Yuri Kamyshkov/ University of Yuri Kamyshkov/ University of TennesseeTennessee

email: kamyshkov@utk.edu email: kamyshkov@utk.edu

Mini-Workshop, WU St. Louis, Mini-Workshop, WU St. Louis, February 11, 2011February 11, 2011

nnnbar transition probability nbar transition probability

2 2

mixed n-nbar QM state

H Hamiltonian on the system

where and are non-relativistic energy operators:

; 2 2

n

n

n n

n n n n n nn n

n

n

E

E

E E

p pE m U E m U

m m

a

a

æ ö÷ç ÷çY = ÷ç ÷÷çè ø

æ ö÷ç ÷ç= ÷ç ÷÷çè ø

= + + = + +

Important assumpti

( ) ( )

5

(i.e. T-invariance is hold)

there is a reference frame where 0

(as CPT required); ( ) / (9 5) 10

gravipotential for and is the same: 0 (S. Lamor

n n n n n

n n

n n n n

p

m m m m m

n n U U U

a a a

-

· ® @ ® =

· =

· = - = ± ´

· D = - =

ons :

( ) ( ) ( )

eaux et al., 1991)

magnetic moment as follows from CPT [BTW, not measured!]

Earth mag. field can be screened down to level

n n n

nT

m m m· = -

·

-mixing amplitude

All beyond SMphysics is here

nnbar transition probability (for given )

( )2 22

22 2

( 2)For sin

( 2)

where is a potential different for neutron and anti-neutron

(e.g. due to non-compensated Earth mag. field; or a

nn n

n

V mm VH P t t

m V V m

V

aa aa a®

é ùæ ö + + D+ ê ú÷ç ÷ç= = ´ ê ú÷ç ÷- ÷ ê úç + + Dè ø ê úë ûh

s part of gravipotential)

is observation time in the experiment, and (if CPT is violated)n nm m mt D = -

In an ideal situation of no suppression i.e.

"vacuum oscillations" : 0 and 0V m= D =

24 is characteristic "oscillation" time [ from present l2 ts10 imi ]nn eVa

at -< ×=h

22

n nnn

tP t

at®

æ öæ ö ÷÷ çç ÷= ´ ÷ = çç ÷÷ çç ÷ ÷çè ø è øh

Suppression of nnbar in intranuclear transitions

22

2

Neutrons inside nuclei are "free" for the time: ~ ~ ~4.5 1030

each oscillating with "free" probability

1and "experiencing free condition" times per sec

binding

nn

t sE MeV

t

Nt

t

-D ´

æ öD ÷ç ÷= ç ÷ç ÷çè ø

=D

h h

2

ond.

1 1Transition probability per second: A

A nn

tP

tt t

æ ö æ öD ÷ ÷ç ç÷= = ´ ÷ç ç÷ ÷ç ç ÷÷ç Dè øè ø

22 1

22

AIntranuclear transition (exponential) lifetime:

1where R~ ~4.5 10 is "nuclear suppression factor"

t

nnnn

s

Rt

tt t

-´D

= = ´D

16 2 56 40Actual nuclear theory suppression calculations for , , , by C. Dover

et al; W.Alberico et al; B.Kopeliovich and J . Hufner, and most recently by

Friedman and Gal (2008) corrected this rough

O D Fe Ar

estimate within a factor of 2

(Friedman and Gal, 2008)22 1(Oxygen) 5 10 s ( 15%)R -» ´ ±

General approach: one of the neutrons in the nucleus transforms toanti-neutron and the latter is annihilated with other nucleons to pions

8Vacuum oscillations: 0.86 10 sec (at ILL, 1994)N N Sensitivity for free neutron search (appearance probability)

2obs

nN N

tP N

Sensitivity for bound neutron search (in nucleon decay expts)

exp

obsn

nucl

tP N

2 where "nuclear suppression factor"nucl N NR Rt t

®= ´

322 10 (SK-2009)nucl yr à

Will use ILL experiment limit as a unit of sensitivity = 1u

Corresponds to sensitivity = 16u

2nucl N N

Rt t®

= ´

Important to know theoretical uncertainty

Important to know theoretical uncertainty

Is nuclear theoryreliable? complete?Is nuclear theoryreliable? complete?

