Gauge Theories for Baryon Number.

Transcription

1 Gauge Theories for Baryon Number. Michael Duerr International Workshop on Baryon and Lepton Number Violation 2017 (BLV 2017) Case Western Reserve University, 18 May 2017

2 Thanks to my collaborators. This talk is based on arxiv: [hep-ph], arxiv: [hep-ph], arxiv: [hep-ph], arxiv: [hep-ph], arxiv: [hep-ph], arxiv: [hep-ph], arxiv: [hep-ph] together with Pavel Fileviez Pérez (CWRU), Manfred Lindner (MPIK), Juri Smirnov (INFN and University Firenze), Mark B. Wise (Caltech) Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 2

3 The Standard Model of particle physics. > Standard Model gauge group: G SM = SU(3) C SU(2) L U(1) Y Field SU(3) C SU(2) L U(1) Y U(1) B U(1) L Q L 3 2 1/6 1/3 0 R 3 1 2/3 1/3 0 d R 3 1 1/3 1/3 0 l L 1 2 1/2 0 1 e R H 1 2 1/ Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 3

4 Baryon number. > Standard Model: > accidental global symmetry of the renormalizable couplings (broken by non-perturbative quantum effects) > stable p and no n n oscillations in the renormalizable SM > Generic GUT: > proton decay due to new gauge interactions > if quarks and leptons in the same multiplet one cannot define baryon number > What do we know about violation of B? [Figure: Viren, arxiv:hep-ex/ ] > Baryon asymmetry of the Universe: γ (n B n B )/n γ > Proton decay (ΔB = 1, ΔL = odd): γ π 0 P + e τ p years Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 4

5 Side remark: lepton number. > Lepton number L conserved at the renormalizable level in the Standard Model as well > What do we know about violation of L? > ν oscillation experiments: ΔL e = 0, ΔL μ = 0, ΔL τ = 0 > ΔL = 2: Majorana neutrino masses (test with 0νββ) [Figure: Mohapatra et al., arxiv:hep-ph/ ] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 5

6 The desert of particle physics. c6 Λ2B QQQL [Weinberg, PRL 43 (1979) 1566] High scale e.g. GUT scale (Λ 1015 GeV) Low scale Electroweak scale (ΛEW 102 GeV) [Figure: Wikipedia] Energy Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 6

7 The desert of particle physics. c6 Λ2B QQQL [Weinberg, PRL 43 (1979) 1566] High scale e.g. GUT scale (Λ 1015 GeV) Low scale Electroweak scale (ΛEW 102 GeV) [Figure: Wikipedia] Energy Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 6

8 The desert of particle physics. c5 ΛL LLHH c6 Λ2B QQQL [Weinberg, PRL 43 (1979) 1566] High scale e.g. GUT scale (Λ 1015 GeV) Low scale Electroweak scale (ΛEW 102 GeV) [Figure: Wikipedia] Energy Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 6

9 The desert of particle physics. c5 ΛL LLHH c6 Λ2B QQQL [Weinberg, PRL 43 (1979) 1566] High scale e.g. GUT scale (Λ 1015 GeV) Low scale Electroweak scale (ΛEW 102 GeV) [Figure: Wikipedia] Energy Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 6

10 The desert of particle physics. c5 ΛL LLHH c6 Λ2B QQQL [Weinberg, PRL 43 (1979) 1566] High scale e.g. GUT scale (Λ 1015 GeV) Low scale Electroweak scale (ΛEW 102 GeV) [Figure: Wikipedia] Energy Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 6

11 The Standard Model of particle physics. > Standard Model gauge group: G SM = SU(3) C SU(2) L U(1) Y Field SU(3) C SU(2) L U(1) Y U(1) B U(1) L Q L 3 2 1/6 1/3 0 R 3 1 2/3 1/3 0 d R 3 1 1/3 1/3 0 l L 1 2 1/2 0 1 e R H 1 2 1/ Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 7

