Subnuclear Physics in the 1970s

Subnuclear Physics in the 1970s IFIC Valencia. 4-8 November 2013 Lecture 4 Measuring the weak mixing angle Polarised electron-deuteron scattering Parity violation in atoms

The charged weak currents (CC) e– ne m– nm t– nt W– W– W– CC: at the vertex incoming and outgoing charges are different, difference taken by W± Space-time structure is V–A Universality: all the couplings are equal (after Cabibbo rotation for quarks) g g g We can simplfy the expression of the currents: Weak charge  chirality: states coupled to W have negative chirality

Electro-weak theory In the EW theory the photon and the massive vector bosons of the weak interactions are introduced as “gauge bosons”, initially mass-less The symmetry spontaneously breaks down (Higgs) giving mass to W± and Z˚, leaving the photon massless The symmetry group is SU(2)U(1). Their fundamental representations contain respectively 3 and 1 objects: the gauge fields, two charged and two neutral W = (W1, W2, W3) = corresponding to the (non Abelian) symmetry SU(2) interact by means of the weak isospin, IW B corresponding to the (Abelian) symmetry U(1) interacts by means of weak ypercharge, YW=2 (Q–IW3) Will see that W+and W+ are (trivial) linear combinations of W1and W2, the photon and the Z are linear combinations of W3 and B

Weak isospin The W±, which mediates CC, couples only to the Left components of leptons and quarks (all of them) Leptons. Each family has two Left leptons: one charged and its neutrino. They are lodged in doublets of weak isospin IW=1/2 Charged leptons are massive and have also a Right component. They are lodged in isospin singlets (IW=0) Quark. Very similar, taking into account Cabibbo mixing.

Electroweak mixing Weinberg angle Wµ = (Wµ1, W µ2, W µ3) is a space time four vector and an isovector (IW=1) in SU(2) Interacts with the leptons charged current Jµ (four-vector and isovector) with the coupling constant g Bmis a four-vector isoscalar (IW=0) Interacts with the leptons neutral current JµY(fourvector-isoscalar)trhough hypercharge with the coupling constant g’ The fields of the physical bosons are C.8 A. Bettini

Unification Relationship with the Fermi constantè Electroweak unification All the vector bosns interactions are determined by the elementary electric charge qe and qW Fermions both left and right are coupled to the Z by the coupling constant The Z-charges are

The neutral currents • NC have important differences from CC • Couple a particle with itself only (ee, not em;uR uR, notuR uB, not uc, …) • Are not V-A,  both Left and Right fields The currents (for the 1˚ family) • The 3x7=21 couplings are determined by two parameters = elementary electric charge and weak angle sin2qW • The Z is universally coupled • couples to both left and right fermions • couples to the Ws • also couples to electrically neutral particles, provided they have Iz ≠0, such as neutrinos • does not couples to states with both Q=0 and Iz =0, such as the gand itself.

Vector boson masses Two constants to be determined by experiments: charge a and mixing angle sin2qW EW unification+Fermi constant (from beta decays etc.) EW theory Experiments (examples to be discussed) modulo small higher order corrections

Measuring the weak mixing • The unification between electromagnetic and weak interactions appears mainly in the NC weak processes. Where we measure the Z-charges that theory gives as functions of a sole parameter, sin2q • Experimentally verified in many processes, at different energy scales • in red to be discussed • Parity violation in atoms (100 eV) • Polarised electron deuteron scattering (GeV) • Asymmetries in e+e– m+m– (10 GeV - 200 GeV) • Deeply inelastic scattering of nm on (several GeV) • Elastic nm electron scattering (MeV)

Inelastic ed scattering Inelastic ed scattering gives information on sin2qW Need detecting interference between Weak NC (small) and EM (large) processes Quark level diagrams on the lefy Experiment done at the LINAC of SLAC at momentum transfer around q21.6 GeV2. Small enough to have a pointlike effective weak interaction Hence Parity violation comes from the product of terms of opposite parity vector electron current times axial quark current axial electron current times quarks vector currents

ed scattering X epol e counter Parity violation appears as an asymmetry Prescott et al. Prepared a circular polarized electron beam. The direction of polarization can be inverted. The flux of electrons scattered by a liquid deuterium target at fixed q2 is measured. The looked for asymmetry is the difference between the fluxes corresponding to the two polarisations e–(polarised) + d e– + X Expected few p.p.m. values Ein Efin Calculation gives (considering only valence quarks) Expected A = 10–4q2 (GeV2) C.Y. Prescott et al. Phys. Lett. 77B (1978) 347; Phys. Lett. 84B (1979) 524

The polarised source Crucial technical development A die LASER (pulsed in phase with the LINAC) goves light at l=710 nm linearly polarised The orientation of the polarisation plane is defined by the direction of the axis of a calcite prism The light beam enters a Pokels cell. It is a crystal with bi-refringence proportional to the square ot the applied electric field – field intensity is chosen to have a l/4 delay). Circular polarisation (photons with helicity + or –) is obtained by rotating the calcite relative to the cell Photons the enter a GaAs crystal, whose surface has been treated to have negative electron affinity. They pump electrons from valence to conduction band, giving them their helicity By rotating the light polarisation plane (the calcite) by an angle FP the electrons helicity varies as cos(2FP) Helicity can be inverted by inverting the electric field on the cell. This can be done often and randomly, in order to minimize drifting effects on the asymmetry N.B. A linear accelerator does not contain magnetic field gradients, hence it does nothing on polarisation

