Higgs-charm Couplings

Higgs-charm Couplings Wai Kin Lai TUM December 21, 2017 MLL Colloquium, TUM

OUTLINE Higgs physics at the LHC

OUTLINE Higgs physics at the LHC H J/ψ + γ as a key channel to measure Hc c coupling

CHRISTMAS WISH Particle physics is able to explain everything

CHRISTMAS WISH Particle physics is able to explain everything hopefully.

STANDARD MODEL SU(3) c SU(2) W U(1) Y with 3 families of fermions and a Higgs field L SM = 1 4 Gaµν G a µν 1 4 WIµν W I µν 1 4 Bµν B µν + Q i L i /DQi L + ūi R i /Dui R + d i R i /Ddi R + L i L i /DLi L + ēi R i /Dei R +(D µh) (D µ H) λ 4 ( H H v2 2 ) 2 + ( g ij uūi R HT ɛq j L gij d d i R H Q j L gij e ēi R H L j L +h.c. ) All known physics: S = d 4 x ( g R ) 16πG + L SM

The Standard Model is very successful! Most accurate prediction in science: Magetic moment of electron µ = gee 2me s ge 2 2 = 0.00115965218073(28) [exp.], 0.00115965218178(77) [O(α 5 ) QED]

The Standard Model is very successful! Most accurate prediction in science: Magetic moment of electron µ = gee 2me s ge 2 = 0.00115965218073(28) [exp.], 0.00115965218178(77) [O(α 5 ) QED] 2 Correct quark charges and number ( of colors! ( ) R = 2 23 2 ( + 3 1 3 σ(e+ e hadrons) σ(e + e µ + µ ) = 3 ) 2 ) = 11 3 above b b threshold

The Standard Model is very successful! Most accurate prediction in science: Magetic moment of electron µ = gee 2me s ge 2 = 0.00115965218073(28) [exp.], 0.00115965218178(77) [O(α 5 ) QED] 2 Correct quark charges and number ( of colors! ( ) R = 2 23 2 ( + 3 1 3 σ(e+ e hadrons) σ(e + e µ + µ ) = 3 ) 2 ) = 11 3 above b b threshold Predicts W ±, Z bosons with right masses! (mw = 80.4 GeV, m Z = 91.2 GeV)

How about the Higgs boson?

HIGGS BOSON IN SM J PC = 0 ++ Unitarize transverse WW WW scattering at high energies Gives masses to W ±, Z: M W = g 2v 2, M Z = M W, sin θ cos θ W = g 1 W Gives masses to fermions via Yukawa couplings: g 2 1 +g2 2 L Yukawa = g ij uū i R HT ɛq j L gij d d i R H Q j L gij e ē i R H L j L + h.c. In terms of fermion mass eigenstates: L Yukawa = i [ ( m i u 1 + h ) ( ū i u i m i d 1 + h ) ( di d i m i e 1 + h ) ] ē i e i. v v v y c = 0.007, y b = 0.024, y t = 0.99 m i = vy i 2

Very small Higgs production cross section! 10 9 proton - (anti)proton cross sections 10 9 10 8 σ tot 10 8 10 7 Tevatron LHC 10 7 10 6 10 6 σ (nb) 10 5 10 4 10 3 10 2 10 1 10 0 10-1 10-2 10-3 10-4 10-5 10-6 σ b σ jet (E T jet > s/20) σ W σ Z σ jet (E jet T > 100 GeV) σ WW σ σ ZZ σ M σ H =125 GeV{ t ggh WH σ VBF 10 5 10 4 10 3 10 2 10 1 10 0 10-1 10-2 10-3 10-4 10-5 10-6 events / sec for L = 10 33 cm -2 s -1 WJS2012 10-7 0.1 1 10 s (TeV) 10-7

HIGGS PRODUCTION g g t ggf H q q W,Z W,Z VBF q q H q q W,Z WH,ZH H W,Z g g t t tth t H t σ(pp H+X) [pb] 2 10 10 pp H (NNLO+NNLL QCD + NLO EW) qqh (NNLO QCD + NLO EW) pp s= 14 TeV LHC HIGGS XS WG 2010 pp 1 pp WH (NNLO QCD + NLO EW) ZH (NNLO QCD +NLO EW) pp tth (NLO QCD) 1 10 100 200 300 400 500 1000 M H [GeV]

HIGGS DECAY Higgs BR + Total Uncert 10 1 1 10 2 ττ cc bb γγ gg Zγ WW ZZ LHC HIGGS XS WG 2013 3 10 µµ 10 4 80 100 120 140 160 180 200 M H [GeV]

The Higgs was discovered in 2012! S/(S+B) Weighted Events / 1.5 GeV 1500 1000 500 0 CMS s Data S+B Fit B Fit Component ±1σ ±2 σ -1 = 7 TeV, L = 5.1 fb Events / 1.5 GeV 1500 1000-1 = 8 TeV, L = 5.3 fb 110 120 130 140 150 m γγ (GeV) s Unweighted 120 130 m γγ (GeV) Entries / 5 GeV 40 30 20 10 CMS -1 s = 8 TeV, L = 5.1 fb data = 125 GeV 0 0 50 100 150 200 m ll (GeV) m H WW VV top Z+jets W+jets Events / 3 GeV 16 14 12 10 8 6 4 2 0 CMS Data Z+X Zγ*, ZZ s m H =125 GeV -1 = 7 TeV, L = 5.1 fb Events / 3 GeV 5 4 3 2 1 0-1 = 8 TeV, L = 5.3 fb 80 100 120 140 160 180 m 4l (GeV) s 6 K D > 0.5 120 140 160 m (GeV) 4l H t H W W+ l l H Z Z l l l l m H = 125.7 ± 0.4 GeV (LHC Run 1)

Results of LHC Run 1: µ i = σ i σ i SM µ i = Bri Br i SM

The Higgs was rediscovered in LHC Run 2!

