An Introduction to Grand Unified Theories

Home , Grand Unified Theory, Harald Fritzsch, X (charge)

An Introduction to Grand Uniﬁed Theories

Dibyakrupa Sahoo

LECTURE – 2

Department of Physics, and Institute of Physics and Applied Physics, Yonsei University, Seoul, South Korea

20 July 2017

1 Contents

Introduction

Generic features of grand uniﬁcation

Examples of grand uniﬁed theories (GUTs)

Phenomenological inﬂuence of GUT inspired ideas

Conclusion

2 Introduction Need to go beyond SM

O Standard Model (SM) is not the ﬁnal theory of particle physics.

O SM has excellent experimental agreement, but many shortcomings also: gravity not included, no explanation for neutrino mass and neutrino oscillation, absence of candidates for dark matter, no logic for several generations of fermions and their mass hierarchy, no physical understanding of the plethora of parameters in the Lagrangian, absence of any mechanism to generate observed baryon asymmetry in our universe, no explanation for the observed smallness of CP violating θ term QCD.

O We shall study grand uniﬁcation and grand uniﬁed theories (GUTs) with an eye on how they help alleviate some of the above ailments of SM.

3 Introduction What is grand uniﬁcation?

O Does the SM gauge group GSM SU(3)C SU(2)L U(1)Y provide an uniﬁed description of electroweak≡ phenomena?× ×

O SU(2)L U(1)Y is product of two disconnected sets of gauge × transformations: SU(2)L comes with coupling strength g and U(1)Y with g0 which are not related by theory, i.e. the ratio,

g0/g = tan θW, has to fixed experimentally. O A truly unified theory of electroweak interaction would use only one independent coupling constant instead of the above two. O The strong interaction is also not unified with electroweak interaction in SM. O The primary aim of grand unification is to describe strong, weak and electromagnetic interactions by a unified coupling constant via embedding SM gauge group inside a larger symmetry group. O Grand Unification Unification of strong and electroweak interactions (without≡ gravity)

4 Introduction

Some excellent resources to start with: O Paul Langacker, Grand Uniﬁed Theories and Proton Decay, Phys. Rep. 72, 185 (1981). O G. Ross, Grand Uniﬁed Theories (Benjamin, 1985). O C. Patrignani et al. (Particle Data Group), Chapter 16, Chin. Phys. C, 40, 100001 (2016).

5 Generic features of grand uniﬁcation Bird’s eye view of grand uniﬁcation

O Basic idea: The SM gauge group GSM is embedded in a larger symmetry group G. So strong and electroweak interactions are merged into one interaction and are described by one coupling constant.

O Basic goal: To break the unifying group G into GSM by spontaneous symmetry breaking(s).

O Constraint: The unifying group G must be large enough to contain GSM as a subgroup. Some possible unifying groups are, Inﬁnite series of groups: SU(n), SO(n), Sp(2n), Exceptional groups: F4, E6, E7, E8.

O Byproducts: Additional symmetries of G restrict some arbitrary features of SM, e.g. family structure and fermion mass hierarchy. New gauge bosons mediating new symmetries emerge which predict some observable phenomena.

6 Generic features of grand uniﬁcation Ratios of Coupling constants in the Unifying Limit

O Assume:

Total number of fermions in our theory = Nf . ∴ total number of left-handed and right-handed fermions = 2Nf . G GSM = SU(3)C SU(2)L U(1)Y . ∃ ⊃ × × G has a single coupling constant gG.

So the other coupling constants gS, g, and g0 are related to gG. O Aim: To ﬁnd out how the coupling constants are related to one another.1

O Step 1: a maximal unifying group Gmax = SU(2Nf ) G GSM. Algebraic∃ relationships amongst coupling constants derived⊃ ⊃ in Gmax is automatically valid in G.

O Step 2: Denote the 2Nf 2Nf dimensional diagonal generators of × Gmax, SU(3)C, SU(2)L and U(1)Y by TG, TC, TL and TY respectively. (α) (i) TG denotes the αth generator of G. Similarly, TA with A C, L, Y ∈ { } denotes the ith generator of SU(3)C, SU(2)L and U(1)Y .

