Baryon and Lepton Number Violation at the TeV Scale

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1 Baryon and Lepton Number Violation at the TeV Scale S. Nandi Oklahoma State University and Oklahoma Center for High Energy Physics : S. Chakdar, T. Li, S. Nandi and S. K. Rai, arxiv: [hep-ph] (Phys. Lett.B718(2012) ), and S. Chakdar, T. Li, S. Nandi and S. K. Rai, (in preparation) Talk at Miami, 2012.

2 Motivation and Goals: To unify quarks and leptons at TeV scale. Have lepto-quark and diquark gauge bosons belonging to a non-adjoint representation of the SM gauge symmetry. To look for baryon and lepton number violating interactions, and explore other phenomenological implications of such an unification at the LHC.

3 Outline of Talk Introduction Models and the Formalism Phenomenological Implications Conclusions and Outlook

4 Introduction In SM, baryon and lepton numbers are accidental global symmetries at the renormalizable level. No fundamental reason for B and L to be exact symmetries. In SM, L number is violated by SM gauge invariant dimension 5 operators. [Weinberg, 1979] In SM, B number is violated by SM gauge invariant dimension 6 operators. [Weinberg, 1979; Wilczek and Zee, 1979] If the ultraviolate mass scale is the Planck s scale, then the generated neutrino masses are too small. Also proton decay rate is too small to be observed.

5 Introduction Stability of the proton was first questioned by Pati and Salam (1973). They proposed SU(4) SU(2) L SU(2) R gauge symmetry in which lepton number is the 4th color. The model has leptoquark gauge bosons that do not cause proton decay. However, they cause K L µe transition : d e, s µ + via leptoquark gauge bosons exchange [Valencia and Willenbrock, 1994] Current limit on B(K L µe) = This gives M LQ > 2300 TeV Beyond the reach of LHC.

6 Introduction Minimal GUT unifying the three SM gauge interactions was proposed by Georgi and Glashow(1973). However, three SM gauge couplings do not unify in non-supersymmetrc SU(5). Also the model has leptoquark and diquark gauge bosons, X and Y which cause proton decay: p e + π 0. Current limit on proton lifetime for this mode years. This give M X, M Y > GeV. Same is true for non-supersymmetric SO(10) GUT.

7 Introduction Leptoquark search at the 7 TeV LHC CMS Collaboration with 36pb 1 of data looked for pair production of leptoquark and each decaying to l q (l = e or µ, and q being a jet) M LQ > 384 GeV. Corresponding limit for the 2nd generation of leptoquark is M LQ > 632 GeV by CMS Collaboration with 2fb 1 of data, M LQ > 685 GeV by ATLAS Collaboration with 1.03fb 1 of data. For 3rd generation of leptoquark, the limits are M LQ > 350 GeV at 95 % CL, by CMS, for LQ decaying to b ν mode with 1.8fb 1 of data. For leptoquark decays to 3rd generation, the limit is very low. In particular, LQ bτ or tt have not been looked for.

8 Model and the formalism Our gauge symmetry is SU(5) SM where SM = SU(3) C SU(2) L U(1) Y. We call it a top SU(5) model. First two families of the SM fermions are charged under SM and singlet under the SU(5), while the third family is charged under SU(5) and singlet under SM. The SM gauge couplings are given by 1 gj 2 = 1 g (g j, 1 1 )2 gy 2 = (g5 Y + 1 )2 (g Y. )2 with j = 1, 2, 3. Thus no unification of the SM couplings is needed. Gives a mechanism for baryon and lepton number violation which is needed for the baryon assymetry of the universe and not present in the SM.

9 Our Model and the formalism Our model is a GUT version of Topcolor and Topflavor model in which the 3rd family is treated differently. TOPCOLOR : SU(3) SU(3) SU(2) L U(1) Y (Hill, 1991) TOPFLAVOR : SU(3) c SU(2) L SU(2) L U(1) Y (Muller and Nandi, 1995) Symmetry Breaking in our Model SU(5) SU(3) C SU(2) L U(1) Y is broken down to the SM gauge symmetry SU(3) C SU(2) L U(1 Y via Higgs mechanism. The theory is unitary and renormalizable

10 Particle content of the model Particles Quantum Numbers Particles Quantum Numbers Q i (1; 3, 2, 1/6) L i (1; 1, 2, 1/2) Ui c (1; 3, 1, 2/3) Nk c (1; 1, 1, 0) Di c (1; 3, 1, 1/3) Ei c (1; 1, 1, 1) F 3 (10; 1, 1, 0) f 3 ( 5; 1, 1, 0) H (1; 1, 2, 1/2) Φ ( 5; 1, 1, 0) U T (5; 3, 1, 1/3) U D (5; 1, 2, 1/2) XT (1; 3, 1, 1/3) XU (10; 1, 1, 1) Xf (5; 1, 1, 0) Xf ( 5; 1, 1, 0) XD (1; 3, 1, 1/3) XD (1; 3, 1, 1/3) XL (1; 1, 2, 1/2) XL (1; 1, 2, 1/2) Table: The complete particle content and the particle quantum numbers under SU(5) SU(3) C SU(2) L U(1) Y gauge symmetry in the top SU(5) model. Here, i = 1, 2 and k = 1, 2, 3.

