adding test for 2L SQCD corrections to mb(Q) in the MSSM

FlexibleSUSY · Apr 7, 2017 · 1fc71ef · 1fc71ef
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diff --git a/meta/MSSM/twoloopbubble.m b/meta/MSSM/twoloopbubble.m
@@ -0,0 +1,141 @@
+(****f* Mathematica/TwoLoopBubbles
+* DESCRIPTION
+*	* This file defines functions for numerical  calculation of two-loop
+* 	vacuum diagrams (bubbles). 
+*	* Two-loop self-energy diagrams with different 
+*	  masses and the momentum expansion, Nuclear Physics B397 (1993) 123-142  
+*
+****)
+
+(* Calculation of Two Loop Bubble *)
+
+(* poles are excluded but only poles!! *)
+
+(* Bubble with two equal masses *)
+
+(* dimension -> mass *)
+
+$CalcPrecition = 15;
+
+(* <<MathWorld`SpecialFunctions`; *)
+
+(****u* TwoLoopBubbles/Clausen
+* DESCRIPTION
+*	* Clausen Function
+*	|latex \begin{eqnarray}
+*	|latex Cl_n(x) & = & \sum\limits_{k=1}^{\infty}\frac{\sin(k x)}{k^n} = 
+*	|latex \frac{i}{2} \left(Li_n(e^{-i x}) - Li_n(e^{i x}) \right), \quad \mathrm{ n~even} \\
+*	|latex Cl_n(x) & = & \sum\limits_{k=1}^{\infty}\frac{\cos(k x)}{k^n} =  
+*	|latex \frac{1}{2} \left(Li_n(e^{-i x}) - Li_n(e^{i x}) \right), \quad \mathrm{ n~odd} 
+*	|latex \end{eqnarray}
+*	
+****)
+
+ClausenCl[n_Integer?EvenQ,x_] := (PolyLog[n, E^(-I x)] - PolyLog[n, E^(I x)])I/2
+ClausenCl[n_Integer?OddQ,x_] :=  (PolyLog[n, E^(-I x)] + PolyLog[n, E^(I x)])/2
+
+(****u* TwoLoopBubbles/Phi
+* DESCRIPTION
+*	* Phi(z) Aux function
+*	|latex \begin{eqnarray}
+*	|latex \Phi(z) & = & 4 \ln 4, \quad z = 1\\
+*	|latex \Phi(z) & = & 4 \sqrt{\frac{z}{1-z}} Cl_2(2 \arcsin\sqrt{z}), \quad  0\leq z < 1\\
+*	|latex \Phi(z) & = & \frac{1}{\lambda}
+*	|latex \left( 2 \ln \left(\frac{1-\lambda}{2}\right)^2  
+*	|latex 	- 4 Li_2 \left(\frac{1-\lambda}{2}\right) - \ln (4 z )^2  + \frac{\pi^2}{3} \right), 
+*	|latex 	\quad\lambda = \sqrt{1 - 1/z}, z > 1
+*	|latex \end{eqnarray}
+*	
+****)
+
+Phi[z_?NumberQ] := N[4 * Sqrt[ z/(1-z) ] * ClausenCl[2, 2 * ArcSin[Sqrt[z]] ],$CalcPrecition] /; (z<1 && z>=0);
+Phi[z_?NumberQ] := N[Sqrt[z /(z-1) ] * ( - 4 PolyLog[2, 1/2 * ( 1 - Sqrt[1 - 1/z] ) ]
+				       + 2 Log[ 1/2 * (1 - Sqrt[1 - 1/z] ) ]^2  
+				       -   Log[ 4 z ]^2 
+				       + Pi^2/3 ), $CalcPrecition ] /; z>1;
+Phi[1] := N[4 Log [4],$CalcPrecition];
+
+(* mass squared! *)
+
+(* mmu - scale *)
+(****u* TwoLoopBubbles/Fin21
+* DESCRIPTION
+*	* Phi21[mm,mm,MM,mmu] - finite part of two-loop bubble with masses 
+*	 two different mm,MM at scale mmu.
