1 A. Bettini LSC, Padova University and INFN Subnuclear Physics in the 1970s 8-May-15 IFIC Valencia. 4-8 November 2013 Lecture 7 Looking inside the nucleons different probes increasing resolution

2 A. Bettini LSC, Padova University and INFN Scattering experiments 8-May-15 To study the internal structure of an object (atom, nucleus, nucleon) we “illuminate” it with a probe beam, which should be as collimated and as monochromatic as possible and we measure the diffraction pattern For nucleons (and nuclei) we use a beam of stable (enough) particles Quasi-monochromatic = all particles have the same energy E within an interval ∆E, with ∆E/E<<1 Consequently they have approximately the same momentum p The beam wave length is = 1/p. Should be < the structure to be studied <D Collimated: all particles have the same direction within an angle << miimum angle to detect  min ∆ p/p<  min In a classical experiment, in the final state we have a scattered particle, namely a particle equal to the beam particles. Measurement of the diffraction pattern = Measurement of the energy E’ and angle  of the scattered particle and build their distributions

3 A. Bettini LSC, Padova University and INFN Scattering experiments 8-May-15 For point-like probes, the diffraction pattern is proportional to the Fourier transform of the density distribution of the target (lecture 1) More precisely this is the density “see” by the beam, namely thevdensity of the charges that interact with the probe electric charge for e and µ probes. They have weak charges too, but effect very smalli weak charge for strong charge for hadronic probes Leptonic probes (e,µ, ) are pointlike  easily extracted information Hadronic probes have a structure  differential cross section is a convolution of the beam and In the elastic collision of spinless (or non polarised) particles there is only one independent variable  E’ and  are completely correlated (see later) In inelastic collision the target does not remain in its initial state, with energy transfer from the probe dependent on the final state. Both E’ and  must be measured

4 A. Bettini LSC, Padova University and INFN Elastic scattering 8-May-15 Consider the elastic collision of a light particle (e.g. e) against a heavy one (nucleus or nucleon) At high energy we can neglect m e 2 and put p=E Complete correlation between energy and scattering angle E–E’ is the energy transferred to the target If the target mass is large E/M<<1, the energy transferred to the target can be neglected (but not the momentum)

5 A. Bettini LSC, Padova University and INFN Rutherford cross section 8-May-15 If the target is pointlike q b =Zq e in the origin  (r) is a  –function and F(q)=1 The scattering amplitude is proportional to the product of the vertices z√  and Z√  and the photon propagator 1/q 2 If the charge of the probe is zq e Geiger e Marsden:  particle

6 A. Bettini LSC, Padova University and INFN Mott cross section 8-May-15 NB. The differential cross section diverges for  0. Consequence of the divergence of the Coulomb potential for r  0. In practice the target is not pointlike Rutherford formula is valid for non relativistic collisions on infinite mass point target When velocity increases the effects of the electron spin become relevant. For elastic scattering, if effects of the target recoil can be neglected the cross section is given by the Mott expression There is an additional actor cos 2 (  /2). It makes the cross section to decrease more quickly with increasing angle. Backward, at 180˚ the Mott cross section goes to zero

7 A. Bettini LSC, Padova University and INFN SLAC 8-May-15 The Stanford Accelerator Center was founded in 1962 The linear electron accelerator is 2 miles long, the longest linear accelerator in the world, and has been operational since 1966 at a maximum energy of 20 GeV

8 A. Bettini LSC, Padova University and INFN SLAC spectrometers 8-May-15 One of the research program was the study of the internal structure of protons and neutrons with the elastic and inelastic scattering of the high energy electron beam J. Friedman, H. Kendall and collaborators at MIT and R. Taylor and collaborators at SLAC designed and built two spectrometers for 8 GeV and 20 GeV. Scattering angle is changed by moving the spectrometers on rails from the control room

9 A. Bettini LSC, Padova University and INFN The optics. 8 GeV 8-May-15 In the vertical plane the focussing is point to point and momenta are dispersed along the focal plane. In the horizontal, the focussing is parallel to point and angles are displaced along the  focal plane The 8 GeV spectrometer decouples the measurement of the angle from that of the momentum using bending magnets that deflect in the vertical plane. Five magnets (two bending dipoles (B) and three focussing quadrupoles (Q)) direct and focus scattered particles into the detectors which are mounted in a heavily shielded enclosure. The whole assembly rides on rails and can be pivoted about the target to change the angle of the scattering of the detected electrons Energy resolution 0.1%

