more simplification of eps

[Karim-Ghorbani]

Hello, I am running the following program:

Vectors k1, k2, p1, p2, q; Indices mu, nu, rho, sigma,m1,n1; Symbols s, t, u, e, mass1, mass2,B,A; Local M1 = 1/B^2 d_(m1,n1)(g(1,p2)+mass2)*g(1,m1)(g(1,p2)-g(1,q)-mass2)g(1,mu)*g6(1)(g_(1,p1)-mass2)g(1,n1)*(g(1,p2)-g(1,q)-mass2)*g(1,nu)*g6_(1) ;

Local M2 = 1/B^2 g_(2,k2)g(2,mu)*g6(2)g_(2,k1)g(2,nu)*g6(2) ; Local M = M1 * M2 ; Trace4,1; Trace4,2; contract;

id p1.p1 = mass2^2 ; id p2.p2 = mass2^2 ; id k1.k1 = mass1^2 ; id k2.k2 = mass1^2 ; *id k1.k2 = p1.q + p2.q -p1.p2; id q.q = 0 ; id mass1 = 0 ; id mass2^2 = 0 ;

Print +s ; .end

I get this output:

M =

• 512k1.k2p1.p2p2.qB^-4
• 512k1.p1k2.p2p2.qB^-4
• 512k1.p2k2.p1p2.qB^-4

• 512e_(k1,k2,p1,p2)p2.q*B^-4

  I would like to get e_(k1,k2,p1,p2) simplified. Would appreciate any hint for this. Thank you Karim

[vermaseren]

Hi,

Question: what do you mean with simplified? This is it. If you can make that simpler, either you have a different meaning for that word, or you made a great breakthrough in mathematics. gamma5 can give Levi-Civita tensors in the answer, particularly in CP violating theories. (is always good for some headaches….)

Cheers

Jos

On 25 Apr 2018, at 12:20, Karim-Ghorbani notifications@github.com wrote:

Hello, I am running the following program:

Vectors k1, k2, p1, p2, q; Indices mu, nu, rho, sigma,m1,n1; Symbols s, t, u, e, mass1, mass2,B,A; Local M1 = 1/B^2 d_(m1,n1)(g(1,p2)+mass2)g(1,m1)(g(1,p2)-g(1,q)-mass2)g(1,mu)g6(1)(g(1,p1)-mass2)g(1,n1)(g(1,p2)-g(1,q)-mass2)g(1,nu)*g6(1) ;

Local M2 = 1/B^2 g_(2,k2)g(2,mu)*g6(2)g_(2,k1)g(2,nu)*g6(2) ; Local M = M1 * M2 ; Trace4,1; Trace4,2; contract;

id p1.p1 = mass2^2 ; id p2.p2 = mass2^2 ; id k1.k1 = mass1^2 ; id k2.k2 = mass1^2 ; *id k1.k2 = p1.q + p2.q -p1.p2; id q.q = 0 ; id mass1 = 0 ; id mass2^2 = 0 ;

Print +s ; .end

I get this output:

M =

• 512k1.k2p1.p2p2.qB^-4
• 512k1.p1k2.p2p2.qB^-4
• 512k1.p2k2.p1p2.qB^-4
• 512*e_(k1,k2,p1,p2)p2.qB^-4

I would like to get e_(k1,k2,p1,p2) simplified. Would appreciate any hint for this. Thank you Karim

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[tueda]

Maybe it would be nice if you use Markdown syntax, especially code block like

L F = 1*2*3;
P;
.end

(Some characters in FORM programs have special meanings in Markdown.)

[Karim-Ghorbani]

Well, I expect the final results in terms of the involved momenta.

Can you please let me know what is e_(k1,k2,p1,p2) in terms of Levi-Civita tensor and external momenta k1, k2, p1, p2.

Thanks Karim

[vermaseren]

That is Schoonschip notation. It is explained in the manual. It means that when the index of a vector is contracted with an index of a function, the vector is placed where the index of the function used to be. This avoids a lot of unnecessary dummy indices.

Jos

On 25 Apr 2018, at 14:38, Karim-Ghorbani notifications@github.com wrote:

Well, I expect the final results in terms of the involved momenta.

Can you please let me know what is e_(k1,k2,p1,p2) in terms of Levi-Civita tensor and external momenta k1, k2, p1, p2.

Thanks Karim

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