Planck 08 Barcelona - Santa Cruz Institute for Particle...

MultiversePredictions

Yasunori Nomura, LJH arXiv:0712.2454

Planck 08 Barcelona

Brian Feldstein, Taizan Watari, LJH hep-ph/060812

Raphael Bousso, Yasunori Nomura, LJH ...

A New Origin for Predictions

An Alternative to Symmetries and Naturalness

I) The Ideas

II) Applications to EWSB, nuclear physics & cosmology

Symmetries

The foundation of explaining why nature is the way it is

3-2-1 & q,u,d,l,e: !,GF ,MZ!MW ,sin"W , ...

BSM Grand unificationTechnicolorSupersymmetryTheories of flavor

...

Limited success over 35 yearsGauge coupling unification

???

CosmologyGiven ,

compute contents of universe:TCMB

B,e

DE

DM

B,e

!

SM BSM

No

Yes -- can’t test

No

No

leptogenesis?

WIMPs?

PGBs?

However...

Why so Little Progress?

Experiments are hard and take many years.

Why no sign of BSM physics at LEP, TeVatron, B factories?

Hard to construct theories with nparams < nobs

(Especially in cosmology)

All simple theories for EWSB are now unnatural.

Need patience -- LHC will be the real watershed.

Why so Little Progress?

Experiments are hard and take many years.

Why no sign of BSM physics at LEP, TeVatron, B factories?

Our ideas of naturalness are wrong.

Need a new tool

Hard to construct theories with nparams < nobs

(Especially in cosmology)

All simple theories for EWSB are now unnatural.

Need patience -- LHC will be the real watershed.

The Multiverse

us

GG

G GG

GG

G

Assume:

Many universes

dN = f (x)dx

Parameters of low energy field theory; or important physical quantities eg Te

landscape, population, transformation to low energy variables

f (x)

Environmental selection dNobs = f (x)n(x)dx

Motivated by string landscape and eternal inflation; ignore difficulties in definitions.

is strongly varying:

Catastrophic Boundaries

In many situations there are catastrophic boundaries --

physics makes a sudden transition

The physics in regions A and B is so different that there is

a sudden change in

x1

x2

AB

xxc

A B

n(x)

n(x)





a sudden change in

x1

x2

AB

xxc

A B

n(x)

n(x)

The crucial assumption:

is peaked towards the boundary

f (x)

xxc

f (x)





a sudden change in

x1

x2

AB

xxc

A B

n(x)

n(x)

The crucial assumption:

is peaked towards the boundary

f (x)

xxc

f (x)

Most observers near boundary

Comparison

Symmetries

Multiverse

Comparison

symmetries restrict the parameter space.

physics of catastrophic boundaries: eg nuclear stability, formation of galaxies.

Symmetries

Multiverse

Comparison



Symmetries

Multiverse

symmetries, representations, symmetry breaking

a multiverse force towards the boundary

Assumptions:

Assumptions:

catastrophic nature of boundary

Comparison



Symmetries

Multiverse

symmetries, representations, symmetry breaking

a multiverse force towards the boundary

Assumptions:

Assumptions:

catastrophic nature of boundary x1

x2

! f

no observers

most universes

Fake and Real Predictions

xxobs

A fake prediction:


xxobs

A fake prediction: f (x)


xxobs


xxobs

A real prediction:


xxobs


xxobs

A real prediction:

xc

Calculated from the physics of the catastrophic boundary

No observers


xxobs


xxobs

A real prediction:

xc

Calculated from the physics of the catastrophic boundary

No observers

f (x)

Most universes

Symmetries & Multiverse

Probable that we will find both types of prediction

Symmetries Multiverse

! !gi/g j !vir

mb/m! (mu,md,me)/mp

Symmetries & Multiverse

Probable that we will find both types of prediction

Symmetries Multiverse

! !gi/g j !vir

mb/m! (mu,md,me)/mp

vmH

mt

Te

!B

??

