More on SM precision measurements. Marina Cobal University of Udine

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1 More on SM precision measurements Marina Cobal University of Udine

2 Processes described by the SM Charged current low energy the theory coincides with Fermi s theory verified in experiments Neutral current processes; the EW unification appears directly verified in experiments 3 bosons interactions (γ, W, Z, H) verified in experiments, except the ones with H Generation of the boson masses through the Higgs NOT verified in experiments LHC Generation of the fermion masses through the Higgs NOT verified in experiments presumably a different mechanism for the neutrino masses If the theory is correct, ALL the interaction constants can be expressed as a funtion of a single free parameter: sin θ W. To verify the theory one needs to measure physics observables and compare the measured value with the theory. The calculation is based on a perturbative method, in which one stops at a given order. The lowest order is called tree level. The higher order are said radiative corrections.

3 Neutral currents Weinberg s angle measurements The unification of the electromagnetic and weak interactions appears expecially in the neutral current processes, NC. In these processes, we can measure the weak charges which in the unified theory are expressed by means of a single parameter sin θ W. Its value must be the same in all cases, at tree level. To compare precision measurements one needs to take into account higher order diagrams as well ( radiative corrections ). This has been verified in a wide range of energies and for different couplings. Non- conservation of atomic parity(scale = ev) Diffusion of polarized electrons on deuterium(gev) Asymmetries in e + e µ + µ (from 10 GeV to 00 GeV) Deep inelastic scattering in ν µ on nuclea (scale= many GeV) ν µ scattering on elettron (scale = MeV) We will discuss this case only

4 Scattering ν µ CHARM Neutrinos (anti-neutrinos) scattering on electrons are purely leptonic processes. The cross section calculation doesn t have therefore theoretical uncertainties (which instead are present in the scattering with nuclea). However, the cross sections are very small and their measurement is difficult. Let s determine the Weinberg angle measuring the cross sections ratio! µ e " #! µ e " e! µ e " #! µ e " The kinematics is such that the scattering happens only at small angles. The transferred momenta are << m Z even if the neutrinos have energies of the order of tenths of GeV.! " s " G F m e E # "(# µ e $ # µ e) "(# µ N $ X) %

5 Cross sections ratio (1/)! (" µ e # $ " µ e # ) Can be distinguished by measuring the helicity summed in squared. ( ) = ( )! " µ e # $ " µ e # =! " µ e + $ " µ e + L+L L+L L+R L+R 5 J=0, J z =0 J=1, J z = 1, one out of three

6 Cross sections ratio (/) L+L L+L L+R L+R 1/3! = G Fm e E " "µ e #,&. $ 1 + sin % ' ( W - ) * sin4 % W / 1 0 L+L L+L 1/3 L+R L+R! = G Fm e E " "µ e #, 1 &. 3 $ 1 + sin % ' ( W - ) * + + sin 4 % W / 1 0 R =! " µ e / E "! "µ e / E " 1# 4sin $ W + 16 = 3 3 sin4 $ W 1# 4sin $ W +16sin 4 $ W

7 Measurement of the fluxes ratio R =! " µ e / E "! "µ e / E " 1# 4sin $ W + 16 = 3 3 sin4 $ W 1# 4sin $ W +16sin 4 $ W Neutrinos and antineutrino fluxes are not monocromatic. They have slightly different energy spectra. The measured ratio is: N (! µ e) # "! ( E! )E! de! R exp = "! ( E! )E! de! N! µ e # ( ) One needs to measure separately the fluxes ratio $ F! " # µ ( E # )E # de # " #µ ( E # )E # de # $ Rates of different processes with well known cross section have been measured. Four indepedent methods developed for crosss-checks. Measured F with the precision ±% Experiment goal sin θ W = ± 0.005

8 Scattering ν µ CHARM "(# µ e $ # µ e) "(# µ N $ X) % 10 4! = G Fm e E " "µ e #,&. $ 1 + sin % ' ( W - ) * sin4 % W / 1 0! = G Fm e E " "µ e #, 1 &. 3 $ 1 + sin % ' ( W - ) * + + sin 4 % W / 1 0 Experimental strategy: To measure the neutrinos and antineutrinos cross sections and take their ratio. R =! " µ e / E "! "µ e / E " 1# 4sin $ W + 16 = 3 3 sin4 $ W 8 1# 4sin $ W +16sin 4 $ W