12 The Standard Model of particle physics. > Extension of the SM gauge group: SU(3) C SU(2) L U(1) Y U(1) B U(1) L Field SU(3) C SU(2) L U(1) Y U(1) B U(1) L Q L 3 2 1/6 1/3 0 R 3 1 2/3 1/3 0 d R 3 1 1/3 1/3 0 l L 1 2 1/2 0 1 e R H 1 2 1/ Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 7

13 The Standard Model of particle physics. > Extension of the SM gauge group: SU(3) C SU(2) L U(1) Y U(1) B U(1) L Field SU(3) C SU(2) L U(1) Y U(1) B U(1) L Gauge theories for B (and L) Q L 3 2 1/6 1/3 0 How to define a realistic theory R 3 1 2/3 1/3 0 where B (and L) are local gauge d R 3 1 1/3 1/3 0 symmetries that can be broken at l L 1 the low 2 (TeV) 1/2 scale? 0 1 e R H 1 2 1/ Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 7

14 Some history. Phys. Rev. 98, 1501 (1955) > heavy particle (= neutrons and protons) gauge transformation: ψ N e α ψ N, ψ P e α ψ P > massless vector boson: gauge coupling must be tiny (α B ) Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 8

15 Some history. Phys. Rev. D 8, 1844 (1973) > Use the Higgs mechanism to break B! Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 9

16 Some history. > Early discussions of gauging B (and L): anomaly cancellation, introduction of new fermions, properties of the gauge boson... > S. Rajpoot, Int. J. Theor. Phys. 27, 689 (1988) > R. Foot, G. C. Joshi, H. Lew, PRD 40, 2487 (1989) > C. D. Carone, H. Murayama, PRD 52, 484 (1995) > H. Georgi, S. L. Glashow, PLB 387, 341 (1996) > First realistic model (sequential/mirror family with B = ±1) > P. Fileviez Pérez, M. B. Wise, PRD 82, (2010) Ruled out: new chiral quarks get mass from SM Higgs change gluon fusion Higgs production + Landau poles > This talk will focus on the following models: > P. Fileviez Pérez, M. B. Wise, JHEP 08 (2011) 068 > MD, P. Fileviez Pérez, M. B. Wise, PRL 110 (2013) > P. Fileviez Pérez, S. Ohmer, H. H. Patel, Phys. Rev. D 90 (2014) Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 10

17 Features of these models. > Framework for the spontaneous breaking of local baryon number at the low scale in agreement with experiments. > Proton is stable (or long-lived) think about the possibility of low-scale unification. > Vector-like fermions F with baryon number to cancel anomalies (with or without color). > Cold dark matter candidate χ: lightest neutral field in the new sector. > Leptophobic gauge boson coupling to SM quarks and new fermions: Z B qq, χχ, FF > New Higgs Boson h B qq, Z B Z B, FF > Connection between the DM and baryon asymmetries. Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 11

18 Outline. > Local baryon number > Baryonic dark matter > Baryon asymmetry > Collider signatures > Towards low-scale unification > Summary Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 12

19 Anomaly cancellation. > New gauge group: Field SU(3) SU(2) U(1)Y U(1)B U(1)L SU(3) SU(2) U(1) Y U(1) B > Baryonic anomalies: A 1 SU(3) 2 U(1) B, A 2 SU(2) 2 U(1) B, A 3 U(1) 2 Y U(1) B, A 4 U(1) Y U(1) 2 B, A 5 (U(1) B ), A 6 U(1) 3 B. 1 3 QL R dr νr er H U(1) B Standard Model SU(2) L SU(2) L A 2 = A 3 = 3 2 > New fermions needed to cancel non-trivial anomalies > A 1 = 0 simplest solution: colorless fields Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 13