II) Predictions:

EWSBNuclearCosmology

!0

h0

!"! lnµ

# 4"2!h4t

An EW Phase BoundaryV (H)

Hv

!("SM) = !0

Assume: SM up to some large scale

EW phase boundary is catastrophic boundary

Scan ht(!SM) = h0

!SM

Brian Feldstein, LJH, Taizan Watari;

hep-ph/0608121

!0

h0

!"! lnµ

# 4"2!h4t

An EW Phase BoundaryV (H)

Hv

!("SM) = !0

Assume: SM up to some large scale

EW phase boundary is catastrophic boundary

Scan ht(!SM) = h0

!SM

Brian Feldstein, LJH, Taizan Watari;

hep-ph/0608121

Environmental predictions for

mt ,mH

! f

Higgs and Top Mass Predictions

p sufficiently large for a tight Higgs mass prediction

relatively insensitive to

SM cutoff

mt =!

176.7+2.2log10

"!SM

1018 GeV

#±3

$GeV

Top and QCD contributions to running2 loop

runningrunning to

pole

mH =!

106+6"

mt!171GeV2GeV

#!2.6

"!s!0.1176

0.002

#±6

$GeV +

25GeVp

! 35GeV"p

What is the future of the field?

“Tip of the Cone”

xxc

! f

NxNb 1 2

1

2

n

n

1 prediction


xxc

! f

NxNb 1 2

1

2

n

n

1 predictionx1

x2

! f

1 prediction, 1 runaway


xxc

! f

NxNb 1 2

1

2

n

n

1 predictionx1

x2

! f


xxc

! f

1 prediction


xxc

! f

NxNb 1 2

1

2

n

n

1 predictionx1

x2

! f


xxc

! f

1 prediction 2 predictionsx1

x2

! f


xxc

! f

NxNb 1 2

1

2

n

n

1 predictionx1

x2

! f


xxc

! f

1 prediction 2 predictionsx1

x2

! f

Tipof the Cone


xxc

! f

NxNb 1 2

1

2

n

n

1 predictionx1

x2

! f


xxc

! f

1 prediction

n predictions

2 predictionsx1

x2

! f

Tipof the Cone

Nuclear Boundaries

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

Figure 5: The location of the observer boundary in mu-md-me space. The neutron and complexnuclei boundaries of Eqs. (21) and (28) are depicted by solid lines (below and above, respectively).Dashed lines represent the deuteron boundary of Eq. (26) (for a = 5.5, 2.2 and 1.3 MeV frombelow). The observed point is represented by little dots.

21

mn < mp +me

mn!mp!me > 8MeV

BD < 0

2d slice

!!,

me

mp,

mu

mp,

md

mp

"Relevant parameters

no stars

no complex nuclei

stars exotic

Yasunori Nomura, LJH

arXiv:0712.2454

Nuclear Boundaries

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0


21

mn < mp +me

mn!mp!me > 8MeV

BD < 0

(10 - 30)%

Closeness to n boundary

2d slice

!!,

me

mp,

mu

mp,

md

mp


no stars

no complex nuclei

stars exotic


arXiv:0712.2454

Nuclear Boundaries

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0


21

mn < mp +me

mn!mp!me > 8MeV

BD < 0

(10 - 30)%


2d slice

!!,

me

mp,

mu

mp,

md

mp


no stars

no complex nuclei

stars exotic


arXiv:0712.2454

DamourDonoghue

arXiv:0712.2968

Nuclear Boundaries

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 40 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 10 me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = me,o

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

md/m

d,o

mu/mu,o

me = 0


21

mn < mp +me

mn!mp!me > 8MeV

BD < 0

(10 - 30)%


2d slice

!!,

me

mp,

mu

mp,

md

mp


no stars

no complex nuclei

stars exotic


arXiv:0712.2454

DamourDonoghue

arXiv:0712.2968

! f Tip of theCone!

mu,d,edetermined by nuclear physics of boundaries

Understanding Coincidences

Why are the three contributions to

comparable?Q(n! pe!)

