Higgs Precision Measurements and Flavor Physics: A Supersymmetric Example
aa r X i v : . [ h e p - ph ] D ec Higgs Precision Measurements and Flavor Physics:A Supersymmetric Example
Review for “Chinese Science Bulletin” and CEPC+SPPC Proposal
Kai Wang and Guohuai Zhu
Zhejiang Institute of Modern Physics and Department of Physics,Zhejiang University, Hangzhou, Zhejiang 310027, CHINA
Rare decays in flavor physics often suffer from Helicity suppress and Loop suppress.Helicity flip is a direct consequence of chiral U (3) symmetry breaking and electroweaksymmetry breaking. The identical feature is also shared by the mass generation of SMfermions. In this review, we use MSSM as an example to illustrate an explicit connectionbetween bottom Yukawa coupling and rare decay process of b → sγ . We take a symmetryapproach to study the common symmetry breaking in supersymmetric correction to bottomquark mass generation and b → sγ . We show that Large Peccei-Quinn symmetry breakingeffect and R -symmetry breaking effect required by b → sγ inevitably lead to significantreduction of bottom Yukawa y b . To compromise the reduction in b ¯ b , a new decay is alsoneeded to keep the Higgs total width as the SM value. I. INTRODUCTION: CHIRAL AND ELECTROWEAK SYMMETRY BREAKING
A SM-like Higgs boson has been discovered at both ATLAS and CMS detectors at the CERNLarge Hadron Collider first via the two cleanest channels, di-photon and four-lepton, with recon-structed invariant mass of 125 GeV[1]. The di-lepton mode was also seen with mass range consis-tent with the four-lepton measurement [2]. Updates from the two collaborations [3, 4] also prefera CP-even spin-zero state J P C = 0 ++ . The over-5 σ evidence of gg → φ → ZZ ∗ → ℓ + i ℓ − i ℓ + j ℓ − j clearly indicates that the boson φ is responsible for electroweak symmetry breaking and should beidentified as the Higgs boson. In addition, both collaborations have also reported the boson de-caying into tau pairs, φ → τ + τ − which is the first evidence at the LHC that the Higgs-like bosonactually couples to SM fermions. However, the final confirmation of whether the Higgs boson isthe standard model (SM) Higgs boson still requires precision measurement of the Higgs couplings.For instance, in the so-called “decoupling limit”, many new physics models beyond the SM alsopredict a light Higgs boson with couplings only differ from the SM ones by 10% or less. There isalso example where the other couplings of this Higgs boson except the bottom Yukawa are verysimilar to the SM Higgs couplings while the bottom Yukawa measurement itself still suffer fromlarge uncertainty. Higgs physics has entered an era of precision measurement and various e + e − colliders as Higgs factory have been proposed as one intensity frontier with controlled backgroundto improve the measurement of Higgs couplings.On the other hand, the other type of intensity frontier as flavor factories have been playingimportant role in searching physics beyond the SM for many years. In this review, we try to illus-trate the direct correlation between physics at two types of intensity frontier, the Higgs precisionmeasurement and flavor physics.Fermion mass is a consequence of chiral symmetry breaking. The Lagrangian of the kineticenergy and gauge interactions of the SM fermion fields is i ¯ Q iL (cid:0)(cid:0) DQ iL + i ¯ u iR (cid:0)(cid:0) Du iR + i ¯ d iR (cid:0)(cid:0) Dd iR + i ¯ ℓ iL (cid:0)(cid:0) Dℓ iL + i ¯ e iR (cid:0)(cid:0) De iR (1)where index i stands for generation. In Eq.1, all the fields carry unbroken gauge symmetry U (1) EM and some are fundamental representation of SU (3) C , Majorana masses are strictly forbidden forthe above fields. Lagrangian in Eq.1 is also invariant under global unitary transformations f i → U ijf f j , f i ∈ { Q iL , u iR , d iR , ℓ iL , e iR } (2)which correspond to accidental chiral symmetries U (3) Q × U (3) u × U (3) d × U (3) ℓ × U (3) e forthree generations. Yukawa couplings y u,d,e of the SM fermions to the Higgs boson, − y iju ¯ Q iL u jR ¯ H − y ijd ¯ Q iL d jR H − y ije ¯ ℓ iL e jR H + h.c., ¯ H = ǫH ∗ , (3)explicitly break the above chiral symmetries and SM fermion masses arise after H developingthe vacuum expectation value. Therefore, SM fermion mass generation is a consequence of bothchiral symmetry breaking and electroweak symmetry breaking.Rare decays in flavor physics often suffer from Helicity suppress and Loop suppress. Forinstance, pseduo-scalar leptonic decay π − → e − ¯ ν e is suppressed by the electron mass. The SMcontribution to B s → µ + µ − is suppressed by the muon mass insertion. Dipole operator ¯ bσ µν sF µν (4)which correspond to b → sγ . Existence of on-shell spin-one photon implies that the helicity in in-volving quark states must be flipped in b → sγ process. Helicity flip also breaks chiral symmetriesand electroweak gauge symmetry. In SM, the helicity flip here corresponds to a mass insertion of m b . Therefore, there may exist a direct correlation between b -quark mass generation and b → sγ .In this review, we use MSSM as an example to illustrate the feature as how contribution to b → sγ may modify the b Yukawa coupling.