20 How many new fermion multiplets?. > Two fermion multiplets Ψ L (1, N, Y 1, B 1 ) and Ψ R (1, M, Y 2, B 2 ) > A 5 (U(1) B ) = 0 requires B 1 = MB 2 /N > Then A 6 U(1) 3 = 0 requires M = N and B B 1 = B 2 > A 2 SU(2) 2 U(1) B cannot be canceled > No solution with two new fermion multiplets [Fileviez Pérez, Ohmer, Patel, arxiv: ] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 14

21 How many new fermion multiplets?. > Three fermion multiplets L (1, N, Y, B 1 ), R (1, N, Y, B 2 ), and χ L (1, M, 0, B 3 ) > Anomaly cancellation requires M = 2N, Y 2 = N 2 /4, B 1 = B 2 = B 3 = 3/N 3 > χ L : fermions with fractional electric charge that cannot decay to SM particles > more general assignments lead to same conclusion > consistent with anomaly cancellation but in conflict with cosmology [Fileviez Pérez, Ohmer, Patel, arxiv: ] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 14

22 How many new fermion multiplets?. > Three fermion multiplets L (1, N, Y, B 1 ), R (1, N, Y, B 2 ), and χ L (1, M, 0, B 3 ) > Anomaly cancellation requires M = 2N, Y 2 = N 2 /4, B 1 = B 2 = B 3 = 3/N 3 > χ L : fermions with fractional electric charge that cannot decay to SM particles > more general assignments lead to same conclusion > consistent with anomaly cancellation but in conflict with cosmology [Fileviez Pérez, Ohmer, Patel, arxiv: ] Anomaly cancellation = phenomenologically viable model Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 14

23 Solution with four fermion multiplets. Ψ L 1, 2, 1 2, 3, Ψ R 1, 2, 1 2 2, 3 2 L 1, 3, 0, 3, χ L 1, 1, 0, [Fileviez Pérez, Ohmer, Patel, arxiv: ] [Ohmer, Patel, arxiv: ] > No fractional charges in the particle spectrum > particle content allows for vector-like masses > Majorana dark matter candidate Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 15

24 A very general solution. All anomalies can be cancelled with the following setup: Field SU(3) SU(2) U(1) Y U(1) B Ψ L N 2 Y 1 B 1 Ψ R N 2 Y 1 B 2 η R N 1 Y 2 B 1 η L N 1 Y 2 B 2 χ R N 1 Y 3 B 1 χ L N 1 Y 3 B 2 Anomaly cancellation demands: B 1 B 2 = 3/(Nn F ), Y 2 = Y 1 1/2 and Y 3 = Y 1 ± 1/2 [Fileviez Pérez, Wise, arxiv: [hep-ph]] [MD, Fileviez Pérez, Wise, arxiv: [hep-ph]] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 16

25 Possible scenarios. Guidelines: > new fields should have direct coupling to SM fields, or > the lightest new particle is neutral and stable. Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 17

26 Possible scenarios. Guidelines: > new fields should have direct coupling to SM fields, or > the lightest new particle is neutral and stable. > N = 1: Use Y 1 = ±1/2, Y 2 = ±1, Y 3 = 0 lightest new fermion can be neutral and a DM candidate Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 17

27 Possible scenarios. Guidelines: > new fields should have direct coupling to SM fields, or > the lightest new particle is neutral and stable. > N = 1: Use Y 1 = ±1/2, Y 2 = ±1, Y 3 = 0 lightest new fermion can be neutral and a DM candidate > N = 3: use at least one hypercharge as for the SM quarks > Scenario I: Y 1 = 1/6, Y 2 = 2/3, Y 3 = 1/3 > Scenario II: Y 1 = 5/6, Y 2 = 4/3, Y 3 = 1/3 > Scenario III: Y 1 = 7/6, Y 2 = 5/3, Y 3 = 2/3 n F = 3: dimension-9 operator for proton decay suppressed, even if cutoff of the theory not very large Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 17

