# Presentation: 325737

## From Quarks to Nuclei to Compact Stars and Back

**Formulating nuclear physics from first principles**

- Mannque Rho, Saclay

## Slide 2

## Weinberg ‘folk theorem’

- “When you use quantum field theory to study
- low-energy phenomena, then according to the
- folk theorem, you're not really making any
- assumption that could be wrong, unless
- of course Lorentz invariance or quantum
- mechanics or cluster decomposition is wrong,
- provided you don't say specifically what the
- Lagrangian is.

- “What is quantum field theory, and what did we think it is?”
-                             hep-th/9702027.

- (‘F-theorem’)

## As long as you let it be the most general 

- As long as you let it be the most general
- possible Lagrangian consistent with the
- symmetries of the theory,  you're simply
- writing down the most general theory you
- could possibly write down.  ... “

- “F-proof”: It’s hard to see how it can go wrong

- ‘F-theorem’ continued

## ‘F-Corollary’ 

- this way to calculate processes involving soft  mesons, that is,  mesons with energy less than about 2 F  1200 MeV. The use of effective quantum field theories has been extended more recently to nuclear physics where although nucleons are not soft they never get far from their mass shell, and for that reason can be also treated by similar methods as the soft pions.

- ‘F-Corollary’

## Nuclear physicists have adopted this point of 

- view, and I gather that they are happy about
- using this new language because it allows one
- to show in a fairly convincing way that what
- they've been doing all along is the correct
- first step in a consistent approximation scheme.”

- ‘F-Corollary’ continued

## Outline

- 1970’s – 1980’s: Cheshire cat, confinement - deconfinement,  MIT bag  Stony  Brook “little bag”  skyrmions
- 1990’s: Weinberg “F-theorem”:  quarks to hadrons to nuclei to dense/hot matter to neutron stars and black holes
- 2000’s: Holographic duality, back to Cheshire cat.

## Objective of Fundamental Principles in Nuclear Physics

- Recover and sharpen the standard nuclear physics approach, put it in the framework of the Standard Model.
- Make precise predictions that play a key ingredient in other areas of science, e.g., solar evolution and neutrino mass.
- Quest for new states of matter created under extreme conditions

## QCD is the First Principle

## QCD Nucleon

***“******Down” quark***

***“******Up” quark***

- MIT Bag (1970’s)

- R ~ 1 fm

## DEUTERON

**DEUTERON**

** **

- Do the bags of R  1 fm overlap?

## Heavy Nucleus

**Heavy Nucleus**

***Grapefruits in the salad bowl !!!???***

***SIZE ***
***CRISIS?***

**NEUTRON**

**PROTON**

## Size Problem

-  MIT bags           pea soup in 208Pb ?

- Spectroscopic
- Factor ~ single
- particleness

-       But
- shell model

- Something
-     amiss

## A Way out

-            Cheshire cat
-  “Origin” of the proton mass

## Cheshire Cat

*Alice in the*
*wonderland*

****

****

## Where does the mass come from?

-       For Molecules, Atoms, Nuclei
- Constituents: protons, neutrons, electrons
- Masses =sum of masses of constituents
-               + tiny binding energy

**Nuclear BE < 1%**

## A ‘Mass’ Problem

- Proton/Neutron Mass=938/940 MeV

- Constituents: Quarks and gluons

-  Proton= uud ;  Neutron= udd

- Sum of “current-quark” masses ≈ 10 MeV

***Where do ~ 99% of the mass come from?***

## QCD Answer 

-  “ *Energy stored in the motion of the *
*   **(nearly) massless quarks and energy in*
*   **massless gluons that connect them”*

- Proton mass ≈ 1 GeV

*“**Mass without mass”*

-  Technically, “chiral symmetry
-    spontaneously broken (SB)”

-  QCD on lattice explains the proton mass
-    within ~ 10% .

- F. Wilczek

- à la Nambu/Goldstone

## Order Parameter

- Quark condensate: <*qq>*

- _

-  <*qq> ≈ -* (0.23±0.03 GeV)3→ Proton
-    mass ≈ 1 GeV
-  Mass disappears when <*qq*>→ 0  ?

- ≠ 0   S broken
- = 0   S restored

- _

- _

**Lattice**
**QCD**

## Stony Brook “Little Bag”

- Shrink the bag to ~ 1/3 fm from ~ 1 fm

-  How?

- SB  pions as (pseudo)Goldstone bosons

- 

- 

- 

- 

- 

- 

- 

- 

- 

- qqq

**qqq**

- Pion pressure

- + “Yukawa”

- G.E. Brown and MR 1979

- <qq>≠0

- <qq>0

-  This reasoning was *not *quite correct!

