Flavor-tuned 125 GeV supersymmetric Higgs boson at the LHC:Test of minimal and natural supersymmetric models

Vernon Barger,1 Peisi Huang,1 Muneyuki Ishida,2 and Wai-Yee Keung3

1Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA2Department of Physics, Meisei University, Hino, Tokyo 191-8506, Japan

3Department of Physics, University of Illinois at Chicago, Illinois 60607, USA(Received 4 July 2012; revised manuscript received 14 November 2012; published 2 January 2013)

We show that an enhanced two-photon signal of the Higgs boson, h, observed with 125 GeV mass by

the ATLAS and CMS collaborations, can be obtained if it is identified principally with the neutral H0u of

the two Higgs doublets of minimal supersymmetry. We focus on sparticles and the pseudoscalar Higgs A

with TeV masses. The off-diagonal element of the (H0u,H

0d) mass matrix in the flavor basis must be

suppressed, and this requires a large Higgsino mass parameter, �� TeV, and large tan�. A minimal

supersymmetric Standard Model sum rule is derived that relates �� and b �b rates, and a �� enhancement

relative to the SM predicts b �b reduction. On the contrary, natural supersymmetry requires j�j<�0:5 TeV, for which �� is reduced and b �b is enhanced. This conclusion is independent of the mA value

and the supersymmetry quantum correction �b. Relative � �� to b �b rates are sensitive to �b.

DOI: 10.1103/PhysRevD.87.015003 PACS numbers: 14.80.Da, 12.60.Jv, 13.85.Qk

A �� enhancement of the 125 GeV Higgs boson signalrelative to the Standard Model (SM) expectation has beenreported by the ATLAS and CMS experiments at the LHC[1,2]. We investigate this in the minimal supersymmetricStandard Model (MSSM) in the region of large mA � TeVby flavor-tuning of the mixing angle� between two neutralcharge conjugation parity even (CP-even) Higgs flavorstatesH0

u andH0d, with the 125 GeV Higgs signal identified

principally withH0u. Then, the b �b decay, which is predicted

to be the dominant decay of the SM Higgs boson, isreduced. The production cross sections of other channelsare correspondingly enhanced, except possibly ��. Werelate the cross-section enhancements/suppressions in��=b �b=�� channels compared with those of the SMHiggs boson. We also consider the consequences for natu-ral supersymmetry (SUSY) [3]. Our focus is on a heavypseudoscalar A and large tan� � hH0

ui=hH0di, a region that

has not yet been constrained by LHC experiments [4].Light stau [5,6] and light stop quark [7] scenarios thathave been considered are outside of our purview.

Ratios of the SUSY Higgs couplings to those of the SMHiggs.—The SUSY Higgs mechanism is based on the twoHiggs doublet model of type II [8–10] with the Hu doubletcoupled to up-type quarks and the Hd doublet coupled todown-type quarks. After spontaneous symmetry breaking,the physical Higgs states are two CP-even neutral Higgs h,H, one CP-odd neutral pseudoscalar A and the chargedHiggs H�.

We focus on the CP-even neutral Higgs boson h and H,which are related to the flavor eigenstates H0

u and H0d by

hffiffiffi2

p ¼ c�H0u � s�H

0d;

Hffiffiffi2

p ¼ s�H0u þ c�H

0d; (1)

where H0u;d is the shorthand for the real part of H0

u;d �hH0

u;di. We use the notation s� ¼ sin�, c� ¼ cos�, and

t� ¼ tan�. Our interest is in large tan�, tan� * 20,and in the decoupling regime with large mA for which� ’ �� �

2 .

The ratios of the h and H couplings to those of the SM

Higgs hSM, denoted as rh;HPP ð� gh;HP �P=ghSMP �PÞ, are given by

rhVV ¼ s���; rhtt ¼ rhcc ¼ c�s�

; rh�� ¼ �s�c�

;

rhbb ¼�s�c�

�1� �b

1þ �b

�1þ 1

t�t�

��;

rHVV ¼ c���; rHtt ¼ rHcc ¼ s�s�

; rH�� ¼ c�c�

;

rHbb ¼c�c�

�1� �b

1þ �b

�1� t�

t�

��

(2)

where we include the 1-loop contribution �b to the b �b cou-pling.�b is the b-quark mass correction factor [11,12], whichmay be sizable, especially if both � and tan� are large.