Q

0me0.5 MeV

!EM1.0 ! 0.5 MeV

!d!u 2.3 ± 0.5 MeV

Q ! 0.8 MeV

Figure 11: Q value for the reaction n " pe!!̄.

where CI # (0.5 – 2) and C! # (0.5 – 2) are strong interaction coe!cients, and we choose

a definition of the QCD scale such that "QCD = 100 MeV. Throughout we use approximate

ranges for mu,o and md,o from Ref. [20]. For complex nuclei the binding energy per nucleon is

Ebin = CB"QCD, with CB # 0.08 another strong interaction coe!cient. The neutron and complex

nuclei boundaries are then described by the inequalities

0 < CI(yd $ yu)v

"QCD$ ye

v

"QCD$ C!" < CB. (55)

In the approximation that the deuteron binding energy, BD, is linear in mu + md in the region of

interest, the stability boundary for the deuteron can be written as

BD

"QCD= C1 $ C2(yd + yu)

v

"QCD> 0, (56)

where C1,2 are two further strong interaction coe!cients. These three boundaries involve just

four independent combinations of Standard Model parameters, yu,d,ev/"QCD and ".

Much of the observer naturalness problem arises because the three terms that contribute to

mn $ mp $ me in Eq. (54) are comparable, as shown in Fig. 11, even though Yukawa couplings

and the ratio of mass scales v/"QCD are expected to range over many orders of magnitude.

The electron mass, yev ! 0.5 MeV and the electromagnetic mass splitting #EM % C!""QCD !1.0 & 0.5 MeV di#er by only about a factor of 2. They both stabilize the neutron, and hence

an unstable neutron requires yd > yu. Not only is this the case, but the isospin breaking term

#d!u % CI(md $ mu) = 2.3 ± 0.5 MeV only just over-compensates the negative terms to give a

40

are determined by the physics of the boundary

comparable?

me, mu, md

Understanding Coincidences

Why are the three contributions to

comparable?Q(n! pe!)

Q

0me0.5 MeV

!EM1.0 ! 0.5 MeV

!d!u 2.3 ± 0.5 MeV

Q ! 0.8 MeV

Figure 11: Q value for the reaction n " pe!!̄.

where CI # (0.5 – 2) and C! # (0.5 – 2) are strong interaction coe!cients, and we choose

a definition of the QCD scale such that "QCD = 100 MeV. Throughout we use approximate

ranges for mu,o and md,o from Ref. [20]. For complex nuclei the binding energy per nucleon is

Ebin = CB"QCD, with CB # 0.08 another strong interaction coe!cient. The neutron and complex

nuclei boundaries are then described by the inequalities

0 < CI(yd $ yu)v

"QCD$ ye

v

"QCD$ C!" < CB. (55)

In the approximation that the deuteron binding energy, BD, is linear in mu + md in the region of

interest, the stability boundary for the deuteron can be written as

BD

"QCD= C1 $ C2(yd + yu)

v

"QCD> 0, (56)

where C1,2 are two further strong interaction coe!cients. These three boundaries involve just

four independent combinations of Standard Model parameters, yu,d,ev/"QCD and ".

Much of the observer naturalness problem arises because the three terms that contribute to

mn $ mp $ me in Eq. (54) are comparable, as shown in Fig. 11, even though Yukawa couplings

and the ratio of mass scales v/"QCD are expected to range over many orders of magnitude.

The electron mass, yev ! 0.5 MeV and the electromagnetic mass splitting #EM % C!""QCD !1.0 & 0.5 MeV di#er by only about a factor of 2. They both stabilize the neutron, and hence

an unstable neutron requires yd > yu. Not only is this the case, but the isospin breaking term

#d!u % CI(md $ mu) = 2.3 ± 0.5 MeV only just over-compensates the negative terms to give a

40

are determined by the physics of the boundary

comparable?

me, mu, md

Simple distributions give

me ! !EM

mu,d !BN

, BD

Cosmological Coincidences

Amount ofDark Energy

Amount ofDark Matter

&Size of primordial

density perturbations

QEDbremsstrahlung

Nuclearburning

t! ! tvir ! tcool (! tburn)

Cosmological Coincidences

Amount ofDark Energy

Amount ofDark Matter

&Size of primordial

density perturbations

QEDbremsstrahlung

Nuclearburning

t! ! tvir ! tcool (! tburn)

1010Why are these time scales all years?

Hard to imagine a symmetry explanation

The Cosmological Constant!