1For details see, Jatinder K. Bajaj and G. Rajasekaran, “The electroweak mixing angle in uniﬁed gauge theories”, Pramana, Vol.14, No.5, May 1980, pp.395-409. 7 Generic features of grand uniﬁcation Ratios of Coupling constants in the Unifying Limit

(α) (i) (β) (j) O Step 3: It is known that gGTG = gCTC , gGTG = gTL and (γ) (k) gGTG = g0TY . There is no reason why α, β, and γ (or i, j and k) should be same. (α) (i) (α) (α) O Step 4: Also TG and TA are normalized such that Tr TG TG is (i) (i) independent of α and Tr TA TA is independent of i, so that:

(α) (β) αβ 2 (i) (j) ij 2 Tr TG TG = δ Tr (TG) , Tr TA TA = δ Tr (TA) . 2 2 2 2 2 2 2 2 = gG Tr (TG) = gS Tr (TC) = g Tr (TL) = g0 Tr TQ , ⇒ g2 Tr T 2 α g2 G ( A) G , where α X for X G, C, L, Y . = 2 = 2 = X = 4 ⇒ gA Tr (TG) αA π ∈ { }

Here for A = C, L, Y we have gA = gS, g, g0 and αA = αS, αL, αY respectively.

2 2 αY Tr (TC) αY Tr (TL) 2 ∴ = 2 and = 2 = tan θW. αS Tr (TY ) αL Tr (TY )

8 Generic features of grand uniﬁcation Ratios of Coupling constants in the Unifying Limit

O Step 5: Since U(1)em SU(2)L U(1)Y we can construct a 2Nf 2Nf ⊂ × × dimensional diagonal generator TQ of U(1)em out of electric charges of all the fermions. The ﬁne structure constant for U(1)em is denoted by α and following the previous step we get,

α Tr T 2 ( L) sin2 θ . α = 2 = W L Tr TQ

O Predicting ratios of coupling constants and finding sin θW: For this we must proceed as follows, construct the required generators, square the generators and evaluate their trace, predict the ratio of coupling constants/fine structure constants from the relations derived before. O Note: The ratios of coupling constants as predicted above are valid at the unification scale. To determine the ratios at other energy scales, renormalization effects must be considered.

9 Generic features of grand uniﬁcation Ratios of Coupling constants in the Unifying Limit: Example with doublets of fermions

O Assumption: Quarks and leptons form doublets under the unifying uα ν group, i.e. for quarks we have and for leptons we have e . dα e Our discussion is independent of number of generations. − O Generators: 16 16 diagonal matrices, ×  uL dL uR dR  ν e ν e z }| { z }| { eL −L z }| { z }| { eR −R  2 2 2 1 1 1 z}|{ z}|{ 2 2 2 1 1 1 z}|{ z}|{ TQ = diag  , , , , , , 0 , 1 , , , , , , , 0 , 1   3 3 3 − 3 − 3 − 3 − 3 3 3 − 3 − 3 − 3 −  | {z } | {z } L R

ν e  uL dL eL −L  ν e z }| { z }| { z}|{ z}|{ uR dR eR −R  1 1 1 1 1 1 1 1 z }| { z }| { z}|{ z}|{ TL = diag  , , , , , , , , 0, 0, 0, 0, 0, 0, 0 , 0   2 2 2 − 2 − 2 − 2 2 − 2 | {z } | {z } R L

 uL dL uR dR  ν e ν e z }| { z }| { eL −L z }| { z }| { eR −R  1 1 1 1 z}|{ z}|{ 1 1 1 1 z}|{ z}|{ TC = diag  , , 0, , , 0, 0 , 0 , , , 0, , , 0, 0 , 0   2 − 2 2 − 2 2 − 2 2 − 2  | {z } | {z } L R

10 Generic features of grand uniﬁcation Ratios of Coupling constants in the Unifying Limit: Example with doublets of fermions

O Traces:

2 16 Tr T , Tr T 2 2, Tr T 2 2. Q = 3 ( L) = ( C) = O Predictions:

α Tr T 2 3 ( C) , α = 2 = 8 S Tr TQ α Tr T 2 3 ( L) sin2 θ 0.375. α = 2 = W = 8 = L Tr TQ

O Note 1: The above results are independent of the actual unifying group as long as it is a subgroup of Gmax which in this case is SU(16) and as long as the doublet scheme is maintained. O Note 2: Large renormalization corrections are required to bring 2 down the value of sin θW from 0.375 to the experimentally measured value 0.23126.