II. TYPE-II 2HDM AND PECCEI-QUINN SYMMETRY
We are interested in the deviation in bottom Yukawa coupling as m b = y b v d + ∆ m b . (5)This is a typical feature Type-II Two-Higgs-Doublet-Model(2HDM) where quark mass generationarises from two different electroweak symmetry breaking sources.Minimal Supersymmetric Standard Model (MSSM) is a natural Type-II 2HDM. The superpo-tential being holomorphic so the ¯ H = ǫH ∗ is forbidden in superpotential. The anomaly cancella-tion conditions for [ SU (2) L ] U (1) Y and Witten anomaly also require the introduction of secondHiggsino, the Fermonic partner of the Higgs boson, so that the Higgsino contributions to anoma-lies vanish. MSSM superpotential is W = y u Qu c H u + y d Qd c H d + y e ℓe c H d + µH u H d (6)The µ is a dimensional parameter which is constrained. µ cannot be zero to avoid massless Hig-gsino and µ cannot be too large either so that the Higgs boson do not decouple. Suppose µ arisefrom a dynamical field S which is SM singlet W ∋ SH u H d . (7)In order to forbid the bare µ -term in the superpotential, we assume there exists a non- R U (1) X symmetry under which S transforms non-trivially s = 0 . Qu c H u : q + u + h u = 0 Qd c H d : q + d + h d = 0 SH u H d : s + h u + h d = 0 (8) U (1) X SU (3) C SU (3) C FIG. 1. Mixed QCD anomaly A [ SU (3) C ] U (1) X . If one compute the mixed QCD anomaly with U (1) X as in Fig.1, one can obtain the anomalycoefficient A [ SU (3) C ] U (1) X = N f q + u + d ) = − N f h u + h d ) = N f s = 0 (9)Therefore, a non-zero s charge results in non-vanishing of mixed QCD- U (1) X anomaly A [ SU (3) C ] U (1) X .The U (1) X can then be identified as Peccei-Quinn (PQ) symmetry which is a global U (1) symme-try with mixed QCD anomaly. The µ -term which corresponds to the Higgsino mass term explicitlybreaks the PQ symmetry.In a full MSSM, PQ symmetry breaking not only appears as Higgsino mixing ˜ H u ˜ H d but alsoappear in scalar potential as V ∋| F H d | = y d µ ∗ H ∗ u ˜ Q ˜ d + y e µ ∗ H ∗ u ˜ ℓ ˜ e (10)where F H d = ∂W∂H d = y d Qd c + y e ℓe c + µH u . (11)When the global U (1) PQ symmetry is broken by anomaly, a pseudo-Goldstone boson is gen-erated with its mass generated by non-perturbative QCD effect. The term in Eq.7 would lead toWeinberg-Wilczek axion which is excluded by K → πa constraint. Therefore, one can introducean extra S term to explicitly break the U (1) PQ into Z known as NMSSM approach or exoticquarks to cancel the above anomaly known as gauged U (1) ′ approach. Coincidently, QCD in-visible axion requires the PQ symmetry breaking scale is the same as the intermediate scale ingravity mediation supersymmetric theory, M /M Pl ∼ M EW . The U (1) X can actually providea simultaneous solution to strong CP problem and the µ -term problem as Kim-Nilles mechanismbased on supersymmetric DFSZ H u H d S /M Pl axion model [5]. III. R -SYMMETRY AND SUPERSYMMETRIC CORRECTIONS TO MASS GENERATION In analogy to the chiral symmetry breaking that is associated with fermion mass generation,the Majorana gaugino mass in supersymmetric theory is associated with R -symmetry breaking. Aglobal U (1) R -transformation is defined as a rotation over the anti-commuting coordinates (Grass-mann variables) θ and ¯ θ R : θ → e iα θ, ¯ θ → e − iα ¯ θ (12)Gauge vector superfields are real so they are neutral under R -transformation. The gaugino com-ponent is then of R -charge 1 as R : λ → e iα λ (13)and gaugino mass term M λ λλ always break the U (1) R -symmetry.One can categorize the soft-supersymmetry breaking Lagrangian based on the PQ and R sym-metries in M λ λλ + ˜ A u ˜ Q ˜ u c H u + ... : (cid:0)(cid:0) RBµH u H d : ✚✚ PQ , (cid:0)(cid:0) RM f ˜ f ∗ ˜ f : . (14)The gaugino mass and ˜ A -terms break R -symmetry. Bµ -term breaks both R and PQ symmetries.The scalar mass term ˜ f ∗ ˜ f is trivial under any unitary transformation.The two global U (1) assignments in MSSM are not uniquely defined. In Table III, we list onesets of assignment of PQ and R charges consistent of SU (5) . Field