+*	|latex \begin{eqnarray}
+*	|latex \Phi_{21}(m^2,m^2,M^2,\mu^2) & = & 
+*	|latex \frac{1}{2} \left((M^2 - 2 m^2) \left( 2 \ln^2 (m^2/\mu^2) - 6 \ln (m^2/\mu^2) + \zeta(2) + 7\right) \\
+*	|latex & + & M^2  \ln (M^2/m^2) \left( 6 - 4 \ln (m^2/\mu^2) - \ln (M^2/m^2) \right) \\
+*	|latex & + & (4 m^2 - M^2) \Phi(z)\right), \quad z = \frac{M^2}{4 m^2}
+*	|latex \end{eqnarray}
+*	
+****)
+
+Fin21[mm_?NumberQ, mm_?NumberQ, MM_?NumberQ, mmu_?NumberQ] :=
+	Module[{z,tmp}, z = MM/(4*mm) ; (* Print[z]; *)
+		    tmp = 0.5 * N[-(2 mm + MM ) ( 2 Log[mm/mmu]^2 - 6 Log[mm/mmu]+ Zeta[2] + 7 )
+		    	      - Log[MM/mm]^2 MM + 2 Log[MM/mm] * ( 3 - 2 Log[mm/mmu]) * MM 
+			      + (4 mm - MM) * Phi[z],$CalcPrecition ];
+	  	    tmp
+	      ];
+(* three different masses *)
+
+LambdaSquared[x_?NumberQ, y_?NumberQ] := (1-x-y)^2-4*x*y;
+
+(* x < 1 and y < 1 *)
+Phi[x_?NumberQ, y_?NumberQ] := 
+        Module[{lambda,tmp}, lambda = Sqrt[LambdaSquared[x,y]]; 
+		tmp := N[ 1/lambda *  
+		( 2 Log[ ( 1 + x - y - lambda )/2 ] * Log[ (1 -x +y - lambda )/2 ] - Log[x]*Log[y]
+		- 2 PolyLog[2, ( 1 + x - y - lambda )/2 ] - 2 PolyLog[2, (1 - x + y - lambda)/2] + Pi^2/3),$CalcPrecition ];
+		tmp
+	      ] /; (LambdaSquared[x,y] > 0 );
+
+Phi[x_?NumberQ, y_?NumberQ] := 
+	Module[{lambda, tmp}, lambda = Sqrt[-LambdaSquared[x,y]];
+		tmp := N[ 2/lambda * ( ClausenCl[2, 2 ArcCos[ (-1 + x + y )/(2 Sqrt[x y] )] ]
+		                      +ClausenCl[2, 2 ArcCos[ (1 + x -y )/(2 Sqrt[x] ) ] ]
+				      +ClausenCl[2, 2 ArcCos[ (1 - x + y )/(2 Sqrt[y] ) ] ]
+				     ), $CalcPrecition];
+		tmp
+	      ] /; (LambdaSquared[x,y] < 0 );
+
+Fin3[mm1_?NumberQ, mm2_?NumberQ, mm3_?NumberQ, mmu_?NumberQ] :=
+	Module[{x,y, tmplist, tmp, mm}, 
+		tmplist = Sort[{mm1,mm2,mm3}];
+		mm = tmplist[[3]];
+		x = tmplist[[1]]/mm;
+		y = tmplist[[2]]/mm;
+		(* Print[x]; Print[y];Print[ LambdaSquared[x,y]]; *)
+		If[LambdaSquared[x,y] == 0,
+		     tmp = N[-1/2 * (x * Log[x]^2 
+			     + ( (x + y - 1) * Log[y]  + 2 x * ( 2 Log[mm/mmu] - 3) ) * Log[x] 
+			     +  y Log[y]^2 
+			     + 2 y Log[y] ( 2 Log[mm/mmu] - 3) 
+			     + (1 + x + y ) * (2 Log[mm/mmu]^2 - 6 Log[mm/mmu] + Zeta[2] + 7)
+			     ) * mm, $CalcPrecition],
+		    tmp = N[mm * (
+		    	1/2 * ( -2 Log[mm/mmu]^2 + 6 Log[mm/mmu] - LambdaSquared[x,y]*Phi[x,y] 
+				- Zeta[2] + Log[x] Log[y] - 7 ) 
+		       -1/2 * x * ( Log[x]^2 + ( Log[y] + 4 Log[mm/mmu] - 6 ) Log[x] + 2 Log[mm/mmu]^2 
+		       		+ Zeta[2] - 6 Log[mm/mmu] + 7 )
+		       -1/2 * y * ( Log[y]^2 + ( Log[x] + 4 Log[mm/mmu] - 6 ) Log[y] + 2 Log[mm/mmu]^2 
