{'fraction_non_alphanumeric': 0.04575365001028172, 'fraction_numerical': 0.022722599218589348, 'mean_word_length': 3.728731161886242, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 2, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 1, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Total Width of 125 GeV Higgs Boson

By using the LHC and Tevatron measurements of the cross sections to various decay channels relative to the standard model Higgs boson, the total width of the putative 125 GeV Higgs boson is determined as 6.1 +7.7-2.9 MeV. We describe a way to estimate the branching fraction for Higgs decay to dark matter. We also discuss a No-Go theorem for the gammagamma signal of the Higgs boson at the LHC.

generally very difficult to determine the total width Γ tot of a narrow resonance like the Higgs boson. Moreover, the determination of this quantity is also an important test of the Higgs mechanism of the Standard Model (SM). A sizable deviation from the SM prediction would directly indicate new physics. The Higgs width can be measured at a γ-γ collider [1] or a µ + µ − collider [2] through its line shape, and such facilities are under consideration.
We will present a simple method to determine the total width Γ tot h 0 of the 125 GeV Higgs signal h 0 by using LHC and Tevatron measurements with the SM Higgs boson h 0 SM as a benchmark. We will apply this method to the data of the putative Higgs-boson signal with mass 125 GeV. Pre-LHC studies [3][4][5][6] were made of a similar ilk.
Outline of the method The h 0 total width is given by the sum of partial widths that can be normalized to the h 0 SM partial widths.
γ AA is the ratio of the h 0 partial width of the AĀ channel to that of h 0 SM . The cross sections of a given channel relative to the h 0 SM expectation is given by where X is the initial parton in the proton participating in the fusion process. Then, we can obtain Γ tot h 0 via measurements of the ratios of Eq. (2) following Eq. (1). Equation (2) is derived from the proportionality of σ(XX → h 0 → AĀ) to the corresponding decay width Γ h 0 →XX and the branching fraction where we use the BF of h 0 SM in Table I, extracted from Ref. [7] and assume γ W W * = γ ZZ * (≡ γ V V ) as is the case for spontaneous symmetry breaking via the SU(2) L Higgs doublet. [8] γ cc can be approximated by unity in Eq. (3) since γ cc is a subleading contribution.
Illustrations of width determination The 5 γ-parameters, (gg, bb, τ + τ − , V V and γγ), can be determined by LHC and Tevatron measurements of the corresponding ratios in Eq. (2).
The observed Higgs-signal cross section at the LHC from various processes relative to the standard model Higgs at m h 0 = 125 GeV are given by CMS [9] and by ATLAS [11]. V V → γγ is determined by CMS from di-jet diphoton events[10]. The bb signal of the second row is inferred from the recent Tevatron data [12]. R is the h 0 total width relative to that of h 0 SM with the same mass. See Eq. (3).
Then the value of Γ tot h 0 is determined by with Γ tot h 0 SM = 4.07 MeV [7]. The small γγ and Zγ contributions can be neglected here.
The experimental values of the ratios of Eq.
(2) at m h 0 = 125 GeV reported by CMS [9,10] and by ATLAS [11] are given in Table II, along with the ratio for the bb channel inferred from the latest Tevatron data [12]. A χ 2 fit gives the estimated values of the γ AA parameters in Table III.
Because of the strong correlations between γ bb,τ τ and γ γγ , loose upper limits are obtained for these quantities from the present data. We obtain the value Γ tot h 0 = 6.1 +7.7 −2.9 MeV. However, the determination will be much improved (see e.g. Refs. [3,5] Table II. One-sigma statistical uncertainties are given. Partial widths of the 125 GeV Higgs Γ h 0 →AĀ and the BF are also given. The total width is estimated to be Γ tot h 0 = 6.1 The γγ cross section seems to be enhanced compared with h 0 SM , although this could be an upward statistical fluctuation. In the SM it is given theoretically by the triangle loop diagrams of the W -boson and top quark. If a new heavy fermion and/or a heavy scalar couple to the SM Higgs, and their masses are generated by the Higgs mechanism, the γ γγ and γ gg are given (see e.g. Ref. [13]) by where the 1st (2nd)  and correspondingly the W W * , ZZ * , bb, τ − τ + channels from gluon fusion are enhanced by γ gg /R = 5.2 ; γγ via gluon fusion is γ gg γ γγ /R = 1.1, almost the same as the SM, while γγ by vector-boson fusion is strongly suppressed, γ γγ /R = 0.12. If the γγ enhancement in the diphoton di-jet events[10] is mainly from V V fusion and the measured value is confirmed, the fourth-generation model will be excluded mass-independently. See also ref. [19]. Similarly, if the enhancement of V V → h 0 → γγ is confirmed, the interpretation of the 125 GeV Higgs signal as the dilaton or radion [14][15][16] will be discarded, since the vector-boson fusion to diphoton cross section is strongly suppressed in these models compared with the SM Higgs.
The loop contributions of a new scalar or a new fermion are proportional to dimensionless where Y f (Y h 0 SS ) is the Yukawa coupling of the new fermion (scalar) and the v is the Higgs GeV. λ f,S = 1 corresponds to the the case that the fermion(scalar) mass is generated by the Higgs mechanism. For a heavy particle with no Higgs mechanism for its mass generation, λ f,S ≪ 1 and γ gg ≃ γ γγ ≃ 1, so the γγ cross section becomes the same as the SM Higgs. To obtain a large enhancement, a m f,S smaller than v is necessary or alternatively the color factor of the new particle is large.
The cross section ratios of various processes relative to the SM Higgs are plotted versus λ f,S in the cases of color-octet fermion (denoted as F 8, also called leptogluon [17]) and coloroctet scalar (S8) in Fig. 1.
The S8 [25] is an interesting possibility. It was discussed in the context of Higgs underproduction [26,27] at LHC for the circumstance that this new scalar has light mass and the Higgs boson has sizable branching fraction to this scalar channel. If the mass of this color-octet scalar is generated by the Higgs mechanism, following Eq.
Color-octet fermion(leptogluon), Color-triplet fermion, and Color-singlet fermion are shown by solid lines with the end points corresponding to λ f = −1(square) and λ f = 1(circle). In Q f = 1 case, the x-coordinates scale with Q 2 f . λ f = 1 corresponds to the case of its mass generated by Higgs mechanism. A color-octet fermion with Q f = 1 is consistent with the red meshed region at λ f ≃ −0.31. For a new scalar, the lengths of the theory lines should be scaled by 1/4; thus, a scalar octet has no overlap with the preferred red meshed region.
of F 8 in Fig. 1, for which (gγ, gV, V γ) = (1.52, 0.67, 2.35). If the Yukawa coupling of the leptogluon is the same as top quark, but the sign of λ is reversed, its mass is estimated to be m F 8 = m t /0.31 ≃ 500 GeV. The corresponding Zγ partial decay width is almost the same as the SM Higgs: γ Zγ = 1.04. Then, a Zγ cross section ratio via gluon fusion 0.69 ± 0.09 is predicted, which is almost the same as gV .
More generally, Fig. 2 is a vector space that can be used in identifying new particle contributions from experimental measurements of the XA.
It is very difficult to obtain V γ > 2 and gγ > 1. This constitutes a NO GO theorem.
Only the F 8 (and F 6) are possible if we limit the charge of the new particle Q f ≤ 1. Similarly, in the Universal Extra Dimension model, where the KK-modes of W -boson, quarks, and leptons contribute to the loop, at most a 50% enhancement of γγ is found for the allowed region of parameters [24].

