Part 1 ! Thomas Blake Warwick Week 2015

An introduction to Flavour Physics

! Part 1 ! Thomas Blake Warwick Week 2015

1 An introduction to Flavour Physics

• What’s covered in these lectures: 1. An introduction to ﬂavour in the SM. ! ➡ A few concepts and a brief history of ﬂavour physics. ! 2.Neutral meson mixing and sources of CP violation. 3.CP violation in the SM. 4.Flavour changing neutral current processes.

2 SM particle content

3 Free parameters of the SM

• 3 gauge couplings

• Higgs mass and vacuum expectation value Flavour parameters • 6 quark masses

• 3 quark mixing angles and one complex phase

• 3 charged lepton masses

• 3 neutrino masses

• 3 lepton mixing angles and (at least) one complex phase

4 Questions for the LHC era?

• What is the mechanism for EW symmetry breaking? ✓ We now know that this is the Higgs mechanism. • What “new physics” lies between the EW and Planck scale? ➡ No idea! There is no evidence for new particles being directly produced at the TeV scale. • What is dark matter? ➡ Again, no idea! Dark matter could be heavy or it could be light. There is no evidence for large missing energy in BSM searches at CMS and ATLAS, which constrains EW scale dark matter, or in direct detection experiments.

• What is the solution to the ﬂavour puzzle?

5 Why is ﬂavour important?

• Most of the free parameters of the SM are related to the ﬂavour sector. ➡ Why are there as so many parameters and why do they have the values they do?

• The ﬂavour sector provides the only source of CP violation in the SM. ➡ Are there additional sources?

• Flavour changing neutral current processes can probe mass scales well beyond those accessible at LHC.

6 Flavour puzzles?

• Why do we have a ﬂavour structure with three generations? ➡ We know we need 3+ generations to get CP violation. Are there more generations to discover?

• Why do the quarks have a ﬂavour structure that exhibits both smallness and hierarchy? ➡ Why is the neutrino ﬂavour sector so different (neither small nor hierarchical)?

• If there is TeV-scale new physics, why doesn’t it manifest itself in FCNCs?

7 Flavour hierarchy?

CKM matrix for quark sector PMNS matrix for neutrino sector

why is the structure so different?

8 Mass hierarchy?

• 12 Large hierarchy in 10 scale between the 9 masses of the 10

fermions. mass [eV] 6 10

• Equivalent to having a 3 10 large hierarchy in the Yukawa couplings. 1

-3 • Why is this hierarchy 10

- - - so large? ν ν ν e µ τ u d s c b t e µ τ

• More on neutrino mass in lectures by Steve Boyd.

9 Flavour in the SM

• Particle physics can be described to excellent precision by a very simple theory:

= (A , )+ (,A , ) ! LSM LGauge a i LHiggs a i with: ➡ Gauge part that deals with the free ﬁelds and their interactions by the strong and electroweak interactions. ➡ Higgs part that gives mass to the SM particles.

10 Flavour in the SM

• The Gauge part of the Lagrangian is experimentally very well veriﬁed, 1 = i ¯ ⇢⇢D F a F µ⌫,a . ! LGauge j j 4g2 µ⌫ a a Xj, X • The ﬁelds are arranged a left-handed doublets and right-handed singlets = QL,uR,dR,LL,eR ! u ⌫ Q = L ,L = L ! L d L e ✓ L◆ ✓ L◆ • There are three replicas of the basic fermion families, which without the Higgs part of the Lagrangian would be identical (huge degeneracy). The Lagrangian is invariant under SU(3) SU(2) U(1) c ⇥ L ⇥ Y 11 Flavour in the SM

• The Higgs part of the Lagrangian, on the other hand, is much more ad-hoc. It is necessary to understand the data but is not stable with respect to quantum corrections (often referred to as the Hierarchy problem). It is also the origin of the ﬂavour structure of the SM.

• Masses of the fermions are generated by the Yukawa mechanism

Q¯i Y ijdj + ... d¯i M ijdj + ... L D R ! L D R Q¯i Y ijdj + ... u¯i M ijuj + ... L U R c ! L U R

12 Flavour in the SM

• Can pick a basis in which one of the Yukawa matrices is diagonal

! yd 00 yu 00 mi Y! D = 0 ys 0 ,YU = V † 0 yc 0 ,yi 0 1 0 1 ⇡ 174GeV 00yb 00yt ! @ A @ A • The matrix V is complex and unitary (V†V = 1).