28 Possible scenarios. Guidelines: > new fields should have direct coupling to SM fields, or > the lightest new particle is neutral and stable. > N = 1: Use Y 1 = ±1/2, Y 2 = ±1, Y 3 = 0 lightest new fermion can be neutral and a DM candidate > N = 3: use at least one hypercharge as for the SM quarks > Scenario I: Y 1 = 1/6, Y 2 = 2/3, Y 3 = 1/3 > Scenario II: Y 1 = 5/6, Y 2 = 4/3, Y 3 = 1/3 > Scenario III: Y 1 = 7/6, Y 2 = 5/3, Y 3 = 2/3 n F = 3: dimension-9 operator for proton decay suppressed, even if cutoff of the theory not very large > N = 8: interesting but non-minimal Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 17

29 Simplest scenario. Consider only uncolored fields: Field SU(3) SU(2) U(1) Y U(1) B Ψ L 1 2 ± 1 2 B 1 Ψ R 1 2 ± 1 2 B 2 η R 1 1 ±1 B 1 η L 1 1 ±1 B 2 χ R B 1 χ L B 2 Anomaly cancellation demands: B 1 B 2 = 3 [MD, Fileviez Pérez, Wise, arxiv: ] [MD, Fileviez Pérez, arxiv: ] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 18

30 What about lepton number. > New gauge group: SU(3) SU(2) U(1) Y U(1) B U(1) L > Purely baryonic anomalies: A 1 SU(3) 2 U(1) B, A 2 SU(2) 2 U(1) B, A 3 U(1) 2 Y U(1) B, A 4 U(1) Y U(1) 2 B, A 5 (U(1) B ), A 6 U(1) 3 B > Purely leptonic anomalies: A 7 SU(3) 2 U(1) L, A 8 SU(2) 2 U(1) L, A 9 U(1) 2 Y U(1) L, A 10 U(1) Y U(1) 2 L > Mixed anomalies:., A 11 (U(1) L ), A 12 U(1) 3 L. A 13 U(1) 2 B U(1) L, A 14 U(1) 2 L U(1) B, A 15 (U(1) Y U(1) L U(1) B ). Field SU(3) SU(2) U(1)Y U(1)B U(1)L QL 3 2 R 3 1 dr ll νr er H 1 2 SM + righthanded ν s A 2 = A 3 = 3 2, A 8 = A 9 = 3 2 Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 19

31 Simplest scenario: lepto-baryons. Assign lepton number to the same fields that cancel the baryonic anomalies Field SU(3) SU(2) U(1) Y U(1) B U(1) L Ψ L 1 2 ± 1 2 B 1 L 1 Ψ R 1 2 ± 1 2 B 2 L 2 η R 1 1 ±1 B 1 L 1 η L 1 1 ±1 B 2 L 2 χ R B 1 L 1 χ L B 2 L 2 Anomaly cancellation demands: B 1 B 2 = 3, L 1 L 2 = 3 [MD, Fileviez Pérez, Wise, arxiv: ] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 20

32 Simplest scenario: lepto-baryons. Assign lepton number to the same fields that cancel the baryonic anomalies Field SU(3) SU(2) U(1) Y U(1) B U(1) L Ψ L 1 2 ± 1 2 B 1 L 1 Ψ R 1 2 ± 1 2 B 2 L 2 η R 1 1 ±1 B 1 L 1 η L 1 1 ±1 B 2 L 2 χ R B 1 L 1 χ L B 2 L 2 Anomaly cancellation demands: B 1 B 2 = 3, L 1 L 2 = 3 [MD, Fileviez Pérez, Wise, arxiv: ] [MD, Fileviez Pérez, arxiv: ] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 20

33 Spontaneous symmetry breaking. > Relevant interactions of the new fields (for B 1 = B 2 ): L h 1 Ψ L Hη R + h 2 Ψ L Hχ R + h 3 Ψ R Hη L + h 4 Ψ R Hχ L + λ 1 Ψ L Ψ R S B + λ 2 η R η L S B + λ 3 χ R χ L S B + h.c. New Higgs: S B (1, 1, 0, B 1 B 2 ) > S B = 0 generates vector-like masses: L M Ψ Ψ L Ψ R + M η η R η L + M χ χ R χ L + h.c. S B (1, 1, 0, 3) ΔB = 3 no proton decay no desert > Remnant Z 2 stabilizes lightest new fermion. Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 21

