Basic Collision Experimental

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Black Event: Event without zero suppression or any on-line data pre-processing.

Collision energy: Referred as $\sqrt{s_{NN}}$ in a center of mass reference frame (Heavy Ion Collisions), or energy per nucleon in fixed target experiments. Some ranges:
  • AGS-BNL: 14.5 AGeV. Berkeley National Lab Alternating Gradient Synchrotron.
  • SPS-CERN: 200 AGeV. Super Proton Synchrotron @ CERN
  • RHIC: $\sqrt{s_{NN}}$ = 200 GeV. Relativistic Heavy Ion Collider @ BNL.

CP violation: Observed during K meson disintegration.

Dalitz decay: 3-body decay, dielectron source. In general: $V {\longrightarrow} e^+e^-X$.
It generates a continuum, in opposition with the two-body meson decay, $V {\longrightarrow} e^+e^-$ that generates 2 peaks.
EX: ${\pi^0}$ Dalitz decay branch (1.2%) ${\pi^0} {\longrightarrow} e^+e^- {\gamma}$ More info about ${\pi^0}$ decay you find at the NIKHEF page

Dalitz plot: Technique to represent all essential kinematical variables, of any three-body final state in a scatter plot or two-dimensional histogram. For a example with masses and the ${p+{\bar{p}} {\longrightarrow} {\pi^0}+{\pi^0}+{\pi^0}}$ decay check COSY-11 web. In general,you could do that if you have relation of the type ${x_1+x_2+x_3 = cte}$.

Drell-Yan (DY) process: A quark and an antiquark are annihilated creating a photon and the photon decays into a leptop pair. For proton proton deep inelastic scattering it can be written like:
${{p+p} \longrightarrow{{\mu^+} +{\mu^-}+X} }$
Being X an hadron. For two quarks, in general:
${{q+{\bar{q}}} \longrightarrow{l +{\bar{l}}} }$
Here you find the DY cross section

Elliptic Flow: Nucleus-nucleus collisions produce an elliptic region of quark-gluon medium. More energetic hadrons squirt out within the plane of interaction than at perpendicular angles, that is, there is a flow in the plane of interaction. We define the elliptic flow streght as the second coefficient of the Fourier expansion of the Lorentz invariant particle distribution ( $v_2$). For a thermal Boltzmann source model:
$E{\frac{d^3N}{dp^3}} = {\frac {d^3N} {m_Tdm_Td{\phi}dy} } {\sum_{n=0}^{\infty}} 2v_2 cos(n({\phi}-{\Phi_R}))$

Infrarred Limit: When a parameter is tending to zero.
For ${\alpha^2({\vert}q^2{\vert})}$ = ${{\alpha^*}+(A{\times}{\frac{\mu^2}{{\vert}q^2{\vert}}})}$, when ${{q^2}{\longrightarrow}0}$, ${{\alpha}={\alpha^*}}$ (infrared stability)

Invariant Mass: Measurement or calculation of the mass that is the same in all reference frames. Here W is the invariant mass of the system of particles, equal to the mass of the decay particle: $ (Wc)^2 = (\Sigma E)^2 + (\Sigma pc)^2$ More details here

Jet: Intensity in a cone of radius R=0.7 in pseudorapidity-azimuthal angle space (${\eta},{\phi}$ cone). If the cone axis is (${\eta_c},{\phi_c}$), a particle i with momentum p is in the jet if:
${ ({\eta}-{\eta_c})^2 + ({\phi}-{\phi_c})^2 < R^2   }$.
The transverse enegy of the jet is thus definend as: $E_T = {\sum}_{i in cone} p_i$

Jet Quenching:. pp hard scattering produces back to back particle jets, but in AA (nucleus-nucleous) collisions, we have a dense quark-gluon medium and the jets are quenched like a shot in the water, and only one usually survives.

Light Cone Variables: Considering the reaction $ a+b {\longrightarrow} d+X $
Using the notation for the 4-momentum of a particle $ a = (a_0,a_T,a_z)$, we define:
  • $d_+ = d_0 +d_z$ : forward light cone momentum
  • $d_- = d_0 -d_z$ : backward light cone momentum
  • $x_+ = {\frac{d_0 +d_z}{b_0+b_z}}$ : forward light cone variable (Lorentz invariant)
  • $x_- = {\frac{d_0 -d_z}{a_0-a_z}}$ : backward light cone variable (Lorentz invariant)
All of them can be expressed as functions of the rapidity or pseudorapidity, or viceversa.

Minimum bias (MB) events: Two definitions:
  • Experimental: non-single diffractive (NSD) inelastice interactions. Usually low pt parton scattering events.
  • Theoretical: non-diffractive inelastic interactions.
Both definitions differ on around 15% at current collider energies. From the Glasgow university site

Multiplicity: Total number N of particles produced in a collision. Since most of the detection methods are only sensitive to charged particles, we speak about charged multiplicity. After Thome, it can be parametrized like:
$<N_{ch}> = 0.88 + 0.44lns + 0.188(lns)^2$
It is common to speak about rapidity distribution of the produced charged particles (charged multiplicity), expressed as ${\frac{dN_{ch}}{dy}} = A(1-x_+)^a(1-x_{-})^-$ where $x_+$, $x_-$ are functions of the rapidity. Since the rapidity is dependent of 2 kinematic variables and the pseudorapidity of only one (angle with the beam axis) and both are equivalent for large momentums, it is more frequently used the pseudrapidity distribution of the produced charged particles.
From the pseudorapidity distibution, using its dependence with the momentum, we obtain the transverse momentum distribution. See also rapidity, pseudorapidity and transverse momentum distribution.