11 Generic features of grand uniﬁcation Ratios of Coupling constants in the Unifying Limit: Example with triplets of fermions

O Assumption: The quarks and leptons form triplets under G, i.e. for  α    u νe quarks we have  dα  and for leptons we have  e .    −  xα E+ O Generators: 24 24 diagonal matrices, ×   uL dL xL ν e E+ uR dR xR ν e E+ eL −L L eR −R R z }| { z }| { z }| { z }| { z }| { z }| {   2 2 2 1 1 1 1 1 1 z}|{ z}|{ z}|{ 2 2 2 1 1 1 1 1 1 z}|{ z}|{ z}|{ TQ = diag  , , , , , , , , , 0 , 1 , +1 , , , , , , , , , , 0 , 1 , +1   3 3 3 − 3 − 3 − 3 − 3 − 3 − 3 − 3 3 3 − 3 − 3 − 3 − 3 − 3 − 3 −  | {z } | {z } L R   u d νe e L L x L −L E+ u d x νe e E+  L L R R R R −R R  z }| { z }| { z}|{ z}|{   1 1 1 1 1 1 z }| { 1 1 z}|{ z }| { z }| { z }| { z}|{ z}|{ z}|{ TL = diag  , , , , , , 0, 0, 0, , , 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0 , 0   2 2 2 2 2 2 2 2   − − − − | {z } | {z } R  L

  uL dL xL ν e E+ uR dR xR ν e E+ eL −L L eR −R R z }| { z }| { z }| { z }| { z }| { z }| {   1 1 1 1 1 1 z}|{ z}|{ z}|{ 1 1 1 1 1 1 z}|{ z}|{ z}|{ TC = diag  , , 0, , , 0, , , 0, 0 , 0 , 0 , , , 0, , , 0, , , 0, 0 , 0 , 0   2 − 2 2 − 2 2 − 2 2 − 2 2 − 2 2 − 2  | {z } | {z } L R

12 Generic features of grand uniﬁcation Ratios of Coupling constants in the Unifying Limit: Example with triplets of fermions

O Traces: 2 2 2 Tr TQ = 8, Tr (TL) = 2, Tr (TC) = 3. O Predictions:

α Tr T 2 3 ( C) 0.375, α = 2 = 8 = S Tr TQ α Tr T 2 1 ( L) sin2 θ 0.25. α = 2 = W = 4 = L Tr TQ

O Note: Here the renormalization corrections required are smaller in comparison with the doublet fermion scenario. This example is for the purpose of illustration only. We shall consider the doublet scenario in our discussion ahead.

13 Generic features of grand uniﬁcation Renormalization effects

O Once the uniﬁed symmetry is broken, the coupling constants undergo different renormalizations and hence their relevant ratios (at low energies) after symmetry breaking are different. Here we use renormalization group.

O Assumption: Uniﬁcation group G breaks down to GSM by a single step SSB at the energy scale MU. O 2 2 For q = MU, we have 1 1 1 1 3 . 2 = 2 = 2 = 2 = 5 αG MU αS MU αL MU αY MU O 2 2 Renormalization group equations: For q < MU, 1 1 q2 = βS ln , α q2 2 M2 S ( ) αS MU − U 1 1 q2 = βL ln , α q2 2 M2 L ( ) αL MU − U 3 1 3 1 3 q2 = βY ln . 5 α q2 5 2 5 M2 Y ( ) αY MU − U 14 Generic features of grand uniﬁcation Renormalization effects