!vir

Catastrophic boundary:must form non-linear proto-

galaxies before CC fuels inflation

Weinberg PRL 1987


!vir



Weinberg PRL 1987

! f

Most universes a dilute inflating

homogeneous gas CC problem solvedAmount of Dark Energy predicted

!! "vir i.e. t! ! tvir


!vir



Weinberg PRL 1987

Martell, Shapiro, Weinberg

astro-ph/9701099

!124 !123 !122 !121 !120 !119

log( !" )

0.0

0.2

0.4

0.6

0.8

Pro

babili

ty d

ensity

1012

109

107

Figure 2: Weighted by “observers per baryon”, the probability distribution for !! de-

pends strongly on specific assumptions about conditions necessary for life. Three curves

are shown, corresponding to di!erent choices for the minimum required mass of a galaxy:

M! = (107, 109, 1012)M". In neither case is the observed value (vertical bar) in the preferred

range. The choice M! = 107M" (also shown in Fig. 1) corresponds to the smallest observed

galaxies. The choice M! = 1012M" minimizes the discrepancy with observation but amounts

to assuming that only the largest galaxies can host observers. By contrast, the Causal En-

tropic Principle does not assume that observers require structure formation, let alone galaxies

of a certain mass; yet its prediction is in excellent agreement with the observed value (see

Fig. 8).

di!erent approach, which is always well-defined. It will allow us to assume nothingmore about observers than that they respect the laws of thermodynamics.

2.3 Weighting by entropy production in the causal diamond

Causal Entropic Principle In this paper we will compute the probability distribu-tion for !! based on the Causal Entropic Principle, which is defined by the following

two conjectures [21]:

(1) The universe consists of one causally connected region, or “causal diamond”.

Larger regions cannot be probed and should not be considered part of the semi-classical geometry.

– 10 –

nobs ! nvir B

!

! f





!vir



Weinberg PRL 1987

Martell, Shapiro, Weinberg

astro-ph/9701099

!124 !123 !122 !121 !120 !119

log( !" )

0.0

0.2

0.4

0.6

0.8

Pro

babili

ty d

ensity

1012

109

107

Figure 2: Weighted by “observers per baryon”, the probability distribution for !! de-

pends strongly on specific assumptions about conditions necessary for life. Three curves

are shown, corresponding to di!erent choices for the minimum required mass of a galaxy:

M! = (107, 109, 1012)M". In neither case is the observed value (vertical bar) in the preferred

range. The choice M! = 107M" (also shown in Fig. 1) corresponds to the smallest observed

galaxies. The choice M! = 1012M" minimizes the discrepancy with observation but amounts

to assuming that only the largest galaxies can host observers. By contrast, the Causal En-

tropic Principle does not assume that observers require structure formation, let alone galaxies

of a certain mass; yet its prediction is in excellent agreement with the observed value (see

Fig. 8).

di!erent approach, which is always well-defined. It will allow us to assume nothingmore about observers than that they respect the laws of thermodynamics.

2.3 Weighting by entropy production in the causal diamond

Causal Entropic Principle In this paper we will compute the probability distribu-tion for !! based on the Causal Entropic Principle, which is defined by the following

two conjectures [21]:

(1) The universe consists of one causally connected region, or “causal diamond”.

Larger regions cannot be probed and should not be considered part of the semi-classical geometry.

– 10 –

nobs ! nvir B

! !126 !125 !124 !123 !122 !121 !120 !119

log( !" )

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Pro

ba

bili

ty d

en

sity

Figure 1: The probability distribution of the vacuum energy measured by typical observers,

computed from the Causal Entropic Principle, is shown as a solid curve. The values consistent

with present cosmological data, in the shaded vertical bar, are well inside the 1! region (shown

in white), and hence, not atypical. For comparison, the dashed line shows the distribution

derived by estimating the number of observers per baryon. Unlike our curve, it assumes

that galaxies are necessary for observers; yet, the observed value is very unlikely under this

distribution. For more details about both curves, see Figures 2 and 8.

In this paper we address the third condition. We will use a novel approach, theCausal Entropic Principle, to argue that the observed value of !! is not unlikely. Ourmain result is shown in Fig. 1.

The Causal Entropic Principle is based on two ideas: any act of observation in-creases the entropy, and spacetime regions that are causally inaccessible should be

disregarded. It assumes that on average, the number of observations will be propor-tional to the amount of matter entropy produced in a causally connected region, !S.

