Beyond Standard Model Effects in Flavour Physics: p.1

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1 Beyond Standard Model Effects in Flavour Physics: Alakabha Datta University of Mississippi Feb 13, 2006 Beyond Standard Model Effects in Flavour Physics: p.1

2 OUTLINE Standard Model (SM) and its Problems. - Flavour Problem - Higgs Problem SM as an effective theory. Beyond Standard Model(BSM) effects in Flavour Physics - What do we learn? Constructing the new Standard Model(nSM). - Probing NP at very high scales beyond reach of colliders Beyond Standard Model Effects in Flavour Physics: p.2

3 THE FLAVOUR PROBLEM The particle content of Standard Model (SM) of particle physics: First Generation ( ) ( ) u ν e SM spin 1 2 d e Gauge Bosons ( spin 1): W ±, Z 0 g(gluons) γ( photon) Higgs ( spin 0) H 0 up quark (u) and down quark (d) do not exist as free particles but are bound inside hadrons. Q(u) = 2 3 e Q(d) = 1 3 e Q(e) = e Q(ν e ) = 0 Beyond Standard Model Effects in Flavour Physics: p.3

4 Bound States: Baryons and Mesons Baryons are qqq bound states: e.g. proton, neutron.. Quarks inside the baryons are held together by the strong force which arise from the exchange of gluons Beyond Standard Model Effects in Flavour Physics: p.4

5 Bound States: Baryons and Mesons Mesons are q q bound states: e.g. pions. Hadrons= Baryons + Mesons Beyond Standard Model Effects in Flavour Physics: p.5

6 Bound States: Nucleus Nucleus is a bound states of proton and neutron held together by the strong force. Inter nucleon force is also a colour force. Beyond Standard Model Effects in Flavour Physics: p.6

7 Bound States: Atoms Atom is a bound states of nucleus and electrons held together by the electromagnetic force. Atom m Nucleus m p,n m quark, electron m Beyond Standard Model Effects in Flavour Physics: p.7

8 Weak Interactions Quarks and Leptons also experience the the weak force Two kinds of Weak Interactions: Charged Current: through the exchange of W ( ) ( ) ± u ν e SM spin 1 2 d e W + W u d d u W + W ν e e ν Beyond Standard Model Effects in Flavour Physics: p.8

9 Beta Decay W + W u d d u W + W ν e e ν n d u p d anti ν W e u n pe ν : beta decay Beyond Standard Model Effects in Flavour Physics: p.9

10 Neutral Current Interactions Neutral Current Interaction are mediated through the exchange of Z 0 e ν and p ν scattering e ν Z _ ν e _ p u u d p ν Z ν Beyond Standard Model Effects in Flavour Physics: p.10

11 Weak Interactions are Different Any quark ( u and d) and lepton ( e and ν e ) can split up into a left handed (LH) and a right handed (RH) piece. u u L + u R p ^ V ^ V s u u u u L R L c c R W ± couple only to LH particles and RH antiparticles. n p + e L + ν er Z 0 couple to both LH particles and RH particles but with different strengths. gluons and photons couple to both LH particles and RH particles with equal strengths. Puzzle: Why are the Weak Interactions different Beyond Standard Model Effects in Flavour Physics: p.11

12 The Higgs( m H < 1 TeV) Quarks and Leptons as well as the weak gauge bosons W ± and Z 0 get masses by interacting with the Higgs boson u R H In SM the neutrino remains massless because there is no ν R W u L H W H Higgs is neutral and has no strong or EM interactions gluons and photons are massless Beyond Standard Model Effects in Flavour Physics: p.12

13 The Particle Masses m e 0.5 MeV m u 5 MeV m d 10 MeV m ν = 0 MeV m W 80 GeV m Z 90 GeV (m p GeV) Puzzle: Higgs boson interaction should result in similar masses for all particle i.e m u m d m e n W m Z Beyond Standard Model Effects in Flavour Physics: p.13

14 Things get more Complicated... There are three generations of quarks and leptons ( ) ( ) I st u(5mev ) ν e (0?) Gen spin 1 2 d(10mev ) e(0.5mev ) II nd Gen ( ) ( ) c(charm, 1.5GeV ) s(strange, 0.2GeV ) ν µ (0?) µ(muon, 0.105GeV ) spin 1 2 III rd Gen ( ) ( ) t(top, 175GeV ) b(bottom, 5GeV ) ν τ (0?) τ(tau, 1.78GeV ) spin 1 2 M III > M II > M I m t 175 GeV m t m W m Z - the only natural quark mass Puzzle:It appears that only the third family is normal the others are abnormal Beyond Standard Model Effects in Flavour Physics: p.14