## Enter Cheshire Catin Infinite Hotel

- Nadkarni, Nielsen and Zahed 1985

-  Bag radius (confinement radius) is a *gauge*
- (“redundant”) degree of freedom
-  **** Low-energy physics should not depend
- upon the bag or confinement size
-  R can be shrunk to zero  skyrmion

**Quarks/gluons**

**“****Smile of the Cheshire Cat”**

## MIT

**Nambu/Goldstone **
**      ****(Pion) Cloud**

**uud**

**uud**

- SB

**MITbag**

**SB little bag**

**skyrmion**

**“****cloudy” bag**

- SB & anomaly

## MIT

- Stony Brook

## Baryon Number 

- Baryon Number

**B**

****

**skyrmion**

**MIT bag**

**total**

**pion**

**quark**

-  Topological invariant

## gA0  “Proton spin”

- SB

- MIT

- Non-topological ~ dynamical

## Nuclei as skyrmions

- Manton, Sutcliffe et al 2008

- Classical, need to be quantized (in progess)

## ‘F-theorem’ applied to nuclei

-  (140), (770), (780), ..., N (940)

-  For *E*  *m**** **(140) * *m**N **(940)*

- LN =*N**† **(i**********t**** **+ ********2**/2M) N + c(N**†**N)**2** + ...*** **

-  galilean invariance etc.

- “*Pionless Lagrangian”*

-  For *E* ~ *m*** *m**N**  *

- Local field

- L = N** + ********************N**

- (*f*/4) Tr(*U**U**†*) +...

*U=exp(2i****/f*****

-    Relevant degrees of freedom: Low-mass hadrons

- Chiral invariance, Lorentz invariance ..

##  Strategy Chiral Lagrangian

-  Pions play a crucial role à la Weinberg
-  Applicable for E < *m******MeV   *
* *Match to highly sophisticated ‘standard
-     nuclear physics approach’ refined since
-     decades:

- Weinberg F-corollary “ ... *it allows one *
*to show in a fairly convincing way that what they've been doing all along is the correct first step in a consistent approximation scheme*”

- 1990 – 2000 : QCD to EFT of nuclei

## How does it fare with Nature?

-  *Parameter free* *calculations*
-        accurate to  better than 97%

-  Thermal *n+p**** d+*******

- th =334±2 mb    (exp: 334.2±0.5 mb)

-  ******th**(3H) =3.035±0.013   (exp: 2.979±.....)
******th**(3He)=-2.198±0.013  (exp: -2.128±.....)

-  *Predictions: solar neutrinos*

-  - + 3He  + 3H

- th=1499±16 Hz   (exp: 1496±4 Hz)

## Solar Neutrino Spectrum

**Solar Neutrino Spectrum**

***pp***

***hep***

## Tortuous History of hep Theory

**                       *****S*****-factor in 10****-20**** MeV-b unit**
**  ****’****52 (Salpeter)        ****	**** ****630****	****    Single particle model**
**  ’****67 (Werntz)      ****	**** 3.7 ****	****    Symmetry group consideration**
**  ’****73 (Werntz)      ****	**** 8.1****	****    Better wave functions (P-wave)**
**  ’****83 (Tegner)                   4********25 ****	****    D-state & MEC**
**  ’****89 (Wolfs)****	****            15.3********4.7       Analogy to ****3****He+n**
**  ’****91 (Wervelman)****	****  57****	****    ****3****He+n with**** shell-model**
**  ****’****91 (Carlson et al.)****	****  ****1.3****	****    VMC with Av14**
**   ’****92 (Schiavilla et al.)****	****1.4-3.1       VMC with Av28 (N+********)**
**   ’****01 (Marcucci et al.)        9.64        CHH with Av18 (N+********) + *****p*****-wave**
**                                                          **

- Tortuous History of *hep**** ***Theory

- 1950-2001

- Serious wave “function overlap” problem

## Bahcall’s challenge to nuclear physics 

**“****The most important unsolved problem in theoretical**
**nuclear physics related to solar neutrinos is the range **
**of values allowed by ****fundamental physics**** for the *****hep***
**production cross section”**

**J. Bahcall, hep-ex/0002018**

**Bahcall’s challenge to nuclear physics **

## Predictions

- Solar neutrino processes

* **p+p **** d+e****+****+**********e**** *
*   *
*S****pp****=*3.94x(1±0.0025) x 10-25 MeV-b
* **p+****3****He **** **4**He+e**+**+**********e*********
*S****hep***=(8.6±1.3) x 10-20 keV-b

- Awaits experiment!

- T.S. Park et al, 2001

## Matter under extreme conditions

**Quest for new states of matter – New physics**

## ‘Phase diagram’ 

## What happens as <qq>  0?

- -

- One possibility is that other
- light degrees of freedom than
- the pions start figuring

## Hidden/emergent gauge symmetries

-  At very low energies, only pions figure

- L=*(f**********2****/4)*Tr[***************U ****************U**†*] + ...

