Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks Investigating Beyond Standard Model Joydeep Chakrabortty Physical Research Laboratory TPSC Seminar, IOP 5th February, 2013 1 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks Standard Model – A Brief Tour Why BSM ? BSM Classification – How do we look into this? Low Scale & High Scale Models. Conclusions 2 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks Standard Model (SM) is now well established as a valid theory of Particle Physics at low energy ∼ 100 GeV (1 GeV ∼ mass of proton). Precision matching of SM’s predictions and experimental observations is spectacular – Discovery of Higgs Scalar ( ? ) (SM is broken spontaneously once Higgs acquires vacuum expectation value – Higgs mechanism). Symmetry Groups Quarks Leptons Scalars (Higgs) Gauge Bosons SU (3) C 3( 3 ) 1 1 Gluon SU (2) L 2(1) 2(1) 2 W U (1) Y NON-ZERO NON-ZERO NON-ZERO B Is it a complete theory? What about Neutrino mass, Dark matter, Baryon Asymmetry of the Universe, and other aesthetic issues, like Unification, Fine tuning ? 3 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks Some recent important issues Both ATLAS and CMS have found a new boson around 122-127 GeV – seems to be SM Higgs. If it is so then its Stability criterion must be adjudged – RGE of Higgs Quartic Coupling λ . New physics includes exotic scalars, fermions, and may have extended gauge sector. The new particles that couple to SM Higgs will affect the RGE of λ – Vacuum Stability must be reexamined. Higgs to di-photon rate – impact on the BSM parameters. The light charged particles (Fermions or Bosons) that couple to SM Higgs and Photon will lead to extra contribution to H → γγ process. Moderate θ 13 can have different impact. Many conclusions in the context of Lepton Flavour Violation (LFV) and Neutrinoless Double Beta Decay ( 0 ννβ ) might be changed. 4 / 35
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Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks Low Energy Models Low energy Model – TeV Scale? Why? Within the reach of the present experiments, like LHC. Either High Scale motivated or Simple Extension (either by particle or symmetry group(s)) of the SM. Left-Right Symmetry – motivated from High scale, where parity symmetry is spontaneously broken. 6 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks PLAN To start with ... What is Left-Right symmetry? Any connection with high scale physics? What is the scale of this theory? Neutrino Mass generation through Type-(I+II) seesaw 0 νββ in LR model at Neutrino Experiments and at the LHC Impact of low energy data on the parameters of this model 7 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks Model Left-Right Symmetry A discrete symmetry that connects Left & Right sector Generic Structure is: SU ( N ) L ⊗ SU ( N ) R Example: SU (2) L ⊗ SU (2) R ⊂ SO (10) SU (3) L ⊗ SU (3) R ⊂ E (6) We will talk about: SU (3) C ⊗ SU (2) L ⊗ SU (2) R ⊗ U (1) B − L Gauge group. SM Extended by: a right-handed neutrino( ν R ), a bidoublet( Φ ), and two triplet Higgs fields( ∆ L/R ) Φ ≡ (2 , 2 , 0) , ∆ L ≡ (3 , 1 , 1) , ∆ R ≡ (1 , 3 , 1) 8 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks Neutrino Mass in LR Model Neutrino Mass generation Few new terms along with the SM Lagrangian: f L l T L Ciσ 2 ∆ L l L + f R l T L = R Ciσ 2 ∆ R l R ¯ l R ( y D Φ + y L ˜ + Φ) l L + V scalar (Φ , ∆ L/R ) Neutral fermion mass matrix: � f L v L � y D v M ν ≡ , y T D v f R v R where < ∆ L > = v L , < ∆ R > = v R . Using the seesaw approximation ( f R v R >> y D v ) we get ) 3 × 3 = f L v L + v 2 ( m light v R y T D f − 1 R y D , ν ( m heavy ) 3 × 3 = f R v R , R (JC, ZD, SG, SP; JHEP 1208 (2012) 008) 9 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks 0 νββ Neutrinoless Double beta decay( 0 νββ ) → ( A, Z + 2) + 2 e − ( A, Z ) − Limit on half-life: T 1 / 2 < 3 × 10 25 yrs (Heidelberg-Moscow experiment using 76 Ge ) Bound on the effective neutrino mass: m eff � 0 . 21 − 0 . 