longitudinal polarization of massive gauge bosons

Hi Alexandra,

I didn't receive any email. Did you use
olivier.mattelaer__AT__uclouvain.be ?

Cheers,

Olivier
On Jun 28, 2012, at 12:01 PM, alexandra wrote:

> New question #201728 on MadGraph5:
> https://answers.launchpad.net/madgraph5/+question/201728
>
> Dear MadGraph team
> -
> I am investigating strong sector sensitivity on multiple scattering
> of longitudinal massive Gauge bosons
> -
> You had already answered me about how to select longitudinal
> polarization on calculating the CX by MadEvent on the Question #197173
> -
> At high energies the CX of logitudinal Gauge boson scattering should
> converge to the CX calculated by scattering of Goldstone bosons of
> linear sigma model
> (equivalence thorem - http://inspirehep.net/record/119348)
> -
> I had done the procedure of separate the longitudinal polarization
> of gauge boson on SM to compare with the scattering of Goldstone
> bosons
> -
> to the sccatering channels I had probed I do not need the quartic H
> coupling, so I used the default SM of Mg5
> -
> I had got some strange numbers to the cross sections
> -
> 1) they do not agree with equivalence theorem
> 2) they do not have the rigth energy behavior (CX decreasing with
> energy)
> -
> the tables of numbers are below the email
> -
> I also send the matrix1.f file on Olivier email to check if I did
> the procedure rigth....
> -
> -
> I then had decided to cross check the results of MG5 at amplitude
> level with linear sigma model.
> -
> Seems that I can do it by a standalone_cpp ouput
> (as explained on Question #189761)
> -
> On this output I also have to choose the longitudinal polarization,
> I have a hint that this should be done on HelAps_sm files
> but aggain I'm not sure about the sintax to change it.
> -
> Thanks a lot for your help/comment
> Alexandra
> -
> -
> begin of tables of CX for SM
> all with 10000 events and MH = 120 Gev
> -----------------------------------------
> ZZ>WW
> -
> only longitudinal (Mad default)
> ECM(Gev) CX(pb)
> 1000 108
> 2000 125
> 4000 181
> 8000 398
> -
> all polarizations
> ECM(Gev) CX(pb)(Mad default) CX(pb)(Calc on unitary gauge)
> 1000 630 617
> 2000 631 619
> 8000 662 620
> -
> linear sigma model (equivalence theorem)
> ECM(Gev) CX(pb)
> 1000 0.45
> 2000 0.11
> 4000 0.027
> 8000 0.0069
> -----------------------------------
> HH>ZZ
> -
> only longitudinal (Mad default)
> ECM(Gev) CX(pb)
> 1000 67
> 2000 68
> 8000 70
> -
> all polarizations
> ECM(Gev) CX(pb)(Mad default) CX(pb)(Calc on unitary gauge)
> 1000 67 69
> 2000 68 70
> 8000 70 70
> -
> linear sigma model (equivalence theorem)
> ECM(Gev) CX(pb)
> 1000 0.19
> 2000 0.05
> 4000 0.013
> 8000 0.0034
> -------------------------------------
>
> --
> You received this question notification because you are a member of
> MadTeam, which is an answer contact for MadGraph5.

Hi Alexandra,

your modifications to the files seems fine to me .

>I then had decided to cross check the results of MG5 at amplitude level with linear sigma model.
>-
>Seems that I can do it by a standalone_cpp ouput
>(as explained on Question #189761)
>-
>On this output I also have to choose the longitudinal polarization, I have a hint that this should be done on HelAps_sm files
>but aggain I'm not sure about the sintax to change it.

In fact, in your case, it should be easier to modify the standalone output instead of standalone_cpp.
Since this output is closer to madevent output and has the same syntax concerning the helicities.

Could you do that? and report if this is in agreement?