�b¼ ��t�

�2�s

3�m̂~gIðm̂2

~g;m̂2~b1;m̂2

~b2Þþ h2t

16�2atIð ��2;m̂2

~t1;m̂2

~t2Þ�;

(3)

Iðx; y; zÞ ¼ � xy lnx=yþ yz lny=zþ zx lnz=x

ðx� yÞðy� zÞðz� xÞ ;

Iðx; y; z ¼ yÞ ¼ ��x� yþ x log

y

x

��ðx� yÞ2;

Iðx; x; xÞ ¼ 1

2x:

(4)

The first (second) term of �b is due to the sbottom-gluino(stop quark—chargino) loop. We nominally take Msusy ¼1TeV and express sparticle masses m̂ in units of Msusy.

The top Yukawa coupling is ht ¼ �mt=vu ¼ �mt=ðvs�Þ and

PHYSICAL REVIEW D 87, 015003 (2013)

1550-7998=2013=87(1)=015003(6) 015003-1 � 2013 American Physical Society

�mt ¼ mtð �mtÞ ¼ 163:5 GeV is the running top quark mass[13]. We consider mQ ¼ mU ¼ mD ¼ Msusy for the squark

masses in the third generation.The off-diagonal element of the stop quark squared

mass matrix is �mtXt where the stop quark mixing parame-ter Xt is given by Xt ¼ At ��=t�. The quantities At, �

and Xt are also defined in units of Msusy as at � At=Msusy,

�� � �=Msusy, and xt � Xt=Msusy ¼ at � ��=t�. Our

sign convention for � and At is the same as [14], oppositeto the sign convention of Ref. [15]. We fix m̂~g ¼ 2,

well above the current LHC reach, m̂~b1¼ m̂~b2

¼ 1, and

m̂~t1 ¼ 0:8, m̂~t2 ¼ 1:2. A stop quark mass difference

m~t2 �m~t1 � 0:4 TeV is chosen in accord with the natural

SUSY prediction [16]. Then �b is well approximatednumerically by

�b ’ ��t�20

�0:26þ

�0:09

j ��j þ 0:6� 0:003

�at

�; (5)

where the first and the second terms in the square bracketare the values of the gluino and the chargino contributions,respectively.

The chargino and neutralino masses have no special roleexcept possibly in b ! s� decay, but consistency withnatural SUSY has been found there [17]. Large mA impliesa large charged HiggsHþ mass and this suppresses theHþloop contribution to b ! s�.

The gg, �� coupling ratios r�gg;�� for � ¼ h, H,A relative to those of hSM are [18]

r�gg ¼ I�tt rhtt þ I�bbr

hbb

I�tt þ I�bb;

r��� ¼74 I

�WWr

hVV � 4

9 I�tt r

htt � 1

9 I�bbr

hbb

74 I

�WW � 4

9 I�tt � 1

9 I�bb

;

(6)

where I�WW;tt;bb represent the triangle-loop contributions to

the amplitudes normalized to the mh ! 0 limit [19–21].The XX ! h ! PP cross section ratios [18] relative to

hSM are obtained from

�P � �PP

�SM

¼ �XX!PP

�XX!hSM!PP

¼ jrhXXrhPPj2Rh

; (7)

Rh ¼ �htot

�hSMtot

¼ 0:57jrhbbj2 þ 0:06jrh��j2 þ 0:25jrhVV j2

þ 0:09jrhggj2 þ 0:03jrhccj2; (8)

where Rh is the ratio of the h total width to that of hSM,�tothSM

¼ 4:14 MeV [22] for mh ¼ 125:5 GeV. The coeffi-

cients in Eq. (8) are the SM Higgs branching fractions.Here we have assumed no appreciable h decays to darkmatter.