15 Quark Mixing The quark generations mix- they talk to each other: ( ) u c t 6f lavours 3f amilies d s b W W b V cb c b V ub u W + W + c V cd d t V ts s 9 possible couplings from transition between up-type (u,c,t) and down-type(d,s,b) quarks : V CKM = V ud V us V ub V cd V cs V cb V td V ts V tb V CKM V CKM = 1 V CKM is a Unitary matrix. Beyond Standard Model Effects in Flavour Physics: p.15

16 Flavour Puzzle: Summary Why are there three generations of quarks and leptons- are there more? Why only the top is heavy with m t m W m Z and the other quarks and leptons are light. Why M III > M II > M I Why is there mixing among generations- what is the origin of V CKM? Why are the weak interactions different from the strong and EM interactions? All these puzzles suggest that the SM is not a complete theory. Solution of these puzzles require BSM physics. Beyond Standard Model Effects in Flavour Physics: p.16

17 Higgs problem Higgs mass problem: m H < 1 TeV from probability conservation( Unitarity) Quantum correction to Higgs mass m 2 H = (m2 H ) classical Λ 2 T ev 2 which SM is valid) Λ TeV (Energy scale up to If m H < 1 TeV then natural value of Λ TeV. New Physics will be observed at T ev and observable at LHC. However it is possible that Λ 10 TeV or higher. Fine tuned cancellation between (m H ) classical and Λ can produce the right Higgs mass. NP is unlikely to be seen at LHC! Beyond Standard Model Effects in Flavour Physics: p.17

18 Effective Field Theory e e photon (γ) photon (γ) z,x... Y _ Y p n p n ATOM ATOM [ E = E em 1 + ( E ] em Λ )n Λ M X, M Y... E em ev, and if Λ = M X >> E em then E em Λ is tiny. Beyond Standard Model Effects in Flavour Physics: p.18

19 Effective Field Theory L = L em + Σ n c n ( O n Λ n ) The operators O n are called higher dimensional operators and are only constructed out of fields/particles in L em. However if we can make very precise measurements we can detect the effects of the higher dimensional operators. The effect of Z exchanges can already be detected in atomic physics experiments. Hence the effects of new particles can be detected at low energies without actually creating them. Beyond Standard Model Effects in Flavour Physics: p.19

20 SM- Effective Field Theory The SM is also an effective field theory. L eff = L SM + Σ n c n ( O n Λ n ) The operators O n are only constructed out of fields/particles in L SM. L eff describes physics for E < Λ but when E Λ it gets replaced by ( or matches on to) to the full NP lagrangian L nsm. L nsm is also an effective theory valid to some scale Λ 1. Our description of nature is in terms of a series/tower of effective theories- one replacing the other as one go up in energy. Of course some people claim they already have a TOE(theory of everything)-string theory. Beyond Standard Model Effects in Flavour Physics: p.20

21 Beyond the SM Standard Model (SM) is not a complete theory- expect deviation from the SM Two ways to search from them: First one is High Energy Experiments- Colliders Basic idea: SM is valid up to E TeV and so at around TeV we should discover new particles New particles can be discovered at high energy colliders: e.g. : Tevatron- Chicago Large Hadron Collider (LHC)- at CERN Beyond Standard Model Effects in Flavour Physics: p.21

22 Low Energy Experiment Test the Standard Model (SM) at low energies by making very precise experiments with high data sample. L eff = L SM + Σ n c n ( O n Λ n ) Deviations from the SM will yield information on the effect of higher dimensional operators and hence on the structure of L nsm. On going and planned experiments: BaBar, Belle- B factories LHCb Super B, Neutrino Factories- future From tiny SM deviations in B decays one can find clues and measure parameters of the underlying new physics (A.Datta and D.London) -Rule out many models of new physics Beyond Standard Model Effects in Flavour Physics: p.22

23 Testing the SM - Quark sector Program: Test SM precisely and look for deviation from SM predictions These deviations will provide clues to what lies beyond the SM Charged current Interactions( via W ± ) causes transitions between up type ( u,c,t) and down type (d,s,b) quarks. Are there neutral current flavour changing interactions (FCNC) transitions among the up type ( u,c,t) and down type (d,s,b) quarks: e.g b sγ, gluon, Z t cγ, gluon, Z Beyond Standard Model Effects in Flavour Physics: p.23

24 Beyond Standard Model Effects in Flavour Physics: p.24 Hence these decays are excellent probes of beyond the SM physics FCNC in the SM Program: In the FCNC are very rare and only arise as quantum corrections or Loops and are suppressed by small CKM elements E.g. B φk s ( b sg) Beyond the SM FCNC may occur at tree level or loops and compete with the SM contribution.