Vacua should be weighted by this factor to account for the rate at which they will be

the cosmological constant gradually [12, 13]. In the string landscape, the vacuum preceding ours waslikely to have had an enormous cosmological constant. Its decay acted like a big bang for the observeduniverse and allowed for e!cient reheating [6].

– 3 –

nobs ! Scausal diamond

!

Bousso, HarnikKribs,Perez

hep-th/0702115

! f




The CC Runaway Problem

! f

!

!vir

Suppose scans!vir

might reach a maximum at some pointf (!vir, ")

This preserves !! "vir but the value cannot be predicted

Need a second catastrophic boundary

The Galaxy Cooling Catastrophe

!vir

no ionization

Bremsstrahlung rate too low

Compute ionization and cooling boundaries

M

Relevant parameters

!, me, mp; "vir, MPl, M


!vir

no ionization



M

! fMc

!virc !m4

em2p

"4 M2Pl! (3"10#3 eV)4

!virc

!virc predicted from proto-galaxy cooling physics:

Relevant parameters



!vir

no ionization



M

! fMc

!virc !m4

em2p

"4 M2Pl! (3"10#3 eV)4

!virc


Relevant parameters


explaining the accident tcool ! tvir


!vir

no ionization



M

Mc !!5 M4

Pl

m1/2e m5/2

p! 1067 GeV! 1010 M"

and as a bonus:

! fMc

!virc !m4

em2p

"4 M2Pl! (3"10#3 eV)4

!virc


Relevant parameters


explaining the accident tcool ! tvir

Solving the CC Runaway Problem

!

!vir

2 scanning parameters and

2 catastrophic boundaries

cooling virialization

Solving the CC Runaway Problem

!

!vir

2 scanning parameters and

2 catastrophic boundaries

cooling virialization

! f

!virc

!c !m4

e m2p

"4 M2Pl! (3"10#3 eV)4

!c

Main Sequence H burning Stars

has same parametric form as

tburnmin !!2 M2

Plm2

e mp

tvir

t! ! tvir ! tcool ! tburn

Nmax !M3

Plm3

p

A Rigid Parameter Set

Proto-galaxy cooling: !vir, Mme

mpNuclear stability

Virialization !

Leaving

Unification near Planck scale

MPl

mp, !



mpNuclear stability

Virialization !

Leaving


MPl

mp, !

What determines ?MPl

mp

Since there is a runaway to large MPl

mp!! "vir #

!mp

MPl

"6



mpNuclear stability

Virialization !

Leaving


MPl

mp, !

What determines ?MPl

mp

Since there is a runaway to large MPl

mp!! "vir #

!mp

MPl

"6

Discreteness of in string landscape! !min

MPl! 10"120

Caveat Bremsstrahlung cooling condition tcool < tdyn

CC stops merging process, so why not just wait?

Anthropic weighting implies a cost to waiting

e.g. preferred tonBousso nWeinberg

Change of regime; cooling problematic

e.g. re-virialization implies that temp of proto-galaxy increases

No discrimination between various n(x)

Generic EWSB Sector

Physics of EWSB

M

SM

8 Electroweak Symmetry Breaking on the Edge of Nu-

clear Stability

The origin of electroweak symmetry breaking is one of the largest mysteries remaining in the

Standard Model. The quadratic divergence of the Higgs mass-squared parameter in the Standard

Model implies that if the scale of new physics M is (much) larger than the weak scale v, the

theory requires fine-tuning. This hierarchy problem was a key motivation for much of the

model building in the last 30 years. What do we know about the scale M? In many (non-

supersymmetric) theories beyond the Standard Model, precision electroweak data indicates a

“little hierarchy problem”: v/M is uncomfortably small, typically of order (10!2 – 10!1) or

smaller (see e.g. [19]). There is also a similar fine-tuning problem in supersymmetric theories,

although its origin is di!erent. A su"ciently heavy Higgs boson typically requires superparticles

to be somewhat heavier than the weak scale, leading to some amount of fine-tuning (see e.g. [20]).

In either case, we find that some amount of unnaturalness is present, at least for the simplest

theories, suggesting that environmental selection may be playing a role. In this section we

investigate how large a hierarchy is to be expected from selection for nuclear stability, and how

the hierarchy depends on which parameters are assumed to scan in the multiverse. In addition,

we study the implications that follow from our universe being very close to the neutron stability

boundary.

