Stores insertion and momenta data and provides a simple interface to manipulate it.
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#include <kinematics.h>
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| static void | replace (csl::Expr &expr, Kinematics const &k1, Kinematics const &k2) |
| | Replaces in an expression the relevant (squared-)momenta corresponding to the replacement of one Kinematics object to another. This function must receive two kinematics of the same size, and replaces in expr the (squared-)momenta of k1 by those of k2. More...
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static Kinematics | merge (Kinematics const &k1, Kinematics const &k2) |
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| static std::vector< size_t > | defaultIndices (size_t N) |
| | Returns the default range of indices form 1 to N. More...
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Stores insertion and momenta data and provides a simple interface to manipulate it.
◆ Kinematics() [1/3]
| mty::Kinematics::Kinematics |
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std::vector< mty::Insertion > const & |
t_insertions | ) |
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explicit |
Initializes the object only from insertions, creates the required momenta.
- Parameters
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| t_insertions | Insertions of the process. |
◆ Kinematics() [2/3]
| mty::Kinematics::Kinematics |
( |
std::vector< mty::Insertion > const & |
t_insertions, |
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std::vector< csl::Tensor > const & |
t_momenta |
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) |
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Initializes the object from insertions and momenta.
Squared momenta are determined from the momenta given as parameters through the relation \( s_{ij} = g_{\mu\nu}p_i^\mu p_j^\nu \).
- Parameters
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| t_insertions | Insertions of the process. |
| t_momenta | External momenta of the process. Should be of the same size as t_insertions. |
◆ Kinematics() [3/3]
| mty::Kinematics::Kinematics |
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std::vector< mty::Insertion > const & |
t_insertions, |
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std::vector< size_t > const & |
indices |
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) |
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Initializes the object from insertions and indices for momenta.
Indices given as parameter determine the name of the different momenta, replacing the default \( p_1, p_2 ..., p_N \) that corresponds to indices \( {1, 2, ..., N} \). The range of indices can be arbitrary provided that its size corresponds to the number of different insertions and that all indices are different. Then squared momenta are determined from the momenta created from the indices through the relation \( s_{ij} = g_{\mu\nu}p_i^\mu p_j^\nu \).
- Parameters
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| t_insertions | Insertions of the process. |
| indices | Indices to initialize momenta names. |
◆ addContraction()
Adds a CSL contraction for momenta.
This function delegates to CSL the responsibility to add the contraction property for \( p_1\cdot p_2 \) calling cgl::TensorParent::addSelfContraction() so that this contraction is simplified when encountered in calculations and replaced by the result.
- Parameters
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| p1 | Left momentum in the contraction. |
| p2 | Right momentum in the contraction. |
| res | Result of the contraction (see squaredMomenta). |
◆ applyIndices()
| Kinematics mty::Kinematics::applyIndices |
( |
std::vector< size_t > const & |
indices | ) |
const |
Creates a new kinemtics object with newly created momenta for the same insertions.
- Parameters
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| indices | Set of indices constructing the momenta for the new Kinematics object. |
- Returns
- The copy of the current Kinematics object with new momenta corresponding to indices.
◆ applyPermutation()
| void mty::Kinematics::applyPermutation |
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std::vector< size_t > const & |
pos | ) |
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Permutes elements inside the Kinematics object, keeping insertions and (squared-)momenta aligned with each other.
- Parameters
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| pos | Permutation. Must be of the same size as the Kinematics object and contain all indices in \( {1, 2, ..., N} \). |
◆ defaultIndices()
| static std::vector<size_t> mty::Kinematics::defaultIndices |
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size_t |
N | ) |
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inlinestatic |
Returns the default range of indices form 1 to N.
- Parameters
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| N | Size of the container to return. |
- Returns
- A std::vector<size_t> equal to \( {1, 2, ..., N} \).
◆ getDegreesOfFreedomFactor()
| csl::Expr mty::Kinematics::getDegreesOfFreedomFactor |
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const |
Returns the combinatorial factor corresponding to the process.
This function takes into account two different factors required in the squared amplitude calculation, namely the number of incoming degrees if freedom to average over them, and the combinatorial factor taking into account indistinguishable outgoing particles. For \( N \) incoming particles indexed by \( i \) and \( M \) groups of indistinguishable outgoing particles of respective sizes \( m_j \), this function returns a symbolic factor equal to
\[ F = \prod _i\dfrac{1}{d_i}\cdot \prod _j \dfrac{1}{m_j!}, \]
with \( d_i \) the number of degrees of freedom of the incoming particle $i$ taking into account spin and gauge representations dimensions.
- Note
- For spin 1 particles, the spin dimension is 2 if the particle is massless, 3 otherwise.
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Indistinguishable particles are particles of the exact same species, with the same complex conjugation property (e.g. \( W^+ \) and \( W^- \) are distinguishable, \( Z \) and \( Z \) are not).
- Returns
- The factor \( F \) calculated as the combinatorial factor for the corresponding squared amplitude.