Q u c e c d c ℓ H u H d θR -charge
15 15 15 75 75 85 25 R -symmetry and Peccei-Quinn symmetry. In MSSM, b -quark mass arises at the tree level from y d Qd c H d . The supersymmetric correctionto m b is effectively Qu c ¯ H u (15)which is known to be Lorentz invariant and gauge invariant in SM. Using charge assignments inTable III, one can substitute them into calculation of effective coupling Qd c ¯ H u as R [ Qd c ¯ H u ] : + − = 0 (16) PQ[ Qd c ¯ H u ] :0 + ( −
1) + 0 = − . (17)Taking two Fermonic component, the R -invariant condition is of R -charge 2 while the aboveterm is 0 so it breaks R -symmetry as well as the PQ symmetry. A trivial realization is that thecorrection can come from the two Higgs mixing term which is known as Bµ -term. Bµ -termexplicitly breaks the PQ and R symmetries as discussed previously. We can conclude that thesupersymmetric correction to SM fermion masses must break PQ and R symmetries in additionto the chiral symmetry and electroweak symmetry. Chiral symmetry breaking is quantized by theYukawa coupling. In the case of m b , the correction is also proportional to H u vev v u which istypically dominated the electroweak symmetry breaking since it is the dominant contribution totop quark mass. Besides y b and v u , the size of correction ∆ m b is then proportional to scales thatbreak the PQ and R symmetries, including Bµ -term, product of µ -term and gaugino masses or A -terms.An inapparent electroweak symmetry breaking source is the Wino-Higgsino mixing as in theneutralino mass matrix N = M − g v d / √ g v u / √ M g v d / √ − g v u / √ − g v d / √ g v d / √ − µg v u / √ − g v u / √ − µ . (18) IV. NON-DECOUPLING MSSM AN EXAMPLE
To illustrate the feature, we take a non-decoupling limit [6, 7] where supersymmetric correctionto b → sγ is maximized to cancel the contribution from light charged Higgs. In this limit, theHiggs boson of 125 GeV is identified as the heavy neutral Higgs H by taking M A around m Z scaleand the charged Higgs H ± is also around O (100 GeV ) as the tree level contribution to chargedHiggs mass M H ± = M A + m W . Such a light charged Higgs may significantly enhance the flavorviolation b → sγ . The 2HDM constraint on b → sγ has pushed the charged Higgs mass to be over300 GeV. Significant cancellation to the light charged Higgs of O (100 GeV ) is then needed fromsupersymmetric particles. As we argued, large supersymmetric correction is a consequence oflarge PQ symmetry breaking and large R symmetry breaking so qualitatively it is easy to see wherethe allowed parameter region lies. At the same time, the inevitable supersymmetric correctionsignificantly modifies the bottom Yukawa coupling. Large reduction in H → b ¯ b then results inlarge reduction of Higgs total width. Since all other Higgs decay channels are at similar level asthe SM predicts, new decay channel is then needed to compromise the reduction of Higgs totalwidth. This feature has been discussed in details by our previous work [7] and we give a briefsummary in this section.In [7], all the numerical analysis are performed with FeynHiggs 2.9.2 [10] with
HiggsBounds3.8.0 [11] and