O β-functions: 11 11 2 3 β F, β F, β 0 F, S = 2 + L = 2 + Y = + −16π −16π 3 5 where F denotes the fermion contribution. O Above results are obtained from the one-loop contributions from the following kind of diagrams: G f gS gS + + G G G G G f

W f gL gL + + W W W W W f

f gY B B f 15 Generic features of grand uniﬁcation Renormalization effects

O Notes: Decoupling theorem is invoked to ignore the contribution of heavy particles. New gauge bosons are all assumed to be sufﬁciently heavy so 2 2 as not to contribute to these one-loop equations for q MU. The non-abelian gauge-boson contributions lead to the negative numbers given for βS and βL, whereas there is no such contribution for the abelian case βY . The fermion contribution F is the same for all the three graphs, assuming that the complete fermion multiplet is light. We ignore Higgs contributions. 2 Tr (TG) 3 We use the doublet scheme of fermions, in which case 2 = . Tr (TY ) 5 Also we have assumed the usual normalization for the non-abelian 2 2 2 generators: Tr (TG) = Tr (TC) = Tr (TL) .

16 Generic features of grand uniﬁcation Renormalization effects

O After algebraic simpliﬁcation results for the ratios of the coupling

constants in the low-energy region ML 100 GeV has the form: ≈ α 3 33 MU = α ln , αS 8 − 8π ML 2 3 55 MU sin θW = α ln . 8 − 24π ML O By rewriting the 1st expression above we get

3 1 1 33 MU = ln . 8 α − αS 8π ML O By substituting the empirical values of the coupling constants for

QCD and QED at the ‘low’ energy scale ML: 1 3 1 3 1 1 5; 50; 45. αS ≈ 8 α ≈ 8 α − αS ≈ This leads to the uniﬁcation scale: 45 8π 15 MU 100 GeV exp × 10 GeV. ≈ × 33 ≈ 17 Generic features of grand uniﬁcation Renormalization effects

15 2 O Using the predicted value of MU 10 GeV we get sin θW 0.21. O Uniﬁcation of coupling constants:≈ ≈

2 gi(Q )

2 GRAND gS(Q ) UNIFICATION

2 g(Q )

2 g0(Q )

q2 2 2 ML MU SU(5), SU(3)C U(1)em DESERT: SU(3)C SU(2)L U(1)Y ⊗ ⊗ ⊗ SO(10), E6

18 Generic features of grand uniﬁcation Phenomenological features: extra gauge bosons and proton decay

O During grand unification, we put quarks and leptons into the same representation of the unifying group G. O This implies that there are gauge bosons (usually denoted by X, Y) that transform quarks to leptons and vice-versa (Baryon number is violated in such processes). O These gauge bosons are called as lepto-quarks (if they mediate the transitions between quarks and leptons) or diquarks (if they mediate quark to quark transitions). Due to their presence, proton decay2 is allowed in grand unified theories: p π0e+. O Observation of proton decay would be a tell-tale→ signature of grand unification, just as observation of 0νββ would be a definitive signature of Majorana neutrinos.

2See the paper: Paul Langacker (1981), “Grand Uniﬁed Theories And Proton Decay”, Physics reports (Review Section of Physics letters) 72, No.4, Pages 185-385, for more details and extensive discussions on proton decay. 19 Generic features of grand uniﬁcation Phenomenological features: extra gauge bosons and proton decay

d e+ u e+ X Y u u d u u u u u

u e+ d ν Y Y u d u d d d u u

u X e+ d Y e+

u d u u d d u u

20 Generic features of grand uniﬁcation Phenomenological features: extra gauge bosons and proton decay

O Let MX = mass of the lepto-quarks (or diquarks). 0 + 2 2 ∴ Amp p π e gG/MX , where gG the coupling strength of the grand unifying→ gauge∼ group. O Neglecting the pion and positron masses in comparison to proton mass, Phase Space Factor ! 2 2 2 ΓP = (gG/MX ) controlled by proton . × mass mP O 2 22 5 By dimensional analysis, ΓP gG/MX mP. 15 ∼ O Putting MX MU 10 GeV,the mean life of proton comes out as ∼ ∼ 1 M4 τ U 1031 years (1) P 5 ∼ ΓP ∼ mp ∼ This is only an order of magnitude estimate. So far no proton decay has been seen experimentally. O Grand uniﬁcation not only predicts the correct value of the electroweak

mixing angle θW, but also the longevity of the proton.

