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| The '''transverse mass''' is a useful quantity to define for use in [[particle physics]] as it is invariant under [[Lorentz boost]] along the z direction. In [[natural units]] it is: | | The individual who wrote the post is known as Jayson Hirano and he totally digs that title. My working day occupation is a travel agent. To play lacross is the factor I love most of all. Mississippi is where her house is but her husband desires them to move.<br><br>Also visit my blog post - psychic chat online ([http://bigpolis.com/blogs/post/6503 visit the following post]) |
| ::<math>m_{T}^2 = m^2 + p_{x}^2 + p_{y}^2 \,</math>
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| :where the z-direction is along the beam pipe and so
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| :<math>p_x</math> and <math>p_y</math> are the momentum perpendicular to the beam pipe and
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| :<math>m</math> is the mass.
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| Hadron collider physicists use another definition of transverse mass, in the case of a decay into two particles:
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| ::<math>M_{T}^2 = (E_{T, 1} + E_{T, 2})^2 - (\overrightarrow{p}_{T, 1} + \overrightarrow{p}_{T, 2})^2</math>
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| :where <math>E_{T}</math> is the transverse energy of each daughter, a positive quantity defined using its true [[invariant mass]] <math>m</math> as:
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| ::<math>E_{T}^2 = m^2 + (\overrightarrow{p}_{T})^2</math>
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| So equivalently,
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| ::<math>M_{T}^2 = m_1^2 + m_2^2 + 2 \left(E_{T, 1} E_{T, 2} - \overrightarrow{p}_{T, 1} \cdot \overrightarrow{p}_{T, 2} \right) </math>
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| For massless daughters, where <math>m_1 = m_2 = 0</math>, the transverse energy simplifies to <math>E_{T} = | \overrightarrow{p}_T |</math>, and the transverse mass becomes
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| ::<math>M_{T}^2 \rightarrow 2 E_{T, 1} E_{T, 2} \left( 1 - \cos \phi \right)</math>
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| :where <math>\phi</math> is the angle between the daughters in the transverse plane:
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| A distribution of <math>M_T</math> has an end-point at the true mother mass: <math>M_T \leq M</math>. This has been used to determine the <math>W</math> mass at the Tevatron.
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| ==References==
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| *{{cite journal | author=J.D. Jackson | authorlink= | title=Kinematics | journal=Particle Data Group | year=2008 | volume= | pages= | url=http://pdg.lbl.gov/2008/reviews/kinemarpp.pdf }} - See sections 38.5.2 (<math>m_{T}</math>) and 38.6.1 (<math>M_{T}</math>) for definitions of transverse mass.
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| *{{cite journal | author=J. Beringer et al. | authorlink= | title=Review of Particle Physics | journal=Particle Data Group | year=2012 | volume= | pages= | url=http://prd.aps.org/abstract/PRD/v86/i1/e010001}} - See sections 43.5.2 (<math>m_{T}</math>) and 43.6.1 (<math>M_{T}</math>) for definitions of transverse mass.
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| [[Category:Particle physics]]
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| [[Category:Kinematics]]
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| [[Category:Special relativity]]
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