25 B φk s -NP models Many NP models can produce deviation from the SM for B φk s In some models the process occurs in loops but is not suppressed by small couplings- in others they arise at tree(classical level)!! Beyond Standard Model Effects in Flavour Physics: p.25

26 Deviations from the SM A very good place to look for deviations from the SM is in CP violating measurements CPV in the SM is large due to a large complex phase in V CKM : CP is not a symmetry or approximate symmetry of Nature. All CPV in SM η - only one phase! SM makes very definite predictions for CPV. Eg CPV in many processes are related. Any New Physics will have new CP phases which are naturally large and will naturally lead to deviations from the SM predictions. Beyond Standard Model Effects in Flavour Physics: p.26

27 CP Violation in the Standard Model In the SM, CP violation is due to a complex phase in the CKM matrix: V CKM λ2 λ Aλ 3 (ρ iη) λ(1 + ia 2 λ 4 η) λ2 Aλ 2 Aλ 3 (1 ρ iη) Aλ 2 1 W W + b V ub u anti b V* ub anti u V ub V ub CP Violation V ub V ub = Im[V ub] η SM: All CP violating effects η ( only one complex phase ) CP violation in various processes are related Beyond Standard Model Effects in Flavour Physics: p.27

28 CP Violation in the Standard Model In the SM, CP violation is due to a complex phase in the CKM matrix: V CKM where λ = λ2 λ Aλ 3 (ρ iη) λ(1 + ia 2 λ 4 η) λ2 Aλ 2 Aλ 3 (1 ρ iη) Aλ 2 1 Note: (i) relative sizes of CKM matrix elements, (ii) large phases occur only in corners: V ub and V td. V CKM Unitarity Triangle: V ud V us V ub e iγ V cd V cs V cb V td e iβ V ts V tb η V ub λv cb γ (ρ,η) α V td λv cb β (1,0) ρ Beyond Standard Model Effects in Flavour Physics: p.28

29 CPV phase in the SM can be probed in B decays: B B (V td ) 2 e 2iβ 2β V ub = V ub e iγ Deviations from the SM values of β or γ will signal NP. Beyond Standard Model Effects in Flavour Physics: p.29

30 CP Violation in the Standard Model SM: Several elements of V CKM are real no CP violation, for e.g B φk s V tb V ts Aλ 2 is real no CP violation in this process. SM makes very specific predictions for CP violation. We have to test them carefully and look for possible deviations from Beyond these Standard predictions. Model Effects in Flavour Physics: p.30

31 NP in B decays? Many NP models can produce deviation from the SM for B φk s, η K s, Kπ - all rare decays in the SM. b ccs η K 0 π 0 K S ω K S φ K 0 f 0 K S π 0 π 0 K S K + K - K 0 K S K S K S sin(2β eff )/sin(2φ e 1ff ) H F A G HEP 2005 PRELIMINARY World Average 0.69 ± 0.03 BaBar 0.50 ± HFAG HEP 2005 HFAG HEP 2005 HEP HFAG 2005 Belle 0.44 ± 0.27 ± 0.05 Average 0.47 ± 0.19 BaBar 0.36 ± 0.13 ± 0.03 Belle 0.62 ± 0.12 ± 0.04 Average 0.50 ± 0.09 BaBar ± 0.10 Belle 0.47 ± 0.36 ± 0.08 Average 0.75 ± 0.24 BaBar ± 0.04 Belle 0.22 ± 0.47 ± 0.08 Average 0.31 ± 0.26 BaBar ± 0.71 ± 0.08 Average ± 0.71 BaBar ± 0.02 HEP HFAG 2005 HFAG HEP 2005 HFAG HEP 2005 HFAG HFAG HEP 2005 Belle 0.95 ± HFAG HEP 2005 HEP Average 0.63 ± 0.30 BaBar 0.41 ± 0.18 ± 0.07 ± 0.11 Belle 0.60 ± 0.18 ± Average 0.51 ± BaBar Belle 2 ± ± 0.36 ± 0.08 Average 0.61 ± L eff = L SM + Σ n c n ( O n Λ n ) Beyond Standard Model Effects in Flavour Physics: p.31