34 Baryonic dark matter. > Dirac DM, SM singlet-like: χ = χ R + χ L > Coupling to the new gauge boson: thermal freeze-out (early Univ.) indirect detection (now) DM SM L g B χγ μ Z μ B (B 2P L + B 1 P R )χ DM annihilation and direct detection direct detection > Model has only six free parameters: M χ, M ZB, g B, B B 1 + B 2 and M h2, θ B DM production at colliders SM χ q χ χ Z B Z B χ q N N [MD, Fileviez Pérez, arxiv: , arxiv: ] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 22

35 Dark matter relic density B = χ q ΩDMh χ Z B q Planck M ZB = 1.5 TeV, g B = 0.5 M ZB = 1.0 TeV, g B = M χ [GeV] > Planck: Ω DM h 2 = ± Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 23

36 Dark matter relic density B = χ q ΩDMh χ Z B q Planck M ZB = 1.5 TeV, g B = 0.5 M ZB = 1.0 TeV, g B = M χ [GeV] > Planck: Ω DM h 2 = ± Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 23

37 Dark matter direct detection. Ω DM h 2 = ± χ χ ZB N N σ SI χn [cm2 ] LUX > Planck: Ω DM h 2 = ± XENON1T B = 1/2 B = M χ [GeV] M ZB [0.5, 5.0] TeV g B [0.1, 0.5] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 24

38 Scalar dark matter. > Scalar DM can arise in these models as well. > If vector-like colored fermions (Q,, d ) cancel the anomalies, they should decay. > Introduce new scalar field X with baryon number B X = 1/3 B Q R : L λ 1 XQ L Q R + λ 2X R L + λ 3Xd R d L + h.c. > Possible annihilation channels: XX Z B qq or XX H SM SM > viable DM candidate in part of the parameter space Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 25

39 Baryon asymmetry and dark matter. > Symmetries of the model: > (B L) SM > Accidental η symmetry in the new sector: Ψ L,R e η Ψ L,R, η L,R e η η L,R, χ L,R e η χ L,R. > Relevant interactions: DM stability L h 1 Ψ L Hη R + h 2 Ψ L Hχ R + h 3 Ψ R Hη L + h 4 Ψ R Hχ L + λ 1 Ψ L Ψ R S B + λ 2 η R η L S B + λ 3 χ R χ L S B + h.c. Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 26

40 Baryon and dark matter asymmetries. > For μ T: Δn s = n + n = 15g μ s 2π 2 g ξ T, > B L asymmetry in the SM sector g: internal degrees of freedom, s: entropy density, g : total number of relativistic degrees of freedom, 2 for fermions, ξ = 1 for bosons. 45 Δ(B L) SM = 4π 2 g T (μ L + μ R + μ dl + μ dr μ νl μ el μ er ), > η charge density 15 Δη = 4π 2 2μΨL + 2μ ΨR + μ χl + μ χr + μ ηl + μ ηr. g T > Baryon asymmetry B SM ƒ = n q n q s 15 = 4π 2 g T 3 μ L + μ R + μ dl + μ dr. P. Fileviez Pérez, H. H. Patel, arxiv: [hep-ph] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 27

41 Baryon and dark matter asymmetries. B SM ƒ Initial Asymmetry = Δ(B L) SM + (15 14B 2) Δη, 198 Baryon Asymmetry Sphalerons (QQQL) 3 ψr ψ L Asymmetric Dark Matter Consistent picture for baryogenesis! 3(3μ L + μ el ) + μ ΨL μ ΨR = 0. P. Fileviez Pérez, H. H. Patel, arxiv: [hep-ph] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 28