9 Elastic scattering ν-e The signal is very rare, and its signature is the presence of an electron. How to distinguish from the background? One can make use of the kinematics. High energies E i + m e = E e + E! 0 = E! sin"! + E e sin" e E i = E! cos"! + E e cos" e E i = E! + E e " E! 1" cos#! E i = E i + m e! E " 1! cos# " ( ) " E e ( 1" cos# e ) ( )! E e ( 1! cos# e ) E e ( ) $ m e ( 1! cos" e ) = m e! E # 1! cos" # 1! cos" e # m e E e m e /E e is very small, so the cosine is very close to 1 1! cos" e! " e E e! e " m e The fundamental kinematical variable to distinguish between signal and background is the product of the electron energy times the squared diffusion angle. One needs to measure both very well.

10 CHARM 10 C.8 A. Bettini 14/1/10

11 CHARM elettrone µ E! E! = 3.8 GeV = 19.3 GeV Data taking p on targett 10 8 ν interactions 1. Huge mass: 69 tons. Good angular resolution low Z absorber (glass) σ(θ)/θ Z/ E 3. Granularity for the vertex definition (to distinguish e from π ) Iarocci s pipes with cells of 1cm 11

12 CHARM: a µ and an e

13 CHARM Final result (1994) sin!e! W = 0.34 ±0.0058(stat.) ± syst ( ) The main background is due to the so-called neutral interactions, which do not have a µ in the final state, since they can give a π. The γ s from the π decay produce a shower like the electron. To distinguish one can use the energy deposit in the scintillator. This, since π γ 4e and the scintillator is crossed by 4 minimum ionizing particles, and not just one. To the price of reducing the statistics, the signal/background ratio is improved and one can verify if the background is understood.

14 M W and M Z. W s leptonic widths Masses (approximately):! M W = g $ " # 8G F % & 1/ = '( G F 1 sin) W = 37.3 sin) W GeV M W M Z = cos! W From the measured value of θ W M W! 80 GeV M Z! 91 GeV W leptonic width (should be equal for the universality) Using the theory:! e" =! µ" =! #" = $ % & g ' ( ) M W 4* = 1 G F M W 3 3 *! 5 MeV NB. In general, the widths are proportional to the third power of the mass.

15 W hadronic width m t > m W! " td = " ts = " tb = 0 To calculate the widths in qq one needs to consider: A factor of 3 since there are 3 colours A mixing matrix V ub << 1! " ub # 0 V cb << 1! " cb # 0 Two types of decays In the same family in different families (small width) All the non-diagonal elements are small, therefore W doesn t decay often in quarks of different families! us "!( W # us) = 3$ V us! e% = 3$ 0.4 $! e% & 35 MeV 3 colours! cd "!( W # cd) = 3$ V cd! e% = 3$ 0. $! e% & 33 MeV! ud "!( W # ud) = 3$ V ud! e% = 3$ $! e% =.84 $! e% & 640 MeV! cs "!( W # cs) = 3$ V cs! e% = 3$ 0.99 $! e% & 660 MeV! W ".04 GeV

16 ! l" #!( W $ l" l ) =! "l " l #!( Z $ " l " l ) =! "l " l = G M 3 F Z $ 3 # % & 1' ( ) Z. Leptonic width g Z! % & ' g I W 3 # Qsin " W cos" W g ( ) * & g ) ' ( cos% W * +! 660 * 1 4 ( ) = M W 4+ M Z & 1) 4, ' ( * + MeV=165 MeV g cos" W c Z = G M F W M Z & 1) cos % W 3, ' ( * +! inv = 3! "l " l #!( Z $ " l " l ) % 495 MeV c Z ν ll 1/ l L l R u L 1/+s s 1/ (/3) s d L 1/+(1/3) s u R d R (/3) s (1/3) s s = sin! W = 0.3! ee =! µµ =! "" = G M 3 F Z 3 # + % 1 $ & ' + ( - s ) *,. + s 4 0! ! 83 MeV /