Proton-proton cross section: It is defined depending of the channel. Schematically it can be written like: ${ {\sigma} = {\sum_{q}} {\int_0^1} {\int_0^1} f_g(y) f_q(x) {\sigma}(xP_1,yP_2) dxdy} $
Where $f_g(y),f_q(x)$ are PDF for the gluon and a quark (depending on "Bjorken x"), and $P_1,P_2$ the four-momenta of the colliding protons. The sum is over the quarks. It depends on the cross section of the quark-gluon scattering (for example, one term is q= u, therefore of ${\sigma_{ug}}$)

Pseudorapidity: From Special relativity ( that is, p = (E, p ) = (p0, p) is a 4-vector)
$ \eta = -ln [{tan(\frac{\theta}{2})}] = {\frac{1}{2}}ln( {\frac{{\vert}p{\vert}+p_z}{{\vert}p{\vert}-p_z} ) } $
  • $ \theta $ : angle with beam axis.
  • $ p_z $ : particle momentum in beam direction (logitudinal).
  • $ {\vert}p{\vert}^2 = {p_T^2+p_z^2} = p_T cosh{\eta} $ : particle momentum (3D).
When the particle is travelling close to the speed of light it is numerically close to the rapidity ( $ {\vert}p{\vert} {\approx} p_0 = E $ and $ \eta {\approx} y$ ) Some values:
$\theta$ 0 5 10 20 30 45 60 80 90
$\eta$ infinite 3.13 2.44 1.74 1.31 0.88 0.55 0.175 0

Rapidity: From Special relativity ( that is, p = (E, p ) = (p0, p) is a 4-vector)
$y = {\frac{1}{2}}ln( {\frac{E+p_{L}}{E-p_{L}} ) } = {\frac{1}{2}}ln( {\frac{p_0+p_z}{p_0-p_z} ) } $
  • $ p_L $ = $ p_z $ : particle momentum in beam direction (logitudinal).
  • E = $ p_0 $ , energy of the particle.
Used because:
  • Particle production is a constant as a function of rapidity( o pseudorapidity).
  • Difference in rapidity of two particles is independent of Lorentz boosts along the beam axis (${\Delta}y ={\Delta}y{\prime}$ )
  • Rapidity distribution is Gaussian.
Taking antilogarithms and from the definition of cosh, its relation with the enery of the particle is:
$p_0 = E = m_Tcosh{y}$ with $m_T^2 = m^2 + p_T^2$ the transverse mass of the particle.

Rapidity gap: Diffractive events are characterized by the absence of significant hadronic particle activity over a large region of rapidity or pseudorapidity. This empty region is called a rapidity gap and can be used as an experimental signature for diffraction.

Scattering length: Scattering amplitude at zero momentum. If scattering amplitude T(q) = a + bq + cq3 + ... , then scattering length T(0) = a. In a square well, it is equivalent to the radius of the square well, and the cross section $ \sigma = \pi a^2 $

Shadowing: the modification of the free nucleon parton density in the nucleus. At the low-momentum fractions, x, observed by collisions at the LHC, shadowing results in a decrease of the multiplicity.

Soft Physics: Physics associated with soft particles in the final state ($p_t < 2 GeV/c)$

Thermal Boltzmann Source: Using the relation rapidity-energy, from the Boltzmann distribution we reach:
$E{\frac{d^3N}{dp^3}} = {\frac {d^3N} {m_Tdm_Td{\phi}dy} } {\propto} Ee^{-E/T} = m_T cosh(y) e^ ({\frac {m_t cosh(y)} {T} })$
Or in the transversal direction:
${\frac{1}{m_T}}{\frac{dN}{dm_T}} {\propto} m_T I_0 ({\frac {p_t sinh({\rho})}) {T}} K_1({\frac {m_t cosh({\rho})} {T} }) $
Where ${\rho} = tanh^{-1} ({\beta_{boost}}) $

V0 vertex: Historically, shape of the verted created after a K0 decay onto a $ \pi^+ $ and $ \pi^-$ . Usually, weak decay of neutral particles, generating 2 charged tracks.

W boson: W is from weak nuclear force. W charge -1, W+ charge +1. Lifetime: 3 x 10−25 s. Rest mass : 80.4 GeV ( 100 proton mass). Spin 1 (as a boson)

Weak force: Changes the flavior of a quark. Present in beta decay. n-> p + e - + $ \nu_{e} $ Since n=udd, p=uud, we saw d -> u + W.

Weinberg angle: $ \theta_{w} =arcsen[g_{1}(g_1^2 + g_2^2)^{-1/2}]$ .Related with symmetry spontaneous violation. g = coupling constant

Z boson: AKA Z0. Like a W boson but with charge 0. Rest mass: 91.2 GeV.
Topic revision: r3 - 2008-04-08, JuanCastillo
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