Cheers,

Olivier

Hi Olivier
I did it to a default point of the parameter space
we have no agreement, but the amplitudes are no so far like the CX values....
-
MadGraph StandAlone:
 -----------------------------------------------------------------------------

n E px py pz m
1 0.5000000E+03 0.0000000E+00 0.0000000E+00 0.4853864E+03 0.1200000E+03
2 0.5000000E+03 0.0000000E+00 0.0000000E+00 -0.4853864E+03 0.1200000E+03
3 0.5000000E+03 0.1090640E+03 0.4373705E+03 -0.1962062E+03 0.9118800E+02
4 0.5000000E+03 -0.1090640E+03 -0.4373705E+03 0.1962062E+03 0.9118800E+02
-----------------------------------------------------------------------------
Matrix element = 0.32059325388539306 GeV^ 0
-----------------------------------------------------------------------------
__________________________
Matrix element to the linear sigma model on mathematica:

-----------------------------------------------
MatrixHHZZp[MH_, MZ_, E_, p1_, p3x_, p3y_, p3z_] := (Sqrt[2]*1.166*10^-5 MH^2) (1 + (3*MH^2)/((4*E^2) - MH^2) + MH^2/(((p3x^2 + p3y^2 + (p3z - p1)^2)) - MZ^2) + MH^2/(((+p3x^2 + p3y^2 + (-p3z - p1)^2)) - MZ^2))
-----------------------------------------------
(result 0.265325)
_____________________________________

I wanted to test annother points before send to you
I guess It is done on check_sa.f, taking of the comment "c"
------
c buff(1)=" 1 0.5630480E+04 0.0000000E+00 0.0000000E+00 0.5630480E+04"
c buff(2)=" 2 0.5630480E+04 0.0000000E+00 0.0000000E+00 -0.5630480E+04"
c buff(3)=" 3 0.5466073E+04 0.4443190E+03 0.2446331E+04 -0.4864732E+04"
c buff(4)=" 4 0.8785819E+03 -0.2533886E+03 0.2741971E+03 0.7759741E+03"
c buff(5)=" 5 0.4916306E+04 -0.1909305E+03 -0.2720528E+04 0.4088757E+04"
-----------------------------
I also already tryied some other ways of modified without success...
-
sory for that,
but could you please tell me how do I change the phase space point?
then I send to you a more detailed analisys
-
thanks
Alexandra

Hi Alexandra,

you need to uncomment all the following lines:
cc Copy down here (or read in) the four momenta as a string.
cc
cc
c buff(1)=" 1 0.5630480E+04 0.0000000E+00 0.0000000E+00
0.5630480E+04"
c buff(2)=" 2 0.5630480E+04 0.0000000E+00 0.0000000E+00
-0.5630480E+04"
c buff(3)=" 3 0.5466073E+04 0.4443190E+03 0.2446331E+04
-0.4864732E+04"
c buff(4)=" 4 0.8785819E+03 -0.2533886E+03 0.2741971E+03
0.7759741E+03"
c buff(5)=" 5 0.4916306E+04 -0.1909305E+03 -0.2720528E+04
0.4088757E+04"
cc
cc Here the k,E,px,py,pz are read from the string into the
momenta array.
cc k=1,2 : incoming
cc k=3,nexternal : outgoing
cc
c do i=1,nexternal
c read (buff(i),*) k, P(0,i),P(1,i),P(2,i),P(3,i)
c enddo
c
cc- print the momenta out
c
c do i=1,nexternal
c write (*,'(i2,1x,5e15.7)') i, P(0,i),P(1,i),P(2,i),P(3,i),
c .dsqrt(dabs(DOT(p(0,i),p(0,i))))
c enddo
c
c CALL SMATRIX(P,MATELEM)
c
c write (*,*) "-------------------------------------------------"
c write (*,*) "Matrix element = ", MATELEM, " GeV^",-
(2*nexternal-8)
c write (*,*) "-------------------------------------------------"

Cheers,

Olivier

On Jun 29, 2012, at 8:11 AM, alexandra wrote:

> Question #201728 on MadGraph5 changed:
> https://answers.launchpad.net/madgraph5/+question/201728
>
> Status: Answered => Open
>
> alexandra is still having a problem:
> Hi Olivier
> I did it to a default point of the parameter space
> we have no agreement, but the amplitudes are no so far like the CX
> values....
> -
> MadGraph StandAlone:
> -----------------------------------------------------------------------------
>
> n E px py
> pz m
> 1 0.5000000E+03 0.0000000E+00 0.0000000E+00 0.4853864E+03
> 0.1200000E+03
> 2 0.5000000E+03 0.0000000E+00 0.0000000E+00 -0.4853864E+03
> 0.1200000E+03
> 3 0.5000000E+03 0.1090640E+03 0.4373705E+03 -0.1962062E+03
> 0.9118800E+02
> 4 0.5000000E+03 -0.1090640E+03 -0.4373705E+03 0.1962062E+03
> 0.9118800E+02
> -----------------------------------------------------------------------------
> Matrix element = 0.32059325388539306 GeV^ 0
> -----------------------------------------------------------------------------
> __________________________
> Matrix element to the linear sigma model on mathematica:
>
> -----------------------------------------------
> MatrixHHZZp[MH_, MZ_, E_, p1_, p3x_, p3y_, p3z_] :=
> (Sqrt[2]*1.166*10^-5 MH^2) (1 + (3*MH^2)/((4*E^2) - MH^2) + MH^2/
> (((p3x^2 + p3y^2 + (p3z - p1)^2)) - MZ^2) + MH^2/(((+p3x^2 + p3y^2
> + (-p3z - p1)^2)) - MZ^2))
> -----------------------------------------------
> (result 0.265325)
> _____________________________________
>
>
> I wanted to test annother points before send to you
> I guess It is done on check_sa.f, taking of the comment "c"
> ------
> c buff(1)=" 1 0.5630480E+04 0.0000000E+00 0.0000000E+00
> 0.5630480E+04"
> c buff(2)=" 2 0.5630480E+04 0.0000000E+00 0.0000000E+00
> -0.5630480E+04"
> c buff(3)=" 3 0.5466073E+04 0.4443190E+03 0.2446331E+04
> -0.4864732E+04"
> c buff(4)=" 4 0.8785819E+03 -0.2533886E+03 0.2741971E+03
> 0.7759741E+03"
> c buff(5)=" 5 0.4916306E+04 -0.1909305E+03 -0.2720528E+04
> 0.4088757E+04"
> -----------------------------
> I also already tryied some other ways of modified without success...
> -
> sory for that,
> but could you please tell me how do I change the phase space point?
> then I send to you a more detailed analisys
> -
> thanks
> Alexandra
>
> --
> You received this question notification because you are a member of
> MadTeam, which is an answer contact for MadGraph5.

Hi Olivier
-
I had made more points on the parameter space
-
(the information that was lacking was that we have to 'make' on every new point)
-
Indeed the result at matrix element level of the selection of only longitudinal polarizaration on MadGraph5 is diferent to the linear sigma model
that, by http://inspirehep.net/record/119348 should be equal to longitudinal gauge boson sccatering on SM
-
I had selected the longitudinal by that same way: on the matrix.f
-
what should we do?
-
below I send the numbers I had got
-
-------------------------------------------------------------------------------
1) -----------------------------------------------------------------------------

n E px py pz m

1 0.5000000E+03 0.0000000E+00 0.0000000E+00 0.4853864E+03 0.1200000E+03

2 0.5000000E+03 0.0000000E+00 0.0000000E+00 -0.4853864E+03 0.1200000E+03

3 0.5000000E+03 0.1090640E+03 0.4373705E+03 -0.1962062E+03 0.9118800E+02

4 0.5000000E+03 -0.1090640E+03 -0.4373705E+03 0.1962062E+03 0.9118800E+02
-----------------------------------------------------------------------------

Matrix element = 0.32059325388539306 GeV^ 0
-----------------------------------------------------------------------------

Matrix element LQT analitical = - 0.257489 GeV^ 0
-----------------------------------------------------------------------------