17 Z. Hadronic widths and total g Z!! uu =! cc = 3 G M 3 F Z 3 " g I W 3 # Qsin " W cos" W * $ 1 # ', % & 3 s ( ) + ( ) = $ + # ' % & 3 s ( ) g cos" W c Z s = sin! W = /! ! 80 MeV. c Z ν ll 1/ l L 1/+s l R u L s 1/ (/3) s d L 1/+(1/3) s u R d R (/3) s (1/3) s! dd =! ss =! bb = 3 G M 3 F Z 3 " * $ 1 # + 1 ', % & 3 s ( ) + $ + 1 ' % & 3 s ( ) - /! ! 370 MeV.! adronica =! uu + 3! dd! 1.67 GeV! Z =! inv + 3! ee +! adronica!.4 GeV

18 Resonant production of W/Z Both W and Z can be produced in a quark-antiquark collider Quarks are not free proton-antiproton collider UA1 (CERN). Discovery in 1983 Z can be produced in eletron-positron colliders as well. precision measurements at LEP (CERN) and SLC (SLAC) Quark-antiquark collisions Energy in the cms ŝ = x q x q s Main process to study u + d! e " + # e They must have same colour They must have correct chirality u + d! e + + " e

19 Resonant production of W/Z u + d! e " + # e Near resonance Breit - Wigner (as for e + e )! ( ud " e # $ e ) = 1 3% & ud & e$ 9 ŝ ŝ # M W! max ( ud " e # $ e ) =! max ( u + d " e + + $ e ) = 4% 3 1 M W & ud & e$ & W = 4% 3 ( ) + & W / ( ) Probability that the colours are the same ' () GeV - * + ' 388 () µb/gev - * +, 8.8 nb Small <<< σ tot 100 mb. The weak interactions are weak! For Z u + u! e " + e + ; d + d! e " + e +! max ( uu " e # e + ) = 4$ 3! max ( dd " e # e + ) == 4$ 3 1 M Z 1 M Z % uu % ee % Z = 4$ 3 % dd % ee % Z & 1 nb An order of magnitude smaller than W & & 388 µb ' 0.8 nb 91.4

20 Cross sections Beam of p = beam with large band of partons (q, g, and some q) Beam of p = beam with a large band of partons ( q, g, and some q) Let s consider the annihilation between a quark and a valence antiquark. If s=630 GeV, the fraction of momentum needed to stay in resonance; < x >! M W s! M Z s! 0.15 OK. There are many 0

21 W and Z production from pp Bandwidth of the parton energies >> W and Z resonance widths The lab reference frame is the pp reference frame, not the qq; This pair, as the originated W or Z, have a longitudinal motion which is different from case to case. ŝ = x d x u s ŝ = x u x u s + similar from du Plus similar from dd Cross section calculation (uncertainties from QCD and PDFs) at s=630 GeV! ( pp " W " e# e ) = $90 s=630 GeV <x> = M W / s 0.15, The valence quarks dominate over the sea. Versus of q = direction of p versus of q = direction of p! ( pp " Z " e + e ) = #10 pb An order of magnitude smaller since M Z >M W and for the weak charges 1 The cross sections and the bosons longitudinal momentum increase quickly with the center of mass energy

22 W l ν l The transverse momenta of q and q are small, therefore also the one of the W. We neglect it. Measurement of M W p Te e W ν e p Te e W θ ν e p e = m W / LAB p e T is the same in the two frames = (m W /) sin θ* CM. W Decay angular distribution in the CM is known: dn dn ##### $ = dn d" * dp T d" * dp T d" * trasf.coordinate Jacobian peak for p T e = m W / Jacobian peak for p T missing = m W / dn dp T = " m $ W # 1 % ' ( p & T dn d) * The transverse momentum of the W (p TW 0) degrades the peak, but does not cancel it. The m W measurement is based on the measurement of the peak energy.

23 Transverse Energy distribution UA1 M W = 8.7±1.0(stat)±.7(syst) GeV Γ W <5.4 GeV UA M W = 80.±0.8(stat)±1.3(syst) GeV Γ W <7 GeV

24 W spin and polarization W! " e! # e In the W CM, the electron energy >> m e. chirality elicity V A W interacts only with Fermions with elicity antifermions with elicity + Total angular momentum: J=S W =1 J z (initial) = λ = 1 J z (final) = λ = 1 d" d# $ d 1 [ %1,%1 ] ' = 1 1+ cos&* () N.B. If it would have been V+A d" d# $ d 1,1 1 ( ) [ ] & = 1 ( 1+ cos%* '( ) ) * + * +, The forward-backward asimmetry is a consequence of the P violation 4 To distinguish V A from V+A one needs to measure the electron polarization.