Possible Dark matter contribution
When we consider the possible decay to dark matter channel, Γ tot h 0 is replaced by the decay width to the visible channels Γ vis h 0 in LHS of Eqs. (1), (3), and (4), while Eq. (2) is unchanged. The Γ tot h 0 in Eq. (2) now includes the partial decay width to the dark matter channel Γ h 0 →DD as [29] Γ tot The detection of the Higgs invisible decays at hadron colliders has been studied in refs. [30,31]. The factor F (≥ 1) is related to the BF to dark matter D by Our method of fitting the quantities of LHS of Eq. (2) now determines γ ′ AA ≡ γ AA /F , not γ AA , since in Eq.
where R is given by the second equality of Eq. (3).
In many models, such as the MSSM in the decoupling limit, the W W * and ZZ * couplings are nearly the same as those of the SM Higgs boson: γ V V ≃ 1. [28] In this case, the value of γ V V /F obtained by our method gives directly the value of 1/F which in turn gives BF (h 0 → DD) following Eq. (8). The best-fit value of γ V V /F in Table III [32] to invisible decay channel is disfavored [33].

Concluding remarks
We have presented a method of determining the total width of the putative 125 GeV Higgs-boson. The measurements of the γγ cross section of the Higgs signal relative to that of the SM will discriminate many candidate models of new physics.
It is difficult to obtain a theoretical enhancement of the γγ signal of more than 2. This constitutes a No-Go theorem. For a charge Q ≤ 1, this theorem is evaded with a new lightmass fermion with color octet(leptogluon) or color-sextet and a negative Higgs coupling.
Such a colored state can be directly tested [34] by LHC experiments.
Measurements of the vector-boson fusion process and the vector-boson bremsstrahlung processes (c.f. Table II) can significantly improve the uncertainty on the total Higgs width estimate.
Accurate measurement of the ratio of the γγ to ZZ * cross sections would determine γ γγ /γ V V , independently of the value of γ gg .
The branching fraction for the decay of the Higgs boson to dark matter can be inferred in the decoupling limit of the W W * and ZZ * couplings of any two Higgs doublet model [35].
The methods presented in this Letter should be useful when higher statistics data are acquired on the Higgs signal. One must be cautious about over-interpreting the data until the Higgs signal is fully established.