Sum rule of cross-section ratios.—In the largemA regionclose to the decoupling limit, � takes a value

� ¼ �� �

2þ (9)

with jj< �2 � �. Then, the rhXX of Eq. (2) are well

approximated by

rhVV ¼ 1; rhtt;cc ¼ 1þ =t�;

rh�� ’ 1� t�; rhbb ’ 1� 1

1þ �b

t�

(10)

through first order in . The rhtt;cc are close to unity becausethose deviations from SM are t� suppressed. Thus,

rhgg ’ rh�� ’ 1; (11)

since the bottom triangle loop function Ihbb is negligible

in Eq. (6). Only rhbb, rh�� can deviate sizably from unity for

large mA and large tan�. Following Eqs. (7) and (8), the�P � �PP=�SM of the other channels are commonlyreduced (enhanced) in correspondence with rhbb > 1(rhbb < 1). We predict the cross sections relative to their

individual SM expectations

�� ¼ �W ¼ �Z ¼ 1

0:6ðrhbbÞ2 þ 0:4; (12)

and

0:4�� þ 0:6�b ¼ 1; (13)

where the SM b �b branching fraction [23] is approximatedas 60%. Equation (12) holds independently of the produc-tion process. Enhanced �� implies reduced �b, as well as

enhanced �W and �Z.Flavor-tuning of mixing angle �.—Note that rhbb;�� ¼ 1

in the exact decoupling limit mA ! 1 for which ¼ 0.Flavor-tuning of to be small but nonzero is necessary toobtain a significant variation of rhbb from unity. Positive

(negative) gives bb reduction (enhancement).The mixing angle � is obtained by diagonalizing the

squared-mass matrix of the neutral Higgs in the u, d basis.Their elements at tree level are

ðM2ijÞtree ¼ M2

Zs2� þm2

Ac2�; M

2Zc

2� þm2

As2�;

� ðM2Z þm2

AÞs�c�; (14)

for ij ¼ 11; 22; 12, respectively, which gives < 0 in allregions of mA. Thus, in order to get b �b reduction, it isnecessary to cancel ðM2

12Þtree by higher order terms �M2ij.

In the 2-loop leading-log (LL) approximation the �M2ij

are given [14,24] by

M2ij ¼ ðM2

ijÞtree þ�M2ij; (15)

where

BARGER, HUANG, ISHIDA, AND KEUNG PHYSICAL REVIEW D 87, 015003 (2013)

015003-2

�M211 ¼ F3

3 �m4t

4�2v2s2�

�t�1�G15

2t�

þ atxt

�1� atxt

12

��1� 2G9

2t��

�M2Zs

2�ð1� F3Þ;

�M222 ¼ �F3

2

�m4t

16�2v2s2�

��1� 2G9

2t�ðxt ��Þ2

�;

�M212 ¼ �F9

4

3 �m4t

8�2v2s2�

��1� 2G9

2t�ðxt ��Þ

�1� atxt

6

��

þM2Zs�c�

�1� F3

2

�; (16)

where Fl ¼ 1=ð1þ lh2t8�2 tÞ with l ¼ 3, 3

2 ,94 and

Gl ¼ � 116�2 ðlh2t � 32��sÞ with l ¼ 15

2 ,92 . The Fl are

due to the wave function renormalization of the Hu fieldand the index l is the numbers of H0

u fields in the effectivepotential of the two Higgs doublet model. F3

4 ’ F943 ’

F322 ’ 1 where is defined by HuðMsÞ ¼ Huð �mtÞ where

¼ F�134

. The formulas of Refs. [14,24] are based on the

expansion Fl ¼ 1� lh2t8�2 t, but our formula of Fl is more

exact and has better approximation at large t. The parame-ter tan� ¼ vu=vd is defined in terms of the Higgs vacuumexpectation values vu;d ¼ hH0

u;di at the minimum of

the 1-loop effective potential at the weak scale � ¼ �mt

and v ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiv2u þ v2

d

q’ 174 GeV, while at, xt, �� have scale

� ¼ Msusy. The relation cot�ð �mtÞ ¼ cot�ðMsÞ�1 will be

used in the following calculation.Numerically �s ¼ �sð �mtÞ ¼ 0:109, giving �32��s ¼

�10:9. Also, ht ¼ �mt=v ¼ 0:939. G152 ;

92¼ 0:0274, 0.0442

and t ¼ logð1TeV�mtÞ2 ¼ 3:62; thus, G15

2t ¼ 0:099, 2G9

2t ¼

0:320, and F3 ¼ 0:892.In the large mA limit, the m2

h expression is

m2h ¼ M2

Zc22�

þ F3

3 �m4t

4�2v2

�t�1�G15

2t�þ

�1� 2G9

2t��x2t � x4t

12

��

�M2Z

�s4�ð1� F3Þ � 2s2�c

2�

�1� F3

2

��; (17)

where the Higgs wave function renormalization factor is retained in the denominator of F3. In the usual expan-sion of the F3 denominator G15