10 A. Bettini LSC, Padova University and INFN The optics. 20 GeV 8-May-15 Scaling up this technique to the 20 GeV spectrometer (and keeping the resolution) would have required a very large vertical displacement A brilliant solution was found by K. Brown and B. Richter who proposed a novel optics arrangement with a central crossover, allowing vertical bending while keeping the vertical dimension within bounds. A simple system of sextupoles was required to correct aberrations

11 A. Bettini LSC, Padova University and INFN Structure functions 8-May-15 Consider the high-energy electron hitting a proton at rest Measure the energy E’ and the scattering angle  Resolving power is inversely proportional to momentum transfer  deep inelastic scattering(DIS) Final statee=group of hadrons of invariant mass W. Not analysed  “inclusive” process In Lab P µ = (m p,0), q µ = (E–E’, q)   E – E’ is the energy transfer in the Lab frame, obtainedmeasuring E’ Useful kinematic variables Q 2 is used just to have a possitive variable in the t chamnel. it is the opposite of the square of the mass of the virtual particle exchanged that probes the target For elastic scattering W = m p  2m p =Q 2  and Q 2 completely correlated For inelastic scattering two kinematic variables  ( and Q 2 ) or (E and E’)

12 A. Bettini LSC, Padova University and INFN Structure functions 8-May-15 W 1 and W 2 are called structure functions W 2 due to interaction of charges; W 1 due to interaction of the magnetic moments (spin-spin) W 1 and W 2 are functions of the kinematic variables In a first approximation, for the experiments we consider W 1 is negligible If the target has a structure the cross section is We drive the electron beam on the target (liquid H2 or liquid D2) Measure energy and angle of the scattered electron (at large momentum transfer). Vary angle and beam energy and extract double differential cross section From the measured E’ and  we calculate Q 2 and. The structure function is given by

13 A. Bettini LSC, Padova University and INFN Results at SLAC May-15 Surprise: while the elastic cross section decreases rapidly with increasing momentum transfer Q 2 the inelastic cross sections at fixed W decrease only slowly with increasing Q 2 are almost independent on W Recall Rutherford It looks like proton contain point-like objects! The first experimental results of a 17 GeV energy beam were published in 1969

14 A. Bettini LSC, Padova University and INFN Feyman explains 8-May-15 Feynman calls “partons” the point-like objects in the proton. They are the quarks Consider the process in a frame in which the proton moves with a very high 4-momentum P µ We can look at the proton as a group of partons all moving with parallel high momenta; we can neglect the transverse momentum components Call x the fraction of 4-momentum of a given parton. The 4-momentum of that parton = xP µ Impulse approximation: the electron-parton collision takes place as if the parton were free We learnt later that this is a consequence of the QCD asymptotic freedom (next lecture) q µ = 4-momentum transferred from e to the parton We can neglect the parton mass m. Write down that it is 0 If this model is correct, the structure function, for a given x, must have the same value for any value of Q 2 (if large enough to provide the resolving power). Bjorken scaling law

15 A. Bettini LSC, Padova University and INFN Point-like constituents 8-May-15 x W 2 has dimensions [energy] –1. One likes better defining an adimensional structure function The scaling law works!

16 A. Bettini LSC, Padova University and INFN Hadrons conposition 8-May-15 3 “valence quarks” determine the hadron quantum numbers the gluons that mediate the colour field quark-antiquark pairs: see-quarks. In the hadron the following processes happen continuously: a gluon materialise in a quark-antiquark pair, which immediately annihilates back, two gluons melt in a pair, etc. In an atom this type of processes is much rare because  s The see contains many u-antiu, d-antid pairs, less s-antis, even less c-antic In total the see, for each falvour, contains as many antiquarks as quarks The probability to find a pair of a flavour decreases with the quark mass For each flavour f there is a distribution of momentum, as a fraction of the total f  f(x)  f(x) dx is the probability that the quark carries a momentum fraction between x and x+dx x f(x) dx is the corresponding momentum fraction For the antiquark the notation is  For the gluons g(x) Quarks f have electric charge z f q e. The antiquark have charge–z f q e Gluons are neutral and have no weak charge: not seen by e or by

17 A. Bettini LSC, Padova University and INFN Structure functions 8-May-15 In the proton: the distributions in x of: up (valence + sea), down (valence + sea), strange (sea), anti-up (sea), anti-down (sea), anti-strange (sea)  6 in tot. (neglecting charm) In the neutron: the distributions in x of: up (valence + sea), down (valence + sea), strange (sea), anti-up (sea), anti-down (sea), anti-strange (sea)  6 in tot. (neglecting charm) Total: 12 functions of x to determine Not all independent Isospin invariance (4) Also (2) Quark sea = antiquark sea (1) We are left with 12–7=5 independent functions to determine We call them We distinguish sea from valence:

