Proces Drella i Yana i potraga za te²kim esticama na hadronskim sudariva ima
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1 Proces Drella i Yana i potraga za te²kim esticama na hadronskim sudariva ima Mentor: izv. prof. dr. sc. Kre²imir Kumeri ki Prirodoslovno-matemati ki fakultet, Fizi ki odsjek Sveu ili²te u Zagrebu velja a 2016.
2 Hadronski sudariva i LHC je smje²ten u tunelu dugom 26.7 km, na dubini od 175 m proton-proton sudari na energiji centra mase s = 13 TeV-a (2015.) primarni ciljevi: potraga za esticama izvan SM, SUSY, tamna materija, samointerakcija Higgsovog bozona
3 dinamika unutar protona rezultira distribucijom impulsa kvarkova distribucije se izraºavaju preko Partonskih distribucijskih funkcija ( PDF) PDF-ove ne moºemo odrediti teorijski ve eksperimentalno stati ki model proton sagra en od dva up-kvarka i jednog down-kvarka u stvarnosti je proton dinami ni sustav kvarkovi izmjenjuju gluone
4 Drell-Yan proces proces su predloºili Sidney Drell i Tung-Mow Yan godine kako bi opisali produkciju leptona u visokoenergetskim sudarima sudarom dva hadrona anihiliraju se kvark i antikvark stvori se virtualni foton ili Z bozon raspada se na par suprotno nabijenih leptona dobivanje korisnih podataka o PDF-ovima omogu uje potragu za te²kim leptonima
5 Udarni presjek za p p γ µ + µ Faktorizacijski teorem σ(pp µ + µ X ) = j ˆσ(q j q j µ + µ )(tok q j i q j iz hadrona)
6 udarni presjek za proces q j q j µ + µ ˆσ = 4α2 π Qq 2 3ŝ tok partona iz hadrona za danu boju i okus 1[ q A 9 j (x 1 )q B j (x 2 ) + q A j (x 1 )qj B (x 2 ) ] dx 1 dx 2 q A j (x 1)dx 1 - broj kvarkova okusa j u hadronu A s udjelom impulsa x 1 q B j (x 2 )dx 2 - broj antikvarkova okusa j u hadronu B s udjelom impulsa x 2
7 diferencijalni udarni presjek za p p γ µ + µ d 2 σ = πα2 1 dx 1 dx 2 3E 2 9 j,boja Q 2 j [ q A j (x 1 )q B j (x 2 ) + q A j (x 1 )q B j (x 2 ) ] uvodimo luminozitet L AB [ (τ) dx jj 1 dx 2 x 1 x 2 q A j (x 1 )q B j (x 2 ) + q A j (x 1 )qj B (x 2 ) ] δ(x 1 x 2 τ) diferencijalni udarni presjek po kvadratu invarijantne mase dσ dm = πα τ [ dx 2 3E 2 m 2 1 Qj 2 q A 3 j τ x j (x 1 )q B j (τ/x 1 ) + q A j (x 1 )qj B (τ/x 1 ) ] 1 Diferencijalni udarni presjek dσ(pp µ + µ ) dm = 8πα2 9m 3 1 τ dx [ 1 4 τ x 1 9 (u(x 1)u(τ/x 1 ) + u(x 1 )u(τ/x 1 ))+ + 1 ] 9 (d(x 1)d(τ/x 1 ) + d(x 1 )d(τ/x 1 ))
8 Diferencijalni udarni presjek
9 Udarni presjek za proces pp Z µ + µ σ(pp µ + µ X ) = j ˆσ(q j q j µ + µ )(tok q j i q j iz hadrona)