42 Dijet searches. > Since the leptophobic gauge boson ZB is produced from quarks, it can decay back to quarks dijet searches q q ZB q q mq = 1 TeV, B1 = 1, B2 = 4/3 BR(ZB ) jj t t P 1000 ATLAS highest-mass dijet event (Event , Run ) Q Q MZB [GeV] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 29

43 Limits on mass vs. gauge coupling. 2 LHC dijet searches 1 gb [MD, Fileviez Pérez, Smirnov, arxiv: ] 0.2 Combination from CMS 27 fb 1 & 36 fb 1 (13 TeV) ATLAS 37.0 fb 1 (13 TeV) ATLAS 3.4 fb 1 (13 TeV); Trigger-object Level Analysis M ZB [GeV] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 30

44 Low-mass region. > New CMS search with ISR jet (CMS-PAS-EXO ) [See talk by A. de Roeck] q coupling, g CMS Preliminary 35.9 fb (13 TeV) Observed Expected ± 1 std. deviation ± 2 std. deviation UA2 CDF Run 1 CDF Run ATLAS13, 15.5 fb, ISR γ -1 ATLAS13, 15.5 fb, ISR jet -1 CMS8, 18.8 fb, Scouting Z Width (indirect) Z' mass (GeV) L g q Z μ qγ μq g B = 3g q Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 31

45 Baryonic Higgs at the LHC. P. Fileviez Pérez, M. B. Wise, arxiv: [hep-ph] MD, P. Fileviez Pérez, J. Smirnov, arxiv: [hep-ph] Cancel the anomalies with vector-like quarks. > Use three copies (analogy to the SM families) B 1 B 2 = 1/3 Scenario III 1 > Scenario I: Y 1 = 1/6, Y 2 = 2/3, Y 3 = 1/3 > Scenario II: Y 1 = 5/6, Y 2 = 4/3, Y 3 = 1/3 > Scenario III: Y 1 = 7/6, Y 2 = 5/3, Y 3 = 2/3 BR(hB) for MhB = 1 TeV hb gg hb W W hb ZZ hb γγ hb Zγ hb t t hb h1h θb BR into photons large compared to SM Higgs, colored new fermions in the loop. [See parallel talk by J. Smirnov] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 32

46 Baryonic Higgs at the LHC. P. Fileviez Pérez, M. B. Wise, arxiv: [hep-ph] MD, P. Fileviez Pérez, J. Smirnov, arxiv: [hep-ph] Cancel the anomalies with vector-like quarks. > Use three copies (analogy to the SM families) B 1 B 2 = 1/3 Scenario III 1 > Scenario I: Y 1 = 1/6, Y 2 = 2/3, Y 3 = 1/3 > Scenario II: Y 1 = 5/6, Y 2 = 4/3, Y 3 = 1/3 > Scenario III: Y 1 = 7/6, Y 2 = 5/3, Y 3 = 2/3 BR(hB) hb gg hb W W hb ZZ hb γγ hb Zγ hb Q Q hb ZBZB [GeV] MhB BR into photons large compared to SM Higgs, colored new fermions in the loop. [See parallel talk by J. Smirnov] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 32

47 Baryonic Higgs at the LHC. MD, P. Fileviez Pérez, J. Smirnov, arxiv: [hep-ph] Di-photon channel can severely constrain the baryonic scale. σ(pp hb) BR(hB γγ) [fb] LHC γγ searches CMS 16.2 fb 1 (13 TeV) fb 1 (8 TeV) ATLAS 15.4 fb 1 (13 TeV) Scenario I: θb = 0 Scenario I: θb = 0.3 Scenario II: θb = 0 Scenario II: θb = 0.3 Scenario III: θb = 0 Scenario III: θb = 0.3 vb [GeV] Lower bound on vb from LHC γγ searches Scenario I: θb = 0, ATLAS Scenario I: θb = 0, CMS Scenario II: θb = 0, ATLAS Scenario II: θb = 0, CMS Scenario III: θb = 0, ATLAS Scenario III: θb = 0, CMS > MhB vb [GeV] MhB [GeV] MhB Dominant production via gluon fusion with colored new fermions in the loop. [See parallel talk by J. Smirnov] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 33