2and G9

2are replaced

by G32: m2

h ¼ M2Zc

22� þ 3 �m4

t

4�2v2 ½tð1 � G3tÞ þ ð1 � 2G3tÞ �ðx2t � x4t

12Þ� � M2Zs

4�

3h2t8�2 t. However, numerically Eq. (17)

significantly increases mh at large Msusy as shown in

Fig. 1. Equation (17) gives increasingmh asMsusy increases

up to �7 TeV, while the usual formula with the expansionapproximation of F3 gives decreasing mh when Msusy >

1:3 TeV and it is not applicable at large Msusy.

The experimental mh determinations from the LHCexperiments are [1,2]

mh¼125:3�0:4�0:4; 126:0�0:4�0:4GeV: (18)

It seems unlikely that the central mh determination willchange much with larger statistics because of the excellentmass resolution in the �� channel. The experimental mh

value is near the maximum possible value ofmh in Eq. (17)

and this constrains the value of xt to jxtj ’ffiffiffi6

p, to maximize

the term x2t � x4t12 . This is known as ‘‘maximal-mixing’’ in

the stop quark mass matrix [16]. In Eq. (17) we requiremh � 124 GeV. This implies

1:95ð� xtminÞ< jxtj< 2:86ð� xtmaxÞ; (19)

where we should note that the positive xt branch is favoredby the SUSY renormalization group prediction [16].By using Eq. (15) the Higgs mixing angle � is deter-

mined from

t2� ¼ 2M212

M222 �M2

11

’ ðm2A þM2

ZÞs2� � 2�M212

ðm2A �M2

ZÞc2� þ ð�M211 � �M2

22Þ;

(20)

�M212 ’ � ��

s2�xt

�1� x2t

6

�558 GeV2 þ 24 � 20

tan�GeV2:

(21)

Defining zð� M2Z=m

2AÞ, �ð� �M2

12=m2AÞ, and �ð� 1

2 �ð�M211 � �M2

22Þ=m2AÞ, is simply given in the first order

of z, �, and � by

¼ �2zþ �

tan�þ �: (22)

We note that rhbb is related to through Eq. (10). With

the xt constraint in Eq. (19), we can derive the allowed

0.5 1 2 3 4 5 10 20 30

116

118

120

122

124

126

128

130

Msusy TeV

mh

GeV

Improved formula 17

Usual formula

FIG. 1 (color online). Msusy dependence of Higgs mass mh bythe improved formula Eq. (17) (solid black) in comparison withthe one by the usual 2LL approximation (dashed blue) with alinear expansion in t of F3. In this illustration xt is taken to be

ffiffiffi6

pfollowing the ‘‘maximal-mixing’’ condition, and tan� ¼ 20.

FLAVOR-TUNED 125 GeV SUPERSYMMETRIC HIGGS . . . PHYSICAL REVIEW D 87, 015003 (2013)

015003-3

4 2 0 2 40.0

0.5

1.0

1.5

in unit of Msusy

xt 0

4 2 0 2 40.0

0.5

1.0

1.5

in unit of Msusy

xt 0

b 1

SUSYNatural

4 2 0 2 40.0

0.5

1.0

1.5

in unit of Msusy

b

x t 0

b

4 2 0 2 40.0

0.5

1.0

1.5

in unit of Msusy

b

x t 0

b

b 1

SUSYNatural

4 2 0 2 40.0

0.5

1.0

1.5

in unit of Msusy

xt 0

4 2 0 2 40.0

0.5

1.0

1.5

in unit of Msusy

xt 0

b 1

SUSYNatural

FIG. 2 (color online). �� dependence of �� ¼ ���=�SM (upper panels), �b ¼ �b �b=�SM (middle panels), and �b ¼ �b �b=�SM

(lower panels) formA ¼ 500 GeV. Their allowed values are between the solid red curve (corresponding to jxtj ¼ xtmax) and the dashedblue curve (corresponding to jxtj ¼ xtmin). Left (right) panels show negative (positive) xt region. Deviations from unity are enlarged fora large negative ��, but there the perturbative calculation is unreliable due to a large quantum correction.