25 First Z from UA1 5 C.8 A. Bettini 14/1/10

26 Z 0! e + e " m = E 1 + E # E 1 E (1! cos") M Z measurement ( )! ( p! 1 + p! ) = E 1 + E + E 1 E! p 1! p! p 1 p cos" m " 4E 1 E sin # / " #100 tan "! ( m ) = m ( ) E 1 "! E 1 # $ % & ' ( ) " +! E # $ E % & ' + " # $! (( ) % tan( / & ' $ O(1) " misurato dalla misura delle tracce % " The E uncertainty (calorimeter) dominates:! ( E) E! ( m ) =! E m E " 4 # 6% ( ) m = 1! m ( ) ( ) m " # 3%! m = 0% E Statistical error on single measurement: σ(m) -3 GeV Scale uncertainty 3.1 GeV (UA1); 1.7 GeV (UA) UA1 (4 Z ee) M Z =93.1±1.0(stat)±3.1(syst) GeV UA M Z =91.5±1.(stat)±1.7(syst) GeV θ E (e +, µ + ) E 1 (e, µ ) ( ) $ 10 6

27 The SM triumph analyses completed on all collected data. No evidence of SM failure! The Weinberg angle must have the same value in all cases, but in the comparison one has to introduce the propre radiative corrections as predicted by theory. The main ones:! (m t " m b ) # m t ln M H The agreement is lost if: m t > GeV From LEP precise measurements of m W and m Z m t =166±7 GeV

28 Precision physics LEP at CERN and SLC at SLAC started to produce physics The SM is a well established theory, well experimentally testes at the % level.. Assuming that the SM is valid, the radiative corrections depend by two observables: the top mass and the Higgs mass: M t and M H Both were unknown until 1995 when the top quark was discovered at Fermilab. M H is still unknown. The top related corrections are related to M t and therefore they are quite sensitive. They gave a precise prediction of M t which was then confirmed by the CDF and D0 experiment. The Higgs related corrections are proportional to logm H and therefore are less sensitive, but, once M t is known, they can predict M H with a certain accuracy. Possible discrepancies could have signalled new physics, but this has not been the case.

29 Resonance The cross sections of the processes: e + +e f + +f (with f e, otherwise the t-channel has to be included as well)are due to the exchanges in the s-channel, at first order Near the resonance ( s m Z ) The exchange of a Z dominates in the s- channel! ( E) = 3" s # e # f %( s $ m Z ) + # / &' ( ) ( )* Γ e partial width in e + e, Γ f partial width in f + f, Γ total width At the peak:! e + +e " f + + f m Z ( ) = 1# m Z $ e $ f $ All events are elementary collisions (with difference with what happens in a hadronic collider)

30 Examples: peak cross section! e + +e " f + + f m Z ( ) = 1# m Z $ e $ f $ How many Z in µ + µ are produced with a luminosity (tipical for LEP) of L=10 35 m s 1 ( ) = 1#! e + + e " µ + + µ m Z $ e $ µ $ = 1# = 5.3%10&6 GeV % 388 µb/gev =.1 nb R = L! = ( m s 1 ) ".1"10 #37 ( m ) = 0.0s 1 About 1/minute How many Z in hadrons are produced? ( ) = 1#! e + + e " adroni m Z $ e $ µ $ = 1# % = 40. nb R = L! = ( m s 1 ) " 4 "10 #36 ( m ) = 0.4s 1

31 Radiative corrections! Born ( E) = 3" E % & E $ m Z # e # f ( ) + (# / ) This expression, called of Born is too simple. There are important radiative corrections. The biggest ones are electromagnetic, well known: ' ( Dominant: initial Bremsstrahlung Other minor EM corrections:

32 Z Lineshape If an electron or a positron irradiates a photon, the collision energy decreases, and becomes resonant at s>m Z. Tails at high energies δσ(peak)= 30%, δm Z 00 MeV The obvious corrections are calculated, the measured curve is corrected, the parameters are extracted (mass, width, peak height) M Z = ± GeV ( ppm) [ ]! Z =.495 ± GeV MS:! Z =.497 ± GeV Observable measured with high precision! 0 = ± nb "# MS:! 0 = ± nb$ % M Z is taken as fundamental constant; in the other two values there are theoretical uncertainties due to the non-perfect knowledge of M H, α s etc