11 Symmetry breaking The Higgs potential breaking the gauge symmetry is given by V = m 2 T UT 2 m 2 D UD 2 + λ T UT λ D UD λ T D UT 2 UD 2 [ + A T ΦU T XT + A D ΦU D H + y ] T D UT 3 UD 2 + H.C., M where < U T >= v T ( I ), < U D >= v D ( 03 2 I 2 2 We assume that V T and V D are in the TeV scale. The masses of the gauge bosons are (D µ U i ) D µ U i = 1 ( ) 2 2 v2 T g 5 Â a3 µ g 3Ãa3 µ i=t,d v2 D g2 5 ( g 5 Â a2 µ g 2Ãa2 µ ) ( 2 v 2 + T 3 + v2 D 2 ( v 2 T + vd 2 ) ( ) Xµ X µ + Y µ Y µ, ) ) ( ) 2 g5 Y Âa1 µ g Y Ãa1 µ,

12 Yukawa couplings L = y u iju c i Q j H + y ν kj N c k L j H + y d ijd c i Q j H +y e ije c i L j H + y u 33F 3 F 3 Φ + y d,e 33 F 3f 3 Φ +y ν k3 N c k f 3Φ + m N kl N c k N c l + H.C., Choose a basis in which up quark mass marix is diagonal. So no mixing between u,c,t. CKM mixing arises from purely down quark sector Need mixing between the first two families and the 3rd family. Done by using dimension 5 operators generated by the fields in the model via renormalizable interaction.

13 CKM mixing The dimension 5 interactions are generated at the renormalizable level by using the vector-like fermions (Xf, XD, XL) with masses 1, 000 TeV. This gives M 1, 000 TeV. L = 1 (y M i3d d i c F 3 ΦU T + ye i3ei c f 3 HU D ) +y3if d 3 Q i HU T + y3if e 3 L i ΦU D + H.C. Correct CKM mixing is generated using M 1, 000 TeV

14 Phenomenological implications Leptoquark gauge bosons X and Y can be pair produced at the LHC via QCD strong interactions. gg X X, Y Ȳ, q q X X, Y Ȳ X and Y subsequently decays to X bτ +, t t; X bτ, t t,y bν τ,y tτ +, tb Consider signal from X X production ( bτ + )(bτ ) Both b and τ can be tagged, so the resonance X in the bτ mode can be reconstructed. [Fig 1] Dominant SM background :pp 2b2τ, 4b, 2j2b, 4j, t t Easily eliminated using suitable cuts.

15 X reonance in the bτ mode at 8 TeV and 7 TeV LHC d /dm b (fb/gev) (b) 2.5 SM ( - b 1 ) Signal ( - b 1 ) Signal ( - b 2 ) 2 SM ( - b 2 ) d /dm b (fb/gev) (b) SM*1e4 ( - b 1 ) Signal ( - b 1 ) Signal ( - b 2 ) SM*1e4 ( - b 2 ) M b (GeV) M b (GeV) Invarint mass distribution for the bτ channel for M X = 800 GeV at 8 TeV LHC and M X = 600 GeV at 7 TeV LHC. Cuts used: p T > 80GeV, η < 2.5, R > 0.2 Also used efficiency for b and τ tagging to be 0.5, mistag rate for light quark 1%, for charmed quark 10%. Also shown are the corresponding backgrounds. Note that for the 600 GeV case, the background has been multiplied by 10.

16 Leptoquark signal at LHC To prove baryon and lepton violation, X need to be reconstructed also in the (t t) mode in addition to the (bτ) mode to show that it is a leptoquark as well as a diquark, and hence baryon and lepton number violating. For heavier leptoquark, one can look for the final state signals such a b bττ, b bν τ ν τ etc. For 8 TeV LHC, our model gives 5 sigma signals events for mass as high as 800 GeV.

17 5σ Reaches for the Leptoquarks in our model at the LHC Reach for b bτ + τ mode At 8 TeV, with luminosities of 10, 20, 30fb 1, the reaches are 620, 660, 680 GeV respectively. At 14 TeV, with luminosities of 30, 100, 300fb 1, the reaches are 1040, 1140, 1240 GeV respect Reach for b bν τ ν τ mode At 8 TeV, with luminosities of 10, 20, 30fb 1, the reaches are 720, 760, 780 GeV respectively. At 14 TeV, with luminosities of 30, 100, 300fb 1, the reaches are 1100, 1200, GeV respectively

18 Summary and Conclusions Presented TeV scale modesl for quark lepton unification in 4 dimensions. Has leptoquark gauge bosons X and Y coupling only to the 3rd family of fermions, and hence produces B and L violation only involving the 3rd family Can be observed as (bτ) and (t t) resonance at the LHC At the 8 TeV LHC, with 30fb 1 luminosity, the discovery reach is 800 GeV. Latest experimental limit from LHC Search for Leptoquark in the bτ mode : CMS-PAS-EXO (CMS Collaboration) M LQ 760 GeV at 95 percent CL