+		       		+ Zeta[2] - 6 Log[mm/mmu] + 7 )
+				), $CalcPrecition]
+		  ];
+		  tmp
+		];
+
+(* additional part *)
+(* Bubble with 1 mass equal to zero *)
+
+Hmine[mm1_?NumberQ, mm2_?NumberQ] := 
+    2 * PolyLog[2, 1-mm1/mm2] + 1/2 * Log[mm1/mm2]^2;
+
+Fin20[mm1_?NumberQ, mm2_?NumberQ, mmu_?NumberQ] :=
+	Module[{tmp}, tmp = N[1/2 * ( - (mm1 + mm2) * ( 7 + Zeta[2] )  
+		            + 6 * (mm1 * Log[mm1/mmu] + mm2 * Log[mm2/mmu])
+			    - 2 * (mm1 * Log[mm1/mmu]^2 + mm2 * Log[mm2/mmu]^2 )
+			   +1/2 * (mm1 + mm2) * Log[mm1/mm2]^2 + (mm1-mm2)*Hmine[mm1,mm2] ),$CalcPrecition]; 
+		      tmp
+	];
diff --git a/test/module.mk b/test/module.mk
@@ -377,6 +377,7 @@ TEST_META := \
 		$(DIR)/test_LoopFunctions.m \
 		$(DIR)/test_MSSM_2L_analytic.m \
 		$(DIR)/test_MSSM_2L_mt.m \
+		$(DIR)/test_MSSM_2L_yb_softsusy.m \
 		$(DIR)/test_MSSM_2L_yt.m \
 		$(DIR)/test_MSSM_2L_yt_loopfunction.m \
 		$(DIR)/test_MSSM_2L_yt_softsusy.m \

diff --git a/test/test_MSSM_2L_yb_softsusy.m b/test/test_MSSM_2L_yb_softsusy.m
@@ -0,0 +1,40 @@
+Needs["TestSuite`", "TestSuite.m"];
+
+Get[FileNameJoin[{"meta", "MSSM", "twoloopbubble.m"}]];
+
+b2l  = Get[FileNameJoin[{"meta", "MSSM", "bquark_2loop_sqcd_decoupling.m"}]];
+b2ls = Get[FileNameJoin[{"meta", "MSSM", "dmbas2.m"}]];
+
+colorCA = 3; colorCF = 4/3; GS = g3;
+zt2 = Zeta[2]; zt3 = Zeta[3];
+MGl = mgl; MT = mt; MB = mb;
+mmgl = mgl^2; mmt = mt^2;
+mmst1 = mst1^2; mmst2 = mst2^2;
+mmsb1 = msb1^2; mmsb2 = msb2^2;
+msd1 = msusy; msd2 = msusy;
+mmsusy = msusy^2; mmu = scale^2;
+Xt = At - MUE CB/SB;
+Xb = Ab - MUE SB/CB;
+s2t = 2 mt Xt/(mmst1 - mmst2);
+s2b = 2 mb Xb/(mmsb1 - mmsb2);
+snb = Sin[ArcSin[s2b]/2];
+
+Delta[mass1_, mass2_, mass3_, x_] := (mass1^2 + mass2^2 + mass3^2 - 2*(mass1*mass2 + mass1*mass3 + mass2*mass3))^x;
+fpart[0, m1_, m2_, scale_]        := Fin20[m1^2, m2^2, scale^2];
+fpart[m1_, m2_, m3_, scale_]      := Fin3[m1^2, m2^2, m3^2, scale^2];
+delta3[m1_, m2_, m3_]             := Delta[m1^2, m2^2, m3^2, -1]; 
+fin[0, mass1_, mass2_]            := Fin20[mass1, mass2, mmu];
+fin[mass1_, mass2_, mass3_]       := Fin3[mass1, mass2, mass3, mmu];
+
+(* check for specific parameter point *)
+point = {
+   g3 -> 1, mst1 -> 100, mst2 -> 200, msb1 -> 300, msb2 -> 400, 
+   msusy -> 500, scale -> 90,
+   mt -> 173, mb -> 3, SB -> TB/Sqrt[1 + TB^2], 
+   CB -> 1/Sqrt[1 + TB^2], Ab -> 100, At -> 110,
+   MUE -> 400, mgl -> 600, TB -> 20
+};
+
+TestEquality[PossibleZeroQ[(b2l - b2ls) //. point // N], True];
+
+PrintTestSummary[];