intranuclear search experiments:Super-K,Soudan-2Frejus

Free neutronsearch limit (ILL)

Bound neutron N-Nbar search experiments Bound neutron N-Nbar search experiments Bound neutron N-Nbar search experiments Bound neutron N-Nbar search experiments

Experiment Year A nyear (1032) Det. eff. Candid. Bkgr. nucl , yr (90% CL)

Kamiokande 1986 O 3.0 33% 0 0.9/yr >0.431032

Frejus 1990 Fe 5.0 30% 0 4 >0.651032

Soudan-2 2002 Fe 21.9 18% 5 4.5 >0.721032

Super-K* 2007 O 245.4 10.4% 20 21.3 >1.81032

Super-K * 2009 O 254.5 12% 23 24 >1.971032

SNO * 2010 D 0.54 41% 2 4.75 >0.3011032

* Not yet published

Observed improvement weaker than SQRT is due to irreducible background of atmospheric ’s.

Still possible to improve a limit(though slowly) but impossible to claim a discovery.

Conversion of Bound Limit to free Oscillation LimitConversion of Bound Limit to free Oscillation LimitConversion of Bound Limit to free Oscillation LimitConversion of Bound Limit to free Oscillation Limit

Experiment Year A nucl , yr (90% CL) R(old), s1 R(new), s1 (old), s (new), s

Kamiokande 1986 O >0.431032 101022 51022 >1.2108 >1.65108

Frejus 1990 Fe >0.651032 141022 ? >1.2108 ?

Soudan-2 2002 Fe >0.721032 141022 ? >1.3108 ?

Super-K* 2007 O >1.771032 101022 51022 >2.36108 >3.34108

Super-K * 2009 O >1.971032 101022 51022 >2.5108 >3.53108

SNO * 2010 D >0.3011032 2.481022 0.821022 >1.96108 >3.4108

V. Kopeliovich 2010, Deuterium

Friedman and Gal 2008, Oxygen

Dover, Gal et. al, old

8 24(from bound) 3.5 10 or 2 10s eVt a -> ´ < ´

n

n

'sp

Claudio Ciofi degli Atti (Perugia U.) is going to look at this (January 2011)

Crossing channel of

the same amplitude

3 3q q

®

®

q

q4q

Proposed by Stuart Raby (2010)

Boris Kopeliovich / SMU

is going (Dec. 2010) to compare

this with 3q 3q crossing channel®

• overlap of two quarks wavefunctions is more probable than for 3 quarks• such 2 quarks might be coming from proton (not only neutron)• 4-antiquark final state annihilates faster

udd

udd

n

n

'sp

q

q4q

All these processes governed by the same crossing amplitude can result into the same indistinguishablefinal state (of ~ 5 pions)

Existing intranuclear NNbar limits will need to be re-evaluated

t

mV

mVtP nn

222

22

2 )2(sin

)2(

More on n More on n nbar suppression: sensitivity to CPT violation nbar suppression: sensitivity to CPT violation

Following Yu. Abov, F. Djeparov, and L. Okun, Pisma ZhETF 39 (1984) 493

• Transitions for free neutrons V=0 are suppressed when

• Suppression possible if m > (due to CPT violation)

obstm

• In the intranuclear transitions where V~10 MeV small provides no additional suppression. Intranuclear transitions Intranuclear transitions are not sensitive to are not sensitive to m !m !

14 (e.g. ~10 )m m eV-D D

• Valid only if 0 , i.e. if n nbar transformation exist

obs

mt

D =h

m (V=0) vs in NNbar search (if 0)

( ) ( )

0 019

9

9

5

8 10

2 10

8 10

/ 9 5 10

KK K

p p p

ee e

n n n

m m m

m m m

m m m

m m m

+ -

-

-

-

-

- < ´

- < ´

- < ´

- = ± ´

Experimental limits on mass difference

Uncertainty of intranuclear suppression

If NNbar transitionwill be observed this will be a new limit

of CPT m test