48 Left right symmetric model. G LR = SU(2) L SU(2) R U(1) B L SM fields > Connects neutrino masses and spontaneous parity violation. > Standard version uses hybrid version of type I and type II seesaw mechanism for neutrino masses. Q L (2, 1, 1/3) Q R (1, 2, 1/3) l L (2, 1, 1) l R (1, 2, 1) Pati, Salam, PRD 10 (1974) 275, Mohapatra, Pati, PRD 11 (1975) 2558, Senjanovic, Mohapatra, PRD 12 (1975) 1502 > Promote gauge group to SU(2) L SU(2) R U(1) B U(1) L He, Rajpoot, PRD 41 (1990) 1636 Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 34

49 Anomaly cancellation: type III seesaw. > Anomalies that need to be cancelled: A 1 SU(2) 2 L U(1) B = 3/2 A 2 SU(2) 2 L U(1) L = 3/2 A 3 SU(2) 2 R U(1) B = 3/2 A 4 SU(2) 2 R U(1) L = 3/2 H L S BL H L > Simplest solution: type III seesaw fields ρ L (3, 1, 3/4, 3/4), ρ R (1, 3, 3/4, 3/4) > Neutrino mass matrix: M 3+2 ν m 1 m 2 D D 0 m 1 0 m 3 m 4 D D = 0 0 m 2 m 5 m 6. D D m 1 m 3 m D D D m 2 m 4 m D D D ν L ν L ρ 0 L ρ 0 L > Two light sterile neutrinos. MD, P. Fileviez Pérez, M. Lindner, arxiv: [hep-ph] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 35

50 Towards low-scale unification. > Step 1: Unification of gauge interactions at the low scale P. Fileviez Pérez, S. Ohmer, arxiv: > Fields in minimal theory for B and L allow for unification at the low scale (proton is stable!) > Step 2: Find UV completion and embed baryon number into a non-abelian gauge symmetry P. Fileviez Pérez, S. Ohmer, arxiv: > If quarks and leptons live in the same multiplets, B and L cannot be defined > With extra matter one can have multiplets with definite baryon number, one of the generators can be identified with baryon number > Color and baryon number can be unified in SU(4) C similar to Pati, Salam, Phys. Rev. D 10 (1974) 275 Fileviez Pérez, Wise, arxiv: Fornal, Rajaraman, Tait, arxiv: [See parallel talk by S. Ohmer for details.] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 36

51 Gauge coupling unification. > Running of gauge couplings 1-loop): k α 1 (M) = α 1 (M Z ) B 2π log(m/m Z) B = b SM + Θ(M M F )n F b new log(m/m F ) log(m/m Z ) > k : normalization > M F : mass scale of the new fermions (here: 500 GeV) > n F : number of new fermion copies P. Fileviez Pérez, S. Ohmer, arxiv: [hep-ph] Αi Α SM 1 1 Α SM 2 1 Α SM 3 1 Α 2 1 Α 1 1 Α Log 10 MGeV > Model with SU(2) triplet: n F unification scale [TeV] k Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 37

52 Gauge coupling unification. > Running of gauge couplings 1-loop): k α 1 (M) = α 1 (M Z ) B 2π log(m/m Z) B = b SM + Θ(M M F )n F b new log(m/m F ) log(m/m Z ) > k : normalization > M F : mass scale of the new fermions (here: 500 GeV) > n F : number of new fermion copies P. Fileviez Pérez, S. Ohmer, arxiv: [hep-ph] Αi Α Α 2 1 Α 3 1 Α 1 SM 1 Α 2 SM 1 Α 3 SM Log 10 MGeV Αi Α L 1 Α 1 1 Α 3 1 ΑB 1 Α Log 10 MGeV Unification of gauge interactions possible with small α B (and α L ) at the low scale. Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 37