• To diagonalise both mass matrices it is necessary to rotate uL and dL separately. Consequently, V also appears in charged current interactions, µ µ µ JW =¯uL dL u¯LV dL ! !

• V is known as the Cabibbo, Kobayashi, Maskawa matrix.

13 Isospin • Proton and neutron have different charges but almost identical masses. ➡ They also have an identical coupling to the strong force.

• In 1932 Heisenberg proposed that they are both part of the an Isospin doublet and can be treated as the same particle with different isospin projections.

p(I, IZ) = (½,½), n(I,IZ) = (½,-½)

• Pions can be arranged as an Isospin triplet,

π+(I, IZ) = (1,+1), π0(I, IZ) = (1, 0) , π-(I, IZ) = (1,-1)

14 Isospin

• Heisenberg proposed that strong interactions are invariant under rotations in Isospin space (an SU(2) invariance). ➡ Isospin was conserved in strong interactions.

• Now know that this is not the correct model but nevertheless it is a useful concept

➡ It works because mu ~ md < ΛQCD ➡ Can be used to predict interaction rates, (p + p d + ⇡+):(p + n d + ⇡0)=2:1 ! !

15 Kaon observation

• In 1947, Rochester and Butler observed two new particles with masses around 500 MeV and relatively long lifetimes.

0 + + + K ⇡ ⇡ K µ ⌫µ S ! !

16 Quark model Iz • Concept of quarks introduced by Gell- Mann, Nishijima and Ne’eman to explain the “zoo” of particles.

• Now understood to be real “fundamental” particles.

• Strangeness conserved by the strong interaction but violated in weak decays.

• Organised by

Y = B + SQ= e(Iz + Y/2)

baryon strangeness number 17 Quark model

• Can only make colour neutral objects: q q¯ ➡ quark anti-quark or three quark combinations (mesons and baryons). Nearly all known q q q particles fall into one of these two categories. ➡ Can also build colour neutral states containing more quarks (e.g. 4 or 5 quark states).

18 Exotic charmonium states

• Several exotic states have recently been discovered: ➡ X(3872) by CDF, Z(4430)+ and Y(4140) by Belle

• These states decay to charmonia and have masses below the b-quark mass. ➡ Z(4430)+ is charged, therefore has minimal quark content ccud • States could be weakly bound molecular D D states or genuine four quark states.

19 Cabibbo angle

• The quark content of the K+ and K0 are (¯ su ) and (¯ sd)

• The main decays of the K+ are + + + 0 + ! K µ ⌫ and K ⇡ e ⌫ ! µ ! e i.e. it decays via the charged current interaction.

• The charged current interaction couples to left-handed doublets, therefore need to construct a doublet that allows s → u and d → u.

• Cabibbo proposed a solution in terms of quark mixing u u = d0 d cos ✓ + s sin ✓ ✓ ◆ ✓ C C ◆

20 Cabibbo angle

• The quark mixing angle, �C, is determined experimentally to be

! sin ✓ 0.22 C ⇡ • Cabibbo’s proposed solution also explained a discrepancy between the weak coupling constant between muon decays and nuclear decay.

• However, this opened up a new problem, why is + 0 + ! [K µ⌫] [K µ µ] ? ! L ! • If the doublet of the weak interaction is the one Cabibbo suggested, can have neural currents 0 J = d¯0 (1 )d0 ! µ µ 5 which introduces tree level FCNCs.

21 GIM mechanism

0 2 2 • Expanding, J =¯s (1 )s sin ✓ + d¯ (1 )d cos ✓ µ µ 5 C µ 5 C +¯s (1 )d sin ✓ cos ✓ ! µ 5 C C + d¯ (1 )s sin ✓ cos ✓ ! µ 5 C C • So was Cabibbo wrong? Glashow, Iliopoulos and Maiani provided a solution in 1970 by adding a second doublet

u ! u c c = , = d0 d cos ✓ + s sin ✓ s0 d sin ✓ + s cos ✓ ✓ !◆ ✓ C C ◆ ✓ ◆ ✓ C C ◆ • The second doublet exactly cancels the FCNC term. Quark mixing led to the prediction of the charm quark.

22 GIM mechanism W ! s u, c d • What happens at loop order? Z0 • For strange decays still have an effective GIM suppression,

2 2 2 2 (V ⇤ V )f(const + m /m )+(V ⇤ V )f(const + m /m ) ! A ⇠ us ud u W cs cd c W • 2 x 2 unitarity implies

! V ⇤ Vud + V ⇤ Vcd =0 0 us cs A ⇡ • FCNC strange decays are very rare, e.g. 0 + 9 (K µ µ)=(6.8 0.1) 10 B L ! ± ⇥ 23 Observation of J/�

• Experimental evidence for charm quark came in 1974.

