backgrounds.md

Generic backrgound models

Here is incomplete list of background-like models - the models that often could be used to describe the background distribution

Polynomial models

Here the list of the most useful polynomial models:

• PolyPos_pdf : positive (non-negative) polynomial
• PolyEven_pdf : positibe (non-negative) symmetric polynomial: p(x)= p(2*x0-x), where x0=0.5*(xmin+xmax)
• Monotonic_pdf : positive (non-negative) polynomial with fixed sign of the first derivative: posynomial either non-decreasing or non-increasing
• Convex_pdf : positive (non-negative) polynomial with fixed signs of the first (non-decreasing or non-increasing) and second (convex or concave) derivatives
• ConvexOnly_pdf : positive (non-negative) polynomial with fixed sign of the second (convex or concave) derivative

Phasespace-based models

Here the list of the most useful phasespace-based models:

• PS2_pdf : 2-body phase space (no parameters)
• PSLeft_pdf : Low edge of N-body phase space
• PSRight_pdf : High edge of L-body phase space from N-body decays
• PSNL_pdf : approximation for L-body phase space from N-body decays
• PS23L_pdf : 2-body phase space from 3-body decays with orbital momenta

Polynomial-based models

• Bkg_pdf : The exponential function, modulated by the positive polynomial. In practice it is the most useful function to describe the combinatorial background
• PSPol_pdf : L-body phase space from N-body decays modulated by a positive polynomial
• Sigmoid_pdf : sigmoid function (atanh) modulated by the positive polynomial
• TwoExpoPoly_pdf : difference of two exponents, modulated by the positive polynomial

Spline-based models

The models, based on B-splines :

• PSpline_pdf : positive (non-negative) spline
• MSpline_pdf : positive (non-negative) monothonic (non-decreasing or non-increasing) spline
• CSpline_pdf : positive (non-negative) monothonic (non-decreasing or non-inclreasing) convex or concave spline
• CPSpline_pdf : positive (non-negative) convex or concave spline