Particle Physics (Phenomenology) Lecture 1/2 Peter Skands, Monash University THEORY PHENOMENOLOGY EXPERIMENT time g a ( − ig s t a ij γ µ ) Figure by T. Sjöstrand q j q i QCD “Jets” INTERPRETATION November 2019, Sydney Spring School on Particle Physics & Cosmology
<latexit sha1_base64="X7BHrRt8e7Fu1Pb2JkiMrpHFU=">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</latexit> 1) Units in Particle Physics ๏ The main particle-physics units of energy is eV (& MeV, GeV) • 1 electron-Volt = kinetic energy obtained by a unit-charge particle (eg an electron or proton) accelerated by potential difference of 1 Volt 1 eV = Q e · 1 V = 1 . 602176565(35) × 10 − 19 C · 1 J / C = 1 . 6 × 10 − 19 J • (So for accelerators, the beam energy in eV is a measure of the corresponding electrostatic potential difference) Planned linear accelerators (ILC, CLIC) could reach E CM ~ 1,000 GeV = 1 TeV ๏ The highest-energy (circular) accelerator LHC ~ 6500 GeV/beam. ๏ ๏ Using E=mc 2 we typically express all masses in units of eV/c 2 J= kg · m2 9 . 1 × 10 − 31 s 2 J s2 m e = 9 . 1 × 10 − 31 kg MeV /c 2 = m e 0 . 511 kg = m 2 MeV /c 2 m µ = 106 eV 5 . 7 × 10 − 12 eV s 2 An example J= 1 . 6 × 10 − 19 MeV /c 2 m τ = 1780 = m 2 (sometimes we forget to say c =3 × 10 8 m / s the 1/c 2 ; it is implied by the 511 × 10 3 eV /c 2 = quantity being mass) 2 � Particle Physics Peter Skands
FOR A RELATIVISTIC Natural Units QUANTUM THEORY ๏ In fact, we use MeV and GeV for everything ! Example: • Define a set of units in which ħ = ϲ = 1 lengths → energies • Action [Energy*Time] : dimensionless ( ħ = 1) E λ All actions are measured in units of ħ ๏ • Velocity [Length/Time] : dimensionless ( ϲ = 1) HEP < 1 fm > 1 GeV All velocities are measured in units of c (i.e., β = v/c) ๏ gamma 1 pm 1 MeV • • Energy : dimension 1 [E] = eV, MeV, GeV, … • Energy : • Mass : dimension 1 (E=mc 2 ) • Mass : X-rays 0.1 nm 10 keV /c 2 ๏ E.g., m e = 0.511 MeV • Time : dimension -1 ([ ħ ]=[E*t]=1) • Time : UV 100 nm 10 eV ๏ Convert: u se ħ = 6.58 x 10 -22 MeV s to convert 1s ๏ E.g., τ μ = 2.2 μ s = 2.2 x 10 -6 s / (6.58 x 10 -16 eV s) = 3.3 x 10 -9 / eV • Length : • Length : dimension -1 (velocity is dimensionless) • Momentum : • Momentum : dimension 1 (same as energy and mass; E 2 -p 2 =m 2 ) � 3 Particle Physics Peter Skands
<latexit sha1_base64="8XlvzAMyjhPDdM5b8qYwQu9Q02k=">ACFnicbVDLSsNAFJ34tr6iLt0MFsGCxqRWTRdCUQSXFawW2hom06kOnSTDzESMoV/hxl9x40IRt+LOv3HSFvF1YC6Hc+7lzj0+Z1Qq2/4wRkbHxicmp6ZzM7Nz8wvm4tKZjGKBSQ1HLBJ1H0nCaEhqipG6lwQFPiMnPvdw8w/vyZC0ig8VQknrQBdhrRDMVJa8sxNftEMYrgP14+28AZsXhOc8l7hS+DeTVaSrNwWPDNvW+Vyd1xoSburusUoWPZfXyRPBi6pnvzXaE4CECjMkZcOxuWqlSCiKGenlmrEkHOEuiQNTUMUENlK+2f14JpW2rATCf1CBfvq94kUBVImga87A6Su5G8vE/zGrHquK2UhjxWJMSDRZ2YQRXBLCPYpoJgxRJNEBZU/xXiKyQVjrJnA7hz8l/yVnRcrat4kpXzkYxjEFVsAqWAcO2AMVcAyqoAYwuAMP4Ak8G/fGo/FivA5aR4zhzDL4AePtE+w7nB8=</latexit> <latexit