We assume that the physics associated with electroweak symmetry breaking is at a scale M

and that the e!ective theory below M is the Standard Model with the Higgs potential

V = m2h h†h +

!h

2(h†h)2. (69)

Integrating out the physics of the electroweak symmetry breaking sector at the scale M will in

general lead to several contributions to m2h, some positive and some negative, which we write as

m2h = (g1(xi) ! g2(xi)) M2, (70)

where the functions g1,2 are both positive. The dimensionless parameters xi are the set of

parameters of the theory above M that substantially a!ect electroweak symmetry breaking.

These parameters are evaluated at the scale M , so that g1,2 are also functions of M through the

logarithmic sensitivity of xi on M : g1,2(xi(M)). Note that m2h here includes the quadratically

divergent radiative corrections in the Standard Model that are regulated by the theory above

M . The parameters xi thus include the Standard Model gauge and Yukawa couplings.

The precise nature of the couplings xi and the functional form of g1,2 are unimportant for

our discussion, so that we write g1(xi) = Ax and g2(xi) = Ay, giving

m2h = (x ! y)AM2, (71)

45


clear Stability
















boundary.



V = m2h h†h +

!h

2(h†h)2. (69)



m2h = (g1(xi) ! g2(xi)) M2, (70)









m2h = (x ! y)AM2, (71)

45

Contains SU(2) gauge contribution

Contains top contribution

> 0 > 0

E

xi


clear Stability
















boundary.



V = m2h h†h +

!h

2(h†h)2. (69)



m2h = (g1(xi) ! g2(xi)) M2, (70)









m2h = (x ! y)AM2, (71)

45v2 = z

AM2

!h

z = y! xHierarchy parameter

y typically O(1)

Scan EWSB Sector v2 = z

AM2

!h

z = y! x

z! 1

z! 1

Natural

Fine tuned

M

z

nstable

nonuclei

Symmetry View1

Scan EWSB Sector v2 = z

AM2

!h

z = y! x

z! 1

z! 1

Natural

Fine tuned

M

z

nstable

nonuclei

Symmetry View

Multiverse View

M

z

nstable

nonuclei

M

z

nstable

nonucleiLittle

HierarchyLarge

Hierarchy

Strongly varying f hierarchy expected

1

Conclusions

x1

x2

! f

Tip of the Cone

Multiverse force towards catastrophic edges

Conclusions

x1

x2

! f

Tip of the Cone


A desperate last resort

A powerful new toolor

Conclusions

x1

x2

! f

Tip of the Cone




me ! !EM mu,d !BN

, BD


!c !m4

e m2p

"4 M2Pl! (3"10#3 eV)4 Mc !

!5 M4Pl

m1/2e m5/2

p! 1067 GeV! 1010 M"

Conclusions

x1

x2

! f

Tip of the Cone




Will LHC confirm unnaturalness of EWSB?

me ! !EM mu,d !BN

, BD


!c !m4

e m2p

"4 M2Pl! (3"10#3 eV)4 Mc !

!5 M4Pl

m1/2e m5/2

p! 1067 GeV! 1010 M"

Even with Symmetries thatprecisely predict

0

0.2

0.4

0.6

0.8

1

1e-20 1e-15 1e-10 1e-05 1 100000 1e+10

g 32(M

*)

!QCD/!QCD,o

0

0.2

0.4

0.6

0.8

1

1e-20 1e-15 1e-10 1e-05 1 100000 1e+10

g 32(M

*)

!QCD/!QCD,o

0

0.2

0.4

0.6

0.8

1

1e-20 1e-15 1e-10 1e-05 1 100000 1e+10

g 32(M

*)

!QCD/!QCD,o

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1e-15 1e-10 1e-05 1 100000

g 32(M

*)

!QCD/!QCD,o

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1e-15 1e-10 1e-05 1 100000

g 32(M

*)

!QCD/!QCD,o

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1e-15 1e-10 1e-05 1 100000

g 32(M

*)

!QCD/!QCD,o

Figure 6: The value of g23(M!) as a function of !QCD/!QCD,o for non-supersymmetric theories

(left) and supersymmetric theories (right). The range of Eq. (29) is depicted by the verticallines, while the corresponding range of g2

3(M!) by the horizontal lines.

between v and !QCD, enhancing P̃!QCD. The distribution and the range of g3(M!) are also

important. For example, if the distribution of g3(M!) were flat in 1/g23(M!) within the range

1/g23(M!) >! b3/16!2, the QCD scale is distributed almost flat in ln !QCD for all !QCD <! M!.