21 Examples of grand uniﬁed theories Example 1: Georgi-Glashow SU(5) model

O The Georgi-Glashow (GG) SU(5) model was the ﬁrst attempt to embed the standard model in an underlying simple group3. The model is the simplest grand uniﬁed theory that is phenomenologically viable. O Gauge bosons represented by the adjoint representation 24 and their decomposition under SU(3)C SU(2)L are as follows: × 24 = (8, 1) + (1, 3) + (1, 1) + (3, 2) + (3∗, 2) | {z } | {z } | {z } | {z } | {z } Gα W ,W0 B X ,Y ¯α ¯α β ( ± ) ( α α) (X ,Y )

where the entries (n3, n2) represent the representations under the SU(3)C and SU(2)L subgroups. O α The 24 contains an octet of gluons Gβ , 4 electro-weak bosons (W±, 0 ¯α ¯α W , B) and 12 new bosons (Xα, Yα, X , Y , where α is the color index) that carry both flavor and color, and hence they mediate Baryon number violating interactions. 3See the paper: G. Georgi, S.L. Glashow (1974). “Unity of All Elementary Particle Forces”. Physical Review Letters 32: 438-441. 22 Examples of grand unified theories Example 1: Georgi-Glashow SU(5) model O Fermions of one family belong to 5∗ + 10 and they are given below:  dc    1 ν  dc  e  2  5  dc   dc  ∗  α  =  3  ≡ e  e  − L  −  ν e L − and  c c 1 1  0 u3 u2 u d   − − − uα  uc 0 uc u2 d2   3 1  10  e+ uc   −uc uc 0 −u3 −d3   α  =  2 1  ≡ dα  u1 −u2 u3 −0 −e+  L   d1 d2 d3 e+ −0 L where the superscript c denotes charge-conjugate. Note that quarks, leptons and anti-quarks (uc and dc) appear together in the above representations. 23 Examples of grand unified theories Example 1: Georgi-Glashow SU(5) model

O Regarding spontaneous symmetry breaking:

SU(5) is spontaneously broken down to SU(3)C SU(2)L U(1)Y by an b a × × adjoint (24) representation Φa(Φa = 0) of Higgs ﬁelds (where a, b = 1, 2, , 5). ··· SU(3)C SU(2)L U(1)Y invariant components of Φ have very large VEVs × 1014 GeV× . ≈ O 14 The Φ therefore generates MX = MY ¦ 10 GeV, 2 2 2 MW = MZ = ml = mq = 0. For MW q ® MU, SU(3)C SU(2)L U(1)Y × × is an approximately unbroken symmetry, and gS, g, and g0 evolve independently. 2 2 2 ∵ MW < q ® MU is barren of any qualitatively new physics, it is called as the DESERT or PLATEAU. A 5-dimensional Higgs representation Ha with a much smaller value of VEV of the order of 100 GeV breaks the SU(3)C SU(2)L U(1)Y × × symmetry down further to SU(3)C U(1)em, generating 2 2 1/2 × MX MY MW MZ (100 GeV) and ml = 0, mq = 0. | − | ∼ ∼ ∼ O 6 6

24 Examples of grand uniﬁed theories Example 1: Georgi-Glashow SU(5) model

O Strong features: SU(5) model has the minimal fermion and Higgs representations.

Quarks and lepton universality is inbuilt ∵ the 5∗ and 10 representations of fermions contain both in the same family.