10 udarni presjek za proces qq Z µ + µ ˆσ = 1 1 gw 4 ŝ [ 1 [ ] (c q 3 12π cos 4 θ W 4(ŝ MZ 2 )2 4 V )2 + (c q A )2][ (c µ V )2 + (c µ A )2] + 6c q A cq V cµ A cµ V tok partona iz hadrona doprinosi lanom 1[ q A 9 j (x 1 )q B j (x 2 ) + q A j (x 1 )qj B (x 2 ) ] dx 1 dx 2 Diferencijalni udarni presjek dσ dm (pp 2 µ+ µ ) = π +6c q A cq V cµ A cµ V gw 4 1 [ 1 cos 4 θ W 4(m 2 MZ 2 )2 4 [ (c q V )2 + (c q A )2][ (c µ V )2 + (c µ A )2] + ] 1 τ dx 1 [4 ] [ 1 τ x 1 9 (u(x [ 1)u(τ/x 1 ) + u(x 1 )u(τ/x 1 )) + (c q 4 V )2 + (c q A )2] ] [(c µ V )2 + (c µ A )2] + 6c q 1 A cq V cµ A cµ V τ dx 1 [1 ] x 1 9 (d(x 1)d(τ/x 1 ) + d(x 1 )d(τ/x 1 )) τ
11 Diferencijalni udarni presjek
12 Ukupni udarni presjek na malim masama dominira EM proces na velikim masama dominira slabi proces
13 Udarni presjek za proces pp γ, Z l + l udarni presjek za anihilaciju partona ˆσ = β(3 β2 ) ( ) ŝ VL 2 48π + V R 2 lijevi i desni parametri vezanja V (γ+z) L,R = Q lq q e 2 + czl c q L,R g 2 ŝ cw 2 (ŝ M Z 2 ) ukupni udarni presjek za proces u kojemu nastaje par suprotno nabijenih leptona σ(pp l + l ) = 1 3 q 1 1 dτ 4ml 2/s τ ( ) dτ ˆσ(qq l + l ) q 1 (x 1 )q 2 (τ/x 2 ) + q 1 (x 1 )q 2 (x 2 ) uzimamo c W = cosθ W, c Zl = c 2 W, Q l = 1
14 BITNE KARAKTERISTIKE SUDARIVAƒA: 1 luminozitet 2 energija centra mase Luminozitet omjer broja dogažaja N u odreženom vremenu t i udarnog presjeka σ L = 1 dn σ dt integriranjem luminoziteta po vremenu, dobivamo integrirani luminozitet L int = Ldt L int = N σ Energija centra mase s = (p 1 + p 2 ) 2 = (E 1 + E 2 ) 2 ( p 1 + p 2 ) 2 s = (2E) 2 s = 2E energija na raspolaganju za stvaranje novih estica
15 Mogu nosti LHC-a
16 Mogu nosti sudariva a energije 100 TeV-a
17 Za²to nam treba sudariva energije s = 100 TeV-a?
18 Zaklju ak analizirali smo Drell-Yan proces te izra unali udarni presjek za proces pp γ, Z l + l promotrili smo kako broj estica ovisi o luminozitetu i energiji centra mase sudariva a za male vrijednosti mase ve u ulogu ima luminozitet, dok je na velikim vrijednostima mase potrebna ve e energija kako bismo proizveli dovoljan broj estica Zahvaljujem se mentoru izv. prof. dr. sc. Kre²imiru Kumeri kom na prenesenom znanju i uloºenom vremenu u ovaj rad!
19 Literatura M. Thomson, Modern Particle Physics, Cambridge University Press (2013) E. Leader and E. Predazzi. An introduction to gauge theories and modern particle physics, Volume 1, Cambridge University Press (1996) A. D. Martin, W. J. Stirling, R. S. Thorne and G. Watt. Parton distributions for the LHC, Eur. Phys. J. C 63 (2009) K. Kumeri ki, I. Picek and B. Radov i. TeV-scale seesaw with quintuplet fermions, Phys. Rev. D 86 (2012) N. Arkani-Hamed, T. Han, M. Mangano, L. T. Wang. Physics Opportunities of a 100 TeV Proton-Proton Collider,arXiv: [hep-ph]
20 HVALA NA PAšNJI!
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