33 Non photonic corrections They are small [O(10 3 )], but very interesting. They allow to test the SM, being sensitive to New Physics. Within the SM particularly interesting are the corrections to the W mass, and therefore the to the well measured quantity M Z /M W " G F M ( t # M b ) $ G F M t Immediatly before the top ( ), the prediction of its mass done from the fit of all existing data was: M t = 166 ± 7 GeV The central value and the first error are obtained assuming M H =300 GeV, the second error is obtained by varying 60<M H <1000 GeV. Present measurement value: M t =174.3±5.1 GeV Correction logm H, very little (10% per M higgs = 1 TeV) but, knowing M t, allows to ppredict an interval for M H

34 Mass and width of the Z The high precision measurement of the mass allows also to measure the beam energy very accurately. ΔE(punto di interazione) = MeV (0-40 ppm) Tidal effects!! M ΔM Z /M Z.3 x 10-5 Z = ±.1 MeV (UA1 and UA about 3%) Γ (cfr. δg F /G F 0.9 x 10-5 ) Z = 495.±.3 MeV ΔΓ Z /Γ Z 0.1% SM prediction (3ν, 3l, 3 colori (u, d, s, c, b) at tree level! Z =.4 GeV! Z mis "! Z albero = 95. ±.3 MeV # 4% ( ) Due to radiative corrections (radiation of g from final f ) ( ) con correz. rad.! Z =.4 GeV [1+ " s M Z # ] $ " s ( M Z ) = 0.1 ± 0.0

35 Z partial widths The LEP experiments measured_ The partial widths in e + e, µ + µ, τ + τ The invisible width to which all the neutrino families contribute, together wiith possible additional neutral particles not included in the SM. The width in cc identifying the secondary vertices The width in bb identifying the secondary Perfect agreement with the theory R e! " adr " e = ± 0.050; R µ! " adr " µ = ± 0.033; R #! " adr " # = ± Test of the universality of the weak interactions for leptons! l = ± MeV [ MS:! l = ± 0.05 MeV]! adr = ±.0 MeV

36 Z hadronic partial widths! adr = ±.0 MeV In events with hadronic jets one cannot in general identify the nature of the quark. One can make it with charm and beauty which have mean lifetime of the order of the picosecond, and can travel for about a millimeter. Vertex detector can identify secondary vertices at a distance of few mm. decay of particles with c or b Kinematic fit to distinguish the two Example: calculate the mean distance crossed by a D and a B of 50 GeV energy l D =! D " D c = #1# 4 #10$13 # 3#10 8 = 3 mm l B =! B " B c = #1#1.5 #10$1 # 3#10 8 = 4.3 mm [ ] [ ] R c! " c / " adr = 0.171± MS: R c = ± R b! " b / " adr = ± MS: R b = ±

37 The number of neutrinos The total width is larger as the number of decay channels increases: and in particular as the neutrino numbers increase (with mass <M Z /). Even more sensitive is the cross section at the peak, which depends strongly from the total width. The contribution to Γ of the 3 neutrinos corresponds to 0% of the total. It is better to use quantities which depend very little from the radiative corrections: σ 0, M Z and the ratio R l =Γ adr /Γ l.! inv "! Z #! adr # 3! l $! inv =! Z! l! 0 = 1" # e # adr $ # Z = 1" M Z # Z # e # adr M Z! 0! l # R l # 3 $ # Z # = 1" R e e M Z! 0! 0 = 1" M Z! inv! l = 1" R e M Z # 0 $ R l $ 3 # adr # e # Z!! 0! 0 =! " Z " Z Measured value! inv " 3! # = " "1.5 MeV N ν =.9840±0.008 It could have been not an integer, in the presence of new physics There are 3 families, and only 3.

38 e + e W + LEPII radiative corrections The theory predictions are fully verified The underlying simmetry is non-abelian The position of the rising edge depends critically from M W and Γ W Tevatron direct measurements (CDF and D0) M W = ± GeV $ da! teor W =.0 1+ " s & %& # ( M Z )! W =.133 ± GeV [ MS:! W =.093 ± 0.00 GeV] ' ) () ( 4 ppm) GeV * " s ( M Z )