There is no room for a νR in the 5∗ + 10 representations. Hence neutrinos remain massless, unless we include νR as an SU(5) singlet. Electric charge, originally a (continuous variable) generator of the U(1) group, is a generator of SU(5), and the commutation relations of this symmetry allow only discrete, rather than continuous, eigenvalues of electric charge. So charge quantization, in this model, occurs as a result of grand uniﬁcation. The quark and lepton charges are related. The sum of charges of the particles in each multiplet is zero. 2 It predicts approximately correct value of sin θW .

25 Examples of grand uniﬁed theories Example 1: Georgi-Glashow SU(5) model

O Weak features:

Each family is placed in a reducible 5∗ + 10 representation. In larger groups each family is usually in an irreducible representation. There is no explanation of why there are several families or of how many there are. The model still has many free parameters. (The model with only one 24 and one 5 Higgs representation has: 1 gauge coupling, 1 θ parameter, 9 Higgs parameters (7 if Φ Φ), 6 quark masses (from which the lepton masses are deduced),→ 6 − mixing angles and 1 CP violating phase.) The model predicts the existence of super heavy (m 1016 GeV) ’t Hooft-Polyakov magnetic monopoles. ≈ The model includes a desert between the W and X(or Y) masses. O Minimal SU(5) GUT is already ruled out by experimental data from proton decay experiments. However, some modiﬁed versions such as supersymmetric SU(5) or ﬂipped SU(5) are still allowed by experimental data.

26 Examples of grand uniﬁed theories Example 2: SO(10) model

O Fritzsch and Minkowski proposed a grand uniﬁed theory4 based on rank-5 group SO(10). O Each family of left-handed fermions is assigned to a 16 dimensional

complex spinor σ+. Consider two distinct subgroups of SO(1)), viz. SU(5) and SU(4) SU(2) SU(2). Under the SU(5) subgroup the × × fermion spinor σ+ for the ﬁrst family decomposes as:

16 = 5∗ + 10 + 1 . |{z} |{z} |{z}c    α  ν νe u eL      c   + c   dα   e uα      e dα − L L

O c T Note: σ+ contains an SU(5) singlet, an antineutrino νeL = Cν¯R. Hence, the SO(10) will in general involve massive neutrinos.

4See the paper: Harald Fritzsch and Peter Minkowski (1975),“Uniﬁed Interactions of leptons and hadrons”, Annals of Physics, Volume-93, Pages 193-266. 27 Examples of grand uniﬁed theories Example 2: SO(10) model

O Of the 45 generators of SO(10), 24 are those of the SU(5) subgroup. The rest 21 generators connect or distinguish between the 5∗, 10 and 1. In order to study their properties it is convenient to consider the subgroup decomposition:

SO(10) SO(6) SO(4) ⊃ × SU(4)C SU(2) SU(2) ∼ × × SU(3)C U(1)0 SU(2)L SU(2)R, (2) ⊃ × × ×

where SU(4)C SU(3)C U(1)0 can be considered an extended color group with leptons⊃ as fourth× color. O With respect to SU(3)C SU(2)L SU(2)R, σ+ decomposes as: × ×

16 = (3, 2, 1) + (1, 2, 1) + (3∗, 1, 2) + (1, 1, 2) . | {z } | {z } | {z } | {z } α c + u νe dα e dα e uc c L − L α L νe L − −

28 Examples of grand uniﬁed theories Example 2: SO(10) model

O SO(10) contains the left-right symmetric SU(2)L SU(2)R U(1)0 electro-weak group as a subgroup. In particular,× the right-handed× fermions (left-handed anti-fermions) transform nontrivially under SU(2)R. The transformation properties of 45 gauge bosons under SU(3)C SU(2)L SU(2)R are: × × 45 = (8, 1, 1) + (1, 3, 1) + (1, 1, 3) + (1, 1, 1) | {z } | {z } | {z } | {z } Gα ,0 ,0 B β (WL± ) (WR± )

+ (3∗, 2, 2) + (3, 2, 2) + (3, 1, 1) + (3∗, 1, 1) . | {z } | {z } | {z } | {z }     X ¯ X Y¯ 0 X0 Y¯ S XS     Y X¯ 0 Y 0 X¯

O α ,0 The ﬁfteen bosons Gβ , WL±,R and B0 are associated with

SU(3)color SU(2)L SU(2)R U(1)0. Now, there are weak bosons × × × corresponding to both SU(2)L and SU(2)R and the lepto-quarks/diquarks X, Y are also larger in number.

