Particle Content SUSY

Definition of Superfields

Chiral superfields in SARAH are defined via the array SuperFields. The general syntax is

SuperField[[/i|i]] = {SuperField Name,  Generations, Components, Transformation Gauge 1,
Transformation Gauge 2..., Transformation Global 1, Transformation Global 2 };

1. Superfield Name: The name for the superfield
2. Generations: The number of generations
3. Components: The basis of the name for the components. Two cases are possible:
   1. The field transforms only trivially under the gauge groups with expanded indices. In this case, the entry is one dimensional.
   2. The field transforms non-trivially under gauge groups with expanded indices. In this case, the entry is a vector or higher dimensional tensor fitting to the dimension of the field. Note, representations larger than the fundamental one are written as tensor products
4. Transformation Gauge X: Transformation under the different gauge groups defined before. For U(1) this is the charge, for non-Abelian gauge groups the dimensions is given as integer respectively negative integer. The dimension D of an irreducible representation is not necessarily unique. Therefore, to make sure, SARAH uses the demanded representation, also the corresponding Dynkin labels have to be added.
5. Transformation Global X: Transformation under the different global symmetries. If only one quantum number is given per superfield per global symmetry, this number is used for the superfield itself but also for the scalar and fermionic component. To define a R symmetry, a list with three entries has to be given. For chiral superfields, the first entry is the charge for the superfield, the second for the scalar component, the third for the fermionic component. For vector superfield, the second entries refers to the gaugino, the third to the gauge boson.

Names of component fields

The names of the component fields are derived from the names of the superfield as explained here

Non-Fundamental representations

More details about the treatment of non-fundamental representations is given here.

Soft-breaking masses

SARAH adds automatically for all chiral superfields soft-breaking squared masses named

m <> "Name of Superfield" <> 2

Examples

1. Fields with expanded indices The definition of the left quark superfield in the MSSM is

   SuperField[[/1|1]] = {q, 3, {uL,  dL},   1/6, 2, 3, {-1,-1,1}};

   The consequence of this definition is

   1. Left up-squarks and quarks are called SuL / FuL
   2. Left down-squarks and quarks are called SdL / FdL
   3. There are three generations
   4. The superfield is named q
   5. The soft-breaking mass is named mq2
   6. The hypercharge is $\frac{1}{6}$
   7. The superfield transforms as 2 under S**U(2)
   8. The superfield transforms as 3 under S**U(3)
   9. The superfield and scalar have R-parity -1, the fermion +1.

2. Fields with no expanded indices The right down-quark superfield is defined in the MSSM as

   SuperField[[/3|3]] = {d, 3, {conj[dR]},  1/3, 1, -3,  {-1,-1,1}};

   The meaning is

   1. The right squarks and quarks are called SdR and FdR
   2. There are three generations
   3. The Superfield name is d
   4. The soft-breaking mass is named md2
   5. The hypercharge is $\frac{1}{3}$
   6. It does not transform under S**U(2)
   7. It does transform as ${\bf \bar{3}}$ under S**U(3)
   8. The superfield and scalar have R-parity -1, the fermion +1.

3. Specification of representation
   Since the 10 under SU(5) is not unique, it is necessary to add the appropriate Dynkin labels, i.e.

   SuperField[[/1|1]] = {Ten, 1, t, {10,{0,1,0,0}},...};

   or

   SuperField[[/1|1]] = {Ten, 1, t, {10,{0,0,1,0}},...};

4. Mixed soft-breaking terms
   In models which contain fields with the same quantum numbers under gauge and global symmetries mixed soft-breaking terms are added. For instance, in models with heavy squarks

   SuperField[[/3|3]] = {d, 3, {conj[dR]},  1/3, 1, -3};
   ...
   SuperField[[/10|10]] = {DH, 3, {conj[dRH]},  1/3, 1, -3};

   the term of the form

   mdDH (conj[SdR] SdRH + SdR conj[SdRH])

   is automatically added. For the MSSM without R-parity violation, the terms

   mlHd (conj[Sl] SHd + Sl conj[SHd])

   are not created, because of the defined, global symmetry.