• Discovery of charmonium (J) at Brookhaven in p + Be → e+ e-X.

• Discovery of charmonium (�) at SLAC in e+e- → hadrons, e+ e-, µ+ µ-

24 �-� puzzle

• Two decays were found for charged strange mesons

! ✓+ ⇡+⇡0 + ! + + ⌧ ⇡ ⇡⇡ ! ! • The � and � had the same mass and lifetime, but the parity of 2π and 3π is different.

➡ Resolution is that the � and � are the same particle and parity is violated in the decay.

25 C and P

• Prior to 1956, it was thought that the laws of physics were invariant under parity, i.e. mirror image of a process is also a valid physical process.

➡ Shown to be violated in β-decays of Co-60 by C. S. Wu (following an idea by T. D. Lee an C. N. Yang).

• Now know that Parity is maximally violated in weak decays.

➡ No right-handed neutrinos.

• C is also maximally violated in weak decays.

➡ No left-handed anti-neutrino.

26 Neutral kaon system

• Ignoring CP violation, the two physical states in the neutral kaon system are K0 K0 K0 + K0 K1 = | i| i and K2 = | i | i ! | i p2 | i p2

under Parity and Charge Conjugation

K0 = K0 , K0 = K0 and K0 = K0 ! P| i | i C| i | i CP| i | i

• For the physical states

K0 = K0 , K0 = K0 and K0 = K0 P|! 1,2i | 1,2i C| 1,2i ⌥| 1 i CP| 1,2i ±| 1,2i

i.e. they are P, C and CP eigenstates as well.

27 Neutral kaon system

• What does this tell us about their decays?

+ ! ⇡ ⇡ ➡ P = +1, C = +1 and CP = +1

+! 0 ⇡ ⇡⇡ ➡ P = -1, C = + 1 and CP = -1

• K2 decays to 3π but the 2π decay would be forbidden if CP is conserved.

28 CP violation

• In 1964, Christensen, Cronin, Fitch and Turlay observed 2π decays of K2 mesons (KL). Observation of CP violation in the kaon system.

Fixed target p + Be experiment at Brookhaven AGS

29 V†V = 1

• The CKM matrix is a complex 3x3 matrix ➡ 9 magnitudes and 9 phases

• Unitary condition ➡ 9 constraints e.g. V! udVub⇤ + VcdVcb⇤ + VtdVtb⇤ =0 2 2 2 ! Vud + Vus + Vub =1 | | | | | | • Can remove a single phase (global phase) and absorb phases into external quark ﬁelds. ➡ 4 parameters, 3 Euler angles and a single complex phase.

• If there were only two generations V would be a real rotation matrix.

30 Im Unitarity triangles VudVub⇤ Re • Unitarity conditions can be represented by triangles in the complex plane. Im ➡ Six triangles with the same area.

• We usually visualise the triangle with almost V V ⇤ equal length sides. td tb Re VudVub⇤ + VcdVcb⇤ + VtdVtb⇤ =0

Re VcdVcb⇤ 31 CKM matrix

• Standard form is to express the CKM matrix in terms of three rotation matrices and one CP violating phase,

! i13 10 0 c13 0 s13e c12 s12 0 VCKM != 0 c23 s23 010 s12 c12 0 0 1 0 +i13 1 0 1 0 s23 c23 s13e 0 c13 001 ! @ A @ A @ A where

cij = cos ✓ij and sij =sin✓ij

32 Wolfenstein parameterisation • Can also exploit the hierarchy of the CKM matrix to write

! 2 3 ! 1 2 A (⇢ i⌘) 2 4 VCKM = 1 A + ( ) ! 0 2 1 O A3(1 ⇢ i⌘) A2 1 ! @ A where

0.22,A 0.82, ⇢¯ 0.13, ⌘¯ 0.35 ' ' ' '

33 CKM picture

1.5 excluded at CL > 0.95 Very complete (and excluded area has CL > 0.95 consistent) picture of the 1.0 m & m ﬂavour structure of the d s SM has been built up in sin 2 0.5 the past 30 years. md ! K

0.0 More on this in lectures 2 and 3 Vub -0.5

-1.0 K CKM f i t t e r sol. w/ cos 2 < 0 Summer 14 (excl. at CL > 0.95) -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

34 Jarlskog invariant

• All of the unitarity triangles have the same area, called the Jarlskog invariant.

