P8P&PHYSICS&AT&LHC. Inelas,c&scaDering&at&LHC& Shahram&Rahatlou. Fisica&delle&Par,celle&Elementari,&Anno&Accademico&

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1 P8P&PHYSICS&AT&LHC Inelas,c&scaDering&at&LHC& Lecture&1& Shahram&Rahatlou Fisica&delle&Par,celle&Elementari,&Anno&Accademico&

2 KINEMATICS E =3.5TeV E =3.5TeV m = 1GeV m = 1GeV p s =7TeV $ >? * = * :? = :; >? =< :; 9 Much higher beam energy needed to achieve same s with fixed target Electron-positron collisions much better with linear colliders. Why? 2

3 PROTON&VS.&ANTI8PROTON < bl'& IBL+, F,*CGbL'& < < Low energy: valence quark are dominate pp 6= p p High energy: gluons and sea quarks become dominant pp ' p p 3

4 CROSS&SECTION&AT&HADRON&COLLIDERS QCD dominates the total cross section Not surprising since these are hadron colliders and strong interaction dominates over EW and QED Interesting processes are order of magnitudes smaller background rejection is the most critical ingredient of all analysis Background discrimination reducible background: processes mimic signal because of misreconstructed objects γ+jet γ+γ irreducible background: processes with same content in final states as signal QCD di-photon production 4

5 BOOST&OF&CENTER&OF&MASS p 1 = x 1 E beam p 2 = x 2 E beam < < θ < < < < g%++a*i-@$al'%b$ ;-K$$N 5::-<'*C>B$A """-OC??C>LB*[ No a-priori knowledge of the boost: xi different and unknown Cannot determine boost unless ALL particles in final states reconstructed Not feasible 5

6 KINEMATIC&VARIABLES `&G/F68&'% WW % cc,$@*c>b-('c%b$a= D jc@l*hb-,ib$ z D <+B'-,IB$ y D D x D D *',A($'A$-@+@$,*L@ B+,IC*LNC,B-@+@$,*L@ % D D '<CNC*J--- <A$LN+'<CNC*J- 1 * -G -G 86G " = 6

7 LORENTZ&INVARIANT&OBSERVABLES Differential cross sections are typically studied as a function of momentum, energy and polar angle for known boost change of reference frame trivial Problems arise with unknown boost Need variables not sensitive to boost pseudo-rapidity intervals Variables unchanged under longitudinal boost transverse momentum 7

8 RAPIDITY&FOR&HIGH&ENERGY&PARTICLES "$%%$&$' 1 -G " % 1 -G ',% " -G % %&G ',% -G ',% %&G -G ',% %&G ',% -G %&G ',% -G 86G P6&.&8$"WW P6&.&8$"WW " = m<<e,p L " = <VII *Q] < *Q] < <VII R< < < R< < < *< < V99 *< < "$%%$&$' V99 -G 86G 8

9 1 -G * -G -G " % -G 3&:'B+,I NO a a -G a " 1 % :? :? -G " % ; :?* -G> " % :?* -G 1 rapidity intervals are invariant under longitudinal boost y 1 y 2 y 1 y 2 = y 1 @y PSEUDO8RAPIDITY&INTERVALS&UNDER&BOOST 9 Boost along z axis:

10 CROSS&SECTION&CALCULATION σ AB = a,b=q,g [ˆσ LO ab + α S (Q 2 ˆσ NLO ab +... ] f a/a (x a, Q 2 f b/b (x b, Q 2 Sum over initial partonic states a,b Parton Density Function hard scattering cross-section 16/5/28 LNFSS8 - Sara Diglio 3 1

11 PARTON&DENSITY&FUNCTIONS 1 3 i = u v, d v, g and sea x = p parton / E beam (*+, -+-.,*/-12*3+, Q 2 = -+-.,*/-*,' $%&6' 7.*.-3,.78 9:%(.732*'*;.'2<.7.(.,7., *;+/A;%BCD$.E+</*3+,.F/*3+,'GHI7+.',+*22/*.<J(.732**;.>K7.(.,7.,2.5;32;;',+,(.*/"*3E. +3A3, LM the x-dependence is parameterised at a fixed scale Q 2 E<.,2.F/N'O 1P > =LK> $=> '.QA</+,O 1P > K =LK> $=> different parameterisations and no.of free parameters used 1 3 is evolved from Q 2 to any other Q 2 by numerically solving the DGLAP equations to various orders (LO,NLO, NNLO 3. the free parameters are determined by fit to data from experimental observables =7*1+- 4RSD.>(.3-.,*' 4L?TRHU?13>.7 *A.*%VU.>(.3-.,*'?:%&?%W 11

12 PARTON&DENSITY&FUNCTION.6.5 quarks: xq(x Q 2 = 1 GeV 2 CTEQ6D fit These & other methods whole set of quarks & antiquarks NB: also strange and charm quarks d V u V valence quarks (u V = u ū are hard x 1:xq V (x (1 x 3 quark counting rules x :xq V (x x.5 Regge theory.1 d S s S c S u S x sea quarks (u S =2ū,...fairly soft (low-momentum x 1:xq S (x (1 x 7 x :xq S (x x.2 12

13 GLUON&DENSITY&FUNCTION Gluons dominate by far at low x LHC dominated mainly by gluon-gluon fusion (hard scattering of 2 gluons at low x 6 5 xq(x, xg(x Q 2 = 1 GeV 2 CTEQ6D fit Different experimental signatures for qq, q-anti-q and qg hard scattering also very different cross sections gluon 1 d S, u S u V x 13

14 PDF&SUM&RULES PDF for partons and anti-partons related through CP symmetry Number of quarks and momentum of proton also provides constraints on different PDF functions 3 valence quarks in proton N u = 1 f p q (x =f q (x f p q (x =f q (x f p g (x =f g (x sum of all parton momenta must add up to proton momentum dx (f u (x fū(x = 2 N d = 1 dx (f d (x f d(x = 1 x i = 1 dx x q f q (x+ q f q (x+f g (x =1 14

15 PICTORIAL&REPRESENTATION&OF&P8P&COLLISION 15

16 HADRON&HADRON&COLLISIONS 16

17 QCD&PROCESS 17