Summary of results from LHC Run 1: Production well tested: ggf, VBF, VH observed, cross sections consistent with SM tth not observed. Decay well tested: γγ, WW, ZZ, τ τ observed, branching ratio consistent with SM H b b not observed Update from Run LHC 2: tth observed, cross section consistent with SM H b b observed, branching ratio consistent with SM But about H c c? (Note that H c c = 3%, H b b = 58%.) So it s very hard to measure Higgs-charm coupling!

Two ways to measure Hc c coupling: Inclusive observable: H c c + X, tag two c-jets Advantage: large rate Disadvantage: c-tagging challenging, signs of coupling degenerate

Two ways to measure Hc c coupling: Inclusive observable: H c c + X, tag two c-jets Advantage: large rate Disadvantage: c-tagging challenging, signs of coupling degenerate Exclusive observable: H J/ψ + γ Advantage: clean signal (J/ψ µ µ), sensitive to both magnitude and sign of coupling Disadvantage: small rate

H Direct amplitude. Indirect amplitude. A = A dir + A indir, Γ α V β V κ Q 2, κ Q =dimensionless Hc c coupling (κ = 1 in SM). Γ sensitive to both magnitide and sign of κ Q. Indirect amplitude determined to percent level. Direct amplitude has large uncertainty. State of the art: O(v 2 ) with light-cone resummation, and O(α s) fixed-order calculation at leading order in v. Γ v 2 10%, Γ αs 60%. Aim of this project: O(v 4 ) corrections to the direct amplitude with light-cone resummation, matching LCDA with color-octet LDME s.

FACTORIZATION Separation of scales: m H m mv

FACTORIZATION Separation of scales: m H m mv Factorized into pqcd SCET NRQCD: σ = H(µ h ) LCDA(µ h ) = H(µ h ) C(µ h, µ s) LDME(µ s) = H(Q) U(Q, m) C(m, m) LDME(m) H(Q) U(Q, m) C(m, m) LDME(mv) (1) µ h m H, µ s m

FACTORIZATION Separation of scales: m H m mv Factorized into pqcd SCET NRQCD: σ = H(µ h ) LCDA(µ h ) = H(µ h ) C(µ h, µ s) LDME(µ s) = H(Q) U(Q, m) C(m, m) LDME(m) H(Q) U(Q, m) C(m, m) LDME(mv) (1) µ h m H, µ s m U(Q, m) resums ln n (m H /m)

Result with O(v 2 ) LDME s and light-cone resummation (courtesy H. S. Chung):

Light cone distribution amplitude (LCDA) φ V (x): 1 1 2 V Q(z)[γ µ, γ ν ][z, 0]Q(0) 0 = f V (ɛ µ V pν V ɛ ν V pµ V ) dx e ip V zx φ V (x) (2) 0 Explicit demonstration of QCD-LCDA factorization for Q Qg final state at leading order at α s in the light-cone limit: H QCD diagrams for QCD-LCDA matching with Q Qg final state at leading order in α s. Diagrams for LCDA with Q Qg final state. Diagram (c) has a gluon emitted from the Wilson line. im = i 2 ee Qκ Q m( 2G F ) 1/2 f V ( ɛ V ɛ γ + ɛ V pγ ɛ γ p ) V 1 dx T(x)φ V (x) (3) p γ p V 0 where T(x) = 1 x(1 x).

Running of φ V (x, µ) governed by Brodsky-Lepage kernel: µ 2 µ 2 φ V (x, µ) = C α s(µ) F 4π 1 0 dy V T (x, y)φ V (y, µ) (4) M = Ch f 1 V 0 dx T(x)φ V (x, µ h ), µ h m H. Resum ln n (m H /m Q ) by running φ(x, µ) from µ s to µ h, µ s m Q. ξ n 1 0 dx (2x 1) n φ V (x, µs) related to LDME s in NRQCD by 1 2 V Q(0)[γ µ, γ ν ] ( n D ) n Q(0) 0 = fv (ɛ µ V pν V ɛ ν V pµ V )( n p V) n 1 0 dx ξ n φ V (x) (5)

With conservative power counting, to relatove order v 4 the following LDME s are included: LDME (abbrev.) LDME relative order φ 1 0 V ψ σ ɛχ 0 1 2Nc v 2 1 m 2 V ψ Q σ ɛ( i 2Ncφ0 2 D ) 2 χ 0 v 2 O 2 1 m 2 V ψ σ i ɛ j ( 2Ncφ0 2 i )2 D (i D j) χ 0 v 4 Q v 4 1 m 4 V ψ Q σ ɛ( i 2Ncφ0 2 D ) 4 χ 0 v 4 O B 1 m 2 V ψ gb ɛχ 0 v 3 2Ncφ0 Q O E1 1 m 3 V ψ (σ (ge D )) ɛ 0 v 3 2Ncφ0 Q O E2 1 m 3 V ψ σ ɛ( D ge ge D )χ 0 v 3 2Ncφ0 Q O E3 1 m 3 V ψ (σ ge)ɛ D χ 0 v 3 Ncφ0 Q Result (preliminary): (Not shown)

SUMMARY AND OUTLOOK Summary: Proof of QCD-LCDA factorization for Q Qg final state at leading order in α s. Matching LCDA to LDME s to O(v 4 ) at leading order in α s, including octet operators. Outlook: Numerical estimate of uncertainties. Propose ways to calculate the relavant LDME s on the lattice. Full O(α sv 2 ) calculation.

Thank you.