53 Baryon number as the fourth color. > Embed SM U(1) B into SU(4) C SU(3) L SU(3) R P. Fileviez Pérez, S. Ohmer, arxiv: > SM fermions d r r D r d Q = b b D b d g g D (4, 3, 1) g Ψ d Ψ Ψ D d c r d c b d c η c Q c ḡ d = c b c η ḡ ( 4, 1, 3) D c r D c b D c η c ḡ D N 1 E + ν L = E N 2 e (1, 3, 3) ν c e + N 3 > extra fermions (anomalies) Ψ c (1, 3, 1) and η (1, 1, 3) > Possible embedding into SU(4) C SU(4) L SU(4) R (plus Z 3 symmetry) [See parallel talk by S. Ohmer for details.] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 38

54 Summary. > I presented simple theories for the spontaneous breaking of baryon number (and lepton number). > Features include: > No proton decay even though B can be broken at the low scale. > DM stability as an automatic consequence of the gauge symmetry. > Leptophobic Z B that can be searched for at colliders. > Unification could be realized at the low scale since the desert is not needed. Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 39

55 Backup slides. Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 1

56 Baryonic dark matter. Condition from anomaly cancellation: B 1 B 2 = 3 two options: B 1 = B 2 B 1 = B 2 = 3/2: > Dirac DM, SM singlet-like: χ = χ R + χ L > Coupling to the Z B : L g B χγ μ Z μ B (B 2P L + B 1 P R )χ > six free parameters (plus extra fermion masses): > Majorana DM with axial coupling to the Z B : L 3 2 g B χγ μ γ 5 χz μ B > five free parameters (plus extra fermion masses): M χ, M ZB, g B, and M h2, θ B [MD, Fileviez Pérez, Smirnov, arxiv: ] M χ, M ZB, g B, B B 1 + B 2, M h2, θ B [MD, Fileviez Pérez, arxiv: , arxiv: ] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 2

57 What about the additional fermions?. > Majorana DM (B 1 = B 2 ): loop-mediated DM annihilation to photons ΩDMh 2 = ± , = MZB 1.2Mχ > Decays of S B : > For θ 0, the branching fractions of the fermion-loop-mediated decays of S B may provide clues about the fermion content of the model at the LHC > Model with SU(2) triplet: WW : ZZ : Zγ : γγ = 20 : 7 : 3 : H.E.S.S. σv χχ γγ [cm 3 s 1 ] FermiLAT Mη = Mχ, MΨ = 2Mχ Mη = 2Mχ, MΨ = 3Mχ Mχ [GeV] [MD, Fileviez Pérez, Smirnov, arxiv: ] > Vector-like model: [Ohmer, Patel, arxiv: ] WW : ZZ : Zγ : γγ = 2 : 1 : 10 3 : 1 Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 3

58 Even lower-mass region. gz m f 90GeV, N f 3 m f 90GeV Ψ M Z' GeV Zwidth m f 450GeV ' Z B model [Dobrescu, Frugiuele, arxiv: ] Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 4

59 Gauging B and L in SUSY setups. > Lepto-baryon fields: J. M. Arnold, P. Fileviez Pérez, B. Fornal, S. Spinner, arxiv: [hep-ph] > U(1) B and U(1) L breaking scale linked to SUSY breaking scale > R-parity must be spontaneously broken > Stable DM candidate > Vector-like family: P. Fileviez Pérez, M. B. Wise, arxiv: [hep-ph] > U(1) B and U(1) L breaking scale linked to SUSY breaking scale > Low B breaking renders the lightest neutralino unstable no DM candidate Michael Duerr Gauge Theories for Baryon Number 18 May 2017 page 5