Esempio n. 1
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def gounaris_sakurai_lineshape(s, m, gamma, m_pi):
    """
      Gounaris-Sakurai shape for rho->pipi
        s     : squared pipi inv. mass
        m     : rho mass
        gamma : rho width
        m_pi  : pion mass
    """
    m2 = m * m
    m_pi2 = m_pi * m_pi
    ss = atfi.sqrt(s)

    ppi2 = (s - 4. * m_pi2) / 4.
    p02 = (m2 - 4. * m_pi2) / 4.
    p0 = atfi.sqrt(p02)
    ppi = atfi.sqrt(ppi2)

    hs = 2. * ppi / atfi.pi() / ss * atfi.log((ss + 2. * ppi) / 2. / m_pi)
    hm = 2. * p0 / atfi.pi() / m * atfi.log((m + 2. * ppi) / 2. / m_pi)

    dhdq = hm * (1. / 8. / p02 - 1. / 2. / m2) + 1. / 2. / atfi.pi() / m2
    f = gamma * m2 / (p0**3) * (ppi2 * (hs - hm) - p02 * (s - m2) * dhdq)

    gamma_s = gamma * m2 * (ppi**3) / s / (p0**3)

    dr = m2 - s + f
    di = ss * gamma_s

    r = dr / (dr**2 + di**2)
    i = di / (dr**2 + di**2)

    return atfi.complex(r, i)
Esempio n. 2
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def helicity_angles_3body(pa, pb, pc):
    """Calculate 4 helicity angles for the 3-body D->ABC decay defined as:
      theta_r, phi_r : polar and azimuthal angles of the AB resonance in the D rest frame
      theta_a, phi_a : polar and azimuthal angles of the A in AB rest frame

    :param pa: 
    :param pb: 
    :param pc: 

    """
    theta_r = atfi.acos(-z_component(pc) / norm(spatial_components(pc)))
    phi_r = atfi.atan2(-y_component(pc), -x_component(pc))

    pa_prime = lorentz_vector(
        rotate_euler(spatial_components(pa), -phi_r,
                     atfi.pi() - theta_r, phi_r), time_component(pa))
    pb_prime = lorentz_vector(
        rotate_euler(spatial_components(pb), -phi_r,
                     atfi.pi() - theta_r, phi_r), time_component(pb))

    w = time_component(pa) + time_component(pb)

    pab = lorentz_vector(-(pa_prime + pb_prime) / scalar(w), w)
    pa_prime2 = lorentz_boost(pa_prime, pab)

    theta_a = atfi.acos(
        z_component(pa_prime2) / norm(spatial_components(pa_prime2)))
    phi_a = atfi.atan2(y_component(pa_prime2), x_component(pa_prime2))

    return (theta_r, phi_r, theta_a, phi_a)
Esempio n. 3
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def generate_rotation_and_boost(moms, minit, meanpt, ptcut, rnd):
    """
    Generate 4-momenta of final state products according to 3-body phase space distribution
      moms   - initial particle momenta (in the rest frame)
      meanpt - mean Pt of the initial particle
      ptcut  - miminum Pt of the initial particle
      rnd    - Auxiliary random tensor
  """

    pt = generate_pt(rnd[:, 0], meanpt, ptcut, 200.)  # Pt in GeV
    eta = generate_eta(rnd[:, 1])  # Eta
    phi = generate_phi(rnd[:, 2])  # Phi

    theta = 2. * atfi.atan(atfi.exp(-eta))  # Theta angle
    p = pt / atfi.sin(theta)  # Full momentum
    e = atfi.sqrt(p**2 + minit**2)  # Energy

    px = p * atfi.sin(theta) * atfi.sin(phi)  # 3-momentum of initial particle
    py = p * atfi.sin(theta) * atfi.cos(phi)
    pz = p * atfi.cos(theta)

    p4 = atfk.lorentz_vector(atfk.vector(px, py, pz),
                             e)  # 4-momentum of initial particle

    rotphi = uniform_random(rnd[:, 3], 0., 2 * atfi.pi())
    rotpsi = uniform_random(rnd[:, 4], 0., 2 * atfi.pi())
    rottheta = atfi.acos(uniform_random(rnd[:, 5], -1, 1.))

