## A critical point of QCD

We performed measurements of quark number susceptibilties on the lattice.
These measurements were made with a lattice spacing of a=1/(8T) where T
is the temperature. Two flavours of staggered quarks were used, with the
quark mass tuned so that m_{π}/m_{ρ}=0.33. At high
temperature the results are close to what weak coupling theories predict.
These results were reported in Lattice 2013. A table of our measurements
is here.

### Talks

- Towards the Continuum Limit for the QCD Critical Point, R. V. Gavai, Lattice 2013
- Controlling errors in simulations for QCD at finite chemical potential, Sourendu Gupta, Lattice 2013
- Susceptibilities in Nf=2 QCD, Saumen Dutta, Lattice 2013

## A critical point of QCD

We have found the critical end point in 2 flavour QCD (circle in purple) through
the analysis of a Taylor expansion of the quark number susceptibility in the
baryon chemical potential μ_{B}.

### Publications

- Phys. Rev. D 78, 114503, 2008
- Phys. Rev. D 73, 014004, 2006
- Phys. Rev. D 72, 054006, 2005
- Phys. Rev. D 71, 114014, 2005
- Phys. Rev. D 68, 034506, 2003

### Talks

- Critical Point and the Onset of Deconfinement, BNL, 2009
- The QCD Critical Point, INT Seattle, 2008
- Extreme QCD, NCSU, 2008
- Quark Matter, 2008
- Strong and Electro-Weak Matter, 2006
- Strangeness in Quark Matter, 2006
- Lattice 2005
- QCD and Dense Matter: From Lattices to Stars, INT Seattle, 2004: Part 1 and Part 2
- Workshop on Finite Density QCD, Nara, 2003
- Lattice 2003

### Projects available

#### Masters' projects

Reworking lattice QCD methods to work on *parallel computers* is
necessary in order to enhance computational abilities in future. This
work can be done by masters' students in physics as well
as applied mathematics. If you would like to do such a project for your
masters' thesis, then you should have good understanding of either quantum
field theory or an object oriented programming language such as C++ or
Fortran 90. It would be an advantage to know both. If you are interested
write to ilgti at theory fullstop tifr dot res period in.

#### Bachelors' projects

The phase diagram of QCD is a seven-dimensional object. It would be interesting to write a program to take sections and projections of this object in any specified plane and draw the corresponding graph. Knowledge of either phase transitions or graphics programming is a pre-requisite for this project.

## Quark number susceptibilities

The fourth order quark number susceptibility χ_{40}
peaks close to T_{c}. This is closely related to the
"Kurtosis" signal for the critical end point. The
fourth (and higher) order susceptibilities were first introduced
by us in 2003.

### Publications

- Phys. Rev. D 78, 114503, 2008
- Phys. Rev. D 73, 014004, 2006
- Phys. Rev. D 72, 054006, 2005
- Phys. Rev. D 68, 034506, 2003
- Phys. Rev. D 67, 034501, 2003
- Phys. Rev. D 65, 094515, 2002
- Phys. Rev. D 65, 054506, 2002
- Phys. Rev. D 64, 074506, 2001

### Projects available

#### Masters' projects

The study of quark number susceptibilties is the most direct signal of the critical end point of QCD. There are straightforward algorithms to generate the quantum field operators which go into determining some of the as yet uncomputed ones. This work can be done as a summer project.

The study of quark number susceptibilties is the most direct signal of the critical end point of QCD. In order to make contact with experiments, one needs to study the diffusion equation and compute the evolution of the susceptibilties through diffusion. This is a possible Maste's thesis. Parts of this problem can also be done as summer projects.