29 Examples of grand uniﬁed theories Example 2: SO(10) model

Patterns of symmetry breaking in SO(10)

M MG SU(5)

Mc M MW SO(10) SU(3)C SU(2)L SU(2)R U(1)0 ≈ SU(3)C SU(2)L U(1)Y × × × × × MR M Mc MG SU(4)C SU(2)L U(1)R SU(3)C SU(2)L U(1)R U(1)0 × × × × ×

30 Examples of grand uniﬁed theories Example 2: SO(10) model

O The SO(10) model is an attractive extension of the SU(5) model in the sense that quarks and leptons are treated much more symmetrically. O There is more freedom in choosing symmetry breaking patterns. So 2 its difﬁcult to uniquely predict sin θW and proton life-time in SO(10). O SO(10) is also left-right symmetric, while SU(5) is not. O SO(10) allows for neutrino mass.

O No desert in between MW and MU. O Some variants of SO(10), for example supersymmetric SO(10), are still allowed by the proton decay data.

31 Phenomenological inﬂuence of GUT inspired ideas

O The following two prominent ideas are currently resurrecting in view of some observed tensions in B decays: Lepto-quarks,

W0 and Z0 bosons. O The new models incorporating lepto-quarks and/or W0, Z0 bosons are, nevertheless, phenomenologically motivated and not necessarily involve uniﬁcation of strong and electroweak coupling constants. O We shall discuss only a few very recent applications of these ideas.

32 Phenomenological inﬂuence of GUT inspired ideas B decay anomalies

O + Lepton universality check in b s` `− decays via RK and RK : → ∗ ( ) + Br B K ∗ µ µ− RK( ) = → ∗ Br B K( )e+e ( ∗ −) → SM exp RK = 1, RK = 0.745 0.09 0.036, ± ± [R. Aaij et al. [LHCb] PRL 113, 151601 (2017)]

¨ +0.110 2 2 2 SM exp 0.660 0.070 0.024 4mµ < q < 1.1GeV RK = 1, RK = −0.113 ± 2 2 2 ∗ ∗ + 0.685 0.069 0.047 1.1GeV < q < 6GeV − ± [S. Bifani, CERN seminar, April 18 (2017)]

O Both RK and RK differ from SM expectation by 2.4σ standard ∗ deviation. ∼

33 Phenomenological inﬂuence of GUT inspired ideas B decay anomalies

O Lepton universality check in b c`−ν decays via RD and RD : → ∗ ¯ ( ) Br B D ∗ τ−ν RD( ) = → ∗ Br B D( )` ν ( ∗ − ) → SM exp RD = 0.300 0.008, RD = 0.407 0.039 0.024, ± ± ± SM exp RD = 0.252 0.003, RD = 0.304 0.013 0.007 ∗ ± ∗ ± ± [results of the heavy ﬂavor averaging group (HFLAG)]

O The RD and RD differ from SM expectation by 2.0σ and 2.7σ ∗ standard deviations respectively. The combined∼ signiﬁcant∼ of disagreement is 3.4σ.

34 Phenomenological inﬂuence of GUT inspired ideas + SM and NP contributions in b s` `− processes →

35 Phenomenological inﬂuence of GUT inspired ideas

SM and NP contributions in b c `−ν →

36 Conclusion

O The idea of grand unification leads to very rich theory and phenomenology. All GUTs predict proton decay due to the presence of extra gauge bosons called lepto-quarks and/or diquarks. O Grand unification has the ability to alleviate many ailments of the SM, but experimental data for proton decay measurements rule out the very simple GUT, the SU(5) GUT. O The concept of lepto-quarks, W0 and Z0 bosons which originally appeared in the literature in the context of GUTs are now being pursued for various other purposes unrelated to grand unification.

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