- Nucleons emerge as skyrmions

- “Current algebra”

-  As energy increases, exploit “gauge symmetry”

- Vector mesons ’, ..., ’, ...figure
- with dropping masses à la Brown-Rho

- Nucleons emerge as instantons or skyrions

*U=exp(2i****/f****) **** SU(N)**L**xSU(N)**R** /SU(N)**V=L+R*

## Gauge symmetry is a redundancy

- Famous case: ***charge-spin separation*** of electron

- e(x)≡ electron, f(x)≡ “new electron,” b(x)≡ “boson”

-  Invariance:

-  Endow with a gauge field:

- “emergent” gauge filed

## What we are concerned with

-  Invariance under

-  “Emergent” SU(N) gauge fields

- Excitation energy  *m**** ~ *800 MeV

- Bando et al 1986
- Harada & Yamawaki 2003

##   Emerging “infinite tower” of vectors

- ’..., ’..., *a**1** ...*

-  5-Dimensionally deconstructed QCD (?)(Son & Stephanov 04)

-  This form descends ALSO from string theory!
-  Harada-Yamawaki theory is a truncated HLS theory
- at the lowest vector mesons 

## Matching HLS toQCD 

- “matching scale”

- QCD (quarks, gluons)

- EFT (pions, vector mesons ...)

- n      nc

- T     Tc

- “*Vector manifestation (VM)” fixed point *

-  ** **** ****Masayasu Harada &**
**    ****Koichi Yamawaki**
**Phys. Rep. 381 (2003) 1-233**

*(T,n)*

- Wilsonian renormalization group flow

## Vector Manifestation 

- “*VM fixed point*”

- All light-quark hadrons lose mass at the VM point

- “VM (or BR) scaling”

- In the chiral limit

## VM scaling in nuclei?

- Dropping mass tagged to <qq>
- Precursor in nuclear structure

- -

-  Warburton ratio
-  carbon-14 dating
-  others

## Warburton Ratio

- Found large enhancement in heavy nuclei

- E. Warburton 91

- Warburton defined/measured in nuclei

- for the weak axial-charge transition

## Prediction

*n**0*

- In units of *m****3*

**A ****                ****Exp**
**12                1.64±0.05**
**50                1.60±0.05**
**205              1.95±0.05**
**208              2.01±0.10**

* **n**0**/2*

- BR scaling

## Carbon-14 dating

**Holt et al 2008**

- Tensor force
- fine-tuned by
- BR scaling!

## Hadronic matter at high temperature and/or density

## Large efforts in heavy-ion collisions 

-         at CERN and RHIC

- But no smoking gun signal yet

- Relegate to the future

## Compact stars andBlack Holes

- High Density Regime

- Questions:

-  What happens as density increases to that of compact stars?
-  Does hadronic physics matter for the collapse of stars?
-  Are the plethora of high density matter observable?

- Assertion:

-  The first – and possibly last (?) – phase change is that
-     kaons condense at relatively low density

## Kaons condense in compact stars

***m******K**********

*********e***

***e******-****** → K******-****** + *********

- density

*M*

**Dropping mass “restores” *****SU(3) s*****ymmetry**

***m************  ~ 0,  m******K****** ~ 1/2  GeV***

- Kaons condense

## Consequences

- A scenario proposed

- A lot of light-mass black holes in the Universe
- “BH-Nothingness” after kaon condensation

## Bethe-Brown Mass

- “Stars more massive than *M**max**BB **≈ *1.6 *M***
-              collapse into black holes”

- What to do?

- Why? Because such massive stars have condensed
- kaons which soften the EOS and trigger instability.

-  “Find a compact star with mass *M > **M**max**BB* ”
-  “Find binary pulsars with mass difference > 4%”

-   If found, the following will be invalidated

-  Maximization of black holes in the Universe
-  Mechanism for “Cosmological Natural Selection”
-  Kaon condensation, VM, “hadronic freedom”

*“**No proof. It’s a conjecture to be checked by nature .”*

## Slide 53

## J0751+1807

- Nice et al 2005

- Observation in neutron star–white dwarf binary of
- 2.2±0.2 *m* led to *pitched activities*

-  strong repulsive N*-*nucleon forces (with N*≥ 3*)
-  crystalline color-superconducting stars
-  etc etc producing ~ one paper a week

- This would unambiguously “kill” the BB conjecture

- But (!) new analysis in 2007 corrects the 2005
- value to 1.26+0.14/-0.12!!

- BB still OK!

## Summary

-  We went to skyrmions from quarks
-  We went to nuclei via skyrmions via F-theorem
-  We went to compact stars via nuclear matter
-     via hidden local symmetry
-  Enter string theory:
-     Sakai and Sugimoto showed (2005) that hadrons
-     at low energy *E < M**KK** *could be described by the
-     5D action ***top-down*** from AdS/CFT:

- Arises also ***bottom-up*** from current algebra by
- “deconstruction”

## Back to Cheshire Cat

- Nucleon is an instanton in 5D≈ a skyrmion in 4D
-         In the infinite tower of vector mesons

*EM form factors*

*Numerically*

- “Dipole”

- “Monopole”

- Close to nature!!

**Hong, Yee, Yi, R  2007; Hashimoto, Sakai, Sugimoto 2008**

**Kim & Zahed 2008**

***First*** confirmation of Sakurai’s 1960’s idea of VD

## Implications on

-    Heavy ions
-  Compact stars ?

- Future

## Thanks for the attention!