Here, b3 is the one-loop beta function coe"cient for g3 evaluated at M!. In this case, we would

obtain P̃!QCDestimated using Eq. (29) to be infinitely small. To avoid this unphysical conclusion,

we can introduce an arbitrary cuto# c on the distribution, 1/g23(M!) <! c. Alternatively, we can

consider that the distribution of g3(M!) is flat in g23(M!). In this case, restricting the range to

be g23(M!) <! c" gives a finite answer to P̃!QCD

. The value of P̃!QCDdepends on c", but we can

make a reasonable conjecture on the value of c", e.g. c" " 1 or " 16!2/b3.

In Fig. 6, we plot the value of g23(M!) as a function of !QCD/!QCD,o obtained using one-

loop renormalization group equations for non-supersymmetric theories (left) and supersymmetric

theories (right). In non-supersymmetric theories, M! is taken to be 1014 GeV, which is the scale

where the SU(3) and U(1) gauge couplings almost meet. (This is the scale where the three

gauge couplings would almost meet if five Higgs doublet fields or a vector-like fermion with the

Higgs quantum numbers were introduced at the electroweak scale.) In supersymmetric theories,

we take M! to be the unification scale, 2 # 1016 GeV, and the scale of superparticle masses to

be mSUSY $ 1 TeV. Dependence of the results on these parameters, however, is weak. From the

figure, we find the probability of !QCD falling in the range of Eq. (29) to be

P̃!QCD$ 0.016

1

c"$ 61#1 1

c", (30)

for non-supersymmetric theories and

P̃!QCD$ 0.038

1

c"$ 26#1 1

c", (31)

20

!QCD

yu,d,e and v

flat f (g23) P!QCD !

130" 1

100

g23(M!)

Predicting

mn < mp +me

BD < 0

me,mu,md

and Closeness to n stability 3 scanning parameters mu = 0

< md +mu >=12

C1

C2!QCD

CI < md!mu >=p!1p!3

!EM

< me >=1

p!3!EM

Success

Predicting

mn < mp +me

BD < 0

me,mu,md

f (ye,yu,yd) ! (yd! yu)!p

p > 3

and Closeness to n stability 3 scanning parameters mu = 0

< md +mu >=12

C1

C2!QCD

CI < md!mu >=p!1p!3

!EM

< me >=1

p!3!EM

Success

The Complex Nuclei Boundary

reasonable value and we will adopt it in our numerics. Using these values,we find that the di!erence in quark masses is also bounded

md ! mu "me + !EM

Z0(23)

ormd ! mu ! 1.67me " 0.83 MeV . (24)

The right hand side of this latter constraint is evaluated at the physicalvalue of the fine structure constant and the QCD scale. It is linear in bothof these quantities.

mu

me

05

1015

20

05

10

15

20

0

5

10

15

20

0

5

10

15

md

Figure 6: The anthropic constraints on md, mu, me in MeV units.

The constraints (20) and (24) are plotted in Fig. 6, which shows a 3Dplot listing the allowed values of each combination of mass. The importantpoint is that the two constraints manage to provide bounds on all three of

the masses. Note that mu and me have no lower anthropic bounds, whilemd is constrained to be non-zero.

We can also take projections into various two-dimensional subsections.The constraints on various combinations of the masses are shown in Fig 7.In each case, the outer range is shown allowing the third mass parameter totake on any allowed value. Also marked by a dashed line on these plots is

15

this constraint isv

vphys! 0.39 (26)

When combined one finds a very restricted range for the vev, under thestated assumptions:

0.39 "v

vphys" 1.64 (27)

which is especially tight if one considers it in the the context of GrandUnification, where the natural range for the vev could extend up to theGUT scale.