The Prescott experiment at SLAC Measure beam polarisation Møller Scattering (elastic e–e– ) in a magnetised Fe foil Pe=[37±1(stat)±0.2(syst)]% Spectrometer selects charged particles of definite momentum (≈80%Ein) Beam intensity= 4x1011 el/pulse Intensity at detectors = 1000 el/pulse Detectors (2 for cross-checks) on the beam analysed by spectrometer Flux is large, cannot count particles Ni is the output signal for the pulse I of the PM of the Cherenkov or the Lead-glass calorimeter Qi is the measured charge of the beam pulse i = integrated beam current Count I is defined as Yi=Ni/Qi Average <Y+> for helicity + and <Y–> for helicity – Check on non polarised beam Aexp=(–2.5±2.2) x 10–5

Asymmetry. First method The following values were chosen for the angle FP between calcite and cell and of the sign of DV on the cell FP=0˚ DV>0 electron helicity + DV<0 electron helicity – FP=45˚ DV>0 electron helicity 0 DV<0 electron helicity 0 FP=90˚ DV>0 electron helicity – DV<0 electron helicity + Expected behaviour Aexpect=Pecos(2 FP) Compatible with 0. OK Opposite values. OK

Asymmetry. Second method Second method. Vary electron helicity Electrons spinsperform precession in the beam transport magnetic structure (remember g–2≠0). The total precession angle depends on the beam energy Ein Measured at dfferent beam energies Ein = 16.2 - 22.2 GeV, q2 = 1. - 1.9 GeV2 The EM amplitude varies as 1/q2 Hence asymmetry A should e proportional to q2 Plot A/Peq2 vs energy

Systematics and result Systematic effects can (do) induce spurious asymmetries Drifts in the PM gain effect is minimised by frequent inversions Beam fluctuations under control, residual effects small enough Variations in beam parameters correlated with helicity changes (dangerous) accurate monitoring of the beam parameters, register data, feedback corrections using micro-processor DEin/Ein<10–6D(A/q2)<0.26x10–5 Total uncertainty = linear sum of statistical ±9% systematic on Pe ±5% systematic on beam parameters ±3.3% A/q2=(–9.5±1.6) x 10–5 GeV–2 Final result sin2qW = 0.224±0.012 (stat) ±0.008 (syst.) ±0.010 (theor.) Theoretical error from the uncertainty on the deuteron quark structure

Atomic parity violationLandmarks

Stark-PV-interference technique Invented by the Bouchats in the 1970s Phys. Lett. 48B (1974) 111 and J. Physique 35 899–927

Atomic parity violation Electrons are bound to atomic nuclei by exchanging photons andZ˚ The latter contribution is too small to be observed as a shift of energy level, but polarisation effects due to the interference between the two amplitudes can be observed Sensitive to electron-quark coupling Energy scale much different from accelerator experiment

Atomic parity violation Precision limiting factors experimental accuracy complexity of the atom system theoretical uncertainties in connecting the measured quantity with the weak charge Expected effect grows with the nuclear charge as Z3 Less uncertain theory for simple atoms  alkaline Good candidate Cesium Only one stable isotope 133Cs, Z = 55, N = 78, A= 133 Atomic level outside closed shell (valence electron) 6s Atom angular momenta J = L + S = 0 + 1/2 = 1/2 Nuclear spin I = 7/2 Total angular momentum F = 3 and 4 Energy difference between F=3 and F=4 9.19 GHz S.L. Gilbert e C. E. Wieman P.R. A,34 (1986) 792 M.C Noecker et al P.R.L. 61 (1988) 310

Theory Dominating contribution is the product of the electron axial current and the nucleon quarks vector current We can define the Z-charges of the nucleons as sums of those of their quarks Considering that T3 and the charge Q are additive, the relations are the same as for quarks Also The interesting interaction is • The effective potential can be calculated consdering that • the wavelength corresponding to the momentum transfer is large compared to the nuclear radius • the electron is non-relativistic, and its wave function becomes A. Bettini

Parity violating effective potential We substitute Calculating effective potential we obtain for neutron and proton We sum over the Z protons and N neutrons of the nucleus obtaining, the total weak potential Notice that the potential is pseudoscalar. As such it mixes levels of opposite parity. We tink to the single valence electron (of the alkaline) as living in the average potential of all the other components of the atom The mixed levels are then S1/2 and P1/2 The matrix element must be calculated is the parity violating “weak charge” There are uncertainties on the radial wave function at the origin R(0) and its gradient dR/dr