32 Flavour Problem The important question: NP at what scale The contribution of NP operators to meson mixing can be represented by higher dimension operators: c NP ( dq) 2 /Λ 2 where q = s, b. The measurement of the K and the B system tell us that Λ 100 TeV!!! if c NP 1 Note K(B) mixing in SM is small because of loop and small parameters like λ = 0.22 For e.g. B mixing Loop V 2 td and V td λ 3 Beyond Standard Model Effects in Flavour Physics: p.32

33 But we expect Λ T ev to stabilize the Higgs mass! c NP has the same suppression as in the SM so Λ TeV strong constraints on the flavour structure of NP expected to be revealed at LHC. or if c NP 1 then flavour physics probes physics at scales way beyond the reach of present or future experiments. Beyond Standard Model Effects in Flavour Physics: p.33

34 Testing the SM - Lepton sector In the SM the neutrino is massless. The neutrino is purely left handed ν L. Mass term is ν L ν R Experiments have now confirmed non zero neutrino masses and mixing- Clear evidence of BSM Physics! Like quarks the leptons have mixing among the three families: V CKM represents the mixing in the quark sector while U MNS represent the mixing in the lepton sector. Neutrino Oscillations : Neutrinos that are produced in reactions( gauge eigenstates are not mass(energy) eigenstates. The two are related by the U MNS matrix [ν] gauge = [U MNS ][ν] mass Beyond Standard Model Effects in Flavour Physics: p.34

35 Neutrino Oscillations- 2 flavour Case ν e (t = 0) > = ν 1 > cos θ + ν 2 > sin θ ν µ (t = 0) > = ν 1 > sin θ + ν 2 > cos θ ν e (t) > = ν 1 > cos θe ie 1t + ν 2 > sin θe ie 2t ν µ (t) > = ν 1 > sin θe ie 1t + ν 2 > cos θe ie 2t E i = m 2 i + p2 p + m2 i 2E Beyond Standard Model Effects in Flavour Physics: p.35

36 Neutrino Oscillations- 2 flavour Case P νe ν e = < ν e ν e (t) > 2 = 1 sin 2 2θ sin 2 [ m2 4E t] P νe ν µ = < ν e ν µ (t) > 2 = sin 2 2θ sin 2 [ m2 4E t] Observation of oscillations established θ 0 (mixing) and m 2 = m 2 2 m 2 1 0( non zero mass). L osc = 4πE m 2 Experiments are set up such that length of source to detector is L L osc. Different experiments have different E and are sensitive to different ranges of m 2. Beyond Standard Model Effects in Flavour Physics: p.36

37 Neutrino Oscillations- General U P MNS = c 12 c 13 s 12 c 13 s 13 e iδ s 12 c 23 c 12 s 23 s 13 e iδ c 12 c 23 s 12 s 23 s 13 e iδ s 23 c 13 K s 12 s 23 c 12 c 23 s 13 e iδ c 12 s 23 c 12 c 23 s 13 e iδ c 23 c 13 where K = diag(1, e iφ 1, e iφ 2 ), s ij = sin θ ij, c ij = cos θ ij. Solar neutrino- from the sun, E 1MeV tan 2 θ 12 = 0.45 θ m 2 = ev 2 Beyond Standard Model Effects in Flavour Physics: p.37

38 Neutrino Oscillations- General Atmospheric neutrino- Produced by cosmic rays at upper atmosphere, E 1GeV sin 2 θ 23 = 0.44 θ m 2 = ev 2 θ 13 is small and only has constraints( reactor angle). δ- CPV phase not measured. Leptonic Mixing is large unlike quark mixing. Eg, compare to the quark mixing sin θ 23 = Mixing in the lepton and the quark sectors are very different!!! Puzzle. Beyond Standard Model Effects in Flavour Physics: p.38

39 Neutrino Masses L eff = L SM + Σ n c n ( O n Λ n ) L HD = Z ij Λ HHL il j M ij Z ij m 2 t Λ m ν = 1eV, Z ij 1, then Λ GeV - energy scale beyond any present or future colliders. The Λ represents the mass of new particles- e.g. mass of a heavy sterile neutrino which mixes with the ordinary neutrinos -Seesaw mechanism. Other possibilities- new scalars. Beyond Standard Model Effects in Flavour Physics: p.39

40 CONCLUSIONS SM leaves many questions about quarks and leptons and Higgs unanswered. Deviation from the SM can be observed by producing new particles at colliders or looking for small deviations at low energies. Hints of deviation from the SM in the quark sector. In the neutrino sector we have already established deviation from SM though the measurement of neutrino masses and mixing. Effects of NP observed in flavour physics will help us understand the physics of new particles discovered in colliders- in some cases they can tell us about physics not accessible at present or future colliders. Beyond Standard Model Effects in Flavour Physics: p.40