Of course, it is also possible that the extra assumption about the con-stancy of the Yukawa couplings is not correct. In the discussions of thestring landscape, there are so many possible vacua that others with di!er-ent values of the Yukawa couplings should be possible. However, our quarkmass constraints should still be relevant for describing the likely values ofthe Higgs vev [19]. Even though extreme cases with disparate scales maybe possible [20], it is plausible that the need for light quarks makes it likelythat the Higgs vev is close to the scale of the strong interactions [19]. More-over, in theories such as supersymmetry which use dynamics to stabilize thefine tuning problem, the anthropic constraint could be an explanation of theoverall scale of supersymmetry breaking.

It may be possible to provide tighter bounds on the masses by consider-ing more specific constraints. One that has been discussed in the literatureis the bound following from the stability of deuterium [3, 21]. The deuteronis very weakly bound and small changes in the masses will su"ce to un-bind it8. This happens for more modest changes than is required for theunbinding of the rest of the elements. Since deuterium is involved in thestandard mechanisms of nucleosynthesis in the early universe and in stars,the lack of a stable deuteron could be the obstacle to providing the elementsneeded for life. However, this bound is less robust that considered above.On the one hand, there may be alternate pathways to the production ofenough elements needed for life. In addition, Weinberg estimates that evenan unstable deuteron could live long enough to generate the elements [1].Moreover, there are extra subtleties in estimating the quark-mass sensitiv-ity of the various two-nucleon systems [23, 24, 25]. For all these reasons,we consider only the most robust of constraints, as discussed above. These

8For example Eugene Golowich (private communication)[22] has estimated that if thescalar coupling is decreased by 5.2%, the deuteron will be unbound. This is half thevariation that we showed was needed to unbind the heavy elements, and would lead to atighter bound of 1.33 for the ratio of Eq. (11).

17

!!,

me

mp,

mu

mp,

md

mp

"

Relevant parameters

Keepingfixed!

md(MeV )

2.5 5 7.5 10 12.5 15 17.5 20

2.5

5

7.5

10

12.5

15

17.5

20

mu (MeV)

me(MeV )

2.5 5 7.5 10 12.5 15 17.5 20

2

4

6

8

10

mu (MeV)

me(MeV )

2.5 5 7.5 10 12.5 15 17.5 20

2

4

6

8

10

md (MeV)

Figure 7: The projection of the anthropic constraints of Fig. 6 into the planesof each pair of masses. The solid lines denote the total allowed region, while thedashed line shows the remaining area if the third mass takes on its physical value.The dot shows the physical values of the masses.

the overall range of the masses when the third mass parameter takes on itsphysical value.

We see that quite small changes in the quark masses would lead to un-livable conditions.

These ranges for the masses can be converted to an allowed range for theHiggs vacuum expectation value, under the additional assumption that theother parameters of the Standard Model (Yukawa and gauge couplings) areheld fixed. This extra assumption could possibly occur in grand unified theo-ries, where there are many attempts to predict gauge and Yukawa couplings.In this situation, the Yukawa couplings could be fixed by the symmetries ofthe grand unified theory, and our quark mass constraints translate directlyinto constraints on the Higgs vev. From our work above on the binding ofnuclei we would then find

v

vphys< 1.64 (25)

at 95% confidence. This constraint is both stronger than and independentfrom the final result of ABDS [3]. The latter was based on the fact that asthe quark masses increases, at fixed Yukawa couplings, the neutron-protonmass di!erence increases until eventually all bound neutrons decay and onlyprotons exist. Thus, that bound constrains md ! mu, while ours constrainsmd+mu. Moreover, our present bound is tight enough that it supersedes thebound on the mass di!erence, because md ! mu can never be greater thanmd+mu. The lower constraint comes from the other process discussed in thissection - the stability of hydrogen atoms against the reaction p+ e " n+ !.If the Higgs vev becomes too small, the proton becomes heavier than theneutron due to electromagnetic interactions and this reaction occurs. Sincethe up, down and electron masses are all proportional to v, one finds that

16

2d projections

Only v scans

neutron

neutron

neutron

neutron

neutron

complexnuclei

complexnuclei

complexnuclei

Damour,Donoghue

arXiv:0712.2968

Dependence of nuclear force on quark masses.

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