BARGER, HUANG, ISHIDA, AND KEUNG PHYSICAL REVIEW D 87, 015003 (2013)

015003-4

region of rhbb for each �� value. Correspondingly,

the allowed regions of ��ð¼ ���=�SM ¼ 10:6ðrh

bbÞ2þ0:4

Þ,�bð¼ �b �b=�SM ¼ ðrh

bbÞ2

0:6ðrhbbÞ2þ0:4

Þ and ��ð¼ ���=�SM ¼ðrh��Þ2

0:6ðrhbbÞ2þ0:4

Þ are given respectively by the two curves in

Fig. 2 where we take tan� ¼ 50.The condition rhbb ¼ 1, or equivalently ¼ 0, t2� ¼ t2�,

defines the boundary that separates �� enhancement andsuppression in the parameter space:

rhbb ¼ 1 , ¼ 0 , �M212

¼ M2Zs2� ��M2

11 � �M222

2t2�: (23)

This condition is independent of mA and the quantum

correction �b. �M212 >M2

Zs2� � �M211��M2

22

2 t2� gives b �b

reduction. Flavor-tuning (FT) with small � requires acancellation of ðM2

12Þtree by the loop-level �M212 contribu-

tion, which requires rather large values of �� and tan�.This possibility was raised in Ref. [25].The region of �� enhancement does not overlap with the

region j ��j< 0:5 of natural SUSY for any value of tan�from 20 to 60. For tan� ¼ 20, j ��j * 2 is necessary for ��enhancement.We give a benchmark point of the FT model in the

MSSM (FT1) and two benchmark points of naturalSUSY (NFT1, NFT2).

�� tan� xt mhðGeVÞ �� �b ��

FT1 �3 20 �2:86 124 1:17 0:89 1:05

NFT1 �0:5 20 2:70 125 0:84 1:11 1:04

NFT2 �0:15 20 2:70 125 0:87 1:08 1:07

(24)

where Msusy ¼ 1 TeV and mA ¼ 0:5 TeV. The relevantsparticle masses are taken commonly with the valuesgiven above Eq. (5). The mh value is predicted byEq. (17). We also note that the predicted values of Bs !�þ�� branching fraction of these benchmark points areconsistent with the experimental measurement [26],ð3:2þ1:4 þ0:5

�1:2stat�0:3systÞ � 10�9 within 2�.

Natural SUSY predictions.—Natural SUSYalways predictsb �b enhancement and �� reduction [27].

mA �� �b ��

mA � 500 GeV 0:82� 0:91 1:06� 1:12 1:04� 1:08

mA � 1000 GeV 0:95� 0:98 1:01� 1:03 1:01� 1:02

(25)

Here we have taken j�j 500 GeV and the other parame-ters are fixed with the values given above Eq. (5).

Concluding remarks.—We have explored the ��, b �band �� signals in the MSSM, relative to SM, and also innatural SUSY. In MSSM an enhancement in the diphotonsignal of the 125 GeV Higgs boson relative to the SMHiggs can be obtained in a flavor-tuned model with

h ¼ H0u provided that j�j is large (TeV) and � is

negative. A �� enhancement is principally due to the

reduction of the b �b decay width compared to hSM. The

ratios of WW and ZZ to their SM values are predicted

to be the same as that of ��. There is also a correspond-

ing reduction of the h to �� signal. The Tevatron evidence

of a Higgs to b �b signal in Wþ Higgs production [29]

does not favor much b �b reduction. The flavor-tuning

of the neutral Higgs mixing angle � requires a large

�� TeV and large tan�. For small j�j<�0:5 TeV of

natural SUSY, �� suppression relative to the SM is

predicted. Thus, precision LHC measurements of the

��, WW, ZZ and b �b signals of the 125 GeV Higgs

boson can test MSSM models.

W.-Y.K. and M. I. thank the hospitality of the NationalCenter for Theoretical Sciences and Academia Sinicawhile this work was completed. M. I. is also gratefulfor hospitality at UW-Madison. This work was sup-ported in part by the U.S. Department of Energy underGrants No. DE-FG02-95ER40896 and No. DE-FG02-12ER41811.

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Z=m2A !

���=�SM ¼ 1� 2:4M2Z=m

2A, independently of tan�. The

smaller mA gives the larger suppression of �� [28]. Then,from the �� deviation from unity, the CP-odd state massmA could be estimated.

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