2) -----------------------------------------------------------------------------

1 0.5000000E+03 0.0000000E+00 0.0000000E+00 0.4853864E+03 0.1200002E+03

2 0.5000000E+03 0.0000000E+00 0.0000000E+00 -0.4853864E+03 0.1200002E+03

3 0.5000000E+03 0.0000000E+00 0.4916140E+03 0.0000000E+00 0.9119032E+02

4 0.5000000E+03 0.0000000E+00 -0.4916140E+03 0.0000000E+00 0.9119032E+02

-------------------------------------------------

Matrix element = 0.17920479992207539 GeV^ 0

-----------------------------------------------------------------------------

Matrix element LQT analitical = - 0.254608 GeV^ 0
-----------------------------------------------------------------------------

3) -----------------------------------------------------------------------------

1 0.5000000E+03 0.0000000E+00 0.0000000E+00 0.4853864E+03 0.1200002E+03

2 0.5000000E+03 0.0000000E+00 0.0000000E+00 -0.4853864E+03 0.1200002E+03

3 0.5000000E+03 0.4916140E+03 0.0000000E+00 0.0000000E+00 0.9119032E+02

4 0.5000000E+03 -0.4916140E+03 0.0000000E+00 0.0000000E+00 0.9119032E+02

-------------------------------------------------

Matrix element = 0.17920479992207539 GeV^ 0

-------------------------------------------------

Matrix element LQT analitical = - 0.254608 GeV^ 0
-----------------------------------------------------------------------------

4)-----------------------------------------------------------------------------

1 0.5000000E+03 0.0000000E+00 0.0000000E+00 0.4853864E+03 0.1200002E+03

2 0.5000000E+03 0.0000000E+00 0.0000000E+00 -0.4853864E+03 0.1200002E+03

3 0.5000000E+03 0.0000000E+00 0.0000000E+00 0.4916140E+03 0.9119032E+02

4 0.5000000E+03 0.0000000E+00 0.0000000E+00 -0.4916140E+03 0.9119032E+02

-------------------------------------------------

Matrix element = 513.84421910674598 GeV^ 0

-------------------------------------------------

Matrix element LQT analitical = 0.169388 GeV^ 0
-----------------------------------------------------------------------------

4)-----------------------------------------------------------------------------

1 0.1000000E+04 0.0000000E+00 0.0000000E+00 0.9927740E+03 0.1199991E+03

2 0.1000000E+04 0.0000000E+00 0.0000000E+00 -0.9927740E+03 0.1199991E+03

3 0.1000000E+04 0.0000000E+00 0.9958340E+03 0.0000000E+00 0.9118467E+02

4 0.1000000E+04 0.0000000E+00 -0.9958340E+03 0.0000000E+00 0.9118467E+02

-------------------------------------------------

Matrix element = 0.17328894976419468 GeV^ 0

-------------------------------------------------

Matrix element LQT analitical = - 0.2415 GeV^ 0

-----------------------------------------------------------------------------

------------------------------------------------------

Mathematica expression:

------------------------------
MW = 80;
MZ = 91.2;
MH = 120;
Gf = 1.166*10^-5;
(**)
S[E_, p1z_, p3x_, p3y_, p3z_] := 4*E^2; (* (p1+p1)^2 *)
T[E_, p1z_, p3x_, p3y_, p3z_] := -(-p3x^2 - p3y^2 - (p3z - p1z)); (* (p1-p3)^2 *)
U[E_, p1z_, p3x_, p3y_, p3z_] := -(-p3x^2 - p3y^2 - (p3z + p1z)^2); (* (p1-p4)^2 && |p4 = -|p3*)
(**)
MatrixHHZZp[MH_, MZ_, S_, T_, U_] := -(Sqrt[2]*1.166*10^-5 MH^2) (1 + (3*MH^2)/(S - MH^2) + MH^2/(T - MZ^2) + MH^2/(U - MZ^2));
(**)
MatrixHHZZp[MH, MZ, S[1000, 992.774, 0, 995.834, 0], T[1000, 992.774, 0, 995.834, 0], U[1000, 992.774, 0, 995.834, 0]]