    moms2 = []
    for m in moms:
        m1 = atfk.rotate_lorentz_vector(m, rotphi, rottheta, rotpsi)
        moms2 += [atfk.boost_from_rest(m1, p4)]

    return moms2
Esempio n. 4
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    def square_dalitz_plot_jacobian(self, sample):
        """
        sample: [mAB^2, mBC^2]
        Return the jacobian determinant (|J|) of tranformation from dmAB^2*dmBC^2 -> |J|*dMpr*dThpr where Mpr, Thpr are defined in (AC) frame.
        """
        mPrime = self.m_prime_ac(sample)
        thPrime = self.theta_prime_ac(sample)

        diff_AC = tf.cast(
            atfi.sqrt(self.maxac) - atfi.sqrt(self.minac), atfi.fptype())
        mAC = atfi.const(0.5) * diff_AC * (
            Const(1.0) + atfi.cos(atfi.pi() * mPrime)) + tf.cast(
                atfi.sqrt(self.minac), atfi.fptype())
        mACSq = mAC * mAC

        eAcmsAC = (atfi.const(0.5) *
                   (mACSq - tf.cast(self.mc2, atfi.fptype()) +
                    tf.cast(self.ma2, atfi.fptype())) / mAC)
        eBcmsAC = (atfi.const(0.5) *
                   (tf.cast(self.md, atfi.fptype())**2.0 - mACSq -
                    tf.cast(self.mb2, atfi.fptype())) / mAC)

        pAcmsAC = atfi.sqrt(eAcmsAC**2.0 - tf.cast(self.ma2, atfi.fptype()))
        pBcmsAC = atfi.sqrt(eBcmsAC**2.0 - tf.cast(self.mb2, atfi.fptype()))

        deriv1 = Pi() * atfi.const(0.5) * diff_AC * atfi.sin(
            atfi.pi() * mPrime)
        deriv2 = Pi() * atfi.sin(atfi.pi() * thPrime)

        return atfi.const(4.0) * pAcmsAC * pBcmsAC * mAC * deriv1 * deriv2
Esempio n. 5
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def helicity_angles_4body(pa, pb, pc, pd):
    """Calculate 4 helicity angles for the 4-body E->ABCD decay defined as:
      theta_ab, phi_ab : polar and azimuthal angles of the AB resonance in the E rest frame
      theta_cd, phi_cd : polar and azimuthal angles of the CD resonance in the E rest frame
      theta_ac, phi_ac : polar and azimuthal angles of the AC resonance in the E rest frame
      theta_bd, phi_bd : polar and azimuthal angles of the BD resonance in the E rest frame
      theta_ad, phi_ad : polar and azimuthal angles of the AD resonance in the E rest frame
      theta_bc, phi_bc : polar and azimuthal angles of the BC resonance in the E rest frame
      phi_ab_cd : azimuthal angle between AB and CD
      phi_ac_bd : azimuthal angle between AC and BD
      phi_ad_bc : azimuthal angle between AD and BC

    :param pa:
    :param pb:
    :param pc:
    :param pd:

    """
    theta_r = atfi.acos(-z_component(pc) / norm(spatial_components(pc)))
    phi_r = atfi.atan2(-y_component(pc), -x_component(pc))

    pa_prime = lorentz_vector(
        rotate_euler(spatial_components(pa), -phi_r,
                     atfi.pi() - theta_r, phi_r),
        time_component(pa),
    )
    pb_prime = lorentz_vector(
        rotate_euler(spatial_components(pb), -phi_r,
                     atfi.pi() - theta_r, phi_r),
        time_component(pb),
    )

    w = time_component(pa) + time_component(pb)

    pab = lorentz_vector(-(pa_prime + pb_prime) / scalar(w), w)
    pa_prime2 = lorentz_boost(pa_prime, pab)

    theta_a = atfi.acos(
        z_component(pa_prime2) / norm(spatial_components(pa_prime2)))
    phi_a = atfi.atan2(y_component(pa_prime2), x_component(pa_prime2))

    return (theta_r, phi_r, theta_a, phi_a)
Esempio n. 6
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def random_rotation_and_boost(moms, rnd):
    """
    Apply random boost and rotation to the list of 4-vectors
      moms : list of 4-vectors
      rnd  : random array of shape (N, 6), where N is the length of 4-vector array
    """
    pt = -5.0 * atfi.log(
        rnd[:, 0]
    )  # Random pT, exponential distribution with mean 5 GeV
    eta = rnd[:, 1] * 3.0 + 2.0  # Uniform distribution in pseudorapidity eta
    phi = rnd[:, 2] * 2.0 * atfi.pi()  # Uniform distribution in phi