! J =Im(V V V ⇤ V ⇤) for i = k andj = l | | ij kl kj il 6 6 • This is a phase convention independent measure of CP violation in the quark sector.

• In the standard notation 2 ! J = c12c13c23s12s13s23 sin

• Small size of the Euler angles means J (and CP violation) is small in the SM.

35 Matter dominated Universe

• From CMB measurements by WMAP + Planck

! nB nB¯ 10 6 10 ! n ⇡ ⇥

• In early (hot) universe expect annihilation to give

! n n ¯ n B ⇡ B ⇡ • i.e. the matter anti-matter imbalance is small ➡ However, still too large to be explained by Electroweak Baryogenesis. CP violation in the SM (quark sector) is too small due to the small size of the mixing angles and large hierarchy of quark masses.

36 Sakharov conditions

• Three conditions needed to generate a matter dominated universe from a symmetric initial state were proposed by A. Sakharov in 1967: 1.C and CP violation. 2.Baryon number violation. 3.A system out of thermal equilibrium.

37 Sakharov conditions • If we start with an equal amount of matter (M) and anti-matter (M̅) and M A ! ! M A ! !

where A and A̅ have baryon numbers NA and -NA.

• If C and CP are violated ! [M A] = [M¯ A¯] ! 6 ! but even with different decay rates, after sufﬁcient time there will be equal amounts of matter/antimatter.

38 Sakharov conditions

• Can get round this problem by having two (or more) competing process M A with probability p ! ! M B with probability 1 p ! ! M¯ A¯ with probabilityp ¯ ! ! M¯ B¯ with probability 1 p¯ ! • Then

N = N p + N (1 p) N ¯ p¯ N ¯ (1 p¯) ! A · B · A · B · =(p p¯)(N N ) ! A B

• Need NA different from NB to generate an asymmetry (i.e. baryon number violation as well as CP violation).

39 Sakharov conditions

• Even then, the system needs to be out of thermal equilibrium or

! [A B + C]=[B + C A] ! ! ! and the asymmetry will be destroyed as fast as it is created.

40 Timeline Observation neutron muon pion + kaon CP violation charm beauty top (1932) (1936) (1947) (1964) (1974) (1977) (1995) !

1940 1950 1960 1970 1980 1990 neutron pion strange charm beauty + top (1920) (1935) quark quark quarks ! ! (1964) (1970) (1973)

Prediction

41 Fin

42 Low energy ﬂavour conserving observables

43 Electric dipole moments

• Classically, EDMs are a measure of the spatial separation of positive and negative charges.

• Can also be measured for fundamental particles (electron, muon, neutron etc).

• Tested using the Zeeman effect, i.e. looking for shift in energy levels under an external electric ﬁeld.

• EDMs are both parity and time reversal symmetries.

! [they can also be viewed as a measure of how spherical the shape of the particle is]

44 Electric dipole moments

• Electron EDM: 29 d < 8.7 10 Science 343 (2014) 6168 e ⇥ • Muon EDM: 19 dµ < 1.9 10 Phys. Rev. D 80 (2009) 052008 ⇥ • Neutron EDM:

26 d < 3.0 10 Phys. Rev. Lett. 97 (2006) 131801 n ⇥ • Probing amazingly small charge separation distances e.g. Neutron were the size of the earth, the EDM corresponds to a charge separation of 10 µm.

45 Magnetic dipole moments

• “Spinning” charge acts as a magnetic dipole with moment µ giving an energy shift in external magnetic ﬁeld,

! E = µ~ B~ · • Prediction of g = 2 (classically g = 1 ) was a big success of the Dirac equation, e.g. in external ﬁeld Aµ 1 e e µ ! (p~ + eA~)2 + B~ eA0 = E µ~ = ~ = g B S~ 2m 2m · 2m ~ ✓ ! ◆

• Receives corrections from higher order processes, e.g. at order �2, ↵ g =2+ ⇡

46 Anomalous magnetic moments • (g-2)e is a powerful precision test of QED 6 (g 2) = (1159.652186 0.000004) 10 ! e ± ⇥ • (g-2)µ receives important Weak and QCD contributions. The latest experimental value from the Brookhaven E821 experiment 6 ! (g 2)µ = (11659208 6) 10 ± ⇥ from Phys. Rev. Lett. 92 (2004) 1618102 is ~3� from the SM expectation.

• Could this be a hint of a NP contribution to (g-2)µ? For a review see Phys. Rept. 477 (2009) 1-110 (arXiv:0902.3360).