sha1_base64="CkYeHJmU4P/6DnCe+nBXawVonDE=">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</latexit> <latexit sha1_base64="8MNyaJx/lh8xno15rZGpZC6vxmQ=">ACP3icbZBPT9tAEMXlFIaCoT2MuqEVUvRHagYA6VUHvpEaQmIMUhGm/GyYpd2+yOI0Wv1kvfAVuvfbSQ6uKzc2IUL8G2mlp9+b0ey8OFfSku/8hZeL5cerX8urbyZnVtvb7xtmOzwghsi0xl5iQGi0qm2CZJCk9yg6Bjhcfx2bepfzxGY2W/qBJj0Nw1QmUgA51K938lOf/zCoyFoDVxzwaOoFo1RlHn1wJixcUdSgyI8o5UZWTPDZXBVhQjwWmrqmr9esNv7u/vhJ9D7kS4GwYtHjT9Wd2JBpvXYb9+GQ0yUWhMSiwthv4OfVKMCSFwqoWFRZzEGcwxK6TKWi0vXJ2f8U3HRnwJDPupcRn9P5ECdraiY5dpwYa2cfeFD7ndQtKwl4p07wgTMXtoqRQnDI+DZMPpEFBauIECPdX7kYgUuHXOTEJ6c/FR0Ws1gu9k62mkcfJ3Hsczesw/sEwvYHjtg39khazPBfrLf7C/7514f7z/3tVt64I3n3nHpR3fQMy8q4M</latexit> 2) Energy and Momentum in Particle Physics for massive particles, m ≠ 0 ๏ We define “4-momentum” as: Q: what does it mean p 0 = � mc that this is a “4-vector”? x µ → x 0 µ = Λ µ m ~ ν x ν v p = � m ~ ~ v = p 1 − � 2 ⇒ p µ → p 0 µ = Λ µ ν p ν = ๏ Zero-component = Relativistic Energy (/c), defined as : ๏ p µ = ( E/c, ~ p ) = ( E/c, p x , p y , p z ) ๏ p 2 = 0 : lightlike; p 2 > 0 : timelike; p 2 < 0 : spacelike Expand γ around small β : 4 � Particle Physics Peter Skands
<latexit sha1_base64="Evz9vRkV1lL2waWs489gLDn+p4=">AB/XicbVDLSgMxFL1TX7W+xsfOTbAIFaTMVE3QtGNywr2Ae1YMmDU1mhiQj1KH4K25cKOLW/3Dn35i2s9Dq4V4nHMvuTl+zJnSjvNl5RYWl5ZX8quFtfWNzS17e6ehokQSWicRj2TLx4pyFtK6ZprTViwpFj6nTX94NfGb91QqFoW3ehRT+B+yAJGsDZS196L7zoiQReoJI6RM6ujrl10ys4U6C9xM1KEDLWu/dnpRSQRNSEY6XarhNrL8VSM8LpuNBJFI0xGeI+bRsaYkGVl06vH6NDo/RQEnToUZT9edGioVSI+GbSYH1QM17E/E/r53o4NxLWRgnmoZk9lCQcKQjNIkC9ZikRPORIZhIZm5FZIAlJtoEVjAhuPNf/ksalbJ7Uq7cnBarl1kcediHAyiBC2dQhWuoQR0IPMATvMCr9Wg9W2/W+2w0Z2U7u/AL1sc3ynmSMg=</latexit> <latexit sha1_base64="2aTwVR743TBLyMkXBFWgfsqw30Q=">ACEXicbVDLSgMxFM3UV62vUZdugkXoxjIzCropFEVwWcE+oC8yaYNTWZCkhHKML/gxl9x40IRt+7c+Tdm2i609UDC4Zx7ufceXzCqtON8W7mV1bX1jfxmYWt7Z3fP3j9oqCiWmNRxCLZ8pEijIakrqlmpCUkQdxnpOmPrzO/+UCkolF4ryeCdDkahjSgGkj9e2S6HV4DEU/+yvwpufBU5h0ONIjP0hEmhqhAnP69tFp+xMAZeJOydFMEetb391BhGOQk1ZkiptusI3U2Q1BQzkhY6sSIC4TEakrahIeJEdZPpRSk8McoABpE0L9Rwqv7uSBXasJ9U5mtqha9TPzPa8c6uOwmNBSxJiGeDQpiBnUEs3jgEqCNZsYgrCkZleIR0girE2IBROCu3jyMml4Zfes7N2dF6tX8zjy4AgcgxJwQWogltQA3WAwSN4Bq/gzXqyXqx362NWmrPmPYfgD6zPH1TLm28=</latexit> <latexit sha1_base64="W6uT/ruMP+gtdLGNOUyXZlz2qac=">ACBnicbVDLSgMxFM3UV62vUZciBIvgqsxUQTdCsQhuhAr2Ae10yKRpG5rMhCQjlKErN/6KGxeKuPUb3Pk3ZtpZaOuBJIdz7iX3nkAwqrTjfFu5peWV1bX8emFjc2t7x97da6golpjUcQi2QqQIoyGpK6pZqQlJE8YKQZjKqp3wgUtEovNdjQTyOBiHtU4y0kXz7UHQ7PIbCT+9LeG1epIeSJ9XbSbfs20Wn5EwBF4mbkSLIUPtr04vwjEnocYMKdV2HaG9BElNMSOTQidWRCA8QgPSNjREnCgvma4xgcdG6cF+JM0JNZyqvzsSxJUa8BUpkOqeS8V/Pase5feAkNRaxJiGcf9WMGdQTGCPSoI1GxuCsKRmVoiHSCKsTXIFE4I7v/IiaZRL7mpfHdWrFxlceTBATgCJ8AF56ACbkAN1AEGj+AZvI368l6sd6tj1lpzsp69sEfWJ8/9MmYKA=</latexit> <latexit