MadGraph5_aMC@NLO

symmetric diagrams info and interference terms

Asked by Arian Abrahantes

Dear MG-team:

1- Is there an straight output in a MG run for the symmetric factors of generated diagrams in a process?

2- suppose a simple situation in the MSSM framework two diagrams where two lightest neutralinos(n1) are forced in the final state after passing through a pair of stops (t1\bar{t1}), I will mark one of the neutrlinos with a "*" and I will only keep these two diagrams in the generation and calculation:

Diag_1:

gg->t1\bar{t1}->t n1 \bar{t} n1*

and Diag_2 permutes n1 and n1*

Diag_2:

gg->t1\bar{t1}->t n1* \bar{t} n1

How does MG deals with the squared matrix element of this two symmetric diagrams

|M|^2 = |fact*diag_1 - fact*diag_2|^2

where fact is the symmetry factor (1/2 in my example) or

|M|^2 = fact * |diag_1 - diag_2|^2

3- Secondly, is there a way that I can extract only the contribution of interference of these diagrams to the total xsection?

thanks in advance,

arian

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Johan Alwall (johan-alwall) said : 		#1

Hello Arian,

The symmetry factor due to identical final-state particles is included in the IDEN factor in matrix.f, together with the averaging over incoming helicities and colors (the actual calculation is done in get_denominator_factor in madgraph/core/helas_objects.py and identical_particle_factor in madgraph/core/base_objects.py).

The matrix element calculation (combination of diagrams) is done in matrix.f, in the lines

      JAMP(1)=+IMAG1*AMP(1)-IMAG1*AMP(2)-AMP(4)-AMP(5)-AMP(6)+AMP(10)
     $ +AMP(11)+AMP(12)
      JAMP(2)=-IMAG1*AMP(1)+IMAG1*AMP(2)-AMP(3)-AMP(7)-AMP(8)+AMP(9)
     $ +AMP(13)+AMP(14)

      MATRIX1 = 0.D0
      DO I = 1, NCOLOR
        ZTEMP = (0.D0,0.D0)
        DO J = 1, NCOLOR
          ZTEMP = ZTEMP + CF(J,I)*JAMP(J)
        ENDDO
        MATRIX1=MATRIX1+ZTEMP*DCONJG(JAMP(I))/DENOM(I)
      ENDDO

The correspondence of amplitudes to diagrams is given in the lines above (note that the 4-particle ggt1t1~ vertex corresponds to two amplitudes). Here, you can easily print out the relative contribution of the interference term only. Note however that MadGraph5 1.4 can not yet deal with negative weights, so if you modify matrix1 to return only the interference term, you might run into trouble since the interference term can be negative. You can use the branch lp:~maddevelopers/madgraph5/negative_weights to enable this calculation (negative weight treatment will be included in version 1.5).

All the best,
Johan

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Arian Abrahantes (arian-abrahantes) said : 		#2

Dear Johan

Thanks for your reply, it was very helpful. My point here is that I am trying to get final x-section values I am not interested in event generation and simulation.

The issue came from the comparison of the following processes:

generate g g > t t~ n1 n1 / z w- w+ h1 h2 h3 sl sr cl cr ul ur dl dr t2 t @1

and

generate g g > t1 t1~, t1 > t n1, t1~ > t~ n1 @1

and for a given parameter card their x-section is respectively

xsect proc 1 = 0.040705 ± 4.64e-05 (pb) (IDEN = 512, 8 diagrams)

xsect proc 2 = 0.039429 ± 4.32e-05 (pb) (IDEN = 256, 4 diagrams)

The relevant point we spotted was that, although the diagram number is reduced by half on the second process, xsections are almost equal ("almost equal" is straight forward to account for since the second process takes away many of the interefernce terms in the calculation of MATRIX). In this specific example missing diagrams in proc2 are completely symmetric to generated ones. And the identical particles factor (IDEN) compensated such lose. Identical particles in final states happens to be tricky states.

By the way is there a documentation for the usage of the branch you proposed. Or is it just straight forward usage?

thank you very much and best regards,

arian

Revision history for this message
Johan Alwall (johan-alwall) said : 		#3

Hello Arian,

Indeed, when you use the decay chain formalism the two sides are different since they are the decay of different particles. You get a symmetry factor only if you have identical decay chains for identical particles.

The negative_weights branch is used just like regular MadEvent, it's just that it can handle negative weights correctly.

All the best,
Johan