    theta = 2.0 * atfi.atan(atfi.exp(-eta))  # Theta angle is a function of eta
    p = pt / atfi.sin(theta)  # Full momentum
    e = atfi.sqrt(p ** 2 + mb ** 2)  # Energy of the Bs

    px = (
        p * atfi.sin(theta) * atfi.sin(phi)
    )  # 3-momentum of initial particle (Bs meson)
    py = p * atfi.sin(theta) * atfi.cos(phi)
    pz = p * atfi.cos(theta)

    boost = atfk.lorentz_vector(
        atfk.vector(px, py, pz), e
    )  # Boost vector of the Bs meson

    rot_theta = atfi.acos(
        rnd[:, 3] * 2.0 - 1.0
    )  # Random Euler rotation angles for Bs decay
    rot_phi = rnd[:, 4] * 2.0 * atfi.pi()
    rot_psi = rnd[:, 5] * 2.0 * atfi.pi()

    # Apply rotation and boost to the momenta in input list
    moms1 = []
    for m in moms:
        m1 = atfk.rotate_lorentz_vector(m, rot_phi, rot_theta, rot_psi)
        moms1 += [atfk.boost_from_rest(m1, boost)]

    return moms1
Esempio n. 7
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sys.path.append("../")
#os.environ["CUDA_VISIBLE_DEVICES"] = ""   # Do not use GPU

import amplitf.interface as atfi
import amplitf.kinematics as atfk
import amplitf.dynamics as atfd
import amplitf.toymc as atft
from amplitf.phasespace.rectangular_phasespace import RectangularPhaseSpace

from ROOT import TFile

if __name__ == "__main__":

    # Four body angular phase space is described by 3 angles.
    phsp = RectangularPhaseSpace(
        ((-1., 1.), (-1., 1.), (-atfi.pi(), atfi.pi())))

    # Fit parameters of the model
    FL = 0.770
    AT2 = 0.200
    S5 = -0.100

    ### Start of model description


    def model(x):
        # Get phase space variables
        cosThetaK = phsp.coordinate(x, 0)
        cosThetaL = phsp.coordinate(x, 1)
        phi = phsp.coordinate(x, 2)
Esempio n. 8
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import sys
import tensorflow as tf

sys.path.append("../")

import amplitf.interface as atfi
import amplitf.kinematics as atfk

atfi.set_seed(2)

rndvec = tf.random.uniform([32, 3], dtype=atfi.fptype())

v = rndvec[:, 0]
th = atfi.acos(rndvec[:, 1])
phi = (rndvec[:, 2] * 2 - 1) * atfi.pi()

p = atfk.lorentz_vector(
    atfk.vector(atfi.zeros(v), atfi.zeros(v), atfi.zeros(v)), atfi.ones(v))

bp = atfk.lorentz_boost(
    p,
    atfk.rotate_euler(atfk.vector(v, atfi.zeros(v), atfi.zeros(v)), th, phi,
                      atfi.zeros(v)))

print(bp)
print(atfk.mass(bp))
Esempio n. 9
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import amplitf.likelihood as atfl
import amplitf.optimisation as atfo
from amplitf.phasespace.rectangular_phasespace import RectangularPhaseSpace

# Import TFA modules
import tfa.toymc as tft

from ROOT import TFile

tf.config.experimental_run_functions_eagerly(False)

if __name__ == "__main__":

    # Four body angular phase space is described by 3 angles.
    phsp = RectangularPhaseSpace(
        ((-1.0, 1.0), (-1.0, 1.0), (-atfi.pi(), atfi.pi())))

    # Fit parameters of the model
    FL = atfo.FitParameter("FL", 0.770, 0.000, 1.000, 0.01)
    AT2 = atfo.FitParameter("AT2", 0.200, -1.000, 1.000, 0.01)
    S5 = atfo.FitParameter("S5", -0.100, -1.000, 1.000, 0.01)

    pars = [FL, AT2, S5]

    ### Start of model description

    @atfi.function
    def model(x):
        # Get phase space variables
        cosThetaK = phsp.coordinate(x, 0)
        cosThetaL = phsp.coordinate(x, 1)