18 A. Bettini LSC, Padova University and INFN How electrons see inside 8-May-15 Structure functions are determined with DIS with electrons, neutrinos and antineutrinos Having different sensitivity to quark charges Electron beams: 3 measurement sets as functions of x Liquid H 2 target for protons Liquid D 2 target for neutrons “isoscalar” targets=nuclei with the same number of protons and neutrons DIS ep DIS en DIS e Nucleus Each quark contributes proportionally to its charge squared NB. 5/18 is the average of the squared charges of up (4/9) and down (1/9)

19 A. Bettini LSC, Padova University and INFN How muon neutrinos see inside 8-May-15 Neutrinos see some flavours and not others, vice versa antineutrinos. Neglecting s Allowed reactions The  lepton becomes a µ – diminishing the charge  at the quark vertex charge must increase Anti-  becomes µ +  the quark charge must diminish Forbidden reactions On point-like target (2 relations) For neutrinos and antineutrinos beams on neutrons we have the same relations. This gives a way to test the consistency of the theory In total we can measure 5 independent functions of x and have 5 unknown structure functions. We can solve the system. The factor 2 comes from the V–A structure

20 A. Bettini LSC, Padova University and INFN How muon neutrinos see 8-May-15 The BEBC+EMI experiment has used neutrino and antineutrino scattering from deuterium to obtain the best measurement of the structure functions on the proton and the neutron separately (Allasia et al., 1985; Jones et al., 1994). A neutrino or antineutrino interaction was identified as coming from a neutron if it had either an even number of prongs, or an odd number of prongs with a proton with momentum less than 150 MeV. All remaining events, with an odd number of prongs and hence a net total charge, were classified as interactions with protons. Misidentifications were corrected on a statistical basis using a Monte Carlo simulation Experiments of increasing precision were performed at CERN and at Fermilab with bubbe chambers (Garagamelle, BEBC, etc.) and with spectromters (CDHSW, CHARM and CHARM2 at CERN, CCFR at Fermi) build on purpose from the 1970s to 1990s

21 A. Bettini LSC, Padova University and INFN Structure function from GGM 8-May-15 The SLAC-MIT values have been divided by 5/18, the mean square charge of the u and d quarks in the proton Neutrino beams are not monochromatic, we do not know the initial energy E (but we know the direction). How can we measure Q 2 =–q  q   We can use the target vertex We then measure the mass W of the hadronic final state and its energy E X Early results from GGM (1973)

22 A. Bettini LSC, Padova University and INFN F2 BEBC 8-May-15 The most evident feature is that F 2 ( p) ≈ 2 F 2 ( n) over most of the kinematic region. This is because the W + emitted in a neutrino interaction must interact with a negatively charged quark, which at high x, has the highest probability of being the valance d quark. Since the neutron has twice the number of valance d quarks as the proton, the neutron structure function is larger. These data clearly indicate the flavor sensitivity of neutrino scattering.

23 A. Bettini LSC, Padova University and INFN Momentum distributions. Gluons 8-May-15 We miss 50%!! 50% of the nucleon momentum is carried by objects that do not have either electric or weak charge. These are the gluons. The gluons contribution is large for x <  0.3 becoming dominant forx<  0.2 Sea quarks contribute mainly for x<  0.1 The valence quarks distributions have maxima at x = They are pretty wide due the Fermi motion in the nucleon (a consequence of the uncertainty principle) Go to zero both for x  0, and for x  1: it is unlikely that a valence quark carry more than some 70% of the nuceon momentum Summing all quark and antiquark contributions we get

24 A. Bettini LSC, Padova University and INFN Scaling violations 8-May-15 Here is a summary of F 2 measurements with different probes and different energies Maximum resolving power was reached at the HERA electron-proton collider at DESY. Electron energy =30 GeV against 800 GeV protons 2.7 < Q 2 < GeV 2 For about x>0.1 scaling law OK At small x values more partons at small Q 2 are observed than foreseen by scaling This was theoretically foreseen in QCD (Dokshitzer, Gribov, Lipatov, Alatrelli, Parisi=DGLAP) Curves are the QCD predictions, fitting the running “constant”  s

25 A. Bettini LSC, Padova University and INFN Why scale law is violated 8-May-15 Consider a quark having fractional momentum x emitting a gluon gluons takes the (longitudinal) momentum fraction x–x’ the momentum fraction of the quark becomes x’<x If Q 2 is not large the resolving power is not sufficient  quark and gluon are not resolved  we measure x If Q 2 is large enough, quark and gluon are resolved and we measure x’  the structure function at fixed small x increase with increasing resolving power Q 2. The effect depends on  s giving a means to determine it From theory we have that allows extracting the gluon distribution function