beyond the standard model @ the tev scale nathaniel craig uc - PowerPoint PPT Presentation

beyond the standard model @ the tev scale nathaniel craig uc santa barbara 2017 ICTP Summer School on Particle Physics

not your advisor’s “beyond the standard Model” wait, that’s not in kolb & turner… bsm is as old as the standard model, giving rise to dominant paradigms (the mssm, wimps, etc.) that fill lectures such as these. but we are in an era rich with data that is challenging these paradigms, so let’s keep an eye on promising alternatives.

outline prologue: effective field theory Part 1: Part 2: Part 3: hierarchy problems hierarchy solutions everything* else naturalness • multiple vacua strong cp problem • • scalar masses • low cutoffs unification • • versions of the • symmetries baryogenesis • • hierarchy problem epilogue: looking to the future

prologue: effective field theory

beyond? see lectures by Y . Nir By standard model , let us take this to mean (1) the observed matter (three generations of quarks & leptons), higgs doublet, and gauge fields. (2) all renormalizable (marginal or relevant) interactions allowed by the field content & gauge symmetries (“totalitarian principle”) BSM entails anything beyond this (new fields or irrelevant operators)

irrelevant? consider scalar field theory in 4 dimensions w/ some polynomial potential:  1 � 2 ∂ µ φ∂ µ φ − 1 2 m 2 φ 2 − 1 4! λφ 4 − 1 Z d 4 x 6! τφ 6 S [ φ ] = in any d, mass dimensions of length & action fixed, [ x ] = − 1 , [ S ] = 0 [ d 4 x ] = − 4 [ m 2 ] = 2 so: [ φ ] = 1 [ λ ] = 0 [ τ ] = − 2 study theory at long distances in scaling limit x µ = sx 0 µ , s → ∞ , x 0 µ fixed φ ( x ) = s (2 � d ) / 2 φ 0 ( x 0 ) keep canonical kinetic term, so work w/  1 � 2 ∂ µ φ 0 ∂ µ φ 0 − 1 2 m 2 s 2 φ 0 2 − 1 4! λ s 0 φ 0 4 − 1 Z d 4 x 0 6! τ s � 2 φ 0 6 S 0 [ φ 0 ] = grows at long constant shrinks distance ( relevant ) ( marginal ) ( irrelevant )

renormalizable? theories with only marginal & relevant operators are renormalizable. historically impose renormalizability in order to preserve predictivity . loops introduce divergences, removed w/ counterterms. fix counterterms with data. renormalizability = finite # of counterterms = predictive (i.e. use some data to fix counterterms, make predictions for other measurements) Z d 4 k in our example, only renormalizes the k 4 ∼ λ 2 log Λ ∼ λ 2 divergence from marginal operator marginal/relevant λφ 4 ⇒ need counterterm operators is δλ Z d 4 k renormalizes new k 4 ∼ τ 2 log Λ but irrelevant ∼ τ 2 irrelevant operator operator φ 6 ρφ 8 ⇒ need counterterm generates δρ adding φ 8 operator then generates φ 10 operator, and so on ad infinitum. need infinite # of measurements to fix all coefficients.

all is not lost can we live with a nonrenormalizable theory? [ d 4 x ] = − 4 [ m 2 ] = 2 [ φ ] = 1 [ λ ] = 0 [ τ ] = − 2 τ has mas dimension -2. at some scale Λ , τ ∼ 1/ Λ 2 . at energies E ≪ Λ , effects of φ 6 on Λ marginal/relevant physics are O(E 2 / Λ 2 ) φ 8 effects are O(E 4 / Λ 4 ), and so on. if we only study physics at E ≪ Λ , can include some irrelevant operators & neglect φ n operators as predictivity long as we only work to O(E N / Λ N ) precision. finite # of irrelevant operators = O(E N / Λ N ) predictive good for E ≪ Λ . as we approach Λ all operators equally important, need uv completion E

effective field theory describing a physical system requires specifying: • Important degrees of freedom: in qft, what fields? • important symmetries: in qft, what interactions? this + renormalizability gives us the standard model. but we can relax renormalizability if in addition we specify • expansion parameters: in qft, what power counting? this last ingredient gives us effective field theory . power counting is usually in distances/energies.

effective field theory two kinds: t0p-down eft bottom-up eft High energy theory is understood, Underlying theory is unknown but useful to have simpler theory or matching is too difficult to at low energies. carry out L ( n ) Theory 1 ??? X L ( n ) X L High → ↓ ↓ low low Theory 2 Theory 2 n n Integrate out & match (matrix write down all interactions elements) at intermediate scale consistent w/ symmetries. couplings not predicted, but fit to data. E.g. theory of weak interactions (fermi effective theory). Waaaay E.g. chiral lagrangian, quantum easier to compute qcd corrections. einstein gravity , or standard model

The standard model as eft if we limit sm to only renormalizable ops, why worry about all this? the Standard model is not uv complete. (1) “quantum” gravity consistent but non-renormalizable, demands uv completion at the planck scale; presumably also involves sm*. (2) we have incontrovertible evidence for additional fields and/or operators beyond sm. 10 5 *what if gravity decouples from sm in the uv? 1 0.50 α ( μ ) running sm gauge couplings into far uv eventually gives landau pole in U(1) Y . would cause fermions to 0.10 0.05 condense in uv. so uv completion of sm is unavoidable! 0.01 100 10 12 10 22 10 32 10 42 μ [ GeV ] Note: not all evidence for bsm comes from high energies; the most compelling is from scales at or below the weak scale.