53 eV Artifact of process like Lepton Number Violation (LNV) by two units Sources: Seesaw models / R-parity Violating SUSY etc. Signals to the presence of “Majorana” nature of neutrinos 10 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks 0 νββ In the standard three generation picture the time period for neutrinoless double beta decay is given as, � � 2 Γ M ν � � | m ee ν | 2 , ln 2 = G � � � m e � where G contains the phase space factors, m e is the electron mass, M ν is the nuclear matrix element. | m ee ν | = | U 2 ei m i | , is the effective neutrino mass that appear in the expression for time period for neutrinoless double beta decay The unitary matrix U is the so called PMNS mixing matrix 11 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks 0 νββ Diagrams contributing to 0 νββ in LR model; (JC, ZD, SG, SP; JHEP 1208 (2012) 008) n p n p W L W L e − e − L L ν i N i e − e − L L W L W L p p n n ( a ) ( b ) Contribution from light and heavy Majorana neutrino intermediate states from two W L exchange p p n n W R W R e − e − R R ν i N i e − e − R R W R W R p p n n ( a ) ( b ) Contribution from light and heavy Majorana neutrinos from two W R exchange 12 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks 0 νββ Diagrams contributing contd. (JC, ZD, SG, SP; JHEP 1208 (2012) 008) n p n p W L W L e − e − L L ν i N i e − e − R R W R W R p p n n ( a ) ( b ) Contribution from light and heavy Majorana neutrino intermediate states from W L and W R exchange n p n p W R W L e − e − L R ∆ −− ∆ −− L R e − e − W L L W R R p p n n Contribution from the charged Higgs intermediate states from W L and W R exchange 13 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks 0 νββ Charged Current interactions of leptons: 3 � g � � ℓ α L γ µ { ( U L ) αi ν Li + ( T ) αi N c Ri } W µ √ L CC = L 2 α = e,µ,τ i =1 � + ℓ α R γ µ { ( S ) ∗ αi ν c Li + ( U R ) ∗ αi N Ri } W µ + h.c. R where complete unitary mixing matrix, U is: � (1 − 1 � U L � � 2 RR † ) U ′ R U ′ T L R U = = − R † U ′ (1 − 1 2 R † R ) U ′ S U R L R with R = m † D M − 1 ∗ R (JC, ZD, SG, SP; JHEP 1208 (2012) 008) 14 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks 0 νββ The half-life is, � M i + p 2 M 4 U ∗ 2 = G |M ν | 2 p 2 T 2 Γ 0 νββ � � U 2 e i W L R e i L e i m i + � ln 2 m 2 M 4 M i � e W R + M 4 M 2 W L W L S ∗ 2 U L e i S ∗ e i m i + e i m i M 4 M 2 W R W R �� + p 2 M 2 T e i U ∗ p 2 M 4 2 + U 2 Lei m i m 2 U 2 Rei M i � W L R e i W L e + � M 2 M 2 M 4 M 2 M i � W R ∆ L W R ∆ R p 2 carries the informations about the Nuclear matrix elements and virtual momentum transfer (JC, ZD, SG, SP; JHEP 1208 (2012) 008) 15 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks 0 νββ For our analysis we consider two cases: (JC, ZD, SG, SP; JHEP 1208 (2012) 008) Type-I dominance : v 2 m light v R y T D f − 1 y D = ν m heavy = fv R R With a harmless choice ( y D is ∝ Identity matrix) we have the light & heavy neutrino mass relation: m i ∝ 1 /M i ⇒ followed from LR-symmetry Type-II dominance : m light = f L v L ν m heavy = f R v R R As an artifact of LR-symmetry ⇒ light & heavy neutrino masses are related as: m i ∝ M i 16 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks 0 νββ We did consider the following zones (JC, ZD, SG, SP; JHEP 1208 (2012) 008): Normal hierarchy (NH) refers to the arrangement which corresponds to m 1 < m 2 << m 3 with � � m 2 1 + ∆ m 2 m 2 1 + ∆ m 2 atm + ∆ m 2 m 2 = sol , m 3 = sol Inverted hierarchy (IH) implies m 3 << m 1 ∼ m 2 with � � m 1 = m 2 3 + ∆ m 2 atm , m 2 = m 2 3 + ∆ m 2 sol + ∆ m 2 atm � ∆ m 2 Quasi degenerate neutrinos correspond to m 1 ≈ m 2 ≈ m 3 >> atm 17 / 35
Outline Standard Model BSM Classification Low Energy Models High Scale Model Remarks 0 νββ The 3 σ ranges of the mass squared differences and mixing angles from global analysis of oscillation data parameter best-fit 3 σ ∆ m 2 sol [10 − 5 eV 2 ] 7.58 6.99-8.18 | ∆ m 2 atm | [10 − 3 eV 2 ] 2.35 2.06-2.67 sin 2 θ 12 0.306 0.259-0.359 sin 2 θ 23 0.42 0.34-0.64 sin 2 θ 13 0.021 0.001-0.044 sin 2 θ 13 for: Daya − Bay : 0 . 023 (best − fit) , 0 . 009 − 0 . 037 (3 σ range) RENO : 0 . 026 (best − fit) 0 . 015 − 0 . 041 (3 σ range) 18 / 35
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