Hi Olivier,
sory
-
I up to date a typo on the mthamatica formula I sent
(not on the numbers)
------------------------
MW = 80;
MZ = 91.2;
MH = 120;
Gf = 1.166*10^-5;
S[E_, p1_, p3x_, p3y_, p3z_] := 4*E^2;
T[E_, p1_, p3x_, p3y_, p3z_] := -(p3x^2 + p3y^2 + (p3z - p1)^2);
U[E_, p1_, p3x_, p3y_, p3z_] := -(p3x^2 + p3y^2 + (p3z + p1)^2);
MatrixHHZZp[MH_, MZ_, S_, T_, U_] := (Sqrt[2]*1.166*10^-5 MH^2) (1 + (3*MH^2)/(S - MH^2) + MH^2/(T - MZ^2) + MH^2/(U - MZ^2));
MatrixHHZZp[MH, MZ, S[500, 485.386, 0, 0, 491.614], T[500, 485.386, 0, 0, 491.614], U[500, 485.386, 0, 0, 491.614]]
------------------
best
Alexandra

Hi Alexandra,

The output of the standalone, is the matrix element square. I don't
that your analytical formula is the equivalent since it returns a
negative number.
So what is it?

Also did you check the value of the various couplings used for the
evaluation of the square matrix element? are in a numerical agreement
with the value that you use in mathematica?
(you can do that by adding some print in the matrix.f file)

Cheers,

Olivier

On Jun 29, 2012, at 3:41 PM, alexandra wrote:

> Question #201728 on MadGraph5 changed:
> https://answers.launchpad.net/madgraph5/+question/201728
>
> alexandra posted a new comment:
> Hi Olivier,
> sory
> -
> I up to date a typo on the mthamatica formula I sent
> (not on the numbers)
> ------------------------
> MW = 80;
> MZ = 91.2;
> MH = 120;
> Gf = 1.166*10^-5;
> S[E_, p1_, p3x_, p3y_, p3z_] := 4*E^2;
> T[E_, p1_, p3x_, p3y_, p3z_] := -(p3x^2 + p3y^2 + (p3z - p1)^2);
> U[E_, p1_, p3x_, p3y_, p3z_] := -(p3x^2 + p3y^2 + (p3z + p1)^2);
> MatrixHHZZp[MH_, MZ_, S_, T_, U_] := (Sqrt[2]*1.166*10^-5 MH^2)
> (1 + (3*MH^2)/(S - MH^2) + MH^2/(T - MZ^2) + MH^2/(U - MZ^2));
> MatrixHHZZp[MH, MZ, S[500, 485.386, 0, 0, 491.614], T[500, 485.386,
> 0, 0, 491.614], U[500, 485.386, 0, 0, 491.614]]
> ------------------
> best
> Alexandra
>
> --
> You received this question notification because you are a member of
> MadTeam, which is an answer contact for MadGraph5.

Hi Olvier
indeed, I had compared with amplitude of the element without square
but even squaring the values does not agree
the non agreement is even worse, by the way
-
the only needed couplings needed for the calculation are Gf Mh and Mz
they are in numeric agreement with the value I use on mathematica
-
from the check output:
Gf = 1.16639000000000003E-005
 aS = 0.11800000000000001
 MZ = 91.188000000000002
 MH = 120.00000000000000
-
I am negleting width effects on my formula
but I saw that add them would not be important in isolated phase space points
-
I'm thinking on more cross checks that I can perform....
cheers
Alexandra

Hello Alexandra,

Did you check that your matrix element expression agrees for some simple Standard Model process? That's a good way to make sure you are using the same normalization and conventions as MG. For example, symmetry factors and average of initial state spins is already included in the MG matrix elements, which is not always the case in other calculations.

All the best,
Johan

Hi Jonathan
HH>ZZ is a simple SM process
I can try another
I had already took care of the average over intial spins ( in this case, there is not)
see that to some ponts the diference (from the square of the number I sent)
is of orders of magnitude
-
I want to remenber that I made this cross check because the cross section of longitudinal sccatering was not decreasing, like expected from a the Higgs unitarization, but increasing
I'll try the same analisys with WW sccatering
best
Alexandra