The standard model as eft what’s the matter with hypercharge? ✓ µ α 2 ◆ α i ≡ g 2 1 1 ∂α i α i ( m Z ) = − b i i i 2 π ln + . . . ∂ ln µ = β i = b i 2 π + . . . ⇒ α i ( µ ) − m Z 4 π b 1 = 41 / 10 b 2 = − 19 / 6 b 3 = − 7 10 sign of U(1) beta function fixed; 5 additional charged states only increase coefficient. all non-trivial 1 U(1)’s run to landau poles in the UV. 0.50 α ( μ ) usual assumption: running cut off 0.10 by unification around 10 15 GeV or 0.05 quantum gravity around 10 18 GeV 0.01 without such a cutoff , landau 10 12 10 22 10 32 10 42 100 pole inevitable. μ [ GeV ]

the smeft treat sm as “bottom-up EFT”, write down all operators consistent with symmetries to given order in power counting 1 dim-5 : 1 operator* Λ ( HL ) 2 schematically dim-6 : 59+4 operators* gauge boson operators four-fermi operators 1 1 1 Λ 2 ( ¯ ψγ µ ψ )( ¯ Λ 2 | H | 2 V µ ν V µ ν Λ 2 ( D µ V µ ν ) 2 ψγ µ ψ ) higgs operators 1 1 1 1 Λ 2 | H † D µ H | 2 Λ 2 ( ∂ µ | H | 2 ) 2 Λ 2 | H | 2 | D µ H | 2 Λ 2 | H | 6 the game: fix/constrain coefficients with data! *Neglecting flavor, i.e. 1 generation at a time.

the smeft henning, lu, melia, murayama ‘15 10000000000 7557369962 2795173575 1000000000 175373592 100000000 75577476 #generations=3 10000000 4614554 5474170 No. of independent ops 3472266 2092441 1000000 261485 257378 100000 90456 44807 15456 10000 11962 3045 1542 993 #generations=1 1000 560 100 84 30 12 10 2 1 (separately counting operators & their hermitian conjugates) 5 6 7 8 9 10 11 12 13 14 15 Mass dimension

the data So far, only one nonzero coefficient. majority of bounds on smeft at or near tev scale; exceptions arise in some high-precision settings (e.g., flavor, edm)

beyond the standard model Look for specific guidance in the shortcomings of the standard model Substance dark matter neutrino mass suggestion unification baryogenesis speculation strong cp problem cc problem ????????????????????????????????????????????????????????? hierarchy problem 10 - 18 10 - 8 10 12 10 22 100 Energy Scale [ GeV ]

beyond the standard model TeV scale Substance dark matter neutrino mass suggestion unification baryogenesis speculation strong cp problem cc problem ????????????????????????????????????????????????????????? hierarchy problem 10 - 18 10 - 8 10 12 10 22 100 Energy Scale [ GeV ]

Part 1: The hierarchy problem

naturalness criteria “ dirac natural :” in theory with fundamental scale Λ , natural size of operator coefficients is c O = O (1) × Λ 4 − ∆ O borne out countless times in nature & simulation. “ technically natural (’t hooft):” coefficients can be much smaller if there is an enhanced symmetry when the coefficient is zero. c O = S × O (1) × Λ 4 − ∆ O where s is a parameter that violates symmetry . philosophical underpinning: quantum corrections respect symmetry; if symmetry is broken, quantum corrections proportional to symmetry breaking.

naturalness in nature dirac’s question: why is m p <<m Pl ? 18 orders of magnitude! answer: qcd scale is dynamically generated by logarithmic evolution of qcd coupling: “dimensional transmutation” α 2 ✓ M P l ◆ 1 1 α 3 ( µ ) = − b 3 ∂α i i 2 π ln + . . . ∂ ln µ = β i = b i ( µ < M P l ) 2 π + . . . ⇒ α 3 ( M P l ) − µ b 3 =-7, so there exists a scale where α 3 →∞ : confinement 1 2 π 1 α 3 ( Λ QCD ) = 0 → Λ QCD = M P l e α s ( MP l ) b 3 m p ∼ Λ QCD Proton acquires most of its mass from confinement, the dimensionless coupling is O(1), totally natural