SUSY Flavor 2.01 [12]. We implement the requirements as• M H : 125 ± GeV;• R γγ = σ γγ obs /σ γγ SM : 1 ∼ ;• Combined direct search bounds from HiggsBound3.8.0;• BR ( B → X s γ ) < . × − ;• BR ( B s → µ + µ − ) < × − .We also calculate the constraint on B + → τ + ν and find the destructive interference between theSM W and the charged Higgs make the MSSM prediction about ∼ smaller than the SMresult of (0 . ± . × − . While the experimental world average is (1 . ± . × − before2012 [8], Belle updated their measurement at ICHEP2012 with much smaller value . +0 . − . × − for hadronic tag of τ [9]. So in the non-decoupling limit, a light charged Higgs with tan β ∼ is well consistent with the new Belle measurement. In addition, the charged Higgs contributionto B → D ( ∗ ) τ ν τ decays are not very significant in the interesting region of M H + and tan β . In FeynHiggs , Higgs boson masses are calculated to full two-loop. To illustrate the qualitative featurehere, we use the leading one-loop expression with only contributions of top Yukawa couplings.Radiative corrections to the Higgs boson mass matrix elements and Higgs decay are [13–15].Figure 2 give the allowed parameter region for the fixed choice of top squark mass as 500 GeVto enhance the correction. The points in blue region pass in addition the constraint of BR ( B → X s γ ) , while the points in black region pass all the constraints, including further the restriction ofBR ( B s → µ + µ − ) . It is clear that the survival region corresponds to large PQ symmetry and R M t Ž L = M t Ž R =
500 GeV M A : 95 GeV --
150 GeVtan Β : 1 -- - - - A t H TeV L Μ H T e V L H + M t Ž L = M t Ž R =
500 GeV
Μ = A t = -
740 GeVtan Β =11
140 160 180 200 220 24050100150200250 M A H GeV L H i gg s M ass H G e V L FIG. 2. (a) Scan Results in [ A t , µ ] plane. The heavy (light) stop scenario with M ˜ Q = M ˜ t = 1 (0 . TeVis shown in the left (right) plot. The red region pass the direct search bounds from HiggsBounds with aheavy CP-even Higgs M H = 125 ± GeV and an enhanced diphoton rate < R γγ < . The blue regionpass in addition the constraint of BR ( B → X s γ ) , while the black region pass all the constraints, includingfurther the restriction of BR ( B s → µ + µ − ) . (b) M h,H,H ± vary with respect to M A for M ˜ t = 500 GeV, A t = − GeV, tan β = 11 , µ = 2300 GeV. symmetry breaking where µ ∼ − − TeV and A t ∼ − GeV. Figure 2-b plots the Higgsmasses respect to M A for one set of benchmark points in the allowed parameter region.When the supersymmetric correction in flavor physics processes is significant, bottom Yukawaalso receives significant corrections while at the same time τ Yukawa is not modified signifi-cantly. Figure 3 shows the correlation between BR ( H → τ + τ − ) normalized by its SM valueand BR ( H → b ¯ b ) normalized by the corresponding SM value as well as the correspondingBR ( t → bH + ) with respect to M H ± by assuming BR ( H + → τ + ν τ ) = 100% for the survivalpoints. In Fig.3-a, the region where R τ + τ − ≃ , H → b ¯ b partial width is much less than its SMvalue but a new decay of H → hh is opened and compromises the reduction of b ¯ b partial widthto make the Higgs total width remaining unchanged. Fig.3-b clearly shows that all the parameterpoints that pass our selections are below the search of light charged Higgs boson via top decay t → bH + with H + → τ + ν τ . R b b R Τ - Τ + æ æ æ æ æ ATLAS Observed CLsData2011 7 TeV 4.6 fb -
120 130 140 150 1600.0000.0050.0100.0150.020 M H + H GeV L B r I t ® b H + M FIG. 3. (a) BR ( H → τ + τ − ) in correlation with BR ( H → b ¯ b ) normalized by the SM values respectively.(b) BR ( t → bH + ) vs M H ± by assuming BR ( H + → τ + ν τ ) = 100% . Red dots are parameter points thatpass all our selection and constraints. V. CONCLUSIONS
