Back to challenge

Challenge Rules

Compute the MS-bar renormalized BNL amplitude graph at the fixed phase-space point below, then submit the leading digits of four complex ratios.

Amplitude Graph

Clean BNL two-loop graph to compute

DOT Definition

digraph BNL {
  num = "1";
  overall_factor = "1";
  overall_factor_evaluated = "1";
  projector = "vbar(0,spenso::bis(4,hedge(0)))
    * u(1,spenso::bis(4,hedge(1)))
    * v(2,spenso::bis(4,hedge(2)))
    * ubar(3,spenso::bis(4,hedge(3)))
    * ebar(4,spenso::mink(4,hedge(4)))
    * ebar(5,spenso::mink(4,hedge(5)))
    * ebar(6,spenso::mink(4,hedge(6)))";

  ext [style=invis]
  ext  -> 0:0 [id=0 particle="e+"];
  ext -> 0:1 [id=1 particle="e-"];

  1:2 -> ext [id=2 particle="mu+"];
  1:3 -> ext [id=3 particle="mu-"];
  2:4 -> ext [id=4 particle="a"];
  3:5 -> ext [id=5 particle="a"];
  4:6 -> ext [id=6 particle="a"];

  0 -> 5 [id=7 particle="a"];
  6 -> 1 [id=8 particle="a"];

  5 -> 6 [id=9 particle="t" lmb_id=0];
  6 -> 2 [id=10 particle="t"];
  2 -> 3 [id=11 particle="t"];
  3 -> 7 [id=12 particle="t"];
  7 -> 4 [id=13 particle="t"];
  4 -> 8 [id=14 particle="t"];
  8 -> 5 [id=15 particle="t"];
  7 -> 8 [id=16 particle="g" lmb_id=1];
}

What To Compute

Compute this MS-bar renormalized amplitude graph for one fixed massless 2 -> 5 kinematic configuration.

Use zero top width, Gamma_t = 0, μr = 1000.0, and evaluate the complex results R0, R1, R2, R3, and R4.

Top Mass Points

Top mass Result label
mt = 600R0
mt = 510R1
mt = 530R2
mt = 400R3
mt = 450R4

What To Submit

On the challenge page, enter the first two digits, not rounded, of the real and imaginary parts of:

R1/R0, R2/R0, R3/R0, R4/R0

Each field should use the signed two-significant-digit style accepted by the form, such as -0.31, +0.20, or 2.3.

Input Kinematics

Use the helicity assignment and four-momenta exactly as shown.

helicities = [-, +, -, +, +, -, +]
momenta = [
 [ 500.0            ,  0.0              ,  0.0              , +500.0             ],
 [ 500.0            ,  0.0              ,  0.0              , -500.0             ],
 [ 163.5141597587927, -155.7860143642699, -12.32488779805292, +48.12167194606676 ],
 [ 146.5267245560251, -18.94527369806406, +33.44069886802352, -141.3961713514227 ],
 [ 162.3143263141399, +4.025183527597962, -151.4903823484999, +58.14122874765845 ],
 [ 296.8259181161096, +175.6763342487531, +137.9119270904214, -195.5089553360614 ],
 [ 230.8188712549325, -4.970229714017088, -7.53735581189216 , +230.6422259937584 ],
]