◆ getIndices()
| std::vector<size_t> const& mty::Kinematics::getIndices |
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const |
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inline |
◆ getInsertions()
| std::vector<mty::Insertion> const& mty::Kinematics::getInsertions |
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const |
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inline |
- Returns
- A const reference to the range of insertions.
◆ getMomenta()
| std::vector<csl::Tensor> const& mty::Kinematics::getMomenta |
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const |
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inline |
- Returns
- A const reference to the range of momenta.
◆ getOrderedMomenta()
| std::vector< csl::Tensor > mty::Kinematics::getOrderedMomenta |
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const |
- Returns
- Returns the momenta in order (p_1, p_2, p_3, ...)
◆ getSquaredMomenta()
| std::vector<csl::Expr> const& mty::Kinematics::getSquaredMomenta |
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| ) |
const |
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inline |
- Returns
- A const reference to the range of squared momenta.
◆ initMomentaSquared()
| void mty::Kinematics::initMomentaSquared |
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std::vector< size_t > const & |
indices | ) |
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private |
Calculates and fills momenta squared from momenta contractions following the expression given in the documentation of squaredMomenta.
- Parameters
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| indices | Range of indices names for momenta to initialize corresponding names for \( s_{ij} \) objects. |
◆ insertion()
Returns the insertion in position i.
- Parameters
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| i | Position of the insertion to get (starts at 0). |
- Returns
- The insertion in position i.
◆ momentum()
| csl::Tensor const& mty::Kinematics::momentum |
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size_t |
i | ) |
const |
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inline |
Returns the momentum in position i.
- Parameters
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| i | Position of the momentum to get (starts at 0). |
- Returns
- The momentum in position i.
◆ replace()
Replaces in an expression the relevant (squared-)momenta corresponding to the replacement of one Kinematics object to another. This function must receive two kinematics of the same size, and replaces in expr the (squared-)momenta of k1 by those of k2.
- Parameters
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| expr | Expression in which the replacement takes place. |
| k1 | Left kinematics, its momenta are replaced. |
| k2 | Right kinematics, its momenta take place in expr. |
◆ setSquaredMomentum()
| void mty::Kinematics::setSquaredMomentum |
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size_t |
i, |
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size_t |
j, |
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csl::Expr const & |
res |
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) |
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private |
Sets a squared momentum from its indices and the corresponding expression.
- Parameters
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| i | Index of the left momentum. |
| j | Index of the right momentum. |
| res | Expression result of the contraction. |
◆ size()
| size_t mty::Kinematics::size |
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| ) |
const |
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inline |
- Returns
- the size of the kinematics objects i.e. the number of insertions / momenta.
◆ squaredMomentumIndex()
| size_t mty::Kinematics::squaredMomentumIndex |
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size_t |
i, |
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size_t |
j |
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) |
| const |
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inlineprivate |
Returns the index corresponding to a given momenta product.
- Parameters
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| i | Index of the left momentum. |
| j | Index of the right momentum. |
- Returns
- The index corresponding to \( s_{ij} \) in the linear range containing squared momenta.
◆ subset()
| Kinematics mty::Kinematics::subset |
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std::vector< size_t > |
pos | ) |
const |
Returns a subset of the Kinematics object taking only some indices.
- Parameters
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| pos | Range of insertions indices of the subset to return. |
- Returns
- The Kinematics object with a subset of insertions and (squared-)momenta containing only objects at given positions given by pos.
◆ operator<<
| std::ostream& operator<< |
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std::ostream & |
out, |
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Kinematics const & |
kin |
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) |
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friend |
Overload of output stream operator for Kinematics object.
- Parameters
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| out | Output stream. |
| kin | Kinematics object to display. |
- Returns
- The modified stream.
◆ indices
| std::vector<size_t> mty::Kinematics::indices |
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private |
Indices of momenta.
Momenta are defined as \( p_i \) with indices \( i \). This member allows the Kinematics to keep this information, considering for example that a set of momenta \( (p_2, p_3, p_1) \) will have indices \( (2, 3, 1) \).
◆ momenta
Set of external momenta of the process.
There are exactly \(N\) momenta for \(N\) insertions.
◆ squaredMomenta
| std::vector<csl::Expr> mty::Kinematics::squaredMomenta |
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private |
Set of squared external momenta for the process.
For \(N\) insertions, there are \(N\) external momenta and \( N(N+1)/2 \) squared momenta defined by
\[ s_{ij} \equiv g_{\mu\nu}p_i^\mu p_j^\nu, \text{ with } i \leq j. \]
For on-shell particles, one has
\[ s_{ii} = m_i^2. \]
This container is linear whereas the data it represents is 2-dimensional, see squaredMomentumIndex() that provides the relation between the 2D index and the physical index for this container. For now this container is redundant and contains both \( s_{ij} \) and \( s_{ji} \) that are equal. This is however not an important overhead and is less error prone that storing a triangle matrix in a linear container.
The documentation for this class was generated from the following files:
1.8.13