Boulder Cs experiment. Scheme The parity violating potential mixes S and P states, making possible a small dipole (E1) transition amplitude between states of the same parity: APNC We measured it by observing its interference with a much larger parity conserving amplitude AST AST = electric dipole transition induced through Stark effect by an external stationary electric field E, which mixes S and P. resonant excitation of transitions 6S7S in the presence of perpendicular crossed electric E and magnetic B fields

Boulder Cs experiment. Continues A(4,4;3,3) B stationary (weak = 7 mT): separates m levels The LASER polarised beam electromagnetic field induces the wanted transitions Cs target is an atomic beam, in order to reduce substantially the Doppler broadening and allowing working with narrow lines Measure the intensity of these radiations to monitor the rates of the LASER induced transitions Transitions to be induced DF =1, Dm =±1

Space structure of the observables The observables whose matrix elements correspond to P conserving processes are scalars, those that violate P are pseudoscalar. Transition to be observed are induced by the LASER field must be proportional to the wave electric field eand to its magnetic field [equivalently to ek] and also to eE The structures of all possible observables are obtained taking the scalar products of e, eke eEwith the availbale vectors (k, E) and axial vectors (B e Ek). The latter are by construction parallel, and consequently equivalent (provided angles are perfectly 90˚) Scalar quantities are e.k zero for EM wave(but not for diffuse radiation) e.E “scalar” polarizability. Gives zero contribution to transitions DF≠0 ek.B magnetic dipole (small).Equivalent toek.µ(with µ electron magnetic moment) eE.B “vectorial” polarizability One pseudoscalar quantitye e.B Parity violating potential. Equivalent toe.s(with s electron spin) (the other expressions are zero or non-independent. Example ek.E= Ee.k=kE.ethat is not independent from B. e)

Transition amplitude The electric dipole transitions ASTare due to the interaction between the wave electric field e and the dipole moment d induced by the stationary electric field E (Stark effect). these are the matrisx elements of beE.B. Hereb is the vector poralizability (spin-orbit) that must be calculated The dipole moment transition amplitudes AM1 are due to the interactions of the wave magnetic field, directed as ke and the magnetic moment m directed as B. Hence: M1ek.µ(“strongly forbidden” transition) The parity non conserving amplitudes APNC due to VPNC e.s For all are different from zero only transitions with m’=m and m’=m±1

Interference maximize minimize For the transition between two given levels m and m’ Interference between the large amplitudes AST and AM1 is zero if Bandk are exactly perpendicular The single interference terms between AST and the small APNC are independent on m and m’. The resulting interference is the weighted sum of the contributions of the different m. It is zero if the positions of the levels are not different. Questa è la funzione del campo B Control of the systematics is vital Need to verify that the directions of the fields and of the beam are relly perpendicular

What do we expect? It is easily shown that the spectrum of the 6S(F=4) 7S(F=3) transition is made of 8 lines, equidistant for weak magnetic fields (Zeeman) The two extreme ones correspond to one transition, m =4  3 and m =–4  –3 respectively, while the other ones are sum of one Dm=1 and one Dm=–1 Stark transitions induced by E Spectrum due to the parity violating potential. Enlarged Expected spectrum We must measure the asymmetry between the intensities at m and –m (expected O(10–6)) The weak magnetic field induces an asymmetry, which can be accurately calculated frequency

Parenthesis. A modern version

The experiment The tuned Fabry Perot cavity effectively amplifies the LASER power by 20 Intensity = 1015 atoms cm–2s–1 Photodiode sensitive at 852/894 nm Circular polarisation can be inverted rapidly We chose the pump LASER frequency to define the levels between which the transition should happen 6S(F=4, m =4 ) 7S(F=3,m=3) and (after 4 h) 6S(F=4, m =–4 ) 7S(F=3,m=–3) • Main experimental points: 4 quasi independent spatial inversion operations • Parity violating interference changes sign for each inversion, while the (much larger) Stark term does not • Inverting E (0.2 Hz) • Inverting B (0.02 Hz) • Inverting circular polarisation. (2 Hz) • Inverting the sign of m by changing the LASER frequency (30 min.)

Results Measured quantity VNPC/b Bouchat et al. 1984 VNPC/b = –1.78±0.26(stat.)±0.12 (syst) mV/cm Noecker et al. 1988 VNPC/b = –1.576±0.034(stat.)±0.008 (syst) mV/cm Polarisability b known from computations b = 27.0 a0 with 5% uncertainty Weak charge is QW= Z(1–4sin2qW)–N = 55 (1–4sin2qW)– 78 for Cs To extract it from the data wave functions and their uncertainties must be known. One obtains (Noecker) QW= –69.4±1.5 (sperim.)±3.8 (theor.) sin2qW = 0.219±0.007±0.018 Present values QW= –73.20±0.35 sin2qW = 0.2385±0.0015 Radiative corrections must be taken into account when comparing with other measurements of sin2qW APV gives the most precise measurement of the coupling between vector weak electron current and d- quark current (u-quark contribution is small)

sin2qW “runs” sin2qW as a function of energy scale. APV: atomic parity violation; APV : asymmetry in polarised Møller scattering; Z-pole measurements; AFB: forward-backward asymmetry at LEP2

Subnuclear Physics in the 1970s