Rare decays in flavor physics often suffer from Helicity suppress and Loop suppress. Helicityflip is a direct consequence of chiral U (3) symmetry breaking and electroweak symmetry breaking.The identical feature is also shared by the mass generation of SM fermions so one would expectthat there exists a general correlation between the helicity flip flavor physics process and SMfermion mass generation. To illustrate the feature, we take a non-decoupling limit [6, 7] wheresupersymmetric correction to b → sγ is maximized to cancel the contribution from light chargedHiggs. In this limit, the Higgs boson of 125 GeV is identified as the heavy neutral Higgs H bytaking M A around m Z scale and the charged Higgs H ± is also around O (100 GeV ) as the treelevel contribution to charged Higgs mass M H ± = M A + m W . Such a light charged Higgs maysignificantly enhance the flavor violation b → sγ . The 2HDM constraint on b → sγ has pushedthe charged Higgs mass to be over 300 GeV. Significant cancellation to the light charged Higgsof O (100 GeV ) is then needed from supersymmetric particles. At the same time, the inevitablesupersymmetric correction significantly modifies the bottom Yukawa coupling. Large reduction in H → b ¯ b then results in large reduction of Higgs total width. Since all other Higgs decay channelsare at similar level as the SM predicts, new decay channel H → hh is then needed to compromisethe reduction of Higgs total width.0A more general approach to study correlation between Yukawa couplings and helicity flippedflavor violation operators is to appear in [16]. ACKNOWLEDGEMENT
KW is supported in part, by the Zhejiang University Fundamental Research Funds for the Cen-tral Universities (2011QNA3017) and the National Science Foundation of China (11245002,11275168).GZ is supported by the National Science Foundation of China (11075139, and 11135006) and Pro-gram for New Century Excellent Talents in University. [1] G. Aad et al. [ATLAS Collaboration], Phys. Lett. B [arXiv:1207.7214 [hep-ex]]. S. Chatrchyan et al. [CMS Collaboration], Phys. Lett. B [arXiv:1207.7235 [hep-ex]].[2] ATLAS Collaboration, ATLAS-CONF-2012-098[3] ATLAS Collaboration, ATLAS-CONF-2012-169[4] CMS Collaboration, CMS-PAS-HIG-12-041[5] J. E. Kim and H. P. Nilles, Phys. Lett. B , 150 (1984). K. S. Babu, I. Gogoladze and K. Wang,Phys. Lett. B , 214 (2003) [hep-ph/0212339].[6] A. Belyaev, Q. -H. Cao, D. Nomura, K. Tobe and C. -P. Yuan, Phys. Rev. Lett. , 061801(2008) [hep-ph/0609079]. S. Heinemeyer, O. Stal and G. Weiglein, Phys. Lett. B , 201 (2012)[arXiv:1112.3026 [hep-ph]]. A. Bottino, N. Fornengo and S. Scopel, Phys. Rev. D , 095013 (2012)[arXiv:1112.5666 [hep-ph]]. N. D. Christensen, T. Han and S. Su, Phys. Rev. D , 115018 (2012)[arXiv:1203.3207 [hep-ph]]. K. Hagiwara, J. S. Lee and J. Nakamura, arXiv:1207.0802 [hep-ph].R. Benbrik, M. G. Bock, S. Heinemeyer, O. Stal, G. Weiglein and L. Zeune, arXiv:1207.1096 [hep-ph].A. Arbey, M. Battaglia, A. Djouadi and F. Mahmoudi, JHEP , 107 (2012) [arXiv:1207.1348 [hep-ph]]. G. Belanger, U. Ellwanger, J. F. Gunion, Y. Jiang, S. Kraml and J. H. Schwarz, arXiv:1210.1976[hep-ph]. M. Drees, arXiv:1210.6507 [hep-ph]. P. Bechtle, S. Heinemeyer, O. St [] l, T. Stefa-niak, G. Weiglein and L. Zeune, arXiv:1211.1955 [hep-ph]. B. Bhattacherjee, M. Chakraborti,A. Chakraborty, U. Chattopadhyay, D. Das and D. K. Ghosh, Phys. Rev. D , 035011 (2013)[arXiv:1305.4020 [hep-ph]]. G. Barenboim, C. Bosch, M. L. Lpez-Ibaez and O. Vives, JHEP ,051 (2013) [arXiv:1307.5973 [hep-ph]]. J. Cao, F. Ding, C. Han, J. M. Yang and J. Zhu, JHEP ,
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