Roni Harnik LBL and UC Berkeley with Daniel Larson and Hitoshi Murayama, hep-ph/0309224
Supersymmetry and Dense QCD? What can we compare b/w QCD and SQCD? Scalars with a chemical potential. Exact Results. SQCD+ Conclusions Feedback is appreciated.
Current results in high density QCD rely on Asymptotic Freedom À QCD Excitations have E» À Q C D Weak Coupling What about. QCD?
Going to lower densities= strong couplings. We can t calculate in QCD Can we find a `QCD-like theory where we can calculate? SQCD is endowed with many exact results. QCD and SQCD `only differ by matter content.
SUSY = Symmetry b/w fermions and bosons Every fermion has a degenerate bosonic superpartner
Extended symmetry + Divergent loops cancel Radiative corrections are under control. Used to cancel the dangerous loops in the SM Higgs sector. 0
The tame behavior of SUSY theories is guaranteed by symmetries. Respected by strong dynamics! In the mid 90 s Seiberg and others made an enormous progress in solving SUSY gauge theories.
What can the exact results tell us? - Moduli space = space of vacua - Light Degrees of freedom - Global symmetries. What can t they tell us? - Size of condensates - Spectrum - Quantative statements
[Alford, hep-ph/0102047]
[Alford, hep-ph/0102047]
Schaffer (2000): Can we hope to reproduce all this for SQCD? NO.
We have the same UV symmetries. But, we are comparing two different theories! Different matter content. Even for =0 theories give different results: e.g. for : QCD give a chiral condensate. SQCD has a moduli-space. in QCD vs. in SQCD. We have `systematic errors. Need a `clean signal!
Baryon number breaking is a `clean signal For =0 : U(1) B is a symmetry of both theories. Both in UV and IR (slight cheat). QCD makes clear predictions
Preparing for SUSY
Start with a complex scalar field Now, add a chemical potential
If a scalar has >m, a BEC is formedscalar gets a vev, symmetry is broken. Can the combination of strong coupling and a small chemical potential, <m, cause symmetry breaking? We will require <m.
We can rewrite- with is a background U(1) gauge field. Very useful: couplings to `Hadrons is determined by gauge invariance!
A Lightening Review
A tool useful to `unify scalars and fermions regular coordinates anti-comuting coordinates Superfields are a function on superspace: e.g. A chiral superfield- Scalar Fermion Auxilary
Kahler potential Superpotential Kahler potential ¾ Kinetic terms. A real function of the fields. example: Superpotential ¾ interacions. A holomorphic function of the fields. example: W does not get renormalized.
An SU(N c ) gauge theory with flavors and `anti-flavors. Symmetries Asymptotically free if. Becomes strong at a scale. What are the d.o.f below? Scale??
Holomorphy- respected by d.o.f and interacions. Symmetries and Spurions- Give charge assignments to couplings and. IR interactions and vevs must respect all symmetries. Decoupling- e.g. Add a mass to one flavor. Match to results for flavors. Anomaly matching- Global anomalies in the UV and the IR must be equal (t Hooft).
Due to holomorphy: The moduli space is parameterized by all the gauge invariant holomorphic operators + constraints. For N f =N c they are: Mesons Baryons with a constraint
We can add a mass to all flavors Symmetries- Check the constraint: Valid for m 0 Constraint is modified by quantum corrections
Due to holomorphy and symmetries: Quantum effect modify the constraint to Enforced by
At finite density fermions and bosons behave differently. A chemical potential breaks SUSY Demand Complimentary to results form QCD
f c As advertised we add a stabilizing mass with m>.???? Breaks the chiral symmetry by hand. What about U(1) B? Convention: q B [Q]=1
f c For =0, the Baryons get a mass:
Chemical potential is a backgroung gauge field: with There is a critical chemical potential < m.
There is a critical chemical potential Agrees with CFL! Strong coupling introduces a smaller critical
There is a critical chemical potential Agrees with CFL! Strong coupling introduces a smaller critical
N f <N c A quick answer for N f =2 : The moduli space contains only mesons In the IR there are no degrees of freedom to break baryon number. Agrees with 2SC phase.
Most robust for 2 and 3 flavors. SUSY stabilization give more `reliable results.
We ve used exact results in supersymmetric gauge theories to understand the phase structure of SQCD+\mu. Only baryon number is a good signal to compare with QCD results. We find a reasonable agreement For the 2sc and CFL phases