 77, 2170 (1996).

axion window: 1μeV ~1 meV(20 cm - 0.2 mm)

�Beff = BeffCs �Beff

Hg

= ±(KCs

�Cs� KHg

�Hg)

]

Cs : electron spin couplings Hg : nuclear spin couplings

75

• The ratio of nuclear spin-precession frequencies of 199Hg and 201Hg atoms for two orientations of magnetic field relative to the Earth’s gravitational fieldB. J. Venema, P. K. Majumder, S. K. Lamoreaux, B. R. Heckel, and E. N. Fortson, Phys. Rev. Lett. 68, 135 (1992).

76

Phase I : systematics

• fB is the magnetic field-dependent precession frequency (including holding field and possible effect from magnetic susceptibility of mass)

• fP is polarization-dependent frequency shift • fSDSRF is the frequency shift due to SDSRF

fB,S = f+± = fB ±�fP +�fSDSRF,

f�⌥ = fB ±�fP ��fSDSRF

B←S←

B→S→

•To reduce the systematics from both magnetic-field and polarization of 3He

�fSDSRF =1

4(�f++ +�f+� ��f�+ ��f��)

77

Baryon asymmetry of Universe and Charge-Parity violation

• Baryon asymmetry of Universe (BAU) :baryon/photon10^-10

• Sakharov proposed charge-parity(CP) violation as one of necessary ingredients(1967)

• CP violation has only been observed in kaon and B meson decay, which can be explained by Kobayashi-Maskawa mechanism (CKM matrix) in Standard Model(SM) : baryon/photon~10^-18

• Require CP violation beyond SM

• Electric dipole moment? Spin-dependent short-range forces?

Kobayashi Maskawa

78

Charge(C), Parity(P) and Time-reversal(T) symmetry

•CP/T operation changes matter to antimatter •Sakharov proposed charge-parity(CP) violation as one of necessary ingredients(1967)

parity(mirror)

Time reversal

+

+ −

+ −+ −

Sakharov79

+

- +

chargeCP

=

• Solenoid

• μ-metal shields

Phase III : Solenoid

80

• Heavier mass:

• BGO, Copper, Lead, gallium,etc

• Shaped mass

• A pocket on the mass fits cell window

• Closer to polarized 3He from unpolarized mass

Phase III : Mass

fSDSRF ←

81

shaped mass can match the cell window