sha1_base64="kvOafV+TE7hEgO7yRzwqFRQw54Y=">AB/3icbVDLSsNAFJ3UV62vqODGzWARXJWkCroRim5cVrAPaGKYTCft0JlkmJkIJXbhr7hxoYhbf8Odf+OkzUJbD1w4nHMv94TCkaVdpxvq7S0vLK6Vl6vbGxube/Yu3tlaQSkxZOWCK7IVKE0Zi0NWMdIUkiIeMdMLRde53HohUNInv9FgQn6NBTCOKkTZSYB+Ie4+n8BJ6KuUBhSKguRDYVafmTAEXiVuQKijQDOwvr5/glJNY4aU6rmO0H6GpKaYkUnFSxURCI/QgPQMjREnys+m90/gsVH6MEqkqVjDqfp7IkNcqTEPTSdHeqjmvVz8z+ulOrwMxqLVJMYzxZFKYM6gXkYsE8lwZqNDUFYUnMrxEMkEdYmsoJwZ1/eZG06zX3tFa/Pas2ro4yuAQHIET4IJz0A3oAlaAINH8AxewZv1ZL1Y79bHrLVkFTP74A+szx8VqZWB</latexit> <latexit sha1_base64="m+ez+K4NIMxg7xApdXwrYKLXcA=">AB+3icbVDLSgMxFM3UV62vsS7dBIvgqsxUQTdC0Y3LCvYB7XTIpJk2NMmEJCOW0l9x40IRt/6IO/GTDsLbT1wL4dz7iU3J5KMauN5305hbX1jc6u4XdrZ3ds/cA/LZ2kCpMmTliOhHShFBmoYaRjpSEcQjRtrR+Dbz249EaZqIBzORJOBoKGhMTJWCt2y7Pd4CmWY9WvI+zUYuhWv6s0BV4mfkwrI0Qjdr94gwSknwmCGtO76njTBFClDMSOzUi/VRCI8RkPStVQgTnQwnd8+g6dWGcA4UbaEgXP198YUca0nPLKTHJmRXvYy8T+vm5r4KphSIVNDBF48FKcMmgRmQcABVQbNrEYUXtrRCPkELY2LhKNgR/+curpFWr+ufV2v1FpX6Tx1Ex+AEnAEfXI6uAMN0AQYPIFn8ArenJnz4rw7H4vRgpPvHIE/cD5/ACmLkzY=</latexit> Reminder: Relativistic Centre-of-Mass The frame in which the total 3-momentum, p = 0 defines the rest frame of a particle, or the CM frame for a system of particles In that frame , the total energy is equal to the invariant mass = E CM For a single particle, at rest p µ = ( m, 0 , 0 , 0) p µ p µ = m 2 µ = E 2 − p 2 = m 2 Lorentz invariant Squared rest mass In any frame For a system of particles: X p µ p µ = p µ p µ = E 2 i CM Lorentz invariant squared invariant mass of the system i How to find the CM frame of (a system of) particles? 1. Sum up their 3-momenta ➜ total p . If it is zero: done 2. If non-zero, find their overall velocity β = p / E 3. Construct and do the relevant (inverse) Lorentz boost. (& Check 1). 5 � Particle Physics Peter Skands
Feynman diagrams and 4-momentum conservation ๏ Consider the QED vertex: time γ → e − + e − e − + e + → γ 1) 2) 3) e → e + γ ๏ What about 4-momentum conservation? 1) Electron at rest decaying to a recoiling electron + a photon? ๏ 2) Two massive particles reacting to produce a massless photon? ๏ 3) Massless photon decaying to two massive electrons? ๏ • This all sounds very strange (even for relativity) � 6 Particle Physics Peter Skands
Feynman diagrams and 4-momentum conservation ๏ Consider the QED vertex: time γ → e − + e − e − + e + → γ 1) 2) 3) e → e + γ ๏ What about 4-momentum conservation? E 2 � p 2 6 = m 2 • At least one of the involved particles must have • Equivalent to Heisenberg Δ E but here expressed in L.I. form • We call such particles virtual ; and say they are off mass shell � 7 Particle Physics Peter Skands
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